Template:RoundBoxTop

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    <title>Template:RoundBoxTop</title>
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        <username>Brawl Stars Gus</username>
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&lt;includeonly&gt;{| cellpadding=&quot;10&quot; cellspacing=&quot;5&quot; style=&quot;width: 100%; background-color: inherit; margin-left: auto; margin-right: auto&quot;
| style=&quot;background-color: {{Robelbox/C1|{{{theme|1}}}}}; border: 1px solid {{Robelbox/C2|{{{theme|1}}}}}; -webkit-border-radius: 8px; -moz-border-radius: 8px; border-radius: 8px&quot; colspan=&quot;1&quot; |&lt;/includeonly&gt;&lt;noinclude&gt;
;One of three parts
:This is a box with rounded corners (visible with selected browsers only.):

This template can be combined with [[Template:RoundBoxNext]] and must conclude with [[Template:RoundBoxBottom]].

==Code examples==
__TOC__
===Default theme===
This code:
  &lt;nowiki&gt;{{RoundBoxTop}}
  Test content using a box of theme = 1.
  {{RoundBoxBottom}}&lt;/nowiki&gt;

produces this box&lt;nowiki&gt;:&lt;/nowiki&gt;
{{RoundBoxTop}}
Test content using a box of theme = 1.
{{RoundBoxBottom}}

===Green theme===
This code:
  &lt;nowiki&gt;{{RoundBoxTop|theme=2}}
  Test content using a box of theme = 2.
  {{RoundBoxBottom}}&lt;/nowiki&gt;

produces this box&lt;nowiki&gt;:&lt;/nowiki&gt;
{{RoundBoxTop|theme=2}}
Test content using a box of theme = 2.
{{RoundBoxBottom}}

==Themes==

{{RoundBoxTop}}
===Theme 1===
;Simple example
:Here is an example of a round box with a theme of 1.
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===Theme 2===
;Simple example
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===Theme 3===
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;Simple example
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===Theme 8===
;Simple example
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===Theme 9===
;Simple example
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===Theme 10===
;Simple example
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===Theme 11===
;Simple example
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===Theme 12===
;Simple example
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;Simple example
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;Simple example
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;Simple example
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;Simple example
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;Simple example
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[[Category:Design templates]]
[[Category:Exclude in print]]
[[Category:RoundBox]]
&lt;/noinclude&gt;</text>
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      <comment>Reverted edits by [[Special:Contributions/Brawl Stars Gus|Brawl Stars Gus]] ([[User_talk:Brawl Stars Gus|talk]]) to last version by [[User:Sophiedriscoll|Sophiedriscoll]] using [[Wikiversity:Rollback|rollback]]</comment>
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;One of three parts
:This is a box with rounded corners (visible with selected browsers only.):

This template can be combined with [[Template:RoundBoxNext]] and must conclude with [[Template:RoundBoxBottom]].

==Code examples==
__TOC__
===Default theme===
This code:
  &lt;nowiki&gt;{{RoundBoxTop}}
  Test content using a box of theme = 1.
  {{RoundBoxBottom}}&lt;/nowiki&gt;

produces this box&lt;nowiki&gt;:&lt;/nowiki&gt;
{{RoundBoxTop}}
Test content using a box of theme = 1.
{{RoundBoxBottom}}

===Green theme===
This code:
  &lt;nowiki&gt;{{RoundBoxTop|theme=2}}
  Test content using a box of theme = 2.
  {{RoundBoxBottom}}&lt;/nowiki&gt;

produces this box&lt;nowiki&gt;:&lt;/nowiki&gt;
{{RoundBoxTop|theme=2}}
Test content using a box of theme = 2.
{{RoundBoxBottom}}

==Themes==

{{RoundBoxTop}}
===Theme 1===
;Simple example
:Here is an example of a round box with a theme of 1.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=2}}
===Theme 2===
;Simple example
:Here is an example of a round box with a theme of 2.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=3}}

===Theme 3===
;Simple example
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{{RoundBoxTop|theme=4}}
===Theme 4===
;Simple example
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{{RoundBoxTop|theme=5}}
===Theme 5===
;Simple example
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{{RoundBoxTop|theme=6}}
===Theme 6===
;Simple example
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{{RoundBoxTop|theme=7}}
===Theme 7===
;Simple example
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===Theme 8===
;Simple example
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===Theme 9===
;Simple example
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{{RoundBoxTop|theme=10}}
===Theme 10===
;Simple example
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{{RoundBoxTop|theme=11}}
===Theme 11===
;Simple example
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===Theme 12===
;Simple example
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===Theme 13===
;Simple example
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===Theme 14===
;Simple example
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===Theme 15===
;Simple example
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{{RoundBoxTop|theme=16}}
===Theme 16===
;Simple example
:Here is an example of a round box with a theme of 16.
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{{RoundBoxTop|theme=17}}
===Theme 17===
;Simple example
:Here is an example of a round box with a theme of 17.
{{RoundBoxBottom}}

[[Category:Design templates]]
[[Category:Exclude in print]]
[[Category:RoundBox]]
&lt;/noinclude&gt;</text>
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        <id>2888076</id>
      </contributor>
      <minor />
      <comment>Protected &quot;[[Template:RoundBoxTop]]&quot;: Highly visible template ([Edit=Allow only autoconfirmed users] (indefinite) [Move=Allow only autoconfirmed users] (indefinite))</comment>
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      <text bytes="3384" sha1="8lbesfna7attn53s3nm6gqa8vk6jyp3" xml:space="preserve">&lt;includeonly&gt;{| cellpadding=&quot;10&quot; cellspacing=&quot;5&quot; style=&quot;width: 100%; background-color: inherit; margin-left: auto; margin-right: auto&quot;
| style=&quot;background-color: {{Robelbox/C1|{{{theme|1}}}}}; border: 1px solid {{Robelbox/C2|{{{theme|1}}}}}; -webkit-border-radius: 8px; -moz-border-radius: 8px; border-radius: 8px&quot; colspan=&quot;1&quot; |&lt;/includeonly&gt;&lt;noinclude&gt;
;One of three parts
:This is a box with rounded corners (visible with selected browsers only.):

This template can be combined with [[Template:RoundBoxNext]] and must conclude with [[Template:RoundBoxBottom]].

==Code examples==
__TOC__
===Default theme===
This code:
  &lt;nowiki&gt;{{RoundBoxTop}}
  Test content using a box of theme = 1.
  {{RoundBoxBottom}}&lt;/nowiki&gt;

produces this box&lt;nowiki&gt;:&lt;/nowiki&gt;
{{RoundBoxTop}}
Test content using a box of theme = 1.
{{RoundBoxBottom}}

===Green theme===
This code:
  &lt;nowiki&gt;{{RoundBoxTop|theme=2}}
  Test content using a box of theme = 2.
  {{RoundBoxBottom}}&lt;/nowiki&gt;

produces this box&lt;nowiki&gt;:&lt;/nowiki&gt;
{{RoundBoxTop|theme=2}}
Test content using a box of theme = 2.
{{RoundBoxBottom}}

==Themes==

{{RoundBoxTop}}
===Theme 1===
;Simple example
:Here is an example of a round box with a theme of 1.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=2}}
===Theme 2===
;Simple example
:Here is an example of a round box with a theme of 2.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=3}}

===Theme 3===
;Simple example
:Here is an example of a round box with a theme of 3.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=4}}
===Theme 4===
;Simple example
:Here is an example of a round box with a theme of 4.
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{{RoundBoxTop|theme=5}}
===Theme 5===
;Simple example
:Here is an example of a round box with a theme of 5.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=6}}
===Theme 6===
;Simple example
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{{RoundBoxTop|theme=7}}
===Theme 7===
;Simple example
:Here is an example of a round box with a theme of 7.
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{{RoundBoxTop|theme=8}}
===Theme 8===
;Simple example
:Here is an example of a round box with a theme of 8.
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{{RoundBoxTop|theme=9}}
===Theme 9===
;Simple example
:Here is an example of a round box with a theme of 9.
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{{RoundBoxTop|theme=10}}
===Theme 10===
;Simple example
:Here is an example of a round box with a theme of 10.
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{{RoundBoxTop|theme=11}}
===Theme 11===
;Simple example
:Here is an example of a round box with a theme of 11.
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{{RoundBoxTop|theme=12}}
===Theme 12===
;Simple example
:Here is an example of a round box with a theme of 12.
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{{RoundBoxTop|theme=13}}
===Theme 13===
;Simple example
:Here is an example of a round box with a theme of 13.
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{{RoundBoxTop|theme=14}}
===Theme 14===
;Simple example
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{{RoundBoxTop|theme=15}}
===Theme 15===
;Simple example
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{{RoundBoxTop|theme=16}}
===Theme 16===
;Simple example
:Here is an example of a round box with a theme of 16.
{{RoundBoxBottom}}

{{RoundBoxTop|theme=17}}
===Theme 17===
;Simple example
:Here is an example of a round box with a theme of 17.
{{RoundBoxBottom}}

[[Category:Design templates]]
[[Category:Exclude in print]]
[[Category:RoundBox]]
&lt;/noinclude&gt;</text>
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  <page>
    <title>Unmanned aerial systems/External links</title>
    <ns>0</ns>
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    <revision>
      <id>2693001</id>
      <parentid>2692989</parentid>
      <timestamp>2024-12-23T12:32:00Z</timestamp>
      <contributor>
        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <minor />
      <comment>Reverted edits by [[Special:Contributions/2.44.173.194|2.44.173.194]] ([[User_talk:2.44.173.194|talk]]) to last version by [[User:ShakespeareFan00|ShakespeareFan00]] using [[Wikiversity:Rollback|rollback]]</comment>
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      <text bytes="5081" sha1="mhhpo518mtpttadlzvl59uyhbd8ozxv" xml:space="preserve">testicles
==External links==
{{col}}
=== Components ===
====Accelerometers====
* [http://www.analog.com/en/prod/0,2877,ADXL202,00.html An Accelerometer]
* [http://www.sparkfun.com/commerce/categories.php?cPath=23_80 Accelerometers]

====Carbon fiber====
* [http://www.hobbylinc.com/htm/mid/mid5720.htm?source=froogle .125&quot; 24&quot; Tube]
* [http://www.hobbylinc.com/htm/mid/mid5704.htm?source=froogle .060&quot; 24&quot; Rod]
* [http://www.hobbylinc.com/htm/mid/mid5743.htm?source=froogle .070&quot; x .437&quot; 24&quot; Strip]
* [http://www.hobbylinc.com/htm/mid/mid5740.htm?source=froogle .019&quot; x .118 24&quot; Strip]
* [http://www.hobbypeople.net/gallery/217925.asp .5&quot; 5' Reinforcing Strip]
* [http://www.jcwhitney.com/webapp/wcs/stores/servlet/Product?storeId=10101&amp;Pr=p_Product.CATENTRY_ID%3A2011293&amp;TID=100&amp;TID=100&amp;productId=2011293&amp;catalogId=10101 Carbon Fiber Sheet 24&quot; x 8&quot;]

====Gyros====
* [http://www.sparkfun.com/commerce/categories.php?cPath=23_85 Gyros]

====Computers====
* [http://www.gumstix.org Gumstixs]
** [http://gumstix.com/store/catalog/product_info.php?products_id=155 Mother Board]
** [http://gumstix.com/store/catalog/product_info.php?products_id=171 WiFi Stick]
** [http://gumstix.com/store/catalog/product_info.php?products_id=157 GPS Stick]
* [http://www.picotux.com/techdatae.html picotux]

====Wireless====
* [http://www.sparkfun.com/commerce/product_info.php?products_id=148 Bluetooth Chip]
* [http://www.sparkfun.com/commerce/product_info.php?products_id=150 Bluetooth USB]

====Solar Cells====
* [http://www.solar-world.com/PowerFilm.htm Powerfilm]
* [http://www.flexcell.com/oem-integrated-solution.php?langue=en Flexcell]

====Blades====
* [http://www.readytoflyfun.com/hepropeller.html 6x4 Heli Props]

====Motors====
* [http://www.tedani.com/tower-pro-bm241009-1100kv-outrunner-brushless-motor-p-556.html?osCsid=b2ba72e8f71da324617fec3ba5696333 55g Brushless]
* [http://www.nitroplanes.com/24oubrmo.html Another 55g Brushless]
* [http://www.aero-fever.com/product_info.php?currency=USD&amp;products_id=48 62g Brushless]

====GPS====
* [http://www.engadget.com/2006/12/18/epson-cranks-out-worlds-smallest-gps-module/ World's Smallest GPS Module]
* [http://gumstix.com/store/catalog/product_info.php?products_id=157 GPS Gumstix]
* [http://www.sparkfun.com/commerce/product_info.php?products_id=7951 Chip]
{{break}}
====Cameras====
* [http://www.spygadgets.com/spy-cameras/micro-cameras.html Micro Cameras]

====Other sites of interest====
* [http://cswww.essex.ac.uk/staff/owen/research.htm#The%20Flying%20Gridswarm,%20and%20the%20UltraSwarm Microheli Gumstix Swarms]
* [http://www.sparkfun.com/commerce/product_info.php?products_id=7906# Cellphone Camera]
* [http://www.sparkfun.com/tutorial/BlueTooth/bluetooth_primer.htm Bluetooth Primer]
* [http://www.uavp.de/index.php?option=com_content&amp;task=view&amp;id=17&amp;Itemid=40 OpenSourceQuadrocopter]

====Software====
* [http://sourceforge.net/projects/wireless/ CUWiN Community Wireless Network] - Mesh networks for everyone.
* [http://sourceforge.net/projects/ivt/ Integrating Vision Toolkit]
* [http://sourceforge.net/projects/aibo/ Cognitive Vision]
* [http://sourceforge.net/projects/reactivision/ reacTIVision]
* [http://sourceforge.net/projects/javavision/ Java Vision Toolkit] - Java toolkit to process 2D and 3D Images
* [http://sourceforge.net/projects/stllcv/ STL like OpenCV wrapper] - Computer vision and machine learning
* [http://sourceforge.net/projects/povclipse/ PovClipse]
* [http://sourceforge.net/projects/vxl/ The VXL Project] - C++ Libs for computer vision and understanding.
* [http://sourceforge.net/projects/fpga-vision/ High Speed Vision System] - Uses FPGA chips.
* [http://sourceforge.net/projects/yarp0/ Yet Another Robot Platform]
* [http://sourceforge.net/projects/estereo/ EStereo] - C++ Computer vision.
* [http://sourceforge.net/projects/gandalf-library/ Gandalf vision and numerical library]
* [http://sourceforge.net/projects/servo-trim/ Servo-Trim]
* [http://sourceforge.net/projects/lmh-calculator/ LMH Rechner]
* [http://sourceforge.net/projects/usbservoctrl/ ACS USB servo controller device driver]
* [http://sourceforge.net/projects/servodriver/ RC-servo driver]
* [http://sourceforge.net/projects/rcfs/ OpenSource RC Flight Simulator]
* [http://sourceforge.net/projects/mrsuite/ MRSuite] - Modular robotics simulator.
* [http://sourceforge.net/projects/servo/ SAM (Servo Actuation Manipulator)] - Controls servo motors via serial port.

{{Col/end}}

===Related links===
*[http://www.autobloggreen.com/2007/10/14/radio-controlled-airplane-can-fly-for-10-hours-on-500-grams-of-h/ 'Radio controlled airplane can fly for 10 hours on 500 grams of hydrogen']
* [http://www.h2daily.com/news/nuvera-to-supply-fuel-cells-for-toro-vehicles-20070405-216-50.html Nuvera to supply fuel cells for vehicles.]
* [http://www.dailymail.co.uk/pages/live/articles/technology/technology.html?in_article_id=447317 Army invests in saucer technology...]

===Related news===
* (2008) [http://www.yankodesign.com/index.php/2008/03/04/roomba-watch-out/ Robots that clean oil spills]

[[Category:Autonomous aerial systems]]</text>
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  <page>
    <title>Social psychology (psychology)/Lectures/Prosocial/Notes</title>
    <ns>0</ns>
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      <text bytes="11527" sha1="j6ug9elvkghxkswz3sqxkzhcvvw9rr0" xml:space="preserve">{{note|There was a glitch with the daylight savings change on the [[UC]] servers which resulted in this lecture not being recorded. On behalf of the university, my apologies. This notes page seeks to provide some additional/accompanying notes instead. Students should feel free to contribute.}}Nigger{{RoundBoxTop|theme=2}}
{{100%done}}
{{TOCright}}
[http://www.slideshare.net/jtneill/lecture-9-prosocial-behaviour View the slides]
==Introduction==
[[../|This lecture]] introduced socio-psychological theory and research about '''[[prosocial behaviour]]''' and '''[[altruism]]'''. These are different concepts, with altruism being a subset of prosocial behaviour in which a prosocial behaviour is undertaken without any thought of personal reward. Prosocial behaviour refers to any behavioural act which further the interests of a group by improving its cohesion, quality of relationships, etc. What is deemed prosocial by one group may be considered by other groups to be antisocial. Antisocial behaviours are those judged to be destructive to group relationships.

An important psychological and philosophical issue for debate is whether there is any such thing as true altruism. The closer one looks at the possible explanations and motivations for prosocial behaviour, the more it seems that its possible to find non-altruistic explanations for prosocial behaviours. This is a rich topic for debate. A related issue is whether altruism is only evident (if at all) in humans or whether other animals are also altruistic e.g., what do you think about this [http://youtube.com/watch?v=Gp7cZ0AWxfI video of a gorilla rescuing a kid at a zoo] (1 min)?

Collectively, prosocial behaviour contributes to [[social capital]], a concept which is explored in the [[Social psychology (psychology)/Tutorials/Australian zeitgeist|Australian zeitgeist]] tutorial.

Prosocial behaviour can be contrasted with [[antisocial behaviour]] which are acts that undermine or otherwise negatively affect social relations within a community.

==When would you help?==
# A collapsed stranger in the street?...
# Some rubbish on a path?...
# Donate blood? organ? money? time?...
# Hitchiker?...
# Someone whose car is broken on the side of the road?...
# ...

What factors influence whether you help or not and why?

==Prosocial behaviour is not just about helping==
The [[{{#titleparts:{{PAGENAME}}|1|}}/Readings/Textbooks/Baumeister and Bushman/2008|Baumeister and Bauman (2008) textbook]] criticises many other social psychology textbook chapters on prosocial behaviour for being overly focused on &quot;helping&quot; and neglecting focus on the prosocial role of [[obedience]] and [[conformity]] (Note that we discussed obedience and conformity earlier in the [[{{#titleparts:{{PAGENAME}}|2|}}/Social thinking|lecture on social thinking]] and, more specifically, on [[social influence]]).

==Reasons for prosocial behaviour==
Reasons for prosocial behaviour include:
* Self-interest
* Improve social status
* Reciprocity - direct or indirect
* Conformity (e.g., to fairness - most people want a balance between underbenefitting and overbenefitting)
* Rule of law (but also note that some acts of disobediance (e.g., [[w:civil disobediance|civil disobediance]]) may ultimately prove to be prosocial rather than antisocial. In this respect, [[w:Kohlberg's stages of moral development|Kohlberg's stages of moral development]] help to give insight to &quot;higher law&quot;) 
* Evolutionary (e.g., kin selection, which is stronger in more life-threatening situations)
* Altruism (is it motivated by empathy for the other; or efforts to relieve one's own personal distress about the other person being distressed?)

==Forgiveness==
Given that often &quot;bad&quot; is stronger than &quot;good&quot;, forgiveness of another for causing harm can be a particularly notable prosocial contribution. Forgiveness involves letting go of anger, resentment, and blaming of one's emotional distress as caused by another's antisocial behaviours.

==Game theory==
In the previous lecture on Groups and Relationships, the commons dilemma and the prisoners' dilemma were discussed as examples of iterative, experimental studies conducted to examine the sociodynamics of competition and cooperation. The collective results of our myriad relational games might be considered as a group's social capital. The net results of various interactions can be loosely understood as negative, neutral, or positive - see the helpful tables and diagrams here: [http://www.synearth.net/Order/UCS2-Science-Order04.html]. Also of relevance here is [[transactional analysis]], Robert S. De Ropp's &quot;The Master Game&quot;, Manning-Clark's straighteners and enlargers, etc. Essentially these and other such &quot;game theory&quot; schemes seek to describe and understand common sociodynamic relational patterns and their consequences.

==Obedience and conformity==
Without obedience and conformity to a rule of law, our social lives would be far more chaotic. Thus, obeying and conforming to social rules is vital for creating and maintaining a community. However, communities evolve and change, thus rules and norms often need to similarly evolve. And there is a danger in a group members becoming overly compliant and conforming, such as classically illustrated in [[w:Milgram's study of obedience|Milgram's 1950's studies of obedience]]. Also, see [[w:Asch conformity experiments|Asch's conformity experiments]]. A more recent example of obedience is a TV show in which contestants were asked to torture. 80% of contestants went to the very end - i.e, administered the ultimate, potentially lethal shock ([http://news.bbc.co.uk/2/hi/europe/8573755.stm] BBC News, 2010; [http://www.telegraph.co.uk/news/worldnews/europe/france/7457780/French-contestants-torture-each-other-on-TV-Game-of-Death.html] Telegraph.co.uk, 2010).

==Motivations for helping==
Batson (1994):
* Egoism – helping benefits the helper – receive rewards or escape punishment.
* Altruism – helping benefits others – no need for reciprocity.
* Collectivism – helping benefits the in-group.
* Principalism – help because of a moral imperative

==[[w:Empathy-altruism|Empathy-altruism hypothesis]]==
Batson (1991) proposed that [[empathy]] motivates people to reduce other people’s distress by helping or comforting:
* If low empathy, people can reduce their own distress by escaping the situation
* If high empathy, emotional response corresponds to feelings of other person redue our distress by reducing other person's distress

Negative relief state theory is the proposition that people help others in order to relieve their own distress.

==Personal determinants of helping==
* Personality - weak predictor, but consider &quot;warmth&quot;
* Competence - more skilled you are in the area of need, the more likely you are to help
* Attributions - recall from social thinking that we have a tendency to blame others' problems on their selves (as opposed to their circumstances, whereas we have a tendency to find external explanations for our own distress. We generally are more likely to help someone if we perceive that their circumstances were externally caused rather than caused by themselves (and thereby &quot;deserved&quot; - see the [[w:Just World Hypothesis|Just World Hypothesis]])
* Personal norms - personal norms for helping based on personal values (e.g., religious beliefs). If we have &quot;helpfulness&quot; as part of our self-concept, then we need to act in consistent ways otherwise we experience [[cognitive dissonance]].

==Emotion and helping==
In general, positive mood increases likelihood of helping, whereas negative mood tends to decrease likelihood of helping. Note, however, that there are logical exceptions to this tendency (e.g., if it will be costsly to one's positive mood one may not help, or if it will relieve one's negative state, one may be more likely to help).

==Interpersonal determinants of helping==
# Females are more likely to receive help
# Attractiveness - more likely to help attractive others.
# Similarity - we are morely likely to help similar others (similarity increases attractiveness &amp; empathy)
# Closeness - more likely to help those we know.
# Deservingness - help those we judge as deserving our help (e.g,. based on reciprocity and attribution).

==Gender==
# Males are more likely to help in &quot;dramatic&quot; circumstances, and broader societal spheres, and they are more likely to help women than men
# Females are more likely to help in &quot;mundane&quot; life, in the local sphere, and are more likely to receive help

==[[Bystander effect]]==
The larger the group, the less likely people are to help because of:
# Diffusion of responsibility: the reduction in feeling responsible that occurs when others are present.
# Pluralistic ignorance: looking to others for cues about how to behave, while they are looking to you; collective misinterpretation.

==Five steps to helping==
Five steps (or barriers) to helping have been proposed (Latane &amp; Darley):
# Notice that something is happening
# Interpret meaning of event - Pluralistic ignorance
# Taking responsibility for providing help - # Diffusion of responsibility
# Know how to help
# Provide help 

==Good Samaritan study==
Darley and Batson (1973)'s classic study found that time (in a rush or not in a rush) had the largest effect. Those in a rush were much less likely to help. [http://faculty.babson.edu/krollag/org_site/soc_psych/darley_samarit.html Summary of the study].

==Bystander-calculus model==
Piliavin, Dovidio, Gaertner, and Clark (1981) offer a social exchange theory model for the bystander effect, according to which bystanders calculate the (perceived) costs &amp; benefits of providing help in three stages:
# Physiological arousal - e.g., witnessing an emergency - the higher the physiological arousal, the  greater chance of helping.
# Labelling the arousal - type of label influences the kind of help offered; e.g., is arousal labelled as personal distress or empathic concern? - usually labelled as personal distress.
# Evaluating the consequences -  weigh up costs of helping, choose action that reduces personal distress at lowest cost.  Costs might include getting hurt, inconvenience, embarrassment etc.

==How can we increase helping?==
# Reduce ambiguity
# Reduce distractions (or make the need for help more obvious)
# Reduce pluralistic ignorance
# Increase personal responsibility (reduce diffusion of responsibility), e.g., reduce anonymity
# Reduce concerns about competence to help
# Reduce audience inhibitions
# Reduce uncertainties of obstacles
# Educate about bystander indifference
# Model helpfulness e.g., positive models in the media.
# Teach moral inclusion - perception of certain people as inside/outside our bounds of moral or ethical concern
# Guilt &amp; concern for self-image - use of compliance tactics
# Learning about / socialising altruism

==Summary and conclusion==
# Prosocial behaviour includes conformity, obedience, and cooperating with others, but may also include disobedience.
# Human culture depends on people following rules.
# Following the rules of society and culture generally brings immense personal and social benefits.
# Is altruism unique to humans?
# Cultural and social variables and situational contingencies can significantly influence whether a person performs prosocial or antisocial behaviours

==External links==
# [https://www.psychvarsity.com/Pluralistic-Ignorance Pluralistic ignorance - Why you won’t raise your hand in the classroom]{{RoundBoxBottom}}

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        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <minor />
      <comment>Reverted edits by [[Special:Contribs/98.186.206.121|98.186.206.121]] ([[User talk:98.186.206.121|talk]]) to last version by 86.128.114.75: reverting vandalism</comment>
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      <text bytes="11523" sha1="b22h5odd7m7xb6rbnykahzxazplldwm" xml:space="preserve">{{note|There was a glitch with the daylight savings change on the [[UC]] servers which resulted in this lecture not being recorded. On behalf of the university, my apologies. This notes page seeks to provide some additional/accompanying notes instead. Students should feel free to contribute.}}

{{RoundBoxTop|theme=2}}
{{100%done}}
{{TOCright}}
[http://www.slideshare.net/jtneill/lecture-9-prosocial-behaviour View the slides]
==Introduction==
[[../|This lecture]] introduced socio-psychological theory and research about '''[[prosocial behaviour]]''' and '''[[altruism]]'''. These are different concepts, with altruism being a subset of prosocial behaviour in which a prosocial behaviour is undertaken without any thought of personal reward. Prosocial behaviour refers to any behavioural act which further the interests of a group by improving its cohesion, quality of relationships, etc. What is deemed prosocial by one group may be considered by other groups to be antisocial. Antisocial behaviours are those judged to be destructive to group relationships.

An important psychological and philosophical issue for debate is whether there is any such thing as true altruism. The closer one looks at the possible explanations and motivations for prosocial behaviour, the more it seems that its possible to find non-altruistic explanations for prosocial behaviours. This is a rich topic for debate. A related issue is whether altruism is only evident (if at all) in humans or whether other animals are also altruistic e.g., what do you think about this [http://youtube.com/watch?v=Gp7cZ0AWxfI video of a gorilla rescuing a kid at a zoo] (1 min)?

Collectively, prosocial behaviour contributes to [[social capital]], a concept which is explored in the [[Social psychology (psychology)/Tutorials/Australian zeitgeist|Australian zeitgeist]] tutorial.

Prosocial behaviour can be contrasted with [[antisocial behaviour]] which are acts that undermine or otherwise negatively affect social relations within a community.

==When would you help?==
# A collapsed stranger in the street?...
# Some rubbish on a path?...
# Donate blood? organ? money? time?...
# Hitchiker?...
# Someone whose car is broken on the side of the road?...
# ...

What factors influence whether you help or not and why?

==Prosocial behaviour is not just about helping==
The [[{{#titleparts:{{PAGENAME}}|1|}}/Readings/Textbooks/Baumeister and Bushman/2008|Baumeister and Bauman (2008) textbook]] criticises many other social psychology textbook chapters on prosocial behaviour for being overly focused on &quot;helping&quot; and neglecting focus on the prosocial role of [[obedience]] and [[conformity]] (Note that we discussed obedience and conformity earlier in the [[{{#titleparts:{{PAGENAME}}|2|}}/Social thinking|lecture on social thinking]] and, more specifically, on [[social influence]]).

==Reasons for prosocial behaviour==
Reasons for prosocial behaviour include:
* Self-interest
* Improve social status
* Reciprocity - direct or indirect
* Conformity (e.g., to fairness - most people want a balance between underbenefitting and overbenefitting)
* Rule of law (but also note that some acts of disobediance (e.g., [[w:civil disobediance|civil disobediance]]) may ultimately prove to be prosocial rather than antisocial. In this respect, [[w:Kohlberg's stages of moral development|Kohlberg's stages of moral development]] help to give insight to &quot;higher law&quot;) 
* Evolutionary (e.g., kin selection, which is stronger in more life-threatening situations)
* Altruism (is it motivated by empathy for the other; or efforts to relieve one's own personal distress about the other person being distressed?)

==Forgiveness==
Given that often &quot;bad&quot; is stronger than &quot;good&quot;, forgiveness of another for causing harm can be a particularly notable prosocial contribution. Forgiveness involves letting go of anger, resentment, and blaming of one's emotional distress as caused by another's antisocial behaviours.

==Game theory==
In the previous lecture on Groups and Relationships, the commons dilemma and the prisoners' dilemma were discussed as examples of iterative, experimental studies conducted to examine the sociodynamics of competition and cooperation. The collective results of our myriad relational games might be considered as a group's social capital. The net results of various interactions can be loosely understood as negative, neutral, or positive - see the helpful tables and diagrams here: [http://www.synearth.net/Order/UCS2-Science-Order04.html]. Also of relevance here is [[transactional analysis]], Robert S. De Ropp's &quot;The Master Game&quot;, Manning-Clark's straighteners and enlargers, etc. Essentially these and other such &quot;game theory&quot; schemes seek to describe and understand common sociodynamic relational patterns and their consequences.

==Obedience and conformity==
Without obedience and conformity to a rule of law, our social lives would be far more chaotic. Thus, obeying and conforming to social rules is vital for creating and maintaining a community. However, communities evolve and change, thus rules and norms often need to similarly evolve. And there is a danger in a group members becoming overly compliant and conforming, such as classically illustrated in [[w:Milgram's study of obedience|Milgram's 1950's studies of obedience]]. Also, see [[w:Asch conformity experiments|Asch's conformity experiments]]. A more recent example of obedience is a TV show in which contestants were asked to torture. 80% of contestants went to the very end - i.e, administered the ultimate, potentially lethal shock ([http://news.bbc.co.uk/2/hi/europe/8573755.stm] BBC News, 2010; [http://www.telegraph.co.uk/news/worldnews/europe/france/7457780/French-contestants-torture-each-other-on-TV-Game-of-Death.html] Telegraph.co.uk, 2010).

==Motivations for helping==
Batson (1994):
* Egoism – helping benefits the helper – receive rewards or escape punishment.
* Altruism – helping benefits others – no need for reciprocity.
* Collectivism – helping benefits the in-group.
* Principalism – help because of a moral imperative

==[[w:Empathy-altruism|Empathy-altruism hypothesis]]==
Batson (1991) proposed that [[empathy]] motivates people to reduce other people’s distress by helping or comforting:
* If low empathy, people can reduce their own distress by escaping the situation
* If high empathy, emotional response corresponds to feelings of other person redue our distress by reducing other person's distress

Negative relief state theory is the proposition that people help others in order to relieve their own distress.

==Personal determinants of helping==
* Personality - weak predictor, but consider &quot;warmth&quot;
* Competence - more skilled you are in the area of need, the more likely you are to help
* Attributions - recall from social thinking that we have a tendency to blame others' problems on their selves (as opposed to their circumstances, whereas we have a tendency to find external explanations for our own distress. We generally are more likely to help someone if we perceive that their circumstances were externally caused rather than caused by themselves (and thereby &quot;deserved&quot; - see the [[w:Just World Hypothesis|Just World Hypothesis]])
* Personal norms - personal norms for helping based on personal values (e.g., religious beliefs). If we have &quot;helpfulness&quot; as part of our self-concept, then we need to act in consistent ways otherwise we experience [[cognitive dissonance]].

==Emotion and helping==
In general, positive mood increases likelihood of helping, whereas negative mood tends to decrease likelihood of helping. Note, however, that there are logical exceptions to this tendency (e.g., if it will be costsly to one's positive mood one may not help, or if it will relieve one's negative state, one may be more likely to help).

==Interpersonal determinants of helping==
# Females are more likely to receive help
# Attractiveness - more likely to help attractive others.
# Similarity - we are morely likely to help similar others (similarity increases attractiveness &amp; empathy)
# Closeness - more likely to help those we know.
# Deservingness - help those we judge as deserving our help (e.g,. based on reciprocity and attribution).

==Gender==
# Males are more likely to help in &quot;dramatic&quot; circumstances, and broader societal spheres, and they are more likely to help women than men
# Females are more likely to help in &quot;mundane&quot; life, in the local sphere, and are more likely to receive help

==[[Bystander effect]]==
The larger the group, the less likely people are to help because of:
# Diffusion of responsibility: the reduction in feeling responsible that occurs when others are present.
# Pluralistic ignorance: looking to others for cues about how to behave, while they are looking to you; collective misinterpretation.

==Five steps to helping==
Five steps (or barriers) to helping have been proposed (Latane &amp; Darley):
# Notice that something is happening
# Interpret meaning of event - Pluralistic ignorance
# Taking responsibility for providing help - # Diffusion of responsibility
# Know how to help
# Provide help 

==Good Samaritan study==
Darley and Batson (1973)'s classic study found that time (in a rush or not in a rush) had the largest effect. Those in a rush were much less likely to help. [http://faculty.babson.edu/krollag/org_site/soc_psych/darley_samarit.html Summary of the study].

==Bystander-calculus model==
Piliavin, Dovidio, Gaertner, and Clark (1981) offer a social exchange theory model for the bystander effect, according to which bystanders calculate the (perceived) costs &amp; benefits of providing help in three stages:
# Physiological arousal - e.g., witnessing an emergency - the higher the physiological arousal, the  greater chance of helping.
# Labelling the arousal - type of label influences the kind of help offered; e.g., is arousal labelled as personal distress or empathic concern? - usually labelled as personal distress.
# Evaluating the consequences -  weigh up costs of helping, choose action that reduces personal distress at lowest cost.  Costs might include getting hurt, inconvenience, embarrassment etc.

==How can we increase helping?==
# Reduce ambiguity
# Reduce distractions (or make the need for help more obvious)
# Reduce pluralistic ignorance
# Increase personal responsibility (reduce diffusion of responsibility), e.g., reduce anonymity
# Reduce concerns about competence to help
# Reduce audience inhibitions
# Reduce uncertainties of obstacles
# Educate about bystander indifference
# Model helpfulness e.g., positive models in the media.
# Teach moral inclusion - perception of certain people as inside/outside our bounds of moral or ethical concern
# Guilt &amp; concern for self-image - use of compliance tactics
# Learning about / socialising altruism

==Summary and conclusion==
# Prosocial behaviour includes conformity, obedience, and cooperating with others, but may also include disobedience.
# Human culture depends on people following rules.
# Following the rules of society and culture generally brings immense personal and social benefits.
# Is altruism unique to humans?
# Cultural and social variables and situational contingencies can significantly influence whether a person performs prosocial or antisocial behaviours

==External links==
# [https://www.psychvarsity.com/Pluralistic-Ignorance Pluralistic ignorance - Why you won’t raise your hand in the classroom]{{RoundBoxBottom}}

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  <page>
    <title>Complex Analysis</title>
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      <contributor>
        <username>Bert Niehaus</username>
        <id>2387134</id>
      </contributor>
      <comment>/* Complex Analysis Part 2 */</comment>
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      <text bytes="12953" sha1="620wje0vpqraod3vadf2fudsrawh4x8" xml:space="preserve">[[File:Wiki2Reveal Logo.png|146px|thumb|Course contains [[v:en:Wiki2Reveal|Wiki2Reveal]] Slides]]
[[File:Mapping f z equal 1 over z.gif|thumb|Moving the argument of function &lt;math&gt;f&lt;/math&gt; in the complex number plane. The point &lt;math&gt;z&lt;/math&gt; has a blue color and &lt;math&gt;f(z)= \frac{1}{z}&lt;/math&gt;  is marked in red color. &lt;math&gt;z&lt;/math&gt; is moved on a curve with  &lt;math&gt;\gamma(t)=t\cdot e^{it}&lt;/math&gt;.]]
[[File:Image of path 1 over z.webm|thumb|Image of path in the complex numbers for the function &lt;math&gt;f(z)=\frac{1}{z}&lt;/math&gt;]]
'''Complex analysis''' is a study of functions of a complex variable. This is a one quarter course in complex analysis at the undergraduate level.

==Articles==

* [[Algebra II]]
* [[Dummy variable]]
* [[Materials Science and Engineering/Equations/Quantum Mechanics]]

== Slides for Lectures ==

=== Chapter 1 - Intoduction ===
* '''[[Complex Numbers/From real to complex numbers|Complex Numbers]]''' - ([https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&amp;title=Complex%20Numbers/From%20real%20to%20complex%20numbers&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Complex%20Numbers&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
** [[w:en:Heine–Borel_theorem|Heine-Borel Theorem]]
* '''[[Riemann sphere|Riemann sphere]]''' - ([https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&amp;title=Riemann%20sphere&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Riemann%20sphere&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
* '''[[Complex_Analysis/Exponentiation_and_square_root|Exponentiation and roots]]''' - ([https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&amp;title=Complex_Analysis/Exponentiation_and_square_root&amp;author=Complex_Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Exponentiation_and_square_root&amp;coursetitle=Complex_Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]

=== Chapter 2 - Topological Foundations ===
* '''[[Complex Analysis/Sequences and series|Sequences and series]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Sequences%20and%20series&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Sequences%20and%20series&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
* [[/Power series/]]
* '''[[Inverse-producing extensions of Topological Algebras/topological algebra|Topological algebra]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Inverse-producing%20extensions%20of%20Topological%20Algebras/topological%20algebra&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=topological%20algebra&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
* [[w:en:Topological space|Topological space]] - Definition: [[Norms, metrics, topology#Definition:_topology|Topology]] 
* '''[[Norms, metrics, topology|Norms, metrics, topology]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Norms,%20metrics,%20topology&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Norms,%20metrics,%20topology&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]

=== Chapter 3 - Complex Derivative ===
* '''[[Holomorphic function|Holomorphic function]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Holomorphic%20function&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Holomorphic%20function&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
* '''[[Complex Analysis/Partial derivative|Partial Derivative]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Partial%20derivative&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Partial%20Derivative&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
* '''[[Cauchy-Riemann Equations|Cauchy-Riemann Equations (CRE)]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Cauchy-Riemann%20Equations&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Cauchy-Riemann%20Equations&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
* '''[[Complex Analysis/Application of Cauchy-Riemann Equations|Application of Cauchy-Riemann Equations]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Application%20of%20Cauchy-Riemann%20Equations&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Application%20of%20Cauchy-Riemann%20Equations&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]

=== Chapter 4 - Curves and Line Integrals ===
* '''[[Line integral|Line integral in &lt;math&gt;\mathbb{R}^n&lt;/math&gt;]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Line%20integral&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Line%20integral&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
* '''[[/Curves/|Curves]]''' - ([https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&amp;title=Complex%20Analysis/Curves&amp;author=Complex_Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Curves&amp;coursetitle=Complex%20Analysis  Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
** [[w:en:Holomorphic function|Wikipedia: holomorphic function]] 
** [[w:en:Integral|Wikipedia:Integral ]]
* '''[[Complex_Analysis/Paths|Paths]]''' - ([https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&amp;title=Complex%20Analysis/Paths&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Paths&amp;coursetitle=Complex%20Analysis  Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]

* '''[[Path Integral|Path Integral]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Path%20Integral&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Path%20Integral&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
  
* [[w:en:Curve integral |Wikipedia: Curve integral]]
* [[w:en:Continuity|Continuity]] and [[w:en:Limit of a sequence|Limit of a sequence]]

* '''[[Complex Analysis/Trace|Trace of Curve]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Trace&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Trace&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
=== Chapter 5 - Holomorphic Functions ===
* '''[[Holomorphic function|Holomorphic function]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Holomorphic%20function&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Holomorphic%20function&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
** [[Holomorphism/Criteria|Criteria]] - ([https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&amp;title=Holomorphism/Criteria&amp;author=Course:Complex_Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Criteria&amp;coursetitle=Complex_Analysis slideset]) [[File:Wiki2Reveal Logo.png|35px]]
** [[w:en:Holomorphic_function#.C3.84quivalent_properties_of_holomorphic_functions_of_one_variable|Wikipedia: Holomorphic function criteria]]
** [[/Differences from real differentiability/]]
** [[w:Conformal_mapping|conformal mappings]]&lt;math&gt;(\ast)&lt;/math&gt;, 
** [[Complex Analysis/Inequalities|Inequalities]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Inequalities&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Inequalities&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
** [[Complex Analysis/rectifiable curve|rectifiable curve]] - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/rectifiable%20curve&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=rectifiable%20curve&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
* '''[[Complex Analysis/Curve Integral|Curve Integral]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Curve%20Integral&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Curve%20Integral&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
* '''[[Complex Analysis/Path of Integration|Path of Integration]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Path%20of%20Integration&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Path%20of%20Integration&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]

* '''[[Complex Analysis/Goursat's Lemma (Details)|Goursat's Lemma (Details)]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Goursat's%20Lemma%20(Details)&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Goursat's%20Lemma%20(Details)&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
* '''[[Complex Analysis/Cauchy's Integral Theorem for Disks|Cauchy's Integral Theorem for Disks]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Cauchy's%20Integral%20Theorem%20for%20Disks&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Cauchy's%20Integral%20Theorem%20for%20Disks&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
  
* '''[[Complex Analysis/Identity Theorem|Identity Theorem]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Identity%20Theorem&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Identity%20Theorem&amp;coursetitle= Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
* '''[[Complex Analysis/Liouville's Theorem|Liouville's Theorem]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Liouville's%20Theorem&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Liouville's%20Theorem&amp;coursetitle= Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]

=== Complex Analysis Part 2 ===

* '''[[Complex Analysis/Chain|Chain]]''' - [https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Chain&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Chain&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]

* '''[[Complex Analysis/cycle|cycle]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/cycle&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=cycle&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
  
* '''[[Laurent Series|Laurent Series]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Laurent%20Series&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Laurent%20Series&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]
  
* '''[[Complex Analysis/Cauchy Integral Theorem|Cauchy Integral Theorem]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/Cauchy%20Integral%20Theorem&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Cauchy%20Integral%20Theorem&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]

* '''[[Cauchy's integral formula|Cauchy's integral formula]]''' - ([https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Cauchy's%20integral%20formula&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=Cauchy's%20integral%20formula&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]) [[File:Wiki2Reveal Logo.png|35px]]

==Lectures==
* [[/Cauchy-Riemann equations/]]
* [[Cauchy Theorem for a triangle]]
* [[Complex analytic function]]
* [[Complex Numbers]]
* [[Divergent series]]
* [[Estimation lemma]]
* [[Fourier series]]
* [[Fourier transform]]
* [[Fourier transforms]]
* [[Laplace transform]]
* [[Riemann hypothesis]]
* [[The Real and Complex Number System]]
* [[Warping functions]]

==Sample exams==

[[/Sample Midterm Exam 1/]]
[[/Sample Midterm Exam 2/]]

==See also==
* [[Boundary Value Problems]]
* [[Introduction to Elasticity]]
* [[The Prime Sequence Problem]]
* [[Wikipedia: Complex analysis]]
*[[Complex number]]
[[Category:Complex analysis| ]]
[[Category:Mathematics courses]]
[[Category:Mathematics]]

&lt;noinclude&gt;
[[de:Kurs:Funktionentheorie]]
&lt;/noinclude&gt;</text>
      <sha1>620wje0vpqraod3vadf2fudsrawh4x8</sha1>
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  </page>
  <page>
    <title>User:Marshallsumter/Radiation astronomy2/Reds</title>
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      <id>2693039</id>
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      <timestamp>2024-12-23T18:18:50Z</timestamp>
      <contributor>
        <username>Yann</username>
        <id>8872</id>
      </contributor>
      <minor />
      <comment>([[c:GR|GR]]) [[c:COM:FR|File renamed]]: [[File:Con00054.jpg]] → [[File:Proton arc over lake Superior.jpg]]</comment>
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      <text bytes="147492" sha1="nzti5gjj4vm5pz9h1ergk72syciqs2a" xml:space="preserve">[[Image:HI6563 fulldisk.jpg|thumb|right|250px|The Sun is observed through a telescope with an H-alpha filter. Credit: Marshall Space Flight Center, NASA.{{tlx|free media}}]]
“In 1926 ... [t]here were no national observatories (except the Naval Observatory), very little chance for guest observing elsewhere, no radio astronomy, no X-ray astronomy, no satellite astronomy, and very little infrared or even '''red astronomy'''!”&lt;ref name=Osterbrock&gt;{{ cite journal
|author=Donald E. Osterbrock
|title=Young Don Menzel's amazing adventures at Lick Observatory
|journal=Journal for the History of Astronomy
|month=May
|year=2002
|volume=33
|issue=111
|pages=95-118
|url=
|arxiv=
|bibcode=2002JHA....33...95O
|doi=
|pmid=
|accessdate=2012-03-12 }}&lt;/ref&gt; Bold added.
{{clear}}

==Astronomy==
{{main|Radiation astronomy/Astronomy}}
[[Image:Mars-19-09-2003.jpeg|thumb|right|250px|A photo of the planet Mars is taken in Straßwalchen (Austria) on September 19, 2003, shortly after its closest approach. Credit: Rochus Hess, http://members.aon.at/astrofotografie.
{{tlx|free media}}]]
With respect to the color '''red''' in '''astronomy''', there are studies of the '''red shift''', which may be considered an entity, sources of red radiation, and the redness of objects.
{{clear}}

==Radiation==
{{main|Radiation}}
[[Image:Glowing Stellar Nurseries.jpg|thumb|right|250px|This is a colour composite image of RCW120. Credit: ESO/APEX/DSS2/ SuperCosmos/ Deharveng(LAM)/ Zavagno(LAM).{{tlx|free media}}]]
[[Image:Color icon red.svg|thumb|right|250px|Nine different shades of red are shown. Credit: [[c:user:Badseed|Badseed]].{{tlx|free media}}]]
[[Image:Rojos.png|thumb|left|250px|Shades of red are shown. Credit: [[c:user:Maulucioni|Maulucioni]].{{tlx|free media}}]]
[[Image:Color icon red v2.svg|thumb|center|250px|This “red icon” shows a broader variety of red. Credit: Mizunoryu, Badseed, Jacobolus.{{tlx|free media}}]]
In [[w:Wavelength|wavelength]]s, red astronomy covers 620 - 750 [[w:Nanometer|nm]].

Infrared or red radiation from a common household radiator or electric heater is an example of thermal radiation, as is the heat emitted by an operating incandescent light bulb. Thermal radiation is generated when energy from the movement of charged particles within atoms is converted to electromagnetic radiation.

'''Infrared''' ('''IR''') light is [[Radiation astronomy/Electromagnetics|electromagnetic radiation]] with longer [[w:wavelength|wavelength]]s than those of [[w:Light|visible light]], extending from the nominal red edge of the visible spectrum at 700 [[w:nanometre|nanometre]]s (nm) to 1&amp;nbsp;mm. This range of wavelengths corresponds to a [[w:Frequency spectrum|frequency]] range of approximately 430&amp;nbsp;[[w:THz|THz]] down to 300&amp;nbsp;[[w:GHz|GHz]],&lt;ref name=Liew&gt;{{ cite book
|author=S. C. Liew
|url=http://www.crisp.nus.edu.sg/~research/tutorial/em.htm
|title=Electromagnetic Waves
|publisher=Centre for Remote Imaging, Sensing and Processing
|accessdate=2006-10-27 }}&lt;/ref&gt; and includes most of the [[w:thermal radiation|thermal radiation]] emitted by objects near room temperature. Infrared light is emitted or absorbed by [[w:molecule|molecule]]s when they change their [[w:Infrared spectroscopy|rotational-vibrational]] movements.

'''Far-red''' light is light at the extreme red end of the visible spectrum, between red and infra-red light. Usually regarded as the region between 710 and 850&amp;nbsp;nm wavelength, it is dimly visible to some human eyes.
{{clear}}

==Planetary sciences==
{{main|Planetary sciences}}
[[Image:Titania (moon) color cropped.jpg|thumb|right|250px|This high-resolution color composite of Titania was made from [[w:Voyager 2|Voyager 2]] images taken January 24, 1986, as the spacecraft neared its closest approach to Uranus. Credit: NASA/JPL. Derivative work: [[c:User:Ruslik0|Ruslik]].{{tlx|free media}}]]
&quot;Far-red light is largely reflected or transmitted by [[w:plants|plants]] on Earth because of the [[w:absorbance|absorbance]] spectrum of [[w:chlorophyll|chlorophyll]], and it is perceived by the plant [[w:photoreceptor protein|photoreceptor]] [[w:phytochrome|phytochrome]]. However, some organisms can use it as a source of energy in photosynthesis.&lt;ref name=Babio&gt;[http://dx.doi.org/10.1016/j.bbabio.2005.05.005]&lt;/ref&gt;&lt;ref name=Quist&gt;[ÖQuist, G. (1969), Adaptations in Pigment Composition and Photosynthesis by Far Red Radiation in Chlorella pyrenoidosa. Physiologia Plantarum, 22: 516–528. doi: 10.1111/j.1399-3054.1969.tb07406.x]&lt;/ref&gt;
Far-red light also is used for vision by certain organisms such as some species of deep-sea fishes.&lt;ref&gt;Douglas, R.H.; Partridge, J.C.; Dulai, K.; Hunt, D.; Mullineaux, C.W.; Tauber, A.Y.; Hynninen, P.H. 1998. Dragon fish see using chlorophyll. Nature. 393(6684): 423-424.&lt;/ref&gt;&lt;ref&gt;[http://www.asknature.org/strategy/3737c9336a6ded86ed50cdd48c210735]&lt;/ref&gt;&lt;ref&gt;[http://www.bio-medicine.org/biology-news/Scientists-discover-unique-microbe-in-Californias-largest-lake-203-1/]&lt;/ref&gt;

The name ''Pomo'', or [[w:Pomo people|Pomo people]], originally meant &quot;those who live at red earth hole&quot; and was once the name of a village in southern [[w:Potter Valley, California|Potter Valley]] near the present-day community of [[w:Pomo, California|Pomo]].&lt;ref name=Kroeber&gt;{{ cite journal
 | author = Alfred L. Kroeber
 | issue = 2
 | journal = University of California Publications in American Archaeology and Ethnology
 | pages = 31–69
 | title = California place names of Indian origin
 | url = http://soda.sou.edu/awdata/030731c1.pdf
 | volume = 12
 | year = 1916 }}.&lt;/ref&gt; It may have referred to local deposits of the red mineral magnesite, used for red beads, or to the reddish earth and clay such as hematite mined in the area.&lt;ref name=McClendon&gt;McClendon and Oswalt 1978:277.&lt;/ref&gt;

Some argue that cosmetic body art was the earliest form of ritual in human culture, dating over 100,000 years ago from the African Middle Stone Age. The evidence for this comes in the form of utilised red mineral pigments (red ochre) including crayons associated with the emergence of ''Homo sapiens'' in Africa.&lt;ref&gt;Power, C. 2010. Cosmetics, identity and consciousness. ''Journal of Consciousness Studies'' 17, 7-8: 73-94.&lt;/ref&gt;&lt;ref&gt;Power, C. 2004. Women in prehistoric art. In G. Berghaus (ed.), ''New Perspectives in Prehistoric Art.'' Westport, CT &amp; London: Praeger, pp. 75-104.&lt;/ref&gt;&lt;ref&gt;Watts, Ian. 2009. Red ochre, body painting and language: in-terpreting the Blombos ochre. In ''The Cradle of Language,'' Rudolf Botha and Chris Knight (eds.), pp. 62–92. Oxford: Oxford University Press.&lt;/ref&gt;&lt;ref&gt;Watts, Ian. 2010. The pigments from Pinnacle Point Cave 13B, Western Cape, South Africa. ''Journal of Human Evolution'' 59: 392–411.&lt;/ref&gt;

A variant of ochre containing a large amount of hematite, or dehydrated iron oxide, has a reddish tint known as &quot;red ochre&quot;. '''Red ochre''', Fe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;, takes its reddish color from the mineral hematite, which is a dehydrated iron oxide.
{{clear}}

==Red minerals==
[[Image:Rhodolite in Matrix-Garnet Group Magnesium iron aluminum silicate Macon County North Carolina 2904.jpg|thumb|right|250px|Rhodolite is the rose-pink to red mineral, a type of garnet, in this magnesium iron aluminum silicate mineral. Credit: Dave Dyet.{{tlx|free media}}]]
[[Image:Breithauptite-229669.jpg|thumb|left|250px|This is a specimen of Breithauptite on calcite from the Samson Mine, St Andreasberg, [[w:Harz Mountains|Harz Mountains]], Lower Saxony, Germany. Credit: Leon Hupperichs.{{tlx|free media}}]]
[[Image:Cinnabarit 01.jpg|thumb|right|250px|Cinnabar is a naturally occurring cochineal-red, towards brownish red and lead-gray, mercury-sulfide mineral. Credit: H. Zell.{{tlx|free media}}]]
[[Image:Crocoite from Tasmania.jpg|thumb|left|250px|This Crocoite specimen is from the Red Lead Mine, [[w:Tasmania|Tasmania]], [[w:Australia|Australia]]. Credit: Eric Hunt.{{tlx|free media}}]]
[[Image:Eudialyte.jpg|thumb|right|250px|Eudialyte is a somewhat rare, red silicate mineral. Credit: [[w:user:Baryonyx|Baryonyx]].{{tlx|free media}}]]
[[Image:Hematite.jpg|thumb|left|250px|Hematite is a blood colored ore. Credit: [[c:user:DanielCD~commonswiki|DanielCD~commonswiki]].{{tlx|free media}}]]
[[Image:MichiganBIF.jpg|thumb|right|250px|This is a close-up of hematitic [[w:banded iron formation|banded iron formation]] specimen from Upper Michigan. Scale bar is 5.0 mm. Credit: [[c:user:Wilson44691|Wilson44691]].{{tlx|free media}}]]
[[Image:Litharge &quot;An der Seilbahn&quot;.jpg|left|thumb|250px|This litharge specimen is from &quot;An der Seilbahn&quot; slag locality, Hüsten, Arnsberg, Sauerland, North Rhine-Westphalia, Germany. Credit: Elmar Lackner, with permission.{{tlx|fairuse}}]]
[[Image:Minium-232908.jpg|right|thumb|250px|Minium druse is on cerussite from the Old Yuma Mine, Tucson Mountains, Arizona. Credit: [[c:user:Robert M. Lavinsky|Robert M. Lavinsky]].{{tlx|free media}}]]
'''Rhodolite''' is a varietal name for rose-pink to red  mineral [[w:pyrope|pyrope]], a species in the [[w:garnet|garnet]] group.

Chemically, rhodolite is an iron-magnesium-aluminium silicate, [(Mg,Fe)&lt;sub&gt;3&lt;/sub&gt;Al&lt;sub&gt;2&lt;/sub&gt;(SiO&lt;sub&gt;4&lt;/sub&gt;)&lt;sub&gt;3&lt;/sub&gt;,] part of the pyrope-[[w:almandine|almandine]] [[w:solid solution|solid-solution]] series, with an approximate garnet composition of ''Py&lt;sub&gt;70&lt;/sub&gt;Al&lt;sub&gt;30&lt;/sub&gt;''.

'''Breithauptite''' is a nickel [[w:antimonide mineral|antimonide mineral]] with the simple formula NiSb. Breithauptite is a metallic opaque copper-red mineral crystallizing in the [[w:Hexagonal (crystal system)|hexagonal]] - dihexagonal dipyramidal [[w:crystal system|crystal system]]. It is typically massive to reniform in habit, but is observed as tabular crystals. It has a [[w:Mohs hardness|Mohs hardness]] of 3.5 to 4 and a specific gravity of 8.23.

It occurs in hydrothermal calcite veins associated with cobalt–nickel–silver ores.

'''Cinnabar''' or '''cinnabarite''' (red mercury(II) sulfide (HgS), native vermilion), is the common ore of mercury. Its color is cochineal-red, towards brownish red and lead-gray. Cinnabar may be found in a massive, granular or earthy form and is bright scarlet to brick-red in color.&lt;ref name=King&gt;{{ cite journal
| journal = Geology Today
| volume = 18
| issue = 5
| pages = 195–9
|title = Minerals Explained 37: Cinnabar
| author = R. J. King
| doi = 10.1046/j.0266-6979.2003.00366.x
| year = 2002 }}&lt;/ref&gt; Generally cinnabar occurs as a vein-filling mineral associated with recent volcanic activity and alkaline hot springs. Cinnabar is deposited by epithermal ascending aqueous solutions (those near surface and not too hot) far removed from their igneous source.

'''Crocoite''' is a mineral consisting of [[w:lead chromate|lead chromate]], [[w:Lead|Pb]][[w:Chromium|Cr]][[w:Oxygen|O]]&lt;sub&gt;4&lt;/sub&gt;. Crystals are of a bright hyacinth-red color. Relative rarity of crocoite is connected with specific conditions required for its formation: an oxidation zone of lead ore bed and presence of ultramafic rocks serving as the source of chromium (in [[w:chromite|chromite]]).

'''Eudialyte''' is a somewhat rare, red silicate mineral, which forms in alkaline igneous rocks, such as nepheline syenites.

'''Hematite''' is the mineral form of iron(III) oxide (Fe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;), one of several iron oxides. Hematite is colored black to steel or silver-gray, brown to reddish brown, or red. Huge deposits of hematite are found in [[w:banded iron formation|banded iron formation]]s.

'''Litharge''' (PbO) is a secondary mineral which forms from the oxidation of galena ores.

'''Minium''' {{chem|Pb|2+|2|Pb|4+|O|4}} is rare and occurs in lead-mineral deposits that have been subjected to severe oxidizing conditions.
{{clear}}

==Theoretical red radiation astronomy==
[[Image:Backyard astronomy 28 - Flickr - planes, space, nature.jpg|thumb|right|250px|The Rosette Nebula (also known as Caldwell 49) is an H II region located near one end of a giant molecular cloud in the Monoceros region of the Milky Way Galaxy. Credit: [https://www.flickr.com/people/158350039@N03 K Bahr].{{tlx|free media}}]]
&quot;[S]ince the majority of carbon and S giants do not possess nearly so much lithium [as has been detected in some red-giant stars], it is necessary to postulate that the production process involves some unusual events.&quot;&lt;ref name=Cameron/&gt;

&quot;[H]elium-burning shell flashes in advanced stages of stellar evolution [may] occasionally induce complete convection of the outer envelope down to the helium-burning shell. If the hydrogen mixing is relatively small for the first 10&lt;sup&gt;7&lt;/sup&gt; seconds, the result may be the production of large amounts of heavy elements by the ''s''-process. When complete mixing commences, the &lt;sup&gt;3&lt;/sup&gt;He in the envelope will be converted to &lt;sup&gt;7&lt;/sup&gt;Be, and the subsequent delayed electron capture to form &lt;sup&gt;7&lt;/sup&gt;Li may allow enough lithium to remain near the surface to account for the very large lithium abundances in some S and carbon red-giant stars. ... the &lt;sup&gt;7&lt;/sup&gt;Li/&lt;sup&gt;6&lt;/sup&gt;Li ratio in these stars should be quite large (&gt; 100).&quot;&lt;ref name=Cameron&gt;{{ cite journal
|author=A. G. W. Cameron
|author2=W. A. Fowler
|title=Lithium and the s-PROCESS in Red-Giant Stars
|journal=The Astrophysical Journal
|month=February
|year=1971
|volume=164
|issue=02
|pages=111-4
|url=http://adsabs.harvard.edu/abs/1971ApJ...164..111C
|arxiv=
|bibcode=1971ApJ...164..111C
|doi=10.1086/150821
|pmid=
|accessdate=2013-08-01 }}&lt;/ref&gt;
{{clear}}

==Entities==
{{main|Radiation astronomy/Entities}}
[[Image:Red Cliffs of Scarborough Tree Root Erosion-01+ (2518248796).jpg|thumb|right|250px|Red Cliffs of Scarborough show tree root erosion. Credit: [https://www.flickr.com/people/34534185@N00 Sheba_Also 43,000 photos].{{tlx|free media}}]]
&quot;[G]alaxies R8 and R10 lie at z = 1.290 - 1.298 while the other 3 are at z = 1.317 - 1.320, i.e., there is a &quot;gap&quot; pf 2500 km s&lt;sup&gt;-1&lt;/sup&gt; in the mean rest frame, though there is no clear segregation on the sky. These may be two separate physical entities (e.g., filaments/sheets/subclusters), but this speculation lies beyond the available data.&quot;&lt;ref name=Liu/&gt;
{{clear}}

==Sources==
{{main|Radiation astronomy/Sources}}
[[Image:Source of Eastern Red Lake - geograph.org.uk - 1823264.jpg|thumb|right|250px|Source of Eastern Red Lake is shown. Credit: [[c:user:Guy Wareham|Guy Wareham]].{{tlx|free media}}]]
&quot;Most of the sources are resolved in [Hubble Space Telescope] HST ''F''814''W'' imaging so they are certainly galaxies and not M stars.&quot;&lt;ref name=Liu/&gt;
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==Objects==
{{main|Radiation astronomy/Objects|Object astronomy}}
[[Image:Red aurora Independence MO.jpg|thumb|right|250px|A view of an all-red aurora is captured in Independence, Mo., on October 24, 2011. Credit: Tobias Billings.{{tlx|fairuse}}]]
&quot;The nature of extremely red objects (EROs) remains an open question in understanding the faint galaxy population at z &gt; 1.&quot;&lt;ref name=Liu&gt;{{ cite book
|author=Michael C. Liu
|author2=Arjun Dey
|author3=James R. Graham
|author4=Charles C. Steidel
|author5=Kurt Adelberger
|title=Extremely Red Galaxies in the Field of QSO 1213-0017: A Galaxy Concentration at z = 1.31, In: ''The Hy-Redshift Universe: Galaxy Formation and Evolution at High Redshift''
|publisher=American Society of Physics
|location=Berkeley, California USA
|date=1999
|volume=193
|editor=Andrew J. Bunker
|editor2=Wil J. M. van Breugel
|pages=344-7
|url=http://adsabs.harvard.edu/full/1999ASPC..193..344L
|arxiv=
|bibcode=1999ASPC..193..344L
|doi=
|pmid=
|isbn=1-58381-019-6
|accessdate=2013-07-30 }}&lt;/ref&gt;
{{clear}}

==Continua==
{{main|Radiation astronomy/Continua}}
[[Image:The red sea Rivera southern of Jordan.png|thumb|right|250px|The red sea Rivera is in southern of Jordan. Credit: [[c:user:Motasem16|Motasem16]].{{tlx|free media}}]]
&quot;The other 3 red galaxies are devoid of strong emission lines, but they do show continuum breaks identifiable as the rest-frame mid-UV breaks at 2640 Å and 2900 Å (Figure 2).&quot;&lt;ref name=Liu/&gt;
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==Absorptions==
{{main|Radiation astronomy/Absorptions|Absorption astronomy}}
[[Image:Radiation Spectrum.png|thumb|right|250px|This figure shows the solar radiation spectrum for direct light at both the top of the Earth's atmosphere (represented by the area in yellow) and at sea level (area in red). Credit: [[w:user:Dragons flight|Robert A. Rohde]].{{tlx|free media}}]]
The sun produces light with a distribution similar to what would be expected from a 5525 K (5250 °C) blackbody, which is approximately the sun's surface temperature. As light passes through the atmosphere, some is absorbed by gases with specific absorption bands. Additional light is redistributed by Rayleigh scattering, which is responsible for the atmosphere's blue color. These curves are based on [National Renewable Energy Laboratory] NREL data for above the atmosphere and at sea level, which are standards adopted by the photovoltaics industry to ensure consistent test conditions and are similar to the light that could be expected in North America. Regions for ultraviolet, visible and infrared light are indicated.

Balmer lines can appear as absorption or emission lines in a spectrum, depending on the nature of the object observed. In stars, the Balmer lines are usually seen in absorption, and they are &quot;strongest&quot; in stars with a surface temperature of about 10,000 kelvin (spectral type A). In the spectra of most spiral and irregular galaxies, [active galactic nuclei] AGNs, H II regions and planetary nebulae, the Balmer lines are emission lines.
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==Emissions==
{{main|Radiation astronomy/Emissions}}
[[Image:The Red Rectangle around the star HD 44179.jpg|thumb|right|250px|The Hubble Space Telescope [Advanced Camera for Surveys] ACS image has H-alpha emission of the Red Rectangle shown in blue. Credit: ESA/Hubble and NASA.{{tlx|free media}}]]
&quot;[T]he extended red emission (ERE) [is] observed in many dusty astronomical environments, in particular, the diffuse interstellar medium of the Galaxy. ... silicon nanoparticles provide the best match to the spectrum and the efficiency requirement of the ERE.&quot;&lt;ref name=Witt&gt;{{ cite journal
|author=Adolf N. Witt
|author2=Karl D. Gordon
|author3=Douglas G. Furton
|title=Silicon Nanoparticles: Source of Extended Red Emission?
|journal=The Astrophysical Journal Letters
|month=July 1,
|year=1998
|volume=501
|issue=1
|pages=L111-5
|url=http://iopscience.iop.org/1538-4357/501/1/L111
|arxiv=astro-ph/9805006
|bibcode=
|doi=10.1086/311453
|pmid=
|accessdate=2013-07-30 }}&lt;/ref&gt;

&quot;The ERE was first recognized clearly in the peculiar reflection nebula called the Red Rectangle by Schmidt, Cohen, &amp; Margon (1980).&quot;&lt;ref name=Witt/&gt;

The '''Red Rectangle Nebula''', so called because of its red color and unique rectangular shape, is a protoplanetary nebula in the Monoceros constellation. Also known as HD 44179, the nebula was discovered in 1973 during a rocket flight associated with the AFCRL Infrared Sky Survey called Hi Star.
{{clear}}

==Bands==
{{main|Radiation astronomy/Bands}}
[[Image:PIA04533.jpg|thumb|250px|right|The Red Rectangle is a proto-planetary nebula. Here is the Hubble Space Telescope Advanced Camera for Surveys (ACS) image. Broadband red light is shown in red. Credit: JPL/NASA.{{tlx|free media}}]]
The &quot;ERE manifests itself through a broad, featureless emission band of 60 &lt; FWHM &lt; 100 nm, with a peak appearing in the general wavelength range 610 &lt; λ&lt;sub&gt;''p''&lt;/sub&gt; &lt; 820 nm.&quot;&lt;ref name=Witt/&gt;

In the Red Rectangle Nebula, diffraction-limited speckle images of it in visible and near infrared light reveal a highly symmetric, compact [[w:bipolar nebula|bipolar nebula]] with X-shaped spikes which imply toroidal dispersion of the circumstellar material. The central binary system is completely obscured, providing no direct light.&lt;ref name=Menshchikov&gt;{{ cite journal
|author=A. B. Men'shchikov
|author2=D. Schertl
|author3=P. G. Tuthill
|author4=G. Weigelt
|author5=L. R. Yungelson
|title=Properties of the close binary and circumbinary torus of the Red Rectangle
|journal=Astronomy and Astrophysics
|month=
|year=2002
|volume=393
|issue=
|pages=867-85
|url=http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2002A%26A...393..867M
|arxiv=astro-ph/0206189
|bibcode=2002A&amp;A...393..867M
|doi=10.1051/0004-6361:20020859
|pmid=
|accessdate=2013-07-30 }}&lt;/ref&gt;

Using various flames such as from a Bunsen burner, &quot;[s]trontium yields two red bands and one orange band.&quot;&lt;ref name=Hartley&gt;{{ cite journal
|author=Walter Noel Hartley
|title=On Some Devices Facilitating the Study of Spectra
|journal=The Astrophysical Journal
|month=December
|year=1907
|url=http://adsabs.harvard.edu/abs/1907ApJ....26..363H
|arxiv=
|bibcode=1907ApJ....26..363H
|doi=10.1086/141513
|pmid=
|accessdate=2013-08-01 }}&lt;/ref&gt;
{{clear}}

==Backgrounds==
{{main|Radiation astronomy/Backgrounds}}
[[Image:Green Red Gradient Background.png|thumb|right|250px|Green to Red Diagonal Gradient background is shown. Credit: [[c:user:Cebarrameda|Cebarrameda]].{{tlx|free media}}]]
&quot;[T]he instrumental response, sky background, and seeing conspire to provide the best images. All the available bands are used to define colors with which we separate cluster members from the background in order to minimize dilution of the weak-lensing signal by unlensed objects.&quot;&lt;ref name=Broadhurst/&gt;

&quot;We select red galaxies with colors redder than the color-magnitude sequence of cluster E/SO galaxies. The sequence forms a well-defined line due to the richness and relatively low redshifts of our clusters. These red galaxies are expected to lie in the background by virtue of ''k''-corrections which are greater than for the red cluster sequence galaxies&quot;.&lt;ref name=Broadhurst/&gt;

&quot;Typically the proportion of blue galaxies used is around 50% of the red background.&quot;&lt;ref name=Broadhurst&gt;{{ cite journal
|author=Tom Broadhurst
|author2=Keiichi Umetsu
|author3=Elinor Medezinski
|author4=Masamune Oguri
|author5=Yoel Rephaeli
|title=Comparison of Cluster Lensing Profiles with ΛCDM Predictions
|journal=The Astrophysical Journal Letters
|month=September 11,
|year=2008
|volume=685
|issue=1
|pages=L9
|url=http://iopscience.iop.org/1538-4357/685/1/L9
|arxiv=
|bibcode=
|doi=10.1086/592400
|pmid=
|accessdate=2013-07-31 }}&lt;/ref&gt;

&quot;[T]he gravitational shear field [is derived] by locally averaging the corrected distortions of color-selected background galaxies of each cluster. ... Maps of the surface number-density distribution of color-selected cluster member galaxies [have been produced], with the gravitational shear of background galaxies overlaid ... Profiles of background red galaxy counts, whose intrinsic slope is relatively shallow [have been observed] ... the utility of the background red galaxies for measuring magnification [has been established].&quot;&lt;ref name=Broadhurst/&gt;

&quot;The distortion profiles measured are among the most accurate constructed to date and the great depth of the Subaru imaging permits magnification profiles to be established with unprecedented detail using the background red galaxy counts.&quot;&lt;ref name=Broadhurst/&gt;
{{clear}}

==Meteors==
{{main|Radiation/Meteors}}
[[Image:Molecular.cloud.arp.750pix.jpg|thumb|right|250px|This cloud of gas and dust is being deleted. Credit: Hubble Heritage Team (STScI/AURA), N. Walborn (STScI) &amp; R. Barbß (La Plata Obs.), NASA.{{tlx|free media}}]]
&quot;[T]he ionization energy of oxygen atoms in a meteor trail can be converted into red-orange emission of atmospheric-system molecular oxygen bands, resulting in a red afterglow in meteor trains associated with fireballs brighter than magnitude -8.&quot;&lt;ref name=Baggaley&gt;{{ cite journal
|author=W. J. Baggaley
|title=The red afterglow in meteor wakes
|journal=Bulletin of the Astronomical Institutes of Czechoslovakia
|month=
|year=1977
|volume=28
|issue=6
|pages=356-9
|url=http://adsabs.harvard.edu/abs/1977BAICz..28..356B
|arxiv=
|bibcode=1977BAICz..28..356B
|doi=
|pmid=
|accessdate=2013-07-31 }}&lt;/ref&gt;

&quot;The red meteors definitely predominated among those with any marked colour.&quot;&lt;ref name=Millman&gt;{{ cite journal
|author=P. M. Millman
|title=Meteor News-South African Meteor Observations, April-May, 1939
|journal=Journal of the Royal Astronomical Society of Canada
|month=August
|year=1939
|volume=33
|issue=08
|pages=260-1
|url=http://adsabs.harvard.edu/full/1939JRASC..33..260M
|arxiv=
|bibcode=1939JRASC..33..260M
|doi=
|pmid=
|accessdate=2013-07-31 }}&lt;/ref&gt;

&quot;Red meteors were rare in all cases, and the shower results fell within the sporadic annual spread of 0.396—0.8% of the total meteors seen. They were generally recorded as being fainter than expected, in line with the scotopic eye's poor red appreciation.&quot;&lt;ref name=McBeath&gt;{{ cite journal
|author=Alastair McBeath
|title=Shower meteor colors
|journal=WGN, Journal of the International Meteor Organization
|month=October
|year=1991
|volume=19
|issue=5
|pages=198-205
|url=http://adsabs.harvard.edu/full/1991JIMO...19..198M
|arxiv=
|bibcode=1991JIMO...19..198M
|doi=
|pmid=
|accessdate=2013-07-31 }}&lt;/ref&gt;
{{clear}}

==Cosmic rays==
{{main|Radiation/Cosmic rays}}
[[Image:243 Ida - August 1993 (16366655925).jpg|thumb|right|250px|Asteroid 243 Ida is seen by the Galileo probe on August 28, 1993. Credit: NASA/JPL/Processed by Kevin M. Gill.{{tlx|free media}}]]
[[Image:243 ida crop.jpg|thumb|right|250px|This is an approximately natural color picture of the asteroid 243 Ida on August 28, 1993. Credit: NASA/JPL.{{tlx|free media}}]]
While 243 Ida has undergone space weathering that has increased its redness, these two images are the same as taken by the Galileo spacecraft with different processing.

&quot;The &lt;sup&gt;22&lt;/sup&gt;Ne/&lt;sup&gt;20&lt;/sup&gt;Ne ratio measured in solar CRs (0.13) agrees with the Ne-A ratio in meteorites (0.12) and is taken here as standard solar system value. The disagreement between solar wind (0.07) and solar flare (0.13) measurements is not understood, but the close similarity between isotopic ratios of C, N, O, and Mg measured in normal solar flares and meteoritic values testifies that, at least, there is no isotopic fractionation in these flares (Mewaldt ''et al.'' 1981; Dietrich and Simpson 1981).&quot;&lt;ref name=Casse/&gt;

&quot;Potential &lt;sup&gt;22&lt;/sup&gt;Ne sources are: (1) young supernova remnants (SNRs) still bearing the print of explosive hydrogen burning, (2) nova outbursts, (3) pulsing red giants, and (4) carbon-rich Wolf-Rayet stars and more generally H-deprived stars.&quot;&lt;ref name=Casse/&gt;

&quot;Pulsing red giants are thought to synthesize &lt;sup&gt;22&lt;/sup&gt;Ne in significant quantities in their helium-burning shells and to eject the processed material brought to the surface via stellar wind and, subsequently, via envelope ejection in the planetary nebula (PN) phase (Iben and Truran 1978). However, the &lt;sup&gt;22&lt;/sup&gt;Ne excess relative to the solar system abundance in the ejected material is (even before dilution) less than the &lt;sup&gt;22&lt;/sup&gt;Ne excess infered at the CR sources.&lt;sup&gt;2&lt;/sup&gt; The weakest point of the red giant scenario is it requires, in an ad hoc fashion, evolved stars near 4 ''M''&lt;sub&gt;ʘ&lt;/sub&gt;, and 4 ''M''&lt;sub&gt;ʘ&lt;/sub&gt; only, to emit most CRs, since virtually no dilution with CRs of any other origin is allowed.&quot;&lt;ref name=Casse/&gt;

&quot;[T]he ability of red giants to accelerate [cosmic rays] CRs is questionable. In the framework of acceleration by stellar winds (Cassé and Paul 1980), they are energetically unfavorable, compared to younger mass-losing objects: mass loss rate ''Ṁ'' ~ 10&lt;sup&gt;-8&lt;/sup&gt; - 10&lt;sup&gt;-9&lt;/sup&gt; yr&lt;sup&gt;-1&lt;/sup&gt; and terminal velocity of the wind ν&lt;sub&gt;w&lt;/sub&gt; ~ 10 km s&lt;sup&gt;-1&lt;/sup&gt; against ''Ṁ'' &gt; 10&lt;sup&gt;-5&lt;/sup&gt; ''M''&lt;sub&gt;ʘ&lt;/sub&gt; yr&lt;sup&gt;-1&lt;/sup&gt; and ν&lt;sub&gt;w&lt;/sub&gt; ~ 2000 km s&lt;sup&gt;-1&lt;/sup&gt; for Wolf-Rayet (W-R) stars.&quot;&lt;ref name=Casse&gt;{{ cite journal
|author=M. Cassé
|author2=J. A. Paul
|title=On the stellar origin of the &lt;sup&gt;22&lt;/sup&gt;Ne excess in cosmic rays
|journal=The Astrophysical Journal
|month=July 15,
|year=1982
|volume=258
|issue=
|pages=860-3
|url=http://adsabs.harvard.edu/full/1982ApJ...258..860C
|arxiv=
|bibcode=1982ApJ...258..860C
|doi=
|pmid=
|accessdate=2013-08-01 }}&lt;/ref&gt;

==Neutrons==
{{main|Radiation/Neutrons}}
[[Image:PIA20353 Ceres Neutron Counts Reflect Hydrogen Abundance.jpg|thumb|right|250px|This map shows a portion of the northern hemisphere of Ceres with neutron counting data acquired by the gamma ray and neutron detector (GRaND) instrument aboard NASA's Dawn spacecraft. Credit: NASA/JPL-Caltech/UCLA/MPS/DLR/IDA/PSI.
{{tlx|free media}}]]
These data reflect the concentration of hydrogen in the upper yard (or meter) of regolith, the loose surface material on Ceres. The color information is based on the number of neutrons detected per second by GRaND. Counts decrease with increasing hydrogen concentration. The color scale of the map is from blue (lowest neutron count) to red (highest neutron count).

Lower neutron counts near the pole suggest the presence of water ice within about a yard (meter) of the surface at high latitudes.

The GRaND data were acquired from Dawn's low-altitude mapping orbit (LAMO) at Ceres, a distance of 240 miles (385 kilometers) from the dwarf planet. The longitude is centered on Occator Crater.

&quot;Seven percent of a normal solar mass contains nearly 2 X 10&lt;sup&gt;51&lt;/sup&gt; iron atoms. The total number of admixed protons is of the order of 4 X 10&lt;sup&gt;50&lt;/sup&gt;. Almost all of these are converted to neutrons by the &lt;sup&gt;12&lt;/sup&gt;C(''p'',γ)&lt;sup&gt;13&lt;/sup&gt;N(e&lt;sup&gt;+&lt;/sup&gt;ν)&lt;sup&gt;13&lt;/sup&gt;C and &lt;sup&gt;13&lt;/sup&gt;C(α,''n'')&lt;sup&gt;16&lt;/sup&gt;O reactions. Since significant synthesis of heavy elements requires the production of 10-10&lt;sup&gt;2&lt;/sup&gt; neutrons per iron nucleus (Clayton ''et al.'' 1961; Seeger, Fowler, and Clayton 1965; Seeger and Fowler 1966), it may be seen that significant ''s''-process production of heavy elements [such as lithium] would occur only if the metal content of the star is less than solar by two orders of magnitude.&quot;&lt;ref name=Cameron/&gt;

&quot;A ratio Rb/Sr ≃ 0.05 [may be derived] for the ''s''-processed material from the He-burning shell ... [involving] the branch in the ''s''-process path at &lt;sup&gt;85&lt;/sup&gt;Kr [that] may be used to determine the neutron density at the time of ''s''-processing. The derived ratio is consistent with predicted neutron densities for operation of the ''s''-process during the interpulse intervals in low-mass asymptotic giant branch (AGB) stars but clearly inconsistent with much higher neutron densities predicted for the running of the ''s''-process in the He-shell thermal pulses of intermediate mass AGB stars and probably also of low-mass AGB stars.&quot;&lt;ref name=Lambert/&gt;

&quot;The absence of &lt;sup&gt;96&lt;/sup&gt;Zr sets an upper limit on the neutron density at the ''s''-process site which is higher than and, therefore, consistent with the limit set by the Rb abundances in related stars.&quot;&lt;ref name=Lambert/&gt;
{{clear}}

==Protons==
{{main|Radiation astronomy/Protons|Proton astronomy}}
[[Image:Proton arc over lake Superior.jpg|thumb|right|250px|Proton arc occurs over Lake Superior. Credit: NOAA Photo Library.{{tlx|free media}}]]
The image on the right shows a proton arc in red as part of the Aurora Borealis.

&quot;The total number of admixed protons in [seven percent of a normal solar mass] is of the order of 4 X 10&lt;sup&gt;50&lt;/sup&gt;.&quot;&lt;ref name=Cameron/&gt;

&quot;Diamond nanocrystals (size 100 nm) emit bright luminescence at 600–800 nm when exposed to green and yellow photons. The photoluminescence, arising from excitation of the nitrogen-vacancy defect centers created by proton-beam irradiation and thermal annealing, closely resembles the extended red emission (ERE) bands observed in reflection nebulae and planetary nebulae. The central wavelength of the emission is 700 nm&quot;.&lt;ref name=Chang&gt;{{ cite journal
|author=Huan-Cheng Chang
|author2=Kowa Chen
|author3=Sun Kwok
|title=Nanodiamond as a Possible Carrier of Extended Red Emission
|journal=The Astrophysical Journal
|month=March 10,
|year=2006
|volume=639
|issue=2
|pages=L63-6
|url=http://iopscience.iop.org/1538-4357/639/2/L63/fulltext/
|arxiv=
|bibcode=2006ApJ...639L..63C
|doi=10.1086/502677
|pmid=
|accessdate=2013-08-01 }}&lt;/ref&gt;
{{clear}}

==Electrons==
{{main|Radiation astronomy/Electrons|Electron astronomy}}
[[Image:BigRed-Sprite.jpg|thumb|right|250px|This is the first color image of a sprite, taken from an aircraft. Credit: [[c:user:Eastview|Eastview]].{{tlx|free media}}]]
[[Image:Sprite from ISS (cropped).jpg|thumb|left|250px|A sprite is seen and photographed from  the ISS (International Space Station). Credit: Image Science and Analysis Laboratory, NASA-Johnson Space Center. &quot;The Gateway to Astronaut Photography of Earth.&quot;.{{tlx|free media}}]]
&quot;The appearance of extensive red emission wings typifies emission lines formed in spherical expanding atmospheres with electron scattering present.&quot;&lt;ref name=Auer&gt;{{ cite journal
|author=Lawrence H. Auer
|author2=David van Blerkom
|title=Electron scattering in spherically expanding envelopes
|journal=The Astrophysical Journal
|month=November 15,
|year=1972
|volume=178
|issue=11
|pages=175-81
|url=http://adsabs.harvard.edu/full/1972ApJ...178..175A
|arxiv=
|bibcode=1972ApJ...178..175A
|doi=
|pmid=
|accessdate=2013-08-01 }}&lt;/ref&gt;

&quot;[E]lectron energization in the lower ionosphere [may be] due to lightning induced transient electromagnetic pulses.&quot;&lt;ref name=Valdivia&gt;{{ cite journal
|author=J. A. Valdivia
|author2=G. Milikh
|author3=K. Papadopoulos
|title=Red sprites: Lightning as a fractal antenna
|journal=Geophysical Research Letters
|month=December 15,
|year=1997
|volume=24
|issue=24
|pages=3169-72
|url=http://onlinelibrary.wiley.com/doi/10.1029/97GL03188/full
|arxiv=
|bibcode=
|doi=10.1029/97GL03188
|pmid=
|accessdate=2013-08-01 }}&lt;/ref&gt;

'''Sprites''' are large-scale [[w:electrical discharge|electrical discharge]]s that occur high above [[w:thunderstorm|thunderstorm]] clouds, or [[w:cumulonimbus|cumulonimbus]], giving rise to a quite varied range of visual shapes flickering in the night sky. They are triggered by the discharges of [[w:positive lightning|positive lightning]] between an underlying [[w:thundercloud|thundercloud]] and the ground.

Sprites appear as luminous reddish-orange flashes. They often occur in clusters within the altitude range 50–90&amp;nbsp;km above the [[Earth]]'s surface. Sporadic visual reports of sprites go back at least to 1886, but they were first photographed on July 6, 1989 by scientists from the University of Minnesota and have subsequently been captured in video recordings many thousands of times.
{{clear}}

==Positrons==
{{main|Radiation astronomy/Positrons|Positron astronomy}}
[[Image:RREA Monte Carlo simulation.png|thumb|right|250px|Monte Carlo simulation of runaway relativistic electron avalanche (RREA) in air. Credit: [[c:user:Becarlson|Becarlson]].{{tlx|free media}}]]
Electrons are shown in black, photons in blue, and positrons in red. The electric field is directed downwards and is only nonzero in the 100-meter thick plane between the two lines.

&quot;The observation of a red supergiant at the site of a peculiar SN I outburst would be a direct means of confirming or refuting the hypothesis that a peculiar SN I explodes in a binary system with a red supergiant.&quot;&lt;ref name=Chugai/&gt;

&quot;The main source of emission of the secondary ejecta in a sufficiently late stage (≥100&lt;sup&gt;d&lt;/sup&gt;) will be the energy of the radioactive Ni&lt;sup&gt;56&lt;/sup&gt; → Co&lt;sup&gt;56&lt;/sup&gt; → Fe&lt;sup&gt;56&lt;/sup&gt; in the surrounding material of the supernova.&quot;&lt;ref name=Chugai/&gt;

&quot;The energy of Co&lt;sup&gt;56&lt;/sup&gt; decay is distributed between γ-ray quanta with an energy of the order of 1 MeV (96%) and positrons (4%).&quot;&lt;ref name=Chugai&gt;{{ cite journal
|author=N. N. Chugai
|title=Possible Binary Nature of Peculiar Type-I Supernovae - is the Satellite a Red Supergiant
|journal=Soviet Astronomy
|month=September/October
|year=1986
|volume=30
|issue=5
|pages=563
|url=http://adsabs.harvard.edu/full/1986SvA....30..563C
|arxiv=
|bibcode=1986SvA....30..563C
|doi=
|pmid=
|accessdate=2013-08-01 }}&lt;/ref&gt;
{{clear}}

==Neutrinos==
{{main|Radiation astronomy/Neutrinos|Neutrino astronomy}}
[[Image:NASA X-ray Telescopes Find Black Hole May Be a Neutrino Factory (19057084225).jpg|thumb|right|250px|The supermassive black hole at the center of the Milky Way may be producing tiny particles, called neutrinos, that have virtually no mass and carry no electric charge. Credit: Smithsonian Institution from the United States.{{tlx|free media}}]]
This Chandra image shows the region around the black hole, known as Sagittarius A*, in low, medium, and high-energy X-rays (red, green, and blue respectively.) There is a connection to outbursts generated by the black hole and seen by Chandra and other X-ray telescopes with the detection of high-energy neutrinos in an observatory under the South Pole.

&quot;[N]on-standard neutrino losses [may have an] impact on the red giant branch (RGB)&quot;.&lt;ref name=Raffelt&gt;{{ cite journal
|author=Georg Raffelt
|author2=Achim Weiss
|title=Non-standard neutrino interactions and the evolution of red giants
|journal=Astronomy and Astrophysics
|month=October
|year=1992
|volume=264
|issue=2
|pages=536-46
|url=http://adsabs.harvard.edu/abs/1992A&amp;A...264..536R
|arxiv=
|bibcode=1992A&amp;A...264..536R
|doi=
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;
{{clear}}

==Gamma rays==
{{main|Gamma-ray astronomy}}
[[Image:Cycle of pulsed gamma rays from the Vela pulsar HI RES.gif|thumb|right|250px|This image shows pulsed gamma rays from the Vela pulsar as constructed from photons detected by Fermi's Large Area Telescope. Credit: Roger Romani (Stanford University) (Lead), Lucas Guillemot (CENBG), Francis Reddy (SPSYS).{{tlx|free media}}]]
The Vela pulsar, which spins 11 times a second, is the brightest persistent source of gamma rays in the sky. The bluer colour in the latter part of the pulse indicates the presence of gamma rays with energies exceeding a billion electron volts (1 GeV). For comparison, visible light has energies between two and three electron volts. Red indicates gamma rays with energies less than 300 million electron volts (MeV); green, gamma rays between 300 MeV and 1 GeV; and blue shows gamma rays greater than 1 GeV. The image frame is 30 degrees across. The background, which shows diffuse gamma-ray emission from the Milky Way, is about 15 times brighter here than it actually is.

A gamma-ray burst (GRB) may have an afterglow at longer wavelengths. Specifically, GRB 000418 has a &quot;very red afterglow [which is] further evidence for dust extinction ... [where] the GRB was associated with a dusty [[star-forming region]].&quot;&lt;ref name=Klose&gt;{{ cite journal
|author=S. Klose
|author2=B. Stecklum
|author3=N. Masetti
|author4=E. Pian
|author5=E. Palazzi
|author6=A. A. Henden
|author7=D. H. Hartmann
|author8=O. Fischer
|author9=J. Gorosabel
|author10=C. Sánchaez-Fernández
|author11=D. Butler
|author12=Th. Ott
|author13=S. Hippler
|author14=M. Kasper
|author15=R. Weiss
|author16=A. Castro-Tirado
|author17=J. Greiner
|author18=C. Bartolini
|author19=A. Guarnieri
|author20=A. Piccioni
|author21=S. Benetti
|author22=F. Ghinassi
|author23=A. Magazzú
|author24=K. Hurley
|author25=T. Cline
|author26=J. Trombka
|author27=T. McClanahan
|author28=R. Starr
|author29=J. Goldstein
|author30=R. Gold
|author31=E. Mazets
|author32=S. Golenetskii
|author33=K. Noeske
|author34=P. Papaderos
|author35=P. M. Vreeswijk
|author36=N. Tanvir
|author37=A. Oscoz
|author38=J. A. Muńoz
|author39=J. M. Castro Ceron
|title=The very red afterglow of GRB 000418: Further evidence for dust extinction in a gamma-ray burst host galaxy
|journal=The Astrophysical Journal
|month=December 10,
|year=2000
|volume=545
|issue=1
|pages=271-6
|url=http://iopscience.iop.org/0004-637X/545/1/271
|arxiv=
|bibcode=
|doi=10.1086/317816
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;
{{clear}}

==X-rays==
{{main|X-ray astronomy}}
[[Image:This image from NASA’s Imaging X-ray Polarimetry Explorer maps the intensity of X-rays coming from the observatory’s first target, the supernova Cassiopeia A.png|thumb|right|250px|This image from NASA’s Imaging X-ray Polarimetry Explorer maps the intensity of X-rays coming from the observatory’s first target, the supernova Cassiopeia A. Credit: NASA.{{tlx|free media}}]]
Colors ranging from cool purple and blue to red and hot white correspond with the increasing brightness of the X-rays. The image was created using X-ray data collected by IXPE between Jan. 11-18.&lt;ref name=Weisskopf/&gt;

NASA’s Imaging X-Ray Polarimetry Explorer which launched Dec. 9, 2021, has delivered its first imaging data since completing its month-long commissioning phase.&lt;ref name=Weisskopf/&gt;

All instruments are functioning well aboard the observatory, which is on a quest to study some of the most mysterious and extreme objects in the universe.&lt;ref name=Weisskopf/&gt;

IXPE first focused its X-ray eyes on Cassiopeia A, an object consisting of the remains of a star that exploded in the 17th century. The shock waves from the explosion have swept up surrounding gas, heating it to high temperatures and accelerating cosmic ray particles to make a cloud that glows in X-ray light. Other telescopes have studied Cassiopeia A before, but IXPE will allow researchers to examine it in a new way.In the image above, the saturation of the magenta color corresponds to the intensity of X-ray light observed by IXPE. It overlays high energy X-ray data, shown in blue, from NASA’s Chandra X-Ray Observatory. Chandra and IXPE, with different kinds of detectors, capture different levels of angular resolution, or sharpness. An additional version of this image is available showing only IXPE data. These images contain IXPE data collected from Jan. 11 to 18.&lt;ref name=Weisskopf/&gt;

After Chandra launched in 1999, its first image was also of Cassiopeia A. Chandra’s X-ray imagery revealed, for the first time, that there is a compact object in the center of the supernova remnant, which may be a black hole or neutron star.&lt;ref name=Weisskopf/&gt;

“The IXPE image of Cassiopeia A is as historic as the Chandra image of the same supernova remnant.”&lt;ref name=Weisskopf&gt;{{ cite web
|author=Martin C. Weisskopf
|title=NASA’s IXPE Sends First Science Image In time for Valentine’s Day
|publisher=NASA
|location=Washington, DC USA
|date=14 February 2022
|url=https://www.nasa.gov/mission_pages/ixpe/index.html
|accessdate=3 September 2022 }}&lt;/ref&gt;

Polarization is a way of looking at how X-ray light is oriented as it travels through space.&lt;ref name=Weisskopf/&gt; The polarization of light contains clues to the environment where the light originated.&lt;ref name=Weisskopf/&gt; IXPE’s instruments also measure the energy, the time of arrival, and the position in the sky of the X-rays from cosmic sources.&lt;ref name=Weisskopf/&gt;

“It demonstrates IXPE’s potential to gain new, never-before-seen information about Cassiopeia A, which is under analysis right now.”&lt;ref name=Weisskopf/&gt;

“The IXPE image of Cassiopeia A is bellissima, and we look forward to analyzing the polarimetry data to learn even more about this supernova remnant.”&lt;ref name=Soffitta&gt;{{ cite web
|author=Paolo Soffitta
|title=NASA’s IXPE Sends First Science Image In time for Valentine’s Day
|publisher=NASA
|location=Washington, DC USA
|date=14 February 2022
|url=https://www.nasa.gov/mission_pages/ixpe/index.html
|accessdate=3 September 2022 }}&lt;/ref&gt;

With polarization data from Cassiopeia A, IXPE will see, for the first time, how the amount of polarization varies across the supernova remnant, which is about 10 light-years in diameter, to create the first-ever X-ray polarization map of the object.&lt;ref name=Landau&gt;{{ cite web
|author=Elizabeth Landau
|title=NASA’s IXPE Sends First Science Image In time for Valentine’s Day
|publisher=NASA
|location=Washington, DC USA
|date=14 February 2022
|url=https://www.nasa.gov/mission_pages/ixpe/index.html
|accessdate=3 September 2022 }}&lt;/ref&gt;

“IXPE's future polarization images should unveil the mechanisms at the heart of this famous cosmic accelerator. To fill in some of those details, we’ve developed a way to make IXPE’s measurements even more precise using machine learning techniques. We’re looking forward to what we’ll find as we analyze all the data.”&lt;ref name=Romani&gt;{{ cite web
|author=Roger Romani
|title=NASA’s IXPE Sends First Science Image In time for Valentine’s Day
|publisher=NASA
|location=Washington, DC USA
|date=14 February 2022
|url=https://www.nasa.gov/mission_pages/ixpe/index.html
|accessdate=3 September 2022 }}&lt;/ref&gt;

IXPE launched on a Falcon 9 rocket from Cape Canaveral, and now orbits 370 miles (600 kilometers) above Earth’s equator.&lt;ref name=Porter&gt;{{ cite web
|author=Molly Porter
|title=NASA’s IXPE Sends First Science Image In time for Valentine’s Day
|publisher=NASA
|location=Washington, DC USA
|date=14 February 2022
|url=https://www.nasa.gov/mission_pages/ixpe/index.html
|accessdate=3 September 2022 }}&lt;/ref&gt;

&quot;The combination of X-ray absorption, red near-IR continuum, polarized optical continuum, and broad lines in the majority of 2MASS [active galactic nucleus] AGNs suggests that they are viewed at an intermediate line of sight with respect to dusty, nuclear material (e.g., torus/disk/wind), as has been proposed for the similarly polarized [broad absorption line] BAL [quasi-stellar object] QSOs.&quot;&lt;ref name=Wilkes&gt;{{ cite journal
|author=Belinda J. Wilkes
|author2=Gary D. Schmidt
|author3=Roc M. Cutri
|author4=Himel Ghosh
|author5=Dean C. Hines
|author6=Brant Nelson
|author7=Paul S. Smith
|title=The X-Ray Properties of 2MASS Red Active Galactic Nuclei
|journal=The Astrophysical Journal
|month=January 10,
|year=2002
|volume=564
|issue=2
|pages=L65-8
|url=http://iopscience.iop.org/1538-4357/564/2/L65/fulltext/
|arxiv=astro-ph/0112433
|bibcode=2002ApJ...564L..65W
|doi=10.1086/338908
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;
{{clear}}

==Ultraviolets==
{{main|Ultraviolet astronomy}}
[[Image:Skylab solar flares in extreme ultraviolet (S74-21921).jpg|thumb|right|250px|Sun photographed by Apollo Telescope Mount through spectroheliometer at a wavelength of 625.3 angstroms. Credit: NASA.{{tlx|free media}}]]
The black areas are the surface of the sun; the reds, yellows and whites are the corona some 70,000 kilometers above the surface.
{{clear}}

==Violets==
{{main|Violet astronomy}}
[[Image:Red beryl.jpg|thumb|right|250px|Beryl variety is red beryl (Violet mine ; Red Emerald), Wah Wah Mts, Beaver Co., Utah, USA. Credit: [[c:user:Géry PARENT|Géry PARENT]].{{tlx|free media}}]]
[[Image:Beryl-Quartz-morganite brazil1.jpg|thumb|left|250px|The morganite has really a hot pink color. Credit: [[c:user:Robert M. Lavinsky|Robert M. Lavinsky]].{{tlx|free media}}]]
A permanganate is the general name for a chemical compound containing the manganate (VII) ion, {{chem|MnO|4|−}}, the conjugate base of permanganic acid. Because the manganese atom is in the +7 oxidation state, permanganate solutions are purple in color and are stable in neutral or slightly alkaline media.

&quot;Emerald is the green variety of the mineral beryl with the chemical composition beryllium aluminium silicate, {{chem|Be|3|Al|2|({{chem|SiO|3}})|6}}. Other varieties of beryls include aquamarine, morganite, heliodor, vanadium beryl, red beryl, yellow beryl, violet beryl and colorless beryl.&quot;&lt;ref name=Yu&gt;{{ cite journal
|author=K. N. Yu, S. M. Tang and T. S. Tay
|title=PIXE studies of emeralds
|journal=X-ray Spectrometry
|date=25 April 2000
|volume=29
|issue=
|pages=267-278
|url=http://www.cityu.edu.hk/nru/pub_j19.pdf
|arxiv=
|bibcode=
|doi=
|pmid=
|accessdate=4 September 2022 }}&lt;/ref&gt;

The dark red color is attributed to Mn&lt;sup&gt;3+&lt;/sup&gt; ions.&lt;ref name=color&gt;{{cite web |title=Color in the beryl group |website=minerals.caltech.edu |accessdate=2009-06-06 |department=Mineral Spectroscopy Server |publisher=California Institute of Technology
|url=https://web.archive.org/web/20110822012424/http://minerals.caltech.edu/FILES/Visible/BERYL/Index.htm }}&lt;/ref&gt;

The pink color of morganite is attributed to Mn&lt;sup&gt;2+&lt;/sup&gt; ions.&lt;ref name=color/&gt; 
{{clear}}

==Superluminals==
{{main|Radiation astronomy/Superluminals|Superluminal astronomy}}
[[Image:GRO J1655-40.jpg|thumb|right|250px|An artist's impression describes GRO J1655-40. Credit: NASA/CXC/A.Hobart.{{tlx|free media}}]]
&quot;[M]ultiwavelength observations of the superluminal X-ray transient GRO J1655-40 [have been performed] during and following the prominent hard X-ray outburst of 1995 March-April.&quot;&lt;ref name=Tavani/&gt;

&quot;The red color of the optical counterpart with E(B - V) = +1.3 ± 0.2, as recently determined by deep 200 nm Hubble Space Telescope (HST) observations in 1995 May (Horne et al. 1996), indicates significant absorption in the direction of GRO J1655-40 (see also B95a). Spectroscopic CTIO observations of GRO J1655-40 carried out in early 1995 May revealed Doppler-shifted high-excitation emission lines superposed on an F-type or early G-type stellar absorption spectrum (Bailyn et al. 1995b, hereafter B95b).&quot;&lt;ref name=Tavani&gt;{{ cite journal
|author=Tavani, M.
|author2=Fruchter, A.
|author3=Zhang, S. N.
|author4=Harmon, B. A.
|author5=Hjellming, R. N.
|author6=Rupen, M. P.
|author7=Bailyn, C.
|author8=Livio, M.
|title=The Dual Nature of Hard X-Ray Outbursts from the Superluminal X-Ray Transient Source GRO J1655-40
|journal=The Astrophysical Journal
|month=December 20,
|year=1996
|volume=473
|issue=12
|pages=L103-6
|url=http://iopscience.iop.org/1538-4357/473/2/L103/fulltext/
|arxiv=astro-ph/9610212
|bibcode=1996ApJ...473L.103T
|doi=10.1086/310406
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;
{{clear}}

==Plasma objects==
{{main|Plasmas/Plasma objects|Plasma objects}}
[[Image:Shifting Plasma (34537472515).jpg|thumb|right|250px|Strands of solar material at the sun's edge shifted and twisted back and forth over a 22-hour period in this footage captured May 2-3, 2017, by NASA’s Solar Dynamics Observatory. Credit: NASA Goddard Space Flight Center from Greenbelt, MD, USA.{{tlx|free media}}]]
In this close-up, the strands are being manipulated by strong magnetic forces associated with active regions. To give a sense of scale, the strands that hover above the sun are more than several times the size of Earth. These images were taken in a wavelength of extreme ultraviolet light, which is typically invisible to our eyes, but was colorized here in red.

The Hessdalen Light HL is an unexplained light usually seen in the Hessdalen valley in the municipality of Holtålen in Sør-Trøndelag county, Norway.

&quot;HL [may be] formed by a cluster of macroscopic Coulomb crystals in a plasma produced by the ionization of air and dust by alpha particles during radon decay in the dusty atmosphere.&quot;&lt;ref name=Paiva/&gt;

&quot;HL are characterized mostly by white color and sometimes by red color. It occurs mostly at night, more often in the winter season and with a peak around midnight.&quot;&lt;ref name=Paiva&gt;{{ cite journal
|author=G.S. Paiva, C.A. Taft
|title=A hypothetical dusty plasma mechanism of Hessdalen lights
|journal=Journal of Atmospheric and Solar-Terrestrial Physics
|month=October
|year=2010
|volume=72
|issue=16
|pages=1200-3
|url=http://www.sciencedirect.com/science/article/pii/S136468261000218X
|arxiv=
|bibcode=
|doi=10.1016/j.jastp.2010.07.022
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;
{{clear}}

==Gaseous objects==
{{main|Gases/Gaseous objects}}
[[Image:Red and Long Dead Abell 24.tif|thumb|right|250px|This red-hued cloud of gas is named Abell 24, and is located in the constellation of Canis Minor (The Lesser Dog). Credit: ESO.{{tlx|free media}}]]
It is something known as a planetary nebula — a burst of gas and dust created when a star dies and throws its outer layers into space. Despite the name, planetary nebulae have nothing to do with planets. The term was coined by William Herschel, who also famously discovered Uranus; in a time of low-resolution astronomy, these nebulous objects appeared to resemble giant planets swimming in a dark cosmos.

A Sun-like star spends most of its life converting hydrogen into helium in its core. In its twilight years the star runs out of fuel and becomes unbalanced; it can no longer resist the inward crush of gravity and the core begins to collapse. The temperature in the core rises dramatically while the cooler outer layers expand, causing the entire star to bloat into a red giant. When the Sun begins its transformation into a red giant it will expand to completely engulf the innermost planets and possibly also the Earth, growing to over 250 times its current radius! Strong winds then expel the gaseous outer layers of the star, forming a shell of gas that spreads out into the vastness of space. The red giant's venting atmosphere will eventually expose its hot, luminous remnant core, which will emit fierce ultraviolet radiation and ionise the surrounding gas. This image shows the faint nebulous glow of a stellar swansong — the bright remnant of a long-dead star.

With respect to &quot;gaseous objects with mass below the H-burning limit. ... the hydrogen-rich gaseous objects with mass below the minimum main sequence mass of ~ 0.08 Msun. ... the minimum mass of a gaseous fragment may be as low as 0.001 Msun.&quot;&lt;ref name=Kumar/&gt;

&quot;The first stage is the initial gravitational collapse phase during which the object moves more or less vertically downward in the H-R diagram. The color of the object is red (or very red) during this stage.&quot;&lt;ref name=Kumar&gt;{{ cite book
|author=Shiv S. Kumar
|title=The Bottom of the Main Sequence and Beyond: Speculations, Calculations, Observations, and Discoveries (1958-2002), In: ''Brown Dwarfs''
|publisher=Astronomical Society of the Pacific
|location=
|date=June 2003
|volume=XXX
|editor=Eduardo Martín
|pages=3-11
|url=http://arxiv.org/abs/astro-ph/0208096
|arxiv=astro-ph/0208096
|bibcode=2003IAUS..211....3K
|doi=
|pmid=
|isbn=
|accessdate=2013-08-02 }}&lt;/ref&gt;

&quot;During [the second evolutionary] stage the object, still luminous, starts sliding down on its cooling curve, and its color gets redder and redder as the surface temperature decreases with time.&quot;&lt;ref name=Kumar/&gt;

==Liquid objects==
{{main|Liquids/Liquid objects|Liquid objects}}
[[Image:Asteroids-20060509.png|thumb|right|250px|A plot of inner solar system asteroids and planets as of 2006 May 9. Credit: [[w:user:Mdf|Mdf]].{{tlx|free media}}]]
Planets (with trajectories) are orange, Jupiter being the outer most in this view. Various asteroid classes are colour coded: 'generic' main-belt are white. Inside the main belt, we have the Aten's (red), Apollo (green) and Amor (blue). Outside the main belt, the Hilda (blue) and the Trojan's (green).

&quot;When solid or liquid objects formed in the early [[Solar System]], either by condensation from the vapor phase or by melting and crystallization of preexisting material, each of these isotopic chronometers is expected to have been reset.&quot;&lt;ref name=Bogard&gt;{{ cite journal
|author=Donald D. Bogard
|title=Impact ages of meteorites: A synthesis
|journal=Meteoritics
|month=May
|year=1995
|volume=30
|issue=05
|pages=244-68
|url=http://adsabs.harvard.edu/full/1995Metic..30..244B
|arxiv=
|bibcode=1995Metic..30..244B
|doi=
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;

&quot;The majority of near-Earth asteroids (NEAs) whose taxonomic types are known belong to Tholen's S-class (Tholen, 1984). The reflectance spectra of S-class asteroids show absorption bands due to pyroxene or olivine or both, and the continuum slopes are moderately red.&quot;&lt;ref name=Howell&gt;{{ cite journal
|author=E. S. Howell
|author2=A. S. Rivkin
|author3=L. A. Lebofsky
|title=Spectral Trends of S-Class Asteroids with Size and Dynamical Population
|journal=Bulletin of the American Astronomical Society
|month=September
|year=1996
|volume=28
|issue=
|pages=1099
|url=http://adsabs.harvard.edu/abs/1996DPS....28.1016H
|arxiv=
|bibcode=1996DPS....28.1016H
|doi=
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;

&quot;The continuum slope of smaller NEAs is much redder than that of meteorite spectra, indicating either a compositional difference, or some space weathering effect.&quot;&lt;ref name=Howell/&gt;
{{clear}}

==Rocky objects==
{{main|Rocks/Rocky objects}}
[[Image:Red Rock Canyon HDR 1.jpg|thumb|right|250px|Look up at the the multicolored Calico Hills in Red Rock Canyon National Conservation Area. Credit: [[c:user:Sixflashphoto|Sixflashphoto]].{{tlx|free media}}]]
&quot;The rocky objects have rather smooth, red spectra (the Mars spectrum has some incompletely-removed terrestrial features). The gas giants have depressed red albedoes. Cloud-covered Venus has a depressed blue albedo.&quot;&lt;ref name=Traub&gt;{{ cite book
|author=Wesley A. Traub
|title=The Colors of Extrasolar Planets, In: ''Scientific Frontiers in Research on Extrasolar Planets''
|publisher=Astronomical Society of the Pacific
|location=San Francisco, California USA
|date=2003
|editor=Drake Deming
|editor2=Sara Seager
|volume=294
|pages=595-602
|url=http://adsabs.harvard.edu/full/2003ASPC..294..595T
|arxiv=
|bibcode=2003ASPC..294..595T
|doi=
|pmid=
|isbn=1-58381-141-9
|accessdate=2013-08-02 }}&lt;/ref&gt;
{{clear}}

==Hydrogens==
{{main|Chemicals/Hydrogens}}
[[Image:Hydrogen spectrum.svg|thumb|right|250px|The spectral series of hydrogen is displayed on a [[w:logarithm|logarithm]]ic scale. Credit: [[c:user:OrangeDog|OrangeDog]].{{tlx|free media}}]]
[[Image:Hydrogen transitions.svg|thumb|right|250px|Electron transitions and their resulting wavelengths for hydrogen. Energy levels are not to scale. Credit: [[c:user:Szdori|Szdori]] and [[c:user:OrangeDog|OrangeDog]].{{tlx|free media}}]]
[[Image:Hydrogen Spectra.jpg|thumb|right|500px|The spectrum shows the lines in the visible due to emission from elemental hydrogen. Credit:[[w:User:Teravolt|Teravolt]].{{tlx|free media}}]]
[[Image:20120831 234435.jpg|thumb|right|250px|Milky Way is viewed by H-Alpha Sky Survey. Credit: David Brown and Douglas Finkbeiner.{{tlx|fairuse}}]]
The emission spectrum of atomic hydrogen is divided into a number of '''spectral series''', with wavelengths given by the [[w:Rydberg formula|Rydberg formula]]. These observed spectral lines are due to electrons moving between energy levels in the atom. The spectral series are important in astronomy for detecting the presence of hydrogen and calculating red shifts. The spectral lines of hydrogen correspond to particular jumps of the electron between [[w:energy level|energy level]]s. The simplest model of the hydrogen atom is given by the [[w:Bohr model|Bohr model]]. When an electron jumps from a higher energy to a lower, a [[w:photon|photon]] of a specific wavelength is emitted.

The spectral lines are grouped into series according to '''n'''. Lines are named sequentially starting from the longest wavelength/lowest frequency of the series, using Greek letters within each series. For example, the {{nowrap|2 &amp;rarr; 1}} line is called &quot;Lyman-alpha&quot; (Ly-α), while the {{nowrap|7 &amp;rarr; 3}} line is called &quot;Paschen-delta&quot; (Pa-δ). Some hydrogen spectral lines fall outside these series, such as the [[w:Hydrogen line|21 cm line]]; these correspond to much rarer atomic events such as [[w:hyperfine structure|hyperfine]] transitions.&lt;ref name=Hyperphysics&gt;{{ cite book
|url=http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/h21.html
|title=The Hydrogen 21-cm Line, In: ''Hyperphysics''
|accessdate=2009-03-18
|publisher=Georgia State University
|date=2004-10-30 }}&lt;/ref&gt; The [[w:fine structure|fine structure]] also results in single spectral lines appearing as two or more closely grouped thinner lines, due to relativistic corrections.&lt;ref name=Liboff&gt;{{ cite book
|author=Richard L. Liboff
|title=Introductory Quantum Mechanics
|publisher=Addison-Wesley
|date=2002
|isbn=0-8053-8714-5 }}&lt;/ref&gt;

The energy differences between levels in the Bohr model, and hence the wavelengths of emitted/absorbed photons, is given by the Rydberg formula&lt;ref name=Bohr&gt;{{ citation
|author=Niels Bohr
|chapter=Rydberg's discovery of the spectral laws
|editor=J. Kalckar
|title=N. Bohr: Collected Works
|publisher=North-Holland Publ.
|location=Amsterdam
|year=1985
|volume=10
|pages=373–9 }}&lt;/ref&gt;:

:&lt;math&gt; {1 \over \lambda} = R \left( {1 \over (n^\prime)^2} - {1 \over n^2} \right) \qquad \left( R = 1.097373 \times 10^7 \ \mathrm{m}^{-1} \right)&lt;/math&gt;
where ''n'' is the initial energy level, ''n&amp;prime;'' is the final energy level, and ''R'' is the [[w:Rydberg constant|Rydberg constant]]. Meaningful values are returned only when ''n'' is greater than ''n&amp;prime;'' and the limit of one over infinity is taken to be zero.

&quot;The familiar red [[w:H-alpha|H-alpha]] [Hα 656 nm] spectral line of hydrogen gas, which is the transition from the shell ''n'' = 3 to the Balmer series shell ''n'' = 2, is one of the conspicuous colors of the universe. It contributes a bright red line to the spectra of [[w:emission nebula|emission]] or ionization nebula, like the [[w:Orion Nebula|Orion Nebula]], which are often [[w:H II region|H II region]]s found in star forming regions. In true-color pictures, these nebula have a distinctly pink color from the combination of visible Balmer lines that hydrogen emits.

A hydrogen-alpha filter is an [[w:optical filter|optical filter]] designed to transmit a narrow [[w:Bandwidth (signal processing)|bandwidth]] of light generally centered on the H-alpha wavelength. They are characterized by a bandpass width that measures the width of the wavelength band that is transmitted.&lt;ref name=Tom&gt;{{ cite book
| url = http://www.astro-tom.com/technical_data/filters.htm
| title = Filters
| publisher = Astro-Tom.com
| accessdate = 2006-12-09 }}&lt;/ref&gt; These filters are manufactured by multiple (~50) layers of [[w:Vacuum deposition|vacuum-deposited]] layers. These layers are selected to produce [[w:interference (wave propagation)|interference]] effects that filter out any wavelengths except at the requisite band.&lt;ref name=Murphy&gt;{{ cite book
| author = D. B. Murphy
|author2=K. R. Spring
|author3=M. J. Parry-Hill
|author4=I. D. Johnson
|author5=M. W. Davidson
| url = http://www.olympusmicro.com/primer/java/filters/interference/index.html
| title = Interference Filters
| publisher = Olympus
| accessdate = 2006-12-09 }}&lt;/ref&gt; Alternatively, an [[w:etalon|etalon]] may be used as the narrow band filter (in conjunction with a &quot;blocking filter&quot; or energy rejection filter) to pass only a narrow (&lt;0.1&amp;nbsp;[[w:nanometer|nm]]) range of wavelengths of light centred around the H-alpha emission line. The physics of the etalon and the dichroic interference filters are essentially the same (relying on constructive/destructive interference of light reflecting between surfaces), but the implementation is different (an interference filter relies on the interference of internal reflections). Due to the high velocities sometimes associated with features visible in H-alpha light (such as fast moving prominences and ejections), solar H-alpha etalons can often be tuned (by tilting or changing the temperature) to cope with the associated [[w:Doppler effect|Doppler effect]].
{{clear}}

==Heliums==
{{main|Chemicals/Heliums}}
[[Image:Helium spectra.jpg|thumb|center|400px|The spectrum shows the lines in the visible due to emission from elemental helium. Credit:[[w:User:Teravolt|Teravolt]].{{tlx|free media}}]]
Helium has at least one weak line in the red.
{{clear}}

==Lithiums==
{{main|Chemicals/Lithiums}}
[[Image:Spectrum Lines of Li.png|thumb|center|400px|This spectrograph shows the visual spectral lines of lithium. Credit: [[w:User:T c951|T c951]].{{tlx|free media}}]]
&quot;[T]he standard solar models have enjoyed tremendous success recently in terms of agreement between the predicted outer structure and the results from helioseismology[, but] some observed properties of the [[Sun (star)|Sun]] still defy explanation, such as the degree of Li depletion&quot; [the &quot;solar Li abundance is roughly a factor of 200 below the meteoritic abundance&quot;].&lt;ref name=King1997&gt;{{ cite journal
|author=Jeremy R. King
|author2=Constantine P. Deliyannis
|author3=Merchant Boesgaard
|title=The &lt;sup&gt;9&lt;/sup&gt;Be Abundances of α Centauri A and B and the Sun: Implications for Stellar Evolution and Mixing
|journal=The Astrophysical Journal
|month=April 1,
|year=1997
|volume=478
|issue=2
|pages=778
|url=http://iopscience.iop.org/0004-637X/478/2/778/pdf/0004-637X_478_2_778.pdf
|arxiv=
|bibcode=
|doi=
|pmid=
|accessdate=2012-07-11 }}&lt;/ref&gt;

In some 824 red giant stars, the Li I 670.78 nm line was detected in several stars, &quot;but only the five objects ... presented a strong line.&quot;&lt;ref name=Monaco&gt;{{ cite journal
|author=L. Monaco
|author2=S. Villanova
|author3=C. Moni Bidin
|author4=G. Carraro
|author5=D. Geisler
|author6=P. Bonifacio
|author7=O. A. Gonzalez
|author8=M. Zoccali
|author9=L. Jilkova
|title=Lithium-rich giants in the Galactic thick disk
|journal=Astronomy &amp; Astrophysics
|month=May
|year=2011
|volume=529
|issue=5
|pages=10
|url=
|arxiv=
|bibcode=2011A&amp;A...529A..90M
|doi=10.1051/0004-6361/201016285
|pmid=
|accessdate=2012-04-16 }}&lt;/ref&gt;

Some of the incontrovertible brown dwarf substellar objects are &quot;identified by the presence of the 670.8&amp;nbsp;nm lithium [I] line. The most notable of these objects was [[w:Gliese 229|Gliese 229]]B, which was found to have a temperature and luminosity well below the stellar range. Remarkably, its near-infrared spectrum clearly exhibited a methane absorption band at 2 micrometres, a feature that had previously only been observed in gas giant atmospheres and the atmosphere of Saturn's moon, Titan. Methane absorption is not expected at the temperatures of main-sequence stars. This discovery helped to establish yet another spectral class even cooler than L dwarfs known as &quot;T dwarfs&quot; for which Gl 229B is the prototype. ... [[w:Lithium|Lithium]] is generally present in brown dwarfs and not in low-mass stars. [T]he presence of the lithium [[w:spectral line|line]] in a candidate brown dwarf's spectrum is a strong indicator that it is indeed substellar. The use of lithium to distinguish candidate brown dwarfs from low-mass stars is commonly referred to as the '''lithium test'''. Some brown dwarfs emit X-rays; and all &quot;warm&quot; dwarfs continue to glow tellingly in the red and infrared spectra until they cool to planetlike temperatures (under 1000&amp;nbsp;K).

&quot;The lithium content of red-giant stars is highly variable (Wallerstein and Conti 1969). The largest amounts of lithium are found in three carbon stars, WZ Cas, WX Cyg, and T Ara, being of the order of 10&lt;sup&gt;-2&lt;/sup&gt; of calcium. ... Boesgaard (1970) has found a similar high lithium abundance in the S star T Sgr. This is a higher ratio of lithium to calcium than is found in T Tauri stars or in meteorites.&quot;&lt;ref name=Cameron/&gt;
{{clear}}

==Berylliums==
{{main|Chemicals/Berylliums}}
[[Image:Beryllium emission spectrum.png|thumb|center|400px|This spectrograph shows the visual spectral lines of beryllium. Credit: [[c:User:Penyulap|Penyulap]].{{tlx|free media}}]]
Beryllium has at least six emission/absorption lines across the red.
{{clear}}

==Borons==
[[Image:Boron emission spectrum.png|thumb|center|400px|This spectrograph shows the visual spectral lines of boron. Credit: [[c:User:Penyulap|Penyulap]].{{tlx|free media}}]]
Boron has a red line near the orange portion of the visual spectrum.
{{clear}}

==Carbons==
[[Image:Carbon Spectra.jpg|thumb|center|400px|The spectrum shows the lines in the visible due to emission from elemental carbon. Credit:[[w:User:Teravolt|Teravolt]].{{tlx|free media}}]]
Carbon has one strong line in the red.
{{clear}}

==Nitrogens==
{{main|Chemicals/Nitrogens}}
[[Image:Nitrogen.Spectrum.Vis.jpg|thumb|center|400px|The spectrum shows the lines in the visible due to emission from elemental nitrogen. Credit:[[c:User:Kurgus|Kurgus]].{{tlx|free media}}]]
[[Image:Cometary Knots Around A Dying Star - GPN-2000-001370.jpg|thumb|right|250px|The red light depicts nitrogen emission ([N II] 658.4 nm); green, hydrogen (H-alpha, 6563A); and blue, oxygen (5007A). These are &quot;cometary knots&quot; in the [[w:Helix nebula|Helix nebula]]. Credit: NASA Robert O Dell Kerry P. Handron Rice University, Houston Texas.{{tlx|free media}}]]
[[Image:Cat's Eye Nebula - GPN-2000-000955.jpg|thumb|left|250px|This NASA Hubble Space Telescope image shows one of the most complex planetary nebulae ever seen, NGC 6543, nicknamed the &quot;Cat's Eye Nebula.&quot; Credit: NASA J.P.Harrington and K.J.Borkowski University of Maryland.{{tlx|free media}}]]
Nitrogen has an emission line at 658.4 nm.

At right is an image gaseous objects (&quot;cometary knots&quot;) discovered in the thousands. These knots are imaged with the Hubble Space Telescope while exploring the Helix nebula, the closest planetary nebula to Earth at 450 light-years away in the constellation Aquarius. Although ground-based telescopes have revealed such objects, astronomers have never seen so many of them. The most visible knots all lie along the inner edge of the doomed star's ring, trillions of miles away from the star's nucleus. Although these gaseous knots appear small, they're actually huge. Each gaseous head is at least twice the size of our solar system; each tail stretches for 100 billion miles, about 1,000 times the distance between the Earth and the Sun. The image was taken in August 1994 with Hubble's Wide Field Planetary Camera 2. The red light depicts nitrogen emission ([NII] 658.4 nm).

The image at the left is a color picture, taken with the Wide Field Planetary Camera-2. It is a composite of three images taken at different wavelengths. (red, hydrogen-alpha; blue, neutral oxygen, 630.0 nm; green, ionized nitrogen, 658.4 nm). This NASA Hubble Space Telescope image shows one of the most complex planetary nebulae ever seen, NGC 6543, nicknamed the &quot;Cat's Eye Nebula.&quot; The image was taken on September 18, 1994. NGC 6543 is 3,000 light-years away in the northern constellation Draco. The term planetary nebula is a misnomer; dying stars create these cocoons when they lose outer layers of gas.
{{clear}}

==Oxygens==
[[Image:Oxygen spectre.jpg|thumb|center|400px|The spectrum shows the lines in the visible due to emission from elemental oxygen. Credit:[[w:User:Teravolt|Teravolt]].{{tlx|free media}}]]
[[Image:M57-spectrum-ru.png|thumb|right|250px|This is a spectrum of Ring Nebula (M57) in range 450.0 — 672.0 nm. Credit: [[c:User:Minami Himemiya|Minami Himemiya]].{{tlx|free media}}]]
Oxygen (O I) has two red lines at 630.0 and 636.4 nm. In the red there are the atomic oxygen transitions of the &quot;forbidden oxygen red doublet at 6300.304 and 6363.776 Å (&lt;sup&gt;1&lt;/sup&gt;D - &lt;sup&gt;3&lt;/sup&gt;P)&quot;&lt;ref name=Cochran&gt;{{ cite journal
|author=Anita L. Cochran, William D. Cochran
|title=Observations of O (&lt;sup&gt;1&lt;/sup&gt;S) and O (&lt;sup&gt;1&lt;/sup&gt;D) in Spectra of C/1999 S4 (LINEAR)
|journal=Icarus
|month=December
|year=2001
|volume=154
|issue=2
|pages=381-90
|url=http://arxiv.org/pdf/astro-ph/0108065v1.pdf
|arxiv=astro-ph/0108065
|bibcode=2001Icar..154..381C
|doi=10.1006/icar.2001.6718
|pmid=
|accessdate=2013-01-16 }}&lt;/ref&gt;. Atmospheric [[w:oxygen|O&lt;sub&gt;2&lt;/sub&gt;]] has a red line at 686.72 nm.

&quot;The oxygen abundance [may be determined] using the oxygen forbidden line at 630nm&quot;&lt;ref name=Spite&gt;{{ cite journal
|author=M. Spite
|author2=F. Spite
|title=Oxygen abundance in metal-poor dwarfs, derived from the forbidden line
|journal=Astronomy and Astrophysics
|month=December
|year=1991
|volume=252
|issue=2
|pages=689-92
|url=
|arxiv=
|bibcode=1991A&amp;A...252..689S
|doi=
|pmid=
|accessdate=2012-07-11 }}&lt;/ref&gt;. &quot;[R]atios [of] O/Fe ... are in agreement with the ratios found in the metal-poor red giants, suggesting that no real difference exists between dwarfs and giants.&quot;&lt;ref name=Spite/&gt;

&quot;The forbidden oxygen line (λ 630.03nm) is weak in dwarf stars&quot;&lt;ref name=Spite/&gt;
 
Several red astronomy emission lines are detected and recorded at normalized intensities (to the oxygen III line) from the [[w:Ring Nebula|Ring Nebula]]. In the red are the two forbidden lines of oxygen ([O I], 630.0 and 636.4 nm), two forbidden lines of nitrogen ([N II], 654.8 nm and [N II], 658.4 nm), the hydrogen line (Hα, 656.3 nm) and a forbidden line of sulfur ([S II], 671.7 nm).
{{clear}}

==Fluorines==
[[Image:Figure-9.-The-light-signature-of-Fluorine.png|thumb|center|400px|This diagram contains the emission and absorption lines for the element fluorine. Credit: Alex Petty.{{tlx|fairuse}}]]
[[Image:Fluorine Spectrum.svg|thumb|center|400px|Spectrum of fluorine uses strong lines from NIST. Credit: [[c:user:Mliu92|Mliu92]].{{tlx|free media}}]]
&quot;Fluorine abundances for red giants of type K, Ba, M, MS, S, SC,N, and J [may be] obtained from the [infrared] rotation-vibration lines of the molecule HF. There appears to be a clear correlation between [F/O] and &lt;sup&gt;12&lt;/sup&gt;C/&lt;sup&gt;16&lt;/sup&gt;O since N stars display F abundances up to 30 times the solar system value. This correlation points toward the He-burning shell as the site of F synthesis. The nuclear chain &lt;sup&gt;14&lt;/sup&gt;N(α,γ)&lt;sup&gt;18&lt;/sup&gt;F(''β''&lt;sup&gt;+&lt;/sup&gt;)&lt;sup&gt;18&lt;/sup&gt;O(p,α)&lt;sup&gt;15&lt;/sup&gt;N(α,γ)&lt;sup&gt;19&lt;/sup&gt;F (where protons come from &lt;sup&gt;13&lt;/sup&gt;C(α,n)&lt;sup&gt;16&lt;/sup&gt;O followed by &lt;sup&gt;14&lt;/sup&gt;N(n,p)&lt;sup&gt;14&lt;/sup&gt;C) operating at the very beginning of He-burning is the most likely for &lt;sup&gt;19&lt;/sup&gt;F production in thermal pulses.&quot;&lt;ref name=Jorissen&gt;{{ cite journal
|author=A. Jorissen
|author2=V.V. Smith
|author3=D.L. Lambert
|title=Fluorine in red giant stars: evidence for nucleosynthesis
|journal=Astronomy and Astrophysics
|month=July
|year=1992
|volume=261
|issue=1
|pages=164-87
|url=http://adsabs.harvard.edu/abs/1992A&amp;A...261..164J
|arxiv=
|bibcode=1992A&amp;A...261..164J
|doi=
|pmid=
|accessdate=2013-08-01 }}&lt;/ref&gt;
{{clear}}

==Neons==
[[Image:Neon spectrum visible.png|thumb|center|400px|This is a visual spectrum of neon showing its many emission lines. Credit: [[c:User:McZusatz|McZusatz]].{{tlx|free media}}]]
Neon has many lines across the red.
{{clear}}

==Irons==
[[Image:Iron spectrum visible.png|thumb|center|400px|Iron spectrum is 400 nm - 700 nm. Credit: [[c:user:McZusatz|McZusatz]].{{tlx|free media}}]]
Iron has two emission lines occurring in the solar corona at 637.451 nm from Fe X and 705.962 nm from Fe XV.&lt;ref name=Swings&gt;{{ cite journal
|author=P. Swings
|title=Edlén's Identification of the Coronal Lines with Forbidden Lines of Fe X, XI, XIII, XIV, XV; Ni XII, XIII, XV, XVI; Ca XII, XIII, XV; a X, XIV
|journal=The Astrophysical Journal
|month=July
|year=1943
|volume=98
|issue=07
|pages=116-28
|url=
|arxiv=
|bibcode=1943ApJ....98..116S
|doi=10.1086/144550
|pmid=
|accessdate=2013-01-18 }}&lt;/ref&gt;
{{clear}}

==Nickels==
{{main|Chemicals/Nickels}}
[[Image:Nickel spectrum visible.png|thumb|center|400px|This is an emission-line spectrum for nickel over the visible range: 400-700 nm. Credit: [[c:User:McZusatz|McZusatz]].{{tlx|free media}}]]
Nickel has an emission line occurring in the solar corona at 670.183 nm from Ni XV.&lt;ref name=Swings/&gt;
{{clear}}

==Rubidiums==
[[Image:Rubidium spectrum visible.png|left|thumb|400px|Rubidium emission spectrum is for 400 nm - 700 nm. Credit: [[c:user:McZusatz|McZusatz]].{{tlx|free media}}]]
[[Image:Die Flammenfärbung des Rubidium.jpg|thumb|right|150px|This image shows the flame test for Rubidium. Credit: [[c:user:Didaktische.Medien|Didaktische.Medien]].
{{tlx|free media}}]]
Rubidium occurs in the mineral [[w:Lepidolite|lepidolite]] and is found through the use of a [[w:Spectroscope|spectroscope]]. Because of the bright red lines in its [[w:Emission spectrum|emission spectrum]].
{{clear}}

==Zirconiums==
[[Image:Zirconium spectrum visible.png|center|thumb|400px|Zirconium spectrum is for 400 nm - 700 nm. Credit: [[c:user:McZusatz|McZusatz]].{{tlx|free media}}]]
&quot;Zirconium isotopic abundances [may be] determined from ZrO bandheads near 6925 Å via synthetic spectra for a sample of S stars.&quot;&lt;ref name=Lambert&gt;{{ cite journal
|author=David L. Lambert
|author2=Verne V. Smith
|author3=Maurizio Busso
|author4=Roberto Gallino
|author5=Oscar Straniero
|title=The Chemical Composition of Red Giants. IV. The Neutron Density at the s-Process Site
|journal=The Astrophysical Journal
|month=September 1,
|year=1995
|volume=450
|issue=09
|pages=302-17
|url=http://adsabs.harvard.edu/abs/1995ApJ...450..302L
|arxiv=
|bibcode=1995ApJ...450..302L
|doi=10.1086/176141
|pmid=
|accessdate=2013-08-01 }}&lt;/ref&gt;
{{clear}}

==Alloys==
{{main|Radiation astronomy/Alloys}}
[[Image:Zincite from Arizona.jpg|thumb|right|250px|This giant chunk of a crystal cluster is enormous. Credit: [https://www.flickr.com/people/cobalt/ cobalt123].{{tlx|free media}}]]
Zincite color depends on the presence of impurities. The zincite found at the Franklin Furnace is red-colored, mostly due to iron and manganese dopants, and is associated with willemite and franklinite. Synthetic crystals can be colorless or can range in color from dark red, orange, or yellow to light green. Bromellite (BeO) is colourless to slightly yellow. Wüstite (FeO) has a grey colour with a greenish tint in reflected light. Bunsenite (NiO) occurs as rare dark green crystal coatings.

&quot;The broad, 60 &lt; FWHM &lt; 100 nm, featureless luminescence band known as extended red emission (ERE) is seen in such diverse dusty astrophysical environments as reflection nebulae&lt;sup&gt;17&lt;/sup&gt;, planetary nebulae&lt;sup&gt;3&lt;/sup&gt;, HII regions (Orion)&lt;sup&gt;12&lt;/sup&gt;, a Nova&lt;sup&gt;11&lt;/sup&gt;, Galactic cirrus&lt;sup&gt;14&lt;/sup&gt;, a dark nebula&lt;sup&gt;7&lt;/sup&gt;, Galaxies&lt;sup&gt;8,6&lt;/sup&gt; and the diffuse interstellar medium (ISM)&lt;sup&gt;4&lt;/sup&gt;. The band is confined between 540-950 nm, but the wavelength of peak emission varies from environment to environment, even within a given object. ... the wavelength of peak emission is longer and the efficiency of the luminescence is lower, the harder and denser the illuminating radiation field is&lt;sup&gt;13&lt;/sup&gt;. These general characteristics of ERE constrain the photoluminescence (PL) band and efficiency for laboratory analysis of dust analog materials.&quot;&lt;ref name=Smith99&gt;{{ cite journal
|author=T. L. Smith
|author2=A. N. Witt
|title=The Photoluminescence Efficiency of Extended Red Emission as a Constraint for Interstellar Dust
|journal=Bulletin of the American Astronomical Society
|month=December
|year=1999
|volume=31
|issue=
|pages=1479
|url=http://adsabs.harvard.edu/abs/1999AAS...195.7406S
|arxiv=
|bibcode=1999AAS...195.7406S
|doi=
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;

&quot;The PL efficiencies measured for HAC and Si-HAC alloys are consistent with dust estimates for reflection nebulae and planetary nebulae, but exhibit substantial photoluminescence below 540 nm which is not observed in astrophysical environments.&quot;&lt;ref name=Smith99/&gt;

&quot;Optical constants measured at normal incidence for iron (Bolotin et al., 1969) and for iron-nickel alloys (Sasovskaya and Noskov, 1974) also predict a red-sloped spectrum.&quot;&lt;ref name=Britt&gt;{{ cite journal
|author=Daniel T. Britt
|author2=Carle M. Pieters
|author3=Peter H. Schultz
|title=Source of the optical red-slope in iron-rich meteorites
|journal=Meteoritics
|month=December
|year=1986
|volume=21
|issue=12
|pages=340-1
|url=http://adsabs.harvard.edu/full/1986Metic..21..340B
|arxiv=
|bibcode=1986Metic..21..340B
|doi=
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;
{{clear}}

==Atmospheres==
{{main|Atmospheres/Astronomy|Atmospheric astronomy}}
[[Image:Jupiter's Great Red Spot - July 10 2017 (35772892350).jpg|thumb|right|250px| Credit: Kevin Gill from Los Angeles, CA, United States.{{tlx|free media}}]]
&quot;Na D and Hα stellar line profiles for a sample of 19 stars in M55 and M13, [may provide] spectral features indicative of mass motions in the atmospheres of red giants.&quot;&lt;ref name=Lyons&gt;{{ cite journal
|author=M. A. Lyons
|author2=S. N. Kemp
|author3=B. Bates
|author4=C. R. Shaw
|title=Mass motions in the atmospheres of red giants in the globular clusters M55 and M13
|journal=Monthly Notices of the Royal Astronomical Society
|month=
|year=1996
|volume=280
|issue=3
|pages=835-48
|url=http://mnras.oxfordjournals.org/content/280/3/835.short
|arxiv=
|bibcode=
|doi=10.1093/mnras/280.3.835
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;

&quot;[O]nly stars with a luminosity above log(L/L&lt;sub&gt;⊙&lt;/sub&gt;)≈2.8 show Hα emission.&quot;&lt;ref name=Lyons/&gt;
{{clear}}

==Materials==
{{main|Chemicals/Materials}}
[[Image:Old Red Sandstone - geograph.org.uk - 1940783.jpg|thumb|right|250px|The Old Red Sandstone is an assemblage of rocks in the North Atlantic region largely of Devonian age. Credit: Anne Burgess.{{tlx|free media}}]]
[[Image:Folded_Old_Red_Sandstone_at_St_Annes_Head_-_geograph.org.uk_-_629204.jpg|thumb|left|250px|Folded Old Red Sandstone rock formation is at St Annes Head in Pembrokeshire, Wales. Credit: Rodney Harris.{{tlx|free media}}]]
A &quot;series of amorphous and crystalline materials: natural coal, amorphous hydrogenated carbon, amorphous hydrogenated silicon carbide, porous silicon, and crystalline silicon nanoparticles [have been investigated to determine the carrier of the Extended Red Emission (ERE)].&quot;&lt;ref name=Ledoux&gt;{{ cite journal
|author=G. Ledoux
|author2=O. Guillois
|author3=F. Huisken
|author4=B. Kohn
|author5=D. Porterat
|author6=C. Reynaud
|title=Crystalline silicon nanoparticles as carriers for the Extended Red Emission
|journal=Astronomy and Astrophysics
|month=October
|year=2001
|volume=377
|issue=10
|pages=707-20
|url=http://adsabs.harvard.edu/abs/2001A%26A...377..707L
|arxiv=
|bibcode=2001A&amp;A...377..707L
|doi=10.1051/0004-6361:20011136
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;
{{clear}}

==Meteorites==
{{main|Rocks/Meteorites|Meteorites}}
[[Image:Roter Kamm impact crater ESA22104135 (cropped).jpeg|thumb|right|250px|On Asteroid Day, the Copernicus Sentinel-2 mission takes us over the Roter Kamm impact crater in Namibia. Credit: European Space Agency.{{tlx|free media}}]]
The circular shape of the crater rim can be seen in the left of the image, just below the centre. The Roter Kamm impact crater is located in the Tsau ǁKhaeb National Park, also known as the Sperrgebiet, a diamond mining area in the Namib Desert, in southwest Namibia. The crater was formed by a meteorite around the size of a large vehicle that collided with Earth approximately 5 million years ago.

The crater has a diameter of 2.5 km and is around 130 m deep. It is clearly visible in the midst of the rust-red dunes, with its rims rising some 40 to 90 m above the surrounding plain. Its floors are covered by sand deposits at least 100 m thick.

&quot;The Raman spectra of some [interplanetary dust particle] IDPs also show red photoluminescence that is similar to the excess red emission seen in some astronomical objects and that has also been attributed to [polycyclic aromatic hydrocarbons] PAH s and hydrogenated amorphous carbon. Moreover, a part of the carbonaceous phase in IDPs and meteorites contains deuterium to hydrogen ratios that are greater than those for terrestrial samples.&quot;&lt;ref name=Allamandola&gt;{{ cite journal
|author=L. J. Allamandola
|author2=S. A. Sandford
|author3=B. Wopenka
|title=Interstellar Polycyclic Aromatic Hydrocarbons and Carbon in Interplanetary Dust Particles and Meteorites
|journal=Science
|month=July 3,
|year=1987
|volume=237
|issue=4810
|pages=56-9
|url=http://www.sciencemag.org/content/237/4810/56.short
|arxiv=
|bibcode=
|doi=10.1126/science.237.4810.56
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;
{{clear}}

==Sun==
{{main|Stars/Sun|Sun (star)}}
[[Image:Sun image through solar telescope.jpg|thumb|right|250px|This is a red image of the Sun taken through a solar telescope. Credit: [[c:User:Totallyhaywire2|Totallyhaywire2]].{{tlx|free media}}]]
As shown in the image at the top of the resource, the Sun is red when imaged in Hα. The additional image at right here is a red image taken through a solar telescope.

&quot;An earlier flare classification is based on [[w:H-alpha|Hα]] spectral observations. The scheme uses both the intensity and emitting surface. The classification in intensity is qualitative, referring to the flares as: ('''f''')aint, ('''n''')ormal or ('''b''')rilliant. The emitting surface is measured in terms of ''millionths'' of the hemisphere and is described below. (The total hemisphere area ''A&lt;sub&gt;H&lt;/sub&gt;'' = 6.2 × 10&lt;sup&gt;12&lt;/sup&gt; km&lt;sup&gt;2&lt;/sup&gt;.)
{| class=&quot;wikitable&quot;
|-
! Classification !! Corrected Area 
|-
!                !! [millionths of hemisphere]
|-
| S || &lt; 100
|-
| 1 || 100 - 250
|-
| 2 || 250 - 600
|-
| 3 || 600 - 1200
|-
| 4 || &gt; 1200
|}
A flare then is classified taking '''S''' or a number that represents its size and a letter that represents its peak intensity, e.g.: '''Sn''' is a ''normal subflare''.&lt;ref name=Hanssen&gt;{{ cite news
 | author = Einar Tandberg-Hanssen, A. Gordon Emslie
| year = 1988
 | title = The physics of solar flares
 | editor = Cambridge University Press }}&lt;/ref&gt;
{{clear}}

==Mercury==
{{main|Liquids/Liquid objects/Mercury}}
[[Image:Mercury-real_color.jpg|thumb|right|250px|This is Mercury in real colors, processed from clear and blue filtered Mariner 10 images. Credit: Images processed by Ricardo Nunes.{{tlx|free media}}]]
&quot;A higher-reflectance, relatively red material occurs as a distinct class of smooth plains that were likely emplaced volcanically; a lower-reflectance material with a lesser spectral slope may represent a distinct crustal component enriched in opaque minerals, possibly more common at depth.&quot;&lt;ref name=Robinson&gt;{{ cite journal
|author=Mark S. Robinson
|author2=Scott L. Murchie
|author3=David T. Blewett
|author4=Deborah L. Domingue
|author5=S. Edward Hawkins III
|author6=James W. Head
|author7=Gregory M. Holsclaw
|author8=William E. McClintock
|author9=Timothy J. McCoy
|author10=Ralph L. McNutt Jr.
|author11=Louise M. Prockter
|author12=Sean C. Solomon
|author13=Thomas R. Watters
|title=Reflectance and Color Variations on Mercury: Regolith Processes and Compositional Heterogeneity
|journal=Science
|month=July 4,
|year=2008
|volume=321
|issue=5885
|pages=66-9
|url=http://www.sciencemag.org/content/321/5885/66.short
|arxiv=
|bibcode=
|doi=10.1126/science.1160080
|pmid=
|accessdate=2013-07-28 }}&lt;/ref&gt;

&quot;The distinctively red smooth plains (HRP) appear to be large-scale volcanic deposits stratigraphically equivalent to the lunar maria (20), and their spectral properties (steeper 
spectral slope) are consistent with magma depleted in opaque materials. The large areal 
extent (&gt;10&lt;sup&gt;6&lt;/sup&gt; km&lt;sup&gt;2&lt;/sup&gt;) of the Caloris HRP is inconsistent with the hypothesis that volcanism was probably shallow and local (10); rather, such volcanism was likely a product of extensive partial melting of the upper mantle.&quot;&lt;ref name=Robinson/&gt;

&quot;Despite the dearth of ferrous iron in silicates, Mercury's surface nonetheless darkens and reddens with time like that of the Moon. This darkening and reddening has been interpreted to be the result of production of nanophase iron (e.g., Pieters et al., 2000; Hapke, 2001), which could be derived from an opaque phase in the crustal material or from delivery by micrometeorite impacts (Noble and Pieters, 2003). On the Moon, deposits that are brighter and redder than the average Moon spectrum appear to be lower in iron (e.g., highland material); deposits that are darker and redder than average are higher in iron (e.g., low-Ti mare material) (Lucey et al., 1995).&quot;&lt;ref name=Kerber&gt;{{ cite journal
|author=Laura Kerber
|author2=James W. Head
|author3=Sean C. Solomon
|author4=Scott L. Murchie
|author5=David T. Blewett
|author6=Lionel Wilson
|title=Explosive volcanic eruptions on Mercury: Eruption conditions, magma volatile 
content, and implications for interior volatile abundances
|journal=Earth and Planetary Science Letters
|month=
|year=2009
|volume=285
|issue=
|pages=263-71
|url=http://www.sciencedirect.com/science/article/pii/S0012821X09002611
|arxiv=
|bibcode=
|doi=10.1016/j.epsl.2009.04.037
|pmid=
|accessdate=2013-07-28 }}&lt;/ref&gt;
{{clear}}

==Venus==
{{main|Gases/Gaseous objects/Venus}}
[[Image:MESSENGER - Venus 630 nm stretch.jpg|thumb|right|250px|This WAC image was taken through a narrow-band filter centered at 630 nanometers. Credit: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington.{{tlx|free media}}]]
&quot;During the MESSENGER mission's second flyby of Venus, the Wide Angle Camera (WAC) of the Mercury Dual Imaging System (MDIS) acquired images through all of its 11 narrow-band color filters of the approaching planet. The surface of Venus is shrouded in clouds, and the WAC images returned from the encounter show this cloud covered view, as seen in a previously released image. However, by processing the WAC images and &quot;stretching&quot; the gray scale used to display the images, subtle differences in the clouds of Venus are revealed, as seen in the image here. This WAC image was taken through a narrow-band filter centered at 630 nanometers, and in this stretched image, global circulation patterns can be seen in the atmosphere of Venus.&quot;&lt;ref name=Campbell&gt;{{ cite book
|author=P. Campbell
|author2=D. Brown
|title=Examining the Details of a Venus 2 Approach Image
|publisher=JHU/APL
|location=Baltimore, Maryland
|date=June 5, 2007
|url=http://messenger.jhuapl.edu/gallery/sciencePhotos/image.php?page=1&amp;gallery_id=2&amp;image_id=327
|accessdate=2012-09-26 }}&lt;/ref&gt;
{{clear}}

==Earth==
{{main|Gases/Gaseous objects/Earth}}
[[Image:Belt_of_venus_from_plane.jpg|thumb|left|250px|The Belt of Venus is imaged at 42,000 feet. Credit: [[c:user:George7378|George7378]].{{tlx|free media}}]]
[[Image:Earth's shadow and Belt of Venus.jpg|thumb|right|250px|The Belt of Venus is shown at ''sunrise'', over a horizon where the sea meets the sky, looking west from [[w:Twin Peaks (San Francisco, California)|Twin Peaks, San Francisco]]. Credit: [https://sites.google.com/site/thebrockeninglory/ Brocken Inaglory].{{tlx|free media}}]]
[[Image:Golden Gate Bridge, the Belt of Venus and the Earth's shadow.jpg|thumb|left|250px|The Belt of Venus is shown at ''sunset'', looking east from the Marin Headlands just north of San Francisco. (Note: there is a thin greyish cloud layer partially obscuring the horizon in this image.) Credit: [https://sites.google.com/site/thebrockeninglory/ Brocken Inaglory].{{tlx|free media}}]]
[[Image:Moon and red blue haze.jpg|thumb|right|250px|The Full moon is rising, as seen through the Belt of Venus. A very small part of the Earth's shadow (dark blue) is also visible in this image, but the horizon here is too high to see more of the Earth's shadow. Credit: [[c:user:Fir0002|Fir0002]].{{tlx|free media}}]]
The '''Belt of Venus''' or '''Venus's Girdle''' is the Victorian-era name for an atmospheric phenomenon seen at sunrise and sunset. Shortly after sunset or shortly before sunrise, the observer is, or is very nearly, surrounded by a pinkish glow (or '''anti-twilight arch''') that extends roughly 10°–20° above the horizon. Often, the glow is separated from the horizon by a dark layer, the Earth's shadow or &quot;dark segment&quot;. The Arch's light rose (pink) color is due to backscattering of reddened light from the rising or setting [[Sun (star)|Sun]].

The first image at left shows the Belt of Venus from 42,000 feet altitude locally above the Earth's surface.

In the image at right is the Belt of Venus, a pink band that is visible above the dark blue of the Earth's shadow, in the same part of the sky. No defined line divides the Earth's shadow and the Belt of Venus; one colored band blends into the other in the sky.

In the image at second left, the Belt of Venus is shown at ''sunset'', looking east from the Marin Headlands just north of San Francisco. There is a thin greyish cloud layer partially obscuring the horizon in this image.

The second image at right shows the full Moon rising as seen through the Belt of Venus.

In the right viewing conditions, a pink (or orange or purple) band is visible in the twilight sky just above the dark blue band of the Earth's shadow. This pink band is called the &quot;anti-twilight arch&quot; or &quot;Belt of Venus&quot;. The name &quot;Belt of Venus&quot; is not connected with the planet Venus; the Belt of Venus is part of Earth's upper atmosphere which is illuminated by the setting or rising sun. It is visible either after the sun ceases to be visible (at sunset) or before the sun becomes visible (at sunrise).&lt;ref name=Cowley&gt;{{cite web
|title=Earth's shadow
|publisher = www.atoptics.co.uk
|author =Les Cowley
|url = http://www.atoptics.co.uk/atoptics/earshad.htm }}&lt;/ref&gt;&lt;ref name=&quot;earth's shadow&quot;&gt;{{cite web
|title=What causes layers in the sunrise and sunset?
|publisher = earthsky.org
|url = http://www.webexhibits.org/causesofcolor/14E.html }}&lt;/ref&gt;

When the sun is near the horizon at sunset or sunrise, the light from the sun is red; this is because the light is reaching the observer through an especially thick layer of the atmosphere, which works as a filter, scattering all but the red light.

From the viewpoint of the observer, the red sunlight directly illuminates small particles in the lower atmosphere on the other side of the sky from the sun. The red light is [[w:backscatter|backscatter]]ed to the observer, and that is why the Belt of Venus appears pink.

The lower the sunset sun descends, the less clearly distinguished the boundary between the Earth's shadow and Belt of Venus becomes. This is because now the setting sun illuminates a thinner part of the upper atmosphere. The red light is not scattered there because there are fewer particles, and the eye only sees the &quot;normal&quot; (usual) blue sky, which is due to [[w:Rayleigh scattering|Rayleigh scattering]] from air molecules. Eventually, both the Earth's shadow and the Belt of Venus dissolve into the darkness of the night sky.&lt;ref name=&quot;earth's shadow&quot;/&gt;
{{clear}}

==Moon==
{{main|Liquids/Liquid objects/Moon}}
[[File:February 2008 total lunar eclipse John Buonomo.jpg|thumb|250px|right|A total lunar eclipse on February 9, 2009, shows the reddish light falling on the moon's surface. Credit: John Buonomo. {{tlx|free media}}]]
[[Image:ESO - Potw1129a (by).jpg|thumb|left|250px|This view of the Moon was taken through a narrowband red filter (H-alpha). Credit: ESO and Andy Strappazzon.{{tlx|free media}}]]
During a lunar eclipse, a very small amount of light from the sun does however still reach the Moon, even when the lunar eclipse is total; this is light which has been [[w:refraction|refracted]] or bent as it passes through the Earth's atmosphere. This sunlight has been [[w:scattering|scattered]] by the dust in the Earth's atmosphere, and thus that light is red, in the same way that sunset and sunrise light is red. This weak red illumination is what causes the eclipsed Moon to be dimly reddish or copper-colored in appearance.&lt;ref name=earth-shadow&gt;{{ cite book
|title=Color and light in nature
|author= David K. Lynch, William Charles Livingston
|url = http://books.google.com/books?id=4Abp5FdhskAC&amp;pg=PA38&amp;lpg=PA38&amp;source=bl&amp;ots=bN3UHSoym0&amp;sig=DIeWBajGeM4ecoPW1KKNmhLyaV0&amp;hl=en&amp;ei=pFe8TLjoLJGqsAPcsemzDw&amp;sa=X&amp;oi=book_result&amp;ct=result&amp;resnum=1&amp;ved=0CBIQ6AEwAA#v=onepage&amp;f=false
|page = 38,39
|publisher=Cambridge University Press; 2 edition
|date=July 2001
|ISBN=978-0-521-77504-5 }}&lt;/ref&gt;

&quot;This image of the crescent Moon [at left] shows sunlight skimming across the heavily pocked surface, filling its craters with shadows. This is a fairly flat region of the Moon, but elsewhere, high mountains can be found, with some peaks reaching about 5000 metres. When backlit by the Sun, these mountains cast long shadows on the lunar surface.&quot;&lt;ref name=Strappazzon&gt;{{ cite book
|author=Andy Strappazzon
|title=Hidden Treasure on Our Doorstep
|publisher=ESO
|location=La Silla, Chile
|date=July 18, 2011
|url=http://www.eso.org/public/images/potw1129a/
|accessdate=2013-07-28 }}&lt;/ref&gt;

&quot;This view of the Moon was taken through a narrowband red filter (H-alpha). The height of the image is about 30 arcminutes.&quot;&lt;ref name=Strappazzon/&gt;

&quot;The MPG/ESO 2.2-metre telescope at La Silla in Chile is a powerful instrument that can capture distant celestial objects, but it has been used here to image a heavenly body that is much closer to home: the Moon.&quot;&lt;ref name=Strappazzon/&gt;
{{clear}}

==Mars==
{{main|Liquids/Liquid objects/Mars}}
[[Image:Mars atmosphere.jpg|thumb|right|250px|The tenuous atmosphere of Mars is visible on the horizon in this low-orbit photo. Credit: NASA.{{tlx|free media}}]]
[[Image:2005-1103mars-full.jpg|thumb|left|250px|Mars is imaged from [[w:Hubble Space Telescope|Hubble Space Telescope]] on October 28, 2005, with dust storm visible. Credit: NASA, ESA, The Hubble Heritage Team (STScI/AURA), J. Bell (Cornell University) and M. Wolff (Space Science Institute).{{tlx|free media}}]]
'''Mars''' is the fourth [[w:planet|planet]] from the [[Sun (star)|Sun]] in the [[Solar System]]. Named after the [[w:Roman mythology|Roman]] [[w:god of war|god of war]], [[w:Mars (mythology)|Mars]], it is often described as the &quot;Red Planet&quot; as the [[w:iron(III) oxide|iron oxide]] prevalent on its surface gives it a [[w:Mars surface color|reddish appearance]].&lt;ref name=&quot;nasa_hematite&quot;&gt;{{ cite book
|title=The Lure of Hematite
|publisher=NASA
|date=March 28, 2001
|url=http://science.nasa.gov/headlines/y2001/ast28mar_1.htm
|accessdate=2009-12-24 }}&lt;/ref&gt; The red-orange appearance of the Martian surface is caused by [[w:iron(III) oxide|iron(III) oxide]], more commonly known as hematite, or rust.&lt;ref name=Peplow&gt;{{ cite book
|author=Mark Peplow
|title=How Mars got its rust
|publisher=MacMillan Publishers Ltd.
|url=http://www.bioedonline.org/news/news-print.cfm?art=953
|accessdate=2007-03-10 }}&lt;/ref&gt; Much of the surface is deeply covered by finely grained [[w:iron(III) oxide|iron(III) oxide]] dust.&lt;ref name=&quot;sci300a&quot;&gt;{{ cite journal
|author=Philip R. Christensen, ''et al''.
|date=June 27, 2003
|title=Morphology and Composition of the Surface of Mars: Mars Odyssey THEMIS Results
|journal=Science
|volume=300
|issue=5628
|pages=2056–61
|doi=10.1126/science.1080885
|pmid=12791998
|bibcode = 2003Sci...300.2056C }}&lt;/ref&gt;&lt;ref name=Golombek&gt;{{ cite journal
|author=Matthew P. Golombek
|date=June 27, 2003
|title=The Surface of Mars: Not Just Dust and Rocks
|journal=Science
|volume=300
|issue=5628
|pages=2043–2044
|doi=10.1126/science.1082927
|pmid=12829771 }}&lt;/ref&gt;
{{clear}}

==Ceres==
{{main|Rocks/Rocky objects/Ceres}}
[[Image:PIA21081 - Water Ice Abundance on Ceres (Animation).jpg|thumb|right|250px|This animation (Figure 1) shows dwarf planet Ceres overlaid with the concentration of hydrogen determined from data acquired by the gamma ray and neutron detector (GRaND) instrument aboard NASA's Dawn spacecraft. Credit: NASA/JPL-Caltech/UCLA/MPS/DLR/IDA/PSI.
{{tlx|free media}}]]
The hydrogen is in the upper yard (or meter) of regolith, the loose surface material on Ceres.

The color scale gives hydrogen content in water-equivalent units, which assumes all of the hydrogen is in the form of H2O. Blue indicates where hydrogen content is higher, near the poles, while red indicates lower content at lower latitudes.

In reality, some of the hydrogen is in the form of water ice, while a portion of the hydrogen is in the form of hydrated minerals (such as OH, in serpentine group minerals). The color information is superimposed on shaded relief map for context.

A second animation (Figure 2) compares the hydrogen content of Ceres' regolith with that of the giant asteroid Vesta, which Dawn orbited from 2011 to 2012. These data show Vesta is a much drier world, with a much lower percent of hydrogen in its regolith. Both maps were produced from data acquired by GRaND.

&quot;Over five hours of observations 15 spectra of asteroid [Ceres] with step 2.46 nm in the region 336 - 746 nm were obtained to see whether the spectral characteristics of the Ceres surface changed with the rotation phase. On processing the observational material, it turned out that the spectra of the asteroid are unusually red (i.e., a remarkable rise of relative reflection coefficients with wave length growth occurs).&quot;&lt;ref name=Golubeva&gt;{{ cite journal
|author=L. F. Golubeva
|author2=D. I. Shestopalov
|title=Spectrometry of Minor Planets. The Possible Reason for Changes in Reflection Spectrum of 1 Ceres
|journal=Solar System Research
|month=
|year=1995
|volume=29
|issue=1
|pages=32-40
|url=http://www.researchgate.net/publication/237006685_Spectrometry_of_minor_planets._The_possible_reason_for_changes_in_reflection_spectrum_of_1_Ceres/file/3deec51b96d02d83d6.pdf
|arxiv=
|bibcode=
|doi=
|pmid=
|accessdate=2013-07-28 }}&lt;/ref&gt;
{{clear}}

==Jupiter==
{{main|Jupiter}}
[[Image:GRS in far infrared.jpg|thumb|right|250px|An infrared image of GRS (top) shows its warm center, taken by the ground based Very Large Telescope. An image made by the Hubble Space Telescope (bottom) is shown for comparison. Credit: NASA/JPL/ESO and NASA/ESA/GSFC.{{tlx|free media}}]]
The Great Red Spot (GRS) is a persistent [[w:anticyclonic storm|anticyclonic storm]], 22° south of Jupiter's equator, which has lasted for at least {{#expr: {{CURRENTYEAR}} - 1830}} years and possibly longer than {{#expr: {{CURRENTYEAR}} - 1665}} years.&lt;ref name=Staff&gt;{{cite book
|author=Staff|date=2007
|url=http://www.space.com/scienceastronomy/solarsystem/jupiter-ez.html
|title=Jupiter Data Sheet&amp;nbsp;– SPACE.com
|publisher=Imaginova|accessdate=2008-06-03 }}&lt;/ref&gt;&lt;ref name=Anonymous&gt;{{cite book
|author=Anonymous|date=August 10, 2000
|url=http://csep10.phys.utk.edu/astr161/lect/jupiter/redspot.html
|title=The Solar System&amp;nbsp;– The Planet Jupiter&amp;nbsp;– The Great Red Spot
|publisher=Dept. Physics &amp; Astronomy&amp;nbsp;– University of Tennessee
|accessdate=2008-06-03}}&lt;/ref&gt; The storm is large enough to be visible through [[Earth]]-based [[w:telescope|telescope]]s. Its dimensions are 24–40,000&amp;nbsp;km west–to–east and 12–14,000&amp;nbsp;km south–to–north. The spot is large enough to contain two or three planets the size of Earth. At the start of 2004, the Great Red Spot had approximately half the longitudinal extent it had a century ago, when it was 40,000&amp;nbsp;km in diameter. The Great Red Spot's latitude has been stable for the duration of good observational records, typically varying by about a degree.

It is not known exactly what causes the Great Red Spot's reddish color. Theories supported by laboratory experiments suppose that the color may be caused by complex organic molecules, red phosphorus, or yet another sulfur compound. The Great Red Spot (GRS) varies greatly in hue, from almost brick-red to pale salmon, or even white. The reddest central region is slightly warmer than the surroundings, which is the first evidence that the Spot's color is affected by environmental factors.&lt;ref name=Fletcher2010&gt;{{ cite journal
|first=Leigh N.|last=Fletcher |first2=G.S.|last2=Orton,|first3=O.|last3=Mousis ''et. al''
|journal=Icarus
|volume=208
|last4=Yanamandra-Fisher
|issue=1
|pages=306–328
|first4=P.
|doi=10.1016/j.icarus.2010.01.005
|last5=Parrish|first5=P.D.|last6=Irwin|first6=P.G.J.|last7=Fisher|first7=B.M.|last8=Vanzi|first8=L.|last9=Fujiyoshi|first9=T.
|title=Thermal structure and composition of Jupiter's Great Red Spot from high-resolution thermal imaging
|year=2010
|format=PDF
|url=http://www.eso.org/public/archives/releases/sciencepapers/eso1010/eso1010.pdf
|ref=Fletcher2010
|bibcode=2010Icar..208..306F }}&lt;/ref&gt; The spot occasionally disappears from the visible spectrum, becoming evident only through the Red Spot Hollow, which is its niche in the South Equatorial Belt. The visibility of GRS is apparently coupled to the appearance of the SEB; when the belt is bright white, the spot tends to be dark, and when it is dark, the spot is usually light. The periods when the spot is dark or light occur at irregular intervals; as of 1997, during the preceding 50 years, the spot was darkest in the periods 1961–66, 1968–75, 1989–90, and 1992–93.&lt;ref name=Beebe&gt;{{ cite book
 |last=Beebe |first=R.
 |date=1997 |edition=2nd
 |title=Jupiter the Giant Planet
 |location=Washington |publisher=Smithsonian Books
 |isbn=1-56098-685-9
 |oclc=224014042
 |ref=Beebe }}&lt;/ref&gt;
{{clear}}

==Comets==
{{main|Radiation astronomy/Comets}}
[[Image:CometLinear.jpg|thumb|right|250px|Armada of &quot;mini-comets&quot; is left behind by Comet LINEAR as observed by the Hubble Space Telescope and the 2.2-meter telescope in Hawaii. Credit: NASA, University of Hawaii, H. Weaver (John Hopkins University).{{tlx|free media}}]]
[[Image:CometWestESO.jpg|thumb|left|250px|Visual photograph of Comet West in early March 1976 shows red gases coming off the comet's head. Credit: Peter Stättmayer (Munich Public Observatory) and ESO.{{tlx|free media}}]]
&quot;My first thought was Hubble Space Telescope does it again! We caught the fish! This is amazing, very exciting, very neat.&quot;&lt;ref name=Weaver&gt;{{ cite book
|author=Harold Weaver
|title=Hubble Discovers Missing Pieces of Comet Linear
|publisher=Hubblesite - Newscenter
|location=Baltimore, Maryland USA
|date=August 7, 2000
|url=http://hubblesite.org/newscenter/archive/releases/2000/27/text/
|accessdate=2013-05-02 }}&lt;/ref&gt;

&quot;Actually, I would have been more amazed if Hubble saw no pieces ... They just had to be there. The amount of heat available from sunlight just isn't enough to boil away something the size of a mountain in so short a time&quot;.&lt;ref name=Lisse&gt;{{ cite book
|author=Carey Lisse
|title=Hubble Discovers Missing Pieces of Comet Linear
|publisher=Hubblesite - Newscenter
|location=Baltimore, Maryland USA
|date=August 7, 2000
|url=http://hubblesite.org/newscenter/archive/releases/2000/27/text/
|accessdate=2013-05-02 }}&lt;/ref&gt;

&quot;On July 27th, ground-based observers had lost sight of the bright core of the comet and were suggesting that the nucleus had totally disintegrated into a pile of dust. ... On Weaver's screen was at least a half dozen &quot;mini-comets&quot; with tails, resembling the shower of glowing fireballs from an aerial firework. They are clustered in the lance-head tip of an elongated stream of dust seen from a ground-based telescope.&quot;&lt;ref name=Villard&gt;{{ cite book
|author=Ray Villard
|author2=Michael Purdy
|title=Hubble Discovers Missing Pieces of Comet Linear
|publisher=Hubblesite - Newscenter
|location=Baltimore, Maryland USA
|date=August 7, 2000
|url=http://hubblesite.org/newscenter/archive/releases/2000/27/text/
|accessdate=2013-05-02 }}&lt;/ref&gt;

At left is an image of Comet West. &quot;Comet West was a stunning sight in the predawn sky of March, 1976, bright with a tall and broad dust tail. ... [T]he comet [was] discovered on photographs taken in August 1975 by Richard West of the European Southern Observatory ... Comet West passed perihelion on February 25, 1976, at a distance of 0.20 a.u. [and] had reached about magnitude -3 at perihelion. Several observers saw it telescopically in daylight, and John Bortle observed it with the naked eye shortly before sunset. ... The following morning, March 7, ... It was brilliant, with a head as bright as Vega (which was nearly overhead) and a huge tail, about 20 degrees tall, straight near the bottom and bending to the left in its upper reaches. The comet quickly faded during March&quot;.&lt;ref name=Hoffman&gt;{{ cite book
|author=Tony Hoffman
|title=Comet West: The Great Comet of 1976
|publisher=Earthlink
|location=
|date=
|url=http://home.earthlink.net/~tonyhoffman/cometwest.htm
|accessdate=2013-05-02 }}&lt;/ref&gt;

&quot;The λλ6300, 6363 Auroral red doublet of [OI] has been measured on digital sky-subtracted spectra of nine cometary nuclei ... The cometary oxygen lines are confined to their nuclear source, so that small apertures include much of the oxygen emission, particularly for small comets with Δ ≳ 1.0 AU.&quot;&lt;ref name=Spinrad&gt;{{ cite journal
|author=Hyron Spinrad
|title=Observations of the red auroral oxygen lines in nine comets
|journal=Publications of the Astronomical Society of the Pacific
|month=December
|year=1982
|volume=94
|issue=12
|pages=1008-16
|url=http://www.jstor.org/stable/10.2307/40678099
|arxiv=
|bibcode=1982PASP...94.1008S
|doi=10.1086/131101
|pmid=
|accessdate=2013-01-21 }}&lt;/ref&gt;
{{clear}}

==Sirius==
{{main|Stars/Sirius}}
[[Image:Sirius A and B Hubble photo.jpg|thumb|right|250px|This Hubble Space Telescope image shows Sirius A, the brightest star in our nighttime sky, along with its faint, tiny stellar companion, Sirius B. Credit: H. Bond (STScI) and M. Barstow (University of Leicester), NASA, ESA.{{tlx|free media}}]]
[[Image:Sirius A &amp; B X-ray.jpg|thumb|left|250px|An X-ray image of the Sirius star system located 8.6 light years from Earth is shown. Credit: NASA/SAO/CXC.{{tlx|free media}}]]
Around 150 AD, the Hellenistic astronomer [[w:Claudius Ptolemy|Claudius Ptolemy]] described Sirius as reddish, along with five other stars, [[w:Betelgeuse|Betelgeuse]], [[w:Antares|Antares]], [[w:Aldebaran|Aldebaran]], [[w:Arcturus|Arcturus]] and [[w:Pollux (star)|Pollux]], all of which are clearly of orange or red hue.&lt;ref name=Holberg2007&gt;{{ cite book
| author=J.B. Holberg
| title=Sirius: Brightest Diamond in the Night Sky
| date=2007
| publisher=Praxis Publishing
| location=Chichester, UK
| isbn=0-387-48941-X }}&lt;/ref&gt; The discrepancy was first noted by amateur astronomer [[w:Thomas Barker (meteorologist)|Thomas Barker]], ... who prepared a paper and spoke at a meeting of the Royal Society in London in 1760.&lt;ref name=Ceragioli1995&gt;{{ cite journal
| author=R. C. Ceragioli
| title=The Debate Concerning 'Red' Sirius
| journal=Journal for the History of Astronomy
| year=1995
| volume=26
| issue=3
| pages=187–226
| bibcode=1995JHA....26..187C
| ref=harv }}&lt;/ref&gt; The existence of other stars changing in brightness gave credence to the idea that some may change in colour too; [[w:Sir John Herschel|Sir John Herschel]] noted this in 1839, possibly influenced by witnessing [[w:Eta Carinae|Eta Carinae]] two years earlier.&lt;ref name=Holberg2007/&gt; [[w:Thomas Jefferson Jackson See|Thomas Jefferson Jackson See]] resurrected discussion on red Sirius with the publication of several papers in 1892, and a final summary in 1926.&lt;ref name=Holberg2007/&gt; He cited not only Ptolemy but also the poet [[w:Aratus|Aratus]], the orator [[w:Cicero|Cicero]], and general [[w:Germanicus|Germanicus]] as colouring the star red, though acknowledging that none of the latter three authors were astronomers, the last two merely translating Aratus' poem ''Phaenomena''.&lt;ref name=Holberg2007/&gt; [[w:Seneca the Younger|Seneca]], too, had described Sirius as being of a deeper red colour than Mars.&lt;ref name=Whittet1999&gt;{{ cite journal
| author=Whittet, D. C. B.
| title=A physical interpretation of the 'red Sirius' anomaly
| journal=Monthly Notices of the Royal Astronomical Society
| year=1999
| volume=310
| issue=2
| pages=355–359
| bibcode=1999MNRAS.310..355W
|doi=10.1046/j.1365-8711.1999.02975.x
| ref=harv }}&lt;/ref&gt; However, not all ancient observers saw Sirius as red. The 1st century AD poet [[w:Marcus Manilius|Marcus Manilius]] described it as &quot;sea-blue&quot;, as did the 4th century [[w:Avienus|Avienus]].&lt;ref name=Holberg2007/&gt; It is the standard star for the color white in ancient China, and multiple records from the 2nd century BC up to the 7th century AD all describe Sirius as white in hue.&lt;ref name=&quot;Jiang1992&quot;&gt;{{ cite journal
| author=江晓原
| year=1992
| title=中国古籍中天狼星颜色之记载
| journal=Ť文学报
| volume=33
| issue=4
| language=Chinese
| ref=harv }}&lt;/ref&gt;&lt;ref name=Jiang1993&gt;{{ cite journal
|author=Jiang, Xiao-Yuan
| title=The colour of Sirius as recorded in ancient Chinese texts
| bibcode=1993ChA&amp;A..17..223J
| journal=Chinese Astronomy and Astrophysics
| volume=17
|issue=2
|pages=223–8
| year=1993
| month=April
| doi=10.1016/0275-1062(93)90073-X
|ref=harv }}&lt;/ref&gt;

In 1985, German astronomers Wolfhard Schlosser and Werner Bergmann published an account of an 8th century [[w:Lombardy|Lombardic]] manuscript, which contains ''De cursu stellarum ratio'' by St. [[w:Gregory of Tours|Gregory of Tours]]. The [[w:Latin|Latin]] text taught readers how to determine the times of nighttime prayers from positions of the stars, and Sirius is described within as ''rubeola''&amp;nbsp;— &quot;reddish&quot;. The authors proposed this was further evidence Sirius B had been a red giant at the time.&lt;ref name=Schlosser198&quot;&gt;{{ cite journal
| author=Schlosser, W.
|author2=Bergmann, W.
| year=1985
| month=November
| title=An early-medieval account on the red colour of Sirius and its astrophysical implications
| journal=Nature
| issue=318
| pages=45–6
| doi=10.1038/318045a0
| volume=318
| ref=harv
|bibcode = 1985Natur.318...45S }}&lt;/ref&gt;
{{clear}}

==Luminous red novas==
{{main|Stars/Novas}}
[[Image:V838 Mon HST.jpg|250px|right|thumb|[[w:V838 Monocerotis|V838 Monocerotis]] in this real visual image from the Hubble Space Telescope is a prototypic luminous red nova. Credit: NASA, ESA and H.E. Bond (STScI).{{tlx|free media}}]]
A '''luminous red nova''' (abbr. ''LRN'', pl. ''luminous red novae'', pl.abbr. ''LRNe'') is a stellar explosion thought to be caused by the merger of two stars. They are characterised by a distinct red colour, and a [[w:light curve|light curve]] that lingers with resurgent brightness in the [[w:infrared|infrared]]. Luminous red novae are not to be confused with standard [[w:nova|nova]]e, explosions that occur on the surface of [[w:white dwarf|white dwarf]] stars. The visible light lasts for weeks or months, and is distinctively red in colour, becoming dimmer and redder over time. As the visible light dims, the infrared light grows and also lasts for an extended period of time, usually dimming and brightening a number of times. Some astronomers believe it to be premature to declare a new class of stellar explosions based on such a limited number of observations. For instance, Pastorello et al. 2007&lt;ref name=Pastorello&gt;http://www.nature.com/nature/journal/v449/n7164/full/nature06282.html&lt;/ref&gt; explained that the event may be due to a type II-p supernova and Todd et al. 2008&lt;ref name=Todd&gt;http://arxiv.org/abs/0809.0510&lt;/ref&gt; pointed out that supernovae undergoing a high level of extinction will naturally be both red and of low luminosity.
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==Red dwarfs==
[[Image:AZCancriCloseup.jpg|thumb|right|250px|This is a real visual image of AZ Cancri. Credit: SDSS Data Release 6.{{tlx|free media}}]]
A '''red dwarf''' is a small and relatively [[w:temperature|cool]] [[w:star|star]] on the [[w:main sequence|main sequence]], either late K or M [[w:spectral type|spectral type]]. Red dwarfs are by far the most common type of star in the Galaxy, at least in the neighborhood of the Sun. [[w:Proxima Centauri|Proxima Centauri]], the nearest star to the Sun, is a red dwarf. Due to their low luminosity, individual red dwarfs cannot easily be observed. From Earth, none are visible to the naked eye.&lt;ref name=Croswell&gt;[http://kencroswell.com/thebrightestreddwarf.html &quot;The Brightest Red Dwarf&quot;], by Ken Croswell (Accessed 6/7/08)&lt;/ref&gt;

{| class=&quot;wikitable&quot; style=&quot;float: right; text-align: center; margin-left: 1em;&quot;
|+ ''Typical characteristics''&lt;ref name=Kaltenegger&gt;{{ cite journal
| author=Lisa Kaltenegger, Wesley A. Traub
| title=Transits of Earth-like Planets
| journal=The Astrophysical Journal
| volume=698
| issue=1
| pages=519-527
| month=June
| year=2009
| doi=10.1088/0004-637X/698/1/519
| bibcode=2009ApJ...698..519K }}&lt;/ref&gt;
! Stellar&lt;br&gt;Class
! Mass&lt;br&gt;([[w:Solar mass|M&lt;sub&gt;ʘ&lt;/sub&gt;]])
! Radius&lt;br&gt;([[w:Solar radius|R&lt;sub&gt;ʘ&lt;/sub&gt;]])
! Luminosity&lt;br&gt;([[w:Solar luminosity|L&lt;sub&gt;ʘ&lt;/sub&gt;]])
! [[w:Effective temperature|T&lt;sub&gt;eff&lt;/sub&gt;]]&lt;br&gt;([[w:Kelvin|K]])
|-
| M0V || 60% || 62% || 7.2% || 3,800
|-
| M1V || 49% || 49% || 3.5% || 3,600
|-
| M2V || 44% || 44% || 2.3% || 3,400
|-
| M3V || 36% || 39% || 1.5% || 3,250
|-
| M4V || 20% || 26% || 0.55% || 3,100
|-
| M5V || 14% || 20% || 0.22% || 2,800
|-
| M6V || 10% || 15% || 0.09% || 2,600
|-
| M7V ||  9% || 12% || 0.05% || 2,500
|-
| M8V ||  8% || 11% || 0.03% || 2,400
|-
| M9V || 7.5% || 8% || 0.015% || 2,300
|}

The red dwarf AZ Cancri is shown in the visual image at right.

&quot;[O]ut [of] a sample of 3,897 red dwarfs ... [the [[w:Kepler (spacecraft)|Kepler Space Telescope]] ]has identified 95 exoplanet candidates circling them. Three of these candidates are roughly Earth-size and orbit within their stars' &quot;Goldilocks zone,&quot; where liquid water (and possibly life as we know it) can exist.&quot;&lt;ref name=Howell2013&gt;{{ cite book
|author=Elizabeth Howell
|title=Closest 'Alien Earth' May Be 13 Light-Years Away
|publisher=Yahoo! News
|location=
|date=February 7, 2013
|url=http://news.yahoo.com/closest-alien-earth-may-13-light-years-away-225759935.html;_ylt=AqKWFaZLTqr7j3HqwwaS3HGs0NUE;_ylu=X3oDMTNscDlubGkzBG1pdANUb3BTdG9yeSBGUARwa2cDMGMwYzFiYzktMGZhYS0zYTcyLTk2MDctNDdlYzM3MDU4NjRjBHBvcwM0BHNlYwN0b3Bfc3RvcnkEdmVyAzgxZDk1Mzc0LTcxMWQtMTFlMi1iZGNkLWY4MzBkYzg1OThkOQ--;_ylg=X3oDMTFpNzk0NjhtBGludGwDdXMEbGFuZwNlbi11cwRwc3RhaWQDBHBzdGNhdANob21lBHB0A3NlY3Rpb25z;_ylv=3
|accessdate=2013-02-07 }}&lt;/ref&gt;
{{clear}}

==Red giants==
[[Image:Mira 1997.jpg|thumb|right|250px|This is a real visual image of the red giant [[w:Mira|Mira]] by the Hubble Space Telescope. Credit: Margarita Karovska (Harvard-Smithsonian Center for Astrophysics) and NASA.{{tlx|free media}}]]
A '''red giant''' is a luminous [[w:giant star|giant star]] The outer atmosphere is inflated and tenuous, making the radius immense and the surface temperature low, somewhere from 5,000 K and lower. The appearance of the red giant is from yellow orange to red, including the [[w:stellar classification|spectral types]] K and M, but also class S stars and most [[w:carbon star|carbon star]]s. The most common red giants are the so-called red giant branch stars (RGB stars). Another case of red giants are the [[w:asymptotic giant branch|asymptotic giant branch]] stars (AGB). To the AGB stars belong the carbon stars of type C-N and late C-R. The stellar limb of a red giant is not sharply-defined, as depicted in many illustrations. Instead, due to the very low mass density of the envelope, such stars lack a well-defined [[w:photosphere|photosphere]]. The body of the star gradually transitions into a '[[w:corona|corona]]' with increasing radii.&lt;ref name=Orange&gt;[http://solarscience.msfc.nasa.gov/feature1.shtml orange sphere of the sun]&lt;/ref&gt;
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==Red supergiants==
[[Image:AB Pyxidis.png|thumb|right|250px|Image shows AB Pyxidis. Credit: Victor M. Blanco telescope.{{tlx|free media}}]]
&quot;'''Red supergiants''' ('''RSG'''s) are [[w:supergiant|supergiant]] stars ([[w:Stellar_classification#Yerkes_spectral_classification|luminosity class]] '''I''') of [[w:spectral classification|spectral type]] K or M. They are the largest stars in the universe in terms of [[w:volume|volume]], although they are not the most [[w:mass|mass]]ive. [[w:Betelgeuse|Betelgeuse]] and [[w:Antares|Antares]] are the best known examples of a red supergiant. These stars have very cool surface temperatures (3500&amp;ndash;4500 K), and enormous radii.  The five largest known red supergiants in the Galaxy are [[w:VY Canis Majoris|VY Canis Majoris]], [[w:VV Cephei A|VV Cephei A]], [[w:V354 Cephei|V354 Cephei]], [[w:RW Cephei|RW Cephei]] and [[w:KW Sagittarii|KW Sagittarii]], which all have radii about 1500 times that of the [S]un (about 7 [[w:astronomical units|astronomical units]], or 7 times as far as the Earth is from the [S]un). The radius of most red giants is between 200 and 800 times that of the Sun. Absolute luminosities may reach -10 magnitude compared to +5 for our Sun.
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==Red clumps==
[[Image:Stellar evolutionary tracks-en.svg|thumb|right|250px|This Hertzsprung-Russell diagram shows the evolution of stars of different masses. The red clump is marked RC on the green line showing the evolution of a star of 2 solar masses. Credit: [[c:user:Jesusmaiz|Jesusmaiz]] and [[c:user:Rursus|Rursus]].{{tlx|free media}}]]
The '''red clump''' is a feature in the [[w:Hertzsprung-Russell diagram|Hertzsprung-Russell diagram]] of stars. The red clump is considered the [[w:metallicity|metal]]-rich counterpart to the [[w:horizontal branch|horizontal branch]]. Stars in this part of the Hertzsprung-Russell diagram are sometimes called ''clump giants''.  These stars are more [[w:luminosity#In astronomy|luminous]] than [[w:main sequence|main sequence]] stars of the same surface temperature (or colder than main sequence stars of comparable luminosity), or above and to the right of the main sequence on the Hertzsprung-Russell diagram.
{{clear}}

==Tip of the red giant branch==
[[Image:Evolutionary track 1m.svg|thumb|right|250px|The evolutionary track of a solar mass, solar metallicity, star from main sequence to post-AGB. Credit: [[c:user:Lithopsian|Lithopsian]].{{tlx|free media}}]]
'''Tip of the red-giant branch''' ('''TRGB''') is a primary [[w:standard candle|distance indicator]] used in [[astronomy]]. It uses the [[w:Luminosity#In astronomy|luminosity]] of the brightest [[w:red giant|red giant branch]] stars in a [[w:galaxy|galaxy]] to gauge the distance to that galaxy. It has been used in conjunction with observations from the [[w:Hubble Space Telescope|Hubble Space Telescope]] to determine the relative motions of the [[w:Local Cluster|Local Cluster]] of galaxies within the [[w:Virgo Supercluster|Local Supercluster]]. ... [There] is a sharp discontinuity in the evolutionary track of the star on the HR diagram.&lt;ref name=&quot;harpaz&quot;&gt;{{ cite book
  | author=Amos Harpaz
| date=1994
  | title=Stellar evolution
| series=Peters Series
  | pages=103&amp;ndash;110
| publisher=A K Peters, Ltd.
  | isbn=1568810121 }}&lt;/ref&gt; This discontinuity is called the tip of the red giant branch. When distant stars at the TRGB are measured in the I-band, their magnitude is somewhat insensitive to their composition of elements with more mass than helium ([[w:metallicity|metallicity]]) and their mass. This makes the technique especially useful as a distance indicator. The TRGB indicator uses stars in the old stellar populations ([[w:Population II|Population II]]).&lt;ref name=&quot;Ferrareseetal2000&quot;&gt;{{ cite journal
  | author=Ferrarese, Laura
|author2=Ford, Holland C.
|author3=Huchra, John
|author4=Kennicutt Robert C. Jr.
|author5=Mould, Jeremy R.
|author6=Sakai, Shoko
|author7=Freedman, Wendy L.
|author8=Stetson, Peter B.
|author9=Madore, Barry F.
|author10=Gibson, Brad K.
|author11=Graham, John A.
|author12=Hughes, Shaun M.
|author13=Illingworth, Garth D.
|author14=Kelson, Daniel D.
|author15=Macri, Lucas
|author16=Sebo, Kim
|author17=Silbermann, N. A.
  | title=A Database of Cepheid Distance Moduli and Tip of the Red Giant Branch, Globular Cluster Luminosity Function, Planetary Nebula Luminosity Function, and Surface Brightness Fluctuation Data Useful for Distance Determinations
  | journal=The Astrophysical Journal Supplement Series
  | year=2000
| volume=128
| issue=2
| pages=431–459
  | bibcode=2000ApJS..128..431F
  | doi=10.1086/313391
| format=abstract
|arxiv = astro-ph/9910501
  | last4=Kennicutt }}&lt;/ref&gt;
{{clear}}

==Interstellar reddening==
[[Image:Interstellar extinction ave curves local group.png|thumb|right|Plot shows the average extinction curves for the MW, LMC2, LMC, and SMC Bar. The curves are plotted versus 1/wavelength to emphasize the UV. Credit: Karl D. Gordon.{{tlx|free media}}]]
The average extinction curves are for the MW, LMC2, LMC, and SMC Bar.&lt;ref name=Gordon&gt;{{Cite journal
  | last = Gordon
  | first = Karl D.
  | author2 = Geoffrey C. Clayton
 | author3 = Karl A. Misselt
 | author4 = Arlo U. Landolt
 | author5 = Michael J. Wolff
  | title = A Quantitative Comparison of the Small Magellanic Cloud, Large Magellanic Cloud, and Milky Way Ultraviolet to Near-Infrared Extinction Curves
  | journal = Astrophysical Journal
  | date = 2003
  | volume = 594
  | issue = 1
  | pages = 279–293
  | bibcode = 2003ApJ...594..279G
  | doi = 10.1086/376774
  | arxiv = astro-ph/0305257
| s2cid = 117180437 }}&lt;/ref&gt;

Interstellar reddening is a phenomenon associated with interstellar extinction where the spectrum of electromagnetic radiation from a radiation source changes characteristics from that which the object originally emitted. Reddening occurs due to the light scattering off dust and other matter in the interstellar medium between source and observer.

In interstellar astronomy, [[w:visible spectrum|visible spectra]] can appear redder due to scattering processes in a phenomenon referred to as [[w:interstellar reddening|interstellar reddening]]&lt;ref name=basicastronomy&gt;See Binney and Merrifeld (1998), Carroll and Ostlie (1996), Kutner (2003) for applications in astronomy.&lt;/ref&gt; — similarly [[w:Rayleigh scattering|Rayleigh scattering]] causes the [[w:Earth's atmosphere|atmospheric]] reddening of the Sun seen in the [[w:sunrise|sunrise]] or [[w:sunset|sunset]] and causes the rest of the sky to have a blue color. This phenomenon is distinct from red''shift''ing because the [[w:atomic spectral line|spectroscopic lines]] are not shifted to other wavelengths in reddened objects and there is an additional [[w:extinction (astronomy)|dimming]] and distortion associated with the phenomenon due to photons being scattered in and out of the [[w:Line-of-sight propagation|line-of-sight]].
{{clear}}

==Star-forming regions==
{{main|Stars/Star-forming regions}}
[[Image:The star formation region NGC 6559.jpg|thumb|right|250px|This region of sky includes glowing red clouds of mostly hydrogen gas. Credit: ESO.{{tlx|free media}}]]
&quot;The gas in the clouds of NGC 6559, mainly hydrogen, is the raw material for star formation. When a region inside this nebula gathers enough matter, it starts to collapse under its own gravity. The center of the cloud grows ever denser and hotter, until thermonuclear fusion begins and a star is born. The hydrogen atoms combine to form helium atoms, releasing energy that makes the star shine. In regions where it is very dense, the dust completely blocks the light behind it, as is the case for the dark isolated patches and sinuous lanes to the bottom left-hand side and right-hand side of the image&quot;.&lt;ref name=ESOofficials&gt;{{ cite book
|author=ESO officials
|title=Dusty Star-Spawning Space Cloud Glows In Amazing Photo
|publisher=Yahoo! News
|location=La Silla, Chile
|date=May 2, 2013
|url=http://news.yahoo.com/dusty-star-spawning-space-cloud-glows-amazing-photo-140759329.html;_ylt=AuvOfcnBLreDFxWBFfhiolaHgsgF;_ylu=X3oDMTRlMXAzbmRkBG1pdANUb3BTdG9yeSBTY2llbmNlU0YgU3BhY2VBc3Ryb25vbXlTU0YEcGtnAzkwY2RjMGI1LTYwNWUtM2I0YS1iOTNmLTJjNjU1N2ZmMzI2ZARwb3MDNwRzZWMDdG9wX3N0b3J5BHZlcgM0M2ZiYWM0MS1iMzMyLTExZTItYWJiYi1iNTZkODJmMTk2NzY-;_ylg=X3oDMTI1MG9icjRhBGludGwDdXMEbGFuZwNlbi11cwRwc3RhaWQDBHBzdGNhdANzY2llbmNlfHNwYWNlLWFzdHJvbm9teQRwdANzZWN0aW9ucw--;_ylv=3
|accessdate=2013-05-02 }}&lt;/ref&gt;

&quot;The Danish 1.54-metre telescope located at ESO’s La Silla Observatory in Chile has captured a striking image of NGC 6559, an object that showcases the anarchy that reigns when stars form inside an interstellar cloud. This region of sky includes glowing red clouds of mostly hydrogen gas, blue regions where starlight is being reflected from tiny particles of dust and also dark regions where the dust is thick and opaque.&quot;&lt;ref name=eso1320a&gt;{{ cite book
|author=eso1320a
|title=The star formation region NGC 6559
|publisher=European Southern Observatory
|location=La Silla Observatory, Chile
|date=May 2, 2013
|url=http://www.eso.org/public/images/eso1320a/
|accessdate=2013-05-02 }}&lt;/ref&gt;

&quot;The two colors of the cloud represent a pair of nebulas. Once the young stars are born, they &quot;energize&quot; the hydrogen surrounding them, ESO officials said. The gas then creates the red wispy cloud — known to astronomers as an &quot;emission nebula&quot; — in the center of the image.&quot;&lt;ref name=Kramer&gt;{{ cite book
|author=Miriam Kramer
|title=Dusty Star-Spawning Space Cloud Glows In Amazing Photo
|publisher=Yahoo! News
|location=La Silla, Chile
|date=May 2, 2013
|url=http://news.yahoo.com/dusty-star-spawning-space-cloud-glows-amazing-photo-140759329.html;_ylt=AuvOfcnBLreDFxWBFfhiolaHgsgF;_ylu=X3oDMTRlMXAzbmRkBG1pdANUb3BTdG9yeSBTY2llbmNlU0YgU3BhY2VBc3Ryb25vbXlTU0YEcGtnAzkwY2RjMGI1LTYwNWUtM2I0YS1iOTNmLTJjNjU1N2ZmMzI2ZARwb3MDNwRzZWMDdG9wX3N0b3J5BHZlcgM0M2ZiYWM0MS1iMzMyLTExZTItYWJiYi1iNTZkODJmMTk2NzY-;_ylg=X3oDMTI1MG9icjRhBGludGwDdXMEbGFuZwNlbi11cwRwc3RhaWQDBHBzdGNhdANzY2llbmNlfHNwYWNlLWFzdHJvbm9teQRwdANzZWN0aW9ucw--;_ylv=3
|accessdate=2013-05-02 }}&lt;/ref&gt;

&quot;These young stars are usually of spectral type O and B, with temperatures between 10 000 and 60 000 K, which radiate huge amounts of high energy ultraviolet light that ionises the hydrogen atoms.&quot;&lt;ref name=Hook/&gt;

&quot;The blue section of the photo — representing a &quot;reflection nebula&quot; — shows light from the newly formed stars in the cosmic nursery being reflected in all directions by the particles of dust made of iron, carbon, silicon and other elements in the interstellar cloud.&quot;&lt;ref name=Kramer/&gt;

'''NGC 6559''' is planetary nebula located at a distance of about 5000 light-years from Earth, in the constellation of Sagittarius.

&quot;NGC 6559 is a cloud of gas and dust located at a distance of about 5000 light-years from Earth, in the constellation of Sagittarius (The Archer). The glowing region is a relatively small object, just a few light-years across, in contrast to the one hundred light-years and more spanned by its famous neighbour, the Lagoon Nebula (Messier 8, eso0936). Although it is usually overlooked in favour of its distinguished companion, NGC 6559 has the leading role in this new picture.&quot;&lt;ref name=Hook&gt;{{ cite book
|author=Richard Hook
|title=An Anarchic Region of Star Formation
|publisher=European Southern Observatory
|location=Garching bei München, Germany
|date=
|url=http://www.eso.org/public/news/eso1320/
|accessdate=2013-05-02 }}&lt;/ref&gt;

&quot;The Milky Way fills the background of the image with countless yellowish older stars. Some of them appear fainter and redder because of the dust in NGC 6559.&quot;&lt;ref name=Hook/&gt;

&quot;This eye-catching image of star formation was captured by the Danish Faint Object Spectrograph and Camera (DFOSC)&quot;.&lt;ref name=Hook/&gt;
{{clear}}

==BL Lacertae objects==
{{main|Stars/Quasars}}
[[Image:H0323bl2.gif|thumb|right|250px|This is an image of H 0323+022 using the red (R) filter. Credit: Renato Falomo, ESO NTT.{{tlx|free media}}]]
QSO B0323+022 is a BL Lacertae object. The image at right is taken with the ESO NTT using the R filter.
{{clear}}

==Starburst galaxy==
[[Image:M82 HST ACS 2006-14-a-large web.jpg|thumb|right|250px|This mosaic image taken by the Hubble Space Telescope of Messier 82 combines exposures taken with four colored filters that capture starlight from visible and infrared wavelengths as well as the light from the glowing hydrogen filaments. Credit: NASA, ESA, and The Hubble Heritage Team (STScI/AURA).{{tlx|free media}}]]
&quot;The presence of ERE has been established spectroscopically in ... the starburst galaxy M82 (Perrin, Darbon, &amp; Sivan 1995).&quot;&lt;ref name=Witt/&gt;

&quot;This mosaic image [at right] is the sharpest wide-angle view ever obtained of M82. The galaxy is remarkable for its bright blue disk, webs of shredded clouds, and fiery-looking plumes of glowing hydrogen blasting out of its central regions.&quot;&lt;ref name=Gallagher&gt;{{ cite book
|author=J. Gallagher
|author2=M. Mountain
|author3=P. Puxley
|title=Happy Sweet Sixteen, Hubble Telescope!
|publisher=HubbleSite.org
|location=Baltimore, Maryland USA
|date=April 24, 2006
|url=http://hubblesite.org/newscenter/archive/releases/2006/14/image/a/
|accessdate=2013-07-30 }}&lt;/ref&gt;

&quot;Throughout the galaxy's center, young stars are being born 10 times faster than they are inside our entire Milky Way Galaxy. The resulting huge concentration of young stars carved into the gas and dust at the galaxy's center. The fierce galactic superwind generated from these stars compresses enough gas to make millions of more stars.&quot;&lt;ref name=Gallagher/&gt;

&quot;In M82, young stars are crammed into tiny but massive star clusters. These, in turn, congregate by the dozens to make the bright patches, or &quot;starburst clumps,&quot; in the central parts of M82. The clusters in the clumps can only be distinguished in the sharp Hubble images. Most of the pale, white objects sprinkled around the body of M82 that look like fuzzy stars are actually individual star clusters about 20 light-years across and contain up to a million stars.&quot;&lt;ref name=Gallagher/&gt;

&quot;The rapid rate of star formation in this galaxy eventually will be self-limiting. When star formation becomes too vigorous, it will consume or destroy the material needed to make more stars. The starburst then will subside, probably in a few tens of millions of years.&quot;&lt;ref name=Gallagher/&gt;

&quot;Located 12 million light-years away, M82 appears high in the northern spring sky in the direction of the constellation Ursa Major, the Great Bear. It is also called the &quot;Cigar Galaxy&quot; because of the elliptical shape produced by the oblique tilt of its starry disk relative to our line of sight.&quot;&lt;ref name=Gallagher/&gt;

&quot;The observation was made in March 2006, with the Advanced Camera for Surveys' Wide Field Channel. Astronomers assembled this six-image composite mosaic by combining exposures taken with four colored filters that capture starlight from visible and infrared wavelengths as well as the light from the glowing hydrogen filaments.&quot;&lt;ref name=Gallagher/&gt;
{{clear}}

==Red shifts==
[[Image:Redshift.svg|thumb|upright|right|250px|[[w:spectral line|Absorption lines]] in the [[w:visible spectrum|visible spectrum]] of a [[w:supercluster|supercluster]] of distant galaxies (right), are compared to absorption lines in the visible spectrum of the Sun (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decreases). Credit: [[c:user:Xorx|Dr. Schorsch]] and [[c:user:Kes47|Kes47]].{{tlx|free media}}]]
&quot;Ideally all intrinsic colours should be found from unreddened stars. This is possible for dwarf and giant stars later than about A0 (Johnson, 1964) ... However, it cannot be used for stars of other spectral classes since they are all relatively infrequent in space, and generally reddened.&quot;&lt;ref name=FitzGerald&gt;{{ cite journal
|author=M. Pim FitzGerald
|title=The Intrinsic Colours of Stars and Two-Colour Reddening Lines
|journal=Astronomy and Astrophysics
|month=February
|year=1970
|volume=4
|issue=2
|pages=234-43
|url=
|arxiv=
|bibcode=1970A&amp;A.....4..234F
|doi=
|pmid=
|accessdate=2011-11-24 }}&lt;/ref&gt;

'''Redshift''' happens when light seen coming from an object that is moving away is [[w:Proportionality (mathematics)|proportion]]ally increased in [[w:wavelength|wavelength]], or shifted to the red end of the [[w:visible spectrum|visible spectrum]]. More generally, where an [[w:Observer (physics)|observer]] detects [[w:electromagnetic radiation|electromagnetic radiation]] outside the [[w:electromagnetic spectrum|visible spectrum]], &quot;redder&quot; amounts to a technical shorthand for &quot;increase in electromagnetic wavelength&quot; &amp;mdash; which also implies lower [[w:frequency|frequency]] and [[w:photon|photon]] energy in accord with, respectively, the [[w:Wave theory of light|wave]] and [[w:Light#Quantum theory|quantum]] theories of light. Redshifts are attributable to the [[w:Doppler effect|Doppler effect]], familiar in the changes in the apparent [[w:Pitch (music)|pitch]]es of sirens and [[w:frequency|frequency]] of the [[w:sound|sound waves]] emitted by speeding vehicles; an observed redshift due to the Doppler effect occurs whenever a light source moves away from an observer.
{{clear}}

==Cosmological redshifts==
[[Image:Observable universe redshift illustration.png|thumb|right|250px|Circular representation of the observable universe is on a redshift scale generated with Celestia software. Credit: [[c:user:Piquito veloz|Piquito veloz]].{{tlx|free media}}]]
All observable universe since the redshift line of z=0.01 to z=1089 (cosmic microwave background). The Solar System at the center z=0.

[[w:Cosmology|Cosmological]] redshift is seen due to the [[w:Metric expansion of space|expansion of the universe]], and sufficiently distant light sources (generally more than a few million [[w:light years|light years]] away) show redshift corresponding to the rate of increase of their distance from Earth.
{{clear}}

==Gravitational redshifts==
[[Image:Gravitational red-shifting.png|thumb|right|250px|Illustration shows gravitational red-shifting. Credit: [[c:user:Vlad2i~commonswiki|Vlad2i~commonswiki]].{{tlx|free media}}]]
[[w:Gravitational redshift|Gravitational redshift]]s are a [[w:general relativity|relativistic]] effect observed in electromagnetic radiation moving out of [[w:Gravitational field|gravitational field]]s.
{{clear}}

==Blue shifts==
[[Image:Andromeda Galaxy 560mm FL.jpg|thumb|right|250px|The Andromeda Galaxy with satellite galaxies Messier 32 (M32) (center left above the galactic nucleus) and Messier 110 (M110) (center left below the galaxy), z = −0.001004 (minus sign indicates blueshift). Credit: [[c:user:David (Deddy) Dayag|David (Deddy) Dayag]].{{tlx|free media}}]]
z = −0.001004 (minus sign indicates blueshift).&lt;ref name=Ned&gt;{{cite web | title = Results for Messier 31 | url = http://ned.ipac.caltech.edu/cgi-bin/objsearch?objname=M+031&amp;extend=no&amp;hconst=73&amp;omegam=0.27&amp;omegav=0.73&amp;corr_z=1&amp;out_csys=Equatorial&amp;out_equinox=J2000.0&amp;obj_sort=RA+or+Longitude&amp;of=pre_text&amp;zv_breaker=30000.0&amp;list_limit=5&amp;img_stamp=YES | work = NASA/IPAC Extragalactic Database | publisher = NASA/Infrared Processing and Analysis Center (IPAC) | accessdate = 28 February 2019 }}&lt;/ref&gt;

The Triangulum Galaxy has a redshift z = -0.000607 ± 0.000010.&lt;ref name=&quot;SIMBAD-M33&quot;&gt;{{cite web | title=M 33 – Galaxy | work=SIMBAD | publisher=Centre de Données astronomiques de Strasbourg | url=http://simbad.u-strasbg.fr/simbad/sim-id?Ident=M33 | accessdate=2009-11-28 }}&lt;/ref&gt;

Messier 32 has a redshift z = −200 ± 6 km/s.&lt;ref name=NGC221&gt;{{ cite web
  | title=NASA/IPAC Extragalactic Database
  | work=Results for NGC 221
  | url=http://nedwww.ipac.caltech.edu/
  | accessdate=2006-11-29 }}&lt;/ref&gt;

A ''decrease'' in wavelength is called blueshift and is generally seen when a light-emitting object moves toward an observer or when electromagnetic radiation moves into a gravitational field.
{{clear}}

==Astrochemistry==
{{main|Astrochemistry}}
[[Image:Turbulent border in Orion Nebula.jpg|thumb|right|250px|These images show the edge of the vast molecular cloud that lies behind the Orion Nebula, 1400 light-years from Earth. Credit: ESO/Goicoechea ''et al''.{{tlx|free media}}]]
The image of the left shows a wide-field view of the region, as seen with the HAWK-I instrument, installed at the Very Large Telescope. A small region is highlighted with a white rectangle, and the rightmost image shows that region in stunning fiery detail, observed with the Atacama Large Millimeter/submillimeter Array (ALMA).

As well as producing beautiful images, molecular clouds are of great interest to astronomers. The clouds are stellar nurseries and at their edge atoms react and form molecules by key astrochemical processes. With the ALMA observations scientists were able to resolve this transition from atomic to molecular gas at the border of the Orion molecular cloud. As Orion is the nearest massive star-forming region it is the ideal target to find out more about these astrochemical processes, and it also offers the possibility to study the interactions of newly formed stars with their surroundings in detail.

Both observations show that this fascinating astrochemical transition from atomic to molecular gas happens in a highly dynamic environment.

&quot;Electron microprobe analyses indicate that the Apollo 15 red glasses with 13.8 wt.% TiO&lt;sub&gt;2&lt;/sub&gt; were produced in a volcanic fire-fountain. They are composed of three chemical groups connected by a pronounced trend. The liquidus phase relations are compatible with the view that the most Mg-rich group (A) was produced by partial melting of Ti-rich cumulates at a depth of about 480 km. The other red glasses (B and C) may have been derived from the group A magma by fractional crystallization at pressures less than 5 kbar.&quot;&lt;ref name=Delano&gt;{{ cite book
|author=J. W. Delano
|title=Chemistry and liquidus phase relations of Apollo 15 red glass Implications for the deep lunar interior, In: ''Lunar and Planetary Science Conference''
|publisher=Pergamon Press
|location=New York
|date=1980
|editor=
|volume=1
|pages=251-88
|url=http://adsabs.harvard.edu/abs/1980LPSC...11..251D
|arxiv=
|bibcode=1980LPSC...11..251D
|doi=
|pmid=
|isbn=
|accessdate=2013-08-02 }}&lt;/ref&gt;
{{clear}}

==Geography==
{{main|Radiation astronomy/Geography}}
[[Image:Red Sea Mountains, Egypt (3280314450).jpg|thumb|right|250px|The Red Sea mountians are reddish. Credit: [https://www.flickr.com/people/78174175@N00 Andrew A. Shenouda from Riyadh, Saudi Arabia].{{tlx|free media}}]]
&quot;Providing very high geometrical resolution and position accuracy and with four multispectral bands, HRSC-AX data delivered even better biotope mapping results than the analysis of aerial photographs. According to Ehlers etal.(2003), the red band, near infrared band and particularly the NDVI ((nIRR)/(nIR–R)) were useful to distinguish vegetation from non-vegetation and to differentiate vegetation types.&quot;&lt;ref name=Otto&gt;{{ cite journal
|author=J.-C. Otto
|author2=K. Kleinod
|author3=O. König
|author4=M. Krautblatter
|author5=M. Nyenhuis
|author6=I. Roer
|author7=M. Schneider
|author8=B. Schreiner
|author9=R. Dikau
|title=HRSC-A data: a new high-resolution data set with multipurpose applications in physical geography
|journal=Progress in Physical Geography
|month=
|year=2007
|volume=31
|issue=2
|pages=179-97
|url=http://ppg.sagepub.com/content/31/2/179.short
|arxiv=
|bibcode=
|doi=10.1177/0309133307076479 
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;

&quot;The HRSC sensor has an enormous potential in vegetation mapping at small scales, particularly the HRSC-AX with its red band introduced for terrestrial observations. ... The HRSC-AX camera is recommended for applications in biogeography.&quot;&lt;ref name=Otto/&gt;
{{clear}}

==Hasselo stadial==
[[Image:Loess Plateau geomorphology——2012-4 - panoramio.jpg|thumb|right|250px|Loess Plateau geomorphology shows reddish color. Credit: 黄河山曲.{{tlx|free media}}]]
The &quot;Hasselo stadial [is] at approximately 40-38,500 &lt;sup&gt;14&lt;/sup&gt;C years B.P. (Van Huissteden, 1990).&quot;&lt;ref name=Vandenberghe&gt;{{ cite journal
|author=J. Vandenberghe
|author2=G. Nugteren
|title=Rapid climatic changes recorded in loess successions
|journal=Global and Planetary Change
|month=
|year=2001
|volume=28
|issue=1-9
|pages=222-30
|url=http://shixi.bnu.edu.cn/field-trips/cooperation/ChinaSweden/the%20link/1.1.4.pdf
|arxiv=
|bibcode=
|doi=
|pmid=
|accessdate=2014-11-06 }}&lt;/ref&gt;

The &quot;Hasselo Stadial [is a glacial advance] (44–39 ka ago)&quot;.&lt;ref name=Nikonov&gt;{{ cite journal
|author=A.A. Nikonov
|author2=M.M. Shakhnovich
|author3=J. van der Plicht
|title=Age of Mammoth Remains from the Submoraine Sediments of the Kola Peninsula and Karelia
|journal=Doklady Earth Sciences
|month=
|year=2011
|volume=436
|issue=2
|pages=308-10
|url=http://cio.eldoc.ub.rug.nl/FILES/root/2011/DoklEarthSciNikonov/2011DoklEarthSciNikonov.pdf?origin=publication_detail
|arxiv=
|bibcode=
|doi=
|pmid=
|accessdate=2014-11-06 }}&lt;/ref&gt; 

The &quot;earliest known astronomy anywhere in the world [is] that of the Australian Aborigines, whose culture has existed for some 40,000 years&quot;.&lt;ref name=Haynes/&gt;

&quot;The Aranda tribes of Central Australia, for example, distinguish red stars from white, blue and yellow stars.&quot;&lt;ref name=Haynes&gt;{{ cite book
|author=R Haynes
|title=Explorers of the southern sky: a history of Australian astronomy
|publisher=Cambridge University Press
|location=Cambridge, England, UK
|date=June 27, 1996
|editor=Raymond Haynes
|editor2=Roslynn Haynes
|editor3=David Malin
|editor4=Richard McGee
|pages=527
|url=http://books.google.com/books?id=XoeiJxMmXZ8C&amp;lr=&amp;source=gbs_navlinks_s
|arxiv=
|bibcode=
|doi=
|pmid=
|isbn=0521365759
|accessdate=2013-08-02 }}&lt;/ref&gt;
{{clear}}

==Astrophysics==
{{main|Radiation astronomy/Astrophysics}}
'''Massive astrophysical compact halo object''', or '''MACHO''', is a general name for any kind of astronomical body that might explain the apparent presence of dark matter in galaxy halos. A MACHO is a body composed of normal baryonic matter, which emits little or no radiation and drifts through interstellar space unassociated with any planetary system. Since MACHOs would not emit any light of their own, they would be very hard to detect. MACHOs may sometimes be black holes or neutron stars as well as brown dwarfs or unassociated planets. White dwarfs and very faint red dwarfs have also been proposed as candidate MACHOs.

==Catalogs==

In 1866, after the new observatory had been completed, [[w:Hans Schjellerup|Schjellerup]] assembled a catalog of red stars.

The Perkins Observatory catalog includes &quot;the full subclasses used are the following: G0, G5, G8, K0, K1, K2, K3, K4, K5, M0, M1, M2, M3, M4, M5, M6, M7, and M8.&quot;&lt;ref name=Keenan&gt;{{ cite journal
|author=Philip C. Keenan
|author2=Raymond C. McNeil
|title=The Perkins catalog of revised MK types for the cooler stars
|journal=The Astrophysical Journal Supplement Series
|month=October
|year=1989
|volume=71
|issue=10
|pages=245-66
|url=http://adsabs.harvard.edu/abs/1989ApJS...71..245K
|arxiv=
|bibcode=1989ApJS...71..245K
|doi=10.1086/191373
|pmid=
|accessdate=2013-08-02 }}&lt;/ref&gt;

==Technology==
{{main|Technology}}
The High Resolution Stereo Camera HRSC-AX150 has the red band of 635-685 nm, and the HRSC-AX047 has 570-680 nm.&lt;ref name=Otto/&gt;
Orcus Patera was imaged by the HRSC:
{{multiple image
|align      = center
|direction  = vertical
|image1     = Orcus Patera by HRSC.jpg
|width      = 800
|caption1   = ''Mars Express'' HRSC views Orcus Patera. Credit: ESA/DLR/FU Berlin (G. Neukum).{{tlx|free media}}
|image2     = Elevation of Orcus Patera and surroundings.jpg
|caption2   = ''Mars Express'' HRSC views Orcus Patera with colors for elevation. Credit: ESA/DLR/FU Berlin (G. Neukum).{{tlx|free media}}
}}
{{clear}}

==Hypotheses==
{{main|Hypotheses}}
# The color astronomies have special values unique to each.

==See also==
{{div col|colwidth=20em}}
* [[Blue astronomy]]
* [[Cyan astronomy]]
* [[Gamma-ray astronomy]]
* [[Green astronomy]]
* [[Infrared astronomy]]
* [[Microwave astronomy]]
* [[Optical astronomy]]
* [[Orange astronomy]]
* [[Radar astronomy]]
* [[Radio astronomy]]
* [[Red astronomy]]
* [[Submillimeter astronomy]]
* [[Violet astronomy]]
* [[Visual astronomy]]
* [[X-ray astronomy]]
* [[Yellow astronomy]]
{{Div col end}}

==References==
{{reflist|2}}

==External links==
* [http://www.genome.jp/ GenomeNet KEGG database]
* [http://www.iau.org/ International Astronomical Union]
* [http://nedwww.ipac.caltech.edu/ NASA/IPAC Extragalactic Database - NED]
* [http://nssdc.gsfc.nasa.gov/ NASA's National Space Science Data Center]
* [http://www.ncbi.nlm.nih.gov/sites/gquery NCBI All Databases Search]
* [http://www.osti.gov/ Office of Scientific &amp; Technical Information]
* [http://www.ncbi.nlm.nih.gov/pccompound PubChem Public Chemical Database]
* [http://www.adsabs.harvard.edu/ The SAO/NASA Astrophysics Data System]
* [http://www.scirus.com/srsapp/advanced/index.jsp?q1= Scirus for scientific information only advanced search]
* [http://cas.sdss.org/astrodr6/en/tools/quicklook/quickobj.asp SDSS Quick Look tool: SkyServer]
* [http://simbad.u-strasbg.fr/simbad/ SIMBAD Astronomical Database]
* [http://nssdc.gsfc.nasa.gov/nmc/SpacecraftQuery.jsp Spacecraft Query at NASA]
* [http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/convcoord/convcoord.pl  Universal coordinate converter]

&lt;!-- footer templates --&gt;
{{tlx|Radiation astronomy resources}}{{Principles of radiation astronomy}}{{tlx|Terminology resources}}{{Sisterlinks|Red astronomy}}

&lt;!-- categories --&gt;
[[Category:Radiation astronomy/Lectures]]
[[Category:Radiation/Lectures]]</text>
      <sha1>nzti5gjj4vm5pz9h1ergk72syciqs2a</sha1>
    </revision>
  </page>
  <page>
    <title>Understanding Arithmetic Circuits</title>
    <ns>0</ns>
    <id>139384</id>
    <revision>
      <id>2693021</id>
      <parentid>2692902</parentid>
      <timestamp>2024-12-23T14:29:59Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Adder */</comment>
      <origin>2693021</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3000" sha1="86st7ms4wex335j50k6jg2woturysi6" xml:space="preserve">
== Adder ==

* Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]]  )
 
{| class=&quot;wikitable&quot;
|-
!  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.20241223.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]]||
|| || 
|}
&lt;/br&gt;
 
=== 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
&lt;/br&gt;

== Barrel Shifter ==
* Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]])
&lt;/br&gt;

'''Mux Based Barrel Shifter'''
* Analysis  ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) 
* Implementation 
&lt;/br&gt;

== Multiplier == 
=== Array Multipliers ===
* Analysis  ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]])
&lt;/br&gt;

=== 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]])
&lt;/br&gt;

=== Booth Multipliers ===
* [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]]
* Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]])
&lt;/br&gt;

== Divider == 
* Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])&lt;/br&gt;

&lt;/br&gt;
&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]

[[Category:Digital Circuit Design]]
[[Category:FPGA]]</text>
      <sha1>86st7ms4wex335j50k6jg2woturysi6</sha1>
    </revision>
    <revision>
      <id>2693092</id>
      <parentid>2693021</parentid>
      <timestamp>2024-12-24T04:46:59Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Adder */</comment>
      <origin>2693092</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3000" sha1="9mg45zzhal7w6rl31x4ua3juu8888dh" xml:space="preserve">
== Adder ==

* Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]]  )
 
{| class=&quot;wikitable&quot;
|-
!  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.20241224.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]]||
|| || 
|}
&lt;/br&gt;
 
=== 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
&lt;/br&gt;

== Barrel Shifter ==
* Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]])
&lt;/br&gt;

'''Mux Based Barrel Shifter'''
* Analysis  ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) 
* Implementation 
&lt;/br&gt;

== Multiplier == 
=== Array Multipliers ===
* Analysis  ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]])
&lt;/br&gt;

=== 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]])
&lt;/br&gt;

=== Booth Multipliers ===
* [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]]
* Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]])
&lt;/br&gt;

== Divider == 
* Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])&lt;/br&gt;

&lt;/br&gt;
&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]

[[Category:Digital Circuit Design]]
[[Category:FPGA]]</text>
      <sha1>9mg45zzhal7w6rl31x4ua3juu8888dh</sha1>
    </revision>
  </page>
  <page>
    <title>User:Drbogdan</title>
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      <contributor>
        <username>Drbogdan</username>
        <id>241794</id>
      </contributor>
      <comment>/* My Links */ adjs</comment>
      <origin>2693017</origin>
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      <text bytes="4245" sha1="p9l51b3xftiy29we07mskddg7jj8xe5" xml:space="preserve">[[File:DrDennisBogdan.jpg|thumb|[http://drbogdan.livejournal.com Dr. Dennis Bogdan]]]

'''Drbogdan''' - My Professional Background Includes [https://www.sciencedirect.com/science/article/abs/pii/0014299970901676 Publishing Medical Research Studies], [https://photos.onedrive.com/share/563AB708D5D054A8!39776?cid=563AB708D5D054A8&amp;resId=563AB708D5D054A8!39776&amp;ithint=photo&amp;migratedtospo=true&amp;redeem=aHR0cHM6Ly8xZHJ2Lm1zL2kvcyFBcWhVME5VSXR6cFdnclpnUDI4Y0ducVVLQkNUaHc Directing Hospital Laboratories], [https://photos.onedrive.com/share/563AB708D5D054A8!39776?cid=563AB708D5D054A8&amp;resId=563AB708D5D054A8!39776&amp;ithint=photo&amp;migratedtospo=true&amp;redeem=aHR0cHM6Ly8xZHJ2Lm1zL2kvcyFBcWhVME5VSXR6cFdnclpnUDI4Y0ducVVLQkNUaHc Lecturing University Students] And [https://archive.ph/YmCTD Contributing As A Grandmaster Editor To Wikipedia]. Also, I Have [https://photos.onedrive.com/share/563AB708D5D054A8!39779?cid=563AB708D5D054A8&amp;resId=563AB708D5D054A8!39779&amp;ithint=photo&amp;migratedtospo=true&amp;redeem=aHR0cHM6Ly8xZHJ2Lm1zL2kvcyFBcWhVME5VSXR6cFdnclpqWXBGQ19sb2FKNVM3OVE Headed Science Fairs] And Have Been Associated With, For A Brief Time, [https://en.wikipedia.org/wiki/Pittsburgh_Symphony_Orchestra The Pittsburgh Symphony Orchestra] And [https://en.wikipedia.org/wiki/Pittsburgh_Ballet_Theatre The Pittsburgh Ballet Theater]. My Professional Background Is Summarized In More Detail On [http://web.archive.org/web/20151003143043/http://home.comcast.net/~drbogdan/publications.html My Publications Page].

==My Links==
* [http://web.archive.org/web/20151003143043/http://home.comcast.net/~drbogdan/publications.html My Publications Page] ([http://archive.today/bXZYs &lt;u&gt;&lt;big&gt;'''a'''&lt;/big&gt;&lt;/u&gt;rchive]/[http://web.archive.org/web/20140128184001/http://home.comcast.net/~drbogdan/publications.html way&lt;u&gt;&lt;big&gt;'''b'''&lt;/big&gt;&lt;/u&gt;ack]/[http://www.webcitation.org/6P1riKsfF web&lt;u&gt;&lt;big&gt;'''c'''&lt;/big&gt;&lt;/u&gt;ite]) 
* [https://drbogdan.wordpress.com/2024/10/08/publications-summary-20241008 My Publications Summary] &amp; [https://drbogdan.wordpress.com/2024/10/08/publications-complete-20241008 Publications Complete]
* [http://web.archive.org/web/20151002151258/http://home.comcast.net/~drbogdan/membersonly/music.html My Original Music] &amp; [http://www.youtube.com/user/joannebogdan/videos My Original Music Videos]
* [http://www.facebook.com/drbogdan My FaceBook] &amp; [https://www.flickr.com/photos/drbogdan/ My Flickr] &amp; [http://drbogdan.livejournal.com My LiveJournal]
* [https://en.wikipedia.org/w/index.php?title=User:Drbogdan&amp;direction=prev&amp;oldid=1232617906 My Wikipedia Page] ([https://archive.ph/YmCTD a]/[https://web.archive.org/web/20240722001545/https://en.wikipedia.org/wiki/User:Drbogdan b]/[https://ghostarchive.org/archive/4oVTp g]&lt;!---/[http://www.webcitation.org/6P1of3jXl c]---&gt;)
* EMail Me (drbogdan) =&gt; @ [[Special:EmailUser/Drbogdan|Wikipedia]] OR @ [mailto:drbogdan@yahoo.com Yahoo]

{| align=center border=3 cellspacing=0 style=&quot;border-width: 5px; border-color: SkyBlue; background: Beige; margin: 2em;&quot;
| style=&quot;text-align: center; padding: 10px 60px 10px 60px;&quot; | 
&lt;small&gt;'''This is a Wikipedia [[w:Wikipedia:User pages|user page]].'''&lt;/small&gt;&lt;br /&gt;&lt;small&gt;This is not an encyclopedia article. If you find this page on any site other than Wikipedia, you are viewing a [[w:Mirror (computing)|mirror site]]. Be aware that the page may be outdated and that the user to whom this page belongs may have no personal affiliation with any site other than Wikipedia itself.  The original page is located at http://en.wikipedia.org/wiki/User:Drbogdan&lt;/small&gt;
|}

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&lt;!-- Metadata: see [[Wikipedia:Persondata]] --&gt; 
&lt;!---
{{Persondata
| NAME              = [[w:User talk:Drbogdan|Dr. Dennis Bogdan]]
| ALTERNATIVE NAMES = [[w:User talk:Drbogdan|Drbogdan]]; [[w:User talk:Drbogdan|Dennis]]
| SHORT DESCRIPTION = [[w:Americans|American]] [[w:Scientist]]
| DATE OF BIRTH     = 12&amp;nbsp;March 1944
| PLACE OF BIRTH    = [[w:Sharon, Pennsylvania]], [[w:USA]]
| DATE OF DEATH     = 
| PLACE OF DEATH    = 
}}
---&gt;</text>
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  </page>
  <page>
    <title>Complex analysis in plain view</title>
    <ns>0</ns>
    <id>171005</id>
    <revision>
      <id>2693022</id>
      <parentid>2692616</parentid>
      <timestamp>2024-12-23T14:30:54Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Geometric Series Examples */</comment>
      <origin>2693022</origin>
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      <text bytes="5241" sha1="qq1vugm2vyr4z3wukgnwg6nxpai8y4l" xml:space="preserve">Many of the functions that arise naturally in mathematics and real world applications can be extended to and regarded as complex functions, meaning the input, as well as the output, can be complex numbers &lt;math&gt;x+iy&lt;/math&gt;, where &lt;math&gt;i=\sqrt{-1}&lt;/math&gt;, in such a way that it is a more natural object to study. '''Complex analysis''', which used to be known as '''function theory''' or '''theory of functions of a single complex variable''', is a sub-field of analysis that studies such functions (more specifically, '''holomorphic''' functions) on the complex plane, or part (domain) or extension (Riemann surface) thereof. It notably has great importance in number theory, e.g. the [[Riemann zeta function]] (for the distribution of primes) and other &lt;math&gt;L&lt;/math&gt;-functions, modular forms, elliptic functions, etc. &lt;blockquote&gt;The shortest path between two truths in the real domain passes through the complex domain.  — [[wikipedia:Jacques_Hadamard|Jacques Hadamard]]&lt;/blockquote&gt;In a certain sense, the essence of complex functions is captured by the principle of [[analytic continuation]].{{mathematics}}

==''' Complex Functions '''== 
* Complex Functions ([[Media:CAnal.1.A.CFunction.20140222.Basic.pdf|1.A.pdf]], [[Media:CAnal.1.B.CFunction.20140111.Octave.pdf|1.B.pdf]], [[Media:CAnal.1.C.CFunction.20140111.Extend.pdf|1.C.pdf]])

* Complex Exponential and Logarithm ([[Media:CAnal.5.A.CLog.20131017.pdf|5.A.pdf]], [[Media:CAnal.5.A.Octave.pdf|5.B.pdf]])

* Complex Trigonometric and Hyperbolic ([[Media:CAnal.7.A.CTrigHyper..pdf|7.A.pdf]], [[Media:CAnal.7.A.Octave..pdf|7.B.pdf]])

'''Complex Function Note'''
: 1. Exp and Log Function Note ([[Media:ComplexExp.29160721.pdf|H1.pdf]])

: 2. Trig and TrigH Function Note ([[Media:CAnal.Trig-H.29160901.pdf|H1.pdf]])

: 3. Inverse Trig and TrigH Functions Note ([[Media:CAnal.Hyper.29160829.pdf|H1.pdf]])

==''' Complex Integrals '''== 
* Complex Integrals ([[Media:CAnal.2.A.CIntegral.20140224.Basic.pdf|2.A.pdf]], [[Media:CAnal.2.B.CIntegral.20140117.Octave.pdf|2.B.pdf]], [[Media:CAnal.2.C.CIntegral.20140117.Extend.pdf|2.C.pdf]])

==''' Complex Series '''== 
* Complex Series ([[Media:CPX.Series.20150226.2.Basic.pdf|3.A.pdf]], [[Media:CAnal.3.B.CSeries.20140121.Octave.pdf|3.B.pdf]], [[Media:CAnal.3.C.CSeries.20140303.Extend.pdf|3.C.pdf]])

==''' Residue Integrals '''==
* Residue Integrals ([[Media:CAnal.4.A.Residue.20140227.Basic.pdf|4.A.pdf]], [[Media:CAnal.4.B.pdf|4.B.pdf]], [[Media:CAnal.4.C.Residue.20140423.Extend.pdf|4.C.pdf]]) 

==='''Residue Integrals Note'''===
* Laurent Series with the Residue Theorem Note ([[Media:Laurent.1.Residue.20170713.pdf|H1.pdf]])
* Laurent Series with Applications Note ([[Media:Laurent.2.Applications.20170327.pdf|H1.pdf]])
* Laurent Series and the z-Transform Note ([[Media:Laurent.3.z-Trans.20170831.pdf|H1.pdf]])
* Laurent Series as a Geometric Series Note ([[Media:Laurent.4.GSeries.20170802.pdf|H1.pdf]])

=== Laurent Series and the z-Transform Example Note === 
* Overview ([[Media:Laurent.4.z-Example.20170926.pdf|H1.pdf]])

====Geometric Series Examples====

* Causality ([[Media:Laurent.5.Causality.1.A.20191026n.pdf|A.pdf]], [[Media:Laurent.5.Causality.1.B.20191026.pdf|B.pdf]]) 

* Time Shift ([[Media:Laurent.5.TimeShift.2.A.20191028.pdf|A.pdf]], [[Media:Laurent.5.TimeShift.2.B.20191029.pdf|B.pdf]]) 

* Reciprocity ([[Media:Laurent.5.Reciprocity.3A.20191030.pdf|A.pdf]], [[Media:Laurent.5.Reciprocity.3B.20191031.pdf|B.pdf]]) 

* Combinations ([[Media:Laurent.5.Combination.4A.20200702.pdf|A.pdf]], [[Media:Laurent.5.Combination.4B.20201002.pdf|B.pdf]]) 

* Properties ([[Media:Laurent.5.Property.5A.20220105.pdf|A.pdf]], [[Media:Laurent.5.Property.5B.20220126.pdf|B.pdf]]) 

* Permutations ([[Media:Laurent.6.Permutation.6A.20230711.pdf|A.pdf]], [[Media:Laurent.5.Permutation.6B.20241223.pdf|B.pdf]], [[Media:Laurent.5.Permutation.6C.20240528.pdf|C.pdf]]) 

* Applications ([[Media:Laurent.5.Application.6B.20220723.pdf|A.pdf]]) 

* Double Pole Case

:- Examples ([[Media:Laurent.5.DPoleEx.7A.20220722.pdf|A.pdf]], [[Media:Laurent.5.DPoleEx.7B.20220720.pdf|B.pdf]]) 

:- Properties ([[Media:Laurent.5.DPoleProp.5A.20190226.pdf|A.pdf]], [[Media:Laurent.5.DPoleProp.5B.20190228.pdf|B.pdf]])

====The Case Examples====
* Example Overview : ([[Media:Laurent.4.Example.0.A.20171208.pdf|0A.pdf]], [[Media:Laurent.6.CaseExample.0.B.20180205.pdf|0B.pdf]])
* Example Case 1 : ([[Media:Laurent.4.Example.1.A.20171107.pdf|1A.pdf]], [[Media:Laurent.4.Example.1.B.20171227.pdf|1B.pdf]])
* Example Case 2 : ([[Media:Laurent.4.Example.2.A.20171107.pdf|2A.pdf]], [[Media:Laurent.4.Example.2.B.20171227.pdf|2B.pdf]])
* Example Case 3 : ([[Media:Laurent.4.Example.3.A.20171017.pdf|3A.pdf]], [[Media:Laurent.4.Example.3.B.20171226.pdf|3B.pdf]])
* Example Case 4 : ([[Media:Laurent.4.Example.4.A.20171017.pdf|4A.pdf]], [[Media:Laurent.4.Example.4.B.20171228.pdf|4B.pdf]])
* Example Summary : ([[Media:Laurent.4.Example.5.A.20171212.pdf|5A.pdf]], [[Media:Laurent.4.Example.5.B.20171230.pdf|5B.pdf]])

==''' Conformal Mapping '''== 
* Conformal Mapping ([[Media:CAnal.6.A.Conformal.20131224.pdf|6.A.pdf]], [[Media:CAnal.6.A.Octave..pdf|6.B.pdf]])

go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]

[[Category:Complex analysis]]</text>
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    </revision>
  </page>
  <page>
    <title>Islam/Praying</title>
    <ns>0</ns>
    <id>203526</id>
    <revision>
      <id>2693088</id>
      <parentid>2252857</parentid>
      <timestamp>2024-12-24T03:42:25Z</timestamp>
      <contributor>
        <username>Tasbihnadir</username>
        <id>2995389</id>
      </contributor>
      <minor />
      <comment>Helping users to do online tasbih.</comment>
      <origin>2693088</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1231" sha1="szpwwnosa2vrvwl1bup3zsx7pfnhx4y" xml:space="preserve">[[File:Taipei Grand Mosque - Tarawih.JPG|thumb|Islamic prayer]]

'''Prayer''' or '''Salah''', is an act of worship which is obligatory for [[Islam/Muslims|muslims]]. Praying is always facing towards the Kiblah&lt;sup&gt;[http://islam.about.com/od/prayer/g/qiblah.htm 1]&lt;/sup&gt;, in the direction of the Ka'aba&lt;sup&gt;[http://muslimvoices.org/kaaba/ 2]&lt;/sup&gt;, in [[Saudi Arabia]]. When a Muslim hits puberty (which is, in Islam, considered to be an adult), they have to pray all 5 prayers, which are: Fajr, Dhuhr, Asr, Maghrib, and Isha. Allah has stated in the [[Islam/Qur'an|Qur'an]], in [http://corpus.quran.com/translation.jsp?chapter=29&amp;verse=45 Surah Ankaboot/Ankabut] (about praying): '''''Recite, [O Muhammad], what has been revealed to you of the Book and establish prayer. Indeed, prayer prohibits immorality and wrongdoing, and the remembrance of Allah is greater. And Allah knows that which you do''''' -Surah Ankaboot/Ankabut, verse 45

They are several verses in the Quran about praying, you can see '''[http://www.questionsonislam.com/article/quranic-verses-about-prayer here]'''.

[[Category:Islamic Studies]]. Muslim usually do tasbih after prayers. Now online [https://tasbihdigital.net/ Tasbih Tools] helps muslim with this.</text>
      <sha1>szpwwnosa2vrvwl1bup3zsx7pfnhx4y</sha1>
    </revision>
    <revision>
      <id>2693090</id>
      <parentid>2693088</parentid>
      <timestamp>2024-12-24T04:28:32Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <comment>you can do this without the unnecessary advertising</comment>
      <origin>2693090</origin>
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      <text bytes="1113" sha1="ebpm3xlo0bqw6r9nmptd462e2fj8c5x" xml:space="preserve">[[File:Taipei Grand Mosque - Tarawih.JPG|thumb|Islamic prayer]]

'''Prayer''' or '''Salah''', is an act of worship which is obligatory for [[Islam/Muslims|muslims]]. Praying is always facing towards the Kiblah&lt;sup&gt;[http://islam.about.com/od/prayer/g/qiblah.htm 1]&lt;/sup&gt;, in the direction of the Ka'aba&lt;sup&gt;[http://muslimvoices.org/kaaba/ 2]&lt;/sup&gt;, in [[Saudi Arabia]]. When a Muslim hits puberty (which is, in Islam, considered to be an adult), they have to pray all 5 prayers, which are: Fajr, Dhuhr, Asr, Maghrib, and Isha. Allah has stated in the [[Islam/Qur'an|Qur'an]], in [http://corpus.quran.com/translation.jsp?chapter=29&amp;verse=45 Surah Ankaboot/Ankabut] (about praying): '''''Recite, [O Muhammad], what has been revealed to you of the Book and establish prayer. Indeed, prayer prohibits immorality and wrongdoing, and the remembrance of Allah is greater. And Allah knows that which you do''''' -Surah Ankaboot/Ankabut, verse 45

They are several verses in the Quran about praying, you can see '''[http://www.questionsonislam.com/article/quranic-verses-about-prayer here]'''.

[[Category:Islamic Studies]]</text>
      <sha1>ebpm3xlo0bqw6r9nmptd462e2fj8c5x</sha1>
    </revision>
  </page>
  <page>
    <title>Dog's behaviour</title>
    <ns>0</ns>
    <id>228750</id>
    <revision>
      <id>2693037</id>
      <parentid>2284169</parentid>
      <timestamp>2024-12-23T17:27:33Z</timestamp>
      <contributor>
        <ip>2603:9000:7AF0:5DA0:E062:6986:D384:5178</ip>
      </contributor>
      <comment>Dog Behaviour (Behaviour By Animal, Canid)</comment>
      <origin>2693037</origin>
      <model>wikitext</model>
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      <text bytes="4877" sha1="aglz91vgtbpcbcb8nde9qowlc2z0xw9" xml:space="preserve">A Dog's Behavior Is A Behavior Of Animals Or Canids.

== Tail chasing ==
This amusing behaviour of dogs is to expend their excess energy. No medical issues are normally connected with it, but if your dog does this constantly, then it might have anal gland problems or flea allergy dermatitis. Chasing one's tail is also called whirling, this is quite natural behaviour often seen among different species of predators.
We often wonder what puppies would do if they caught their tails. One snap of the teeth is probably enough to teach most puppies that their tails are indeed attached to their bodies. Watching a puppy chase its tail can be very funny. If you laugh and give your puppy attention when it chases its tail, your puppy may chase its tail more often when it wants more attention from you. Whether they learn that their tails are always going to be following them around or they just don't play as much anymore, older dogs tend not to chase their tails like puppies do. When older dogs chase their tails, it can be a sign that a trip to the veterinarian might be a good idea. For example, older dogs might chase their tails if they have fleas or worms. Tail chasing in older dogs can also be a sign of a behavioral problem. Like humans, dogs can develop compulsive disorders. Sometimes these disorders cause dogs to chew or lick themselves. In other cases, they can cause them to chase their tails for no apparent reason.

== Eating feces ==
The habit is just plain gross. Reasons may vary behind Coprophagia (the medical term for consuming feces). She does so, maybe because she is hungry or could be because she likes the taste and the smell. It’s possible that she is missing key nutrients from her diet. She might just think it's fun. It’s definitely not a behaviour humans want to dwell on. Eating feces is normal with many different animal species. In dogs, it is not part of the digestive process, but it is a normal cleaning behaviour in mother dogs with pups. Some dogs eat stool even without puppies in a misguided attempt to clean either the yard or their kennel. This can easily turn into a habit.
Another reason can be malnourished dogs who lack nutrients in their diet or are unable to digest the nutrients in their food may resort to eating partially digested food in poop in order to meet their nutritional needs. Consult your vet about the best diet for your dog, and also to rule out any existing medical problem associated with coprophagia, the scientific name for the act of dogs eating their own or other animals’ feces.

== Howling ==
Wait, what! We thought wolves howl, but yes, dogs howl too at times. Another strange way of behaviour. Since wolves and dogs share the same ancestor, it could be just a behaviour passed on from their ancestral cousins. According to the behaviorists, howling is instinctively rewarding and necessary for dogs. 
Howling is one of many forms of vocal communication used by dogs. Dogs howl to attract attention, to make contact with others and to announce their presence. Some dogs also howl in response to high-pitched sounds, such as emergency vehicle sirens or musical instruments.

== Humping ==
Dogs humping objects, toys, and other dogs does not always mean sexual behaviour. The dog humps because he is excited and seeking attention. This behavior could bring quite an embarrassment when the dog does it to you that is why you can always use toys to redirect your dog. Toys always work well. Dogs often mount and hump their littermates, other playmates, people, and toys. Some experts believe that this behavior functions as practice for future sexual encounters. As puppies reach sexual maturity, they start to mount other dogs in sexual contexts. Often, during courtship, females in heat mount and hump their male “suitors.” Female dogs also commonly mount and hump other females when one or both are in heat.

== Head tilting ==
Your dog's eyes always trained(?) on you with her head tilt a little. Chances are, she is hoping you are going to give her a treat. But sometimes her direct eye contact means threatening. She is annoyed for some good reason and it's time you pamper her.
Even though dogs can hear frequencies we can’t, they’re actually not as good as humans at finding out where a sound is coming from. Some experts believe that when a dog tilts its head, it’s trying to adjust the pinnae, or outer ears, to better detect where a sound is coming from. So when you’re making a weird noise, your dog might be thinking, “That’s weird. I better find out if that sound is really coming from my human.”

== Sniffing other dog's butt ==
This is dog’s way of saying ‘’hello, nice to meet you’’, to another dog. In the human world, this behaviour can land one in jail, but in dog's world this is a socially acceptable form of greeting.

[[Category:Animal psychology]]</text>
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    </revision>
    <revision>
      <id>2693038</id>
      <parentid>2693037</parentid>
      <timestamp>2024-12-23T17:29:50Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>Reverted edits by [[Special:Contributions/2603:9000:7AF0:5DA0:E062:6986:D384:5178|2603:9000:7AF0:5DA0:E062:6986:D384:5178]] ([[User_talk:2603:9000:7AF0:5DA0:E062:6986:D384:5178|talk]]) to last version by [[User:Cromium|Cromium]] using [[Wikiversity:Rollback|rollback]]</comment>
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      <text bytes="5211" sha1="bjjnnqqr0cd4rkpe2pzodnq8qmjqw5m" xml:space="preserve">{{cleanup|grammar, spelling--good article, just listing the things to work on in this article. Keep up the work!}}
Dogs have fair share of behaviour to other animals that are truly baffling. As humans, it’s hard for us to make sense of many dog’s body language and social cues. Our pet dogs' desire to sniff butts, hump legs, and chase their own tails just doesn't make sense to us.

== Tail chasing ==
This amusing behaviour of dogs is to expend their excess energy. No medical issues are normally connected with it, but if your dog does this constantly, then it might have anal gland problems or flea allergy dermatitis. Chasing one's tail is also called whirling, this is quite natural behaviour often seen among different species of predators.
We often wonder what puppies would do if they caught their tails. One snap of the teeth is probably enough to teach most puppies that their tails are indeed attached to their bodies. Watching a puppy chase its tail can be very funny. If you laugh and give your puppy attention when it chases its tail, your puppy may chase its tail more often when it wants more attention from you. Whether they learn that their tails are always going to be following them around or they just don't play as much anymore, older dogs tend not to chase their tails like puppies do. When older dogs chase their tails, it can be a sign that a trip to the veterinarian might be a good idea. For example, older dogs might chase their tails if they have fleas or worms. Tail chasing in older dogs can also be a sign of a behavioral problem. Like humans, dogs can develop compulsive disorders. Sometimes these disorders cause dogs to chew or lick themselves. In other cases, they can cause them to chase their tails for no apparent reason.

== Eating feces ==
The habit is just plain gross. Reasons may vary behind Coprophagia (the medical term for consuming feces). She does so, maybe because she is hungry or could be because she likes the taste and the smell. It’s possible that she is missing key nutrients from her diet. She might just think it's fun. It’s definitely not a behaviour humans want to dwell on. Eating feces is normal with many different animal species. In dogs, it is not part of the digestive process, but it is a normal cleaning behaviour in mother dogs with pups. Some dogs eat stool even without puppies in a misguided attempt to clean either the yard or their kennel. This can easily turn into a habit.
Another reason can be malnourished dogs who lack nutrients in their diet or are unable to digest the nutrients in their food may resort to eating partially digested food in poop in order to meet their nutritional needs. Consult your vet about the best diet for your dog, and also to rule out any existing medical problem associated with coprophagia, the scientific name for the act of dogs eating their own or other animals’ feces.

== Howling ==
Wait, what! We thought wolves howl, but yes, dogs howl too at times. Another strange way of behaviour. Since wolves and dogs share the same ancestor, it could be just a behaviour passed on from their ancestral cousins. According to the behaviorists, howling is instinctively rewarding and necessary for dogs. 
Howling is one of many forms of vocal communication used by dogs. Dogs howl to attract attention, to make contact with others and to announce their presence. Some dogs also howl in response to high-pitched sounds, such as emergency vehicle sirens or musical instruments.

== Humping ==
Dogs humping objects, toys, and other dogs does not always mean sexual behaviour. The dog humps because he is excited and seeking attention. This behavior could bring quite an embarrassment when the dog does it to you that is why you can always use toys to redirect your dog. Toys always work well. Dogs often mount and hump their littermates, other playmates, people, and toys. Some experts believe that this behavior functions as practice for future sexual encounters. As puppies reach sexual maturity, they start to mount other dogs in sexual contexts. Often, during courtship, females in heat mount and hump their male “suitors.” Female dogs also commonly mount and hump other females when one or both are in heat.

== Head tilting ==
Your dog's eyes always trained(?) on you with her head tilt a little. Chances are, she is hoping you are going to give her a treat. But sometimes her direct eye contact means threatening. She is annoyed for some good reason and it's time you pamper her.
Even though dogs can hear frequencies we can’t, they’re actually not as good as humans at finding out where a sound is coming from. Some experts believe that when a dog tilts its head, it’s trying to adjust the pinnae, or outer ears, to better detect where a sound is coming from. So when you’re making a weird noise, your dog might be thinking, “That’s weird. I better find out if that sound is really coming from my human.”

== Sniffing other dog's butt ==
This is dog’s way of saying ‘’hello, nice to meet you’’, to another dog. In the human world, this behaviour can land one in jail, but in dog's world this is a socially acceptable form of greeting.

[[Category:Animal psychology]]</text>
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      <text bytes="72563" sha1="tdzozrrvxzekmx8aybeogbsmrdgspuv" xml:space="preserve">'''No Orders, Beautiful flowers were blooming from Childhood! Let us pick up your most beautiful moments...'''
[[File:Salzburg Cathedral (Inside) - Mozart Baptized place 1. - Mozart-Complexes World under Water (Modernist View).jpg|thumb|Piano Kids, on that day, modern colours, lights and technologies made Mozart's birthplace (Washing) -Salzburg Cathedral like a world (palace) under the biggest water - Blue Sea]]
[[File:Beautiful landscapes surrounding Mozart's birthplace - Heavenly Spring flowing from Alps Moutain.jpg|thumb|Heavenly Ice-spring from Alps Mountain]]
[[File:Mozart from Green Nature 1.jpg|thumb|Mozart comes from Green Mountain and Nature]]
[[File:Models for Chaoshan Family Tourism - Taifo Hall.jpg|thumb|Uncle Han -the piano teacher and his wife Yang, Gao (Cynthia) were volunteeringly pictured outside the door of Taifo Hall in Chaoshan. They are promoting it for Family Tourism there. It's a beautiful time in all family members' memories, as a piano song told in life story...]]
[[File:Beautiful Sunset View of Oceanic City from top building during COVID-19 period.jpeg|thumb|Beautiful Sunset View of Oceanic City during COVID-19 period]]
[[File:Small items in Commons Life of 2019 Spring 2.jpg|thumb|Flaming Katy and piano-peers as Micro-landscape in classroom ]]
[[File:An Oil Painting watched since born.jpeg|thumb|Oil Painting: Forest Cabin in front of Fuji(or Helan) Mountain 'hanging on the wall']]

 Oh, dear piano pupils, we have seen so many beautiful landscapes, across the times and spaces. Now, firstly, getting into East- your nature and self-meditation, let us try to take the Pentatonic Scales Exercises for relaxing you 'busy heart' and focusing your attention back to piano...

*[[Portal:Pentatonic Impressionism (China Wu Sheng) in the view of Neo-classical Piano Techniques-training]]

'''Afterwards, we can take further great life-tasks in piano...'''

[[File:Piano Lecture of Dalian Library (Music) delivered by Jason (Jixun) on October 13th, 2024.jpg|thumb|2024 Piano Lecture of Dalian Library (Music) Delivered by Jason (Jixun), Han and His Piano Pupils Team Associated by Family members and Library workers]]

''' Lecture Speech Conclusion'''
[[File:The Chinese characterastics speech of Piano pupils' art technique training and musicality athletics cultivation (Report Conclusion of Jixun, Han - Jason's team lecture on the date of October 13th, 2024 at Dalian Library).pdf|thumb|The Chinese characterastics speech of Piano pupils' art technique training and musicality athletics cultivation (Report Conclusion of Jixun, Han - Jason's team lecture on the date of October 13th, 2024 at Dalian Library)]]
'''Waiting Translation'''
'''New Time and Fresh Air from 2024'''
*[[Portal:Fresh Air of Piano after COVID-19 and beginning up a Recovering New Time of Openness from 2024]]

===='''Firstly, passing by a Skyline of Citylife Night-Skyline'''====

[[File:Flowing City (Lin Hai), Player and Teacher JMC,Han (Jason).ogg|thumb| Flowing City from 'Forest Sea', JMC,Han
[[File:Dalian Urban Night Skyline from Xiao Ping Island Mountain-top No.2.jpg|thumb|Dalian Urban Night Skyline from Xiao Ping Island Mountain-top No.2]]  ]]

===='''New Era is coming...:(New Teaching List)'''====
[[File:Skiing Statue made during my rollers-skating.jpg|thumb|Skiing Statue shows Spirit (like piano)]]
[[File:The new situation of bubbles-fish statue.jpg|thumb|Ice &amp; Snow Bubbles-fish are welcoming]]
[[File:Mmexport1614470203508.jpg|thumb|Picture of piano lessons still under Covid-19 situation]]
Etude in the Advanced level - Sir Chopin's famous Black-keys (Flatten G Major) Etude:
[[File:Chopin Black-keys Flat G Etude (Exercise), player JMC, Han.ogg|thumb| Black-keys: An Etude your teacher has no chance in childhood, but still hurries up to be better]]
[[File:Chopin Impromptus Op.29, JMC, Han.ogg|thumb|Chopin Impromptus Op.29, JMC, Han - Deep Fast Waltz-thinking in Quiet Gentleman's Self-Expression (Improvising)]]
[[File:Sogdian whirl with large pipa.jpg|thumb| (Public Domain Work: See original page: https://commons.m.wikimedia.org/wiki/File:Sogdian_whirl_with_large_pipa.jpg#mw-jump-to-license): Could you find some musicality similarly with Chopin's Black-keys' Pentatonic?]]
True Fairland - a piano melody of The Nutcracker (Dance of Sugar Plum Fairy): the advanture from childhood realizes your piano dream-&quot;Fingering Ballet&quot; 
[[File:The Nutcracker (Dance of Sugar Plum Fairy), Piano performer JMC, Han.ogg|thumb|The piano performance of &lt;Dance of the Sugar Plum Fairy&gt; in 'The Nutcracker' (Ballet Re-edited Piano Melody)]]

Czerny 299 etudes were designed for the smart&amp;strong fingering&amp;modelling of hands and a pair of Vienna school's ears for the harmony...such as No.23...
[[File:Czerny 299 No. 23 JMC,Han.ogg|thumb|Czerny 299 No. 23, player JMC,Han]]
A peacefully  praying Sinfonia of Sir Bach is freshly added in the &quot;New exam book's list' during this COVID-19 period, to which you can have a relaxing hear and try (Don't worry, listening, it's enough time, you knew,  'Andatino'-Peacefully walking, and to sing by hands, in a small Baroque place :
[[File:Sinfonia No.11 - 3Ps Invention, Bach, JMC,Han.ogg|thumb|Sinfonia No.11 Andatino- 3Ps Invention, Bach, Teacher JMC,Han (COVID-19 Protection Time)]]

Encouragement in Italy Smart Fashion, but needs the very carefully fingering-techniques training (Long time, advanced), feet-edges' staccato, sentence-Pizzicato, flowing streams...Italian artist techniques always attract our eyeballs... Let us attempt to... make out your own Italy style! Cheer up!
[[File:Domenico Scarlatti G Major Sonata, JMC,Han.ogg|thumb| Domenico Scarlatti G Major Sonata (In COVID-19 Pandemic Period), JMC,Han.ogg]]
'''A good teaching video result played by Yixuan, Wang:'''

http://m.kugou.com/mv/?hash=f00b36624f27b091b79e3f30e158aa03&amp;sruserid=640650901

Baroque staccato techniques were always in a reasonable, confident, relaxing(wrists), fluent and vivid - 'Enough manners' of the Era, which needs us apply very careful fingering trainings. In a view of the whole structure, according to ears' musical suitable habits(psychological), I gave 1st section a twice repetitions, and then a throughout 2nd section to the Code. Hopefully, French Suite would make us brave, confident and relaxed. (but it also need years' accumulation of hand working to let those out and better) Have a try? Good luck!
[[File:BWV.816 Gigue-French Suites No.5 Bach, Player JMC, Han.ogg|thumb|BWV.816 Gigue-French Suites No.5 Bach, Player JMC, Han]]
(By turning to Wikimedia Commons, you will find two versions under its 'historical tree', currently. They are showing different stages we can reach. The first version was kept because it's relatively slower and more stable that in the basic stage we can make notes heard staccato and clear. After feeling suitable in this stage, we need to improve its tempo and get Gigue Dances' happy, vivid,,dialoguing with moods, jumping and  wrists' breathing naturally. It needs time to train your hands frequently, untill relaxing but accurately. Main Difficulties: Stiffen wrists, Cramp and Tiredness... Now, it's the time of yourself...)

Hi! We, piano kids: Imaging a scene, let us hands-dances with the good manners and a earnest mind in a beautiful Baroque palace. It's easy and natural...
[[File:Primary Bach No. 16 March, Player JMC, Han.ogg|thumb|'Primary Bach No. 16 March' -A peaceful Bach-melody for all 'Piano Kids'...]]

Sir Debussy's Arabesque Suites (The second suite) is also in the list.
The musicality in my world is: 
It's the legend of Butterfly in birds' chorus... it took us to a Life-mountain behind our living garden facing a quiet sea...
Watching, in some time of one section, you can also hear Monet's 'Quiet Morning' upon the sea...
Alongside Butterfly's dance-suite, imagination is beginning. Oh, listening... (Main meaning referenced from my main page)
What about it in your world and imagination?
'''Sound teaching demonstration:'''
[[File:Claude Debussy - 2nd Arabic Suite (Arabesque) - Spring Butterfly, Performer JMC, Han.wav|thumb|2nd Arabic Suite- Spring Butterfly (Impressionism Singing -Main Natural Lines&amp;Breathes from Sir Debussy)]]

'''Good video teaching result from  a 12 years' old little girl piano-pupil Mo Zhou:'''
http://m.kugou.com/mv/?hash=b50e133a360fa8d30cdcd9fca4163e73&amp;sruserid=640650901
(Photographer: Ms. Yang, Gao)


Listening! boys and girls, Dvorak's Humor-jumping and Homesick-expressing:
 A true Czech-homeland heart,
but 
Dancing... somewhere in American Countryside
[[File:Flatten G Humoresque Dvorak, Player JMC,Han.ogg|thumb|Flatten G Humoresque, A. Dvorak, Player JMC,Han]]
[[File:One Town-view from Cesky Krumlov Castle.jpeg|thumb| Krumlov Castle-town's view]]

====Xinran, Yu - a lovely Chinese little piano girl's 'Ink-Mountain &amp; Green Rivers' view of &lt;The Cowherd's Flute&gt; ====
'''Comment:'''
&quot;Before taking the national examination and the  exhibition competition, we together listened and learned to the net-editions of young master Lang Lang and Yujia Wang...(regarding with this famous little melody of Chinese tradition)
I think in this melody, she tried out her best for the techniques-training and the musicality in her age... from a little performer's view. Therefore,I gave the comment-Excellent.
Close your eyes, thinking of a little lovely girl happily playing among ink-mountains and the green rivers, with a water buffalo, some birds followed, and her smart flute... let us relax in the Chinese Ink-Landscape and listen to this little melody...(referenced partly from the writing in Wikimedia Commons page)
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 02:28, 27 May 2021 (UTC)

==== Zichen Tao - A little Chinese snowgirl's hardworking of D Major Sonatina====

'''Comment:'''

D Major Sonatina is still piano Children's favorites to perform and show... taken to the national grade examination, daily performed with each other, and also to city's piano Competition &amp;Exhibition. That's an educational case lasting for many years in Dalian.
This edition is played by a lovely and white Chinese girl - Zichen, Tao. She and her mother took the very responsibility to check the wrong notes, improve the learning progress, and make the performing manners and designs for the stage-show... 
Therefore, in my view as her piano teacher, this edition is already great in her age...(though hand-running details need to improve for her age). Hopefully, her family can enjoy this piano experience, companying with this melody in her childhood. (Partly referenced from her Wikimedia Commons' page)
[[File:D major Sonatina , Piano student Zichen Tao.ogg|thumb| D major Sonatina (Kuhlau's) played by piano pupil Zichen Tao]]

==== Meng's Performance and Comments after learning in the reality from Jason M. C.,Han in Children's Corner: ====
[[File:Children's corner of Meng.ogg|thumb| Meng Meng (nick name)'s edition of Doctorial in Children's Corner: Currently, the Fourth Version was her most beautiful one self-made in classroom before Piano Grade Test Exanimation. Regarding with all editions' comments and reasons, please reference to the original file in Wikimedia Commons]]
[[File:MM Good classroom F major 1838 Grande valse brillante.ogg|thumb|MM Good classroom F major 1838 Grande valse brillante]]
'''[[Portal: Part of Comments - 'for students' Examination Performance, Piano tutor's teaching self-reflexivity and possible some requirements of Pedalling Sound-effects with Artist Fashion of Post-impressionism'  | Part of Comments - 'for students' Examination Performance, Piano tutor's teaching self-reflexivity and possible some requirements of Pedalling Sound-effects with Artist Fashion of Post-impressionism']]'''
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 04:15, 12 October 2018 (UTC)

==== Kim Hui's 'Doctoral Training','Under the sunshine' in Children's Corner: ====

'''Comments for Kim Hui's first draft:'''
1. She did the second theme (associated) well 'much deeper like vocally singing out a better life in New Era under the sunshine, on a piece of small area in a rainforest'...

2. Her Korean dance (Wikipedia introduction: https://en.wikipedia.org/wiki/Korean_dance) has been done well, in which I can hear traditional drum-points in bass-part and crossing hand to tremble part. 

3. I can hear Time-travelling and space-shaking to the past through a 'Dark-cave', from..., minutes 1.30-1.40... But, I think: if 'dramatically' and 'significantly' in dynamics (loudness), it would be better to show...

4. I can hear Forest's Evensong in Coda part - 'dim.' to the silence of night and a 'rit.' slowing down to the sleeping dream, and even several night-birds' dreaming voices...But, please make a much gentler taste (not so hurry up and not so strong) of those pictures. Meanwhile, I hope you can get a better &amp; coherent control of the rhythm among different sections.

5. I knew, regarding with 'peak-parts', she had made many attempts 'drumming beats rights and keeping those connections clear'. However, still, in minutes 1.04 and 1.59, I felt it's a little bit 'rough', and needed to be handled in of the solidification... Oh, maybe, I am so severe... sorry, I should give you the encouragement. 

Main comment: 'Under the sunshine' is suitable to Kim Hui's fashion and can be kept in her performance list. Her first draft and its preparation has given me an enjoyable teaching experience and many beautiful memories of life. It's fluent and vivid, expressive and dedicated. Thanks, Kim Hui! More colours and lights would be added from technique details, from her independent fingering and some traditional piano manners, meanwhile, the rhythm should be balanced well in the future. There are many developing zones of 'this painting' she can better and draw out for her future.[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 21:22, 17 October 2018 (UTC)
===== Kim Hui's second 'Show-Time' in classroom - Poem of Music (Piano Etude) =====
'''Teacher's Demonstration:''' 
[[File:Poem of music.ogg|thumb|Poem of music  JMC, Han]]
'''Student's Second Performance - Poem of Music: ''' 
[[File:Poem of Music (Piano Etude) - Student Kim Hui.ogg|thumb|Poem of Music (Piano Etude) - Student Kim Hui]]
'''Comments for Kim Hui's first draft:'''
1. She has mainly got the technique-points, but a little bit of rough in some details, such as the minutes 0.30-0.31 - 'Tail-closing part' of a sentence - in the progression of 'Diminished Seventh Chord-Arpeggio'... However, as her first draft and the random collection from a normal classroom, I thought it's well-done. we can wish its further 'Developing Zone', in the view of piano education.
2. In 'Coda Part' of Poem of Music (Piano Etude), she was able to show a great controllability of the 'Legato' between two hands, as the pieces of falling leaves slowly flying-upon the surface of water. Sometimes, it was evenly better than mine. I hoped she could manage it in a better way.
3. She showed some thoughts of musicality... However, 'Techniques-points' still wasted much of her energy. I think the total Dynamics in physics will be improved soon. 
(waiting more)  
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 14:53, 23 May 2019 (UTC)

===== Kim Hui can reach the  advanced level of piano performance in this 'Little Children's Corner' =====
Though It's still Covid-19 Health-protection Time, after Home-self-Training Time, some classroom face-mask covering &amp; health-good-protection lessons and an examination of China Culture&amp;Tourism Ministry, She can play this 'Doctoral Etude' which is dreamed  many piano pupils, with impressionism style. As her teacher, I didn't think It's a simple Etude which was expressed in many scenes, but with the big universe imagination and impression. Therefore, we have trained it as Meng's approach and further developed it. 
Indeed, I think she performed far greater than this edition, right in that online  national examination. She got it, Congratulation! Let us listen to her ...
[[File:Debussy-Children's Corner-Doctorial Etude, Piano pupil Jinghui Jin (Kim).ogg|thumb|Debussy-Children's Corner-Doctorial Etude, Piano pupil Jinghui Jin (Kim)]]

==== 'Colourful Clouds Running After Moon' impressed into the Heart of Xinyi, Hua (Hua family's Heart-sweet girl from 'Painting Imagery')====
'''Comments for the first draft of Xinyi, Hua:''' 

1. I like her treatment of the prelude part in 'Colourful Clouds Running After Moon'. It's light and soft like silky clouds up-bridging alongside moonlight towards a round moon above the dark-blue sea. However, please try to link each silky pentatonic-arpeggio weave as a smooth whole from the bottom to the top, and from the left hand to the right hand. If so, her progress will be enlarged;

2. I can hear the situation 'Colourful Clouds Running After Moon' appeared in many linking parts before and later. She was attempting to give an acceleration imitating this procedure from a slower speed to a fast one, and between two hands' echo-following from a loose density to a tight one... However, if obviously, it will be better;

3. Like 0.58 to 1.03 minutes, I can hear that in some parts, she would like to make a returning sound-boomerang (Wikipedia introduction: https://en.wikipedia.org/wiki/Boomerang) up-rising 'to the moon' and down-landing upon the sea-surface. If a small time of middle reaction was canceled out by her proficiency, we will appreciate the musical beauty in a much more advanced situation;

4. In 1.22 to 1.30 minutes, I know she would like to make a silky veil, with the colourful clouds as material, upon moon's beautiful face by her right hand. It's a little bit of pity that the controlling ability of relative loudness made she carried this willing but harder to realize. Meanwhile, this veil needed to be smooth. Oh, sorry, I am so critical... indeed, she did not bad;

5. There is a hard hurt in 1.36 minute - it's still a repetition of bass-chord though she has already attempted her best to grasp the bass large chord through left hand's opening degrees (Little girl, I knew you had tried your best. Though the momentum was great, I still need to point it out.);

6. 2.12 - 2.40 minutes is the part - 'Bright Moon up-rising above the harvest sea'. This is a grand scene which needs great forces from students' forearms and a fast reactions for some flexible connections to arpeggio-parts... Congratulations, little girl, she have got it, though it's a little bit slower. She have given out a great momentum;

7. In the Moon-tail part, she has expressed her great musicality to make moon disappear in the dawn of sea;

8. Many ornamentations she has done well, though still some need to be gently breezing in the impressionism of Chinese landscape painting.

[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 12:22, 24 October 2018 (UTC)
===== 'Pure White Dove' in Young Teenager Xinyi's Eyes =====
[[File:Dove in the eyes of Young Teenager girl Xinyi, Hua.ogg|thumb|'Pure White Dove' ('La Paloma' - 'No More' in English) in the eyes of Young Teenager girl Xinyi, Hua]]
'''Congratulation to your beautifully singing of the 'Melodic lines' behind the right hand's octaves-grasping!'''
'''Comments:''' 
1. Four biggest designs appeared: around B50 (Minutes 1.36),  B55 (Minutes 1.48), B58 (Minutes 1.54) and B62 (Minutes 2.01) - four Peak-currents, we'd like to throw (rit.) the 'missing notes' into the air and rotate them a little bit more slowly - like to send, wait and feel Dove's messages across the ocean in a self-holding &amp; self-releasing intoxication. She tried her best to make them out, but not quite clearly and still need much time to grow up... 

2. I liked her coda part (from B65 Minutes 2.08 to the end): She was so sure about two hands' March-doubling, as a confirmation of future and belief; or to say, she transformed her 'missing' in the melody to be a true hope of tomorrow, or someday... Evenly, I thought it's better than mine... 

3. For more than half years, we have worked hard to help her link all octave-grasping pearls out of melodic lines in singing breaths. She almost got it successfully, through small breaks... 

4. Some 'Spanish Dotted notes' and 'Triples-wandering', with the rhythm of Spanish Dance Habanera-Andante (Wikipedia introduction: https://en.wikipedia.org/wiki/Contradanza) can be fulfilled, but some not really... I am happy she recognized them and paid more attentions to... It's waiting time that she could perform much better.

5. Yes, I had to say: still some small faults there... The good usage of pedalling almost hide some, but... also a little bit rough... Oh, I didn't want to be a so severe teacher. Rather than, much more good wishes of her growth should be given. Okay, hopefully, she enjoyed it. 
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 12:57, 4 April 2019 (UTC)

'''Teacher's Demonstration for standards above and Further Progress (Advanced Level):''' [[File:Dove With Spanish Sense in Piano JMC.Han.ogg|thumb|Dove With Spanish Sense in Piano JMC.Han (It was once used by the photography gallery of music friend User:PigeonIP - https://commons.wikimedia.org/wiki/User:PigeonIP/Tauben/2019_April_1-10 and the main page La Paloma in wikipedia )]]
'''More information and reading - articles (list) about 'Dove', please watch:''' https://en.wikipedia.org/wiki/La_Paloma

==== Malagueña Dream from a little Chinese girl - Yinuo's heart (A promise ... to piano) in a small beach-side classroom ====
[[File:Student edition - Malagueña Suite (modified for piano) played by Yinuo, Liu.ogg|thumb|Student edition - Malagueña Suite (modified for piano) played by Yinuo, Liu]]

'''Comments for the first draft of Yinuo, Liu:'''

1. We can hear the impression of Flamenco rhythmic pattern (Compás) (Wikipedia introduction: https://en.wikipedia.org/wiki/Flamenco) diffusing from some simple rhythm-components of a parts in a total ABA structure of Malagueña Suite. This is what I - the tutor and the little girl -learner would like to express through three more different accompaniment bass-forms, including pizzicatos, small slurring breathes and some opposite weights..., which imitated some of Classical Guitar's handling ways. Thanks to the little girl Yinuo, you have realized most of our designs! Congratulations!

2. I really like her beautiful Cante jondo - associated 'vocal' lines by right hand which was balanced &amp; flying above the flamenco accompaniment of the left hand when the second thematic melody began. It's a deep, profound and emotions-rich singing, almost from a beautiful Spanish girl's natural expression for the missing, the reasoning of life &amp; Universe when facing a 'deep and far' sea. Though if the dynamics would be dramatically and the singing would be much deeper, the emotional atmosphere would be better: I thought to only a girl of her 11 years' old age, she has already attempted her best to understand those across cultures;

3. I like the middle B's fantastical view of holiday beach under the sunshine, which was almost formed by white waves from blue sea. It's relaxable, dreamful and graceful, like a girl poet's walk alongside a small sand bay...  (Yinuo, you knew, if you can make the 'rit. - A Tempo' much more nature like the real tides of sea and the speed tiny faster, the progress zone will be enlarged);

4. I know in two middle long 'vocal' ornaments, she would like to show us ' the blackbirds or the nightingales of its gardens...' However, if making it much more smoothly, expressively, and flexibly, even a little bit down-slowed, her Spanish 'tasteful' fashion will be more beautiful; 

5. Repeated A part is better to be different in small details which can show the ability of hands and the variation of music.
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 13:35, 24 October 2018 (UTC)

==== Für Elise in piano boy Zhe's eyes ====
'''Teacher's demonstration in classroom for better:'''[[File:For Elise (Für Elise) Beethoven JMC Han.ogg|thumb|For Elise (Für Elise) Beethoven JMC Han]]
'''Student's performance in classroom:'''
[[File:Für Elise -Student Performance Zhe,Zhang.ogg|thumb|Für Elise in piano boy Zhe's eyes]]
==== D major Sonatina (Kuhlau) - Piano-pupil girl Mengshuang's 'Strong Willpower and Persistence' ====
'''Teacher's demonstration in classroom for better:'''
[[File:D major sonatina 2nd movement Kuhlau (played by Jason).ogg|thumb|D major sonatina 2nd movement Kuhlau - Teacher JMC. Han]]
'''Student's performance in classroom:'''
[[File:D major Sonatina (Kuhlau) - the version from piano-student Meng Shuang, Wang.ogg|thumb|D major Sonatina (Kuhlau) - the version from piano-student Meng Shuang, Wang. This classroom version has been selected by https://commons.wikimedia.org/wiki/User:Rsteen/Artists_from_Denmark/2019_August_1-10]]
'''Comments and Statements:'''
1. Totally to say, the main melody fast-run by the right hand has kept its fluency, transparency and clearance. It's very hard in piano training for herself, owe to that her hands-shape was a little bit of 'frozen'. Thanks for your hard-working in the training. Congratulation!

2. Her musicality in this melody has also been motivated out - unrestrained and natural in the expression.

3. Left hand's accompaniment was in good triplet-treatment, but please light and dedicate a little bit... It's to say: the controllability still needs to improve.

4. Some heads of sentences and smaller phrases need to be match together between two hands in a better way - some parts, because of small ornamentations and dotted notes, weren't quite well...

5. I am very happy that you (in your 12th year of life) were willing to play out the middle 'rit. - A Tempo' in a comparison ('rit.' was slowing down the waiting, then, 'A Tempo' for the Peak expression in return). However, it was still a little bit rough (before its right time). You can try to modify it in a better view. 
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 03:08, 2 August 2019 (UTC)

==== How to play Mozart's Classics? ====
===== Work from Mozart's earlier time - Turkish March =====
 '''Teacher's Demonstration in classroom:'''
'''Video:'''
[[File:Turkey March Video-Mozart-Jason Han.webm|thumb|Turkish March (Video) for Mozart's; JMC, Han]]
'''Sound:'''
[[File:Turkey March for Mozart and Memory JMC, Han.ogg|thumb|Turkish March (Sound) for Mozart's and Memory (many times used in peer Tokfo/Vienna Gallery - such as https://commons.wikimedia.org/wiki/User:Tokfo/Vienna/2019_January_26-28 ); JMC, Han]]

==== Sure, Ma's boy-view of Mozart's 'Turkish March' ====
[[File:Sure, Ma's Version of 'Turkish March' in piano classroom for piano education.ogg|thumb|'Turkish March' - an old mysterious Turkey story in piano student (Jason's piano pupil) boy Sure, Ma's classroom edition. Thanks, this good teaching &amp; Learning result was selected by Tokfo/Vienna Gallery: https://commons.wikimedia.org/wiki/User:Tokfo/Vienna/2019_April_25-27 ]]
'''Further Comments for his first draft:'''
1. It's very difficult for a young boy to manage Turkish March's speed in a smooth way... He tried his best to keep it stable and unified, and almost did achieve it. (Turkish March is easily to make people play faster and faster until crazily broken. He tried to solve it by giving a slower beginning )  But, it's a little bit of too serious,afraid to touch wrong. Indeed, I heard his another time, in which he totally open himself and relax from nature... We could give him more hopes.
2. His melodic flow of scale-phrases (legato) are quite fluent and natural, which shows his scale-playing and fingering were quite great. But, a small break occurred around 1.14 to 1.17 minutes could be caused by the stiff right wrist (too tried) and no-good fingering design. He should frequently move second and third fingers in a much smarter way. To a young boy in his age, it should already be 'okay'.
3. When the theme occurred in the second time, it's better to give a dynamics-difference in contrast. My mother-Ms Song said: it's like an old story (sound) heard from a far distance to near somewhere - mysteriously. However, he gave a very tight connection, as if it was linked with the previous section. 
4. He tried his best to take the Worldwide difficult challenge - 'Broken-chordal Arpeggiated-octaves' (Around 2.00 to 2.14 minutes). I gave him a 'LIKE' that he had taken this challenge which even many pianists or teachers made some 'faults' as their heart pities - You can hear the edition of Romuald Greiss' in Wikipedia and several my previous times... However, this boy achieved it after many trainings time after time... Though later half one, compared with the beginning, might be in lower distinguishing degree, he didn't make any 'breaks', which comforted my teaching way so much. Thanks, boy Sure!
5. The final problem would occur in 'Alberti Bass' (left hand) of Coda part. Coming to it, you will feel easy to give up, which required more endeavors to control your hands in narrow and elaborate dealing way. He did it good, but lost in the counting of number (B111), and further, the connection with the final 'Square-opening Dance' (a small break). other things, such as the strength, are fine in his age.
6. In addition, I am planning to add a 'Turkish Stop' by a final pedaling. I didn't know whether he could, someday. 
Overall, I gave him an Excellent Comment. Hopefully, he will play better after better in his growth. [[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 14:13, 8 March 2019 (UTC)

'''Further Comments for his second draft:'''
1. As his teacher, I am very happy to hear several great designs we have made in classrooms can be achieved in the second draft, according to the background knowledge of 'Turkey March' I taught, such as the final 'Turkey Stop' (not really in modern piano, but a little bit similar) and the Bass-points-layer (simulating the military drum) beneath the long fast running scale-phrases of right hand (middle section)... Cool boy, thanks that you can remember your teacher's words! Congratulation!
2. Yes, right after the chance of Music library Report-performance in local we have made and getting back, you improved the edition's speed and fluency. You can evenly save 15 seconds, contrasted with before, which showed that your fingering &amp; running ability of hands had been greatly improved. However, the disadvantage is that it's easier to make some small motives uneven and rough (touching wrong notes) without purpose, which needs more your careful attention and exactness about details.
3. I knew you tried your best to face the peak challenge Mozart made to all people - making broken-progression of octaves message (middle part) and hearing out its hidden melodic lines. Great! However, it's still a little bit beyond your ability that its distinction with chords-effect weren't so clear. No matter, Sure boy, more exercises, it will be better.
In all, progressing soon which shows the potential, thanks to your performances1 There is still the developing zone waiting for you. 
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 15:08, 25 April 2019 (UTC)

==== Clever Girl Jia Xin's Clever view of Sir Bach's 3-parts Invention ====
'''Teacher's Demonstration for Future Development:''' 
[[File:3 Parts Invention 8th- from Sir Bach.ogg|thumb|3 Parts Invention 8th- from Sir Bach's BWV 794 – Sinfonia No. 8 in F major ]]
''' Jia Xin's Performance:'''
[[File:3-parts Invention No. 8 (F major) in piano-girl Jia Xin's view.ogg|thumb|3-parts Invention No. 8 (F major) in piano-girl Jia Xin's view]]
'''Comments of her first draft:'''
1. Totally, 3 parts are ranged in Bach's harmony, to a girl in her age - 12 years old. It's not easier to make so clear layers out. I was satisfied with this point, after heard every time; 
2. I can hear piano techniques for polyphonic &amp; counterpoint music like Bach's, such as cannon, intimation between two hands, up-climbing shoulder by shoulder, dialogues, long-notes down-pressed for different parts' SHE (sentence-head-enhancement), long-notes kept for parts' division and maintaining, fingering grouping in one hand for 2 parts, parts' continuously melting into one for the summarization, and..., Baroque ornamentation... mentioned for long. For those trainings, and further, the internalization into her own mind-analysis, we had searched information &amp; knowledge through Wikipedia, two more manuscripts, books and other webs online, further, spent classroom time to reason, analyse, train and fix note by note for long time... In this case, I gave her hard-working a 'Like' again; 
3. There would also be some problems regarding with recording pressure and her memory...: some big ones - left hand's relatively weak ability in managing two parts, small mistakes (like B18's f note played as sharp f - around 1.13 minute, B21's final g isn't raised there - around 1.23-1.24 minutes, and others...), small ornaments in a little bit of rough view and a much more graceful manner in Coda part. (sorry, to such a 12 years old girl, my suggestions could be so severe. But when listening, they are directly in my ears...) 
4. She did really pay her attention to Dynamics, but please better - lighter, smarter and more obviously...
5. The speed of later part is better than the slower earlier part. 
Overall, I also gave her an excellent comment for her performance (Live) in classroom. For further development, she can listen to my edition and the one in 'Inventions and Sinfonias (Bach)' - Wikipedia article (I thought it's great, but I didn't like too many speed-variations in Bach's works. It's better more reasonable: https://en.wikipedia.org/wiki/Inventions_and_Sinfonias_(Bach) )
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 07:33, 9 March 2019 (UTC)
==== Yixuan's piano-view and traveling landscapes ====
'''First view (only 9 years old) of Sir Bach's 2-parts Inventions'''

[[File:Bach 2-parts Invention, played by Yixuan Wang (Only 9 years old).ogg|thumb|Bach 2-parts Invention, played by Yixuan Wang (Only 9 years old)]]
'''Comments from teacher:'''
1. Musical parts and space-dimensions were much clearer than before, which reflected the little girl Yixuan's hard-working continuously after her piano examination...
2. I can hear the heads of musical sentences which were highlighted by each hand when required. I can also hear cannon-following, doubling and countermelody which were clearly shown into her performance. It's quite necessary for students in this age - 9 years old. In certain degree, she is already a good and careful student in piano.
3. Still, the controllability and the stability of hands, especially the turn of her 3rd, 4th and 5th fingers, need to be improved, which caused some small faults, such as 0.49-0.50 minutes (Bar 22) - a recovered B in right 3rd finger, 0.54-0.55 minutes (Bar 25) - 3rd, 4th &amp; 5th fingers of left hand, and a small disharmonic note - flatten B in the right hand - 0.32 (Bar 14)...
4. It's great that I can hear Baroque staccatos were in their graceful manners - like imperfect pearls required by its era. She almost did it...
5. Totally saying: it must be a very hard-job for a student in 9 years old to play Bach's 2-parts Invention. She bravely took up this life-task and successfully completed - this point should be affirmed. Congratulation! You can do more further...
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 02:28, 6 September 2019 (UTC)


'''MARIAGE D'AMOUR (Dreaming Wedding Ceremony) and its Educational Story:''' 

It's only no more than 2 weeks she did get the main techniques, after taking a Covid-19 Protection piano lesson and further test(Face-mask covering and breathe-prevention…).Then, she went back home and made a hard self-working exercise. Afterwards, around 10 days, this edition can come out. Why was she so keen on making it? She told me... One of her family's friends would like a piece of background music for his wedding ceremony, and they knew she was a good piano pupil.They invited her to take this task. She online self found out her long dreaming piece, and felt very happy for them. She thought only hard-working at home can realize this dream in this 'Hard Recovery Time'. She has beautifully taken this life-task for a very short time, and finally I could find a beautiful smile on her face... Though there were still some small faults in teacher's view, such as the biggest 1.02-1.03...
('''Problems:'''
Mentioned one is because of the distance of the Tenth-grasping is out of her hand-shape and ability in this age - rolling but touching a wrong note; In addition, the breathing of each sentence's tail somehow is with a longer responded break... Further, the Pedaling for the coherence from natural breathing need to improve; The final departing dropping notes were too noisy... which needs to be quiet,rit. and peaceful...), 
her hands' ability (especially the big chords-grasping, whole-viewing, locating, and sight-reading) was improved by her own endeavors (Maybe... subjects-divided examination-taking online through self-video-recording,in this special time, motivated her self-management...). This point made me feel happy... Hopefully, the friend of her family enjoyed their wedding ceremony with this own and LIVE background music, luckily as in a fantastic, peaceful and forever-lasting life-dream of happiness.

In future, Hoping: Yixuan, you can play this fantastic wedding song of piano (fluently and heart-touchingly) for more families and share their friendship, love and happiness...
Little girl pupil, thank you!^_^
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 01:55, 24 September 2020 (UTC)

[[File:CCzerny 299 Etude No. 27, Piano student Yixuan Wang, Tutor Jason Han.oggzerny 299 Etude No. 27, Piano student Yixuan Wang, Tutor Jason Han.ogg|thumb|
Czerny 299 Etude No. 27, Piano student Yixuan Wang, Tutor Jason Han.ogg]]
I have taught two children this Etude-a girl and also a boy (with outcomes). They played all well in very different musicalities. One is like a fast gym meeting 299's standards. The other-hers is with a good sound effect -light and peaceful after her grade examination. Both I all like. 
Regarding with how to train this sound effect with pedal, Please see my etudes'platform:
https://en.m.wikiversity.org/wiki/Portal:Piano_Etudes_as_Poems

'''G major Sonata L.349 - Yixuan Wang's New Attempt of Italian Baroque Style of A. Scarlatti'''
A. Scarlatti's Sonatas are quite hard for young students and young teenagers to train and perform.However, Yixuan is fine, I thought.
It needs a very fast &amp; light fingering of Scale &amp; Arpeggios and different STACCATOing keyboard-touching way, meanwhile, the exaggerating fluency of simple patterns... I thought she somehow had touched at her own little age. Just, more from nature, more details-care and the flexibility of hands&amp;body could make things better. 
At her age, it's already fine.Thanks to the recent striving in this still hard time of COVID-19 Recovery. [[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 02:31, 20 August 2021 (UTC)
[[File:G major Sonata L.349, Piano Pupil Yixuan, Wang.ogg|thumb|A, Scarlatti L.349 Sonata, Piano-pupil Yixuan, Wang]]

It's very hard to train Scarlatti's Italian Style of technique skills... However, Yixuan, Wang has never given up... 
during this COVID-19 Time...-Protecting herself with masks, meanwhile, playing times after times... Finally, we can get some senses of fast, airily,lightly and breezily... Yes, there may also be some problems, like- it's very easy to be stressful and breathless on the stage...But to her age, do you think it's already good... 
Therefore, I recorded it in a video and published it on a musical platform -Kugou, and a educational platform - Youku, as to remember her growth: 

http://m.kugou.com/mv/?hash=f00b36624f27b091b79e3f30e158aa03&amp;sruserid=640650901

====Piano Pupil Mo Zhou's Smart Growth and Hard-working learning of Techniques  ====

The video of Mo Zhou's most beautiful performance of Debussy's work- 2re Arabesque (I call it 'Butterfly's Dream') :
Kugou musical platform -
http://m.kugou.com/mv/?hash=547cb2c1e2f57a9e8ec66e8ecf36c269&amp;sruserid=640650901
Youku educational part -
http://v.youku.com/v_show/id_XNTgxNzA2Njk2MA==.html?x&amp;sharefrom=android&amp;sharekey=9631de9a76de1af3d601221019590cd26

(Published on the musical platform of Kugou and the educational part of Youku; the classroom volunteering photographer is Ms. Yang Gao) 

'''Piano Pupil Mo, Zhou's Violin simulation of Cremer's Etude's Art'''

Catching the hands' positions (somehow borrowed from voilin's) is almost the hardest point to train.One focuses on left hand's Notes-Slipping; the other regards with the interval Position-switching (2 notes) check of right hand frequently.
Though this little girl has a pair of smart&amp;slim hands, she attempted her best. You can hear the most part's effect LIVE in classroom...
In this point, I gave a 'LIKE'.

[[File:Cramer Etude, Performed by Piano Pupil Mo, Zou.ogg|thumb|Cramer Etude, Performed by Piano Pupil Mo, Zhou]]

'''A, Scarlatti L.349 Sonata - A Italian Style Taste of Baroque Music'''
''Comments:''
Mo,Zhou's hands are very smart, regarding with which some very tiny actions she can take, though they aren't quite big. Yes, she has been always willing to enlarge her hands.
This point, but somehow, associate her to take this Italian Baroque Style (Rocca) quite easy. 
Yes, I thought she was fine regarding with much more details.(though it's LIVE that very few unexpected faults could be caused by the stress of the recording).

I thought: to her performance, my teaching is working well. She did many requirements... Let us listen to her.[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 03:25, 20 August 2021 (UTC)
 

[[File:G major Sonata L.349, Piano pupil Mo, Zhou.ogg|thumb|File:G major Sonata L.349, Piano pupil Mo, Zhou.ogg]]

==== Brilliant Snow-ball boy (Yu) of Zhang family is praying for his father working in New Zealand ====
[[File:Pupil Yu,Zhang's edition - e minor sonata of Sir Haydn.ogg|thumb|E minor sonata of Sir Haydn was played by Piano student Yu, Zhang in classroom]]
'''(Waiting better)'''
Could you understand how hard Sir Haydn's &amp; Mozart's mature sonata-structuralism and Classical Countermelody (from String Quartet: https://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozart) were for the training of such a young boy or some students around this aget? Oh, looking back, I, myself, also did feel hard... However, this boy and another older piano sister did really insist on doing so. Today, they can give their own editions - very different with own personalities and natures. 
Another point I would like to say: It's only one week's time that this boy was fighting for 'a good hearing' of his father. Afterwards, a modified recording edition soon got out, which showed his proficiency and quality...Good boy!
To be honest, reviewing the past year, in order to train Sir Haydn's melody, we researched many ways together, including mathematics... Sometimes, evenly felt hopeless... Playing from childhood, Haydn's style is quite simple to me - models, switching, sonata structure..., but to students, they didn't quite like the sense of thinking being structured... And at the very beginning, I even didn't understand why they felt difficult... Recognizing something, We began to make many games, and evenly counting out some scores for the achievement of his 'fried chicken legs'...
Here, from rhythm to notation, and from melodic interaction to parts-division, I felt it's much clearer, more fluent and stable, than before... His ability of coordination has also been improved, though still some problems. I dared and felt confidential to say: it's a great edition of himself. Hopefully, he can progress further.
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 16:08, 4 April 2019 (UTC) Now, he made it much more fluent and accurate, and also played out his own fashion, though some details still need to be modified. Honestly to say, I thought somehow he got his progress in this period which we can hear...[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 03:28, 2 August 2019 (UTC)

'''Comments'''

It's the second time of piano boy Yu Zhang's teaching result show. In this time, he chose the melody &lt;Under the Sunshine&gt; - a Chinese fork teaching melody as one subject of national examination and also a performance of one piano competition in Dalian.
In my view as his teacher, he gave a very different view of this melody, compared with girls'. He paid more attentions to the whole view of melody's energy, strength, fluency and the joyfulness in Under the Sunshine, but didn't too much care about the details of some parts. However, on the stage, it showed a very great expression as from boy's situation... Good luck and happy experiment. After some practices, in the classroom we together recorded it and submit it up... (Referenced Partly from his page in Wikimedia Commons)


==== How to play Chinese Folk tune - 'Kids' Dance' with Chinese kids' fashion? Listen to little girl Kunlu's performance ====
'''Teacher's Demonstration in classroom:'''
[[File:Kid's Dance Chinese Folk Piano Player Jason M. C.,Han.ogg|thumb|Kid's Dance - 'Kid's Dance', from a folk piano-tune in China National Grading Book, was personally performed here, as a gift for all piano-kids' 'Happy 2019 Lucky Pig Year']]
'''Student Kunlu's Performance in classroom:'''
[[File:Kid's Dance (Chinese) - Student Kunlu, Han.ogg|thumb|Student Kunlu, Han's (Han family's girl born as bright as dewdrop in Kun - Saturn of Wuxing) good performance of Kid's Dance (Chinese)]]
'''Teacher's Comments:'''
Totally to say: Though She can play better editions (many better ones, last winter), in this sound file, she showed the coherence, fluency, flexibility and stability ( as Chinese fork-tune required). Hearing such a smart Chinese girl playing such a fugue-cannoning song, you will feel: it's a right song designing for a right girl... I think that's one meaning of piano-performance. Though spending much time, We did also research special 'Chinese supplemental positions &amp; Dialogues' in polyphony together, which gave us many beautiful memories... Further more, in this age, her staccatos, slurs and Tenuto have been performed quite well, which helped her to keep a unified speed to the end. 
Taking back a step, there must still be some small faults in classroom (without purposes) that I have to point out: such as B18's  #C blowing to D a little bit, the attention didn't get back in B41 head A which made a small break, and a small mistake of 'Recovered C' rather than #C... In order to dream of its accuracy and pentatonic harmony, it's a hard-working that we have already come over many problems and mistakes... Therefore, I think she fulfilled herself and achieved many things from 'Kid's Dance'. Hopefully, she enjoys the procedure of music-carving. [[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 15:07, 4 April 2019 (UTC)
===== Kunlu's Crystal Heart on International Children's Day -  Kleine Kinder Kleine Sorgen (Little Child) =====
'''Teacher's Comments:'''
1. The degrees of proficiency, fluency (and internal speed) have been improved, right on International Children's Day. 
2. I preferred her treble part very much - so cool, pure, clean and refreshing, which reflected her crystal heart in childhood.
3. The grasping of big chords - stronger, that's great - but needs to be more accurately and deep (The word 'deep' wasn't always 'loud' and 'heavy'). Please try to understand this point. Yes, it needs to show the hardness of growth (to young teenager), but also the achievement 'to be stronger and more confident of yourself...' [[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 03:32, 28 June 2019 (UTC)
[[File:Internationl Children&amp;#039;s Day Gifts - 2. Kleine Kinder Kleine Sorgen (Little Child, Piano-modification of Germany Song).ogg|thumb| Kleine Kinder Kleine Sorgen (Little Child, Piano-modification of Germany Song), played by Kunlu, Han]]

==== Teacher's Shares of his own home-works from childhood (Open) - Jason, Han====
====='''M. Moszkowsky Etude (Op.72 No.5) - &quot;C major's Fluency, Clarification, Sunshine and Love'''=====
New Beginning with...: M. Moszkowsky Etude (Op.72 No.5) played by Jixun Han (Jason) for piano teaching. It's long time that my piano classroom on the cloud in wikiversity hasn't update its situation. After so many things, now I can partly return to English writing world. The first Etude I would like to upload is still MM Edute which gave me so fluent and clean mind in my childhood. Oh, 38 years old, and after a wedding ceremony with my real lover, my fingers would not be so great as around 15s'... However, I would like to update its situation and new editions untill great someday. Now, let's began with this new melody. It's taught to my good Chinese boy pupil named Guoguo (fruit zeyu, Cui) when I grasped up and recorded. Yes, this little boy will also play well. Let's listen to my version, firstly. Thanks Jason M. C., Han (talk) 13:26, 20 November 2024 (UTC)

More information, please see https://en.wikipedia.org/wiki/List_of_compositions_by_Moritz_Moszkowski

Homework Requirements (challenges):

1. B23-B24(B stands for Musical Bar): By right hand, heads of every 4-notes group make a down-going semi-notes scale, which needs a very careful&amp;exact arpegio-fingering with a whole—palm holded and also thumb-measuring ability. Meanwhile, the left hand is making a whole-tenth measure, but arranged upon every  two chords' link. The semi-notes scale is also its fixed channel accordingly. This point is very different to follow and be made accurately and perfectly, which needs long-time training.

2. B49-50 It's almost a two-hands doubling for playing arpeggio-phrase.But not really!  You can watch the second phrase- fingering! Your left hand need a smallish shape. Meanwhile, the little finger's head of last phrase need to jump out a minor third distance down. It's very hard to control and also not a doubling.
(Hard for playing, but good for sounding, if out. Therefore, dears, have a try like mine...)
Yours little uncle Han [[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 14:15, 25 November 2024 (UTC) 
[[File:M. Moszkowsky Etude (Op.72 No.5) played by Jixun Han (Jason) for piano teaching.wav|thumb|M. Moszkowsky Etude (Op.72 No.5) played by Jixun Han (Jason) for piano teaching]]

===== '''Beethoven's Moonlight Sonata''' =====
Indeed, Beethoven left a historical challenge (difficulty) but the continuously creative inspiration to understand the techniques &amp; musicality of all his movements, equally to all people. We can attempt different approaches and own personal life-experiences to understand them, and discuss out some possible results.   
[[File:Moonlight Sonata - 3rd Movement of Sharp c minor Sonata Beethoven.ogg|thumb|Moonlight Sonata - 3rd Movement of Sharp c minor Sonata after a library presentation of Beethoven (Further, thanks to the April-collections of Tokfo Gallery (Vienna: https://commons.wikimedia.org/wiki/User:Tokfo/Vienna/2019_April_28-30) and Sir James Gallery (Bonn:https://commons.wikimedia.org/wiki/User:Sir_James/Bonn/2019_April_29) - great encouragements!)]]
'''3rd Movement- 'Moonlights Storming' - Techniques Analysis from Notation-reading ('Presto agitato' of Breitkopf &amp; Hartel Company and Berlin Arts Collage also compared with Old New York Edition - as the remembrance of one monitor):'''
'''Musicality:''' In a grandly general view, it's like...in a crazily running (very fast) race, viewed from the window, moonlights have been dismembered upon deep Lake Lucerne (many fragmental sections composed together). 
[[File:Vienna Beethoven Monument (with angels and children surrounding).jpg|thumb| Beethoven's Monument in Vienna]]
[[File:Beside Beethoven's Musicality.jpg|thumb| A third-person's Watching of Beethoven's Musicality]]
For its musicality cultivation, I could give a similar sense of its situation, like in Picasso's works- such as Picasso's Guernica (Ceridwen's Creative Commons Attribution-Share Alike 2.0 Generic license) For achieving it, a little bit of dark-moods anger and sadness faced from the unfairness and out of control could be inputted, after all technique points were trained in the dexterity. Therefore, from emotion to say, I thought the video right after getting back from UK and the lost one in Newcastle central station were better than this time. [[File:3rd movement of Sonata &amp;#039;Moonlight&amp;#039; Rocking Video JMC, Han (Jason).webm|thumb|3rd movement of moonlight sonata; Rocking Video JMC, Han (Jason)]] However, I satisfied with it, right like in life and after the presentation. From this point, we can see: Beethoven, as a piano master, has super-reached too much before the time - even abstractionism and postmodernism (deconstructionism).
'''2nd Movement - 'a little Fantasy Moonflower blooming between two rocky layers' - Techniques Analysis from Notation-reading (Allegretto of Breitkopf &amp; Hartel Company and Berlin Arts Collage):'''
1. Parts-distinguishing way can be applied to pick up the main melodic points from its background and legato them into lines. 
'''( Notice: Here, from the historical observation, a thing needs to be clarified: Baroque-regression (back-reasoning) was usually made by classical composers (in Vienna school: Mozart, Haydn and Beethoven etc.), especially in their later years of life for calming down the dramatical emotions, and keeping Life's Reasonability. Meanwhile, from Haydn, they discussed and created classical counterpoints from symphony and string quartet together, to modify creative inspirations. Beethoven also inherited it. Therefore, when we play some in piano, we need to analyse and apply some special techniques, commonly used in classical polyphony, to pick up the main from the background, sentence by sentence, as an era-responding.)[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 03:38, 15 May 2019 (UTC)'''
2. Octaves-bridging and chords-connections for big hands, into their hidden melodies, are the most difficulties, which need your frequent exercises, sentence by sentence. (Painful but worthful! Finally, flexible and skillful... )
3. Long keeping-notes, in certain parts, are important for the continuity of the tune and the texture, without broken.
4. It's better in light and tender keyboard-touching way to make melodic lines clear and 'the little flower' smile lightly.
5. 'Rondo' (ABA) formation can be applied to understand its repetitions, responding and structure.    
[[File:Moonlight Sonata (Sharp c minor Sonata) 2nd Movement Beethoven JMC,Han.ogg|thumb|Moonlight Sonata - a little fantasy flower between two rocky layers]][[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 14:51, 14 May 2019 (UTC)
=====  Blue Danube is always flowing from heart and life, with the vitality as spring: =====
Children and young teenagers, let us swim in this life-long river, to see some beautiful landscapes!
[[File:Blue Denube in my heart.jpg|thumb|Blue Denube in my heart]]
[[File:Blue Danube (Exercise and variations-collections in piano) JMC, Han.ogg|thumb|Blue Danube (Exercise and variations-collections in piano) JMC, Han]]
=====  Pachelbel's Canon is always the canon (polyphonic technique) since Baroque Era, but in '''Modern Piano's Pop Variations''' =====
[[File:Pachelbel&amp;#039;s Canon in Pop Variations (Geoge Winston Notation) Player Jason, Han.ogg|thumb| Pachelbel's Canon in Pop Variations (George Winston Notation) Player Jason, Han]]
'''Story of teaching &amp; learning (from Wikimedia Commons):'''
Regarding with this piano melody, there is a long story in my heart... Oh, did you hear Mag-pie's singing (I like 'pie' in the tail of this word) in the first draft? Yes, it was attracted and landing on the tree outside my balcony... You can clearly hear it at the beginning and in the tail in my first draft... Almost, it would like to share my memory...

Long long ago, my old brother on my mother's side used to be one hero of my life and fashion... On each holiday, he was always able to find great music pieces, MTVs, transcripts , and scientific fictions, from foreign countries, such as American and Japan (Summer)... and brought &amp; shared with me... Then, I attempted my best to exercise them into the reality, which included this song - Canon Variations from pianist George Winston... Those memories have never faded out, but in my deep sea. To now, evenly did I think Canon was from US and a POP song... After seeking the exact information in Wikipedia, I found it's Pachelbel's Canon in D and Baroque Era and German, rather than C and Modern and Pop in American... and with a 'Gigue for Violins and Basso Continuo',  it's not only for piano in many parts than our 3 parts in original piano edition. However either, I still like it very much and would like call it American POP in my music world...

Then after, a male colleague in my working college said to me: Jason, on my wedding ceremony, I would like to play it for a girl... Could you give me a simple one? Then, searching online, I found a simple (middle level) notation and an original (advanced level) notation, I downloaded both, and chose the simple one for him Three months, he was able to play it from 0 level (he wasn't able to read the notation)... I thought piano would have give him a good memory of wedding...

Following, I found a girl felt bored about her piano examination... Then, by choosing the simple transcript and inserting into her lessons... it made my tutoring classrooms really beautiful, relaxable, magical and peaceful... 

Now, I have time to play the original edition out... One long dream of my heart is going to be fullfilled... Though my hands in several points didn't make my perfectionism satisfied contrasted with before, especially the tenth-cross design between the left hand and the right hand, I knew it's my life, and fate?... I prefered to update its situations for bettering continuously... if having time...

Compared with the firstly draft, I thought the second was much down-calmed and peaceful...Somehow, I preferred the first draft, but a little bit of 'fast'... I cannot make the decision...then, kept two. However either, I still felt very happy the little natural friend - mag-pie can join... For this reason, I kept it. Hopefully, you will enjoy...
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 04:50, 16 September 2019 (UTC)
===== KV.265 12 Variations on Ah vous dirai-je, Maman - 'Twinkle Twinkle Little Star' =====
Analysis (Waiting)
[[File:KV.265 12 Variations on Ah vous dirai-je, Maman Mozart JMC, Han.ogg|thumb|KV.265 12 Variations on Ah vous dirai-je, Maman Mozart JMC, Han]]
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 08:43, 7 October 2019 (UTC)
=====''' 'The beautiful views of Scotti-highlands' from Thompson's Book (Advanced Level) - Teaching and demonstration '''=====
[[File:The beautiful views of Scotti-highlands (Teaching demonstration - video; Jason, Han).webm|thumb| After the performance in local Crossing-year 2019-2020 Library Concert and many further exercises, a good edition in classroom got out - Piano kids, always, you knew:  No pains, No gains]]
For its musicality and academic thoughts, please visit Wikiverty's Portal of Piano education(The Section: The beautiful views of Scotti-highlands' in a Far-land Home (Academic thoughts, musicality, literature-writing and case-realization)):
*[[Portal:Green Sleeves (Impressionist Visualization)]]
*[[Portal: Sir J.S.BACH and His contributions to Piano Kids' Reasonable Life]]
[[File:C minor Prelude Bach (BWV847), Performer JMC, Han.wav|thumb|C minor Prelude Bach (BWV847)]]

==== 'Swan's Dream Upon the lake' - Little Girl  'Wenxin's' (Brilliant &amp; Sweet literatures in arts ) Performance====
'''Teacher's Demonstration:''' 
[[File:The Dying Swan - black angel JMC Han.ogg|thumb| Musicality from watching 'The Dying Swan - the black angel', performed by JMC Han]]
'''Wenxin's Performance:''' 
1. Techniques-recovery: The Arpeggio-training of left hand in the accompaniment was the biggest challenge to not only a piano-child at her age - no more than 12 (In Chinese culture, Kid's first year was in mother's womb. Thereby, I asked her - how old are you, and she gave the number '13'...),  to me and evenly some expertise pianists. (Camille Saint-Saëns's 'The Swan' on wikipedia or other social editions). The arpeggio-accompaniment is travelling in rich variations of tunes, which caused left hand much harder to expand, shrink and positions-change. Therefore, it spent us more than half a year to train and recover her hand's dexterity from a small failure of her piano life in the Grade Test, just like 'Princess Swan's' experience. Now, totally to say, she got an excellent situation in which children at her age can perform. Thanks to your hard-working!  
2. Musicality-cultivation: Usually, she showed a very great musicality in the first page - to the minute (Approximately 1.05) - tender, expending, lyrical and expressive... However, it's really a hardness to keep it throughout the second section - a shading &amp; wandering heart-road in the growth. The attention has to be paid too much on the exactness of left hand's arpeggio-travelling. With a pity, still, some notes were beaten wrongly. But oppositely again, we can see: Princess Swan, in her period of Darkness growth - facing Satan, turning into a dark angel and only appearing in night... She really faced a hardness and the difficulty of life, right as beating wrong notes, getting out some noises and travelling a little bit slowly and roughly in a channel. In this view, perhaps that the difficulties can be transformed- in the musical needs and with a small fashion. Congratulation, more exercises, haha!
3. Together, we gave two great designs: one is the 'Big Brightness' began from the minute (Approximately 2.03) when the main theme happens again; and the other is 'Swan's Departure like Sound of Fall-Leaves rotating upon Lake's Surface' (from minute 2.49 to the end)... She almost achieved some - the mood calmed down very much and stably progressed to further with a confidence. However, a little bit of disfluency made the impression fade, somehow. Meanwhile, a 'rit. to a tempo' turned inversely - what a pity. 

Totally to say, musicality, at her age, was preciously showing in this time's performance. The hard-working of recovery and exercises, during many classes, touched my heart very much. (I knew that...)  More trainings of Arpeggio-running (dominate sevenths) and its fluency can help her achieve more in the future. Wenxin, thanks to you for letting us appreciate this world-famous melody in piano.     
 
[[File:Growth of Swan in eyes of the little girl - Wenxi, Zhang.ogg|thumb|Growth of Swan in the eyes of the little girl - Wenxi, Zhang]]
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 16:06, 5 May 2019 (UTC)
==== Listen to Mother's Old Story! - A beautiful and quiet little girl's Good Wish ====
'''Teacher's Demonstration:'''
[[File:Mother&amp;#039;s Old story - China Impression.ogg|thumb| Listen to Mother's Old story - China Impression (JMC, Han - teacher's domenstration)]]
'''Student's Performance:'''
[[File:Listen to Mother&amp;#039;s Old Story - Piano Pupil Yiwen, Cui.ogg|thumb| Listen to Mother's Old Story- Piano Pupil Yiwen, Cui]]
'''Teacher's Comments:'''
Yiwen, Cui (Direct translation of her Chinese name - A beautiful girl who is good at the translation of art and literature, from Cui family), at the age of 10, is a quite and beautiful girl. She got a good life effect from this Chinese piano-kid's song - 'Listen to Mother's Old Story': making her family and parents happy, getting some confidences through this piano song from the examination, showing her fashion in my library concert held for piano kids... After those more above, frequent exercises, and getting her permission, I can submit this classroom-recording edition. Though in the tail I found a note lost... and some parts of her left hand might run much more fluently... , I think her emotional background of this music reached to a good level, and those polyphonic parts can be clearly heard two layers, their cannoning, and so on... Congratulation! 
'''(Words from the description in Wikimedia Commons page)'''
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 01:04, 8 August 2019 (UTC)

==== Moonlight upon Lotus Pool (Summer) - Letters-Accompaniment Improvising Chinese Pop-song with both Classical Tradition and Pentatonic Scale ====

'''Teacher's Comment:'''
1. I am very excited that you (only 10-years-old) understood Letter-To-Accompaniment Improvising sheet and its approach in a very fast way.
2. It's great you can use both Pentatonic Arpeggios and Tenth-Rolling-Bass-dropping in your accompaniment (You can make Tenth-rolling Bass in a more fluent view, I thought) 
3. We can feel the musical scene from your musicality - In a beautiful summer night, Walking along a lotus pool, you and your family members were enjoying the moonlight and a breeze of cool wind...  
4. In future, hopefully, you can improve your 'new learns' to a higher level.
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 01:04, 8 August 2019 (UTC)

''' Xuan, Lee's Second Attempt - Pearl of the Orient'''

==== 'Mother in the candlelight' - A little girl (Siqi)'s heart-words for her mother's birthday - in the growth and in the dreams...  ====

'''Heart-story:'''
Regarding with this piano-song, there is a little story about this little commons' girl: Usually, her parents were very busy in the family's restaurant... I and my mother saw she had independently managed herself well and grew up alone for many years... In this year - 2019, time was near her mother's birthday. In the KTV (a place like karaoke bar, but for small single groups of people in rooms, with TV in the middle for singing ), she heard this song - 'Mother in the candlelight' and found her parents enjoyed singing it very much. Then, she decided to play it as a gift to her mother, right on mother's birthday. It's my biggest honour to be together sight-reading the notation, making the re-designs and re-editions of this song into piano - like, Prelude, Introduction-theme 1st, theme 2nd, Development and Peak, a small Repetition and Coda... She learnt in a very fast and hard-working way that merely around one month she played it in this level. And finally, she got her heart-sweet - playing it for her mother, as a birthday gift.(Wikimedia Commons' original page, 2019)

'''Comments from teacher:'''
1. The musical emotions were very rich and expressive, especially the 'Peak-Calling for mother' (2.53 minutes - 3.53 minutes). I almost can hear 'Mum...' (or Mumu...) for many times in a kid's tear-drops and in the candlelight... by your right hand's touchable singing...
2. I liked our 'Flanger tr. Ornaments' very much (I thought it's from Mozartian). I am very happy you can put it in for soon time...
3. I am very happy in the Coda-tail, you can get my suggestion - ending by a Major Seventh Progression-Arpeggio. This point should give the thanks to my mentor - Ray. I quite enjoy its special colour... 
4. Your strong and mixed left hand accompaniment must have been trained for many times. I knew it's a hard-working job, but tender and flexible a little bit... better?
5. The singing of right hand and its 'breathing' were quite natural and fine, sentence by sentence..., but the total speed is too slower than normal, which reflect the running ability of the left hand needed to improve. I knew: to your 9-years-old hands, it's a very hard requirement... However,  waiting the up-grown, I have the confidence you can hands-sing it in a much more fluent way...
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 14:10, 5 September 2019 (UTC)

'''Night's Piano-Song - The depth of China Pop-Piano (and Siqi's Heart-Try)'''
''Comments:''
She made the depth of two peak notes but in light touching way. I thought also that she did this Pop-piano's musicality in a poet's Night-thinking... 
She is suitable for the performance of this-type-'songs' and improvising (still at little age and need to prepare in time).
Let us listen to her and feel her expression.

==== The Cowherd's Flute played by a little girl piano pupil - Guo Guo (Nickname: Happy fruits)  ====
This edition has already been her best attempt, regarding with its landscape-painting style, lovely Cowherd's Flute we can refer to Wikipedia introduction (Seeking key words 'The Cowboy's Flute' in). It's recorded as a beautiful memory of her piano-learning and her Childhood. Let us listen to her:
[[File:The Cowboy&amp;#039;s Flute - Yuxuan, Lu (Guo Guo).ogg|thumb|The Cowherd's Flute - Yuxuan, Lu (Guo Guo)]]

====  Clementi Sonata Op35 No. 5 (Movement 1st), played by Piano pupil Yixuan, Qiao ====
Clementi's Sonata-Op35 No. 5 was a so long and difficult piece for students around their ninth year. Therefore, we have divided it into many small sections and taught. She learnt in progress. Meanwhile, this little and beautiful girl (She was beautifully good at dancing, somehow rather than piano.) has already attempted her best in exercising and recording. I thought it recorded her good piano-learning experiences and those memories of childhood. Regarding with further information about this work, please refer to the educational portal: https://en.wikiversity.org/wiki/Portal:Sonatinas_from_Kids%27_corner_near_heaven#Muzio_Clementi . Let us listen to her:
[[File:Clementi Sonatina Op35. No 5 Movement 1st Piano pupil YIxuan, Qiao.ogg|thumb|Clementi Sonatina Op35. No 5 Movement 1st Piano pupil YIxuan, Qiao]]
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 02:42, 18 October 2019 (UTC)

====Little and Little, Twinkling Stars - Little Piano-Kids' Playground====
Say 'Hello' to our 'Little Goldman'
[[File:Vienna Trip - The Little Goldman- Strauss Family.jpg|thumb|Hand-making my  own picture of Strauss Family's Little Goldman]]
* [[Portal:Little and Little, Twinkling Stars - Little Piano-Kids' Playground| Little and Little, Twinkling Stars - Little Piano-Kids' Playground]]</text>
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      <text bytes="72564" sha1="5hxvhvhv2hdwtfw71ffi8xju57jht3d" xml:space="preserve">'''No Orders, Beautiful flowers were blooming from Childhood! Let us pick up your most beautiful moments...'''
[[File:Salzburg Cathedral (Inside) - Mozart Baptized place 1. - Mozart-Complexes World under Water (Modernist View).jpg|thumb|Piano Kids, on that day, modern colours, lights and technologies made Mozart's birthplace (Washing) -Salzburg Cathedral like a world (palace) under the biggest water - Blue Sea]]
[[File:Beautiful landscapes surrounding Mozart's birthplace - Heavenly Spring flowing from Alps Moutain.jpg|thumb|Heavenly Ice-spring from Alps Mountain]]
[[File:Mozart from Green Nature 1.jpg|thumb|Mozart comes from Green Mountain and Nature]]
[[File:Models for Chaoshan Family Tourism - Taifo Hall.jpg|thumb|Uncle Han -the piano teacher and his wife Yang, Gao (Cynthia) were volunteeringly pictured outside the door of Taifo Hall in Chaoshan. They are promoting it for Family Tourism there. It's a beautiful time in all family members' memories, as a piano song told in life story...]]
[[File:Beautiful Sunset View of Oceanic City from top building during COVID-19 period.jpeg|thumb|Beautiful Sunset View of Oceanic City during COVID-19 period]]
[[File:Small items in Commons Life of 2019 Spring 2.jpg|thumb|Flaming Katy and piano-peers as Micro-landscape in classroom ]]
[[File:An Oil Painting watched since born.jpeg|thumb|Oil Painting: Forest Cabin in front of Fuji(or Helan) Mountain 'hanging on the wall']]

 Oh, dear piano pupils, we have seen so many beautiful landscapes, across the times and spaces. Now, firstly, getting into East- your nature and self-meditation, let us try to take the Pentatonic Scales Exercises for relaxing you 'busy heart' and focusing your attention back to piano...

*[[Portal:Pentatonic Impressionism (China Wu Sheng) in the view of Neo-classical Piano Techniques-training]]

'''Afterwards, we can take further great life-tasks in piano...'''

[[File:Piano Lecture of Dalian Library (Music) delivered by Jason (Jixun) on October 13th, 2024.jpg|thumb|2024 Piano Lecture of Dalian Library (Music) Delivered by Jason (Jixun), Han and His Piano Pupils Team Associated by Family members and Library workers]]

''' Lecture Speech Conclusion'''
[[File:The Chinese characterastics speech of Piano pupils' art technique training and musicality athletics cultivation (Report Conclusion of Jixun, Han - Jason's team lecture on the date of October 13th, 2024 at Dalian Library).pdf|thumb|The Chinese characterastics speech of Piano pupils' art technique training and musicality athletics cultivation (Report Conclusion of Jixun, Han - Jason's team lecture on the date of October 13th, 2024 at Dalian Library)]]
'''Waiting Translation'''

'''New Time and Fresh Air from 2024'''
*[[Portal:Fresh Air of Piano after COVID-19 and beginning up a Recovering New Time of Openness from 2024]]

===='''Firstly, passing by a Skyline of Citylife Night-Skyline'''====

[[File:Flowing City (Lin Hai), Player and Teacher JMC,Han (Jason).ogg|thumb| Flowing City from 'Forest Sea', JMC,Han
[[File:Dalian Urban Night Skyline from Xiao Ping Island Mountain-top No.2.jpg|thumb|Dalian Urban Night Skyline from Xiao Ping Island Mountain-top No.2]]  ]]

===='''New Era is coming...:(New Teaching List)'''====
[[File:Skiing Statue made during my rollers-skating.jpg|thumb|Skiing Statue shows Spirit (like piano)]]
[[File:The new situation of bubbles-fish statue.jpg|thumb|Ice &amp; Snow Bubbles-fish are welcoming]]
[[File:Mmexport1614470203508.jpg|thumb|Picture of piano lessons still under Covid-19 situation]]
Etude in the Advanced level - Sir Chopin's famous Black-keys (Flatten G Major) Etude:
[[File:Chopin Black-keys Flat G Etude (Exercise), player JMC, Han.ogg|thumb| Black-keys: An Etude your teacher has no chance in childhood, but still hurries up to be better]]
[[File:Chopin Impromptus Op.29, JMC, Han.ogg|thumb|Chopin Impromptus Op.29, JMC, Han - Deep Fast Waltz-thinking in Quiet Gentleman's Self-Expression (Improvising)]]
[[File:Sogdian whirl with large pipa.jpg|thumb| (Public Domain Work: See original page: https://commons.m.wikimedia.org/wiki/File:Sogdian_whirl_with_large_pipa.jpg#mw-jump-to-license): Could you find some musicality similarly with Chopin's Black-keys' Pentatonic?]]
True Fairland - a piano melody of The Nutcracker (Dance of Sugar Plum Fairy): the advanture from childhood realizes your piano dream-&quot;Fingering Ballet&quot; 
[[File:The Nutcracker (Dance of Sugar Plum Fairy), Piano performer JMC, Han.ogg|thumb|The piano performance of &lt;Dance of the Sugar Plum Fairy&gt; in 'The Nutcracker' (Ballet Re-edited Piano Melody)]]

Czerny 299 etudes were designed for the smart&amp;strong fingering&amp;modelling of hands and a pair of Vienna school's ears for the harmony...such as No.23...
[[File:Czerny 299 No. 23 JMC,Han.ogg|thumb|Czerny 299 No. 23, player JMC,Han]]
A peacefully  praying Sinfonia of Sir Bach is freshly added in the &quot;New exam book's list' during this COVID-19 period, to which you can have a relaxing hear and try (Don't worry, listening, it's enough time, you knew,  'Andatino'-Peacefully walking, and to sing by hands, in a small Baroque place :
[[File:Sinfonia No.11 - 3Ps Invention, Bach, JMC,Han.ogg|thumb|Sinfonia No.11 Andatino- 3Ps Invention, Bach, Teacher JMC,Han (COVID-19 Protection Time)]]

Encouragement in Italy Smart Fashion, but needs the very carefully fingering-techniques training (Long time, advanced), feet-edges' staccato, sentence-Pizzicato, flowing streams...Italian artist techniques always attract our eyeballs... Let us attempt to... make out your own Italy style! Cheer up!
[[File:Domenico Scarlatti G Major Sonata, JMC,Han.ogg|thumb| Domenico Scarlatti G Major Sonata (In COVID-19 Pandemic Period), JMC,Han.ogg]]
'''A good teaching video result played by Yixuan, Wang:'''

http://m.kugou.com/mv/?hash=f00b36624f27b091b79e3f30e158aa03&amp;sruserid=640650901

Baroque staccato techniques were always in a reasonable, confident, relaxing(wrists), fluent and vivid - 'Enough manners' of the Era, which needs us apply very careful fingering trainings. In a view of the whole structure, according to ears' musical suitable habits(psychological), I gave 1st section a twice repetitions, and then a throughout 2nd section to the Code. Hopefully, French Suite would make us brave, confident and relaxed. (but it also need years' accumulation of hand working to let those out and better) Have a try? Good luck!
[[File:BWV.816 Gigue-French Suites No.5 Bach, Player JMC, Han.ogg|thumb|BWV.816 Gigue-French Suites No.5 Bach, Player JMC, Han]]
(By turning to Wikimedia Commons, you will find two versions under its 'historical tree', currently. They are showing different stages we can reach. The first version was kept because it's relatively slower and more stable that in the basic stage we can make notes heard staccato and clear. After feeling suitable in this stage, we need to improve its tempo and get Gigue Dances' happy, vivid,,dialoguing with moods, jumping and  wrists' breathing naturally. It needs time to train your hands frequently, untill relaxing but accurately. Main Difficulties: Stiffen wrists, Cramp and Tiredness... Now, it's the time of yourself...)

Hi! We, piano kids: Imaging a scene, let us hands-dances with the good manners and a earnest mind in a beautiful Baroque palace. It's easy and natural...
[[File:Primary Bach No. 16 March, Player JMC, Han.ogg|thumb|'Primary Bach No. 16 March' -A peaceful Bach-melody for all 'Piano Kids'...]]

Sir Debussy's Arabesque Suites (The second suite) is also in the list.
The musicality in my world is: 
It's the legend of Butterfly in birds' chorus... it took us to a Life-mountain behind our living garden facing a quiet sea...
Watching, in some time of one section, you can also hear Monet's 'Quiet Morning' upon the sea...
Alongside Butterfly's dance-suite, imagination is beginning. Oh, listening... (Main meaning referenced from my main page)
What about it in your world and imagination?
'''Sound teaching demonstration:'''
[[File:Claude Debussy - 2nd Arabic Suite (Arabesque) - Spring Butterfly, Performer JMC, Han.wav|thumb|2nd Arabic Suite- Spring Butterfly (Impressionism Singing -Main Natural Lines&amp;Breathes from Sir Debussy)]]

'''Good video teaching result from  a 12 years' old little girl piano-pupil Mo Zhou:'''
http://m.kugou.com/mv/?hash=b50e133a360fa8d30cdcd9fca4163e73&amp;sruserid=640650901
(Photographer: Ms. Yang, Gao)


Listening! boys and girls, Dvorak's Humor-jumping and Homesick-expressing:
 A true Czech-homeland heart,
but 
Dancing... somewhere in American Countryside
[[File:Flatten G Humoresque Dvorak, Player JMC,Han.ogg|thumb|Flatten G Humoresque, A. Dvorak, Player JMC,Han]]
[[File:One Town-view from Cesky Krumlov Castle.jpeg|thumb| Krumlov Castle-town's view]]

====Xinran, Yu - a lovely Chinese little piano girl's 'Ink-Mountain &amp; Green Rivers' view of &lt;The Cowherd's Flute&gt; ====
'''Comment:'''
&quot;Before taking the national examination and the  exhibition competition, we together listened and learned to the net-editions of young master Lang Lang and Yujia Wang...(regarding with this famous little melody of Chinese tradition)
I think in this melody, she tried out her best for the techniques-training and the musicality in her age... from a little performer's view. Therefore,I gave the comment-Excellent.
Close your eyes, thinking of a little lovely girl happily playing among ink-mountains and the green rivers, with a water buffalo, some birds followed, and her smart flute... let us relax in the Chinese Ink-Landscape and listen to this little melody...(referenced partly from the writing in Wikimedia Commons page)
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 02:28, 27 May 2021 (UTC)

==== Zichen Tao - A little Chinese snowgirl's hardworking of D Major Sonatina====

'''Comment:'''

D Major Sonatina is still piano Children's favorites to perform and show... taken to the national grade examination, daily performed with each other, and also to city's piano Competition &amp;Exhibition. That's an educational case lasting for many years in Dalian.
This edition is played by a lovely and white Chinese girl - Zichen, Tao. She and her mother took the very responsibility to check the wrong notes, improve the learning progress, and make the performing manners and designs for the stage-show... 
Therefore, in my view as her piano teacher, this edition is already great in her age...(though hand-running details need to improve for her age). Hopefully, her family can enjoy this piano experience, companying with this melody in her childhood. (Partly referenced from her Wikimedia Commons' page)
[[File:D major Sonatina , Piano student Zichen Tao.ogg|thumb| D major Sonatina (Kuhlau's) played by piano pupil Zichen Tao]]

==== Meng's Performance and Comments after learning in the reality from Jason M. C.,Han in Children's Corner: ====
[[File:Children's corner of Meng.ogg|thumb| Meng Meng (nick name)'s edition of Doctorial in Children's Corner: Currently, the Fourth Version was her most beautiful one self-made in classroom before Piano Grade Test Exanimation. Regarding with all editions' comments and reasons, please reference to the original file in Wikimedia Commons]]
[[File:MM Good classroom F major 1838 Grande valse brillante.ogg|thumb|MM Good classroom F major 1838 Grande valse brillante]]
'''[[Portal: Part of Comments - 'for students' Examination Performance, Piano tutor's teaching self-reflexivity and possible some requirements of Pedalling Sound-effects with Artist Fashion of Post-impressionism'  | Part of Comments - 'for students' Examination Performance, Piano tutor's teaching self-reflexivity and possible some requirements of Pedalling Sound-effects with Artist Fashion of Post-impressionism']]'''
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 04:15, 12 October 2018 (UTC)

==== Kim Hui's 'Doctoral Training','Under the sunshine' in Children's Corner: ====

'''Comments for Kim Hui's first draft:'''
1. She did the second theme (associated) well 'much deeper like vocally singing out a better life in New Era under the sunshine, on a piece of small area in a rainforest'...

2. Her Korean dance (Wikipedia introduction: https://en.wikipedia.org/wiki/Korean_dance) has been done well, in which I can hear traditional drum-points in bass-part and crossing hand to tremble part. 

3. I can hear Time-travelling and space-shaking to the past through a 'Dark-cave', from..., minutes 1.30-1.40... But, I think: if 'dramatically' and 'significantly' in dynamics (loudness), it would be better to show...

4. I can hear Forest's Evensong in Coda part - 'dim.' to the silence of night and a 'rit.' slowing down to the sleeping dream, and even several night-birds' dreaming voices...But, please make a much gentler taste (not so hurry up and not so strong) of those pictures. Meanwhile, I hope you can get a better &amp; coherent control of the rhythm among different sections.

5. I knew, regarding with 'peak-parts', she had made many attempts 'drumming beats rights and keeping those connections clear'. However, still, in minutes 1.04 and 1.59, I felt it's a little bit 'rough', and needed to be handled in of the solidification... Oh, maybe, I am so severe... sorry, I should give you the encouragement. 

Main comment: 'Under the sunshine' is suitable to Kim Hui's fashion and can be kept in her performance list. Her first draft and its preparation has given me an enjoyable teaching experience and many beautiful memories of life. It's fluent and vivid, expressive and dedicated. Thanks, Kim Hui! More colours and lights would be added from technique details, from her independent fingering and some traditional piano manners, meanwhile, the rhythm should be balanced well in the future. There are many developing zones of 'this painting' she can better and draw out for her future.[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 21:22, 17 October 2018 (UTC)
===== Kim Hui's second 'Show-Time' in classroom - Poem of Music (Piano Etude) =====
'''Teacher's Demonstration:''' 
[[File:Poem of music.ogg|thumb|Poem of music  JMC, Han]]
'''Student's Second Performance - Poem of Music: ''' 
[[File:Poem of Music (Piano Etude) - Student Kim Hui.ogg|thumb|Poem of Music (Piano Etude) - Student Kim Hui]]
'''Comments for Kim Hui's first draft:'''
1. She has mainly got the technique-points, but a little bit of rough in some details, such as the minutes 0.30-0.31 - 'Tail-closing part' of a sentence - in the progression of 'Diminished Seventh Chord-Arpeggio'... However, as her first draft and the random collection from a normal classroom, I thought it's well-done. we can wish its further 'Developing Zone', in the view of piano education.
2. In 'Coda Part' of Poem of Music (Piano Etude), she was able to show a great controllability of the 'Legato' between two hands, as the pieces of falling leaves slowly flying-upon the surface of water. Sometimes, it was evenly better than mine. I hoped she could manage it in a better way.
3. She showed some thoughts of musicality... However, 'Techniques-points' still wasted much of her energy. I think the total Dynamics in physics will be improved soon. 
(waiting more)  
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 14:53, 23 May 2019 (UTC)

===== Kim Hui can reach the  advanced level of piano performance in this 'Little Children's Corner' =====
Though It's still Covid-19 Health-protection Time, after Home-self-Training Time, some classroom face-mask covering &amp; health-good-protection lessons and an examination of China Culture&amp;Tourism Ministry, She can play this 'Doctoral Etude' which is dreamed  many piano pupils, with impressionism style. As her teacher, I didn't think It's a simple Etude which was expressed in many scenes, but with the big universe imagination and impression. Therefore, we have trained it as Meng's approach and further developed it. 
Indeed, I think she performed far greater than this edition, right in that online  national examination. She got it, Congratulation! Let us listen to her ...
[[File:Debussy-Children's Corner-Doctorial Etude, Piano pupil Jinghui Jin (Kim).ogg|thumb|Debussy-Children's Corner-Doctorial Etude, Piano pupil Jinghui Jin (Kim)]]

==== 'Colourful Clouds Running After Moon' impressed into the Heart of Xinyi, Hua (Hua family's Heart-sweet girl from 'Painting Imagery')====
'''Comments for the first draft of Xinyi, Hua:''' 

1. I like her treatment of the prelude part in 'Colourful Clouds Running After Moon'. It's light and soft like silky clouds up-bridging alongside moonlight towards a round moon above the dark-blue sea. However, please try to link each silky pentatonic-arpeggio weave as a smooth whole from the bottom to the top, and from the left hand to the right hand. If so, her progress will be enlarged;

2. I can hear the situation 'Colourful Clouds Running After Moon' appeared in many linking parts before and later. She was attempting to give an acceleration imitating this procedure from a slower speed to a fast one, and between two hands' echo-following from a loose density to a tight one... However, if obviously, it will be better;

3. Like 0.58 to 1.03 minutes, I can hear that in some parts, she would like to make a returning sound-boomerang (Wikipedia introduction: https://en.wikipedia.org/wiki/Boomerang) up-rising 'to the moon' and down-landing upon the sea-surface. If a small time of middle reaction was canceled out by her proficiency, we will appreciate the musical beauty in a much more advanced situation;

4. In 1.22 to 1.30 minutes, I know she would like to make a silky veil, with the colourful clouds as material, upon moon's beautiful face by her right hand. It's a little bit of pity that the controlling ability of relative loudness made she carried this willing but harder to realize. Meanwhile, this veil needed to be smooth. Oh, sorry, I am so critical... indeed, she did not bad;

5. There is a hard hurt in 1.36 minute - it's still a repetition of bass-chord though she has already attempted her best to grasp the bass large chord through left hand's opening degrees (Little girl, I knew you had tried your best. Though the momentum was great, I still need to point it out.);

6. 2.12 - 2.40 minutes is the part - 'Bright Moon up-rising above the harvest sea'. This is a grand scene which needs great forces from students' forearms and a fast reactions for some flexible connections to arpeggio-parts... Congratulations, little girl, she have got it, though it's a little bit slower. She have given out a great momentum;

7. In the Moon-tail part, she has expressed her great musicality to make moon disappear in the dawn of sea;

8. Many ornamentations she has done well, though still some need to be gently breezing in the impressionism of Chinese landscape painting.

[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 12:22, 24 October 2018 (UTC)
===== 'Pure White Dove' in Young Teenager Xinyi's Eyes =====
[[File:Dove in the eyes of Young Teenager girl Xinyi, Hua.ogg|thumb|'Pure White Dove' ('La Paloma' - 'No More' in English) in the eyes of Young Teenager girl Xinyi, Hua]]
'''Congratulation to your beautifully singing of the 'Melodic lines' behind the right hand's octaves-grasping!'''
'''Comments:''' 
1. Four biggest designs appeared: around B50 (Minutes 1.36),  B55 (Minutes 1.48), B58 (Minutes 1.54) and B62 (Minutes 2.01) - four Peak-currents, we'd like to throw (rit.) the 'missing notes' into the air and rotate them a little bit more slowly - like to send, wait and feel Dove's messages across the ocean in a self-holding &amp; self-releasing intoxication. She tried her best to make them out, but not quite clearly and still need much time to grow up... 

2. I liked her coda part (from B65 Minutes 2.08 to the end): She was so sure about two hands' March-doubling, as a confirmation of future and belief; or to say, she transformed her 'missing' in the melody to be a true hope of tomorrow, or someday... Evenly, I thought it's better than mine... 

3. For more than half years, we have worked hard to help her link all octave-grasping pearls out of melodic lines in singing breaths. She almost got it successfully, through small breaks... 

4. Some 'Spanish Dotted notes' and 'Triples-wandering', with the rhythm of Spanish Dance Habanera-Andante (Wikipedia introduction: https://en.wikipedia.org/wiki/Contradanza) can be fulfilled, but some not really... I am happy she recognized them and paid more attentions to... It's waiting time that she could perform much better.

5. Yes, I had to say: still some small faults there... The good usage of pedalling almost hide some, but... also a little bit rough... Oh, I didn't want to be a so severe teacher. Rather than, much more good wishes of her growth should be given. Okay, hopefully, she enjoyed it. 
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 12:57, 4 April 2019 (UTC)

'''Teacher's Demonstration for standards above and Further Progress (Advanced Level):''' [[File:Dove With Spanish Sense in Piano JMC.Han.ogg|thumb|Dove With Spanish Sense in Piano JMC.Han (It was once used by the photography gallery of music friend User:PigeonIP - https://commons.wikimedia.org/wiki/User:PigeonIP/Tauben/2019_April_1-10 and the main page La Paloma in wikipedia )]]
'''More information and reading - articles (list) about 'Dove', please watch:''' https://en.wikipedia.org/wiki/La_Paloma

==== Malagueña Dream from a little Chinese girl - Yinuo's heart (A promise ... to piano) in a small beach-side classroom ====
[[File:Student edition - Malagueña Suite (modified for piano) played by Yinuo, Liu.ogg|thumb|Student edition - Malagueña Suite (modified for piano) played by Yinuo, Liu]]

'''Comments for the first draft of Yinuo, Liu:'''

1. We can hear the impression of Flamenco rhythmic pattern (Compás) (Wikipedia introduction: https://en.wikipedia.org/wiki/Flamenco) diffusing from some simple rhythm-components of a parts in a total ABA structure of Malagueña Suite. This is what I - the tutor and the little girl -learner would like to express through three more different accompaniment bass-forms, including pizzicatos, small slurring breathes and some opposite weights..., which imitated some of Classical Guitar's handling ways. Thanks to the little girl Yinuo, you have realized most of our designs! Congratulations!

2. I really like her beautiful Cante jondo - associated 'vocal' lines by right hand which was balanced &amp; flying above the flamenco accompaniment of the left hand when the second thematic melody began. It's a deep, profound and emotions-rich singing, almost from a beautiful Spanish girl's natural expression for the missing, the reasoning of life &amp; Universe when facing a 'deep and far' sea. Though if the dynamics would be dramatically and the singing would be much deeper, the emotional atmosphere would be better: I thought to only a girl of her 11 years' old age, she has already attempted her best to understand those across cultures;

3. I like the middle B's fantastical view of holiday beach under the sunshine, which was almost formed by white waves from blue sea. It's relaxable, dreamful and graceful, like a girl poet's walk alongside a small sand bay...  (Yinuo, you knew, if you can make the 'rit. - A Tempo' much more nature like the real tides of sea and the speed tiny faster, the progress zone will be enlarged);

4. I know in two middle long 'vocal' ornaments, she would like to show us ' the blackbirds or the nightingales of its gardens...' However, if making it much more smoothly, expressively, and flexibly, even a little bit down-slowed, her Spanish 'tasteful' fashion will be more beautiful; 

5. Repeated A part is better to be different in small details which can show the ability of hands and the variation of music.
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 13:35, 24 October 2018 (UTC)

==== Für Elise in piano boy Zhe's eyes ====
'''Teacher's demonstration in classroom for better:'''[[File:For Elise (Für Elise) Beethoven JMC Han.ogg|thumb|For Elise (Für Elise) Beethoven JMC Han]]
'''Student's performance in classroom:'''
[[File:Für Elise -Student Performance Zhe,Zhang.ogg|thumb|Für Elise in piano boy Zhe's eyes]]
==== D major Sonatina (Kuhlau) - Piano-pupil girl Mengshuang's 'Strong Willpower and Persistence' ====
'''Teacher's demonstration in classroom for better:'''
[[File:D major sonatina 2nd movement Kuhlau (played by Jason).ogg|thumb|D major sonatina 2nd movement Kuhlau - Teacher JMC. Han]]
'''Student's performance in classroom:'''
[[File:D major Sonatina (Kuhlau) - the version from piano-student Meng Shuang, Wang.ogg|thumb|D major Sonatina (Kuhlau) - the version from piano-student Meng Shuang, Wang. This classroom version has been selected by https://commons.wikimedia.org/wiki/User:Rsteen/Artists_from_Denmark/2019_August_1-10]]
'''Comments and Statements:'''
1. Totally to say, the main melody fast-run by the right hand has kept its fluency, transparency and clearance. It's very hard in piano training for herself, owe to that her hands-shape was a little bit of 'frozen'. Thanks for your hard-working in the training. Congratulation!

2. Her musicality in this melody has also been motivated out - unrestrained and natural in the expression.

3. Left hand's accompaniment was in good triplet-treatment, but please light and dedicate a little bit... It's to say: the controllability still needs to improve.

4. Some heads of sentences and smaller phrases need to be match together between two hands in a better way - some parts, because of small ornamentations and dotted notes, weren't quite well...

5. I am very happy that you (in your 12th year of life) were willing to play out the middle 'rit. - A Tempo' in a comparison ('rit.' was slowing down the waiting, then, 'A Tempo' for the Peak expression in return). However, it was still a little bit rough (before its right time). You can try to modify it in a better view. 
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 03:08, 2 August 2019 (UTC)

==== How to play Mozart's Classics? ====
===== Work from Mozart's earlier time - Turkish March =====
 '''Teacher's Demonstration in classroom:'''
'''Video:'''
[[File:Turkey March Video-Mozart-Jason Han.webm|thumb|Turkish March (Video) for Mozart's; JMC, Han]]
'''Sound:'''
[[File:Turkey March for Mozart and Memory JMC, Han.ogg|thumb|Turkish March (Sound) for Mozart's and Memory (many times used in peer Tokfo/Vienna Gallery - such as https://commons.wikimedia.org/wiki/User:Tokfo/Vienna/2019_January_26-28 ); JMC, Han]]

==== Sure, Ma's boy-view of Mozart's 'Turkish March' ====
[[File:Sure, Ma's Version of 'Turkish March' in piano classroom for piano education.ogg|thumb|'Turkish March' - an old mysterious Turkey story in piano student (Jason's piano pupil) boy Sure, Ma's classroom edition. Thanks, this good teaching &amp; Learning result was selected by Tokfo/Vienna Gallery: https://commons.wikimedia.org/wiki/User:Tokfo/Vienna/2019_April_25-27 ]]
'''Further Comments for his first draft:'''
1. It's very difficult for a young boy to manage Turkish March's speed in a smooth way... He tried his best to keep it stable and unified, and almost did achieve it. (Turkish March is easily to make people play faster and faster until crazily broken. He tried to solve it by giving a slower beginning )  But, it's a little bit of too serious,afraid to touch wrong. Indeed, I heard his another time, in which he totally open himself and relax from nature... We could give him more hopes.
2. His melodic flow of scale-phrases (legato) are quite fluent and natural, which shows his scale-playing and fingering were quite great. But, a small break occurred around 1.14 to 1.17 minutes could be caused by the stiff right wrist (too tried) and no-good fingering design. He should frequently move second and third fingers in a much smarter way. To a young boy in his age, it should already be 'okay'.
3. When the theme occurred in the second time, it's better to give a dynamics-difference in contrast. My mother-Ms Song said: it's like an old story (sound) heard from a far distance to near somewhere - mysteriously. However, he gave a very tight connection, as if it was linked with the previous section. 
4. He tried his best to take the Worldwide difficult challenge - 'Broken-chordal Arpeggiated-octaves' (Around 2.00 to 2.14 minutes). I gave him a 'LIKE' that he had taken this challenge which even many pianists or teachers made some 'faults' as their heart pities - You can hear the edition of Romuald Greiss' in Wikipedia and several my previous times... However, this boy achieved it after many trainings time after time... Though later half one, compared with the beginning, might be in lower distinguishing degree, he didn't make any 'breaks', which comforted my teaching way so much. Thanks, boy Sure!
5. The final problem would occur in 'Alberti Bass' (left hand) of Coda part. Coming to it, you will feel easy to give up, which required more endeavors to control your hands in narrow and elaborate dealing way. He did it good, but lost in the counting of number (B111), and further, the connection with the final 'Square-opening Dance' (a small break). other things, such as the strength, are fine in his age.
6. In addition, I am planning to add a 'Turkish Stop' by a final pedaling. I didn't know whether he could, someday. 
Overall, I gave him an Excellent Comment. Hopefully, he will play better after better in his growth. [[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 14:13, 8 March 2019 (UTC)

'''Further Comments for his second draft:'''
1. As his teacher, I am very happy to hear several great designs we have made in classrooms can be achieved in the second draft, according to the background knowledge of 'Turkey March' I taught, such as the final 'Turkey Stop' (not really in modern piano, but a little bit similar) and the Bass-points-layer (simulating the military drum) beneath the long fast running scale-phrases of right hand (middle section)... Cool boy, thanks that you can remember your teacher's words! Congratulation!
2. Yes, right after the chance of Music library Report-performance in local we have made and getting back, you improved the edition's speed and fluency. You can evenly save 15 seconds, contrasted with before, which showed that your fingering &amp; running ability of hands had been greatly improved. However, the disadvantage is that it's easier to make some small motives uneven and rough (touching wrong notes) without purpose, which needs more your careful attention and exactness about details.
3. I knew you tried your best to face the peak challenge Mozart made to all people - making broken-progression of octaves message (middle part) and hearing out its hidden melodic lines. Great! However, it's still a little bit beyond your ability that its distinction with chords-effect weren't so clear. No matter, Sure boy, more exercises, it will be better.
In all, progressing soon which shows the potential, thanks to your performances1 There is still the developing zone waiting for you. 
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 15:08, 25 April 2019 (UTC)

==== Clever Girl Jia Xin's Clever view of Sir Bach's 3-parts Invention ====
'''Teacher's Demonstration for Future Development:''' 
[[File:3 Parts Invention 8th- from Sir Bach.ogg|thumb|3 Parts Invention 8th- from Sir Bach's BWV 794 – Sinfonia No. 8 in F major ]]
''' Jia Xin's Performance:'''
[[File:3-parts Invention No. 8 (F major) in piano-girl Jia Xin's view.ogg|thumb|3-parts Invention No. 8 (F major) in piano-girl Jia Xin's view]]
'''Comments of her first draft:'''
1. Totally, 3 parts are ranged in Bach's harmony, to a girl in her age - 12 years old. It's not easier to make so clear layers out. I was satisfied with this point, after heard every time; 
2. I can hear piano techniques for polyphonic &amp; counterpoint music like Bach's, such as cannon, intimation between two hands, up-climbing shoulder by shoulder, dialogues, long-notes down-pressed for different parts' SHE (sentence-head-enhancement), long-notes kept for parts' division and maintaining, fingering grouping in one hand for 2 parts, parts' continuously melting into one for the summarization, and..., Baroque ornamentation... mentioned for long. For those trainings, and further, the internalization into her own mind-analysis, we had searched information &amp; knowledge through Wikipedia, two more manuscripts, books and other webs online, further, spent classroom time to reason, analyse, train and fix note by note for long time... In this case, I gave her hard-working a 'Like' again; 
3. There would also be some problems regarding with recording pressure and her memory...: some big ones - left hand's relatively weak ability in managing two parts, small mistakes (like B18's f note played as sharp f - around 1.13 minute, B21's final g isn't raised there - around 1.23-1.24 minutes, and others...), small ornaments in a little bit of rough view and a much more graceful manner in Coda part. (sorry, to such a 12 years old girl, my suggestions could be so severe. But when listening, they are directly in my ears...) 
4. She did really pay her attention to Dynamics, but please better - lighter, smarter and more obviously...
5. The speed of later part is better than the slower earlier part. 
Overall, I also gave her an excellent comment for her performance (Live) in classroom. For further development, she can listen to my edition and the one in 'Inventions and Sinfonias (Bach)' - Wikipedia article (I thought it's great, but I didn't like too many speed-variations in Bach's works. It's better more reasonable: https://en.wikipedia.org/wiki/Inventions_and_Sinfonias_(Bach) )
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 07:33, 9 March 2019 (UTC)
==== Yixuan's piano-view and traveling landscapes ====
'''First view (only 9 years old) of Sir Bach's 2-parts Inventions'''

[[File:Bach 2-parts Invention, played by Yixuan Wang (Only 9 years old).ogg|thumb|Bach 2-parts Invention, played by Yixuan Wang (Only 9 years old)]]
'''Comments from teacher:'''
1. Musical parts and space-dimensions were much clearer than before, which reflected the little girl Yixuan's hard-working continuously after her piano examination...
2. I can hear the heads of musical sentences which were highlighted by each hand when required. I can also hear cannon-following, doubling and countermelody which were clearly shown into her performance. It's quite necessary for students in this age - 9 years old. In certain degree, she is already a good and careful student in piano.
3. Still, the controllability and the stability of hands, especially the turn of her 3rd, 4th and 5th fingers, need to be improved, which caused some small faults, such as 0.49-0.50 minutes (Bar 22) - a recovered B in right 3rd finger, 0.54-0.55 minutes (Bar 25) - 3rd, 4th &amp; 5th fingers of left hand, and a small disharmonic note - flatten B in the right hand - 0.32 (Bar 14)...
4. It's great that I can hear Baroque staccatos were in their graceful manners - like imperfect pearls required by its era. She almost did it...
5. Totally saying: it must be a very hard-job for a student in 9 years old to play Bach's 2-parts Invention. She bravely took up this life-task and successfully completed - this point should be affirmed. Congratulation! You can do more further...
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 02:28, 6 September 2019 (UTC)


'''MARIAGE D'AMOUR (Dreaming Wedding Ceremony) and its Educational Story:''' 

It's only no more than 2 weeks she did get the main techniques, after taking a Covid-19 Protection piano lesson and further test(Face-mask covering and breathe-prevention…).Then, she went back home and made a hard self-working exercise. Afterwards, around 10 days, this edition can come out. Why was she so keen on making it? She told me... One of her family's friends would like a piece of background music for his wedding ceremony, and they knew she was a good piano pupil.They invited her to take this task. She online self found out her long dreaming piece, and felt very happy for them. She thought only hard-working at home can realize this dream in this 'Hard Recovery Time'. She has beautifully taken this life-task for a very short time, and finally I could find a beautiful smile on her face... Though there were still some small faults in teacher's view, such as the biggest 1.02-1.03...
('''Problems:'''
Mentioned one is because of the distance of the Tenth-grasping is out of her hand-shape and ability in this age - rolling but touching a wrong note; In addition, the breathing of each sentence's tail somehow is with a longer responded break... Further, the Pedaling for the coherence from natural breathing need to improve; The final departing dropping notes were too noisy... which needs to be quiet,rit. and peaceful...), 
her hands' ability (especially the big chords-grasping, whole-viewing, locating, and sight-reading) was improved by her own endeavors (Maybe... subjects-divided examination-taking online through self-video-recording,in this special time, motivated her self-management...). This point made me feel happy... Hopefully, the friend of her family enjoyed their wedding ceremony with this own and LIVE background music, luckily as in a fantastic, peaceful and forever-lasting life-dream of happiness.

In future, Hoping: Yixuan, you can play this fantastic wedding song of piano (fluently and heart-touchingly) for more families and share their friendship, love and happiness...
Little girl pupil, thank you!^_^
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 01:55, 24 September 2020 (UTC)

[[File:CCzerny 299 Etude No. 27, Piano student Yixuan Wang, Tutor Jason Han.oggzerny 299 Etude No. 27, Piano student Yixuan Wang, Tutor Jason Han.ogg|thumb|
Czerny 299 Etude No. 27, Piano student Yixuan Wang, Tutor Jason Han.ogg]]
I have taught two children this Etude-a girl and also a boy (with outcomes). They played all well in very different musicalities. One is like a fast gym meeting 299's standards. The other-hers is with a good sound effect -light and peaceful after her grade examination. Both I all like. 
Regarding with how to train this sound effect with pedal, Please see my etudes'platform:
https://en.m.wikiversity.org/wiki/Portal:Piano_Etudes_as_Poems

'''G major Sonata L.349 - Yixuan Wang's New Attempt of Italian Baroque Style of A. Scarlatti'''
A. Scarlatti's Sonatas are quite hard for young students and young teenagers to train and perform.However, Yixuan is fine, I thought.
It needs a very fast &amp; light fingering of Scale &amp; Arpeggios and different STACCATOing keyboard-touching way, meanwhile, the exaggerating fluency of simple patterns... I thought she somehow had touched at her own little age. Just, more from nature, more details-care and the flexibility of hands&amp;body could make things better. 
At her age, it's already fine.Thanks to the recent striving in this still hard time of COVID-19 Recovery. [[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 02:31, 20 August 2021 (UTC)
[[File:G major Sonata L.349, Piano Pupil Yixuan, Wang.ogg|thumb|A, Scarlatti L.349 Sonata, Piano-pupil Yixuan, Wang]]

It's very hard to train Scarlatti's Italian Style of technique skills... However, Yixuan, Wang has never given up... 
during this COVID-19 Time...-Protecting herself with masks, meanwhile, playing times after times... Finally, we can get some senses of fast, airily,lightly and breezily... Yes, there may also be some problems, like- it's very easy to be stressful and breathless on the stage...But to her age, do you think it's already good... 
Therefore, I recorded it in a video and published it on a musical platform -Kugou, and a educational platform - Youku, as to remember her growth: 

http://m.kugou.com/mv/?hash=f00b36624f27b091b79e3f30e158aa03&amp;sruserid=640650901

====Piano Pupil Mo Zhou's Smart Growth and Hard-working learning of Techniques  ====

The video of Mo Zhou's most beautiful performance of Debussy's work- 2re Arabesque (I call it 'Butterfly's Dream') :
Kugou musical platform -
http://m.kugou.com/mv/?hash=547cb2c1e2f57a9e8ec66e8ecf36c269&amp;sruserid=640650901
Youku educational part -
http://v.youku.com/v_show/id_XNTgxNzA2Njk2MA==.html?x&amp;sharefrom=android&amp;sharekey=9631de9a76de1af3d601221019590cd26

(Published on the musical platform of Kugou and the educational part of Youku; the classroom volunteering photographer is Ms. Yang Gao) 

'''Piano Pupil Mo, Zhou's Violin simulation of Cremer's Etude's Art'''

Catching the hands' positions (somehow borrowed from voilin's) is almost the hardest point to train.One focuses on left hand's Notes-Slipping; the other regards with the interval Position-switching (2 notes) check of right hand frequently.
Though this little girl has a pair of smart&amp;slim hands, she attempted her best. You can hear the most part's effect LIVE in classroom...
In this point, I gave a 'LIKE'.

[[File:Cramer Etude, Performed by Piano Pupil Mo, Zou.ogg|thumb|Cramer Etude, Performed by Piano Pupil Mo, Zhou]]

'''A, Scarlatti L.349 Sonata - A Italian Style Taste of Baroque Music'''
''Comments:''
Mo,Zhou's hands are very smart, regarding with which some very tiny actions she can take, though they aren't quite big. Yes, she has been always willing to enlarge her hands.
This point, but somehow, associate her to take this Italian Baroque Style (Rocca) quite easy. 
Yes, I thought she was fine regarding with much more details.(though it's LIVE that very few unexpected faults could be caused by the stress of the recording).

I thought: to her performance, my teaching is working well. She did many requirements... Let us listen to her.[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 03:25, 20 August 2021 (UTC)
 

[[File:G major Sonata L.349, Piano pupil Mo, Zhou.ogg|thumb|File:G major Sonata L.349, Piano pupil Mo, Zhou.ogg]]

==== Brilliant Snow-ball boy (Yu) of Zhang family is praying for his father working in New Zealand ====
[[File:Pupil Yu,Zhang's edition - e minor sonata of Sir Haydn.ogg|thumb|E minor sonata of Sir Haydn was played by Piano student Yu, Zhang in classroom]]
'''(Waiting better)'''
Could you understand how hard Sir Haydn's &amp; Mozart's mature sonata-structuralism and Classical Countermelody (from String Quartet: https://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozart) were for the training of such a young boy or some students around this aget? Oh, looking back, I, myself, also did feel hard... However, this boy and another older piano sister did really insist on doing so. Today, they can give their own editions - very different with own personalities and natures. 
Another point I would like to say: It's only one week's time that this boy was fighting for 'a good hearing' of his father. Afterwards, a modified recording edition soon got out, which showed his proficiency and quality...Good boy!
To be honest, reviewing the past year, in order to train Sir Haydn's melody, we researched many ways together, including mathematics... Sometimes, evenly felt hopeless... Playing from childhood, Haydn's style is quite simple to me - models, switching, sonata structure..., but to students, they didn't quite like the sense of thinking being structured... And at the very beginning, I even didn't understand why they felt difficult... Recognizing something, We began to make many games, and evenly counting out some scores for the achievement of his 'fried chicken legs'...
Here, from rhythm to notation, and from melodic interaction to parts-division, I felt it's much clearer, more fluent and stable, than before... His ability of coordination has also been improved, though still some problems. I dared and felt confidential to say: it's a great edition of himself. Hopefully, he can progress further.
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 16:08, 4 April 2019 (UTC) Now, he made it much more fluent and accurate, and also played out his own fashion, though some details still need to be modified. Honestly to say, I thought somehow he got his progress in this period which we can hear...[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 03:28, 2 August 2019 (UTC)

'''Comments'''

It's the second time of piano boy Yu Zhang's teaching result show. In this time, he chose the melody &lt;Under the Sunshine&gt; - a Chinese fork teaching melody as one subject of national examination and also a performance of one piano competition in Dalian.
In my view as his teacher, he gave a very different view of this melody, compared with girls'. He paid more attentions to the whole view of melody's energy, strength, fluency and the joyfulness in Under the Sunshine, but didn't too much care about the details of some parts. However, on the stage, it showed a very great expression as from boy's situation... Good luck and happy experiment. After some practices, in the classroom we together recorded it and submit it up... (Referenced Partly from his page in Wikimedia Commons)


==== How to play Chinese Folk tune - 'Kids' Dance' with Chinese kids' fashion? Listen to little girl Kunlu's performance ====
'''Teacher's Demonstration in classroom:'''
[[File:Kid's Dance Chinese Folk Piano Player Jason M. C.,Han.ogg|thumb|Kid's Dance - 'Kid's Dance', from a folk piano-tune in China National Grading Book, was personally performed here, as a gift for all piano-kids' 'Happy 2019 Lucky Pig Year']]
'''Student Kunlu's Performance in classroom:'''
[[File:Kid's Dance (Chinese) - Student Kunlu, Han.ogg|thumb|Student Kunlu, Han's (Han family's girl born as bright as dewdrop in Kun - Saturn of Wuxing) good performance of Kid's Dance (Chinese)]]
'''Teacher's Comments:'''
Totally to say: Though She can play better editions (many better ones, last winter), in this sound file, she showed the coherence, fluency, flexibility and stability ( as Chinese fork-tune required). Hearing such a smart Chinese girl playing such a fugue-cannoning song, you will feel: it's a right song designing for a right girl... I think that's one meaning of piano-performance. Though spending much time, We did also research special 'Chinese supplemental positions &amp; Dialogues' in polyphony together, which gave us many beautiful memories... Further more, in this age, her staccatos, slurs and Tenuto have been performed quite well, which helped her to keep a unified speed to the end. 
Taking back a step, there must still be some small faults in classroom (without purposes) that I have to point out: such as B18's  #C blowing to D a little bit, the attention didn't get back in B41 head A which made a small break, and a small mistake of 'Recovered C' rather than #C... In order to dream of its accuracy and pentatonic harmony, it's a hard-working that we have already come over many problems and mistakes... Therefore, I think she fulfilled herself and achieved many things from 'Kid's Dance'. Hopefully, she enjoys the procedure of music-carving. [[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 15:07, 4 April 2019 (UTC)
===== Kunlu's Crystal Heart on International Children's Day -  Kleine Kinder Kleine Sorgen (Little Child) =====
'''Teacher's Comments:'''
1. The degrees of proficiency, fluency (and internal speed) have been improved, right on International Children's Day. 
2. I preferred her treble part very much - so cool, pure, clean and refreshing, which reflected her crystal heart in childhood.
3. The grasping of big chords - stronger, that's great - but needs to be more accurately and deep (The word 'deep' wasn't always 'loud' and 'heavy'). Please try to understand this point. Yes, it needs to show the hardness of growth (to young teenager), but also the achievement 'to be stronger and more confident of yourself...' [[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 03:32, 28 June 2019 (UTC)
[[File:Internationl Children&amp;#039;s Day Gifts - 2. Kleine Kinder Kleine Sorgen (Little Child, Piano-modification of Germany Song).ogg|thumb| Kleine Kinder Kleine Sorgen (Little Child, Piano-modification of Germany Song), played by Kunlu, Han]]

==== Teacher's Shares of his own home-works from childhood (Open) - Jason, Han====
====='''M. Moszkowsky Etude (Op.72 No.5) - &quot;C major's Fluency, Clarification, Sunshine and Love'''=====
New Beginning with...: M. Moszkowsky Etude (Op.72 No.5) played by Jixun Han (Jason) for piano teaching. It's long time that my piano classroom on the cloud in wikiversity hasn't update its situation. After so many things, now I can partly return to English writing world. The first Etude I would like to upload is still MM Edute which gave me so fluent and clean mind in my childhood. Oh, 38 years old, and after a wedding ceremony with my real lover, my fingers would not be so great as around 15s'... However, I would like to update its situation and new editions untill great someday. Now, let's began with this new melody. It's taught to my good Chinese boy pupil named Guoguo (fruit zeyu, Cui) when I grasped up and recorded. Yes, this little boy will also play well. Let's listen to my version, firstly. Thanks Jason M. C., Han (talk) 13:26, 20 November 2024 (UTC)

More information, please see https://en.wikipedia.org/wiki/List_of_compositions_by_Moritz_Moszkowski

Homework Requirements (challenges):

1. B23-B24(B stands for Musical Bar): By right hand, heads of every 4-notes group make a down-going semi-notes scale, which needs a very careful&amp;exact arpegio-fingering with a whole—palm holded and also thumb-measuring ability. Meanwhile, the left hand is making a whole-tenth measure, but arranged upon every  two chords' link. The semi-notes scale is also its fixed channel accordingly. This point is very different to follow and be made accurately and perfectly, which needs long-time training.

2. B49-50 It's almost a two-hands doubling for playing arpeggio-phrase.But not really!  You can watch the second phrase- fingering! Your left hand need a smallish shape. Meanwhile, the little finger's head of last phrase need to jump out a minor third distance down. It's very hard to control and also not a doubling.
(Hard for playing, but good for sounding, if out. Therefore, dears, have a try like mine...)
Yours little uncle Han [[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 14:15, 25 November 2024 (UTC) 
[[File:M. Moszkowsky Etude (Op.72 No.5) played by Jixun Han (Jason) for piano teaching.wav|thumb|M. Moszkowsky Etude (Op.72 No.5) played by Jixun Han (Jason) for piano teaching]]

===== '''Beethoven's Moonlight Sonata''' =====
Indeed, Beethoven left a historical challenge (difficulty) but the continuously creative inspiration to understand the techniques &amp; musicality of all his movements, equally to all people. We can attempt different approaches and own personal life-experiences to understand them, and discuss out some possible results.   
[[File:Moonlight Sonata - 3rd Movement of Sharp c minor Sonata Beethoven.ogg|thumb|Moonlight Sonata - 3rd Movement of Sharp c minor Sonata after a library presentation of Beethoven (Further, thanks to the April-collections of Tokfo Gallery (Vienna: https://commons.wikimedia.org/wiki/User:Tokfo/Vienna/2019_April_28-30) and Sir James Gallery (Bonn:https://commons.wikimedia.org/wiki/User:Sir_James/Bonn/2019_April_29) - great encouragements!)]]
'''3rd Movement- 'Moonlights Storming' - Techniques Analysis from Notation-reading ('Presto agitato' of Breitkopf &amp; Hartel Company and Berlin Arts Collage also compared with Old New York Edition - as the remembrance of one monitor):'''
'''Musicality:''' In a grandly general view, it's like...in a crazily running (very fast) race, viewed from the window, moonlights have been dismembered upon deep Lake Lucerne (many fragmental sections composed together). 
[[File:Vienna Beethoven Monument (with angels and children surrounding).jpg|thumb| Beethoven's Monument in Vienna]]
[[File:Beside Beethoven's Musicality.jpg|thumb| A third-person's Watching of Beethoven's Musicality]]
For its musicality cultivation, I could give a similar sense of its situation, like in Picasso's works- such as Picasso's Guernica (Ceridwen's Creative Commons Attribution-Share Alike 2.0 Generic license) For achieving it, a little bit of dark-moods anger and sadness faced from the unfairness and out of control could be inputted, after all technique points were trained in the dexterity. Therefore, from emotion to say, I thought the video right after getting back from UK and the lost one in Newcastle central station were better than this time. [[File:3rd movement of Sonata &amp;#039;Moonlight&amp;#039; Rocking Video JMC, Han (Jason).webm|thumb|3rd movement of moonlight sonata; Rocking Video JMC, Han (Jason)]] However, I satisfied with it, right like in life and after the presentation. From this point, we can see: Beethoven, as a piano master, has super-reached too much before the time - even abstractionism and postmodernism (deconstructionism).
'''2nd Movement - 'a little Fantasy Moonflower blooming between two rocky layers' - Techniques Analysis from Notation-reading (Allegretto of Breitkopf &amp; Hartel Company and Berlin Arts Collage):'''
1. Parts-distinguishing way can be applied to pick up the main melodic points from its background and legato them into lines. 
'''( Notice: Here, from the historical observation, a thing needs to be clarified: Baroque-regression (back-reasoning) was usually made by classical composers (in Vienna school: Mozart, Haydn and Beethoven etc.), especially in their later years of life for calming down the dramatical emotions, and keeping Life's Reasonability. Meanwhile, from Haydn, they discussed and created classical counterpoints from symphony and string quartet together, to modify creative inspirations. Beethoven also inherited it. Therefore, when we play some in piano, we need to analyse and apply some special techniques, commonly used in classical polyphony, to pick up the main from the background, sentence by sentence, as an era-responding.)[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 03:38, 15 May 2019 (UTC)'''
2. Octaves-bridging and chords-connections for big hands, into their hidden melodies, are the most difficulties, which need your frequent exercises, sentence by sentence. (Painful but worthful! Finally, flexible and skillful... )
3. Long keeping-notes, in certain parts, are important for the continuity of the tune and the texture, without broken.
4. It's better in light and tender keyboard-touching way to make melodic lines clear and 'the little flower' smile lightly.
5. 'Rondo' (ABA) formation can be applied to understand its repetitions, responding and structure.    
[[File:Moonlight Sonata (Sharp c minor Sonata) 2nd Movement Beethoven JMC,Han.ogg|thumb|Moonlight Sonata - a little fantasy flower between two rocky layers]][[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 14:51, 14 May 2019 (UTC)
=====  Blue Danube is always flowing from heart and life, with the vitality as spring: =====
Children and young teenagers, let us swim in this life-long river, to see some beautiful landscapes!
[[File:Blue Denube in my heart.jpg|thumb|Blue Denube in my heart]]
[[File:Blue Danube (Exercise and variations-collections in piano) JMC, Han.ogg|thumb|Blue Danube (Exercise and variations-collections in piano) JMC, Han]]
=====  Pachelbel's Canon is always the canon (polyphonic technique) since Baroque Era, but in '''Modern Piano's Pop Variations''' =====
[[File:Pachelbel&amp;#039;s Canon in Pop Variations (Geoge Winston Notation) Player Jason, Han.ogg|thumb| Pachelbel's Canon in Pop Variations (George Winston Notation) Player Jason, Han]]
'''Story of teaching &amp; learning (from Wikimedia Commons):'''
Regarding with this piano melody, there is a long story in my heart... Oh, did you hear Mag-pie's singing (I like 'pie' in the tail of this word) in the first draft? Yes, it was attracted and landing on the tree outside my balcony... You can clearly hear it at the beginning and in the tail in my first draft... Almost, it would like to share my memory...

Long long ago, my old brother on my mother's side used to be one hero of my life and fashion... On each holiday, he was always able to find great music pieces, MTVs, transcripts , and scientific fictions, from foreign countries, such as American and Japan (Summer)... and brought &amp; shared with me... Then, I attempted my best to exercise them into the reality, which included this song - Canon Variations from pianist George Winston... Those memories have never faded out, but in my deep sea. To now, evenly did I think Canon was from US and a POP song... After seeking the exact information in Wikipedia, I found it's Pachelbel's Canon in D and Baroque Era and German, rather than C and Modern and Pop in American... and with a 'Gigue for Violins and Basso Continuo',  it's not only for piano in many parts than our 3 parts in original piano edition. However either, I still like it very much and would like call it American POP in my music world...

Then after, a male colleague in my working college said to me: Jason, on my wedding ceremony, I would like to play it for a girl... Could you give me a simple one? Then, searching online, I found a simple (middle level) notation and an original (advanced level) notation, I downloaded both, and chose the simple one for him Three months, he was able to play it from 0 level (he wasn't able to read the notation)... I thought piano would have give him a good memory of wedding...

Following, I found a girl felt bored about her piano examination... Then, by choosing the simple transcript and inserting into her lessons... it made my tutoring classrooms really beautiful, relaxable, magical and peaceful... 

Now, I have time to play the original edition out... One long dream of my heart is going to be fullfilled... Though my hands in several points didn't make my perfectionism satisfied contrasted with before, especially the tenth-cross design between the left hand and the right hand, I knew it's my life, and fate?... I prefered to update its situations for bettering continuously... if having time...

Compared with the firstly draft, I thought the second was much down-calmed and peaceful...Somehow, I preferred the first draft, but a little bit of 'fast'... I cannot make the decision...then, kept two. However either, I still felt very happy the little natural friend - mag-pie can join... For this reason, I kept it. Hopefully, you will enjoy...
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 04:50, 16 September 2019 (UTC)
===== KV.265 12 Variations on Ah vous dirai-je, Maman - 'Twinkle Twinkle Little Star' =====
Analysis (Waiting)
[[File:KV.265 12 Variations on Ah vous dirai-je, Maman Mozart JMC, Han.ogg|thumb|KV.265 12 Variations on Ah vous dirai-je, Maman Mozart JMC, Han]]
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 08:43, 7 October 2019 (UTC)
=====''' 'The beautiful views of Scotti-highlands' from Thompson's Book (Advanced Level) - Teaching and demonstration '''=====
[[File:The beautiful views of Scotti-highlands (Teaching demonstration - video; Jason, Han).webm|thumb| After the performance in local Crossing-year 2019-2020 Library Concert and many further exercises, a good edition in classroom got out - Piano kids, always, you knew:  No pains, No gains]]
For its musicality and academic thoughts, please visit Wikiverty's Portal of Piano education(The Section: The beautiful views of Scotti-highlands' in a Far-land Home (Academic thoughts, musicality, literature-writing and case-realization)):
*[[Portal:Green Sleeves (Impressionist Visualization)]]
*[[Portal: Sir J.S.BACH and His contributions to Piano Kids' Reasonable Life]]
[[File:C minor Prelude Bach (BWV847), Performer JMC, Han.wav|thumb|C minor Prelude Bach (BWV847)]]

==== 'Swan's Dream Upon the lake' - Little Girl  'Wenxin's' (Brilliant &amp; Sweet literatures in arts ) Performance====
'''Teacher's Demonstration:''' 
[[File:The Dying Swan - black angel JMC Han.ogg|thumb| Musicality from watching 'The Dying Swan - the black angel', performed by JMC Han]]
'''Wenxin's Performance:''' 
1. Techniques-recovery: The Arpeggio-training of left hand in the accompaniment was the biggest challenge to not only a piano-child at her age - no more than 12 (In Chinese culture, Kid's first year was in mother's womb. Thereby, I asked her - how old are you, and she gave the number '13'...),  to me and evenly some expertise pianists. (Camille Saint-Saëns's 'The Swan' on wikipedia or other social editions). The arpeggio-accompaniment is travelling in rich variations of tunes, which caused left hand much harder to expand, shrink and positions-change. Therefore, it spent us more than half a year to train and recover her hand's dexterity from a small failure of her piano life in the Grade Test, just like 'Princess Swan's' experience. Now, totally to say, she got an excellent situation in which children at her age can perform. Thanks to your hard-working!  
2. Musicality-cultivation: Usually, she showed a very great musicality in the first page - to the minute (Approximately 1.05) - tender, expending, lyrical and expressive... However, it's really a hardness to keep it throughout the second section - a shading &amp; wandering heart-road in the growth. The attention has to be paid too much on the exactness of left hand's arpeggio-travelling. With a pity, still, some notes were beaten wrongly. But oppositely again, we can see: Princess Swan, in her period of Darkness growth - facing Satan, turning into a dark angel and only appearing in night... She really faced a hardness and the difficulty of life, right as beating wrong notes, getting out some noises and travelling a little bit slowly and roughly in a channel. In this view, perhaps that the difficulties can be transformed- in the musical needs and with a small fashion. Congratulation, more exercises, haha!
3. Together, we gave two great designs: one is the 'Big Brightness' began from the minute (Approximately 2.03) when the main theme happens again; and the other is 'Swan's Departure like Sound of Fall-Leaves rotating upon Lake's Surface' (from minute 2.49 to the end)... She almost achieved some - the mood calmed down very much and stably progressed to further with a confidence. However, a little bit of disfluency made the impression fade, somehow. Meanwhile, a 'rit. to a tempo' turned inversely - what a pity. 

Totally to say, musicality, at her age, was preciously showing in this time's performance. The hard-working of recovery and exercises, during many classes, touched my heart very much. (I knew that...)  More trainings of Arpeggio-running (dominate sevenths) and its fluency can help her achieve more in the future. Wenxin, thanks to you for letting us appreciate this world-famous melody in piano.     
 
[[File:Growth of Swan in eyes of the little girl - Wenxi, Zhang.ogg|thumb|Growth of Swan in the eyes of the little girl - Wenxi, Zhang]]
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 16:06, 5 May 2019 (UTC)
==== Listen to Mother's Old Story! - A beautiful and quiet little girl's Good Wish ====
'''Teacher's Demonstration:'''
[[File:Mother&amp;#039;s Old story - China Impression.ogg|thumb| Listen to Mother's Old story - China Impression (JMC, Han - teacher's domenstration)]]
'''Student's Performance:'''
[[File:Listen to Mother&amp;#039;s Old Story - Piano Pupil Yiwen, Cui.ogg|thumb| Listen to Mother's Old Story- Piano Pupil Yiwen, Cui]]
'''Teacher's Comments:'''
Yiwen, Cui (Direct translation of her Chinese name - A beautiful girl who is good at the translation of art and literature, from Cui family), at the age of 10, is a quite and beautiful girl. She got a good life effect from this Chinese piano-kid's song - 'Listen to Mother's Old Story': making her family and parents happy, getting some confidences through this piano song from the examination, showing her fashion in my library concert held for piano kids... After those more above, frequent exercises, and getting her permission, I can submit this classroom-recording edition. Though in the tail I found a note lost... and some parts of her left hand might run much more fluently... , I think her emotional background of this music reached to a good level, and those polyphonic parts can be clearly heard two layers, their cannoning, and so on... Congratulation! 
'''(Words from the description in Wikimedia Commons page)'''
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 01:04, 8 August 2019 (UTC)

==== Moonlight upon Lotus Pool (Summer) - Letters-Accompaniment Improvising Chinese Pop-song with both Classical Tradition and Pentatonic Scale ====

'''Teacher's Comment:'''
1. I am very excited that you (only 10-years-old) understood Letter-To-Accompaniment Improvising sheet and its approach in a very fast way.
2. It's great you can use both Pentatonic Arpeggios and Tenth-Rolling-Bass-dropping in your accompaniment (You can make Tenth-rolling Bass in a more fluent view, I thought) 
3. We can feel the musical scene from your musicality - In a beautiful summer night, Walking along a lotus pool, you and your family members were enjoying the moonlight and a breeze of cool wind...  
4. In future, hopefully, you can improve your 'new learns' to a higher level.
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 01:04, 8 August 2019 (UTC)

''' Xuan, Lee's Second Attempt - Pearl of the Orient'''

==== 'Mother in the candlelight' - A little girl (Siqi)'s heart-words for her mother's birthday - in the growth and in the dreams...  ====

'''Heart-story:'''
Regarding with this piano-song, there is a little story about this little commons' girl: Usually, her parents were very busy in the family's restaurant... I and my mother saw she had independently managed herself well and grew up alone for many years... In this year - 2019, time was near her mother's birthday. In the KTV (a place like karaoke bar, but for small single groups of people in rooms, with TV in the middle for singing ), she heard this song - 'Mother in the candlelight' and found her parents enjoyed singing it very much. Then, she decided to play it as a gift to her mother, right on mother's birthday. It's my biggest honour to be together sight-reading the notation, making the re-designs and re-editions of this song into piano - like, Prelude, Introduction-theme 1st, theme 2nd, Development and Peak, a small Repetition and Coda... She learnt in a very fast and hard-working way that merely around one month she played it in this level. And finally, she got her heart-sweet - playing it for her mother, as a birthday gift.(Wikimedia Commons' original page, 2019)

'''Comments from teacher:'''
1. The musical emotions were very rich and expressive, especially the 'Peak-Calling for mother' (2.53 minutes - 3.53 minutes). I almost can hear 'Mum...' (or Mumu...) for many times in a kid's tear-drops and in the candlelight... by your right hand's touchable singing...
2. I liked our 'Flanger tr. Ornaments' very much (I thought it's from Mozartian). I am very happy you can put it in for soon time...
3. I am very happy in the Coda-tail, you can get my suggestion - ending by a Major Seventh Progression-Arpeggio. This point should give the thanks to my mentor - Ray. I quite enjoy its special colour... 
4. Your strong and mixed left hand accompaniment must have been trained for many times. I knew it's a hard-working job, but tender and flexible a little bit... better?
5. The singing of right hand and its 'breathing' were quite natural and fine, sentence by sentence..., but the total speed is too slower than normal, which reflect the running ability of the left hand needed to improve. I knew: to your 9-years-old hands, it's a very hard requirement... However,  waiting the up-grown, I have the confidence you can hands-sing it in a much more fluent way...
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 14:10, 5 September 2019 (UTC)

'''Night's Piano-Song - The depth of China Pop-Piano (and Siqi's Heart-Try)'''
''Comments:''
She made the depth of two peak notes but in light touching way. I thought also that she did this Pop-piano's musicality in a poet's Night-thinking... 
She is suitable for the performance of this-type-'songs' and improvising (still at little age and need to prepare in time).
Let us listen to her and feel her expression.

==== The Cowherd's Flute played by a little girl piano pupil - Guo Guo (Nickname: Happy fruits)  ====
This edition has already been her best attempt, regarding with its landscape-painting style, lovely Cowherd's Flute we can refer to Wikipedia introduction (Seeking key words 'The Cowboy's Flute' in). It's recorded as a beautiful memory of her piano-learning and her Childhood. Let us listen to her:
[[File:The Cowboy&amp;#039;s Flute - Yuxuan, Lu (Guo Guo).ogg|thumb|The Cowherd's Flute - Yuxuan, Lu (Guo Guo)]]

====  Clementi Sonata Op35 No. 5 (Movement 1st), played by Piano pupil Yixuan, Qiao ====
Clementi's Sonata-Op35 No. 5 was a so long and difficult piece for students around their ninth year. Therefore, we have divided it into many small sections and taught. She learnt in progress. Meanwhile, this little and beautiful girl (She was beautifully good at dancing, somehow rather than piano.) has already attempted her best in exercising and recording. I thought it recorded her good piano-learning experiences and those memories of childhood. Regarding with further information about this work, please refer to the educational portal: https://en.wikiversity.org/wiki/Portal:Sonatinas_from_Kids%27_corner_near_heaven#Muzio_Clementi . Let us listen to her:
[[File:Clementi Sonatina Op35. No 5 Movement 1st Piano pupil YIxuan, Qiao.ogg|thumb|Clementi Sonatina Op35. No 5 Movement 1st Piano pupil YIxuan, Qiao]]
[[User:Jason M. C., Han|Jason M. C., Han]] ([[User talk:Jason M. C., Han|discuss]] • [[Special:Contributions/Jason M. C., Han|contribs]]) 02:42, 18 October 2019 (UTC)

====Little and Little, Twinkling Stars - Little Piano-Kids' Playground====
Say 'Hello' to our 'Little Goldman'
[[File:Vienna Trip - The Little Goldman- Strauss Family.jpg|thumb|Hand-making my  own picture of Strauss Family's Little Goldman]]
* [[Portal:Little and Little, Twinkling Stars - Little Piano-Kids' Playground| Little and Little, Twinkling Stars - Little Piano-Kids' Playground]]</text>
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  <page>
    <title>Social Victorians/People/Bourke</title>
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      <text bytes="54184" sha1="gkk7fap114nyv77jbj63k8vjsd3cqmo" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
* Mrs. Guendoline Bourke
* Lady Florence Bourke
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father.

== Overview ==
Although the Hon. Algernon Henry Bourke was born in Dublin in 1854 and came from a family whose title is in the Peerage of Ireland,&lt;ref name=&quot;:6&quot;&gt;1911 England Census.&lt;/ref&gt; he seems to have spent much of his adult life generally in England and especially in London.

Mrs. Guendoline Bourke was a noted horsewoman and an excellent shot, exhibited at dog shows successfully and was &quot;an appreciative listener to good music.&quot;&lt;ref&gt;&quot;Vanity Fair.&quot; ''Lady of the House'' 15 June 1899, Thursday: 4 [of 44], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004836/18990615/019/0004.&lt;/ref&gt; She was reported as attending many social events without her husband, usually with a quick description of what she wore.

The Hon. Algernon Bourke and Mr. Algernon, depending on the newspaper article, were the same person. Calling him Mr. Bourke in the newspapers, especially when considered as a businessman or (potential) member of Parliament, does not rule out the son of an earl.

== Acquaintances, Friends and Enemies ==

=== Mr. Algernon Bourke ===

* [[Social Victorians/People/Montrose|Marcus Henry Milner]], &quot;one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys&quot;&lt;ref name=&quot;:8&quot;&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 2a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;
* Caroline, Duchess of Montrose — her &quot;legal advisor&quot; on the day of her marriage to Marcus Henry Milner&lt;ref&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 1b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;

== Organizations ==

=== The Hon. Algernon Bourke ===
* Eton
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Stock Exchange
* Willis's Rooms&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;
*One of the directors, the Franco-English Tunisian Esparto Fibre Supply Company, Ltd.&lt;ref&gt;''Money Market Review'', 20 Jan 1883 (Vol 46): 124.&lt;/ref&gt;
*One of the directors, the Frozen Lake, Ltd., with Admiral Maxse, Lord [[Social Victorians/People/Beresford|Marcus Beresford]], [[Social Victorians/People/Williams|Hwfa Williams]]&lt;ref&gt;&quot;The Frozen Lake, Limited.&quot; ''St James's Gazette'' 08 June 1894, Friday: 15 [of 16], Col. 4a [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/18940608/085/0015. Print p. 15.&lt;/ref&gt;
*[[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)

=== Mr. Algernon Bourke ===

* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt;

== Timeline ==
'''1872 February 8''', Richard Bourke, 6th Earl of Mayo was assassinated while inspecting a &quot;convict settlement at Port Blair in the Andaman Islands ... by Sher Ali Afridi, a former Afghan soldier.&quot;&lt;ref&gt;{{Cite journal|date=2024-12-01|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo.&lt;/ref&gt; The Hon. Algernon's brother Dermot became the 7th Earl at 19 years old.

'''1876 November 24, Friday''', the Hon. Algernon Bourke was one of 6 men (2 students, one of whom was Bourke; 2 doctors; a tutor and another man) from Cambridge who gave evidence as witnesses in an inquest about the death from falling off a horse of a student.&lt;ref&gt;&quot;The Fatal Accident to a Sheffield Student at Cambridge.&quot; ''Sheffield Independent'' 25 November 1876, Saturday: 7 [of 12], Col. 5a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000181/18761125/040/0007. Print title: ''Sheffield and Rotherham Independent'', n. p.&lt;/ref&gt;

'''1884 May 3, Saturday''', the &quot;Rochester Conservatives&quot; announced that they would &quot;bring forward the Hon. Algernon Bourke, brother of Lord Mayo, as their second candidate,&quot;&lt;ref&gt;&quot;Election Intelligence.&quot; ''Yorkshire Gazette'' 03 May 1884, Saturday: 4 [of 12], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000266/18840503/011/0004.&lt;/ref&gt; but because he could not be the first candidate, Bourke declined.&lt;ref&gt;&quot;Rochester.&quot; London ''Daily Chronicle'' 09 May 1884, Friday: 3 [of 8], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/18840509/049/0003.&lt;/ref&gt;

'''1884 June 18, Wednesday''', Mr. Algernon Bourke was on a committee to watch a [[Social Victorians/Timeline/1884#18 June 1884, Wednesday|Mr. Bishop's &quot;thought-reading&quot; experiment]], which was based on a challenge by Henry Labourchere made the year before. This &quot;experiment&quot; took place before a fashionable audience.

'''1885 October 3, Saturday''', the Hon. Algernon Bourke was named as the Conservative candidate for Clapham in the Battersea and Clapham borough after the Redistribution Bill determined the electoral districts for South London.&lt;ref&gt;&quot;South London Candidates.&quot; ''South London Press'' 03 October 1885, Saturday: 9 [of 16], Col. 5b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18851003/096/0009. Print p. 9.&lt;/ref&gt; The Liberal candidate, who won, was Mr. J. F. Moulton.

'''1886 July 27, Tuesday''', Algernon Bourke attended a service honoring a memorial at St. Paul's for his father, who had been assassinated.&lt;ref&gt;&quot;Memorial to the Late Earl of Mayo.&quot; ''Northern Whig'' 28 July 1886, Wednesday: 6 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000434/18860728/143/0006. Print p. 6.&lt;/ref&gt;

'''1886 September 2, Thursday''', Mr. Algernon Bourke was part of a group of mostly aristocratic men taking part in [[Social Victorians/Timeline/1886#8 September 1886, Wednesday|a &quot;trial-rehearsal&quot; as part of Augustus Harris's production]] ''A Run of Luck'', about sports.

'''1886 October 2, Saturday''', the Duke of Beaufort and the Hon. Algernon Bourke arrived in Yougal: &quot;His grace has taken a residence at Lismore for a few weeks, to enjoy some salmon fishing on the Blackwater before the close of the season.&quot;&lt;ref&gt;&quot;Chippenham.&quot; ''Wilts and Gloucestershire Standard'' 02 October 1886, Saturday: 8 [of 8], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001955/18861002/142/0008. Print p. 8.&lt;/ref&gt;

'''1887 December 15''', Hon. Algernon Bourke and Guendoline Stanley were married at St. Paul's, Knightsbridge, by Bourke's uncle the Hon. and Rev. George Bourke. Only family members attended because of &quot;the recent death of a near relative of the bride.&quot;&lt;ref&gt;&quot;Court Circular.&quot; ''Morning Post'' 16 December 1887, Friday: 5 [of 8], Col. 7c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18871216/066/0005.&lt;/ref&gt;

'''1888 July 26''', [[Social Victorians/People/Montrose|Caroline Graham Stirling-Crawford]] (known as Mr. Manton for her horse-breeding and -racing operations) and Marcus Henry Milner married.&lt;ref name=&quot;:12&quot;&gt;&quot;Hon. Caroline Agnes Horsley-Beresford.&quot; {{Cite web|url=https://thepeerage.com/p6863.htm#i68622|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt; According to the ''Nottingham Evening Post'' of 31 July 1888,&lt;blockquote&gt;LONDON GOSSIP.

(From the ''World''.)

The marriage of &quot;Mr. Manton&quot; was the surprise as well the sensation of last week. Although some wise people noticed a certain amount of youthful ardour in the attentions paid by Mr. Marcus Henry Milner to Caroline Duchess of Montrose at '''Mrs. Oppenheim's ball''', nobody was prepared for the sudden ''dénouement''; '''and it''' were not for the accidental and unseen presence [[Social Victorians/People/Mildmay|a well-known musical amateur]] who had received permission to practice on the organ, the ceremony performed at half-past nine on Thursday morning at St. Andrew's, Fulham, by the Rev. Mr. Propert, would possibly have remained a secret for some time to come. Although the evergreen Duchess attains this year the limit of age prescribed the Psalmist, the bridegroom was only born in 1864. Mr. &quot;Harry&quot; Milner (familiarly known in the City as &quot;Millions&quot;) was one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys, and Mr. Algernon Bourke, the head of the house (who, of course, takes a fatherly interest in the match) went down to Fulham to give away the Duchess. The ceremony was followed by a ''partie carrée'' luncheon at the Bristol, and the honeymoon began with a visit to the Jockey Club box at Sandown. Mr. Milner and the Duchess of Montrose have now gone to Newmarket. The marriage causes a curious reshuffling of the cards of affinity. Mr. Milner is now the stepfather of the [[Social Victorians/People/Montrose|Duke of Montrose]], his senior by twelve years; he is also the father-in-law of [[Social Victorians/People/Lady Violet Greville|Lord Greville]], Mr. Murray of Polnaise, and [[Social Victorians/People/Breadalbane|Lord Breadalbane]].&lt;ref name=&quot;:8&quot; /&gt;&lt;/blockquote&gt;'''1888 December 1st week''', according to &quot;Society Gossip&quot; from the ''World'', the Hon. Algernon Bourke was suffering from malaria, presumably which he caught when he was in South Africa:&lt;blockquote&gt;I am sorry to hear that Mr. Algernon Bourke, who married Miss Sloane-Stanley a short time ago, has been very dangerously ill. Certain complications followed an attack of malarian fever, and last week his mother, the Dowager Lady Mayo, and his brother, Lord Mayo, were hastily summoned to Brighton. Since then a change for the better has taken place, and he is now out of danger.&lt;ref&gt;&quot;Society Gossip. What the ''World'' Says.&quot; ''Hampshire Advertiser'' 08 December 1888, Saturday: 2 [of 8], Col. 5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18881208/037/0002. Print title: ''The Hampshire Advertiser County Newspaper''; print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;'''1889 – 1899 January 1''', the Hon. Algernon Bourke was &quot;proprietor&quot; of White's Club, St. James's Street.&lt;ref name=&quot;:9&quot;&gt;&quot;The Hon. Algernon Bourke's Affairs.&quot; ''Eastern Morning News'' 19 October 1899, Thursday: 6 [of 8], Col. 7c [of7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001152/18991019/139/0006. Print p. 6.&lt;/ref&gt;

'''1889 June 8, Saturday''', the Hon. Algernon Bourke contributed some art he owned to the collection of the Royal Institute of Painters in Water-Colours' [[Social Victorians/Timeline/1889#8 June 1889, Saturday|exhibition of &quot;the works of the 'English Humourists in Art.'&quot;]]

'''1892''', the Hon. Algernon Bourke privately published his ''The History of White's'', the exclusive gentleman's club.

'''1893 February 11, Tuesday''', Algernon Bourke opened Willis's Restaurant:&lt;blockquote&gt;Mr. Algernon Bourke has in his time done many things, and has generally done them well. His recently published history of White's Club is now a standard work. White's Club itself was a few years ago in its agony when Mr. Bourke stepped in and gave it a renewed lease of life. Under Mr. Bourke's auspices &quot;Willis's Restaurant&quot; opened its doors to the public on Tuesday last in a portion of the premises formerly so well known as Willis's Rooms. This new venture is to rival the Amphitryon in the matter of cuisine and wines; but it is not, like the Amphitryon, a club, but open to the public generally. Besides the restaurant proper, there are several ''cabinets particuliers'', and these are decorated with the very best of taste, and contain some fine portraits of the Georges.&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Letter from the Linkman.&quot; ''Truth'' 20 April 1893, Thursday: 25 [of 56], Col. 1a [of 2]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025# https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025]. Print p. 855.&lt;/ref&gt;&lt;/blockquote&gt;'''1893 November 30, Thursday''', with Sir Walter Gilbey the Hon. Algernon Bourke &quot;assisted&quot; in &quot;forming [a] collection&quot; of engravings by George Morland that was exhibited at Messrs. J. and W. Vokins’s, Great Portland-street.&lt;ref&gt;&quot;The George Morland Exhibition at Vokins's.&quot; ''Sporting Life'' 30 November 1893, Thursday: 4 [of 4], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000893/18931130/058/0004.&lt;/ref&gt;

'''1895 February 23, Saturday''', the Hon. Algernon Bourke attended the [[Social Victorians/Timeline/1895#23 February 1895, Saturday|fashionable wedding of Laurence Currie and Edith Sibyl Mary Finch]].

'''1895 August 24, Saturday''', &quot;Marmaduke&quot; in the Graphic says that Algernon Bourke &quot;opened a cyclists' club in Chelsea.&quot;&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Court and Club.&quot; The ''Graphic'' 24 August 1895, Saturday: 11 [of 32], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18950824/017/0011. Print p. 223.&lt;/ref&gt;

'''1895 October''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#24 October 1902, Friday|opened the Prince's ice-skating rink for the season]].

'''1896 June 29, Monday''', Algernon Bourke published a letter to the editor of the ''Daily Telegraph'':&lt;blockquote&gt;To the Editor of “The Daily Telegraph.”

Sir — Permit me to make my bow to the public. I am the manager of the Summer Club, which on two occasions bas been the subject of Ministerial interpellation in Parliament. The Summer Club is a small combination, which conceived the idea of attempting to make life more pleasant in London by organising breakfast, luncheon, and teas in Kensington Gardens for its members. This appears to have given offence in some way to Dr. Tanner, with the result that the catering arrangements of the club are now &quot;by order&quot; thrown open to the public. No one is more pleased than I am at the result of the doctor's intervention, for it shows that the idea the Summer Club had of using the parks for something more than mere right of way bas been favourably received. In order, however, that the great British public may not be disappointed, should they all come to lunch at once, I think it necessary to explain that the kitchen, which by courtesy of the lessee of the kiosk our cook was permitted to use, is only 10ft by 5ft; it has also to serve as a scullery and pantry, and the larder, from which our luxurious viands are drawn, is a four-wheeled cab, which comes up every day with the food and returns after lunch with the scraps. Nevertheless, the Summer Club says to the British public — What we have we will share with you, though it don't amount to very much — I am, Sir, your obedient servant,

ALGERNON BOURKE.

White's Club, June 27&lt;ref&gt;&quot;The Summer Club.&quot; ''Daily Telegraph &amp; Courier'' (London) 29 June 1896, Monday: 8 [of 12], Col. 2b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18960629/072/0008. Print title: ''Daily Telegraph'', p. 8.&lt;/ref&gt;&lt;/blockquote&gt;'''1896 July 4, Saturday''', &quot;Marmaduke&quot; in the ''Graphic'' took Bourke's side on the Summer Club in Kensington Park:&lt;blockquote&gt;Most of us have noticed that if we read in the newspapers the account of some matter which we are personally acquainted with the account will generally contain several errors. I have also noticed that when a question is asked in the House of Commons regarding some matter about which I know all the facts the question and the official answer to it frequently contain serious errors. Last week Mr. Akers-Douglas was asked in the House to explain how it was that Mr. Algernon Bourke obtained permission to open the &quot;Summer Club&quot; in Kensington Gardens, and he was questioned upon other particulars connected with the same matter. Both the questions and the official reply showed considerable ignorance of the facts. There has been from time immemorial a refreshment kiosk in Kensington Gardens. Mr. Bourke obtained from the tenant of this permission to use the kitchen for the benefit of the &quot;Summer Club,&quot; and to supply the members of the latter with refreshments. It was a purely commercial transaction. Mr. Bourke then established some wicker seats, a few tables, a tent, and a small hut upon a lawn in the neighbourhood of the kiosk. To do this he must have obtained the permission of Mr. Akers-Douglas, as obviously he would otherwise have been immediately ordered to remove them. Mr. Akers-Douglas equally obviously would not have given his sanction unless he had been previously informed of the objects which Mr. Bourke had in view — to wit, that the latter intended to establish a club there. That being the case, it is difficult to understand for what reason Mr. Akers-Douglas has now decided that any member of the public can use the chairs, tables, and tent belonging to the &quot;Summer Club,&quot; can insist upon the club servants attending upon him, and can compel them to supply him with refreshments. Mr. Akers-Douglas should have thought of the consequences before he granted the permission.&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Court and Club.&quot; The ''Graphic'' 04 July 1896, Saturday: 14 [of 32], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18960704/029/0014. Print p. 14.&lt;blockquote&gt;&lt;/blockquote&gt;&lt;/ref&gt;&lt;/blockquote&gt;'''1896 August 10, Monday''', the Morning Leader reported that the Hon. Algernon Bourke, for the Foreign Office, received Li Hung Chang at St. Paul's:&lt;blockquote&gt;At St. Paul's Li Hung was received by Field-Marshal Simmons, Colonel Lane, the Hon. Algernon Bourke, of the Foreign Office (who made the necessary arrangements for the visit) and Canon Newbolt, on behalf of the Dean and Chapter. A crowd greeted Li with a cheer as he drove up in Lord Lonsdale’s striking equipage, and his Excellency was carried up the steps in an invalid chair by two stalwart constables. He walked through the centre door with his suite, and was immediately conducted by Canon Newbolt to General Gordon’s tomb in the north aisle, where a detachment of boys from the Gordon Home received him as a guard of honor.

Li inspected the monument with marked interest, and drew the attention of his suite to the remarkable likeness to the dead hero. He laid a handsome wreath of royal purple asters, lilies, maidenhair fern, and laurel, tied with a broad band of purple silk, on the tomb.

The visit was not one of inspection of the building, but on passing the middle aisle the interpreter called the attention of His Excellency to the exquisite architecture and decoration of the chancel. Li shook hands in hearty English fashion with Canon Newbolt and the other gentlemen who had received him, and, assisted by his two sons, walked down the steps to his carriage. He returned with his suite to Carlton House-terrace by way of St. Paul’s Churchyard, Cannon-st., Queen Victoria-st., and the Embankment.&lt;ref&gt;&quot;At St. Paul's.&quot; ''Morning Leader'' 10 August 1896, Monday: 7 [of 12], Col. 2b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18960810/134/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;'''1896 August 19, Wednesday''', the ''Edinburgh Evening News'' reported on the catering that White's Club and Mr Algernon Bourke arranged for the visiting Li Hung Chang:&lt;blockquote&gt;It is probably not generally known (says the &quot;Chef&quot;) that Mr Algernon Bourke, manager of White's Club, London, has undertaken to the whole of the catering for our illustrious visitor front the Flowery Land. Li Hung Chang has five native cooks in his retinue, and the greatest good fellowship exists between them and their English ''confreres'', although considerable difficulty is experienced in conversation in understanding one another's meaning. There are between 40 and and 50 to cater for daily, besides a staff about 30; that Mr Lemaire finds his time fully occupied. The dishes for his Excellency are varied and miscellaneous, and from 14 to 20 courses are served at each meal. The bills of fare contain such items as bird's-nest soup, pigs' kidneys stewed in cream, boiled ducks and green ginger, sharks' fins, shrinips and prawns stewed with leeks and muscatel grapes, fat pork saute with peas and kidney beans. The meal usually winds with fruit and sponge cake, and freshly-picked green tea as liqueur.&lt;ref&gt;&quot;Li Hung Chang's Diet.&quot; ''Edinburgh Evening News'' 19 August 1896, Wednesday: 3 [of 4], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000452/18960819/057/0003.&lt;/ref&gt;&lt;/blockquote&gt;

'''1896 November 6, Friday''', Algernon Bourke was on the committee for [[Social Victorians/Timeline/1896#1896 November 6, Friday|the Prince's Club ice-skating rink, which opened on this day]].&lt;p&gt;

'''1896 November 25, Wednesday''', Mr. and Mrs. Algernon Bouke attended [[Social Victorians/Timeline/1896#23 November 1896, Monday23 November 1896, Monday|Lord and Lady Burton's party for Derby Day]].&lt;p&gt;
'''1896 December 4, Friday''', the Orleans Club at Brighton was robbed:&lt;blockquote&gt;The old building of the Orleans Club at Brighton, which opens its new club house at 33, Brunswick-terrace to-day, was the scene of a very ingenious burglary during the small hours of yesterday morning. The greater portion of the club property had already been removed to the new premises, but Mr Algernon Bourke, his private secretary, and some of the officials of the club, still occupied bed-rooms at the house in the King’s-road. The corner shop of the street front is occupied by Mr. Marx, a jeweller in a large way of business, and upon his manager arriving at nine o'clock he discovered that the place had been entered through hole in the ceiling, and a great part of a very valuable stock of jewelry extracted. An examination of the morning rooms of the club, which runs over Mr. Marx's establishment reveal a singularly neat  specimen of the burglar's art. A piece of the flooring about 15in square had been removed by a series of holes bored side by side with a centre-bit, at a spot where access to the lofty shop was rendered easy by a tall showcase which stood convemently near. A massive iron girder had been avoided by a quarter of an inch, and this circumstance and the general finish of the operation point to an artist in his profession, who had acquired an intimate knowledge of the premises. The club doors were all found locked yesterday morning, and the means of egress adopted by the thief are at present a mystery.&lt;ref&gt;&quot;Burglary at Brighton.&quot; ''Daily Telegraph &amp; Courier'' (London) 05 December 1896, Saturday: 5 [of 12], Col. 7a [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18961205/090/0005. Print title: ''Daily Telegraph''; p. 5.&lt;/ref&gt;&lt;/blockquote&gt;

'''1897 July 2, Friday''', the Hon. A. and Mrs. A. Bourke and Mr. and Mrs. Bourke attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House.&lt;p&gt;

'''23 July 1897 — or 30 July 1897 – Friday''', Guendonline Bourke attended [[Social Victorians/Timeline/1897#23 July 1897, Friday|Lady Burton's party at Chesterfield House]]. &lt;blockquote&gt;Far the prettiest women in the room were Lady Henry Bentinck (who looked perfectly lovely in pale yellow, with a Iong blue sash; and Mrs. Algernon Bourke, who was as smart as possible in pink, with pink and white ruchings on her sleeves and a tall pink feather in her hair.&lt;ref&gt;&quot;Lady Burton's Party at Chesterfield House.&quot; ''Belper &amp; Alfreton Chronicle'' 30 July 1897, Friday: 7 [of 8], Col. 1c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004151/18970730/162/0007. Print title: ''Belper and Alfreton Chronicle''; n.p.&lt;/ref&gt;&lt;/blockquote&gt;

'''1898 January 5, Wednesday''', the ''Irish Independent'' reported that &quot;Mr Algernon Bourke, the aristocratic stock broker ... was mainly responsible for the living pictures at the Blenheim Palace entertainment.&lt;ref&gt;&quot;Mr Algernon Bourke ....&quot; ''Irish Independent'' 05 January 1898, Wednesday: 6 [of 8], Col. 2c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001985/18980105/115/0006.&lt;/ref&gt;&lt;p&gt;

'''1899 January 10, Tuesday''', the Brighton Championship Dog Show opened:&lt;blockquote&gt;Princess of Wales a Winner at the Ladies’ Kennel Club Show.

[Exclusive to &quot;The Leader.&quot;)

The Brighton Championship Dog Show opened in the Dome and Corn Exchange yesterday, and was very well patronised by visitors and exhibitors. Among the latter was H.R.H. the Princess of Wales, who did very well; and others included Princess Sophie Duleep Singh, Countess De Grey, Sir Edgar Boehm, the Hon Mrs. Algernon Bourke, Lady Cathcart, Lady Reid, Mr. Shirley (chairman of the Kennel Club), and the Rev. Hans Hamiiton (president of the Kennel Club).

The entry of bloodhounds is one of the best seen for some time; the Great Danes are another stronyg lot; deerhounds are a fine entry, all good dogs, and most of the best kennels represented; borzois are another very stylish lot. The bigger dogs are, as usual, in the Corn Exchange and the &quot;toy&quot; dogs in the Dome. To everyone's satsfaction the Princess of Wales carried off two first prizes with Alex in the borzois class.&lt;ref&gt;&quot;Dogs at Brighton.&quot; ''Morning Leader'' 11 January 1899, Wednesday: 8 [of 12], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18990111/142/0008. Print p. 8.&lt;/ref&gt;&lt;/blockquote&gt;'''1899 January 11, Wednesday''', Guendoline Bourke attended [[Social Victorians/Timeline/1899#11 January 1899, Wednesday|a luncheon Stanfield-hall, home of Mr. and Mrs. Basil Montogomery, for Princess Henry of Battenberg]], that also included the Countess of Dudley (sister of Mrs. Montgomery), General Oliphant, and the Mayor and Mayoress of Romsey.

'''1899 February 7, Tuesday''', Guendoline Bourke was a member of the very high-ranking committee organizing a [[Social Victorians/Timeline/1899#1899 February 7, Tuesday|ball at the Hotel Cecil on 7 February 1899]].

'''1899 June 1, Thursday''', the Hon. Algernon and Guendoline Bourke attended the wedding of her brother, Sloane Stanley and Countess Cairns at Holy Trinity Church, Brompton.&lt;ref&gt;&quot;Marriage of Mr. Sloane Stanley and Countess Cairns.&quot; ''Hampshire Advertiser'' 03 June 1899, Saturday: 6 [of 8], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18990603/049/0006. Print p. 6.&lt;/ref&gt;&lt;p&gt;

'''1899 October 19, Thursday''', the Hon. Algernon Bourke had a bankruptcy hearing:&lt;blockquote&gt;The public examination of the Hon. Algernon Bourke was held before Mr Registrar Giffard yesterday, at the London Bankruptcy Court. The debtor, described as proprietor of a St. James's-street club, furnished a statement of affairs showing unsecured debts £13,694 and debts fully secured £12,800, with assets which are estimated at £4,489 [?]. He stated, in reply to the Official Receiver, that he was formerly a member of the Stock Exchange, but had nothing to do with the firm of which he was a member during the last ten years. He severed his connection with the firm in May last, and believed he was indebted to them to the extent of £2,000 or £3,000. He repudiated a claim which they now made for £37,300. In 1889 he became proprietor of White's Club, St. James's-street, and carried it on until January 1st last, when he transferred it to a company called Recreations, Limited. One of the objects of the company was to raise money on debentures. The examination was formally adjourned.&lt;ref name=&quot;:9&quot; /&gt;&lt;/blockquote&gt;'''1899 November 8, Wednesday''', the Hon. Algernon Bourke's bankruptcy case came up again:&lt;blockquote&gt;At Bankruptcy Court, yesterday, the case the Hon. Algernon Bourke again came on for hearing before Mr. Registrar Giffard, and the examination was concluded. The debtor has at various times been proprietor of White’s Club, St. James’s-street, and the Orleans’ Club, Brighton, and also of Willis's Restaurant, King-street, St. James's. He attributed his failure to losses sustained by the conversion of White’s Club and the Orleans' Club into limited companies, to the payment of excessive Interest on borrowed money, and other causes. The liabilities amount to £26,590, of which £13,694 are stated to be unsecured, and assets £4,409.&lt;ref&gt;&quot;Affairs of the Hon. A. Bourke.&quot; ''Globe'' 09 November 1899, Thursday: 2 [of 8], Col. 1c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001652/18991109/020/0002. Print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;

'''1899 December 23, Saturday''', &quot;Mr. Algernon Bourke has departed for a tour in Africa, being at present the guest of his brother in Tunis.&quot;&lt;ref&gt;&quot;The Society Pages.&quot; ''Walsall Advertiser'' 23 December 1899, Saturday: 7 [of 8], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001028/18991223/143/0007. Print p. 7.&lt;/ref&gt;

'''1900 February 15, Thursday''', Miss Daphne Bourke, the four-year-old daughter of the Hon. Algernon and Mrs. Bourke was a bridesmaid in the wedding of Enid Wilson and the Earl of Chesterfield, so presumably her parents were present as well.&lt;ref&gt;&quot;London Day by Day.&quot; ''Daily Telegraph'' 15 February 1900, Thursday: 8 [of 12], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/19000215/175/0008. Name in British Newspaper Archive: ''Daily Telegraph &amp; Courier'' (London). Print p. 8.&lt;/ref&gt;

'''1900 September 16''', the Hon. Algernon Bourke became the heir presumptive to the Earldom of Mayo when his older brother Captain Hon. Sir Maurice Archibald Bourke died.

'''1900 October 06, Saturday''', the ''Weekly Irish Times'' says that Mr. Algernon Bourke, now heir presumptive to the earldom of Mayo, &quot;has been for some months lately staying with Mr. Terence Bourke in Morocco.&quot;&lt;ref&gt;&quot;Society Gossip.&quot; ''Weekly Irish Times'' 06 October 1900, Saturday: 14 [of 20], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001684/19001006/121/0014. Print p. 14.&lt;/ref&gt;

'''1901 May 30, Thursday''', the Hon. Mrs. Algernon Bourke attended the fashionable Ladies' Kennel Association Dog Show.

'''1901 July 4, Thursday''', Guendoline and Daphne Bourke attended a children's party hosted by the Countess of Yarborough:&lt;blockquote&gt;The Countess of Yarborough gave a charming children's party on Thursday (4th) afternoon at her beautiful house in Arlington Street. The spacious ballroom was quite filled with little guests and their mothers. Each little guest received a lovely present from their kind hostess. The Duchess of Beaufort, in grey, and with a large black picture hat, brought her two lovely baby girls, Lady Blanche and Lady Diana Somerset, both in filmy cream [Col. 2b–3a] lace frocks. Lady Gertrude Corbett came with her children, and Ellen Lady Inchiquin with hers. Lady Southampton, in black, with lovely gold embroideries on her bodice, brought her children, as also did Lady Heneage and Mr. and Lady Beatrice Kaye. Lady Blanche Conyngham, in écru lace, over silk, and small straw hat, was there; also Mrs. Smith Barry, in a lovely gown of black and white lace. The Countess of Kilmorey, in a smart grey and white muslin, brought little Lady Cynthia Needham, in white; Mrs. Arthur James, in black and white muslin; and the Countess of Powys, in mauve silk with much white lace; Lady Sassoon, in black and white foulard; Victoria Countess of Yarborough, came on from hearing Mdme. Réjane at Mrs. Wernher's party at Bath House; and there were also present Lord Henry Vane-Tempest, the Earl of Yarborough, Lady Naylor-Leyland's little boys; the pretty children of Lady Constance Combe, Lady Florence Astley and her children, and Lady Meysey Thompson (very smart in mauve and white muslin) with her children; also Hon. Mrs. Algernon Bourke, in pale grey, with her pretty little girl.&lt;ref&gt;&quot;The Countess of Yarborough ....&quot; ''Gentlewoman'' 13 July 1901, Saturday: 76 [of 84], Col. 2b, 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010713/381/0076. Print p. xxxvi.&lt;/ref&gt;&lt;/blockquote&gt;'''1901 July 20, Saturday''', the ''Gentlewoman'' published the Hon. Mrs. Algernon Bourke's portrait (identified with &quot;Perthshire&quot;) in its 3rd series of &quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot;&lt;ref&gt;&quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot; ''Gentlewoman'' 20 July 1901, Saturday: 31 [of 60], Col. 4b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010720/141/0031. Print n.p.&lt;/ref&gt; Their daughter Daphne appears in the portrait as well.

'''1901 September 12, Thursday''', Mrs. Guendoline Bourke's name is listed as Gwendolen Bourke, but the spelling is not what she objected to:&lt;blockquote&gt;Mr. Underhill, the Conservative agent, mentioned to the Revising Barrister (Mr. William F. Webster) that the name of the Hon. Mrs. Gwendolen Bourke was on the list in respect of the house, 75, Gloucester-place. The lady had written to him to say that she was the Hon. Mrs. Algernon Bourke and that she wished that name to appear on the register. In reply to the Revising Barrister, Mr. Underhill said that “Algernon” was the '''name the lady’s husband'''.

Mr. Cooke, the rate-collector, said that Mrs. Bourke had asked to be addressed Mrs. Algernon Bourke, but that the Town Clerk thought the address was not a correct one. The lady signed her cheques Gwendolen.”

Mr. Underhill said the agents frequently had indignant letters from ladies because they were not addressed by their husband’s Christian name.

The Revising Barrister — lf a lady gave me the name of Mrs. John Smith I should say I had not got the voter’s name. The name Gwendolen must remain.&lt;ref&gt;&quot;Ladies’ Names.&quot; ''Morning Post'' 12 September 1901, Thursday: 7 [of 10], Col. 3a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19010912/130/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;'''1902 September 4, Thursday''', the ''Daily Express'' reported that &quot;Mrs. Algernon Bourke is staying with Lord and Lady Alington at Scarborough.&quot;&lt;ref&gt;&quot;Onlooker.&quot; &quot;My Social Diary.&quot; &quot;Where People Are.&quot; ''Daily Express'' 04 September 1902, Thursday: 5 [of 8], Col. 1b? [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020904/099/0005. Print p. 4, Col. 7b [of 7].&lt;/ref&gt;

'''1902 October 24, Friday''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#24 October 1902, Friday|opened the Prince's ice-skating rink for the season]], which he had been doing since 1895.

'''1902 December 9, Tuesday''', Guendonline Bourke attended [[Social Victorians/Timeline/1900s#9 December 1902, Tuesday|Lady Eva Wyndham-Quin's &quot;at home,&quot; held at the Welch Industrial depot]] for the sale Welsh-made Christmas gifts and cards. Bourke wore &quot;a fur coat and a black picture hat.&quot;&lt;ref&gt;&quot;A Lady Correspondent.&quot; &quot;Society in London.&quot; ''South Wales Daily News'' 11 December 1902, Thursday: 4 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000919/19021211/082/0004. Print p. 4.&lt;/ref&gt;

'''1903 March 17, Tuesday''', Guendoline Bourke staffed a booth at a [[Social Victorians/Timeline/1900s#1903 March 17, Tuesday|sale of the Irish Industries Association]] on St. Patrick's Day with [[Social Victorians/People/Mayo|Lady Mayo]], [[Social Victorians/People/Dudley|Georgina Lady Dudley]] and [[Social Victorians/People/Beresford|Miss Beresford]]. A number of other aristocratic women were also present at the sale in other booths, including [[Social Victorians/People/Londonderry|Lady Londonderry]] and [[Social Victorians/People/Lucan|Lady Lucan]].

'''1903 June 23, Tuesday''', Guendoline and Daphne Bourke were invited to a [[Social Victorians/Timeline/1900s#1903 June 23, Tuesday|children's party at Buckingham Palace for Prince Eddie's birthday]].

'''1905 February 17, Friday''', the Dundee ''Evening Post'' reported that Algernon Bourke &quot;set up a shop in Venice for the sale of art treasures and old furniture.&quot;&lt;ref&gt;&quot;Social News.&quot; Dundee ''Evening Post'' 17 February 1905, Friday: 6 [of 6], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000582/19050217/105/0006. Print p. 6.&lt;/ref&gt;

'''1905, last week of July''', Guendoline Bourke and daughter Daphne Bourke — who was 10 years old — attended [[Social Victorians/Timeline/1900s#Last week of July, 1905|Lady Cadogan's children's party at Chelsea House]]. Daphne was &quot;One of loveliest little girls present.&quot;&lt;ref&gt;&quot;Court and Social News.&quot; ''Belfast News-Letter'' 01 August 1905, Tuesday: 7 [of 10], Col. 6b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/19050801/157/0007. Print p. 7.&lt;/ref&gt;

'''1913 May 7, Wednesday''', Guendoline Bourke presented her daughter Daphne Bourke at court:&lt;blockquote&gt;Mrs. Algernon Bourke presented her daughter, and wore blue and gold broché with a gold lace train.&lt;ref&gt;&quot;Social and Personal.&quot; London ''Daily Chronicle'' 08 May 1913, Thursday: 6 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/19130508/120/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;The ''Pall Mall Gazette'' has a description of Daphne Bourke's dress, but what exactly &quot;chiffon [[Social Victorians/Terminology#Hoops|paniers]]&quot; means in 1913 is not clear:&lt;blockquote&gt;Court dressmakers appear to have surpassed all previous records in their efforts to make the dresses for to-night’s Court as beautiful as possible. Noticeable among these is the dainty presentation gown to be worn by Miss Bourke, who will be presented by her mother, the Hon. Mrs. Algernon Bourke. This has a skirt of soft white satin draped with chiffon [[Social Victorians/Terminology#Hoops|paniers]] and a bodice veiled with chiffon and trimmed with diamanté and crystal embroidery. Miss Bourke’s train, gracefully hung from the shoulders, is of white satin lined with pale rose pink chiffon and embroidered with crystal and diamanté.&lt;ref&gt;&quot;Fashion Day by Day. Lovely Gowns for To-night's Court.&quot; ''Pall Mall Gazette'' 07 May 1913, Wednesday: 13 [of 18], Col. 1a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/19130507/199/0013. Print n.p.&lt;/ref&gt;&lt;/blockquote&gt;

== Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball ==
According to both the ''Morning Post'' and the ''Times'', the Hon. Algernon Bourke was among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]] at the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]].&lt;ref name=&quot;:2&quot; /&gt;&lt;ref name=&quot;:3&quot; /&gt; Based on the people they were dressed as, Guendonine Bourke was probably in this procession but it seems unlikely that Algernone Bourke was.

[[File:Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.jpg|thumb|alt=Black-and-white photograph of a standing woman richly dressed in an historical costume with a headdress and a very large fan|Hon. Guendoline Bourke as Salammbô. ©National Portrait Gallery, London.]]
=== Hon. Guendoline Bourke ===
[[File:Alfons Mucha - 1896 - Salammbô.jpg|thumb|left|alt=Highly stylized orange-and-yellow painting of a bare-chested woman with a man playing a harp at her feet|Alfons Mucha's 1896 ''Salammbô''.]]
Lafayette's portrait (right) of &quot;Guendoline Irene Emily Bourke (née Sloane-Stanley) as Salammbô&quot; in costume is photogravure #128 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot;&gt;&quot;Devonshire House Fancy Dress Ball (1897): photogravures by Walker &amp; Boutall after various photographers.&quot; 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.&lt;/ref&gt; The printing on the portrait says, &quot;The Hon. Mrs. Algernon Bourke as Salammbo.&quot;&lt;ref&gt;&quot;Mrs. Algernon Bourke as Salammbo.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158491/Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.&lt;/ref&gt;

==== Newspaper Accounts ====
The Hon. Mrs. A. Bourke was dressed as

* Salambo in the Oriental procession.&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''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.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“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.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}
*&quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“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.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}

==== Salammbô ====
Salammbô is the eponymous protagonist in Gustave Flaubert's 1862 novel.&lt;ref name=&quot;:5&quot;&gt;{{Cite journal|date=2024-04-29|title=Salammbô|url=https://en.wikipedia.org/w/index.php?title=Salammb%C3%B4&amp;oldid=1221352216|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Salammb%C3%B4.&lt;/ref&gt; Ernest Reyer's opera ''Salammbô'' was based on Flaubert's novel and published in Paris in 1890 and performed in 1892&lt;ref&gt;{{Cite journal|date=2024-04-11|title=Ernest Reyer|url=https://en.wikipedia.org/w/index.php?title=Ernest_Reyer&amp;oldid=1218353215|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Ernest_Reyer.&lt;/ref&gt; (both Modest Mussorgsky and Sergei Rachmaninoff had attempted but not completed operas based on the novel as well&lt;ref name=&quot;:5&quot; /&gt;). Alfons Mucha's 1896 lithograph of Salammbô was published in 1896, the year before the ball (above left).[[File:Algernon Henry Bourke Vanity Fair 20 January 1898.jpg|thumb|alt=Old colored drawing of an elegant elderly man dressed in a 19th-century tuxedo with a cloak, top hat and formal pointed shoes with bows, standing facing 1/4 to his right|''Algy'' — Algernon Henry Bourke — by &quot;Spy,&quot; ''Vanity Fair'' 20 January 1898]]
=== Hon. Algernon Bourke ===
[[File:Hon-Algernon-Henry-Bourke-as-Izaak-Walton.jpg|thumb|left|alt=Black-and-white photograph of a man richly dressed in an historical costume sitting in a fireplace that does not have a fire and holding a tankard|Hon. Algernon Henry Bourke as Izaak Walton. ©National Portrait Gallery, London.]]
'''Lafayette's portrait''' (left) of &quot;Hon. Algernon Henry Bourke as Izaak Walton&quot; in costume is photogravure #129 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot; /&gt; The printing on the portrait says, &quot;The Hon. Algernon Bourke as Izaak Walton.&quot;&lt;ref&gt;&quot;Hon. Algernon Bourke as Izaak Walton.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158492/Hon-Algernon-Henry-Bourke-as-Izaak-Walton.&lt;/ref&gt;

This portrait is amazing and unusual: Algernon Bourke is not using a photographer's set with theatrical flats and props, certainly not one used by anyone else at the ball itself. Isaak Walton (baptised 21 September 1593 – 15 December 1683) wrote ''The Compleat Angler''.&lt;ref&gt;{{Cite journal|date=2021-09-15|title=Izaak Walton|url=https://en.wikipedia.org/w/index.php?title=Izaak_Walton&amp;oldid=1044447858|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Izaak_Walton.&lt;/ref&gt; A cottage Walton lived in and willed to the people of Stafford was photographed in 1888, suggesting that its relationship to Walton was known in 1897, raising a question about whether Bourke could have used the fireplace in the cottage for his portrait. (This same cottage still exists, as the [https://www.staffordbc.gov.uk/izaak-waltons-cottage Isaak Walton Cottage] museum.)

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{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)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

=== Mr. and Mrs. Bourke ===
The ''Times'' made a distinction between the Hon. Mr. and Mrs. A. Bourke and Mr. and Mrs. Bourke, including both in the article.&lt;ref name=&quot;:3&quot; /&gt; Occasionally this same article mentions the same people more than once in different contexts and parts of the article, so they may be the same couple. (See [[Social Victorians/People/Bourke#Notes and Question|Notes and Question]] #2, below.)

== Demographics ==
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;
=== Residences ===
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1890: 33 Cadogan Terrace
*1891: 33 Cadogan Terrace, Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

== Family ==
*Hon. Algernon Henry Bourke (31 December 1854 – 7 April 1922)&lt;ref&gt;&quot;Hon. Algernon Henry Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p29657.htm#i296561|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
*Guendoline Irene Emily Sloane-Stanley Bourke (c. 1869 – 30 December 1967)&lt;ref name=&quot;:1&quot;&gt;&quot;Guendoline Irene Emily Stanley.&quot; {{Cite web|url=https://www.thepeerage.com/p51525.htm#i515247|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
#Daphne Marjory Bourke (5 April 1895 – 22 May 1962)

=== Relations ===
*Hon. Algernon Henry Bourke (the 3rd son of the [[Social Victorians/People/Mayo|6th Earl of Mayo]]) was the older brother of Lady Florence Bourke.&lt;ref name=&quot;:0&quot; /&gt;

==== Other Bourkes ====
*Hubert Edward Madden Bourke (after 1925, Bourke-Borrowes)&lt;ref&gt;&quot;Hubert Edward Madden Bourke-Borrowes.&quot; {{Cite web|url=https://www.thepeerage.com/p52401.htm#i524004|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p52401.htm#i524004.&lt;/ref&gt;
*Lady Eva Constance Aline Bourke, who married [[Social Victorians/People/Dunraven|Windham Henry Wyndham-Quin]] on 7 July 1885;&lt;ref&gt;&quot;Lady Eva Constance Aline Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p2575.htm#i25747|title=Person Page|website=www.thepeerage.com|access-date=2020-12-02}} https://www.thepeerage.com/p2575.htm#i25747.&lt;/ref&gt; he became 5th Earl of Dunraven and Mount-Earl on 14 June 1926.
== Writings, Memoirs, Biographies, Papers ==

=== Writings ===
* Bourke, the Hon. Algernon. ''The History of White's''. London: Algernon Bourke [privately published], 1892.
* Bourke, the Hon. Algernon, ed., &quot;with a brief Memoir.&quot; ''Correspondence of Mr Joseph Jekyll with His Sister-in-Law, Lady Gertrude Sloane Stanley, 1818–1838''. John Murray, 1893.
* Bourke, the Hon. Algernon, ed. ''Correspondence of Mr Joseph Jekyll''. John Murray, 1894.

=== Papers ===
* Where are the papers for the Earl of Mayo family? Are Algernon Bourke's papers with them?

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
== Footnotes ==
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      <text bytes="54196" sha1="m1w0maacf0913j6b2ne60dnykq6gvnp" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
* Mrs. Guendoline Bourke
* Lady Florence Bourke
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father.

== Overview ==
Although the Hon. Algernon Henry Bourke was born in Dublin in 1854 and came from a family whose title is in the Peerage of Ireland,&lt;ref name=&quot;:6&quot;&gt;1911 England Census.&lt;/ref&gt; he seems to have spent much of his adult life generally in England and especially in London.

Mrs. Guendoline Bourke was a noted horsewoman and an excellent shot, exhibited at dog shows successfully and was &quot;an appreciative listener to good music.&quot;&lt;ref&gt;&quot;Vanity Fair.&quot; ''Lady of the House'' 15 June 1899, Thursday: 4 [of 44], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004836/18990615/019/0004.&lt;/ref&gt; She was reported as attending many social events without her husband, usually with a quick description of what she wore.

The Hon. Algernon Bourke and Mr. Algernon, depending on the newspaper article, were the same person. Calling him Mr. Bourke in the newspapers, especially when considered as a businessman or (potential) member of Parliament, does not rule out the son of an earl.

== Acquaintances, Friends and Enemies ==

=== Mr. Algernon Bourke ===

* [[Social Victorians/People/Montrose|Marcus Henry Milner]], &quot;one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys&quot;&lt;ref name=&quot;:8&quot;&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 2a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;
* Caroline, Duchess of Montrose — her &quot;legal advisor&quot; on the day of her marriage to Marcus Henry Milner&lt;ref&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 1b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;

== Organizations ==

=== The Hon. Algernon Bourke ===
* Eton
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Stock Exchange
* Willis's Rooms&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;
*One of the directors, the Franco-English Tunisian Esparto Fibre Supply Company, Ltd.&lt;ref&gt;''Money Market Review'', 20 Jan 1883 (Vol 46): 124.&lt;/ref&gt;
*One of the directors, the Frozen Lake, Ltd., with Admiral Maxse, Lord [[Social Victorians/People/Beresford|Marcus Beresford]], [[Social Victorians/People/Williams|Hwfa Williams]]&lt;ref&gt;&quot;The Frozen Lake, Limited.&quot; ''St James's Gazette'' 08 June 1894, Friday: 15 [of 16], Col. 4a [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/18940608/085/0015. Print p. 15.&lt;/ref&gt;
*[[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)

=== Mr. Algernon Bourke ===

* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt;

== Timeline ==
'''1872 February 8''', Richard Bourke, 6th Earl of Mayo was assassinated while inspecting a &quot;convict settlement at Port Blair in the Andaman Islands ... by Sher Ali Afridi, a former Afghan soldier.&quot;&lt;ref&gt;{{Cite journal|date=2024-12-01|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo.&lt;/ref&gt; The Hon. Algernon's brother Dermot became the 7th Earl at 19 years old.

'''1876 November 24, Friday''', the Hon. Algernon Bourke was one of 6 men (2 students, one of whom was Bourke; 2 doctors; a tutor and another man) from Cambridge who gave evidence as witnesses in an inquest about the death from falling off a horse of a student.&lt;ref&gt;&quot;The Fatal Accident to a Sheffield Student at Cambridge.&quot; ''Sheffield Independent'' 25 November 1876, Saturday: 7 [of 12], Col. 5a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000181/18761125/040/0007. Print title: ''Sheffield and Rotherham Independent'', n. p.&lt;/ref&gt;

'''1884 May 3, Saturday''', the &quot;Rochester Conservatives&quot; announced that they would &quot;bring forward the Hon. Algernon Bourke, brother of Lord Mayo, as their second candidate,&quot;&lt;ref&gt;&quot;Election Intelligence.&quot; ''Yorkshire Gazette'' 03 May 1884, Saturday: 4 [of 12], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000266/18840503/011/0004.&lt;/ref&gt; but because he could not be the first candidate, Bourke declined.&lt;ref&gt;&quot;Rochester.&quot; London ''Daily Chronicle'' 09 May 1884, Friday: 3 [of 8], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/18840509/049/0003.&lt;/ref&gt;

'''1884 June 18, Wednesday''', Mr. Algernon Bourke was on a committee to watch a [[Social Victorians/Timeline/1884#18 June 1884, Wednesday|Mr. Bishop's &quot;thought-reading&quot; experiment]], which was based on a challenge by Henry Labourchere made the year before. This &quot;experiment&quot; took place before a fashionable audience.

'''1885 October 3, Saturday''', the Hon. Algernon Bourke was named as the Conservative candidate for Clapham in the Battersea and Clapham borough after the Redistribution Bill determined the electoral districts for South London.&lt;ref&gt;&quot;South London Candidates.&quot; ''South London Press'' 03 October 1885, Saturday: 9 [of 16], Col. 5b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18851003/096/0009. Print p. 9.&lt;/ref&gt; The Liberal candidate, who won, was Mr. J. F. Moulton.

'''1886 July 27, Tuesday''', Algernon Bourke attended a service honoring a memorial at St. Paul's for his father, who had been assassinated.&lt;ref&gt;&quot;Memorial to the Late Earl of Mayo.&quot; ''Northern Whig'' 28 July 1886, Wednesday: 6 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000434/18860728/143/0006. Print p. 6.&lt;/ref&gt;

'''1886 September 2, Thursday''', Mr. Algernon Bourke was part of a group of mostly aristocratic men taking part in [[Social Victorians/Timeline/1886#8 September 1886, Wednesday|a &quot;trial-rehearsal&quot; as part of Augustus Harris's production]] ''A Run of Luck'', about sports.

'''1886 October 2, Saturday''', the Duke of Beaufort and the Hon. Algernon Bourke arrived in Yougal: &quot;His grace has taken a residence at Lismore for a few weeks, to enjoy some salmon fishing on the Blackwater before the close of the season.&quot;&lt;ref&gt;&quot;Chippenham.&quot; ''Wilts and Gloucestershire Standard'' 02 October 1886, Saturday: 8 [of 8], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001955/18861002/142/0008. Print p. 8.&lt;/ref&gt;

'''1887 December 15''', Hon. Algernon Bourke and Guendoline Stanley were married at St. Paul's, Knightsbridge, by Bourke's uncle the Hon. and Rev. George Bourke. Only family members attended because of &quot;the recent death of a near relative of the bride.&quot;&lt;ref&gt;&quot;Court Circular.&quot; ''Morning Post'' 16 December 1887, Friday: 5 [of 8], Col. 7c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18871216/066/0005.&lt;/ref&gt;

'''1888 July 26''', [[Social Victorians/People/Montrose|Caroline Graham Stirling-Crawford]] (known as Mr. Manton for her horse-breeding and -racing operations) and Marcus Henry Milner married.&lt;ref name=&quot;:12&quot;&gt;&quot;Hon. Caroline Agnes Horsley-Beresford.&quot; {{Cite web|url=https://thepeerage.com/p6863.htm#i68622|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt; According to the ''Nottingham Evening Post'' of 31 July 1888,&lt;blockquote&gt;LONDON GOSSIP.

(From the ''World''.)

The marriage of &quot;Mr. Manton&quot; was the surprise as well the sensation of last week. Although some wise people noticed a certain amount of youthful ardour in the attentions paid by Mr. Marcus Henry Milner to Caroline Duchess of Montrose at '''Mrs. Oppenheim's ball''', nobody was prepared for the sudden ''dénouement''; '''and it''' were not for the accidental and unseen presence [[Social Victorians/People/Mildmay|a well-known musical amateur]] who had received permission to practice on the organ, the ceremony performed at half-past nine on Thursday morning at St. Andrew's, Fulham, by the Rev. Mr. Propert, would possibly have remained a secret for some time to come. Although the evergreen Duchess attains this year the limit of age prescribed the Psalmist, the bridegroom was only born in 1864. Mr. &quot;Harry&quot; Milner (familiarly known in the City as &quot;Millions&quot;) was one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys, and Mr. Algernon Bourke, the head of the house (who, of course, takes a fatherly interest in the match) went down to Fulham to give away the Duchess. The ceremony was followed by a ''partie carrée'' luncheon at the Bristol, and the honeymoon began with a visit to the Jockey Club box at Sandown. Mr. Milner and the Duchess of Montrose have now gone to Newmarket. The marriage causes a curious reshuffling of the cards of affinity. Mr. Milner is now the stepfather of the [[Social Victorians/People/Montrose|Duke of Montrose]], his senior by twelve years; he is also the father-in-law of [[Social Victorians/People/Lady Violet Greville|Lord Greville]], Mr. Murray of Polnaise, and [[Social Victorians/People/Breadalbane|Lord Breadalbane]].&lt;ref name=&quot;:8&quot; /&gt;&lt;/blockquote&gt;'''1888 December 1st week''', according to &quot;Society Gossip&quot; from the ''World'', the Hon. Algernon Bourke was suffering from malaria, presumably which he caught when he was in South Africa:&lt;blockquote&gt;I am sorry to hear that Mr. Algernon Bourke, who married Miss Sloane-Stanley a short time ago, has been very dangerously ill. Certain complications followed an attack of malarian fever, and last week his mother, the Dowager Lady Mayo, and his brother, Lord Mayo, were hastily summoned to Brighton. Since then a change for the better has taken place, and he is now out of danger.&lt;ref&gt;&quot;Society Gossip. What the ''World'' Says.&quot; ''Hampshire Advertiser'' 08 December 1888, Saturday: 2 [of 8], Col. 5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18881208/037/0002. Print title: ''The Hampshire Advertiser County Newspaper''; print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;'''1889 – 1899 January 1''', the Hon. Algernon Bourke was &quot;proprietor&quot; of White's Club, St. James's Street.&lt;ref name=&quot;:9&quot;&gt;&quot;The Hon. Algernon Bourke's Affairs.&quot; ''Eastern Morning News'' 19 October 1899, Thursday: 6 [of 8], Col. 7c [of7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001152/18991019/139/0006. Print p. 6.&lt;/ref&gt;

'''1889 June 8, Saturday''', the Hon. Algernon Bourke contributed some art he owned to the collection of the Royal Institute of Painters in Water-Colours' [[Social Victorians/Timeline/1889#8 June 1889, Saturday|exhibition of &quot;the works of the 'English Humourists in Art.'&quot;]]

'''1892''', the Hon. Algernon Bourke privately published his ''The History of White's'', the exclusive gentleman's club.

'''1893 February 11, Tuesday''', Algernon Bourke opened Willis's Restaurant:&lt;blockquote&gt;Mr. Algernon Bourke has in his time done many things, and has generally done them well. His recently published history of White's Club is now a standard work. White's Club itself was a few years ago in its agony when Mr. Bourke stepped in and gave it a renewed lease of life. Under Mr. Bourke's auspices &quot;Willis's Restaurant&quot; opened its doors to the public on Tuesday last in a portion of the premises formerly so well known as Willis's Rooms. This new venture is to rival the Amphitryon in the matter of cuisine and wines; but it is not, like the Amphitryon, a club, but open to the public generally. Besides the restaurant proper, there are several ''cabinets particuliers'', and these are decorated with the very best of taste, and contain some fine portraits of the Georges.&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Letter from the Linkman.&quot; ''Truth'' 20 April 1893, Thursday: 25 [of 56], Col. 1a [of 2]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025# https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025]. Print p. 855.&lt;/ref&gt;&lt;/blockquote&gt;'''1893 November 30, Thursday''', with Sir Walter Gilbey the Hon. Algernon Bourke &quot;assisted&quot; in &quot;forming [a] collection&quot; of engravings by George Morland that was exhibited at Messrs. J. and W. Vokins’s, Great Portland-street.&lt;ref&gt;&quot;The George Morland Exhibition at Vokins's.&quot; ''Sporting Life'' 30 November 1893, Thursday: 4 [of 4], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000893/18931130/058/0004.&lt;/ref&gt;

'''1895 February 23, Saturday''', the Hon. Algernon Bourke attended the [[Social Victorians/Timeline/1895#23 February 1895, Saturday|fashionable wedding of Laurence Currie and Edith Sibyl Mary Finch]].

'''1895 August 24, Saturday''', &quot;Marmaduke&quot; in the Graphic says that Algernon Bourke &quot;opened a cyclists' club in Chelsea.&quot;&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Court and Club.&quot; The ''Graphic'' 24 August 1895, Saturday: 11 [of 32], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18950824/017/0011. Print p. 223.&lt;/ref&gt;

'''1895 October''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#24 October 1902, Friday|opened the Prince's ice-skating rink for the season]].

'''1896 June 29, Monday''', Algernon Bourke published a letter to the editor of the ''Daily Telegraph'':&lt;blockquote&gt;To the Editor of “The Daily Telegraph.”

Sir — Permit me to make my bow to the public. I am the manager of the Summer Club, which on two occasions bas been the subject of Ministerial interpellation in Parliament. The Summer Club is a small combination, which conceived the idea of attempting to make life more pleasant in London by organising breakfast, luncheon, and teas in Kensington Gardens for its members. This appears to have given offence in some way to Dr. Tanner, with the result that the catering arrangements of the club are now &quot;by order&quot; thrown open to the public. No one is more pleased than I am at the result of the doctor's intervention, for it shows that the idea the Summer Club had of using the parks for something more than mere right of way bas been favourably received. In order, however, that the great British public may not be disappointed, should they all come to lunch at once, I think it necessary to explain that the kitchen, which by courtesy of the lessee of the kiosk our cook was permitted to use, is only 10ft by 5ft; it has also to serve as a scullery and pantry, and the larder, from which our luxurious viands are drawn, is a four-wheeled cab, which comes up every day with the food and returns after lunch with the scraps. Nevertheless, the Summer Club says to the British public — What we have we will share with you, though it don't amount to very much — I am, Sir, your obedient servant,

ALGERNON BOURKE.

White's Club, June 27&lt;ref&gt;&quot;The Summer Club.&quot; ''Daily Telegraph &amp; Courier'' (London) 29 June 1896, Monday: 8 [of 12], Col. 2b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18960629/072/0008. Print title: ''Daily Telegraph'', p. 8.&lt;/ref&gt;&lt;/blockquote&gt;'''1896 July 4, Saturday''', &quot;Marmaduke&quot; in the ''Graphic'' took Bourke's side on the Summer Club in Kensington Park:&lt;blockquote&gt;Most of us have noticed that if we read in the newspapers the account of some matter which we are personally acquainted with the account will generally contain several errors. I have also noticed that when a question is asked in the House of Commons regarding some matter about which I know all the facts the question and the official answer to it frequently contain serious errors. Last week Mr. Akers-Douglas was asked in the House to explain how it was that Mr. Algernon Bourke obtained permission to open the &quot;Summer Club&quot; in Kensington Gardens, and he was questioned upon other particulars connected with the same matter. Both the questions and the official reply showed considerable ignorance of the facts. There has been from time immemorial a refreshment kiosk in Kensington Gardens. Mr. Bourke obtained from the tenant of this permission to use the kitchen for the benefit of the &quot;Summer Club,&quot; and to supply the members of the latter with refreshments. It was a purely commercial transaction. Mr. Bourke then established some wicker seats, a few tables, a tent, and a small hut upon a lawn in the neighbourhood of the kiosk. To do this he must have obtained the permission of Mr. Akers-Douglas, as obviously he would otherwise have been immediately ordered to remove them. Mr. Akers-Douglas equally obviously would not have given his sanction unless he had been previously informed of the objects which Mr. Bourke had in view — to wit, that the latter intended to establish a club there. That being the case, it is difficult to understand for what reason Mr. Akers-Douglas has now decided that any member of the public can use the chairs, tables, and tent belonging to the &quot;Summer Club,&quot; can insist upon the club servants attending upon him, and can compel them to supply him with refreshments. Mr. Akers-Douglas should have thought of the consequences before he granted the permission.&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Court and Club.&quot; The ''Graphic'' 04 July 1896, Saturday: 14 [of 32], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18960704/029/0014. Print p. 14.&lt;blockquote&gt;&lt;/blockquote&gt;&lt;/ref&gt;&lt;/blockquote&gt;'''1896 August 10, Monday''', the Morning Leader reported that the Hon. Algernon Bourke, for the Foreign Office, received Li Hung Chang at St. Paul's:&lt;blockquote&gt;At St. Paul's Li Hung was received by Field-Marshal Simmons, Colonel Lane, the Hon. Algernon Bourke, of the Foreign Office (who made the necessary arrangements for the visit) and Canon Newbolt, on behalf of the Dean and Chapter. A crowd greeted Li with a cheer as he drove up in Lord Lonsdale’s striking equipage, and his Excellency was carried up the steps in an invalid chair by two stalwart constables. He walked through the centre door with his suite, and was immediately conducted by Canon Newbolt to General Gordon’s tomb in the north aisle, where a detachment of boys from the Gordon Home received him as a guard of honor.

Li inspected the monument with marked interest, and drew the attention of his suite to the remarkable likeness to the dead hero. He laid a handsome wreath of royal purple asters, lilies, maidenhair fern, and laurel, tied with a broad band of purple silk, on the tomb.

The visit was not one of inspection of the building, but on passing the middle aisle the interpreter called the attention of His Excellency to the exquisite architecture and decoration of the chancel. Li shook hands in hearty English fashion with Canon Newbolt and the other gentlemen who had received him, and, assisted by his two sons, walked down the steps to his carriage. He returned with his suite to Carlton House-terrace by way of St. Paul’s Churchyard, Cannon-st., Queen Victoria-st., and the Embankment.&lt;ref&gt;&quot;At St. Paul's.&quot; ''Morning Leader'' 10 August 1896, Monday: 7 [of 12], Col. 2b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18960810/134/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;'''1896 August 19, Wednesday''', the ''Edinburgh Evening News'' reported on the catering that White's Club and Mr Algernon Bourke arranged for the visiting Li Hung Chang:&lt;blockquote&gt;It is probably not generally known (says the &quot;Chef&quot;) that Mr Algernon Bourke, manager of White's Club, London, has undertaken to the whole of the catering for our illustrious visitor front the Flowery Land. Li Hung Chang has five native cooks in his retinue, and the greatest good fellowship exists between them and their English ''confreres'', although considerable difficulty is experienced in conversation in understanding one another's meaning. There are between 40 and and 50 to cater for daily, besides a staff about 30; that Mr Lemaire finds his time fully occupied. The dishes for his Excellency are varied and miscellaneous, and from 14 to 20 courses are served at each meal. The bills of fare contain such items as bird's-nest soup, pigs' kidneys stewed in cream, boiled ducks and green ginger, sharks' fins, shrinips and prawns stewed with leeks and muscatel grapes, fat pork saute with peas and kidney beans. The meal usually winds with fruit and sponge cake, and freshly-picked green tea as liqueur.&lt;ref&gt;&quot;Li Hung Chang's Diet.&quot; ''Edinburgh Evening News'' 19 August 1896, Wednesday: 3 [of 4], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000452/18960819/057/0003.&lt;/ref&gt;&lt;/blockquote&gt;

'''1896 November 6, Friday''', Algernon Bourke was on the committee for [[Social Victorians/Timeline/1896#1896 November 6, Friday|the Prince's Club ice-skating rink, which opened on this day]].&lt;p&gt;

'''1896 November 25, Wednesday''', Mr. and Mrs. Algernon Bouke attended [[Social Victorians/Timeline/1896#23 November 1896, Monday23 November 1896, Monday|Lord and Lady Burton's party for Derby Day]].&lt;p&gt;
'''1896 December 4, Friday''', the Orleans Club at Brighton was robbed:&lt;blockquote&gt;The old building of the Orleans Club at Brighton, which opens its new club house at 33, Brunswick-terrace to-day, was the scene of a very ingenious burglary during the small hours of yesterday morning. The greater portion of the club property had already been removed to the new premises, but Mr Algernon Bourke, his private secretary, and some of the officials of the club, still occupied bed-rooms at the house in the King’s-road. The corner shop of the street front is occupied by Mr. Marx, a jeweller in a large way of business, and upon his manager arriving at nine o'clock he discovered that the place had been entered through hole in the ceiling, and a great part of a very valuable stock of jewelry extracted. An examination of the morning rooms of the club, which runs over Mr. Marx's establishment reveal a singularly neat  specimen of the burglar's art. A piece of the flooring about 15in square had been removed by a series of holes bored side by side with a centre-bit, at a spot where access to the lofty shop was rendered easy by a tall showcase which stood convemently near. A massive iron girder had been avoided by a quarter of an inch, and this circumstance and the general finish of the operation point to an artist in his profession, who had acquired an intimate knowledge of the premises. The club doors were all found locked yesterday morning, and the means of egress adopted by the thief are at present a mystery.&lt;ref&gt;&quot;Burglary at Brighton.&quot; ''Daily Telegraph &amp; Courier'' (London) 05 December 1896, Saturday: 5 [of 12], Col. 7a [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18961205/090/0005. Print title: ''Daily Telegraph''; p. 5.&lt;/ref&gt;&lt;/blockquote&gt;

'''1897 July 2, Friday''', the Hon. A. and Mrs. A. Bourke and Mr. and Mrs. Bourke attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House.&lt;p&gt;

'''23 July 1897 — or 30 July 1897 – Friday''', Guendonline Bourke attended [[Social Victorians/Timeline/1897#23 July 1897, Friday|Lady Burton's party at Chesterfield House]]. &lt;blockquote&gt;Far the prettiest women in the room were Lady Henry Bentinck (who looked perfectly lovely in pale yellow, with a Iong blue sash; and Mrs. Algernon Bourke, who was as smart as possible in pink, with pink and white ruchings on her sleeves and a tall pink feather in her hair.&lt;ref&gt;&quot;Lady Burton's Party at Chesterfield House.&quot; ''Belper &amp; Alfreton Chronicle'' 30 July 1897, Friday: 7 [of 8], Col. 1c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004151/18970730/162/0007. Print title: ''Belper and Alfreton Chronicle''; n.p.&lt;/ref&gt;&lt;/blockquote&gt;

'''1898 January 5, Wednesday''', the ''Irish Independent'' reported that &quot;Mr Algernon Bourke, the aristocratic stock broker ... was mainly responsible for the living pictures at the Blenheim Palace entertainment.&lt;ref&gt;&quot;Mr Algernon Bourke ....&quot; ''Irish Independent'' 05 January 1898, Wednesday: 6 [of 8], Col. 2c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001985/18980105/115/0006.&lt;/ref&gt;&lt;p&gt;

'''1899 January 10, Tuesday''', the Brighton Championship Dog Show opened:&lt;blockquote&gt;Princess of Wales a Winner at the Ladies’ Kennel Club Show.

[Exclusive to &quot;The Leader.&quot;)

The Brighton Championship Dog Show opened in the Dome and Corn Exchange yesterday, and was very well patronised by visitors and exhibitors. Among the latter was H.R.H. the Princess of Wales, who did very well; and others included Princess Sophie Duleep Singh, Countess De Grey, Sir Edgar Boehm, the Hon Mrs. Algernon Bourke, Lady Cathcart, Lady Reid, Mr. Shirley (chairman of the Kennel Club), and the Rev. Hans Hamiiton (president of the Kennel Club).

The entry of bloodhounds is one of the best seen for some time; the Great Danes are another stronyg lot; deerhounds are a fine entry, all good dogs, and most of the best kennels represented; borzois are another very stylish lot. The bigger dogs are, as usual, in the Corn Exchange and the &quot;toy&quot; dogs in the Dome. To everyone's satsfaction the Princess of Wales carried off two first prizes with Alex in the borzois class.&lt;ref&gt;&quot;Dogs at Brighton.&quot; ''Morning Leader'' 11 January 1899, Wednesday: 8 [of 12], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18990111/142/0008. Print p. 8.&lt;/ref&gt;&lt;/blockquote&gt;'''1899 January 11, Wednesday''', Guendoline Bourke attended [[Social Victorians/Timeline/1899#11 January 1899, Wednesday|a luncheon Stanfield-hall, home of Mr. and Mrs. Basil Montogomery, for Princess Henry of Battenberg]], that also included the Countess of Dudley (sister of Mrs. Montgomery), General Oliphant, and the Mayor and Mayoress of Romsey.

'''1899 February 7, Tuesday''', Guendoline Bourke was a member of the very high-ranking committee organizing a [[Social Victorians/Timeline/1899#1899 February 7, Tuesday|ball at the Hotel Cecil on 7 February 1899]].

'''1899 June 1, Thursday''', the Hon. Algernon and Guendoline Bourke attended the wedding of her brother, Sloane Stanley and Countess Cairns at Holy Trinity Church, Brompton.&lt;ref&gt;&quot;Marriage of Mr. Sloane Stanley and Countess Cairns.&quot; ''Hampshire Advertiser'' 03 June 1899, Saturday: 6 [of 8], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18990603/049/0006. Print p. 6.&lt;/ref&gt;&lt;p&gt;

'''1899 October 19, Thursday''', the Hon. Algernon Bourke had a bankruptcy hearing:&lt;blockquote&gt;The public examination of the Hon. Algernon Bourke was held before Mr Registrar Giffard yesterday, at the London Bankruptcy Court. The debtor, described as proprietor of a St. James's-street club, furnished a statement of affairs showing unsecured debts £13,694 and debts fully secured £12,800, with assets which are estimated at £4,489 [?]. He stated, in reply to the Official Receiver, that he was formerly a member of the Stock Exchange, but had nothing to do with the firm of which he was a member during the last ten years. He severed his connection with the firm in May last, and believed he was indebted to them to the extent of £2,000 or £3,000. He repudiated a claim which they now made for £37,300. In 1889 he became proprietor of White's Club, St. James's-street, and carried it on until January 1st last, when he transferred it to a company called Recreations, Limited. One of the objects of the company was to raise money on debentures. The examination was formally adjourned.&lt;ref name=&quot;:9&quot; /&gt;&lt;/blockquote&gt;'''1899 November 8, Wednesday''', the Hon. Algernon Bourke's bankruptcy case came up again:&lt;blockquote&gt;At Bankruptcy Court, yesterday, the case the Hon. Algernon Bourke again came on for hearing before Mr. Registrar Giffard, and the examination was concluded. The debtor has at various times been proprietor of White’s Club, St. James’s-street, and the Orleans’ Club, Brighton, and also of Willis's Restaurant, King-street, St. James's. He attributed his failure to losses sustained by the conversion of White’s Club and the Orleans' Club into limited companies, to the payment of excessive Interest on borrowed money, and other causes. The liabilities amount to £26,590, of which £13,694 are stated to be unsecured, and assets £4,409.&lt;ref&gt;&quot;Affairs of the Hon. A. Bourke.&quot; ''Globe'' 09 November 1899, Thursday: 2 [of 8], Col. 1c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001652/18991109/020/0002. Print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;

'''1899 December 23, Saturday''', &quot;Mr. Algernon Bourke has departed for a tour in Africa, being at present the guest of his brother in Tunis.&quot;&lt;ref&gt;&quot;The Society Pages.&quot; ''Walsall Advertiser'' 23 December 1899, Saturday: 7 [of 8], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001028/18991223/143/0007. Print p. 7.&lt;/ref&gt;

'''1900 February 15, Thursday''', Miss Daphne Bourke, the four-year-old daughter of the Hon. Algernon and Mrs. Bourke was a bridesmaid in the wedding of Enid Wilson and the Earl of Chesterfield, so presumably her parents were present as well.&lt;ref&gt;&quot;London Day by Day.&quot; ''Daily Telegraph'' 15 February 1900, Thursday: 8 [of 12], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/19000215/175/0008. Name in British Newspaper Archive: ''Daily Telegraph &amp; Courier'' (London). Print p. 8.&lt;/ref&gt;

'''1900 September 16''', the Hon. Algernon Bourke became the heir presumptive to the Earldom of Mayo when his older brother Captain Hon. Sir Maurice Archibald Bourke died.

'''1900 October 06, Saturday''', the ''Weekly Irish Times'' says that Mr. Algernon Bourke, now heir presumptive to the earldom of Mayo, &quot;has been for some months lately staying with Mr. Terence Bourke in Morocco.&quot;&lt;ref&gt;&quot;Society Gossip.&quot; ''Weekly Irish Times'' 06 October 1900, Saturday: 14 [of 20], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001684/19001006/121/0014. Print p. 14.&lt;/ref&gt;&lt;p&gt;

'''1901 May 30, Thursday''', the Hon. Mrs. Algernon Bourke attended the fashionable Ladies' Kennel Association Dog Show.&lt;p&gt;

'''1901 July 4, Thursday''', Guendoline and Daphne Bourke attended a children's party hosted by the Countess of Yarborough:&lt;blockquote&gt;The Countess of Yarborough gave a charming children's party on Thursday (4th) afternoon at her beautiful house in Arlington Street. The spacious ballroom was quite filled with little guests and their mothers. Each little guest received a lovely present from their kind hostess. The Duchess of Beaufort, in grey, and with a large black picture hat, brought her two lovely baby girls, Lady Blanche and Lady Diana Somerset, both in filmy cream [Col. 2b–3a] lace frocks. Lady Gertrude Corbett came with her children, and Ellen Lady Inchiquin with hers. Lady Southampton, in black, with lovely gold embroideries on her bodice, brought her children, as also did Lady Heneage and Mr. and Lady Beatrice Kaye. Lady Blanche Conyngham, in écru lace, over silk, and small straw hat, was there; also Mrs. Smith Barry, in a lovely gown of black and white lace. The Countess of Kilmorey, in a smart grey and white muslin, brought little Lady Cynthia Needham, in white; Mrs. Arthur James, in black and white muslin; and the Countess of Powys, in mauve silk with much white lace; Lady Sassoon, in black and white foulard; Victoria Countess of Yarborough, came on from hearing Mdme. Réjane at Mrs. Wernher's party at Bath House; and there were also present Lord Henry Vane-Tempest, the Earl of Yarborough, Lady Naylor-Leyland's little boys; the pretty children of Lady Constance Combe, Lady Florence Astley and her children, and Lady Meysey Thompson (very smart in mauve and white muslin) with her children; also Hon. Mrs. Algernon Bourke, in pale grey, with her pretty little girl.&lt;ref&gt;&quot;The Countess of Yarborough ....&quot; ''Gentlewoman'' 13 July 1901, Saturday: 76 [of 84], Col. 2b, 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010713/381/0076. Print p. xxxvi.&lt;/ref&gt;&lt;/blockquote&gt;'''1901 July 20, Saturday''', the ''Gentlewoman'' published the Hon. Mrs. Algernon Bourke's portrait (identified with &quot;Perthshire&quot;) in its 3rd series of &quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot;&lt;ref&gt;&quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot; ''Gentlewoman'' 20 July 1901, Saturday: 31 [of 60], Col. 4b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010720/141/0031. Print n.p.&lt;/ref&gt; Their daughter Daphne appears in the portrait as well.&lt;p&gt;

'''1901 September 12, Thursday''', Mrs. Guendoline Bourke's name is listed as Gwendolen Bourke, but the spelling is not what she objected to:&lt;blockquote&gt;Mr. Underhill, the Conservative agent, mentioned to the Revising Barrister (Mr. William F. Webster) that the name of the Hon. Mrs. Gwendolen Bourke was on the list in respect of the house, 75, Gloucester-place. The lady had written to him to say that she was the Hon. Mrs. Algernon Bourke and that she wished that name to appear on the register. In reply to the Revising Barrister, Mr. Underhill said that “Algernon” was the '''name the lady’s husband'''.

Mr. Cooke, the rate-collector, said that Mrs. Bourke had asked to be addressed Mrs. Algernon Bourke, but that the Town Clerk thought the address was not a correct one. The lady signed her cheques Gwendolen.”

Mr. Underhill said the agents frequently had indignant letters from ladies because they were not addressed by their husband’s Christian name.

The Revising Barrister — lf a lady gave me the name of Mrs. John Smith I should say I had not got the voter’s name. The name Gwendolen must remain.&lt;ref&gt;&quot;Ladies’ Names.&quot; ''Morning Post'' 12 September 1901, Thursday: 7 [of 10], Col. 3a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19010912/130/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;'''1902 September 4, Thursday''', the ''Daily Express'' reported that &quot;Mrs. Algernon Bourke is staying with Lord and Lady Alington at Scarborough.&quot;&lt;ref&gt;&quot;Onlooker.&quot; &quot;My Social Diary.&quot; &quot;Where People Are.&quot; ''Daily Express'' 04 September 1902, Thursday: 5 [of 8], Col. 1b? [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020904/099/0005. Print p. 4, Col. 7b [of 7].&lt;/ref&gt;&lt;p&gt;

'''1902 October 24, Friday''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#24 October 1902, Friday|opened the Prince's ice-skating rink for the season]], which he had been doing since 1895.

'''1902 December 9, Tuesday''', Guendonline Bourke attended [[Social Victorians/Timeline/1900s#9 December 1902, Tuesday|Lady Eva Wyndham-Quin's &quot;at home,&quot; held at the Welch Industrial depot]] for the sale Welsh-made Christmas gifts and cards. Bourke wore &quot;a fur coat and a black picture hat.&quot;&lt;ref&gt;&quot;A Lady Correspondent.&quot; &quot;Society in London.&quot; ''South Wales Daily News'' 11 December 1902, Thursday: 4 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000919/19021211/082/0004. Print p. 4.&lt;/ref&gt;

'''1903 March 17, Tuesday''', Guendoline Bourke staffed a booth at a [[Social Victorians/Timeline/1900s#1903 March 17, Tuesday|sale of the Irish Industries Association]] on St. Patrick's Day with [[Social Victorians/People/Mayo|Lady Mayo]], [[Social Victorians/People/Dudley|Georgina Lady Dudley]] and [[Social Victorians/People/Beresford|Miss Beresford]]. A number of other aristocratic women were also present at the sale in other booths, including [[Social Victorians/People/Londonderry|Lady Londonderry]] and [[Social Victorians/People/Lucan|Lady Lucan]].

'''1903 June 23, Tuesday''', Guendoline and Daphne Bourke were invited to a [[Social Victorians/Timeline/1900s#1903 June 23, Tuesday|children's party at Buckingham Palace for Prince Eddie's birthday]].

'''1905 February 17, Friday''', the Dundee ''Evening Post'' reported that Algernon Bourke &quot;set up a shop in Venice for the sale of art treasures and old furniture.&quot;&lt;ref&gt;&quot;Social News.&quot; Dundee ''Evening Post'' 17 February 1905, Friday: 6 [of 6], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000582/19050217/105/0006. Print p. 6.&lt;/ref&gt;

'''1905, last week of July''', Guendoline Bourke and daughter Daphne Bourke — who was 10 years old — attended [[Social Victorians/Timeline/1900s#Last week of July, 1905|Lady Cadogan's children's party at Chelsea House]]. Daphne was &quot;One of loveliest little girls present.&quot;&lt;ref&gt;&quot;Court and Social News.&quot; ''Belfast News-Letter'' 01 August 1905, Tuesday: 7 [of 10], Col. 6b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/19050801/157/0007. Print p. 7.&lt;/ref&gt;

'''1913 May 7, Wednesday''', Guendoline Bourke presented her daughter Daphne Bourke at court:&lt;blockquote&gt;Mrs. Algernon Bourke presented her daughter, and wore blue and gold broché with a gold lace train.&lt;ref&gt;&quot;Social and Personal.&quot; London ''Daily Chronicle'' 08 May 1913, Thursday: 6 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/19130508/120/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;The ''Pall Mall Gazette'' has a description of Daphne Bourke's dress, but what exactly &quot;chiffon [[Social Victorians/Terminology#Hoops|paniers]]&quot; means in 1913 is not clear:&lt;blockquote&gt;Court dressmakers appear to have surpassed all previous records in their efforts to make the dresses for to-night’s Court as beautiful as possible. Noticeable among these is the dainty presentation gown to be worn by Miss Bourke, who will be presented by her mother, the Hon. Mrs. Algernon Bourke. This has a skirt of soft white satin draped with chiffon [[Social Victorians/Terminology#Hoops|paniers]] and a bodice veiled with chiffon and trimmed with diamanté and crystal embroidery. Miss Bourke’s train, gracefully hung from the shoulders, is of white satin lined with pale rose pink chiffon and embroidered with crystal and diamanté.&lt;ref&gt;&quot;Fashion Day by Day. Lovely Gowns for To-night's Court.&quot; ''Pall Mall Gazette'' 07 May 1913, Wednesday: 13 [of 18], Col. 1a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/19130507/199/0013. Print n.p.&lt;/ref&gt;&lt;/blockquote&gt;

== Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball ==
According to both the ''Morning Post'' and the ''Times'', the Hon. Algernon Bourke was among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]] at the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]].&lt;ref name=&quot;:2&quot; /&gt;&lt;ref name=&quot;:3&quot; /&gt; Based on the people they were dressed as, Guendonine Bourke was probably in this procession but it seems unlikely that Algernone Bourke was.

[[File:Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.jpg|thumb|alt=Black-and-white photograph of a standing woman richly dressed in an historical costume with a headdress and a very large fan|Hon. Guendoline Bourke as Salammbô. ©National Portrait Gallery, London.]]
=== Hon. Guendoline Bourke ===
[[File:Alfons Mucha - 1896 - Salammbô.jpg|thumb|left|alt=Highly stylized orange-and-yellow painting of a bare-chested woman with a man playing a harp at her feet|Alfons Mucha's 1896 ''Salammbô''.]]
Lafayette's portrait (right) of &quot;Guendoline Irene Emily Bourke (née Sloane-Stanley) as Salammbô&quot; in costume is photogravure #128 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot;&gt;&quot;Devonshire House Fancy Dress Ball (1897): photogravures by Walker &amp; Boutall after various photographers.&quot; 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.&lt;/ref&gt; The printing on the portrait says, &quot;The Hon. Mrs. Algernon Bourke as Salammbo.&quot;&lt;ref&gt;&quot;Mrs. Algernon Bourke as Salammbo.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158491/Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.&lt;/ref&gt;

==== Newspaper Accounts ====
The Hon. Mrs. A. Bourke was dressed as

* Salambo in the Oriental procession.&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''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.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“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.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}
*&quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“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.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}

==== Salammbô ====
Salammbô is the eponymous protagonist in Gustave Flaubert's 1862 novel.&lt;ref name=&quot;:5&quot;&gt;{{Cite journal|date=2024-04-29|title=Salammbô|url=https://en.wikipedia.org/w/index.php?title=Salammb%C3%B4&amp;oldid=1221352216|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Salammb%C3%B4.&lt;/ref&gt; Ernest Reyer's opera ''Salammbô'' was based on Flaubert's novel and published in Paris in 1890 and performed in 1892&lt;ref&gt;{{Cite journal|date=2024-04-11|title=Ernest Reyer|url=https://en.wikipedia.org/w/index.php?title=Ernest_Reyer&amp;oldid=1218353215|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Ernest_Reyer.&lt;/ref&gt; (both Modest Mussorgsky and Sergei Rachmaninoff had attempted but not completed operas based on the novel as well&lt;ref name=&quot;:5&quot; /&gt;). Alfons Mucha's 1896 lithograph of Salammbô was published in 1896, the year before the ball (above left).[[File:Algernon Henry Bourke Vanity Fair 20 January 1898.jpg|thumb|alt=Old colored drawing of an elegant elderly man dressed in a 19th-century tuxedo with a cloak, top hat and formal pointed shoes with bows, standing facing 1/4 to his right|''Algy'' — Algernon Henry Bourke — by &quot;Spy,&quot; ''Vanity Fair'' 20 January 1898]]
=== Hon. Algernon Bourke ===
[[File:Hon-Algernon-Henry-Bourke-as-Izaak-Walton.jpg|thumb|left|alt=Black-and-white photograph of a man richly dressed in an historical costume sitting in a fireplace that does not have a fire and holding a tankard|Hon. Algernon Henry Bourke as Izaak Walton. ©National Portrait Gallery, London.]]
'''Lafayette's portrait''' (left) of &quot;Hon. Algernon Henry Bourke as Izaak Walton&quot; in costume is photogravure #129 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot; /&gt; The printing on the portrait says, &quot;The Hon. Algernon Bourke as Izaak Walton.&quot;&lt;ref&gt;&quot;Hon. Algernon Bourke as Izaak Walton.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158492/Hon-Algernon-Henry-Bourke-as-Izaak-Walton.&lt;/ref&gt;

This portrait is amazing and unusual: Algernon Bourke is not using a photographer's set with theatrical flats and props, certainly not one used by anyone else at the ball itself. Isaak Walton (baptised 21 September 1593 – 15 December 1683) wrote ''The Compleat Angler''.&lt;ref&gt;{{Cite journal|date=2021-09-15|title=Izaak Walton|url=https://en.wikipedia.org/w/index.php?title=Izaak_Walton&amp;oldid=1044447858|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Izaak_Walton.&lt;/ref&gt; A cottage Walton lived in and willed to the people of Stafford was photographed in 1888, suggesting that its relationship to Walton was known in 1897, raising a question about whether Bourke could have used the fireplace in the cottage for his portrait. (This same cottage still exists, as the [https://www.staffordbc.gov.uk/izaak-waltons-cottage Isaak Walton Cottage] museum.)

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{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)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

=== Mr. and Mrs. Bourke ===
The ''Times'' made a distinction between the Hon. Mr. and Mrs. A. Bourke and Mr. and Mrs. Bourke, including both in the article.&lt;ref name=&quot;:3&quot; /&gt; Occasionally this same article mentions the same people more than once in different contexts and parts of the article, so they may be the same couple. (See [[Social Victorians/People/Bourke#Notes and Question|Notes and Question]] #2, below.)

== Demographics ==
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;
=== Residences ===
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1890: 33 Cadogan Terrace
*1891: 33 Cadogan Terrace, Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

== Family ==
*Hon. Algernon Henry Bourke (31 December 1854 – 7 April 1922)&lt;ref&gt;&quot;Hon. Algernon Henry Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p29657.htm#i296561|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
*Guendoline Irene Emily Sloane-Stanley Bourke (c. 1869 – 30 December 1967)&lt;ref name=&quot;:1&quot;&gt;&quot;Guendoline Irene Emily Stanley.&quot; {{Cite web|url=https://www.thepeerage.com/p51525.htm#i515247|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
#Daphne Marjory Bourke (5 April 1895 – 22 May 1962)

=== Relations ===
*Hon. Algernon Henry Bourke (the 3rd son of the [[Social Victorians/People/Mayo|6th Earl of Mayo]]) was the older brother of Lady Florence Bourke.&lt;ref name=&quot;:0&quot; /&gt;

==== Other Bourkes ====
*Hubert Edward Madden Bourke (after 1925, Bourke-Borrowes)&lt;ref&gt;&quot;Hubert Edward Madden Bourke-Borrowes.&quot; {{Cite web|url=https://www.thepeerage.com/p52401.htm#i524004|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p52401.htm#i524004.&lt;/ref&gt;
*Lady Eva Constance Aline Bourke, who married [[Social Victorians/People/Dunraven|Windham Henry Wyndham-Quin]] on 7 July 1885;&lt;ref&gt;&quot;Lady Eva Constance Aline Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p2575.htm#i25747|title=Person Page|website=www.thepeerage.com|access-date=2020-12-02}} https://www.thepeerage.com/p2575.htm#i25747.&lt;/ref&gt; he became 5th Earl of Dunraven and Mount-Earl on 14 June 1926.
== Writings, Memoirs, Biographies, Papers ==

=== Writings ===
* Bourke, the Hon. Algernon. ''The History of White's''. London: Algernon Bourke [privately published], 1892.
* Bourke, the Hon. Algernon, ed., &quot;with a brief Memoir.&quot; ''Correspondence of Mr Joseph Jekyll with His Sister-in-Law, Lady Gertrude Sloane Stanley, 1818–1838''. John Murray, 1893.
* Bourke, the Hon. Algernon, ed. ''Correspondence of Mr Joseph Jekyll''. John Murray, 1894.

=== Papers ===
* Where are the papers for the Earl of Mayo family? Are Algernon Bourke's papers with them?

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
== Footnotes ==
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      <text bytes="57070" sha1="ni7incprr1k1yua7bf3btry29ovmhz2" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
* Mrs. Guendoline Bourke
* Lady Florence Bourke
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father.

== Overview ==
Although the Hon. Algernon Henry Bourke was born in Dublin in 1854 and came from a family whose title is in the Peerage of Ireland,&lt;ref name=&quot;:6&quot;&gt;1911 England Census.&lt;/ref&gt; he seems to have spent much of his adult life generally in England and especially in London.

Mrs. Guendoline Bourke was a noted horsewoman and an excellent shot, exhibited at dog shows successfully and was &quot;an appreciative listener to good music.&quot;&lt;ref&gt;&quot;Vanity Fair.&quot; ''Lady of the House'' 15 June 1899, Thursday: 4 [of 44], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004836/18990615/019/0004.&lt;/ref&gt; She was reported as attending many social events without her husband, usually with a quick description of what she wore.

The Hon. Algernon Bourke and Mr. Algernon Bourke, depending on the newspaper article, were the same person. Calling him Mr. Bourke in the newspapers, especially when considered as a businessman or (potential) member of Parliament, does not rule out the son of an earl, who would normally be accorded the honorific of ''Honorable''.

== Acquaintances, Friends and Enemies ==

=== Algernon Bourke ===

* [[Social Victorians/People/Montrose|Marcus Henry Milner]], &quot;one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys&quot;&lt;ref name=&quot;:8&quot;&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 2a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;
* Caroline, Duchess of Montrose — her &quot;legal advisor&quot; on the day of her marriage to Marcus Henry Milner&lt;ref&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 1b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;

=== Guendoline Bourke ===

* Lord and Lady Alington, Belvedere House, Scarborough

== Organizations ==

=== The Hon. Algernon Bourke ===
* Eton
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Stock Exchange ( – 1901 [at least])
* [[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)
* Willis's Rooms&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;

==== Boards of Directors ====
*1883: One of the directors, the Franco-English Tunisian Esparto Fibre Supply Company, Ltd.&lt;ref&gt;''Money Market Review'', 20 Jan 1883 (Vol 46): 124.&lt;/ref&gt;
*1891: One of the founders, the Discount Banking Company, Ltd., which says Algernon Bourke is a director of District Messenger Services and News Company, Ltd.&lt;ref&gt;&quot;Public Company.&quot; ''Nottingham Journal'' 31 October 1891, Saturday: 4 [of 8], Col. 8a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001896/18911031/099/0004. Print title: ''The Nottingham Daily Express'', p. 4.&lt;/ref&gt;
*1894: One of the directors, the Frozen Lake, Ltd., with Admiral Maxse, Lord [[Social Victorians/People/Beresford|Marcus Beresford]], [[Social Victorians/People/Williams|Hwfa Williams]]&lt;ref&gt;&quot;The Frozen Lake, Limited.&quot; ''St James's Gazette'' 08 June 1894, Friday: 15 [of 16], Col. 4a [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/18940608/085/0015. Print p. 15.&lt;/ref&gt;

=== Mr. Algernon Bourke ===

* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt;

== Timeline ==
'''1872 February 8''', Richard Bourke, 6th Earl of Mayo was assassinated while inspecting a &quot;convict settlement at Port Blair in the Andaman Islands ... by Sher Ali Afridi, a former Afghan soldier.&quot;&lt;ref&gt;{{Cite journal|date=2024-12-01|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo.&lt;/ref&gt; The Hon. Algernon's brother Dermot became the 7th Earl at 19 years old.

'''1876 November 24, Friday''', the Hon. Algernon Bourke was one of 6 men (2 students, one of whom was Bourke; 2 doctors; a tutor and another man) from Cambridge who gave evidence as witnesses in an inquest about the death from falling off a horse of a student.&lt;ref&gt;&quot;The Fatal Accident to a Sheffield Student at Cambridge.&quot; ''Sheffield Independent'' 25 November 1876, Saturday: 7 [of 12], Col. 5a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000181/18761125/040/0007. Print title: ''Sheffield and Rotherham Independent'', n. p.&lt;/ref&gt;

'''1884 May 3, Saturday''', the &quot;Rochester Conservatives&quot; announced that they would &quot;bring forward the Hon. Algernon Bourke, brother of Lord Mayo, as their second candidate,&quot;&lt;ref&gt;&quot;Election Intelligence.&quot; ''Yorkshire Gazette'' 03 May 1884, Saturday: 4 [of 12], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000266/18840503/011/0004.&lt;/ref&gt; but because he could not be the first candidate, Bourke declined.&lt;ref&gt;&quot;Rochester.&quot; London ''Daily Chronicle'' 09 May 1884, Friday: 3 [of 8], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/18840509/049/0003.&lt;/ref&gt;

'''1884 June 18, Wednesday''', Mr. Algernon Bourke was on a committee to watch a [[Social Victorians/Timeline/1884#18 June 1884, Wednesday|Mr. Bishop's &quot;thought-reading&quot; experiment]], which was based on a challenge by Henry Labourchere made the year before. This &quot;experiment&quot; took place before a fashionable audience.

'''1885 October 3, Saturday''', the Hon. Algernon Bourke was named as the Conservative candidate for Clapham in the Battersea and Clapham borough after the Redistribution Bill determined the electoral districts for South London.&lt;ref&gt;&quot;South London Candidates.&quot; ''South London Press'' 03 October 1885, Saturday: 9 [of 16], Col. 5b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18851003/096/0009. Print p. 9.&lt;/ref&gt; The Liberal candidate, who won, was Mr. J. F. Moulton.

'''1886 July 27, Tuesday''', Algernon Bourke attended a service honoring a memorial at St. Paul's for his father, who had been assassinated.&lt;ref&gt;&quot;Memorial to the Late Earl of Mayo.&quot; ''Northern Whig'' 28 July 1886, Wednesday: 6 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000434/18860728/143/0006. Print p. 6.&lt;/ref&gt;

'''1886 September 2, Thursday''', Mr. Algernon Bourke was part of a group of mostly aristocratic men taking part in [[Social Victorians/Timeline/1886#8 September 1886, Wednesday|a &quot;trial-rehearsal&quot; as part of Augustus Harris's production]] ''A Run of Luck'', about sports.

'''1886 October 2, Saturday''', the Duke of Beaufort and the Hon. Algernon Bourke arrived in Yougal: &quot;His grace has taken a residence at Lismore for a few weeks, to enjoy some salmon fishing on the Blackwater before the close of the season.&quot;&lt;ref&gt;&quot;Chippenham.&quot; ''Wilts and Gloucestershire Standard'' 02 October 1886, Saturday: 8 [of 8], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001955/18861002/142/0008. Print p. 8.&lt;/ref&gt;

'''1887 December 15''', Hon. Algernon Bourke and Guendoline Stanley were married at St. Paul's, Knightsbridge, by Bourke's uncle the Hon. and Rev. George Bourke. Only family members attended because of &quot;the recent death of a near relative of the bride.&quot;&lt;ref&gt;&quot;Court Circular.&quot; ''Morning Post'' 16 December 1887, Friday: 5 [of 8], Col. 7c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18871216/066/0005.&lt;/ref&gt;

'''1888 July 26''', [[Social Victorians/People/Montrose|Caroline Graham Stirling-Crawford]] (known as Mr. Manton for her horse-breeding and -racing operations) and Marcus Henry Milner married.&lt;ref name=&quot;:12&quot;&gt;&quot;Hon. Caroline Agnes Horsley-Beresford.&quot; {{Cite web|url=https://thepeerage.com/p6863.htm#i68622|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt; According to the ''Nottingham Evening Post'' of 31 July 1888,&lt;blockquote&gt;LONDON GOSSIP.

(From the ''World''.)

The marriage of &quot;Mr. Manton&quot; was the surprise as well the sensation of last week. Although some wise people noticed a certain amount of youthful ardour in the attentions paid by Mr. Marcus Henry Milner to Caroline Duchess of Montrose at '''Mrs. Oppenheim's ball''', nobody was prepared for the sudden ''dénouement''; '''and it''' were not for the accidental and unseen presence [[Social Victorians/People/Mildmay|a well-known musical amateur]] who had received permission to practice on the organ, the ceremony performed at half-past nine on Thursday morning at St. Andrew's, Fulham, by the Rev. Mr. Propert, would possibly have remained a secret for some time to come. Although the evergreen Duchess attains this year the limit of age prescribed the Psalmist, the bridegroom was only born in 1864. Mr. &quot;Harry&quot; Milner (familiarly known in the City as &quot;Millions&quot;) was one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys, and Mr. Algernon Bourke, the head of the house (who, of course, takes a fatherly interest in the match) went down to Fulham to give away the Duchess. The ceremony was followed by a ''partie carrée'' luncheon at the Bristol, and the honeymoon began with a visit to the Jockey Club box at Sandown. Mr. Milner and the Duchess of Montrose have now gone to Newmarket. The marriage causes a curious reshuffling of the cards of affinity. Mr. Milner is now the stepfather of the [[Social Victorians/People/Montrose|Duke of Montrose]], his senior by twelve years; he is also the father-in-law of [[Social Victorians/People/Lady Violet Greville|Lord Greville]], Mr. Murray of Polnaise, and [[Social Victorians/People/Breadalbane|Lord Breadalbane]].&lt;ref name=&quot;:8&quot; /&gt;&lt;/blockquote&gt;'''1888 December 1st week''', according to &quot;Society Gossip&quot; from the ''World'', the Hon. Algernon Bourke was suffering from malaria, presumably which he caught when he was in South Africa:&lt;blockquote&gt;I am sorry to hear that Mr. Algernon Bourke, who married Miss Sloane-Stanley a short time ago, has been very dangerously ill. Certain complications followed an attack of malarian fever, and last week his mother, the Dowager Lady Mayo, and his brother, Lord Mayo, were hastily summoned to Brighton. Since then a change for the better has taken place, and he is now out of danger.&lt;ref&gt;&quot;Society Gossip. What the ''World'' Says.&quot; ''Hampshire Advertiser'' 08 December 1888, Saturday: 2 [of 8], Col. 5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18881208/037/0002. Print title: ''The Hampshire Advertiser County Newspaper''; print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;'''1889 – 1899 January 1''', the Hon. Algernon Bourke was &quot;proprietor&quot; of White's Club, St. James's Street.&lt;ref name=&quot;:9&quot;&gt;&quot;The Hon. Algernon Bourke's Affairs.&quot; ''Eastern Morning News'' 19 October 1899, Thursday: 6 [of 8], Col. 7c [of7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001152/18991019/139/0006. Print p. 6.&lt;/ref&gt;

'''1889 June 8, Saturday''', the Hon. Algernon Bourke contributed some art he owned to the collection of the Royal Institute of Painters in Water-Colours' [[Social Victorians/Timeline/1889#8 June 1889, Saturday|exhibition of &quot;the works of the 'English Humourists in Art.'&quot;]]

'''1892''', the Hon. Algernon Bourke privately published his ''The History of White's'', the exclusive gentleman's club.

'''1893 February 11, Tuesday''', Algernon Bourke opened Willis's Restaurant:&lt;blockquote&gt;Mr. Algernon Bourke has in his time done many things, and has generally done them well. His recently published history of White's Club is now a standard work. White's Club itself was a few years ago in its agony when Mr. Bourke stepped in and gave it a renewed lease of life. Under Mr. Bourke's auspices &quot;Willis's Restaurant&quot; opened its doors to the public on Tuesday last in a portion of the premises formerly so well known as Willis's Rooms. This new venture is to rival the Amphitryon in the matter of cuisine and wines; but it is not, like the Amphitryon, a club, but open to the public generally. Besides the restaurant proper, there are several ''cabinets particuliers'', and these are decorated with the very best of taste, and contain some fine portraits of the Georges.&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Letter from the Linkman.&quot; ''Truth'' 20 April 1893, Thursday: 25 [of 56], Col. 1a [of 2]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025# https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025]. Print p. 855.&lt;/ref&gt;&lt;/blockquote&gt;'''1893 November 30, Thursday''', with Sir Walter Gilbey the Hon. Algernon Bourke &quot;assisted&quot; in &quot;forming [a] collection&quot; of engravings by George Morland that was exhibited at Messrs. J. and W. Vokins’s, Great Portland-street.&lt;ref&gt;&quot;The George Morland Exhibition at Vokins's.&quot; ''Sporting Life'' 30 November 1893, Thursday: 4 [of 4], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000893/18931130/058/0004.&lt;/ref&gt;

'''1895 February 23, Saturday''', the Hon. Algernon Bourke attended the [[Social Victorians/Timeline/1895#23 February 1895, Saturday|fashionable wedding of Laurence Currie and Edith Sibyl Mary Finch]].

'''1895 August 24, Saturday''', &quot;Marmaduke&quot; in the Graphic says that Algernon Bourke &quot;opened a cyclists' club in Chelsea.&quot;&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Court and Club.&quot; The ''Graphic'' 24 August 1895, Saturday: 11 [of 32], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18950824/017/0011. Print p. 223.&lt;/ref&gt;

'''1895 October''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#24 October 1902, Friday|opened the Prince's ice-skating rink for the season]].

'''1896 June 29, Monday''', Algernon Bourke published a letter to the editor of the ''Daily Telegraph'':&lt;blockquote&gt;To the Editor of “The Daily Telegraph.”

Sir — Permit me to make my bow to the public. I am the manager of the Summer Club, which on two occasions bas been the subject of Ministerial interpellation in Parliament. The Summer Club is a small combination, which conceived the idea of attempting to make life more pleasant in London by organising breakfast, luncheon, and teas in Kensington Gardens for its members. This appears to have given offence in some way to Dr. Tanner, with the result that the catering arrangements of the club are now &quot;by order&quot; thrown open to the public. No one is more pleased than I am at the result of the doctor's intervention, for it shows that the idea the Summer Club had of using the parks for something more than mere right of way bas been favourably received. In order, however, that the great British public may not be disappointed, should they all come to lunch at once, I think it necessary to explain that the kitchen, which by courtesy of the lessee of the kiosk our cook was permitted to use, is only 10ft by 5ft; it has also to serve as a scullery and pantry, and the larder, from which our luxurious viands are drawn, is a four-wheeled cab, which comes up every day with the food and returns after lunch with the scraps. Nevertheless, the Summer Club says to the British public — What we have we will share with you, though it don't amount to very much — I am, Sir, your obedient servant,

ALGERNON BOURKE.

White's Club, June 27&lt;ref&gt;&quot;The Summer Club.&quot; ''Daily Telegraph &amp; Courier'' (London) 29 June 1896, Monday: 8 [of 12], Col. 2b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18960629/072/0008. Print title: ''Daily Telegraph'', p. 8.&lt;/ref&gt;&lt;/blockquote&gt;'''1896 July 4, Saturday''', &quot;Marmaduke&quot; in the ''Graphic'' took Bourke's side on the Summer Club in Kensington Park:&lt;blockquote&gt;Most of us have noticed that if we read in the newspapers the account of some matter which we are personally acquainted with the account will generally contain several errors. I have also noticed that when a question is asked in the House of Commons regarding some matter about which I know all the facts the question and the official answer to it frequently contain serious errors. Last week Mr. Akers-Douglas was asked in the House to explain how it was that Mr. Algernon Bourke obtained permission to open the &quot;Summer Club&quot; in Kensington Gardens, and he was questioned upon other particulars connected with the same matter. Both the questions and the official reply showed considerable ignorance of the facts. There has been from time immemorial a refreshment kiosk in Kensington Gardens. Mr. Bourke obtained from the tenant of this permission to use the kitchen for the benefit of the &quot;Summer Club,&quot; and to supply the members of the latter with refreshments. It was a purely commercial transaction. Mr. Bourke then established some wicker seats, a few tables, a tent, and a small hut upon a lawn in the neighbourhood of the kiosk. To do this he must have obtained the permission of Mr. Akers-Douglas, as obviously he would otherwise have been immediately ordered to remove them. Mr. Akers-Douglas equally obviously would not have given his sanction unless he had been previously informed of the objects which Mr. Bourke had in view — to wit, that the latter intended to establish a club there. That being the case, it is difficult to understand for what reason Mr. Akers-Douglas has now decided that any member of the public can use the chairs, tables, and tent belonging to the &quot;Summer Club,&quot; can insist upon the club servants attending upon him, and can compel them to supply him with refreshments. Mr. Akers-Douglas should have thought of the consequences before he granted the permission.&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Court and Club.&quot; The ''Graphic'' 04 July 1896, Saturday: 14 [of 32], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18960704/029/0014. Print p. 14.&lt;blockquote&gt;&lt;/blockquote&gt;&lt;/ref&gt;&lt;/blockquote&gt;'''1896 August 10, Monday''', the Morning Leader reported that the Hon. Algernon Bourke, for the Foreign Office, received Li Hung Chang at St. Paul's:&lt;blockquote&gt;At St. Paul's Li Hung was received by Field-Marshal Simmons, Colonel Lane, the Hon. Algernon Bourke, of the Foreign Office (who made the necessary arrangements for the visit) and Canon Newbolt, on behalf of the Dean and Chapter. A crowd greeted Li with a cheer as he drove up in Lord Lonsdale’s striking equipage, and his Excellency was carried up the steps in an invalid chair by two stalwart constables. He walked through the centre door with his suite, and was immediately conducted by Canon Newbolt to General Gordon’s tomb in the north aisle, where a detachment of boys from the Gordon Home received him as a guard of honor.

Li inspected the monument with marked interest, and drew the attention of his suite to the remarkable likeness to the dead hero. He laid a handsome wreath of royal purple asters, lilies, maidenhair fern, and laurel, tied with a broad band of purple silk, on the tomb.

The visit was not one of inspection of the building, but on passing the middle aisle the interpreter called the attention of His Excellency to the exquisite architecture and decoration of the chancel. Li shook hands in hearty English fashion with Canon Newbolt and the other gentlemen who had received him, and, assisted by his two sons, walked down the steps to his carriage. He returned with his suite to Carlton House-terrace by way of St. Paul’s Churchyard, Cannon-st., Queen Victoria-st., and the Embankment.&lt;ref&gt;&quot;At St. Paul's.&quot; ''Morning Leader'' 10 August 1896, Monday: 7 [of 12], Col. 2b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18960810/134/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;'''1896 August 19, Wednesday''', the ''Edinburgh Evening News'' reported on the catering that White's Club and Mr Algernon Bourke arranged for the visiting Li Hung Chang:&lt;blockquote&gt;It is probably not generally known (says the &quot;Chef&quot;) that Mr Algernon Bourke, manager of White's Club, London, has undertaken to the whole of the catering for our illustrious visitor front the Flowery Land. Li Hung Chang has five native cooks in his retinue, and the greatest good fellowship exists between them and their English ''confreres'', although considerable difficulty is experienced in conversation in understanding one another's meaning. There are between 40 and and 50 to cater for daily, besides a staff about 30; that Mr Lemaire finds his time fully occupied. The dishes for his Excellency are varied and miscellaneous, and from 14 to 20 courses are served at each meal. The bills of fare contain such items as bird's-nest soup, pigs' kidneys stewed in cream, boiled ducks and green ginger, sharks' fins, shrinips and prawns stewed with leeks and muscatel grapes, fat pork saute with peas and kidney beans. The meal usually winds with fruit and sponge cake, and freshly-picked green tea as liqueur.&lt;ref&gt;&quot;Li Hung Chang's Diet.&quot; ''Edinburgh Evening News'' 19 August 1896, Wednesday: 3 [of 4], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000452/18960819/057/0003.&lt;/ref&gt;&lt;/blockquote&gt;

'''1896 November 6, Friday''', Algernon Bourke was on the committee for [[Social Victorians/Timeline/1896#1896 November 6, Friday|the Prince's Club ice-skating rink, which opened on this day]].&lt;p&gt;

'''1896 November 25, Wednesday''', Mr. and Mrs. Algernon Bouke attended [[Social Victorians/Timeline/1896#23 November 1896, Monday23 November 1896, Monday|Lord and Lady Burton's party for Derby Day]].&lt;p&gt;
'''1896 December 4, Friday''', the Orleans Club at Brighton was robbed:&lt;blockquote&gt;The old building of the Orleans Club at Brighton, which opens its new club house at 33, Brunswick-terrace to-day, was the scene of a very ingenious burglary during the small hours of yesterday morning. The greater portion of the club property had already been removed to the new premises, but Mr Algernon Bourke, his private secretary, and some of the officials of the club, still occupied bed-rooms at the house in the King’s-road. The corner shop of the street front is occupied by Mr. Marx, a jeweller in a large way of business, and upon his manager arriving at nine o'clock he discovered that the place had been entered through hole in the ceiling, and a great part of a very valuable stock of jewelry extracted. An examination of the morning rooms of the club, which runs over Mr. Marx's establishment reveal a singularly neat  specimen of the burglar's art. A piece of the flooring about 15in square had been removed by a series of holes bored side by side with a centre-bit, at a spot where access to the lofty shop was rendered easy by a tall showcase which stood convemently near. A massive iron girder had been avoided by a quarter of an inch, and this circumstance and the general finish of the operation point to an artist in his profession, who had acquired an intimate knowledge of the premises. The club doors were all found locked yesterday morning, and the means of egress adopted by the thief are at present a mystery.&lt;ref&gt;&quot;Burglary at Brighton.&quot; ''Daily Telegraph &amp; Courier'' (London) 05 December 1896, Saturday: 5 [of 12], Col. 7a [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18961205/090/0005. Print title: ''Daily Telegraph''; p. 5.&lt;/ref&gt;&lt;/blockquote&gt;

'''1897 July 2, Friday''', the Hon. A. and Mrs. A. Bourke and Mr. and Mrs. Bourke attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House.&lt;p&gt;

'''23 July 1897 — or 30 July 1897 – Friday''', Guendonline Bourke attended [[Social Victorians/Timeline/1897#23 July 1897, Friday|Lady Burton's party at Chesterfield House]]. &lt;blockquote&gt;Far the prettiest women in the room were Lady Henry Bentinck (who looked perfectly lovely in pale yellow, with a Iong blue sash; and Mrs. Algernon Bourke, who was as smart as possible in pink, with pink and white ruchings on her sleeves and a tall pink feather in her hair.&lt;ref&gt;&quot;Lady Burton's Party at Chesterfield House.&quot; ''Belper &amp; Alfreton Chronicle'' 30 July 1897, Friday: 7 [of 8], Col. 1c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004151/18970730/162/0007. Print title: ''Belper and Alfreton Chronicle''; n.p.&lt;/ref&gt;&lt;/blockquote&gt;

'''1898 January 5, Wednesday''', the ''Irish Independent'' reported that &quot;Mr Algernon Bourke, the aristocratic stock broker ... was mainly responsible for the living pictures at the Blenheim Palace entertainment.&lt;ref&gt;&quot;Mr Algernon Bourke ....&quot; ''Irish Independent'' 05 January 1898, Wednesday: 6 [of 8], Col. 2c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001985/18980105/115/0006.&lt;/ref&gt;&lt;p&gt;

'''1899 January 10, Tuesday''', the Brighton Championship Dog Show opened:&lt;blockquote&gt;Princess of Wales a Winner at the Ladies’ Kennel Club Show.

[Exclusive to &quot;The Leader.&quot;)

The Brighton Championship Dog Show opened in the Dome and Corn Exchange yesterday, and was very well patronised by visitors and exhibitors. Among the latter was H.R.H. the Princess of Wales, who did very well; and others included Princess Sophie Duleep Singh, Countess De Grey, Sir Edgar Boehm, the Hon Mrs. Algernon Bourke, Lady Cathcart, Lady Reid, Mr. Shirley (chairman of the Kennel Club), and the Rev. Hans Hamiiton (president of the Kennel Club).

The entry of bloodhounds is one of the best seen for some time; the Great Danes are another stronyg lot; deerhounds are a fine entry, all good dogs, and most of the best kennels represented; borzois are another very stylish lot. The bigger dogs are, as usual, in the Corn Exchange and the &quot;toy&quot; dogs in the Dome. To everyone's satsfaction the Princess of Wales carried off two first prizes with Alex in the borzois class.&lt;ref&gt;&quot;Dogs at Brighton.&quot; ''Morning Leader'' 11 January 1899, Wednesday: 8 [of 12], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18990111/142/0008. Print p. 8.&lt;/ref&gt;&lt;/blockquote&gt;'''1899 January 11, Wednesday''', Guendoline Bourke attended [[Social Victorians/Timeline/1899#11 January 1899, Wednesday|a luncheon Stanfield-hall, home of Mr. and Mrs. Basil Montogomery, for Princess Henry of Battenberg]], that also included the Countess of Dudley (sister of Mrs. Montgomery), General Oliphant, and the Mayor and Mayoress of Romsey.

'''1899 February 7, Tuesday''', Guendoline Bourke was a member of the very high-ranking committee organizing a [[Social Victorians/Timeline/1899#1899 February 7, Tuesday|ball at the Hotel Cecil on 7 February 1899]].

'''1899 June 1, Thursday''', the Hon. Algernon and Guendoline Bourke attended the wedding of her brother, Sloane Stanley and Countess Cairns at Holy Trinity Church, Brompton.&lt;ref&gt;&quot;Marriage of Mr. Sloane Stanley and Countess Cairns.&quot; ''Hampshire Advertiser'' 03 June 1899, Saturday: 6 [of 8], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18990603/049/0006. Print p. 6.&lt;/ref&gt;&lt;p&gt;

'''1899 October 19, Thursday''', the Hon. Algernon Bourke had a bankruptcy hearing:&lt;blockquote&gt;The public examination of the Hon. Algernon Bourke was held before Mr Registrar Giffard yesterday, at the London Bankruptcy Court. The debtor, described as proprietor of a St. James's-street club, furnished a statement of affairs showing unsecured debts £13,694 and debts fully secured £12,800, with assets which are estimated at £4,489 [?]. He stated, in reply to the Official Receiver, that he was formerly a member of the Stock Exchange, but had nothing to do with the firm of which he was a member during the last ten years. He severed his connection with the firm in May last, and believed he was indebted to them to the extent of £2,000 or £3,000. He repudiated a claim which they now made for £37,300. In 1889 he became proprietor of White's Club, St. James's-street, and carried it on until January 1st last, when he transferred it to a company called Recreations, Limited. One of the objects of the company was to raise money on debentures. The examination was formally adjourned.&lt;ref name=&quot;:9&quot; /&gt;&lt;/blockquote&gt;'''1899 November 8, Wednesday''', the Hon. Algernon Bourke's bankruptcy case came up again:&lt;blockquote&gt;At Bankruptcy Court, yesterday, the case the Hon. Algernon Bourke again came on for hearing before Mr. Registrar Giffard, and the examination was concluded. The debtor has at various times been proprietor of White’s Club, St. James’s-street, and the Orleans’ Club, Brighton, and also of Willis's Restaurant, King-street, St. James's. He attributed his failure to losses sustained by the conversion of White’s Club and the Orleans' Club into limited companies, to the payment of excessive Interest on borrowed money, and other causes. The liabilities amount to £26,590, of which £13,694 are stated to be unsecured, and assets £4,409.&lt;ref&gt;&quot;Affairs of the Hon. A. Bourke.&quot; ''Globe'' 09 November 1899, Thursday: 2 [of 8], Col. 1c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001652/18991109/020/0002. Print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;

'''1899 December 23, Saturday''', &quot;Mr. Algernon Bourke has departed for a tour in Africa, being at present the guest of his brother in Tunis.&quot;&lt;ref&gt;&quot;The Society Pages.&quot; ''Walsall Advertiser'' 23 December 1899, Saturday: 7 [of 8], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001028/18991223/143/0007. Print p. 7.&lt;/ref&gt;

'''1900 February 15, Thursday''', Miss Daphne Bourke, the four-year-old daughter of the Hon. Algernon and Mrs. Bourke was a bridesmaid in the wedding of Enid Wilson and the Earl of Chesterfield, so presumably her parents were present as well.&lt;ref&gt;&quot;London Day by Day.&quot; ''Daily Telegraph'' 15 February 1900, Thursday: 8 [of 12], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/19000215/175/0008. Name in British Newspaper Archive: ''Daily Telegraph &amp; Courier'' (London). Print p. 8.&lt;/ref&gt;

'''1900 September 16''', the Hon. Algernon Bourke became the heir presumptive to the Earldom of Mayo when his older brother Captain Hon. Sir Maurice Archibald Bourke died.

'''1900 October 06, Saturday''', the ''Weekly Irish Times'' says that Mr. Algernon Bourke, now heir presumptive to the earldom of Mayo, &quot;has been for some months lately staying with Mr. Terence Bourke in Morocco.&quot;&lt;ref&gt;&quot;Society Gossip.&quot; ''Weekly Irish Times'' 06 October 1900, Saturday: 14 [of 20], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001684/19001006/121/0014. Print p. 14.&lt;/ref&gt;&lt;p&gt;

'''1901 May 30, Thursday''', the Hon. Mrs. Algernon Bourke attended the fashionable [[Social Victorians/Timeline/1900s#1901 May 30, Thursday|Ladies' Kennel Association Dog Show at the Botanic Garden]].&lt;p&gt;

'''1901 July 4, Thursday''', Guendoline and Daphne Bourke attended a children's party hosted by the Countess of Yarborough:&lt;blockquote&gt;The Countess of Yarborough gave a charming children's party on Thursday (4th) afternoon at her beautiful house in Arlington Street. The spacious ballroom was quite filled with little guests and their mothers. Each little guest received a lovely present from their kind hostess. The Duchess of Beaufort, in grey, and with a large black picture hat, brought her two lovely baby girls, Lady Blanche and Lady Diana Somerset, both in filmy cream [Col. 2b–3a] lace frocks. Lady Gertrude Corbett came with her children, and Ellen Lady Inchiquin with hers. Lady Southampton, in black, with lovely gold embroideries on her bodice, brought her children, as also did Lady Heneage and Mr. and Lady Beatrice Kaye. Lady Blanche Conyngham, in écru lace, over silk, and small straw hat, was there; also Mrs. Smith Barry, in a lovely gown of black and white lace. The Countess of Kilmorey, in a smart grey and white muslin, brought little Lady Cynthia Needham, in white; Mrs. Arthur James, in black and white muslin; and the Countess of Powys, in mauve silk with much white lace; Lady Sassoon, in black and white foulard; Victoria Countess of Yarborough, came on from hearing Mdme. Réjane at Mrs. Wernher's party at Bath House; and there were also present Lord Henry Vane-Tempest, the Earl of Yarborough, Lady Naylor-Leyland's little boys; the pretty children of Lady Constance Combe, Lady Florence Astley and her children, and Lady Meysey Thompson (very smart in mauve and white muslin) with her children; also Hon. Mrs. Algernon Bourke, in pale grey, with her pretty little girl.&lt;ref&gt;&quot;The Countess of Yarborough ....&quot; ''Gentlewoman'' 13 July 1901, Saturday: 76 [of 84], Col. 2b, 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010713/381/0076. Print p. xxxvi.&lt;/ref&gt;&lt;/blockquote&gt;'''1901 July 20, Saturday''', the ''Gentlewoman'' published the Hon. Mrs. Algernon Bourke's portrait (identified with &quot;Perthshire&quot;) in its 3rd series of &quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot;&lt;ref&gt;&quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot; ''Gentlewoman'' 20 July 1901, Saturday: 31 [of 60], Col. 4b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010720/141/0031. Print n.p.&lt;/ref&gt; Their daughter Daphne appears in the portrait as well.&lt;p&gt;

'''1901 September 12, Thursday''', Mrs. Guendoline Bourke's name is listed as Gwendolen Bourke, but the spelling is not what she objected to:&lt;blockquote&gt;Mr. Underhill, the Conservative agent, mentioned to the Revising Barrister (Mr. William F. Webster) that the name of the Hon. Mrs. Gwendolen Bourke was on the list in respect of the house, 75, Gloucester-place. The lady had written to him to say that she was the Hon. Mrs. Algernon Bourke and that she wished that name to appear on the register. In reply to the Revising Barrister, Mr. Underhill said that “Algernon” was the '''name the lady’s husband'''.

Mr. Cooke, the rate-collector, said that Mrs. Bourke had asked to be addressed Mrs. Algernon Bourke, but that the Town Clerk thought the address was not a correct one. The lady signed her cheques Gwendolen.”

Mr. Underhill said the agents frequently had indignant letters from ladies because they were not addressed by their husband’s Christian name.

The Revising Barrister — lf a lady gave me the name of Mrs. John Smith I should say I had not got the voter’s name. The name Gwendolen must remain.&lt;ref&gt;&quot;Ladies’ Names.&quot; ''Morning Post'' 12 September 1901, Thursday: 7 [of 10], Col. 3a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19010912/130/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;'''1902 September 4, Thursday''', the ''Daily Express'' reported that &quot;Mrs. Algernon Bourke is staying with Lord and Lady Alington at Scarborough.&quot;&lt;ref&gt;&quot;Onlooker.&quot; &quot;My Social Diary.&quot; &quot;Where People Are.&quot; ''Daily Express'' 04 September 1902, Thursday: 5 [of 8], Col. 1b? [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020904/099/0005. Print p. 4, Col. 7b [of 7].&lt;/ref&gt;&lt;p&gt;

'''1902 October 24, Friday''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#24 October 1902, Friday|opened the Prince's ice-skating rink for the season]], which he had been doing since 1895.

'''1902 December 9, Tuesday''', Guendonline Bourke attended [[Social Victorians/Timeline/1900s#9 December 1902, Tuesday|Lady Eva Wyndham-Quin's &quot;at home,&quot; held at the Welch Industrial depot]] for the sale Welsh-made Christmas gifts and cards. Bourke wore &quot;a fur coat and a black picture hat.&quot;&lt;ref&gt;&quot;A Lady Correspondent.&quot; &quot;Society in London.&quot; ''South Wales Daily News'' 11 December 1902, Thursday: 4 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000919/19021211/082/0004. Print p. 4.&lt;/ref&gt;

'''1903 March 17, Tuesday''', Guendoline Bourke staffed a booth at a [[Social Victorians/Timeline/1900s#1903 March 17, Tuesday|sale of the Irish Industries Association]] on St. Patrick's Day with [[Social Victorians/People/Mayo|Lady Mayo]], [[Social Victorians/People/Dudley|Georgina Lady Dudley]] and [[Social Victorians/People/Beresford|Miss Beresford]]. A number of other aristocratic women were also present at the sale in other booths, including [[Social Victorians/People/Londonderry|Lady Londonderry]] and [[Social Victorians/People/Lucan|Lady Lucan]].

'''1903 June 23, Tuesday''', Guendoline and Daphne Bourke were invited to a [[Social Victorians/Timeline/1900s#1903 June 23, Tuesday|children's party at Buckingham Palace for Prince Eddie's birthday]].

'''1905 February 17, Friday''', the Dundee ''Evening Post'' reported that Algernon Bourke &quot;set up a shop in Venice for the sale of art treasures and old furniture.&quot;&lt;ref&gt;&quot;Social News.&quot; Dundee ''Evening Post'' 17 February 1905, Friday: 6 [of 6], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000582/19050217/105/0006. Print p. 6.&lt;/ref&gt;

'''1905, last week of July''', Guendoline Bourke and daughter Daphne Bourke — who was 10 years old — attended [[Social Victorians/Timeline/1900s#Last week of July, 1905|Lady Cadogan's children's party at Chelsea House]]. Daphne was &quot;One of loveliest little girls present.&quot;&lt;ref&gt;&quot;Court and Social News.&quot; ''Belfast News-Letter'' 01 August 1905, Tuesday: 7 [of 10], Col. 6b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/19050801/157/0007. Print p. 7.&lt;/ref&gt;

'''1913 May 7, Wednesday''', Guendoline Bourke presented her daughter Daphne Bourke at court:&lt;blockquote&gt;Mrs. Algernon Bourke presented her daughter, and wore blue and gold broché with a gold lace train.&lt;ref&gt;&quot;Social and Personal.&quot; London ''Daily Chronicle'' 08 May 1913, Thursday: 6 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/19130508/120/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;The ''Pall Mall Gazette'' has a description of Daphne Bourke's dress, but what exactly &quot;chiffon [[Social Victorians/Terminology#Hoops|paniers]]&quot; means in 1913 is not clear:&lt;blockquote&gt;Court dressmakers appear to have surpassed all previous records in their efforts to make the dresses for to-night’s Court as beautiful as possible. Noticeable among these is the dainty presentation gown to be worn by Miss Bourke, who will be presented by her mother, the Hon. Mrs. Algernon Bourke. This has a skirt of soft white satin draped with chiffon [[Social Victorians/Terminology#Hoops|paniers]] and a bodice veiled with chiffon and trimmed with diamanté and crystal embroidery. Miss Bourke’s train, gracefully hung from the shoulders, is of white satin lined with pale rose pink chiffon and embroidered with crystal and diamanté.&lt;ref&gt;&quot;Fashion Day by Day. Lovely Gowns for To-night's Court.&quot; ''Pall Mall Gazette'' 07 May 1913, Wednesday: 13 [of 18], Col. 1a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/19130507/199/0013. Print n.p.&lt;/ref&gt;&lt;/blockquote&gt;'''1904 September 15, Thursday''', according to what was at the time called the ''Irish Daily Independent and Nation'', Algernon Bourke was living in Venice and not in the UK at this point:&lt;blockquote&gt;Algernon Bourke, who usually lives in Venice, has spent some time in England during the present summer, and has now gone on a fishing expedition to Sweden, accompanied by his brother, Lord Mayo. Lady Mayo has been staying meanwhile in Ireland, and has had a visit from her mother, Lady Maria Ponsonby, who is a sister of Lend Obventry.&lt;ref name=&quot;:10&quot;&gt;&quot;Society Notes.&quot; ''Irish Independent'' 15 September 1904, Thursday: 4 [of 8], Col. 5b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001986/19040915/131/0004. Print title: ''Irish Daily Independent and Nation'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;'''1909 May 22, Saturday''', Algernon Bourke appears to have been living in Pisa. A columnist for the ''Queen'' reported on the Royal School of Art Needlework:&lt;blockquote&gt;Lady Leconfield [?] was there, also her sister-in-law, the Dowager Lady Mayo, only just back from her winter on the Continent, when she spent most of the time at Pisa, where her son Mr Algernon Bourke has also been staying. The latter is a great connoisseur as regards [art?] notably in what is really good in the way of old Italian sculpture and carving. He and his handsome wife have a place near to Putney, and this winter again Mr Bourke, as the result of his Italian travels, has been sending home such relics of the old Italian palace gardens as as stone and marble carved vases, garden seats, and what-not of the kind — not all for himself and his own gardens by any means, I fancy; but his friends, relying on his knowledge in such matters, get him when abroad to choose for [them?] the adornment of their English terraces and gardens.&lt;ref&gt;&quot;My Social Diary.&quot; The ''Queen'' 22 May 1909, Saturday: 31 [of 86], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19090522/203/0031. Print p. 871.&lt;/ref&gt;&lt;/blockquote&gt;

== Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball ==
According to both the ''Morning Post'' and the ''Times'', the Hon. Algernon Bourke was among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]] at the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]].&lt;ref name=&quot;:2&quot; /&gt;&lt;ref name=&quot;:3&quot; /&gt; Based on the people they were dressed as, Guendonine Bourke was probably in this procession but it seems unlikely that Algernone Bourke was.

[[File:Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.jpg|thumb|alt=Black-and-white photograph of a standing woman richly dressed in an historical costume with a headdress and a very large fan|Hon. Guendoline Bourke as Salammbô. ©National Portrait Gallery, London.]]
=== Hon. Guendoline Bourke ===
[[File:Alfons Mucha - 1896 - Salammbô.jpg|thumb|left|alt=Highly stylized orange-and-yellow painting of a bare-chested woman with a man playing a harp at her feet|Alfons Mucha's 1896 ''Salammbô''.]]
Lafayette's portrait (right) of &quot;Guendoline Irene Emily Bourke (née Sloane-Stanley) as Salammbô&quot; in costume is photogravure #128 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot;&gt;&quot;Devonshire House Fancy Dress Ball (1897): photogravures by Walker &amp; Boutall after various photographers.&quot; 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.&lt;/ref&gt; The printing on the portrait says, &quot;The Hon. Mrs. Algernon Bourke as Salammbo.&quot;&lt;ref&gt;&quot;Mrs. Algernon Bourke as Salammbo.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158491/Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.&lt;/ref&gt;

==== Newspaper Accounts ====
The Hon. Mrs. A. Bourke was dressed as

* Salambo in the Oriental procession.&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''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.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“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.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}
*&quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“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.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}

==== Salammbô ====
Salammbô is the eponymous protagonist in Gustave Flaubert's 1862 novel.&lt;ref name=&quot;:5&quot;&gt;{{Cite journal|date=2024-04-29|title=Salammbô|url=https://en.wikipedia.org/w/index.php?title=Salammb%C3%B4&amp;oldid=1221352216|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Salammb%C3%B4.&lt;/ref&gt; Ernest Reyer's opera ''Salammbô'' was based on Flaubert's novel and published in Paris in 1890 and performed in 1892&lt;ref&gt;{{Cite journal|date=2024-04-11|title=Ernest Reyer|url=https://en.wikipedia.org/w/index.php?title=Ernest_Reyer&amp;oldid=1218353215|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Ernest_Reyer.&lt;/ref&gt; (both Modest Mussorgsky and Sergei Rachmaninoff had attempted but not completed operas based on the novel as well&lt;ref name=&quot;:5&quot; /&gt;). Alfons Mucha's 1896 lithograph of Salammbô was published in 1896, the year before the ball (above left).[[File:Algernon Henry Bourke Vanity Fair 20 January 1898.jpg|thumb|alt=Old colored drawing of an elegant elderly man dressed in a 19th-century tuxedo with a cloak, top hat and formal pointed shoes with bows, standing facing 1/4 to his right|''Algy'' — Algernon Henry Bourke — by &quot;Spy,&quot; ''Vanity Fair'' 20 January 1898]]
=== Hon. Algernon Bourke ===
[[File:Hon-Algernon-Henry-Bourke-as-Izaak-Walton.jpg|thumb|left|alt=Black-and-white photograph of a man richly dressed in an historical costume sitting in a fireplace that does not have a fire and holding a tankard|Hon. Algernon Henry Bourke as Izaak Walton. ©National Portrait Gallery, London.]]
'''Lafayette's portrait''' (left) of &quot;Hon. Algernon Henry Bourke as Izaak Walton&quot; in costume is photogravure #129 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot; /&gt; The printing on the portrait says, &quot;The Hon. Algernon Bourke as Izaak Walton.&quot;&lt;ref&gt;&quot;Hon. Algernon Bourke as Izaak Walton.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158492/Hon-Algernon-Henry-Bourke-as-Izaak-Walton.&lt;/ref&gt;

This portrait is amazing and unusual: Algernon Bourke is not using a photographer's set with theatrical flats and props, certainly not one used by anyone else at the ball itself. Isaak Walton (baptised 21 September 1593 – 15 December 1683) wrote ''The Compleat Angler''.&lt;ref&gt;{{Cite journal|date=2021-09-15|title=Izaak Walton|url=https://en.wikipedia.org/w/index.php?title=Izaak_Walton&amp;oldid=1044447858|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Izaak_Walton.&lt;/ref&gt; A cottage Walton lived in and willed to the people of Stafford was photographed in 1888, suggesting that its relationship to Walton was known in 1897, raising a question about whether Bourke could have used the fireplace in the cottage for his portrait. (This same cottage still exists, as the [https://www.staffordbc.gov.uk/izaak-waltons-cottage Isaak Walton Cottage] museum.)

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{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)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

=== Mr. and Mrs. Bourke ===
The ''Times'' made a distinction between the Hon. Mr. and Mrs. A. Bourke and Mr. and Mrs. Bourke, including both in the article.&lt;ref name=&quot;:3&quot; /&gt; Occasionally this same article mentions the same people more than once in different contexts and parts of the article, so they may be the same couple. (See [[Social Victorians/People/Bourke#Notes and Question|Notes and Question]] #2, below.)

== Demographics ==
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;
=== Residences ===
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1890: 33 Cadogan Terrace
*1891: 33 Cadogan Terrace, Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1904: Algernon Bourke was &quot;usually liv[ing] in Venice&quot;&lt;ref name=&quot;:10&quot; /&gt;
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

== Family ==
*Hon. Algernon Henry Bourke (31 December 1854 – 7 April 1922)&lt;ref&gt;&quot;Hon. Algernon Henry Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p29657.htm#i296561|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
*Guendoline Irene Emily Sloane-Stanley Bourke (c. 1869 – 30 December 1967)&lt;ref name=&quot;:1&quot;&gt;&quot;Guendoline Irene Emily Stanley.&quot; {{Cite web|url=https://www.thepeerage.com/p51525.htm#i515247|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
#Daphne Marjory Bourke (5 April 1895 – 22 May 1962)

=== Relations ===
*Hon. Algernon Henry Bourke (the 3rd son of the [[Social Victorians/People/Mayo|6th Earl of Mayo]]) was the older brother of Lady Florence Bourke.&lt;ref name=&quot;:0&quot; /&gt;

==== Other Bourkes ====
*Hubert Edward Madden Bourke (after 1925, Bourke-Borrowes)&lt;ref&gt;&quot;Hubert Edward Madden Bourke-Borrowes.&quot; {{Cite web|url=https://www.thepeerage.com/p52401.htm#i524004|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p52401.htm#i524004.&lt;/ref&gt;
*Lady Eva Constance Aline Bourke, who married [[Social Victorians/People/Dunraven|Windham Henry Wyndham-Quin]] on 7 July 1885;&lt;ref&gt;&quot;Lady Eva Constance Aline Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p2575.htm#i25747|title=Person Page|website=www.thepeerage.com|access-date=2020-12-02}} https://www.thepeerage.com/p2575.htm#i25747.&lt;/ref&gt; he became 5th Earl of Dunraven and Mount-Earl on 14 June 1926.
== Writings, Memoirs, Biographies, Papers ==

=== Writings ===
* Bourke, the Hon. Algernon. ''The History of White's''. London: Algernon Bourke [privately published], 1892.
* Bourke, the Hon. Algernon, ed., &quot;with a brief Memoir.&quot; ''Correspondence of Mr Joseph Jekyll with His Sister-in-Law, Lady Gertrude Sloane Stanley, 1818–1838''. John Murray, 1893.
* Bourke, the Hon. Algernon, ed. ''Correspondence of Mr Joseph Jekyll''. John Murray, 1894.

=== Papers ===
* Where are the papers for the Earl of Mayo family? Are Algernon Bourke's papers with them?

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
== Footnotes ==
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    <title>Social Victorians/People/Montrose</title>
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      <text bytes="24087" sha1="4uactvxo5jbsf0rfm3hsf2j6cxeg2l4" xml:space="preserve">== Overview ==
The &quot;aristocratic lady writer&quot; [[Social Victorians/People/Lady Violet Greville |Lady Violet Greville]] (Beatrice Violet Graham Greville) was the daughter of James Graham, 4th Duke of Montrose and Caroline Graham, Duchess of Montrose, who married two more times after the Duke of Montrose died in 1874. The 5th Duchess, sister in law of Lady Violet Graham the writer, was also named Violet: Violet Hermione (née Graham) Graham.

Known on the track as Mr Manton, Caroline Graham ran a successful stable and had a larger-than-life and, apparently, difficult personality. In &quot;The Vagaries of 'Mr Manton,&quot; the ''Dundee Evening Telegraph'' reports stories about Caroline, Duchess of Montrose's temper, her loss of a lady's maid she had mistreated and her demand that she be carried up the new elevator shaft by a groomsman:&lt;blockquote&gt;The death of the Dowager-Duchess Montrose has deprived sporting society of one of its most remarkable figures and smoking-room raconteurs of inexhaustible material. &quot;Mr Manton's&quot; notoriously violent temper was responsible for most of the anecdotes of her vagaries, and for her success on the turf not having been what it might have been had she been able to keep her temper and her trainers. Some three years ago I told the story — a true one — of her Grace's maid who, determined to avenge the insults heaped on her while doing her mistress's hair before dinner, carefully plaited it in and out of the back of the chair, and when the Duchess was thus firmly secured to a not very light piece furniture, gave her a violent box on the ear, walked out of the room, and five minutes later left the house, her luggage having by arrangement with the other servants already been despatched to the station. The sequel is characteristic of the late Duchess. She declared she would never again run such risk, and had a special backless seat purchased; and on none other would she sit when having her hair done for several months after the aforesaid maid's departure. Another story is fairly common property — of how, when trying by herself to work a new lift in her house, before the engineers had passed it ready for use, she was carried down into the &quot;well,&quot; whence she shouted violent expletives at her servants above, until a footman secured and descended a ladder at considerable risk, and carried the lady up under one arm. She brought an action against the lift-makers to recover damages for &quot;shock to the system,&quot; but lost the day. Mr Milner, her third husband, and now her widower, was born nearly 50 years after the lady whose loss he doubtless mourns. — ''Woman''.&lt;ref&gt;&quot;Woman&quot; [pseud]. &quot;The Vagaries of 'Mr Manton.&quot; ''Dundee Evening Telegraph'' 22 November 1894, Thursday: 2 [of 4], Col. 2c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000453/18941122/008/0002. Print title: The ''Evening Telegraph''; n.p.&lt;/ref&gt;&lt;/blockquote&gt;Caroline Graham, 4th Duchess died in 1894, but Marcus Henry Milner, her 3rd husband, more than 40 years younger than she was, attended the [[Social Victorians/1897 Fancy Dress Ball |Duchess of Devonshire's 2 July 1897 fancy-dress ball]] with the 5th Duke and Duchess.

== Also Known As ==
*Family name: Graham
*Duke of Montrose
**Douglas Beresford Malise Ronald Graham, 5th Duke (30 December 1874 – 10 December 1925)&lt;ref&gt;{{Cite journal|date=2020-08-04|title=Douglas Graham, 5th Duke of Montrose|url=https://en.wikipedia.org/w/index.php?title=Douglas_Graham,_5th_Duke_of_Montrose&amp;oldid=971139213|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Duchess of Montrose
**Caroline Agnes Horsley-Beresford Graham (30 December 1836 – 16 November 1894)
**Violet Hermione Graham Graham (24 July 1876 – 21 November 1940)
*Caroline Agnes Horsley-Beresford Graham Stirling-Crawford Milner was also known as Mr. Manton for her horse-breeding and -racing operations.
*Marcus Henry Milner: &quot;Mr. 'Harry' Milner (familiarly known in the City as 'Millions').&quot;&lt;ref name=&quot;:3&quot;&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 2a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;

== Acquaintances, Friends and Enemies ==

=== Marcus Henry Milner ===

* Mr. [[Social Victorians/People/Mildmay|F. B. (Francis Bingham) Mildmay]]
* Mr. St. John Wontner, &quot;the well-known solicitor practising in the West End police-courts&quot;&lt;ref name=&quot;:4&quot;&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 1b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;

== Organizations ==

* Messrs. Bourke and Sandys: &quot;one of the zealous assistants of that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:3&quot; /&gt; headed by [[Social Victorians/People/Bourke|Algernon Bourke]]

== Timeline ==
'''1836 October 15''', James Graham and Caroline Agnes Horsley-Beresford married.&lt;ref name=&quot;:1&quot;&gt;&quot;Hon. Caroline Agnes Horsley-Beresford.&quot; {{Cite web|url=https://thepeerage.com/p6863.htm#i68622|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt;

'''1874 December 30''', James Graham, 4th Duke of Montrose, died.

'''1876 January 22''', Caroline Agnes Horsley-Beresford Graham and William Stuart Stirling-Crawford married.&lt;ref name=&quot;:1&quot; /&gt;

'''1876 July 24''', Douglas Beresford Malise Ronald Graham and Violet Hermione Graham married.&lt;ref name=&quot;:2&quot;&gt;&quot;Violet Hermione Graham.&quot; {{Cite web|url=https://thepeerage.com/p5396.htm#i53952|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt;

'''1888 July 26''', Caroline Agnes Horsley-Beresford Graham Stirling-Crawford and Marcus Henry Milner married.&lt;ref name=&quot;:1&quot; /&gt; According to the ''Nottingham Evening Post'' of 31 July 1888,&lt;blockquote&gt;METROPOLITAN NOTES. [FROM LONDON CORRESPONDENTS.] London, Monday Evening.

Society has not had for some time so piquant a piece of gossip to deal with as that arising out of the marriage of the Dowager Duchess of Montrose a few days since with Mr. Milner. In any case, the union of bride of seventy with a bridegroom of twenty-four would have caused remark, but this has created the more because of the extreme secrecy with which it is surrounded. The church authorities at St. Andrew's, Fulham, where the ceremony was performed, knew nothing, l am told, of the condition of the parties to the suit until the licence was in their hands, and though the Duchess was arrayed in bridal costume there was no lady either with her or in the church at the time, she being accompanied only by Mr. [[Social Victorians/People/Bourke|Algernon Bourke]], who was stated to be her legal adviser, the bridegroom being similarly supported only by lawyer, in the person of Mr. St. John Wontner, the well-known solicitor practising in the West End police-courts.

The bridegroom, who had earned the necessary residential qualification by staying at [[Social Victorians/London Clubs#Queen's|the Queen's Club]], led his wife, after the ceremony, into the vestry, where the marriage settlements were signed; but they did not drive away, the Duchess departing as she had come with Mr. Bourke. How the news of the wedding first reached the friends is not the least curious part of the story, which runs that Mr. [[Social Victorians/People/Mildmay|Mildmay]], the Liberal Unionist member for Totnes, who is a personal acquaintance the bridegroom, happened go to St. Andrew's to practice upon the organ at the time the ceremony was to take place, and, to his astonishment, saw his friend being married. The reason given at the church for the extreme quietude of the wedding was that there had recently been a death in one of the families.&lt;ref name=&quot;:4&quot; /&gt;&lt;/blockquote&gt;'''1888 November 22''', the Duchess of Montrose was in court about an unpaid bill; there is also a mention of a visit by the Prince of Wales:&lt;blockquote&gt;In the Queen's Bench Division, London, on Wednesday, Mr Sanders, carrying on business as an orchid grower at St Alban's, commenced an action against the Duchess of Montrose to recover £1,730 for orchids supplied and for furnishing a conservatory at Newmarket. A sum of £700 was paid into court, and the remaining £1,000 was disputed on the ground that the orchids had not been supplied to order. For the plaintiff it was stated that her grace had expressed herself delighted with the orchids, but thought there were too many white flowers. She said the Prince of Wales was coming there to dinner, and asked plaintiff whether he thought he could supply in time some coloured plants. The plaintiff said he could, and in his evidence said the original arrangement was that he should supply 1,000 orchids for 1,000 guineas. Several experts were examined, and expressed the opinion that the prices charged for work done and orchids supplied were fair. The further hearing of the case was adjourned.&lt;ref&gt;&quot;Action against 'Mr Manton.' The Prince of Wales and the Orchids.&quot; ''South Wales Daily News'' 22 November 1888, Thursday: 2 [of 4]. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000919/18881122/028/0002.&lt;/ref&gt;&lt;/blockquote&gt;'''1894 July 28, Saturday''', the ''Aberdeen Evening Express'' published a report about conflict between the Duchess and Mr. Milner:&lt;blockquote&gt;Racing circles are following with eager interest the conflict between &quot;Mr Manton&quot; and her husband the manner in which the latter's annuity is to be paid. When the Dowager-Duchess Montrose married Mr Harry Milner she assigned to him three thousand year out of the five thousand pounds that came to her under the will of Mr Stirling Crawfurd, the understanding being that all the instalments should be paid to the credit of the Duchess's account with her bankers in London. Mr Milner was a party to this arrangement, but he has now revoked it, to the indignation of his wife, who is contesting the matter hotly.

It is now six years since the Dowager-Duchess made her last matrimonial experiment. Her husband was at the time one of the zealous assistants of that well-known firm of stockbrokers, Messrs Bourke &amp; Sandys; and Mr [[Social Victorians/People/Bourke|Algernon Bourke]], the head the firm, went down to Fulham to give her away. The honeymoon began with a visit to the Jockey Club box Sandown and ended at the Lake of Geneva. Even now Mr Henry Milner is only in his thirtieth year, while his wife first saw the light in 1818, and was married to the fourth Duke of Montrose close on thirty years before her present husband was born.


Lady Breadalbane and Lady Greville, who is still Lady Violet Greville when writing plays, never took Mr Henry Milner seriously as a stepfather, nor is he regarded with the veneration due to a parent by the comparatively venerable Duke of Montrose.&lt;ref name=&quot;:0&quot;&gt;&quot;'Mr Manton' and Mr Harry Milner.&quot; ''Aberdeen Evening Express'', 28 July 1894, Saturday: 2 [of 6], Col. 7c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000444/18940728/022/0002.&lt;/ref&gt;&lt;/blockquote&gt;

'''1894 November 16, Friday''', Caroline, Duchess of Montrose, died:&lt;blockquote&gt;Caroline, Duchess of Montrose, passed away at 1.20 this morning. The duchess was well known in the racing world as &quot;Mr Manton,&quot; and at the time of her death had some 17 horses in training, including Shrine, Grand Duke, Medora, Adoration, Lady Caroline, Broad Corrie None the Wiser, Jocasta Mecca, and Beggar's Opera. Last year her Grace won 11 races, the stakes amounting to over £4,000. The principal winners were Mecca, which was successful in several valuable juvenile races, and Medora, who won the Goodwood Stewards' Cup. Her chief success in the handicap department this year was achieved in the Cezarewitch, the &quot;All scarlet&quot; being carried into third place by the seven year old mare Shrine. The deceased Duchess had, during her long career, owned some of the best known race horses of the century, including the filly Thebais, who secured the One Thousand Guineas and the Oaks in 1891, and the Liverpool Autumn Cup three years later. Her Grace was very shrewd in equine matters, and her opinion was often sought by some of the highest personages in the country in regard to the purchase of thoroughbreds. Deceased had this year leased most of the Sefton Farm yearlings to Sir Frederick Johnstone, and they are now in training at Kingsclere. She struck all her horses out of Lincoln, Liverpool, and Manchester engagements on October 30th. The Duchess was a daughter of the second Baron Decies. She was born in 1818, and married, firstly, the fourth Duke of Montrose, who died in 1874; secondly, Mr William Stuart Stirling Crawford, who died in 1883; and thirdly, Mr Henry Miller [sic], who survives her. The deceased expired at her London residence in Belgrave-square, where she had been lying ill for several weeks. Although her illness had caused much anxiety to her family, her immediate death was not expected, and on Sunday a slight improvement being noticcd, the present Duke and Duchess left for Scotland, where they now are. Up to midnight no change appeared, but shortly afterwards her breathing became laboured, and she passed away quietly from sudden failure the heart, in the presence of her two daughters, [[Social Victorians/People/Lady Violet Greville|Baroness Greville]] and the [[Social Victorians/People/Breadalbane|Marchioness of Breadalbane]].&lt;ref&gt;&quot;Death of the Duchess of Montrose ('Mr Manton').&quot; ''Hull Daily Mail'' 16 November 1894, Friday: 3 [of 4], Col. 5c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000323/18941116/031/0003.&lt;/ref&gt;&lt;/blockquote&gt;

'''1897 June 28, Monday''', according to the ''Morning Post'', Douglas, 5th Duke and Violet, Duchess of Montrose were invited to the 28 June [[Social Victorians/Diamond Jubilee Garden Party|Queen's Garden Party]], the official end of the Diamond Jubilee celebrations in London.&lt;ref&gt;“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''  ''&lt;nowiki&gt;https://www.britishnewspaperarchive.co.uk/viewer/BL/0000174/18970629/032/0004&lt;/nowiki&gt;'' and ''&lt;nowiki&gt;https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970629/032/0005&lt;/nowiki&gt;''.&lt;/ref&gt;

'''1897 July 2''', Douglas, 5th Duke of Montrose and Violet, Duchess of Montrose attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House.

== Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball ==
At the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]], Douglas Graham, 5th Duke of Montrose (at #170 in the list of people who attended), sat at Table 6.

Violet Graham, Duchess of Montrose (at 186) sat at Table 8. According to the ''Westminster Gazette'', &quot;[t]he Duchess of Montrose wore a sapphire-blue velvet gown, with muslin fichu and powdered hair.&quot;&lt;ref&gt;“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.&lt;/ref&gt;{{rp|Col. 1}}

Harry&lt;ref&gt;&quot;Personal Paragraphs.&quot; Dublin ''Evening Telegraph'' 01 August 1902 Friday: 2 [of 4], Col. 8b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002093/19020801/053/0002.&lt;/ref&gt; ([[Social Victorians/People/Milner|Marcus Henry) Milner]] (at 612) — Caroline, Duchess of Montrose's 3rd husband — was dressed as a &quot;Chasseur, Louis XV., ... after the picture by Van Loo; coat, Louis XV. period; turquoises richly embroidered on skirts, cuffs, breast, and pockets with beautiful gold embroidery; laced shirt and jabot, buff riding breeches; hat, three cornered, laced and edged with gold.&quot;&lt;ref&gt;“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.&lt;/ref&gt;{{rp|42, Col. 1a}}

== Demographics ==
*Nationality: Anglo-Irish

== Family ==
*James Graham, 3rd Duke of Montrose (8 September 1755 – 30 December 1836)&lt;ref&gt;&quot;James Graham, 3rd Duke of Montrose.&quot; {{Cite web|url=https://thepeerage.com/p2815.htm#i28142|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt;
*Lady Jemima Elizabeth Ashburnham (1 January 1762 – 17 September 1786)&lt;ref&gt;&quot;Lady Jemima Elizabeth Ashburnham.&quot; {{Cite web|url=https://thepeerage.com/p1159.htm#i11589|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt;
*#Unknown son Graham
*Lady Caroline Maria Montagu (10 August 1770 – 24 March 1847)&lt;ref&gt;&quot;Lady Caroline Maria Montagu.&quot; {{Cite web|url=https://thepeerage.com/p2883.htm#i28825|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt;
#Lady Georgiana Charlotte Graham (– 13 February 1835)
#Lady Emily Graham Foley (– 1 January 1900)
#Lady Caroline Graham (– 24 March 1875)
#Lady Lucy Graham (25 September 1793 – 16 September 1875)
#'''James Graham, 4th Duke of Montrose''' (16 July 1799 – 30 December 1874)
#Lord Montagu William Graham (2 February 1807 – 21 June 1878)


*Caroline Agnes Horsley-Beresford Graham Stirling-Crawfurd Milner (c. 1818?&lt;ref name=&quot;:0&quot; /&gt; – 16 November 1894)&lt;ref name=&quot;:1&quot; /&gt;
*James Graham, 4th Duke of Montrose (16 July 1799 – 30 December 1874)&lt;ref&gt;&quot;James Graham, 4th Duke of Montrose.&quot; {{Cite web|url=https://thepeerage.com/p2815.htm#i28143|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt;
#Beatrice Violet Graham, [[Social Victorians/People/Lady Violet Greville | Lady Violet Greville]] (13 February 1842 – 29 Feb 1932)
#Agnes Caroline Graham ( – 8 May 1873)
#James John Graham, Marquess of Graham (7 Feb 1845 – 31 Jan 1846)
#James Graham, Marquess of Graham (22 Jun 1847 – 3 Apr 1872)
#'''Douglas Beresford Malise Ronald Graham, 5th Duke of Montrose''' (7 November 1852 – 10 December 1925)
#Alma Imogen Leonora Charlotta Graham, later [[Social Victorians/People/Breadalbane|Marchioness of Breadalbane]] (7 Sep 1854 – 10 May 1932)
*William Stuart Stirling-Crawfurd (Crawford?) ( – 23 February 1883),&lt;ref&gt;&quot;William Stuart Stirling-Crawford.&quot; {{Cite web|url=https://thepeerage.com/p6863.htm#i68623|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt; her second husband
*Marcus Henry Milner (16 April 1864 – 16 January 1939),&lt;ref&gt;&quot;Marcus Henry Milner.&quot; {{Cite web|url=https://thepeerage.com/p6863.htm#i68624|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt; her third husband (He was 22; she was 68 if she was 16 at her first marriage, in 1836.)


*Douglas Beresford Malise Ronald Graham, 5th Duke of Montrose (7 November 1852 – 10 December 1925)&lt;ref&gt;&quot;Douglas Beresford Malise Ronald Graham, 5th Duke of Montrose.&quot; {{Cite web|url=https://thepeerage.com/p5396.htm#i53951|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt;
*Violet Hermione (née Graham) Graham ( – 21 November 1940)&lt;ref name=&quot;:2&quot; /&gt;
#'''James Graham, 6th Duke of Montrose''' (1 May 1878 – 20 January 1954)
#Helen Violet Graham (1 July 1879 – 27 August 1945)
#Hermione Emily Graham Cameron (22 February 1882 –1978)
#Douglas Malise Graham (14 October 1883 – 20 November 1974)
#Alastair Mungo Graham (12 May 1886 – 1976)


* James Graham, 6th Duke of Montrose (1 May 1878 – 20 January 1954)&lt;ref&gt;&quot;James Graham, 6th Duke of Montrose.&quot; {{Cite web|url=https://www.thepeerage.com/p10991.htm#i109901|title=Person Page|website=www.thepeerage.com|access-date=2023-04-13}} https://www.thepeerage.com/p10991.htm#i109901.&lt;/ref&gt;
* Lady Mary Louise [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton|Douglas-Hamilton]] (1 November 1884 – 21 February 1957)&lt;ref&gt;&quot;Lady Mary Louise Douglas-Hamilton.&quot; {{Cite web|url=https://www.thepeerage.com/p10990.htm#i109900|title=Person Page|website=www.thepeerage.com|access-date=2023-04-13}} https://www.thepeerage.com/p10990.htm#i109900.&lt;/ref&gt;

# '''James Angus Graham, 7th Duke of Montrose''' (2 May 1907 – 10 February 1992)
# Lady Mary Helen Alma Graham (11 April 1909  – 7 February 1999)
# Lord Ronald Malise Hamilton Graham (20 September 1912 – 11 June 1978)
# Lady Jean Sibyl Violet Graham (7 November 1920 – 13 October 2017)


=== Algernon William Fulke Greville's Family ===
*Fulke Southwell Greville-Nugent, 1st Baron Greville (17 February 1821 – 25 January 1883)
*Lady Rosa Emily Mary Anne Nugent Greville-Nugent
#Algernon Greville-Nugent, 2nd Baron Greville (1841–1909)
#Hon. George Frederick Greville-Nugent (1842–1897)
#Hon. Robert Southwell Greville-Nugent (26 March 1847 – 1912)
#Hon. Reginald James Macartney Greville-Nugent (1848–1878)
#Hon. Patrick Emilius John Greville-Nugent (6 August 1852 – 1925), married Ermengarda Ogilvy on 5 June 1882
#Hon. Mildred Charlotte Greville-Nugent (d. 1906), married Alexius Huchet, Marquis de La Bêdoyére on 26 August 1869

=== Relations ===

* Lady Caroline Maria Montagu was the daughter of the [[Social Victorians/People/Manchester|Duke of Manchester]].

== Questions and Notes ==
#Douglas Graham, 5th Duke of Montrose, is [[Social Victorians/People/Lady Violet Greville | Lady Violet Greville]]'s brother.
#The Boston Guardian reports this:&lt;blockquote&gt;The Dowager Duchess of Montrose, who died last week at the age of 76, was a well-known figure on the turf, running her horses in the name of &quot;Mr. Manton.&quot; Her first husband was the father of the present Duke of Montrose, and she has retained the title derived from this union through two succeeding matrimonial arrangements. Her second husband, Mr. Stirling Crawfurd [sic], was a wealthy land-owner, and when he died, 11 years ago, he left her a large fortune and a château at Cannes. Five years later society was startled by the announcement that the Duchess then a woman of 70 [confirming that she was born in 1818], had taken for her third husband Mr. Harry Milner, a young man of 24, who had previously been engaged with an aristocratic stockbroking firm in the City. The Duchess had a life-rent annuity of £5,000 a year, and of this she assigned £3,000 a year to Mr. Milner, on the understanding that all the annuity cheques were to be paid into her account. This arrangement was adhered to until early in the present year, when Mr. Mlner countermanded the order. The result has been domestic differences and lawsuits, to which the Duchess's death has put a stop. On the turf her &quot;all scarlet&quot; colours were well-known on many race-courses, among them most celebrated of her victories being those of Thebaia, who won the Thousand Guineas and the Oaks in 1881. It is understood that her château at Cannes, one of the most beautiful in the neighbourhood, is now the property of Lord Rendel, better known as Mr. Stuart Rendel, the entertainer of Mr. Gladstone.&lt;ref&gt;&quot;'Mr. Manton.'&quot; ''Boston Guardian'' 24 November 1894, Saturday: 6 [of 8], Col. 5b. ''British Newspaper'' Archive http://www.britishnewspaperarchive.co.uk/viewer/bl/0001888/18941124/098/0006.&lt;/ref&gt;&lt;/blockquote&gt;
#Personal details about Caroline, Duchess of Montrose, especially around the race track:&lt;blockquote&gt;&quot;Mr. Manton&quot; has been a familiar figure in the paddock at every great English race meeting. Next to that of the venerable Sir John Astley, it was probably the best known. The duchess was tall and straight and heavily built. In her youth she had been rather good looking, a woman of a high-bred English type. On the racecourse she wore tailor-made clothes of a very horsey cut, including check gowns, covert coats, white cravats with horseshoe pins, and felt hats. She was in the habit of bidding for yearlings in public and of superintending the stables personally.&lt;ref&gt;&quot;The Late 'Mr. Manton.' Death of the Duchess of Montrose. A Well-Known Sportswoman Gone.&quot; ''Western Mail'' 17 November 1894, Saturday: 7 [of 8]. ''British Newspaper'' Archive http://www.britishnewspaperarchive.co.uk/viewer/bl/0000104/18941117/037/0007.&lt;/ref&gt;&lt;/blockquote&gt;

== Footnotes ==
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    <title>Social Victorians/Timeline/1900s</title>
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      <contributor>
        <username>Scogdill</username>
        <id>1331941</id>
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      <comment>/* 1901 */</comment>
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      <text bytes="114644" sha1="rc5f52jut5onfibo3iwi17c4takf4i0" xml:space="preserve">[[Social Victorians/Timeline/1850s | 1850s]] [[Social Victorians/Timeline/1860s | 1860s]] [[Social Victorians/Timeline/1870s | 1870s]] [[Social Victorians/Timeline/1880s | 1880s]] [[Social Victorians/Timeline/1890s | 1890s]] 1900s

==1900==
1900, early, [[Social Victorians/People/Mathers|MacGregor and Moina Mathers]] were living at 87 Rue Mozart, Paris (Howe 203).
===January 1900===
====1 January 1900, Monday, New Year's Day====
====13 January 1900, Tuesday====
&lt;blockquote&gt;THE HOUSEHOLD TROOPS. ENTERTAINMENT AT HER MAJESTY'S.

The Prince and Princess of Wales, accompanied by Princess Victoria and Prince Charles of Denmark, attended the entertainment to aid the widows and orphans of her Majesty's Household Troops, organised by Mrs. Arthur Paget and presented under the direction of Mr. H. Beerbohm Tree at Her Majesty's Theatre last night.

... [The major part of this story is the program of the entertainment, in which [[Social Victorians/People/Muriel Wilson|Muriel Wilson]], among others, played an important part.]

Among those present at the entertainment were: The Prince and Princess of Wales, Princess Victoria of Wales, and Prince Charles of Denmark, the French Ambassador, the Russian Ambassador, the Portuguese Minister, Count Mensdorff, the Austrian Embassy, Prince and Princess Demidoff, Prince and Princess Hatzfeldt, Prince and Princess Alexis Dolgorouki, Count and Countess Roman Potocki, Count and Countess Alexander Münister, the Duke and Duchess of Devonshire, the Marquis of Downshire, the Earl and Countess of Cork, the Earl and Countess of Westmorland, the Earl and Countess of Gosford, the Earl of Lathom, the Countess of Ancaster, the Countess of Wilton, the Countess of Yarborough, the Countess of Huntingdon, Viscount Curzon, Lord and Lady Farquhar, Lord and Lady Savile, Lord Rowton, Lord Westbury, Baroness d'Erlanger, Count and Countess Seilern, Lord and Lady Ribblesdale, Lord and Lady Hothfield, Lord and Lady Raincliffe, Lord Wandsworth, Lord Charles Montagu, Lady Cunard, Sir Edgar and Lady Helen Vincent, Lady Kathleen and Mr. Pilkington, Lady Violet Brassey, Lady Grey Egerton, the Hon. Humphry and Lady Feodorowna Sturt, Lady Ripley, Lady Katherine Coke, Lady Agneta Montagu, Lady Tatton Sykes, Lady Templemore, Lady Florence Grant, Lady Garrick, Lady Pearson, Lady Constance Haddon, Sir F. Burdett, the Hon. M. Charteris, Sir A. de la Rue, Sir Frederick and Lady Milner, the Hon. E. Stonor, Sir Edward and Lady Sassoon, Mrs. Joseph Chamberlain, the Hon. Mrs. Lawrence, the Hon. Mrs. Napier, Sir Charles Forbes, Mrs. Bradley Martin, Mrs. Cornwallis West, Mr. Arnold Morley, Mr. L. Neumann, Madame Vagliano, Mr. Gillett, Mrs. Godfrey Samuelson, Mrs. Reginald Ward, Mr. and Mrs. Arthur Wilson, Mr. Menzies, Mr. Dreyfous [sic], Mrs. George Coats, Mr. Hartmann, Mrs. Rube, Mrs. Neumann, Mr. Lukach, Mrs. Candy, Mr. Bargrave Deane, Mr. L. V. Harcourt, Mrs. Oppenheim, Mrs. Lionel Phillips, Mr. King. Mr. James Finch, Mrs. Clayton Glyn, Miss Van Wart, Mr. Hall Walker, Mr. Drexell, Mrs. Van Raalte, Mr. Alfred Beit, Mr. Douglas Uzielli, Mrs. Alfred Harmsworth, Mr. Munday, Mrs. William James, Mrs. Newhouse, Mrs. Max Waechter, Mr. G. Prentis, Mrs. M'Calmont, Mr. Blacklock, Mrs. Ausell, Captain Holford (Equerry to the Prince of Wales), Mr. De Nino, Mrs. Keyser, Mrs. Fleming, Mrs. Breitmeyer, Mrs. Wernher, Mrs. Armour, Mr. Van Alan, Mrs. Ewart, Mrs. Carl Meyer, Mrs. Powell, Mr. Hambro, Colonel Charles Allen, Colonel Cunningham, Mrs.Hutchinson, Mrs. Schumacher, Colonel Kennard, Mrs. Fludyer, Mrs. Williamson, Mr. Thellusson, Mr. Sackville West, Captain M'Neil, Mrs. Dalrymple Hamilton, Mrs. Penn Curzon, Mrs. Hamar Bass, Mrs. Kuhliug, General Stracey, Mrs. Jeffcock, Colonel Thynne. (1900-02-14 Morning Post).&lt;/blockquote&gt;

====17 January 1900, Saturday====

1900 February 17, Lady Greville writes about the amateur theatricals Muriel Wilson is involved in: &lt;blockquote&gt;The most notable social event of the week was the amateur performance of tableaux at Her Majesty's Theatre. One is accustomed to the amateurs under every aspect, leaping in where angels fear to tread, essaying the most difficult parts, dabbling in the arts of music and literature, but so full and rich and interesting a performance has rarely been given before. To begin with, there was a masque, modelled on the Elizabethan lines, with song and dance, and special music composed for the occasion by Mr. Hamish McCunn, dresses statuesque and graceful, and a bevy of pretty women to carry out the idea.

One original feature there was, too, which certainly did not present itself before our Virgin Queen, and that was the graceful fencing of Miss Lowther, who looked an ideal young champion in her russet suit and jaunty little cap. A very young debutante appeared in the person of Miss Viola Tree, who, dressed in the nest diaphanous garments, acted with a grace and lightness that promises well for her future career. Mrs. Crutchly, as &quot;Glory,&quot; appeared amid a din of thunder and a rosy glare of limelight, and clashed her cymbals in truly determined fashion. An element of wildness suited to the character, distinguished her agreeable posturing, and her high spiked crown gave distinct individuality to the representation. Mrs. Martineau, Hebe-like in a white robe and a large crown of roses, as if she had just stepped out of a picture by Leighton, then danced and took the palm for poetry and suppleness of movement; Miss [[Social Victorians/People/Muriel Wilson|Muriel Wilson]], meanwhile, having daringly shot up through a trap-door in scarlet robes with a flaming torch, announced herself as &quot;War,&quot; and beckoned to Glory, Victory, and Prosperity, when they finished their performance, to sit beside her on her throne. &quot;Rumour,&quot; alias Mr. Gervase Cary Elwes, sang an excellent topical song, attired in a quaint garb covered with interrogations, and carrying an electric telegraph-post in her hand. Lady Maud Warrender, as &quot;Pity,&quot; advanced from a barge that had just arrived, and sang a doleful ditty which made one wish &quot;Pity&quot; might combine a sense of gaiety. But as Mrs. Willie James, in the part of &quot;Mercy,&quot; dressed as a nurse, recited some bright lines anent Tommy, to the accompaniment of distant fifes and drums, the audience decided to take this as a satisfactory compensation.

All being now harmoniously arranged, &quot;War&quot; performed a sleight-of-hand feat, divested herself of her red dress, her headgear of flaming serpents, and her glistening breastpiece, and appeared in virgin white, crowned with roses, as “Peace,&quot; surrounded by “Music&quot; in a gorgeous gown of gold tissue, by “Painting,&quot; “Science,&quot; and “Literature.&quot; A pleasant finaleof gay music brought the Masque to a close, and left a decidedly agreeable and novel impression behind it.

Tableaux then followed, all more or less well grouped by well-known artists, and represented by beautiful women of Society. Among the familiar faces were Lady St. Oswald, Lady Mary Sackville, Miss Agatha Thynne, Mrs. Fitz Ponsonby, Lady Maitland, Madame von André, &amp;c., but neither Lady Helen Vincent, Lady De Grey, Lady Cynthia Graham, the Duchess of Portland, nor many other well-known and lovely ladies took part in the performance.

Finally, came the Patriotic Tableau, which had evidently engaged all the energies of the organisers of the fête. On a high throne, with a most realistic lion, open-mouthed and fierce-looking, beside her, sat Lady Westmoreland as &quot;Great Britain,&quot; a stately and dignified figure in white satin, draped in a red cloak and crowned with a large wreath of laurel. The stage on each side was lined by genuine stalwart Guardsmen, and to the sound of lively martial music, composed and conducted by Sir Arthur Sullivan, slowly advanced a procession of Great Britain's dependencies, figured by ladies magnificently costumed, their long jewelled trains borne by two little pages in cloth of gold brocade coats, with black silk legs. Very beautiful were the blendings of the colours in this tableau, artistically designed by Mr. Percy Anderson. Lady Claude Hamilton, as &quot;British Columbia,&quot; moved with stately gait in a robe of palest green; Lady Feo Sturt glittered barbarically with jewels; her headdress and her bosom were covered with gems. As the typical representative of &quot;India,&quot; she was dressed in apricot colour and bore branches of hibiscus in her hands. Mrs. Hwfa Williams, in blazing red, carried a parrot and some red flowers. The Hon. Barbara Lister looked lovely and picturesque in her violet robes under a massive wreath of wisteria blossoms; Lady Raincliffe, wearing a curious high head-dress, was dressed in white to represent &quot;Canada.&quot; &quot;Rhodesia&quot; made one of the prettiest figures in her khaki gown and cloak, with the coquettish hat and feathers and the red trimming associated with the Colonial Volunteers. &quot;Natal&quot; appeared appropriately clad all in black, while little &quot;Nigeria,&quot; for the nonce, wore spotless white robes. /

Miss Muriel Wilson spoke an ode, and looked striking in apricot and white, with a high diamond crown and a long standing-up white feather. None of the ladies suffered from shyness; they showed thorough acquaintance with the stage, and moved easily thereon. In fact, costumes, arrangements, music, and the glorious feast of beauty left nothing to be desired.

The final impression in one's mind was that the stage produces strange effects. It idealises some faces, hardens others, and alters many. The large wreaths, almost grotesque in size, proved eminently becoming, and the Grecian draperies carried away the palm for beauty. After them our modern dress seems stiff, angular, and inartistic. The whole performance was one to be commended, and will no doubt be as successful financially as it was from the aesthetic and spectacular point of view.

Mrs. James Stuart Wortley, who died last week, will be regretted by every class of society. This lady, a beauty in her youth, devoted the latter part of her life entirely to works of charity. She founded the East London Nursing Society, to the tender and skilful ministrations of which many a poor woman owes her return to health, and in every philanthropic scheme, emigration, the befriending of young servants, and the education of youth, she took a lively interest. Her clear sense, her logical grasp of subjects and her immense activity were of infinite service in everything she undertook, and her memory will smell sweet in the hearts of the many who loved and depended on her.

I really wonder at the patience of the British taxpayer. During the snow of this week Belgravia, Eaton, and other fashionable squares, remained a morass of slush, ice, and half-melted snow. The pavements as slippery as glass had not been cleansed, and only at the risk of one's life one made one's way from street to street. (Greville 7, Col. 1a-2a)&lt;/blockquote&gt;

'''25 January 1900, Thursday'''

David Lindsay, [[Social Victorians/People/Crawford and Balcarres|Lord Balcarres]] and Constance Lilian Pelly married:
&lt;blockquote&gt;
MARRIAGE OF LORD BALCARRES.

The marriage of Lord Balcarres, M.P. for North Lancashire, eldest son of the Earl of Crawford of Balcarres House, Fife, and Haigh Hall, Wigan, to Miss Pelly, daughter of the late Sir H. Peily, Bart., and granddaughter of the Earl of Wemyss, was solemnised yesterday (Thursday) at St Margaret's Church, Westminster, in the presence of a large gathering of friends.

Among the invited guests were the Earl and Countess of Crawford, the Dowager Countess of Crawford, the Earl of Wemyss, Lord and Lady Elcho, the Hon. E. Lindsay, the Hon. Lionel Lindsay, the Hon. Ronald Lindsay, Lord and Lady Cowper, Mr. A. J. Balfour, the Hon. L. Greville, and many othsrs. The service was fully choral, and was conducted by the Bishop of Stepney, assisted by the the Rev. Canon Gore. Mr Yorke, the stepfather of the bride, gave her away. She wore a dress of white velvet, draped with old Brussels lace, the gift of the Dowager Countess of Crawford: chiffon veil and wreath of natural orange blossoms. Her only ornament was a Maltese cross of diamonds, also the gift of the Dowager Countess of Crawford.

There were nine bridesmaids. Miss Pelly, sister of the bride) [sic], the Hon. Mary Vasey, the Hon. Cynthia Charteris, Miss Brodrick, Miss Sybil Brodrick, Miss Benita Pelly, the Hon. Aline Menjendie, Miss Daisy Benson, and Miss Madeline Bourke. They were attired alike in costumes of white de chine, with lace insertions, with blue chiffon hat, trimmed with plumes of white and blue ostrich feathers. They carried bouquets of violets, and wore red enamel brooches with diamond centres and pearl drops, the gifts of the bridegroom. The Hon E. Lindsay supported his brother as best man.

At the conclusion of the ceremony the guests drove to the town residence of the bride's mother in Queen Anne's Gate, where the wedding reception was held. Later in the day the newly-married couple left town for Wrest Park, Ampthill, kindly lent them for the honeymoon by Earl and Countess Cowper. Princess Louise (the Marchioness of Lorne) sent the bride a handsome silver basket as a wedding present.&lt;ref&gt;&quot;Marriage of Lord Balcarres.&quot; ''Dundee Courier'' 26 January 1900 Friday: 4 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000164/19000126/105/0004.&lt;/ref&gt;
&lt;/blockquote&gt;

===February===
1900, February, a brief account of the Matherses' Isis ceremony appeared in &quot;the New York periodical the ''Humanist'', February 1900&quot; (Howe 201).

==== 15 February 1900, Thursday ====
A number of familiar people took part in [[Social Victorians/People/Arthur Stanley Wilson|Enid Wilson]]'s wedding to the Earl of Chesterfield:&lt;blockquote&gt;This afternoon, at St. Mark's Church, North Audley-street, the [[Social Victorians/People/Chesterfield|Earl of Chesterfield]] is to be married to Miss Enid Wilson, second daughter of Mr. Charles Wilson, M.P., of Marter Priory, Yorkshire, and 41, Grosvenor-square. The bride, who will be given away by her father, will wear a dress of white crêpe de chine wrought with silver and trimmed with fine old lace and ermin. The bridesmaids will be Miss Gladys Wilson, sister of the bride, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], her cousin, Lady Aldra Acheson, daughter of the Earl [[Social Victorians/People/Gosford|and Countess of Gosford]], Lady Mary Willoughby, daughter of the [[Social Victorians/People/Ancaster|Earl and Countess of Ancastor]], Lady Marjorie Carrington, daughter of [[Social Victorians/People/Carrington|Earl and Countess Carrington]], Miss Daphne Bourke, the four-year-old daughter of the [[Social Victorians/People/Bourke|Hon. Algernon and Mrs. Bourke]], [[Social Victorians/People/Balfour|Miss Balfour]], and [[Social Victorians/People/Paget Family|Miss Paget]]. Lace Empire dresses and long bright red cloth Directoire coats trimmed with sable and hats to match. They will carry sable muffs, the gifts to them of the bridegroom. Viscount Ednam, the [[Social Victorians/People/Dudley|Earl and Countess of Dudley]]'s only son, aged six, and Lord Wendover, the only son of Earl and Countess Carrington, aged something over four, will be the youthful trainbearers. After the wedding Mrs. Charles Wilson will hold a reception at 41, Grosvenor-square. The Prince of Wales has given Lord Chesterfield a remarkably handsome embossed silver cigarbox, lined with cedar, monogrammed and coroneted, accompanied by a letter written by his Royal Highness to the bridegroom, cordially wishing him every happiness. The Duke of Fife's gift is a cedar-lined plain silver cigarette-case.&lt;ref&gt;&quot;London Day by Day.&quot; ''Daily Telegraph'' 15 February 1900, Thursday: 8 [of 12], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/19000215/175/0008. Name in British Newspaper Archive: ''Daily Telegraph &amp; Courier'' (London). Print p. 8.&lt;/ref&gt;&lt;/blockquote&gt;Another, more local report: &lt;blockquote&gt;There was very large and fashionable assembly at St. Mark’s Church, North Audley-street, London, on Thursday afternoon, to witness the very pretty wedding of the Right Hon. the Earl of Chesterfield, P.C., of Holme Lacey, Hereford, and Miss Enid Wilson, fourth daughter of Mr. Charles H. Wilson, M.P. for Hull, of Warter Priory, York, and 41, Grosvenor-square, London. The service was fully choral, and the church handsomely decorated.

There were seven bridesmaids in attendance upon the bride. These young ladies were Miss Gladys Wilson (sister). Miss Muriel Wilson (cousin of the bride). Lady Mary Willoughby, Lady Alexandra Acheson, Lady Marjorie Carrington, Miss Dorothy Paget, and Miss Alice Balfour, who were in costumes of quaint, old-fashioned riding coats of red cloth, with white muslin skirts.

The local guests included Sir James and Lady Reckitt, Sir James and Lady Woodhouse, Lord and Lady Herries, Mr. Philip Hodgson, Lord and Lady Raincliffe, Mr. and Mrs. Kenneth Wilson, Mr. and Mrs. Stanley Wilson, Mr. and Mrs. Strickland Constable.

Presents wore also received from Commander Bethell (silver candlestick). Hr. and Mrs. George A. Duncombe, Beverley (Louis XV. sofa). Mr. and Mrs. Frank Lambert, Beverley (inlaid writing table), Colonel and Mrs. Goddard, Cottingham (silver mirror), Mr. Haslewood Taylor, Beverley (pair of prints). (1900-02-21 Beverley Echo)&lt;/blockquote&gt;

==== 27 February, 1900, Tuesday ====
Mardi Gras

===April 1900===

==== 8 April 1900, Sunday ====
Palm Sunday

====14 April 1900, Saturday====
Wynn Westcott assumed W. A. Ayton was on, as he wrote, &quot;the Committee to investigate the G. D. which contains Yeats, Bullock and I suppose Ayton&quot; (Howe 217).

====20 April 1900, Friday====
The R.R. et A.C. was code named Research and Archaeological Association (Howe 226)

====21 April 1900, Saturday====
The Inner Order of the Golden Dawn met at 116 Netherwood Road, West Kensington (Howe 227).

===May 1900===
====26 May 1900, Saturday====
Arthur Sullivan is visited by &quot;Sir George Martin, the organist at St. Paul's Cathedral, and Colonel Arthur Collins, one of the royal equerries&quot; to get him to write a Te Deum thanking God for the end of the Boer War (Ainger, Michael. Gilbert and Sullivan: a Dual Biography. P. 381.).

====30 May 1900, Wednesday====
Derby Day.

According to the Morning Post, &lt;quote&gt;The Derby Day. / The Archbishops of Canterbury and York hold a Reception of Colonial and Missionary Church Workers in the Great Hall of the Church House, 4.30 to 6.30. / ... May Fair and Bazaar, St. George's Drill Hall, Davies-street, Berkeley-square, opened by Lady Edward Spencer Churchill, 2.30.&lt;/quote&gt; (&quot;Arrangements for This Day.&quot; The Morning Post Wednesday, 30 May 1900: p. 7 [of 12], Col. 6C)

===June 1900===
Summer 1900: WBY summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

==== 3 June 1900, Sunday ====
Whit Sunday (Pentecost)

Whitsun party at Sandringham House, described by Lord Knutsford in his letters and summarized by Anita Leslie, whose parent's generation remembered some of these people Knutsford mentions as present:

* The Prince and Princess of Wales
* Princess Victoria
* Other daughters of the Prince and Princess of Wales
* Lord Knutsford
* [[Social Victorians/People/Ripon|Lord and Lady Gladys de Grey]]
* Luís De Soveral
* Tosti
* [[Social Victorians/People/Durham|Hon. George Lambton]]
* [[Social Victorians/People/Churchill|Lady Randolph Churchill]]
* [[Social Victorians/People/Holford|Holford]]
* Lady Musgrave

Leslie's summary of Knutsford's letters:&lt;blockquote&gt;The Whitsun party that year included Lord and Lady de Grey, De Soveral, whose caustic wit always lightened Edward's humour, Tosti, the famous baritone-songwriter (Alexandra and her daughters were so musical — strumming away ''à quatre mains'' while Totti's voice made chandeliers vibrate in after-dinner songs), the Hon. George Lambton (racing trainer), and Lady Randolph Churchill, &quot;just back from her hospital ship which had been a boon in South Africa, but fractiously insisting she is going to marry George Cornwallis-West.&quot;

Lord Knutsford describes the chattering guests travelling in that special train coach from St. Pancras to Wolverton Station where the house party was met by royal carriages with officious flunkeys in red livery who dealt with the luggage — and ''such'' luggage! Big trunks had to be brought for a few days' stay so that the correct attire could be produced for every meal and outing.

How exciting to drive through a forest of rhododendrons and to disembark in front of Sandringham House. The royal host and hostess stood in the hall to welcome their guests. After handshakes Queen Alexandra sat down to pour tea. Dinner was at 9 &lt;small&gt;P&lt;/small&gt;.&lt;small&gt;M&lt;/small&gt;. (at Sandringham all clocks were kept half an hour ahead of time). Footmen informed the gentlemen what waistcoats were to be worn. Ladies' maids scurried to the ironing rooms. At nine, having assembled in the drawing room, each man was told whom he must escort into dinner and where to sit. This saved hesitation and embarrassment. On this occasion Knutsford describes the Prince giving his arm to Lady de Grey, while Alexandra walked beside De Soveral and Lord de Grey escorted the unmarried Princess Victoria. There were, of course, no cocktails, but exquisite wines accompanied each course. The Prince never drank more than a glass or so of claret at dinner and a brandy after the last course.

When the ladies left the dining room cigarettes and cigars were brought by footmen. Heavy drinking was never encouraged, and / after half an hour the gentlemen moved to the drawing room to chat with the ladies, until Alexandra rose and they retired to their bedrooms where the ladies' maids would be waiting to unlace them from their gorgeous satin and velvet gowns. Hard as the existence of a servant might be, they were perhaps consoled by the colossal meals offered in recompense for late hours. A five-course breakfast could be consumed by every scullery maid if she so desired, and many a working-class mother strove to &quot;get her daughter's knees under a good table.&quot;

When the ladies had disappeared upstairs the men went to the billiards room, where the Prince, who idolised his dogs, would roar with laughter when his black bulldog nipped the legs of players. No one could go to bed before Edward, but at twelve-thirty he would certainly retire. There was no thought of any hanky-panky after hours at Sandringham. That would have been considered bad taste and an insult to the royal hostess.

On Sunday morning the breakfast gong sounded at 10 &lt;small&gt;A&lt;/small&gt;.&lt;small&gt;M&lt;/small&gt;. Then came church and a stroll in the garden until lunch at one-thirty. After a fairly heavy meal the ladies went upstairs to change into walking skirts and strong boots. The whole party then underwent a slow three-hour walk to the kennels and stables and farm. Talk was almost entirely about animals — dogs, pedigree cattle and, of course, race horses. Knutsford noticed Alexandra's &quot;touching girl-like love&quot; for every stone and corner of Sandrringham. She reminded him of &quot;a bird escaped from a cage.&quot;

Certainly the royal pair were never so happy as in this big Norfolk house, which they regarded as home, but guests grew weary of trying to do the right thing. Knutsford found dinner very wearing, with the conversation in mingled English and French: &quot;they drop from one to another in the same sentence.&quot;

Then came the local Whitsunday sports. Off drove the house party — Lady de Grey and Holford in the first carriage with Edward. Knutsford found himself in the second carriage with Princess Victoria and Lady Randolph Churchill and Lady Musgrave. The ladies wore coloured blouses and contrasting skirts and jackets over their blouses, white gloves and feather boas. A brisk wind nearly blew off their huge hats. Lady Musgrave in particular had difficulty with her concoction. &quot;Send it to the bazaar!&quot; cried Alexandra, and everyone roared with laughter.

Sandringham parties were called &quot;informal,&quot; but what a relief, nevertheless, when they all got back to the station in those regal carriages followed by the four horse-drawn vans of luggage.

In this spring of 1900 the visitors departed to their homes full to / the brim of food and anecdote. Jennie, who had been argumentative all weekend, would almost immediately marry her young George. Gladys de Grey would get on her newly installed phone to admirer number one, the Hon. Reginald Listen, or if he was not available to admirer number two, Sir John Listen-Kaye. Ladies were now able to ring the men up and guardedly converse instead of sending dangerous notes. Servants might overhear but there would be nothing ''on paper''.&lt;ref&gt;Leslie, Anita. ''The Marlborough House Set''. Doubleday, 1973.&lt;/ref&gt;{{rp|195–197}}&lt;/blockquote&gt;

====26 June 1900, Tuesday====
There was apparently a regular celebration of Arthur Collins' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902.

==== 28 June 1900, Thursday ====
Lady Randolph Churchill and George Cornwallis-West married at St. Paul's, Knightsbridge.&lt;ref&gt;Martin, Ralph G. ''Lady Randolph Churchill : A Biography''. Cardinal, 1974. Internet Archive: https://archive.org/details/ladyrandolphchur0002mart_w8p2/.&lt;/ref&gt;{{rp|220–223}}

===July 1900===
====27 July 1900, Friday====
The [[Social Victorians/People/Albert Edward, Prince of Wales|Prince of Wales]] had dinner at the Arthur Wilsons’:&lt;blockquote&gt;[[Social Victorians/People/Arthur Stanley Wilson|Mr and Mrs Arthur Wilson]] were honoured with the presence of the Prince of Wales at dinner on Friday night. Amongst the guests were the Portuguese Minister, Count Mensdorff, Duke of Roxburghe, Lady Georgina Curzon, Captain and Lady Sarah Wilson (arrived that morning from South Africa), Lord and Lady Tweedmouth, Lord Herbert Vane Tempest, Viscount Villiers, Lady Norreys, Lady Gerard, [[Social Victorians/People/Keppel|Hon Mrs Keppel]], Sir Edward and Lady Colebrook, Mr and Mrs Grenfell, Lady Lister Kaye, Mrs Arthur Paget, Mr and Mrs Arthur Sassoon, Hon. W. Erskine, Mr and Mrs J. Menzies, General Oliphant, Miss Jane Thornewell, Mrs Kenneth Wilson, and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]]. (1900-07-30 Hull Daily Mail)&lt;/blockquote&gt;

===October 1900===
====31 October 1900, Wednesday====
Halloween.
===November 1900===
====5 November 1900, Monday====
Guy Fawkes Day
====9 November 1900, Friday====
A debutante dance for Miss Helyar: &lt;quote&gt;In honour of the coming of age of Miss Helyar, a small dance was given by Lady Savile, at Rufford Abbey, last night. The number of invitations was not so large as it would have been but for the war. The house party included Mrs. and Miss Cavendish Bentinck, Lady Juliet Lowther, Lady Evelyn Ward, Lady Mabel Crichton, Mrs Kenneth Wilson, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Sir Berkeley Sheffield, Miss Sheffield, Lord Hyde, Lord Herbert, the Hon. B. Ward, the Hon. E. FitzGerald, the Hon. W. Erskine, Mr. Laycock, Captain Brinton, the Hon. George Peel, Mr. Harris, Captain Tharp, Captain Heneage, and the Hon. G. Portman.&lt;/quote&gt; (1900-11-10 Yorkshire Post)

====27 November 1900, Tuesday====
Arthur Sullivan's funeral: &lt;quote&gt;At eleven o'clock on Tuesday, November 27th, the [366/367] funeral procession set forth from Victoria Street, Westminster, on its mournful way, first to the Chapel Royal, St. James's, where, by command of the Queen, part of the Burial Service was to take place, and thence to St. Paul's. Throughout the line of route flags drooped at half-mast, whilst beneath them people crowded in their thousands, bare-headed and in silence, waiting to pay their last tribute of respect and gratitude to the lamented master whose genius had done so much to brighten their lives for the past five-and-twenty years. [new paragraph] Into the Royal Chapel, where Arthur Sullivan had begun his career as a chorister, was borne the casket containing his remains. On either side stood men and women famous in society and the wider world of Art in all its branches. The Queen was represented by Sir Walter Parratt, Master of Music, who was the bearer of a wreath with the inscription: &quot;A mark of sincere admiration for his musical talents from Queen Victoria.&quot; Sir Hubert Parry represented the Prince of Wales; the German Emperor was represented by Prince Lynar, Attache of the German Embassy; Prince and Princess Christian by Colonel the Hon. Charles Eliot, and the Duke of Cambridge by General Bateson.

Among the congregation at the Chapel Royal were seen the United States Ambassador; the Earl and Countess of Strafford; Theresa, Countess of Shrewsbury; the Countess of Essex; Lord Glenesk; Lord Rowton; Lord Crofton; Lady Catherine Coke; the Dean of Westminster; Lady Bancroft; Lady [367/368] Barnby; Mr. Arthur Chappell; Mr. and Mrs. F. C. Burnand; Mr. Arthur W. Pinero; Mr. Haddon Chambers; Lieutenant Dan Godfrey; Signor Tosti; Mr. George Grossmith; Mr. Rutland Barrington; Miss Macintyre; Mrs. Ronalds; Canon Duckworth; Lady Lewis; Miss Ella Russell; Mr. Augustus Manns; Mr. Charles Wyndham; Captain Basil Hood; the Chairman and Secretary of Leeds Musical Festival; and Representatives of various British Musical Associations.

The Pall-bearers were Sir Squire Bancroft, Mr. Francois Cellier, Colonel A. Collins (one of the Royal Equerries), Sir Frederick Bridge, Sir George Lewis, Sir Alexander Mackenzie, Sir George Martin, and Sir John Stainer. [new paragraph] he chief mourners were Mr. Herbert Sullivan (nephew), Mr. John Sullivan (uncle), Mrs. Holmes, and Miss Jane Sullivan (nieces), Mr. Wilfred Bendall (Sullivan's secretary), Mr. B. W. Findon, Mr. Edward Dicey, Mr. C. W. Mathews, Mrs. D'Oyly Carte, Dr. Buxton Browne, Mr. Arthur Wagg, Mr. Fred Walker, Mr. Dreseden and Sir Arthur's servants. [new paragraph] Much to their regret, neither Mr. Gilbert nor Mr. Carte was able to attend the funeral. The first was on the Continent for the benefit of his health, the second was laid up by serious illness. The present writer also, having been absent from London at the time, has not the advantage of an eye-witness to give a graphic description of the funeral obsequies of his old friend; and so, rather than attempt to paint the picture from imagination, he gladly avails himself [368/369] again of the courtesy of his brother-author who is so generous as to lend the aid of his experience. [new paragraph] In these sympathetic words, Mr. Findon describes the scenes and incidents in which, as a chief mourner, he took part at the Chapel Royal and St. Paul's Cathedral: &lt;blockquote&gt;&quot;. . . As the casket was borne into the Chapel, it was impossible to avoid thinking of those days when Sullivan himself had worn the gold and scarlet coat of a Chapel Royal Chorister, and his sweet young voice had rung through the sacred edifice. Then the world and its honours lay before him, but we doubt if even in the most sanguine moments of impulsive boyhood he imagined the greatness that one day would be his, or that his bier would pass within those honoured walls amid the silent demonstration of a mourning people. The anthem, 'Yea, though I walk through the valley of the shadow of death,' from his oratorio 'The Light of the World,' was beautifully sung, and the pathos of the music bathed many a face in tears, and touched a tender spot in more than one loving heart. Another of the dead master's exquisite thoughts, ' Wreaths for our graves the Lord has given,' brought the Service at the Chapel Royal to an end, and the procession passed on its way to St. Paul's Cathedral, which was crowded with sympathetic spectators.

&quot;Clerical etiquette and cathedral dignity compelled the beginning of the Burial Service anew, and when the coffin had been lowered into the crypt there came the most poignant moment of the long ceremonial. [new paragraph] &quot;Close to the open vault sat the members of the Savoy Opera Company, including his life-long friend, Mr. Francois Cellier, who had been associated as chef d'orchestre with all his comic operas, and, after [369/370] the Benediction had been given, they sang in voices charged with emotion the touching chorus, 'Brother, thou art gone before us,' from ' The Martyr of Antioch.' The effect was quite remarkable, inasmuch as it was one of those incidents which come but rarely in a life-time.&quot;&lt;/blockquote&gt;It was not in London alone that people mourned for Arthur Sullivan on that November day. Throughout Great Britain and Ireland, on the Continent of Europe, in America and farther across the seas, thousands of fond and grateful hearts ached with grief at the thought that England's dear master of melody had passed away into the silent land. From high-born personages and from people of low estate came floral emblems, wreaths, crosses, and lyres innumerable. Conspicuous among them was a beautiful harp of purple blossoms with strings — one broken — of white violets. To this offering was attached a card bearing the inscription:&lt;blockquote&gt;In Memoriam

ARTHUR SEYMOUR SULLIVAN

Born 13 May, 1842. Died 22 Nov., 1900

FROM MR. D'OYLY CARTE'S &quot;ROSE OF PERSIA&quot; TOURING COMPANY IN TOKEN OF THEIR AFFECTIONATE REGARD
&lt;poem&gt;Dear Master, since thy magic harp is broken,
Where shall we find new melodies^ to sing?
The grief we feel may not in words be spoken;
Our voices with thy songs now heav'nward wing.
Whilst on thy tomb we lay this humble token
Of love which to thy memory shall cling.&lt;/poem&gt;
BELFAST,
24th November, 1900.&lt;/blockquote&gt; [370/371] These simple lines but half expressed the love and esteem in which Sir Arthur Sullivan was held by all whose privilege it was to have been associated with him, and to have served, however humbly, his proud and brilliant life-cause.&lt;/quote&gt; (Cellier, François, and Cunningham Bridgeman. Gilbert and Sullivan and their operas: with recollections and anecdotes of D. Pp. 366-371. Google Books: http://books.google.com/books?id=Au05AAAAIAAJ.)

====30 November 1900, Friday====
The wedding between Lady Randolph Churchill and George Cornwallis West at St. Paul's, Knightsbridge, occurred about this time. [[Social Victorians/People/Muriel Wilson|Muriel Wilson]] attended, as did much of Society (1900-07-30 Times).

===December 1900===
===25 December 1900, Tuesday====
Christmas Day
====26 December 1900, Wednesday====
Boxing Day
===Works Cited===
*[1900-02-14 Morning Post] &quot;The Household Troops. Entertainment at Her Majesty's.&quot; Morning Post 14 February 1900, Wednesday: 3 [of 10], Col. 1a–2b [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19000214/014/0003 (accessed February 2020).
*[1900-07-30 Hull Daily Mail] &quot;Social Record.&quot; Hull Daily Mail 30 July 1900, Monday: 2 [of 6], Col. 5a [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000324/19000730/007/0002 (accessed July 2019).
*[1900-07-30 Times] &quot;Court Circular.&quot; Times, 30 July 1900, p. 6. The Times Digital Archive, http://tinyurl.galegroup.com/tinyurl/AHR8r5. Accessed 20 June 2019.
*[1900-11-10 Yorkshire Post] &quot;Court and Personal.&quot; Yorkshire Post 10 November 1900, Saturday: 6 [of 14], Col. 4c [of 8]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000687/19001110/099/0006 (accessed July 2019).
*Greville, Lady Violet. &quot;Place aux Dames.&quot; The Graphic 17 February 1900, Saturday: 7 [of 40], Col.1a–2a, 2c [of 3]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000057/19000217/008/0007 (accessed July 2019). [Col. 2c only for the last 2 paragraphs, not really relevant to Muriel Wilson]

==1901==
===January===
&quot;There were no winter performances of opera at Covent Garden in those times: there was, in 1901, only a summer season&quot; (Baring-Gould II 704, n. 14, quoting Rolfe Boswell).
====1 January 1901, Tuesday, New Year's Day====
====16 January 1901, Wednesday====
Arnold Dolmetsch sent out notices that he was moving to 85 Charlotte Street, Fitzroy Square (Campbell 137-38).

====22 January 1901, Tuesday====
Queen Victoria died at Osborne House, on the Isle of Wight.

====23 January 1901, Wednesday====
Edward VII formally proclaimed “King of Great Britain and Ireland and Emperor of India, Defender of the Faith” &quot;at Temple Bar, on St. Paul's Cathedral steps and at the Royal Exchange.&quot; &quot;The Privy Council met in St. James' Palace at 2 o'clock in the afternoon for the purpose of signing the accession proclamation of Edward VII. The attendance at the meeting of the Council was more than 200.&quot; (Merrill, Arthur Lawrence, and Henry Davenport Northrop. Life and Times of Queen Victoria: Containing a Full Account of the Most Illustrious Reign of Any Soveriegn in the History of the World, Including the Early Life of Victoria; Her Accession to the Throne and Coronation; Marriage to Prince Albert; Great Events During Her Brilliant Reign; Personal Traits and Characteristics That Endeared Her to Her People; Graphic Descriptions of Her Charming Home Life; Noble Qualities as Wife and Mother; Royal Castles; Public Receptions; Wonderful Growth of the British Empire, Etc. To Which is Added the Life of King Edward VII., and Sketches of the Members of the Royal Family. Philadelphia, PA: World Bible House, 1901. Page 437. Google Books: http://books.google.com/books?id=Kx48AQAAIAAJ)

====26 January 1901, Saturday====
Arnold Dolmetsch gave a performance at his new domicile at 85 Charlotte Street, Fitzroy Square (Campbell 137-38).

===February 1901===
====2 February 1901, Saturday====
Queen Victoria’s funeral at St. George’s Chapel, Windsor Chapel. Consuelo (Vanderbilt), Duchess of Marlborough was there: &lt;blockquote&gt;The service itself was magnificent. The stalls of the Knights of the Garter were occupied by the German Emperor and a dazzling array of kings, queens, ambassadors extraordinary, Indian princes, Colonial dignitaries, generals, admirals and courtiers. Consuelo wore the prescribed deep black mourning and crepe veil, which rather suited her, and it had the effect of extracting what she describes as a 'rare compliment' from her husband who remarked: 'If I die, I see you will not remain a widow long' — a conceit which suggests that he was more of his father's son than he cared to acknowledge.

Consuelo later reflected that the funeral of Queen Victoria was a moment when it truly appeared that no other country in the world had an aristocrac so magnificent, nor a civil service so dedicated, which is precisely what was intended. The great doors were flung open as the royal cortege mounted the steps, a boom of distant guns and clanging swords the only sound other than the funeral march, until Margot Asquith broke the reverential silence with a quip. Consuelo thoroughly enjoyed herself at the reception in the Waterloo Chamber afterwards too. (Stuart, Amanda Mackenzie. Consuelo and Alva Vanderbilt: The Story of a Daughter and a Mother in the Gilded Age. New York and London: HarperCollins, 1005. Page 228. Google Books: http://books.google.com/books?id=44mhoIv12rEC)&lt;/blockquote&gt; Also Henry James saw the funeral procession.

====3 February 1901, Sunday====
1901 February 2–4?: Queen Victoria lay in state for 2 days between her funeral and her interment.

====4 February 1901, Monday====
Queen Victoria’s interment at Frogmore Mausoleum, Windsor Great Park.
====23 February 1901, Saturday====
The wedding of Hugh Richard Arthur, 2nd Duke of Westminster and Constance Edwina Cornwallis-West (1901-02-23 Cheshire Observer).

===March 1901===
Sometime in March 1901 Arthur Conan Doyle and Fletcher Robinson &quot;were on a golfing holiday at the Royal Links Hotel at Cromer in Norfolk,&quot; where Robinson told Doyle a Dartmoor legend of &quot;a spectral hound&quot; (Baring-Gould II 113).

Doyle's &quot;The Hound of the Baskervilles&quot; began publication in the ''Strand'' in January 1902.

===April 1901===
====18-20 April 1901, Thursday-Saturday====
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] and Mrs. Beerbohm Tree took part in 3 performances of &lt;quote&gt;Masks and Faces. The matinées have been organized by [[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]], of Tranby Croft, in aid of the local fund of the Soldiers’ and Sailors’ Families Association. It was originally intended that the matinées should have been given in January last, but, owing to the death of Queen Victoria, they were postponed until Thursday, Friday, and Saturday last week. Additional interest was centered in the event, owing to the cast including no less a name than that of Mrs. Beerbohm Tree, while the fact that Miss Muriel Wilson was to appear as Peg Woffington aroused expectation.&lt;/quote&gt; (1901-04-25 Stage)

===May 1901===

==== '''1901 May 30, Thursday''' ====
The London ''Daily Express'' reported on the opening of the Ladies' Dog Show:&lt;blockquote&gt;There was a very large attendance yesterday at the Botanic Gardens for the summer fête of the Ladies’ Kennel Association, which is under the patronage of the Queen, and the charming grounds had quite the aspect of a garden-party at tea-time, when the band played under the trees.

Among well-known exhibitors to be seen were Sir Claud and Lady Alexander, who was showing a number of cats, Lady Aberdeen, Lady Angela Foster, and the Princess de Moniglyon, who took a first prize. Neither Lady Decies nor Lady Maitland was exhibiting on this occasion. Others to be seen were Lady Algernon Gordon-Lennox in black and white, Mrs., Algernon Bourke all in mauve, the Duchess of Newcastle, Mrs. Baillie of Dochfour, and Mrs. Greville.

The Dogs’ Brigade Parade, which takes place to-day at 4.30, will be in aid of the Princess of Wales' Soldiers and Sailors' Widows and Orphans Fund.&lt;ref&gt;&quot;At the Botanic Gardens.&quot; ''Daily Express'' 31 May 1901, Friday: 4 [of 8], Col. 7a [of 7]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/BL/0004848/19010531/086/0004?browse=true https://www.britishnewspaperarchive.co.uk/viewer/BL/0004848/19010531/086/0004]. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;The ''Birmingham Daily Gazette'' has a different list of names:&lt;blockquote&gt;Yesterday the annual show of the Ladies' Kennel Association was held in the Royal Botanical Gardens, Regent's Park, and attracted a highly fashionable gathering. Among the ladies represented were Princess Victor Dhuleep Singh, Princess Sophie Dhuleep Singh, the Marchioness of Nottingham, the Duchess of Sutherland, the Countess of Aberdeen, Lady Evelyn Ewart, Lady Helen Forbes, the Hon. Mrs. Baillie, Lady Moor, the Hon. Mrs. Alwyne Greville, the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], Lady Alwyne Compton, Lady Chetwode, Lady Cathcart, Lady Angela Forbes, the Hon. Mrs. Fellowes, Lady Gooch, Princess de Montglyon, and Viscountess Southwell, Mrs. Samuelson, Miss Serena, Mrs. Bosanquet, Mrs. Williams, and Mrs. Ingle Bepler. Cats and poultry are also exhibited.&lt;ref&gt;&quot;Ladies' Dog Show.&quot; ''Birmingham Daily Gazette'' 31 May 1901, Friday: 6 [of 8], Col. 5b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000667/19010531/124/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1901===
Summer 1901: William B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).
====17 June 1901, Monday====
&lt;quote&gt;The &quot;Women Writers&quot; held their dinner at the Criterion on Monday, the 17th. Now Mr. Stephen Gwynn, in his paper entitled &quot;A Theory of Talk,&quot; roundly asserts that women are less amusing than men. He says that there is no reason in nature why they should be, but that their inferiority is obvious. He points out that &quot;thirty or forty men will meet at seven o'clock, dine together, and pass the evening very agreeably till midnight. Imagine thirty or forty women called upon to do the same; would they be able to amuse themselves?&quot; It seems almost a pity that the exclusiveness of the women writers would not allow Mr. Gwynn personally to observe whether they were amused or bored on Monday night. In number there were nearly two hundred, and there certainly did not appear to be any lack of enjoyment or of laughter, but then it is also a fundamental belief with men that women are early adepts at hiding their true feelings. / Lucas Malet occupied the chair, and her carefully prepared speech was read out by Miss Sydney Phelps. Standing at the base of the statue of one of the world's greatest authors, and that, we regret to say, not a woman but a &quot;mere man,&quot; Miss Phelps, speaking for Lucas Malet, said there was good cause for women to congratulate themselves that, whereas there had been Thackeray, Dickens, the brothers Kingsley, and Wilkie Collins among authors, authoresses could boast of George Eliot, Mrs. Gaskell, [33 Col B / 34 Col A] Miss Yonge, &amp;c, and she felt that in the future they might equal, she would not say rival, their &quot;brother man.&quot; At this courageous vaunt our glance involuntarily strayed to the statue, anticipating that it would be moved to at least a wink; but overwhelmed, perhaps, by the presence of so many &quot;sisterwomen,&quot; it gave no sign. The speech was long, lasting for over thirty minutes. It touched on the evils of lowering work to what might be a present commercial but fleeting value; it contained much that was excellent, and tendered some good sound advice; perhaps it dwelt a trifle too insistently upon the obvious, and it was serious even to solemnity. But then &quot;women are so serious.&quot; / Mme. Sarah Grand's reply was couched in far lighter vein. It slipped into the anecdotal, and was altogether more in the masculine line of after-dinner speaking. It offered no advice save on the advisability of laughter; it lingered for a moment on the sorrows of misinterpretation and misunderstanding, and included some amusing examples. Mme. Sarah Grand possesses a sympathetic voice, and is very pleasant to listen to. / It is characteristic of the gravity with which even in play hours women regard their &quot;work&quot; that the majority of guests preferred the more serious matter of Lucas Malet to the light personal note of Mme. Grand. The dinner itself was very good, and it was noticeable that whilst at the Authors' dinner on May 1 but few women availed themselves of the permission to smoke, at the women's function scarcely one was without a cigarette. Coffee was served at the table, and afterwards the company broke up into groups. / The committee numbered among its members Miss Beatrice Harraden, Mrs. Steel, Mrs. Craigie, Miss Christabel Coleridge, Miss Violet Hunt, and many other favourite writers. In the company present there were Dr. Jex-Blake, Mrs. Ady, Dr. Margaret Todd, Miss Adeline Sergeant, Mrs. Mona Caird, Mrs. Burnett-Smith, Mme. Albanesi, Miss Nora Maris, Miss Kenealy, and others; and the following presided at the tables : Lucas Malet, Mme. Sarah Grand, Mrs. de la Pasture, Miss Montresor, the Lady Mayoress, Mrs. L. T. Meade, Mrs. Alec Tweedie, Mrs. Walford, Mrs. B. M. Croker, Miss Violet Hunt, Miss Beatrice Harraden, Mrs. Belloc Lowndes, Miss Violet Brooke-Hunt, Miss Thorneycroft Fowler.&lt;/quote&gt; (&quot;The Women Writers' Dinner.&quot; The Author. Vol. XII, No. 2. 1 July 1901. Pp. 33–34.)

====26 June 1901, Wednesday====
There was apparently a regular celebration of Arthur Collins' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902.

====29 June 1901, Saturday====
&quot;To-day sees the public inauguration of the Horniman Musem at Forest Hill. This collection of marvels from many lands, gathered together by a member of the Horniman family, has been generously presented to the public and housed in a handsome new building — set in the midst of fifteen acres, which are now dedicated to use as a public park. The entrance to the museum will be free.&quot; (&quot;The Horniman Museum.&quot; Illustrated London News (London, England), Saturday, June 29, 1901; pg. 928; Issue 3245, Col. B)

===July 1901===
====19 July 1901, Friday====
[[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]] hosted a concert at the Wilson house in Grosvenor-place in London: &lt;quote&gt;Mr. and Mrs. Arthur Wilson lent their house in Grosvenor-place on Friday afternoon for Miss Gwendoline Brogden’s concert. Miss Brogden, who is only eleven years old, is quite a prodigy. She sings quite exquisitely, and great many people, including Lady de Grey and Mrs. Arthur Wilson, are much interested in her future, which promises to be a very brilliant one. Lady Maud Warrender, Miss Rosamond Tufton, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Mr. Bernard Ralt, Signor Ancona, and Signor Tosti, all promised to assist at the concert, and the tickets were a guinea each.&lt;/quote&gt; (1901-07-24 Beverley Echo)

==== 25 July 1901, Thursday, 2:30 p.m. ====
The wedding of William Dixon Mann Thomson — Captain Mann Thomson in the Life Guards — and Violet Hemsley Duncan. Captain Mann Thomson's father had died in 1899. (Guests' names with their gifts set as an unordered list here, to save space; it was typeset as a long list of paragraphs in the newspaper story.)&lt;blockquote&gt;MARRIAGE OF CAPTAIN MANN THOMSON AND MISS DUNCAN.

The marriage of Captain Mann Thomson, Royal Horse Guards, and Miss Violet Duncan, eldest daughter of Mr. A. Lauderdale Duncan, Knossington Grange, Oakham, took place in St. Peter's Chnrch, Eaton-square, London, on Thursday, the inst., 2.30 p.m. The bride, who was given away her father, wore a dress of white satin, draped with white and old Brussels lace, wreath of orange blossoms, and tulle veil. Her ornaments were pearls. She was attended by seven bridesmaids, viz.: — Miss Adèle, Miss Marjory, and Miss Esmè Duncan, sisters; Miss Dorothy and Miss Sybil Thompson, cousins of the bride; Miss Villiers, cousin of the bridegroom; and Miss Joan Dawson. They wore dresses of the palest pink silk, covered with pink gauze, collars of white lace, and pale pink chiffon baby hats. The bride's train was carried by Miss Duncan, her youngest sister. The bridesmaids carried bouquets of pink carnations, and wore diamond brooches in the shape of a violet with sapphire centre, the gifts the bridegroom. A detachment of non-commissioned officers and men of the bridegroom's troop lined the aisle during the ceremony. The bridegroom was supported by the Earl Arran as best man. The officiating clergy were the Rev. Ravenscroft Stewart, Vicar of All Saints', Ennismore-gardens, the Rev. G. Tanner, Rector of St. Peter's, Knossington, Leicestershire, and the Rev. H. Trower. After the ceremony, a reception was held at 8, Rutland-gate, the residence of Mr. and Mrs. Lauderdale Duncan. Among those present were the Duke and Duchess of Westminster, Dowager Countess of Chesterfield, Sir William and Lady Houldsworth, the Hon. C. and Mrs. Stanhope, Miss Hay, Lord and Lady Eglinton, Lord and Lady Castlereagh, Lord Ernest St. Maur, Lord and Lady Pembroke, Mrs. Adair, Mrs. Mann Thomson, Miss Mann Thompson, Earl Arran, Lord Cecil Manners, Mrs. and Miss Wilton Phipps, and many others. Later, the bride and bridegroom left for Dover, ''en route'' for the Continent, where they will spend the honeymoon. The bride's travelling dress was of pale blue crepe-de-chine, and black hat. There were about five hundred gifts from relations and friends. The following is a list:—

* Bridegroom to Bride — Large diamond spray
* Mrs. Mann Thomson (mother of bridegroom) — Diamond ring, diamond and sapphire bangle, and cheque
* Mr. Lauderdale (father of bride) — Diamond and sapphire necklace
* Mrs. Duncan (mother of bride) — Silver-mounted travelling bag
* Dowager Lady Hay (bride's aunt) — Silver tea service
* Miss Mann Thomson (bridegroom's sister) — Brougham
* Mr. and Mrs. Butler Duncan (uncle and aunt) — Gold-mounted claret jug
* The Misses Jackson (bridegroom's aunts) — Silver plate
* Mr. H. Mann Thomson (brother) — Silver-mounted portmanteau
* Mr. Charles Hunt — Diamond and pearl brooch
* Miss Adele Duncan — Gold match-box
* The Earl Arran — Gold cigarette case
* Mr. and Mrs. Lucas — Bracelet
* Earl of Arran — Set of diamond and pearl studs
* Capt. and Lady Riddell — Bracelet
* Mrs. and Miss Wilton Phipps — Gold and ruby buckle
* Hon. H. Stanhope, R.N. — Brilliant buckle
* Mr. and Mrs. Pennington — Ruby necklace
* Mr. A. Butler Duncan — Necklace (old design)
* Mr. and Mrs. Gervase Beckett — Sleeve links
* Duke and Duchess of Westminster—Pair of silver candlesticks
* Duchess of Roxburgh—Dresden china coffee service
* The Countess of Shaftesbury — Walking-stick
* The Earl of Arran — Umbrella
* Lady Napier Magdala — Snuff-box
* Sir Richard Waldie Griffith — Fan
* Officers of the Royal Horse Guards — Massive silver vase
* Lady Houldsworth — Silver inkstand
* Viscount Ingestre — Silver waiter
* Miss Hay — Silver coffee pot
* Lady Hay — Silver tea caddy
* The Countess of Chesterfield — Silver and brilliant-mounted photo frame
* Lord Manners — Set four silver candlesticks
* Lord and Lady Eglinton — Silver cigarette box
* Earl and Countess of Ancaster — Pair of silver peppers
* Lady Augusta Noel — Book-slide
* Mr. and Mrs. Bradley-Martin — Old china coffee service in case
* Mr. and Lady Wilfred Renshaw — Leather-covered book, &quot;Where It?&quot;
* Mrs. Duncan — Silver-mounted stationery case and blotter
* Sir Arthur Fludyer — Hunting crop
* Lady Katherine Cole — Walking-stick
* Lord Hamilton — Oak card table
* Sir John Kelk — Writing case
* Capt. Hon. E. St. Aubyn — Set of silver spoons in case
* Capt. and Mrs. Burns-Hartopp — Set of silver asparagus tongs in case
* Capt. Trotter — Silver sealing-wax stand
* Capt. E. W. Clowes — Silver tobacco box
* Mr. and Mrs. Sands Clayton — Silver scent bottle
* Mr. and Mrs. John Hunt Clayton — Thermometer in silver-mounted case
* Mr. and Mrs. Evan Hanbury — Clock
* Major Atherley — Cigarette box
* Mr. and Mrs. Richard Tryon — Card case
* Mr. and Mrs. Hamilton Stubber — Table mirror in silver frame
* Mr. and Mrs. Gretton — Pair of silver candlesticks
* Miss Adele Duncan — Silver tea service
* Hon. G. Crichton — Silver-mounted paper-knife
* Mrs. Norman Lampson — Parasol
* Capt. Gregson — Photo, &quot;Guards at Pretoria&quot;
* Mr. Alfred Keyser — Leather bag
* Mr. and Mrs. Armytage — lvory paper knife
* Mrs. Boyce — Leather tray with two painted china plaques
* Mr. and Mrs. A. B. Norman — Silver-mounted paper knife
* The Master of Elibank — Pair of silver ash trays
* Mr. Adrian Rose — Pair of silver toast racks
* Mr. Archibald Smith — Hunting crop
* Major Bradford Atkinson — Walking-stick
* Mr. and Mrs. Stanhope — Painted china tea service
* Mr. G. A. Grant — Stationery case
* Mrs. Charles Inge — Copper and brass jardiniere
* Col. and Mrs. Makins — Hunting crop
* Mr. G. F. Trotter — Walking stick
* Mr. and Misses Cardwell — Fan
* Mrs. Dana — Thermometer
* Mrs. Nugent — Card case
* Mr. and Mrs. Ovey — Tortoiseshell box
* Mr. F. Peake — Writing table
* Capt. Boyce — Embroidered table cover
* Mrs. Duncan — Dressing bag case
* Mr. F. C. Fardell and Miss Gilbert Day — Brocaded satin cushion
* Mr. and Mrs. Niel Robson — Visiting book
* Mrs. R. B. Hay — Silver salts in case
* Mr. and Mrs. Harold Broadbent — Pair silver peppers in case
* —— Set silver knives in case
* Mr. and Mrs. Greville Clayton — Six silver vases in case
* Mr. and Mrs. Reginald H. Lewis — Pair silver peppers
* Lord Ernest St. Maur — Set four silver fruit spoons in case
* Rev. Geo. and Mrs. Tanner — Pair of silver salts
* Capt. Thomson's Valet and Groom — Pair of silver peppers
* Mr. Alick Duncan — Silver jug
* Mr. and Mrs. A. Brocklehurst — Silver timepiece in case
* Lieut.-Col. and Mrs. Blackburn — Silver fruit spoon
* Mr. and Lady Georgiana Mure — Silver-mounted ink [sic]
* Mrs. Gerald Fitzgerald — Silver-mounted inkstand
* Mrs. Ruthven — Set of silver knives in case
* Mrs. Blair — Umbrella
* Mrs. Willie Lawson — Hunting crop
* —— Three driving whips
* —— Tea tray
* Mr. and Mrs. Ramsay — Umbrella
* Mr. George Hunt — Silver flower bowl
* Mr. and Mrs. Reginald Cookson — Silver biscuit box
* Mr. Arthur and V. James — Silver two-handled cup and cover
* Mr. Robbio Stubber — Pair of silver scent bottles
* Mr. and Mrs. Geo. Baird — Silver bowl
* Mr. and Mrs. Harrison Broadley — Pair of silver flower vases
* Mrs. Grant—Silver flower-pot stand
* Mrs. Villiers — Silver corkscrew
* Capt. Spender Clay — Antique silver snuffbox
* Mr. and Mrs. Weir — Silver bacon dish
* Mr. Baird — Pair of silver candlesticks
* Mr. Athol Hay — Silver sugar bowl
* Capt. Ewing — Pair of silver fruit dishes
* Mr. and Mrs. C. J. Phillips — Pair of silver baskets
* Miss Esmé Duncan — Silver box
* Mr. and Mrs. Ronald Paton — lvory paper knife
* Dr. Freshfleld — Work case
* Mrs. Arkwright — Silver-mounted blotter
* Mr. and Mrs. Peake — Silver-mounted stationery case
* Miss Goddard — Book
* Mr. D. Baird — Silver inkstand
* J. G. and Jane B. Hay — lnkpot, with silver watch top
* Mr. and Mrs. Wadsworth Ritchie — Pair of silver dishes in case
* Mr. and Mrs. Guy Fenwick — Set of twelve silver knives in case
* Jane and Uncle Willie — Silver sugar basin in case
* Mr. and Miss Millington Knowles — Set of four silver dessert spoons in ease
* Herbert and Lady Beatrix Herbert — Silver flower dish
* Mr. and Mrs. J. B. Thorneycroft — Four silver candlesticks
* Mr. and Mrs. Russell? M [illegible, ink has spread] — Silver bowl [Col. 2c / Col. 3a]
* Mr., Mrs., and the Misses Wm. Cooper — Fan
* Miss Winearls — Silver-mounted scent bottle
* Sir Ernest Cassel — Diamond and enamel brooch
* Mr. John S. Cavendish — Gold pencil case
* —— Diamond and sapphire bracelet
* Miss Lottie Coats — Diamond and pearl brooch
* Hon. T. Robarts — Diamond brooch
* Mr. and Mrs. Chas. E. Hay — Enamel and pearl miniature holder
* Evelyn Ward — Cornomandel [sic] box
* Mr. and Mrs. Slade — China clock
* Lieut.-Col. Jervoise — Fan
* Mr. and Mrs. J. B. Fergusson—Set of four silver menu holders
* Mr. Guy R. F. Dawson — Silver card case
* Rev. E. V. and Mrs. Hodge — Silver dish
* Mr. C. S. and Mrs. Newton — Silver waiter
* Mrs. Metcalfe — Gold, turquoise, and ruby brooch
* Lord and Lady Erne — Set of three gilt decorated liqueur decanters
* Mr. and Mrs. Chas. Grant — Two silver-mounted spirit decanters
* Mr. and Mrs. George Baird — Set of three cut-glass decanters
* Mr. Peter Cookson—Pair of silver-mounted decanters
* Mrs. Featherstonehaugh — China ornament
* Aunt Mary — China coffee service in case
* Mr. H. S. Sykes — Silver-mounted telegram form case
* Capt. Meade — Pair of engraved claret jugs
* Lord and Lady Binning — Silver-mounted claret jug
* Mr. and Mrs. Baldock — Silver-mounted water jug, with inscription
* Mrs. and the Misses Chaplin — Pair of gilt decorated vases
* —— Silver-mounted claret jug
* Kittie, Margie, Hestie, Walter, Phillip, and Millicent Tanner — Pair of silver peppers case
* Mr. J. R. J. Logan — Silver-mounted claret jug
* Miss Ethel Baird — Painted china box
* Mrs. D. A. Neilson — Pair of female figures with Cupids
* M. M. Phillips — Painted china miniature box
* Lady Waldie Griffith — Stationery case
* —— Painted two-fold screen
* Miss Mabel Fitzgerald — Silver-mounted vase
* Major Bouverie — Silver-mounted match holder
* —— Enamelled inkstand and candlesticks to match
* Mrs. Duncan — Stationery case and blotter
* —— Silver-mounted stationery case
* —— Tortoiseshell and silver-mounted paper-knife
* Miss Mills — Dresden china vase, cover, and stand
* —— Six Vols. of Ruskin's &quot;Modern Painters&quot;
* Mrs. W. Baird — Leather bag
* Miss Langridge — Four silver spoons
* Miss Kirk and Miss Hemsley — Silver-mounted photo frame
* Miss Nessie Hemsley — Silver-mounted photo frame
* Captain and Mrs. St. Aubyn Loftus — Silver vase
* Decima Walker Leigh — Pair of silver-mounted menu stands
* Mrs. Charles Thomson — Mirror in silver frame
* Miss Reese — Silver crumb scoop
* —— Silver-mounted seal and case
* Mary Abercorn Alexander and Gladys Hamilton — Silver inkstand
* Mr. and Mrs. Cecil Chaplin — Silver pen, pencil, and knife in case
* Miss Gwendoline Brassey — Silver-mounted ice pail
* Mr. and Mrs. and Misses Clifford Chaplin — Pair of silver candlesticks
* Mr. and Mrs. Magee — lvory paper knife
* Misses Dorothy and Maude Pilcher — Scent bottle
* Miss Ashton — Silver-mounted clock
* Mrs. William Clarence and Miss Watson — Silver crumb scoop
* Major and Mrs. Ed. Baird — Egg-boiler on silver stand
* Mr. A. F. H. Fergusson — Pair of silver coffee pots
* —— Table mirror
* —— Pair of silver vases
* Mrs. R. B. Mnir — Silver fox ornament
* Mr. H. Brassey and Mr. H. R. Molynenx — Silver teapot
* —— Pair of silver sauce boats
* Mr. and Mrs. Heathcote — Silver cream jug
* Misses Thompson — Silver photo frame
* Mr. C. D. Rose — Pair of silver fruit dishes
* Mr. T. Archibald Hope — Silver toast-rack
* Mr. and Mrs. Robert Hunt — Pair of silver sauce boats
* Major and Mrs. Candy — Pair of silver fruit baskets
* Misses Trefusis — Silver-mounted owl mustard-pot
* Mrs. Frank Chaplin — Silver photo frame
* Major Vaughan Lee — Silver waiter
* Major Byng — Pair of silver menu stands
* Lady Wilton — Silver photo stand
* Geoffrey and Sibyll Palmer — Scent bottle
* Dr. Clement Godson — Silver salad cruet
* Mr. Mackenzie — Silver cigar case
* Mr. G. Colvin White — Set of four silver trays
* Mr. Edgar Brassey — Silver pipe lighter
* Miss Emily Dawson — Photo frame
* Mrs. Gerald FitzGerald — Silver match-box holder
* A. Barns — Silver waiter
* Miss Palmer — Letter-clip and dish
* Mr. and Mrs. Aubrey Coventry — Photo frame
* —— Silver bowl three feet
* Mr. and Mrs. Hornsby — Openwork silver basket
* —— Antique silver box
* Mr. and Mrs. H. R. Baird — Silver coffee-pot
* —— Pair of silver salts
* Mr. Hugh Wanemley — Silver-gilt match-box
* Captain Gordon Wilson — Silver snuff-box
* Mrs. Whitelaw — Silver mustard-pot
* Mrs. Palmer — Silver spoon
* Mr. Dudley Majoribanks — Silver bowl and cover
* Mr. Wilfred F. Ricardo — Pair silver candlesticks
* Indoor Servants at Knossington Grange and 8, Rutland Gate — Breakfast warmer and two silver entree dishes and covers
* Outdoor Servants at Knossington Grange — Silver stationery case
* Mr. Waterman (coachman) — Driving-whip
* Mr. Alexander (coachman) and Mrs. Alexander — lnk-stand
* Villagers of Knossington — Silver sugar bowl, sugar tongs, and cream ewer in case
* Silver vase, with inscription — &quot;Capt. Mann Thomson, Royal Horse Guards, from the Estate and Household at Dalkeith, on the occasion of his marriage, 25th July, 1901.&quot;
* Miss Baldock — Pair of scent bottles
* Captain Cook — Paper-knife
* Sir A. Baird — Pair of silver muffineers
* Rev. H. W. Trower — Pair of silver peppers
* Mr. T. Vandeleur — Silver cigarette box
* Lady Miller — Silver milk jug
* Mr. Hedworth Barclay — Silver muffineer
* Miss May A. Jackson — Photo frame
* Mr. Geoffrey Heneage — Silver ash tray
* Mr. and Mrs. R. B. Hay — Pair silver mustard-pots
* Mrs. George Charteris — Silver-mounted calendar
* Royal School of Art Needlework, Exhibition-road — Silvered copper heart-shaped box
* Mr. A. C. Newbigging — Silver fox ornament
* Mr. S. Schreiber — Silver match box
* Mr. and Mrs. J. H. J. Phillips — Silver muffineers
* Mr. and Mrs. Fyfe Jameson — Silver flask
* Mrs. Beaumont Lubbock — Silver bon-bon dish
* Lord Castlereagh — Salad bowl
* Captain Hambro — Silver card case
* Lord Longford — Silver bowl
* Captain —— Silver waiter
* Mrs. Forester — Silver frame
* Mrs. Martin — Tea cloth
* Mr. and Mrs. Cooper — Whip
* Earl Lonsdale — Silver tray
* Lady Augusta Fane — Red box
* Mr. Paul Phipps — Clippers
* Mr. E. Herlick — lnkstand&lt;ref&gt;&quot;Marriage of Captain Mann Thomson and Miss Duncan.&quot; ''Grantham Journal'' 27 July 1901 Saturday: 2 [of 8], Cols. 2a–3b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000400/19010727/003/0002.&lt;/ref&gt;
&lt;/blockquote&gt;

===August 1901===
====30 August 1901, Friday====
[[Social Victorians/People/Horos|The Horoses]] (troublesome members of the Golden Dawn) were thrown out of 99 Gower Street and moved to Gloucester Crescent (King 89 91).
===October 1901===
====31 October 1901, Thursday====
Halloween.
===November 1901===
====5 November 1901, Tuesday====
Guy Fawkes Day
===December 1901===
====25 December 1901, Wednesday====
Christmas Day
====26 December 1901, Thursday====
Boxing Day
===Works Cited===
*[1901-02-23 Cheshire Observer] &quot;Duke of Westminster. Brilliant Function.&quot; Cheshire Observer 23 February 2901, Saturday: 6 [of 8], Col. 1a–6c [of 8]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000157/19010223/114/0006 (accessed July 2019).
*[1901-04-25 Stage] &quot;Provinces.&quot; &quot;Amateurs.&quot; The Stage 25 April 1901, Thursday: 11 [of 24], Col. 3c, 4b–c [of 5]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001179/19010425/028/0011 (accessed July 2019).
*[1901-07-24 Beverley Echo] &quot;Stray Notes.&quot; Beverley Echo 24 July 1901, Wednesday: 2 [of 4], Col. 4b [of 6]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001561/19010724/037/0002 (accessed July 2019).

==1902==
Sometime in 1902, London publisher [[Social Victorians/People/Working in Publishing#George Newnes|George Newnes]] published an edition of [[Social Victorians/People/Arthur Conan Doyle|Arthur Conan Doyle]]'s first (1892) collection of Holmes stories.
===January 1902===
====1 January 1902, Wednesday, New Year's Day====
===February 1902===

==== 13 February 1902, Thursday ====

King Edward VII and Queen Alexandra were present with some of their friends at Niagara, which must have been an ice-skating rink. Mr. and [[Social Victorians/People/Churchill|Mrs. George West]] are Lady Randolph Churchill and George Cornwallis-West.&lt;blockquote&gt;SOCIAL &amp; PERSONAL

Royalty at Niagara.

Quite a record audience was present at Niagara yesterday, when the free skating and waltzing competitions were skated off to the sound of gay music in a brightly lighted, warm atmosphere.

The royal box made a goodly show with its trappings of Oriental hangings and decorations of palms.

The Royal Box.

The King and Queen were accompanied by Princess Victoria and Prince and Princess Charles of Denmark, the Prince and Princess of Wales having previously arrived. Their Majesties were conducted to the spacious box by Mr. Hayes Fisher.

All the royal ladies wore black, the Queen adding a bunch of yellow Lent lilies to her sombre attire. Her two daughters lightened their mourning with touches of white, and the Princess of Wales wore a bunch of violets in her toque, with a twist of white.

In the adjoining box, among members of the suite were the Countess of Gosford, Earl Howe, Mr. Sidney Greville, Mr. H. J. Stonor, Lieut.-Colonel Davidson, Lieut.-Colonel Legge, and Viscount Crichton.

In boxes on the other side of the royal box were Lady Alice Stanley, with the Ladies Acheson, the Countess of Derby, Countess De Grey and Lady Juliet Lowther, [Col. 3c/4b] Mr. and [[Social Victorians/People/Churchill|Mrs. George West]] [Lady Randolph Churchill and George Cornwallis-West], Sir Edgar and Lady Helen Vincent, the Duchess of Bedford and the Marquis of Tavistock, [[Social Victorians/People/de Soveral|M. de Soveral, the Portuguese Minister]], and Viscount and Viscountess Falmouth.

Others to be picked out in the crowd were Consuelo Duchess of Manchester, Viscountess Coke and Mrs. Ellis, Lady Archibald Campbell and her son, Mrs. Grenander, Lord and Lady Lilford, Mr. and Mrs. Edward Stonor, Mrs. [[Social Victorians/People/Bourke|Algernon Bourke]], Mr. Algernon Grosvenor, and Mr. and Mrs. Hwfa Williams.

The royal party took a great interest in the contests, and especially applauded the Swedish couple in their graceful evolutions. Their Majesties remained over an hour, the royal party taking their departure shortly after five.&lt;ref&gt;&quot;Social &amp; Personal.&quot; ''Daily Express'' 14 February 1902, Friday: 4 [of 8], Cols. 3c–4b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020214/088/0004. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

===March 1902===
The last time Bret Harte and Arthur Collins saw each other: &quot;They dined at the Royal Thames Yacht Club, and Collins found his 'poor old friend' 'saldly aged and broken, but genial and kind as ever.' They sat an hour at a music hall and Harte wrote afterwards to thank Collins for having 'forced him out.'&quot; (Nissen, Axel. Bret Harte: Prince and Pauper. Jackson, MS: U P of Mississippi, 2000: 262)
===April 1902===
====9 April 1902, Wednesday====
According to a letter to Lady Gregory, [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] dictated &quot;2000 words in an hour and a half&quot; &quot;to a typewriter; he was working on his novel (Wade 370). At this point, a typewriter was a person who used the machine called typewriter to type.
====10 April 1902, Thursday====
[[Social Victorians/People/William Butler Yeats|W. B. Yeats]] wrote to Lady Gregory from 18 Woburn Buildings about working on his novel &quot;-- dictating to a typewriter&quot; (Wade 370).

===May 1902===
====5 May 1902, Monday====
Bret Harte died. Arthur Collins does not seem to have been there at his death; “his dear friend Madame Van de Velde and her attendants” were, though (Pemberton, T. Edgar. The Life of Bret Harte. Dodd, Meade, 1903. http://books.google.com/books?id=eZMOAAAAMAAJ). Not sure when the funeral occurred, but he is buried “in quiet Frimly churchyard,” (341) and &lt;quote&gt;In accordance with his well-known views on such subjects the funeral was a very simple one. Among the few who followed him to his ivy-lined grave were Mrs. Bret Harte, his son and daughter-in-law, Mr. and Mrs. Francis King Harte, his daughter, Miss Ethel Harte, Madame Van de Velde, Colonel Collins, Mr. A.S. Boyd, and a small cluster of grief-stricken friends.&lt;/quote&gt; (Pemberton, T. Edgar. The Life of Bret Harte. Dodd, Meade, 1903. http://books.google.com/books?id=eZMOAAAAMAAJ (accessed November 2014).

====8 May 1902, Thursday====
&lt;quote&gt;On Thursday, May 8, 1902, in the squat, mid-Victorian church of St. Peter's in the Surrey village of Frimley, a group of about twenty people had come to show their final respects to Francis Bret Harte. Outside it was raining steadily . In the subdued light from the stained-glass windows, one cold discern a small group at the front of the church consisting of Anna Harte, her son Frank, her daughter-in-law Aline, and her daughter Ethel. Another small group was formed around Madame Van de Velde, including one of her unmarried daughters, Miss Norris (the sister of her son-in-law Richard Norris), and Mrs. Clavering Lyne. Of Harte's closest friend, only Arthur Collins and Alexander Stuart Boyd were present. Pemberton had written to Frank the day before that he wished to attend the funeral but that in his &quot;deplorable state of health&quot; it was impossible for him to travel. Beside the small group of family and old friends, the rest of the people who heard the service conducted by the rector of Frimley, Reverend W. Basset, were recent acquaintances from among the local gentry. As one newspaper noted: &quot;The funeral was of the simplest possible character and the phrase 'this our brother' had a peculiar poignancy, for, though a group of villagers stood in the rain under the trees as the hearse arrived, there were few in the church, who had not the right to call Mr. Bret Harte friend.&quot; The simplicity of the service was in keeping with Bret Harte's wishes.&lt;/quote&gt; (Nissen, Axel. Bret Harte: Prince and Pauper. Jackson, MS: U P of Mississippi, 2000: 263)
===June 1902===
Summer 1902: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until Yeats bought the Tower at Ballylee. (I got this from Wade?)
====3 June 1902, Tuesday====
[[Social Victorians/People/William Butler Yeats|W. B. Yeats]] wrote Arnold Dolmetsch, asking him to &quot;chair ... a lecture he [was] soon to give&quot;: &quot;You are the only one, I suppose, in the world now, who knows anything about the old music that was half speech, and I need hardly say that neither [[Social Victorians/People/Florence Farr|Miss Farr]] nor myself, could have done anything in this matter of speaking to notes without your help&quot; (Campbell 142).
====7-9 June 1902, Saturday-Monday====
The [[Social Victorians/People/Warwick|Earl and Countess of Warwick]] hosted a house party: &lt;quote&gt;The Earl and Countess of Warwick entertained a distinguished house party from Saturday to yesterday, including the Grand Duke Michael of Russia and the Countess of Torby, the Earl and Countess of Craven, the Earl and Countess of Kilmorey, Earl Cairns, Lord and Lady Savile, Lord Chesham, Sir Frederick and Lady Milner, Colonel and Lady Gwendoline Colvin. Lady Margaret Orr-Ewing, Lady Eva Dugdale. Mrs. Kenneth Wilson, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Right Hon. H. Chaplin, M.P., Hon. H. Stonor, Mr. J. Pease, M.P., Captain Brinton, and Captain J. Forbes.&lt;/quote&gt; (1902-06-10 Manchester Courier and Lancashire General Advertiser)

====10 June 1902, Tuesday====
[[Social Victorians/People/Florence Farr|Florence Farr]]'s first public performance in which she &quot;recit[ed] to her own accompaniment on the psaltery was at the Hall of Clifford's Inn, Fleet Street, on 10 June 1902 (Campbell 144, n. 18).

==== 12 June 1902, Thursday====
12 June 1902: &lt;quote&gt;Thursday, the 12th inst., being the grand day of Trinity term at Gray's-inn, the Treasurer (Mr. Herbert Reed, K.C.) and the Masters of the Bench entertained at dinner the following guests: The Right Hon. Lord Strathoona and Mount Royal, the Right Hon. Lord Avebury, the Right Hon. H. H. Asquith, K.C, M.P., the Right Hon. Sir Frank Lascelles, G.C.B. (British Minister at Berlin), General Sir Edward Brabant, K.C.B., the Right Hon. Sir Edward Carson (Solicitor-General), Sir Squire Bancroft, Colonel Alfred Egerton, C.B. (Equerry to H.R.H. the Duke of Connaught), Mr. Austen Chamberlain,M.P., Colonel Royds, M.P., and Mr. Frank Dicksee, R.A. The Benchers present in addition to the Treasurer were H.R H. the Duke of Connaught, Lord Ashbourne, Lord Shand, Mr. Henry Griffith, Sir Arthur Collins, K.C, Mr. Hugh Shield, K.C, His Honour Judge Bowen Rowlands, K.C, Mr. James Sheil, Mr. Arthur Beetham, Mr. John Rose, Mr. Paterson, Mr. Mulligan, K.C, Mr. Mattinson, K.C, Mr. Macaskie, K.C., Mr. C. A. Russell, K.C., Mr. Montague Lush, K.C., Mr. Dicey, C B., Mr. Barnard, Mr. H. C. Richards, K.C., M.P., Mr. Duke, K.C., M.P., Sir Julian Salomons, K.C., with the Preacher (the Rev. Canon C. J. Thompson, D.D.).&lt;/quote&gt; (The Solicitor's Journal and Reporter. June 21, 1902. Volume XLVI. 1901-1902 [November 2, 1901, to October 25, 1902]: 588. Google Books: http://books.google.com/books?id=9T84AQAAIAAJ&amp;pg=PA588).

====26 June 1902, Thursday====
Edward VII crowned King of England. 26 June 1902.

There was apparently a regular celebration of Arthur Collins' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in May 1902, so the celebration with Harte present did not take place this year. Did it take place at all?

===July 1902===
====3 July 1902, Thursday====
[[Social Victorians/People/Mathers|MacGregor and Moina Mathers]] were living at 28 Rue Saint Vincent, Buttes Montmartre, Paris (Howe 244).

===September 1902===
''Tristan and Isolde'' at the Covent Garden.
====25 September 1902, Thursday====
&quot;There were no winter performances of opera at Covent Garden in those times .... In 1902 an autumnal series was added, and there were several Wagner nights, the last of which was on Thursday, 25 September, when Philip Brozel and Blanch Marchesi were starred in ''Tristan and Isolda'' with Marie Alexander as Brangane&quot; (Baring-Gould II 704, n. 14, quoting Rolfe Boswell).

===October 1902===

==== 24 October 1902, Friday ====
The ''Daily Express'' reported on the annual opening of the Prince's ice-skating rink, revealing who had an interest in skating:&lt;blockquote&gt;PRINCE’S RINK OPENS.

The first ice of the season was skated upon yesterday. It was the carefully-prepared ice which Mr. H. W. Page and Mr. Nightingale offer to the members of Prince’s Skating Club, in Knightsbridge, and was in grand condition.

The [[Social Victorians/People/Bourke|Hon. Algernon Bourke]] opened the rink for the seventh season, and in the afternoon and evening the West End patronized the popular club to skate or to lounge to the pleasant strains of the Viennese band.

[[Social Victorians/People/Princess Louise|Princess Louise]] is again at the head of the ladies’ committee, with the [[Social Victorians/People/Portland|Duchess of Portland]] and [[Social Victorians/People/Londonderry|Marchioness of Londonderry]] as co-members, and Lord Edward Cecil and many other well-known skaters are identified with the committee work.

The skating hours are from 9.30 to 1 and 3 to 7, and on Sundays 3 to 7 only.&lt;ref&gt;&quot;Prince's Rink Opens.&quot; ''Daily Express'' 25 October 1902, Saturday: 5 [of 8], Col. 6c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19021025/132/0005.&lt;/ref&gt;&lt;/blockquote&gt;

====31 October 1902, Friday====
Halloween.
===November 1902===
====5 November 1902, Wednesday====
Guy Fawkes Day.

==== 8 November 1902, Saturday ====
The Earl and Countess of Warwick hosted a shooting party at Easton Lodge:&lt;blockquote&gt;The [[Social Victorians/People/Warwick|Earl and Countess of Warwick]] are entertaining a large party at Easton Lodge this week-end for [?] shooting, and among their guests are the Grand Duke Michael of Russia and Countess Torby, the Duc d'Alba, the Duke of Sutherland, Earl Howe, Earl Cairns, Lord Dalmeny, Lord Herbert Vane-Tempest, the Hon. John and Lady [Choely?] Scott-Montagu, the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], the Right Hon. Henry Chaplin, M.P., General and Mrs. Arthur Paget, and Miss Leila Paget, Miss Naylor, Miss Deacon, and Mr W. M. Low.&lt;ref&gt;&quot;Guests at Easton Lodge.&quot; ''Birmingham Mail'' 08 November 1902, Saturday: 2 [of 6], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000644/19021108/091/0002. Print title: ''Birmingham Daily Mail''; p. 2.&lt;/ref&gt;&lt;/blockquote&gt;

====29 November 1902, Saturday====
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]]’s cousin, Lady Hartopp, was involved in a divorce case:
&lt;blockquote&gt;Society Women in a Law Court Case.

Mr. Justice Barnes’s Court is now crowded by society people. What is the strange fascination which brings elegantly dressed ladies, accustomed to luxurious surroundings and all the external refinements of life, to sit for hours in stuffy court, where the accommodation is all the plainest, and the surroundings are none too attractive. It would need some assurance to invite a Belgravian Countess, or the wife of Mayfair Millionaire to spend the morning under such conditions unless there were the attraction of a very strong piece of scandal. One could not presume to suggest she should attend Missionary meeting, or social reform movement, under any such conditions. At least I must confess that I never heard of one being packed with a West End crowd as the Court just now. Of course it cannot be mere idle curiosity. Our higher education for girls must have cured Mother Eve’s failing long ago. Cynics suggest that it is the survival in our highly-civilised modern conditions of that instinct of the wild creature which incites attack on the wounded or injured fellow. Wild birds will sometimes peck injured bird to death. Are these fair and soft-voiced ladies animated by the same spirit when they throng witness the ordeal through which a woman of their own class is passing?

The Latest Divorce Case.

Lady Hartopp, the heroine of the story which has been occupying the tongues and thoughts of the upper ten thousand for the last 48 hours, is a member of a well-known and wealthy family, and is herself remarkable for her beauty. Her two sisters are as famous for their charms as herself, and society has given them many flattering titles. The daughters of Mr. C. H. Wilson, the great shipowner, whose sails are on every sea, are as favoured by Fortune as Venus. Miss Muriel Wilson, the society beauty, is a cousin of Lady Hartopp, and Lady Chesterfield is her sister. It was at Tranby Croft, near Hull, the residence of Mr. and Mrs. Arthur Wilson, that the famous baccarat case occurred some years ago. Lady Hartopp is the niece of Mr. Arthur Wilson, and no doubt recollects that incident, and all the consequent stir. It attracted all the more notice at the time, because the then Prince of Wales had taken part in the game; but the Prince, who had nothing to be ashamed of, with characteristic straightforwardness, asked to go into the box and state all he knew. (1902-11-29 Norwich Mercury)&lt;/blockquote&gt;

===December 1902===

==== 9 December 1902, Tuesday ====
&quot;Severe weather&quot; did not prevent Lady Eva Wyndham's &quot;at home&quot; from being a success:&lt;blockquote&gt;Lady Wyndham-Quin's &quot;At Home.&quot;

The severe weather proved to be no detriment to the many visitors who had accepted Lady Eva Wyndham-Quin's invitation to an &quot;at home&quot; at the Welch Industrial depot on Tuesday afternoon, and the admirers and purchasers of the fascinating Christmas gifts were numerous. Lady Eva received her quests wearing a coat of Persian paw and a white feather toque, whilst her two tittle daughters the Misses Olein and Kethlean Wyndham-Quin wore pelisses and hats of pale blue Welsh frieze, trimmed with grebe. Amongst those present were Lady George Hamilton, all in black; Lady Brassey, wearing a lovely sable cape; the [[Social Victorians/People/Bourke|Hon. Mrs Algernon Bourke]], in a fur coat and a black picture hat; and the Hon. Mrs Herbert, of Llanever; Mrs Brynmor Jones was fall of her coming visit to Paris to see her young daughter, and Mrs Richard Helme came with her son, Mr Ernest Helme. Mrs Brenton and her sister, Mrs Ashurst Morris, were also present, as were Lady Eafield, the Dowager Lady Hylton, Lady Dennison Pender [Ponder?], and Lady Blanche Conyngham. Mrs Grinnell Milne brought Miss Murray end Mrs Shelley Bontens, and Mrs James Head came in for a few minutes. Everybody bought largely and the Welsh Christmas cards were an attractive feature, as were some artistic muff chains. Another specimen of Welsh lace sent by Miss Jenkins, of Denbighshire, was much admired and resembles Irish lace both in style and design.&lt;ref&gt;&quot;A Lady Correspondent.&quot; &quot;Society in London.&quot; ''South Wales Daily News'' 11 December 1902, Thursday: 4 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000919/19021211/082/0004. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

====16 December 1902, Tuesday====
A poem satirizing Florence Farr and Arnold Dolmetsch was published in ''Punch''.
====25 December 1902, Thursday====
Christmas Day
====26 December 1902, Friday====
Boxing Day
===Works Cited===
*[1902-06-10 Manchester Courier and Lancashire General Advertiser] &quot;Court and Personal.&quot; Manchester Courier and Lancashire General Advertiser 10 June 1902, Tuesday: 5 [of 10], Col. 3c [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000206/19020610/033/0006 (accessed July 2019).
*[1902-11-29 Norwich Mercury] &quot;Society Women in a Law Court Case.&quot; And &quot;The Latest Divorce Case.&quot; Norwich Mercury 29 November 1902, Saturday: 5 [of 12], Col. 1b [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001669/19021129/072/0005 (accessed July 2019).

==1903==
From sometime in 1891 to sometime in 1903 Eduoard de Reszke was &quot;a leading bass&quot; at the New York Metropolitan Opera (Baring-Gould II 112, n. 114).

&quot;[I]n England in 1903, gramophone distinctly meant the Berliner-Gramophon &amp; Typewriter disc machine, while cyclinder machines were known as phonographs or graphophones &quot; (Baring-Gould II 745, n. 15).

Gerald Balfour was &quot;largely responsible for getting the important Land Acts of 1903 under way&quot; (O'Connor 163).

In a display of &quot;too little, too late,&quot; on March 18, the day after St. Patrick's Day, the ''Daily Mail'' talks about events in London and Dublin in honor of St. Patrick's Day:&lt;blockquote&gt;The bells of St. George’s Chapel, Windsor Castle, were rung yesterday morning in honour of Ireland’s patron Saint. Sprays of shamrock were worn as “button-holes” by some of the residents in Windsor, Eton, and the surrounding districts.&lt;p&gt;

For the first time on record, St. Patrick’s Day was observed as a general holiday in Dublin. A large crowd witnessed the ceremony of the trooping of the colour by the 4th Battalion Royal Warwickshire Regiment, in Upper Yard, Dublin Castle. The Lord Lieutenant, on horseback, attended by his staff, was present.&lt;ref&gt;&quot;A Sale of National Work.&quot; ''Daily News'' (London) 18 March 1903, Wednesday: 12 [of 12], Col. 5c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/19030318/236/0012. Print p. 12.&lt;/ref&gt;&lt;/blockquote&gt;

===January 1903===
====1 January 1903, Thursday, New Year's Day====
====3 January 1903, Saturday====
Madame Troncey was doing a portrait of [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] (Wade 392).

=== March 1903 ===

==== 1903 March 17, Tuesday ====
Aristocratic women supporting Irish-made laces, needlework, and clothing:&lt;blockquote&gt;It was unfortunate weather for the St. Patrick’s Day sale of the Irish Industries Association, yesterday afternoon; but, in spite of this disadvantage, the rooms were crowded, and orders wore being given and taken on all sides. [[Social Victorians/People/Londonderry|Lady Londonderry]] was, as usual, presiding over the laces of the London depôt, though she often left her stall to her assistants and went about receiving her friends. The lace shown on her stall was beautiful. The needlepoint, Limerick, and Carrickmacross flounces, collars, and coatees finding many buyers during the afternoon. The Dowager Lady Downshire presided over the Association’s stall of embroideries, and Lady Gage arrived betimes to arrange them, wearing a dress of black lace over white, trimmed with appliques, also in black and white. Lady Aberdeen, as usual indefatigable, was at the Association’s stall of knitting, carving, and baskets. And Mrs. Marjoribanks was with her, showing in her own white dress how well Irish tweeds can look when made up. Lady Marjorie Gordon was also helping her mother. As for the 21 stalls representing the various cottage industries, these were once again covered with the beautiful work the Irish peasants, or (as in the case of the Gentlewomen’s Guild Handicrafts, the Ulster Ladies’ Work depôt, and the Irish School of Art Needlework) with work done by Irish ladies. The art needlework done by the Irish School needs little recommendation, it known so well for its excellence. And there were beautiful things on its stall this year, including many portières and some very finely-worked pictures. The stall was in charge of [[Social Victorians/People/Mayo|Lady Mayo]], [[Social Victorians/People/Dudley|Georgina Lady Dudley]], [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], and [[Social Victorians/People/Beresford|Miss Beresford]]. [[Social Victorians/People/Lucan|Lady Lucan]], being always on the watch for extending the sale of the tweeds woven by the Castlebar Homespun Industry, this year shows some of a rather heavy description, made for motor coats, and one of these was on show yesterday afternoon. A pretty coat it looked, too, being carried out in cream cloth, with strapped back, and narrow collar of black velvet. Toys and furniture came from the Cushenhall and the Killarney Industries respectively, and were by no means the least patronised yesterday afternoon, whilst there was steady sale of little bunches of shamrock, which came from poor Ulster lady, who grows and gathers the plant for such occasions as these. The sale is continued to-day from 12 until 6.&lt;ref&gt;&quot;A Sale of National Work.&quot; ''Daily News'' (London) 18 March 1903, Wednesday: 12 [of 12], Col. 5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/19030318/236/0012. Print p. 12.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1903===
Summer 1903: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

==== 1903 June 23, Tuesday ====
A children's party at Buckingham Palace:&lt;blockquote&gt;(From the Court Circular.)

Their Majesties gave a children’s party in the garden of the Palace this afternoon in honour of the ninth birthday his Highness Prince Edward of Wales, at which their Royal Highnesses the Prince and Princess of Wales with their children, Princess Louise, Duchess of Fife, and the Duke of Fife, with their children, the Princess Victoria and their Serene Highnesses the Duke and Duchess of Teck, with their children, were present.

The following, with their children, some of whom were unable to obey their Majesties' command, had the honour of receiving invitations: The Duke and Duchess of Beaufort, the Duke and Duchess of Buccleuch and Lady Constance Scott, the Duke and Duchess of Leeds, the Duke and Duchess of Marlborough, the Duke and Duchess of Portland, the Duke and Duchess of Sutherland, Catherine, Duchess of Westminster, the Marquis and Marchioness of Granby, the Marquis and Marchioness of Hamilton, the Countess of Airlie, the Earl and Countess of Albemarle, the Countess of Antrim, the Earl and Countess Carrington, the Earl and Countess of Dalkeith, the Earl and Countess of Denbigh and Desmond, the Earl and Countess of Essex, the Earl and Countess of Mar and Kellie, the Earl and Countess of Normanton, the Earl and Countess of Pembroke and Montgomery, the Earl and Countess of Selborne, the Earl and Countess of Stradbroke, the Countess de Mauny-Talvande, Viscount and Viscountess Chelsea, Viscount and Viscountess Castlereagh, Viscount and Viscountess Churchill, Viscount and Viscountess Coke, Viscount and Viscountess Cranborne, Viscount and Viscountess Falmouth, Lord and Lady Balfour of Burleigh, Lord and Lady De Ramsey, Lady Farquhar, Lady Cynthia Graham, Lord and Lady Hastings, Lord and Lady Hillingdon, Lord and Lady Knollys, Lord and Lady Lurgan, Lord and Lady St. Oswald, Lord and Lady Settringto, Lord and Lady Alice Stanley, Lord and Lady Suffield, Lord and Lady Wolverton, Mr and the Hon. Mrs. Gervase Beckett. Hon. [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], Mr. and the Hon. Mrs. Lionel Cust, Hon. Mrs. Geoffrey Glyn, Lientenant-Colonel Hon. Charles and Mrs. Harbord, Hon. Charles and Mrs. Hardinge, Hon. Sydney and Lady Mary Holland, Hon. Derek and Mrs. Keppel, Hon. George and Mrs. Keppel, Hon. Frederick and Mrs. Lambton, Hon. Lancelot and Mrs. Lowther, Sir Richard and Hon. Lady Musgrave, Hon H. and Lady Feodorowna Sturt, Hon. Dorothy Violet and Hon. Alexandra Vivian, Mr and Lady Aline Beaumont, Mr. and Lady Katherine Brand, Mr. and Lady Violet Brassey, Mr. and Lady Moyra Cavendish, Mr. and Lady Evelyn Cavendish, Sir E. and Lady Colebroke, Captain and Lady Jane Combe, Sir H. and Lady de Trafford, Mr. and Lady Eva Dugdale, Sir E. and Lady Edmonstone, Major-General Sir R. and Lady Beatrice Pole-Carew, Sir G. and Lady Maud Warrender, Mr. and Mrs. Rupert Beckett, Revd. Canon and Mrs. Dalton, Mr. and Mrs. Farquharson of Invercauld, Mr. and Mrs. W. Grenfell, Mr. and Mrs. A. Hay-Drummond, Mr. and Mrs. W. James, Mr. and Mrs. Blundell Leigh, Mr. and Mrs. Sartoris.&lt;ref&gt;&quot;Prince Eddie's Birthday.&quot; ''Daily News'' (London) 24 June 1903, Wednesday: 7 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/19030624/197/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

=== August–September 1903 ===

==== 20 and 25 August and 3 September 1903 ====
The 1903 America's Cup yacht race in New York Harbor with Nathaniel Herreshoff's ''Reliance'' for the US and Sir Thomas Lipton's ''Shamrock III'' for the UK,&lt;ref&gt;{{Cite journal|date=2022-09-11|title=1903 America's Cup|url=https://en.wikipedia.org/w/index.php?title=1903_America%27s_Cup&amp;oldid=1109663279|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/1903_America%27s_Cup.&lt;/ref&gt; the 12th challenge for the cup and &quot;the most expensive Cup challenge in history.&quot;&lt;ref name=&quot;:0&quot;&gt;{{Cite web|url=https://www.americascup.com/history/26_LIPTONS-THIRD-CHALLENGE|title=LIPTON’S THIRD CHALLENGE|last=Cup|first=America's|website=37th America's Cup|language=en|access-date=2024-07-02}} https://www.americascup.com/history/26_LIPTONS-THIRD-CHALLENGE.&lt;/ref&gt; The first race was run on 20 August 1903, the 2nd on 25 August and the 3rd on 3 September.&lt;ref name=&quot;:0&quot; /&gt; Because the ''Reliance'' won the first 3 races, the best 3-out-of-5 race ended after the 3rd one.

===October 1903===
Sometime in October 1903, [[Social Victorians/People/Arthur Conan Doyle|Arthur Conan Doyle]]'s &quot;The Adventure of the Empty House,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 331).
====31 October 1903, Saturday====
Halloween.
===November 1903===
Sometime in November 1903 Arthur Conan Doyle's &quot;The Adventure of the Norwood Builder,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 415).
====5 November 1903, Thursday====
Guy Fawkes Day
===December 1903===
Sometime in December 1903 Arthur Conan Doyle's &quot;The Adventure of the Dancing Men,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 529).
====16 December 1903, Wednesday====
&quot;On 16 December, Punch satirised an activity in which Dolmetsch was concerned. [[Social Victorians/People/Florence Farr|Florence Farr]] was acting as secretary for a newly-formed fellowship known as 'The Dancers', a body whose aim was to 'fight the high and powerful devil, solemnity'. In a poem entitled L'Allegro up to date, the final stanza is devoted to Dolmetsch:
&lt;poem&gt;:The old forgotten dancing-lore,
:The steps we cannot understand,
:DOLMETSCH agrees to take in hand,
:These on the well-trod stage anon,
:When next our learned sock is on,
:We’ll show, while ARNOLD, Fancy’s child,
:Tootles his native wood-wind wild.&lt;/poem&gt;
This verse is curiously prophetic for Dolmetsch had not yet introduced the recorder into his concerts, although he occasionally included a flute. Dolmetsch did know something of the steps of the old dances but it was his wife who later researched the subject most thoroughly and wrote two books on the subject.&quot; (Campbell 151–52)

===25 December 1903, Friday===
Christmas Day
====26 December 1903, Saturday====
Boxing Day
===Works Cited===
*Baring-Gould.
*Campbell.

==1904==
===January 1904===
Sometime in January 1904 [[Social Victorians/People/Arthur Conan Doyle|Arthur Conan Doyle]]'s &quot;The Adventure of the Solitary Cyclist,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 399).
===March 1904===
Sometime in March 1904 Arthur Conan Doyle's &quot;The Adventure of Black Peter,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 384).

===April 1904===
Sometime in April 1904, Arthur Conan Doyle's &quot;The Adventure of Charles Augustus Milverton,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 558, n. 1, and 559).

===June 1904===
Sometime in June 1904 Arthur Conan Doyle's &quot;The Adventure of the Three Students,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 370).

Summer 1904: [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

===July 1904===
Sometime in July 1904, Arthur Conan Doyle's &quot;The Adventure of the Golden Pince-Nez,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 351).
===August 1904===
Sometime in August 1904, Arthur Conan Doyle's &quot;The Adventure of the Missing Three-Quarter,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 476).

===September 1904===
Sometime in September 1904, Arthur Conan Doyle's &quot;The Adventure of the Abbey Grange,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 491).

==1905==
===April 1905===
====3 April 1905, Monday====
[[Social Victorians/People/William Butler Yeats|W. B. Yeats]] wrote to Lady Gregory from Dublin, saying he had &quot;dictated a rough draft of a new Grania second act to Moore's typewriter&quot; (Wade 368).
===June 1905===
Summer 1905: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).
===July 1905===
====10 July 1905, Monday====
1905 July 10, the Austro-Hungarian Ambassador hosted a dinner party:&lt;blockquote&gt;The Austro-Hungarian Ambassador entertained the Duke and Duchess of Connaught and Princess Patricia of Connaught at dinner at the Embassy in Belgrave-square on Monday evening. There were also present the Spanish Ambassador and Mme. Bernabé, the United States Ambassador and Mrs. and Miss Whitelaw Reid, Princess Hohenlohe, Prince Francis of Teck, Princess Teano, the Earl of Essex, the Earl and Countess of Crewe, Viscount Villiers, Viscount Errington, Viscount Newry, Mrs. J. Leslie, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Mr. R. Graham, Mrs. Astor, Lady Maud Warrender, Prince Furstenburg, Count Szenchenyi, Captain A. Meade, and Miss Pelly and Colonel Murray in attendance on the Duke and Duchess.&lt;ref&gt;&quot;Court Circular.&quot; ''Times'', 12 July 1905, p. 7. ''The Times Digital Archive'', http://tinyurl.galegroup.com/tinyurl/AHRNq6. Accessed 20 June 2019.&lt;/ref&gt;&lt;/blockquote&gt;

==== Last week of July, 1905 ====
Lady Cadogan hosted a children's party at Chelsea House:&lt;blockquote&gt;Lady Cadogan’s children’s party last week at Chelsea House was one of the prettiest sights imaginable. Her grandchildren, the little Chelseas, came to help entertain the guests, and nearly all the smart women in London brought their small folk. One of loveliest little girls present was Daphne Bourke, Mrs. [[Social Victorians/People/Bourke|Algernon Bourke]]’s only child; and Lady De Trafford’s young daughter Violet was much admired, and Lady Maud Ramsden’s little people were among daintiest of the small children.&lt;ref&gt;&quot;Court and Social News.&quot; ''Belfast News-Letter'' 01 August 1905, Tuesday: 7 [of 10], Col. 6b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/19050801/157/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

===October 1905===

==== 1905 October 14, Saturday ====
A &quot;send-off dinner&quot; for Jerome K. Jerome before his trip to the U.S. occurred at the Garrick Club &quot;the other evening&quot; before October 14:&lt;blockquote&gt;Jerome K. Jerome has undertaken a six months lecturing tour in the United States. I believe that this tour will be a great success, particularly when the Americans come to realise that Mr. Jerome is not only a humorous writer but a brilliant, serious writer with very genuine pathos. His appeal on this side has not, perhaps, gone home to the English people as much as it should, but the quick-witted Americans will not be slow to recognise his talents of both kinds, nor will they fail to appreciate the significance of the fact that the other evening a send-off dinner was given to Mr. Jerome at the Garrick Club. The hosts of the evening were Mr. Pett Ridge and Mr. W. W. Jacobs, which shows that there is no such thing as literary jealousy among our best humorists.

The presence of quite a galaxy of novelists to the dinner to Mr. Jerome, including Mr. Barrie, Sir Arthur Conan Doyle, Mr. Max Pemberton, Mr. H. G. Wells, Mr. G. B. Burgin, Mr. Arthur Morrison, and Mr. Israel Zangwill, serve to indicate the existence of a pleasant brotherhood among the writers of fiction. The readers of ''Three Men in a Boat'' may be interested to know that there were also present Mr. Jerome's companions in that famous journey — Mr. Carl Hentschel and Mr. C. Wingrove.

When I have named further the presence of three artists in Mr. A. S. Boyd, Mr. John Hassall, and Mr. Will Owen, and two journalists in Dr. Robertson Nicoll and [[Social Victorians/People/Rook|Mr. Clarence Rook]], I have given some record of an exceedingly pleasant dinner party. The essential point, however, of this enumeration of names is that many of them are among the most highly honoured of Englishmen in the United States, and that thus Mr. Jerome cannot fail to reap additional benefit from this dinner so thoughtfully given in his honour by Mr. Jacobs and Mr. Pett Ridge.&lt;ref&gt;S., C. K. &quot;A Literary Letter.&quot; ''The Sphere'' 14 October 1905, Saturday: 16 [of 20], Col. 2a–c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001861/19051014/022/0016. Print p. 56.&lt;/ref&gt;&lt;/blockquote&gt;

===November 1905===
Sometime in November 1905, &quot;Arnold Dolmetsch was again asked to provide music for a Been Greet season in New York — an engagement that brought about his first meeting with two young actors on their first American tour, Sybil Thorndike, and her brother, Russell&quot; (Campbell 169). Dolmetsch's return to the US; was [[Social Victorians/People/Horniman|Annie Horniman]] still with the Thorndikes?

==1906==
===March 1906===
====5 March 1906====
&quot;Mr. Frederick John Horniman, who died on March 5, in his seventy-first year, was the son of that well-known Quaker and tea-merchant, John Horniman, who made a magnificent fortune by retailing tea in air-tight packets, and, like his father, devoted both time and wealth to charitable objects. A great traveller, both for business and pleasure, Mr. Horniman gathered togther an admirable collection of curios, and this is housed at Forest Hill in the museum that bears his name. His private benefactions were also large. Mr. Horniman, who was a Liberal, sat in two Parliaments, representing Penrhyn and Falmouth Boroughs in one. He did not seek re-election in January last.&quot; (&quot;The World's News.&quot; Illustrated London News (London, England), Saturday, March 10, 1906; pg. 338; Issue 3490, Col. C)
===June 1906===
Summer 1906: [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

==1907==
===April 1907===
April 1907, [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] went to Italy with Lady Gregory (Harper 80 28).
===June 1907===
Summer 1907: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

'''1907 June 22, Saturday'''
The annual dinner of the Correctors of the Press was held at De Keyser's Royal Hotel:&lt;blockquote&gt;The London Association of Correctors of the Press held their annual dinner at De Keyser’s Royal Hotel on Saturday. The Chairman was the Lord Mayor, and among his supporters were Sir John Cockburn, Colonel David Bruce, Colonel Earl Church, Lieutenant-Colonel Alsager Pollock, Sheriff Dunn, Mr. J. W. Cleland, M.P., Mr. R. Donald, Mr. T. Seccombe, Mr. Francis H. Skrine, Major H. F. Trippel, Mr. Walter Haddon, Mr. W. Pett Ridge, Mr. W. H. Helm, Mr. R. Warwick Bond, Mr. F. W. Rudler, Major Vane Stow, [[Social Victorians/People/Rook|Mr. Clarence Rook]], Mr. J. Randall (Chairman of the Association), Mr. Foxen, and Mr. Feldwick. Proposing the toast of &quot;Literature,” Mr. W. H. Helm speculated as to what would follow the banning of &quot;Mary Barton&quot; by the Education Committee of the London County Council. In his opinion &quot;The Swiss Family Robinson&quot; was a more immoral book, because beyond any other work it had fostered the Micawber view of life. (Laughter.) The LORD MAYOR [init caps large, rest sm, throughout], submitting the toast of &quot;The Readers' Pension Fund,” apologised for appearing in morning dress. The reason was that he had been to the King’s Garden Party at Windsor, and whlle he was returning to London by motor something burst. (Laughter.) Only that morning he had arrived from Berlin, where he learned some lessons useful to people who give dinners. When the Oberburgomeister of Berlin proposed the health of, say, the Lord Mayor of London, there was an end of the business. He did not push forward the Houses of Parliament, the Navy and Army, or even Literature. (Laughter.) Being a practical people the Germans when they met for a particular purpose applied themselves to no other, and the English would well to copy them. (Hear, hear.) Mr. J. RANDALL said that last year the Association helped five readers and one reader’s widow to pensions, and this year it had done the same for two readers and two widows. One of the men assisted last March had taught himself Greek, Arabic, and Sanscrit, and in leisure moments amused himself by making object glasses for microscopes and telescopes. At this very gathering there was a printer’s reader who was Hebrew scholar. (Hear, hear.) With regard to finance Mr. Randall was happy to say that this dinner would enable the Association to establish a fourth pension. (Cheers.) The Lord Mayor, [[Social Victorians/People/Borthwick|Lord Glenesk]] (President of the Readers' Pensions Committee), the Clothworkers’ Company, and the Cutlers’ Company had contributed ten guineas each, and the total addition to the fund resulting from the dinner was £l90. During the evening excellent entertainment was provided by Miss Helena Foxen, Miss Kathleen Dwyer, Mr. T. C. Bell, Mr. P. E. Syrett, Mr. Prank Rhodes, and Mr. E. Croft-Williams, the last-named being the hon. musical director.&lt;ref&gt;&quot;Correctors of the Press.&quot; ''Morning Post'' 24 June 1907, Monday: 4 [of 14], Col. 3c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19070624/074/0004. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

===November 1907===
====10 November 1907====
&lt;quote&gt;On 10 November, Dolmetsch, 'awfully tired and disquieted with overwork', writes to Horne, 'longing for Florence'.

7, Bayley Street&lt;br /&gt;W.C.&lt;br /&gt;My concert went very well last night. Melodie quite distinguished herself, and a sister of [[Social Victorians/People/George Bernard Shaw|Bernard Shaw]] Lucy Carr Shaw sang delightfully. …&lt;br /&gt;But Symmons [sic] … did not go before 1 o'cl. and yet, by the first post this morning, I got a charming poem on Rameau. … He must have spent all night on it.&lt;/quote&gt; (Campbell 120)

==1908==
In 1908 Sidney Paget died in 1908 in some &quot;untimely&quot; fashion (Baring-Gould II 239).

=== April 1908 ===

==== 1908 April 9, Thursday ====
The Provisional Committee for the Shakespeare Memorial demonstration at the Lyceum Theatre met at the Hôtel Métropole:&lt;blockquote&gt;SHAKESPEARE MEMORIAL.

A meeting of the Provisional Committee for the forthcoming Shakespeare Memorial demonstration at the Lyceum Theatre was held yesterday at the Hôtel Métropole. Mr. T. P. O’Connor, M.P., presided, and there were present : The Earl of Lytton, Mr. Percy Alden, M.P., Mr. Henry Ainley, Mr. Percy Ames, Mr. Robert Barr, Mr. Arthur à Beckett, Mr. Austin Brereton, Mr. Acton Bond (General Director of the British Empire Shakespeare Society), Mr. Dion Boucicault, Mrs. Bateman-Crowe, Professor Boss, Mr. Norreys Connell, Mr. W. M. Crook, Mr. John Cutler, K.C., Mr. J. Comyns Carr, Mr. Ernest Carpenter, the Rev. P. H. Ditchfleld, Mr. Robert Donald, Mr. A. C. Forster Boulton, M.P., Mr. and Mrs. Laurence Gomme, Mr. A. A. Gardiner, Mr. C. T. Hunt (hon. secretary London Shakespeare League), Mr. Laurence Housman, Mr. J. A. Hobson. Mr. Ford Madox Hueffer, Mr. Selwyn Image, Mr. Henry Arthur Jones, Mr. Jerome K. Jerome, Mr. Frederick Kerr, Miss Gertrude Kingston, Professor Knight, Mr. Matheson Lang, the Hon. Mrs. Alfred Lyttelton, Miss Lillah McCarthy, Mr. Justin Huntly McCarthy, Colonel Henry Mapleson, Dr. Gilbert Murray, Mr. T. Fairman Ordish, Mr. A. W. Pinero, Mr. Ernest Rhys, [[Social Victorians/People/Rook|Mr. Clarence Rook]], the Rev. J. Cartmel Robinson, Mr. George Radford, M.P., Mr. Clement Shorter, Mr. Otto Salimann (hon. secretary of the Elizabethan Society), [[Social Victorians/People/George Bernard Shaw|Mr. Bernard Shaw]], Mr. H. W. Smith, Mr. Herbert Trench, [[Social Victorians/People/Todhunter|Dr. Todhunter]], and Mr. James Welch. It was agreed that the Lyceum demonstration should take place in May, and a resolution should be moved in favour of the establishment of a National Theatre as a memorial to Shakespeare.&lt;ref&gt;&quot;Shakespearea Memorial.&quot; ''Morning Post'' 10 April 1908, Friday: 7 [of 12], Col. 3c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19080410/126/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1908===
Summer 1908: [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

==== 1908 June 21, Sunday ====
Very large demonstration for women's suffrage in Hyde Park coming from &quot;seven points in London.&quot;&lt;blockquote&gt;WOMAN'S VOTE.
SUFFRAGISTS' GREAT MARCH TO HYDE PARK TODAY.

WHITE DEMONSTRATION.

AMUSING ADDRESS TO M.P.'s. FROM RIVER LAUNCH.

From seven points in London to-day seven big prossesions will march to Park, and there jointly demand the Parliamentary franchise for women.

The whole town will be alive with demonstrating suffragists. The streets will resound with the cry of &quot;Votes for Women.&quot; In Hyde Park eighty speakers will voice the demand from twenty platforms.

London has been divided into districts for the purposes of the mighty demonstration, and each of theee has an assembling place, from which the processions will move off to Hyde Park, as given in the following official list: —

A. — Euston-road. — Form up at 12 o'clock, east of Euston Station. Start at 1 p.m. March via Euston-road, Portland-place, Upper Regent-street, Oxford-street, to the Marble Arch.

B. — Trafalgar-square. — Form up 12.30. Start 1.30. March via Pall Mall, Regent-street, Piccadilly, Berkeley-street, and Mount-street to the Grosvenor Gate.

C. — Victoria Embankment. [sic] Form up 12.30. Start from Westminster Bridge 1.30. March via Victorla-street, Grosvenor-place, to Hyde Park Corner.

D. — Chelsea Embankment. — Form up 12.30. Start 1.30. March via Oakley-street, King's-road, Sloane-square, Sloane-street to Albert Gate.

E. — Kensington High-street. — Form up 1 o'clock. Start 1.30. March via Kensington into the Alexandra Gate of the Park.

F. — Paddington Station. — Form up 1 p.m. Start 2 p.m. March via Victoria Gate into Hyde Park.

G. — Marylebone-road. — Form up 12.30. Start 1.30. March via Seymour-place, Seymour-street, and Into the Park close to the Marble Arch.

The demonstrators will come from all parts of the country, some seventy special trains being run from the big towns in the provinces. These will be met at the London stations by white-garbed &quot;Captains&quot; and &quot;Stewards,&quot; and their occupants marshalled in proper divisions.

Literature and the drama will be represented in several of the processions. Mr. and Mrs. Bernard Shaw will join in Trafalgar-square, and so will Mr. Pett Ridge. Starting from Euston-road will be a coach carrying Mrs. Parkhurst, Miss Beatrice Harraden, Mrs. Mona Caird, and Miss Elizabeth Robins.

Mrs. Israel Zangwill will chaperon a party on a coach from the Thames Embankment, which will include Professor and Mrs. Ayrton, Madame Sarah Grand, Miss Lillah McCarthy (Mrs. Granville Barker), Miss Marian McCarthy, Mr. Lucien Wolf, Professor Perry, F.R.S. (scientist), Mrs. H. G. Wells, Mrs. Alice Meynell, and Suffragist leaders from Sweden, Finland, and Norway. In Finland women not only have the vote, but they sit in Parliament. Madame Stromberg, from that country, is now in London attending the Horse Show at Olympia, and will be present at to-day's demonstration. Mr. H. Nevinson and Mr. H. N. Brailsford will walk in the Embankment procession.

On the Kensington four-in-hand coach will be:— [[Social Victorians/People/Rook|Mrs. Clarence Rook]], Mrs. Jopling Rowe, Mlle. Stavance (Norwegian editor and authoress), Mrs. French Sheldon, F.R.G.S., and Miss Christine Silver. 

...

In addition to seven four-horse coaches — one for each procession — there will be more than sixty brakes, filled with country suffragists, and elaborately decorated. [Story continues.]&lt;ref&gt;&quot;Women's Vote. Suffragists' Great March to Hyde Park To-day. White Demonstration. Amusing Address to M.P.'s from River Launch.&quot; ''Lloyd's Weekly Newspaper'' 21 June 1908, Sunday: 1 [of 28], Col. 1a–c [of 5], 2, Col. 5. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003216/19080621/002/0001. Print p. 1.&lt;/ref&gt;&lt;/blockquote&gt;

===Works Cited===
*Baring-Gould

==1909==
===January 1909===
====1 January 1909====
Rev. [[Social Victorians/People/Ayton|W. A. Ayton]] died (Howe 85 10-11).
===June 1909===
Summer 1909: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

== Bibliography ==
#&quot;Calendar for the Year 1900.&quot; Jumk.de Webprojects. https://kalender-365.de/public-holidays.php?yy=1900. Accessed November 2023.
#Howe

== Footnotes ==
&lt;references /&gt;</text>
      <sha1>rc5f52jut5onfibo3iwi17c4takf4i0</sha1>
    </revision>
  </page>
  <page>
    <title>Social Victorians/People/Mayo</title>
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      <text bytes="19123" sha1="7fbpw3hvmnhzgs6o4k607mf5vs7u1ki" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:6&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* See also the [[Social Victorians/People/Bourke|Bourke page]]
* Earl of Mayo (in the Peerage of Ireland)
** Richard Southwell Bourke, 6th Earl of Mayo (12 August 1867 – 8 February 1872)
** Dermot Robert Wyndham Bourke, 7th Earl of Mayo (8 February 1872 – 31 December 1927)
*Baron Connemara
**Robert Bourke, 1st and last Baron Connemara (12 May 1887 – 3 September 1902)&lt;ref name=&quot;:2&quot;&gt;&quot;Robert Bourke, 1st and last Baron Connemara.&quot; {{Cite web|url=https://www.thepeerage.com/p5752.htm#i57514|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p5752.htm#i57514.&lt;/ref&gt;
* The [[Social Victorians/People/Bourke|Hon. Algernon Bourke]]
* [[Social Victorians/People/Bourke|Lady Florence Bourke]]

==Overview==
Richard Bourke, 6th Earl of Mayo was assassinated while inspecting a convict settlement at Port Blair in the Andaman Islands. Robert Bourke, 1st Baron Connemara and Lady Susan Georgiana Ramsay divorced in a sensational case in which she successfully sued for divorce on the grounds of adultery (with her maid Hannah Moore) and cruelty (infecting her with venereal disease).

[[Social Victorians/People/Bourke|Algernon Bourke]], 3rd son of the 6th Earl, was successful in the stock market and, by and large, in business.

In 1912, when Blanche, Dowager Countess of Mayo was 86 years old, the ''Woodford Times'' summarized her like this:&lt;blockquote&gt;The Dowager Countess of Mayo and Lady Costance Mure the only surviving daughters of the first Lord Leconfield, the inheritor of the famous house and estate of Petworth, and consequently aunts of Mr. George Wyndham. Their mother was one of the Blunts. of Crabbet Park, Sussex, which makes them kinswomen of Mr. Wilfrid Scawen Blunt, poet, Egyptophil and counsel for Arabi Pasha is his trial. The Dowager Lady Mayo is the widow — as she has been for forty years past — of the Governor-General of India, who was assassinated while on a tour of the Andamas Islands. Subsequently the Government voted her a pension, which she still enjoys. She was an extra woman of the Bedchamber for over a quarter of a century, and until the death of Queen Victoria. Beside Lord Mayo, her children are the Hon. [[Social Victorians/People/Bourke|Algernon Bourke]], who was at one time on the Stock Exchange; Lady Eva Wyndham-Quin; Lady Florence Bourke; and the Hon. Terence Bourke, who is British Vice-Consul at Bizerta.&lt;ref&gt;&quot;The Dowager Countess of Mayo ....&quot; ''Woodford Times'' 29 November 1912, Friday: 6 [of 8], Col. 6c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004344/19121129/159/0006. Print n.p.&lt;/ref&gt;&lt;/blockquote&gt;

==Acquaintances, Friends and Enemies==
==Timeline==
'''1863 November 21''', Robert Bourke and Lady Susan Georgiana Ramsay married.&lt;ref name=&quot;:3&quot;&gt;&quot;Lady Susan Georgiana Ramsay.&quot; {{Cite web|url=https://www.thepeerage.com/p23213.htm#i232124|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p23213.htm#i232124.&lt;/ref&gt;

'''1872 February 8''', Richard Bourke, 6th Earl of Mayo was assassinated while inspecting a &quot;convict settlement at Port Blair in the Andaman Islands ... by Sher Ali Afridi, a former Afghan soldier.&quot;&lt;ref&gt;{{Cite journal|date=2024-12-01|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo.&lt;/ref&gt;

'''1872 November 20''', Hon. Edward Roden Bourke and Emma Mary Augusta Hatch married.&lt;ref name=&quot;:5&quot;&gt;&quot;Emma Mary Augusta Hatch.&quot; {{Cite web|url=https://www.thepeerage.com/p5751.htm#i57507|title=Person Page|website=www.thepeerage.com|access-date=2021-08-27}} https://www.thepeerage.com/p5751.htm#i57507.&lt;/ref&gt;

'''1880 February 4, Wednesday''', ball at Palmerstown House hosted by the Earl of Mayo:&lt;blockquote&gt;A grand ball was given on Wedneeday night at Palmerstown House, the seat of the Earl of Mayo. The ball was given by the noble earl to the friends and admirers of his father, in acknowledgment of their munificence in erecting, by subscription, a new family mansion as a memorial to the late earl. The new house, which is to be called the Memorial House, has just been completed. It is a handsome building, picturesquely situated on an elevated site, a short distance from the old mansion. The large hall, which is to be called the Memorial Hall, was set apart as the ballroom. It was handsomely decorated with evergreens, exotics, &amp;c., and when lit up in the most effective and tasteful style, presented a gay and brilliant appearance. A distinguished company have been staying at Palmerstown House, including the Marchioness of Blandford, Lady Georgina Spencer Churchill, the Hon. Algernon Bourke, Lady Margaret Bourke, Lord Capel, Mr. George Darner, Hon. Charles Lascelles, Hon. Henry and Mrs. Henry Bourke, the Countess of Stradbroke, Lady Sophia Rous [?], the Marchioness of Conyngham and the Ladies Conyngham, Lord Arthur Butler, the Hon. Bernard and Hon. Mrs. FitzPatrick, Mr. lon Trant Hamilton, M.P., and Mrs. Hamilton. Amongst those invited were:— The Duke and Duchess of Leinster, and the Ladies Fitzgerald, the Marquis of Kildare, the Marquis and Marchioness of Drogheda, Mr. and the Hon. Mrs. Skeffington Smyth, Mrs. and Miss Kavanagh, Borris House; Colonel Thackwell, 38th Regiment, and Mrs. Thackwell, the officers 38th Regt., &amp;c.&lt;ref&gt;&quot;Ball at Palmerstown House.&quot; ''Kilkenny Moderator'' 07 February 1880, Saturday: 2 [of 4], Col. 7c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002957/18800207/028/0002. Print title: ''Kilkenny Moderator and Leinster Advertiser'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;'''1886 July 27, Tuesday''', the Bourkes attended a service honoring a memorial at St. Paul's for the Earl of Mayo, who had been assassinated&lt;blockquote&gt;A memorial erected to the late Earl of Mayo was unveiled yesterday in the crypt of St. Paul's Cathedral, by Lord Cranbrook. Among those present were — The Dowager Countess of Mayo, Lord and Lady Drogheda, Lord and Lady Ashbourne, Lord Headfort, Lord John Manners, M.P.; Lord Barrington, Lord Leconfield, Lord and Lady Mayo, Right Hon. Beresford Hope, M.P.; Lord Stalbridge, Sir Peter Lumsden, Sir Owen Burne, Colonel Nigel Kingscote, Hon. Percy Wyndham, Mr. Henry Doyle, Mr. George Batten, Mr. E. Lawson, the Right Hon. Gerard Noel, General Fraser, V.C., M.P.; Canon Liddon, Mr. [[Social Victorians/People/Bourke|Algernon Bourke]], Lady Florence Bourke, and the late Lord Mayo’s six brothers — General Bourke, Right Hon. Robert Bourke, M.P.; Rev. George Bourke, Mr. Charles Bourke, C.B.; Major Bourke, and Mr. Henry Bourke. The following is the inscription at foot of the monument:— &quot;Sacred to the memory of Richard South [sic] well Bourke, Earl of Mayo, and for nearly four years Viceroy of India. He discharged the duties of his high office with conspicuous ability. Wise, kindly, just, and energetic, he won the affection of those about him, and the respect of neighbouring Princes; his work for his God and his Queen thus begun was laid aside when, struck down, alas! by the hand of assassin, he yielded up his soul to Christ on the 8th of February, 1872.&quot;&lt;ref&gt;&quot;Memorial to the Late Earl of Mayo.&quot; ''Northern Whig'' 28 July 1886, Wednesday: 6 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000434/18860728/143/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;'''1887 December 15''', [[Social Victorians/People/Bourke|Hon. Algernon Bourke]] and Guendoline Stanley married.&lt;ref name=&quot;:1&quot;&gt;&quot;Guendoline Irene Emily Stanley.&quot; {{Cite web|url=https://www.thepeerage.com/p51525.htm#i515247|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;

'''1889 June 8, Saturday''', the Earl of Mayo contributed some art he owned to the collection of the Royal Institute of Painters in Water-Colours' [[Social Victorians/Timeline/1889#8 June 1889, Saturday|exhibition of &quot;the works of the 'English Humourists in Art.'&quot;]]

'''1890 November 27''', Robert Bourke, 1st Baron Connemara and Lady Susan Georgiana Ramsay divorced in a sensational case in which she successfully sued for divorce on the grounds of adultery (with her maid Hannah Moore) and cruelty (infecting her with venereal disease).&lt;ref&gt;&quot;Another Society Scandal. Connemara Divorce Suit. Shocking Disclosures.&quot; ''South Wales Echo'' 27 November 1890 Thursday: 3 [of 4], Cols. 2a–3a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000902/18901127/031/0003.&lt;/ref&gt; This story is repeated essentially verbatum in a number of newspapers.

'''1892 March 5, Saturday''', two generations of men of the Bourke family are mentioned in this article reporting on &quot;the first reverse&quot; in Capt. the Hon. Maurice Bourke's career. Notable is that the Bourkes were &quot;one of the first aristocratic families of which the members took to the Stock Exchange.&quot;&lt;blockquote&gt;Capt. the Hon. Maurice Bourke, who has just been reprimanded in connection with the stranding of the Victoria, is the brother of the present Lord Mayo, and comes of an enterprising family. The Bourkes have pushed their way with remarkable energy in various professions, but are specially noticeable as one of the first aristocratic families of which the members took to the Stock Exchange. Before the Bourkes took it up the &quot;house&quot; was at a discount in Belgravia; it is now at a premium. Both Mr. Henry Bourke and Major Edward Bourke, uncles of Captain Bourke, and Mr. [[Social Victorians/People/Bourke|Algernon Bourke]], his brother, have reaped considerable incomes as the fruits of their enterprise. Captain Bourke has been singularly lucky In the navy in the matter of promotion, being one of those fortunate mariners who have served on the Queen's yacht. This is the first reverse in his career.&lt;ref&gt;&quot;Captain. the Hon. Maurice Bourke.&quot; ''Carlow Nationalist'' 05 March 1892, Saturday: 9 [of 10], Col. 2b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004580/18920305/082/0009. Print title ''Supplement to the Nationalist and Leinster Times''; n. p.&lt;/ref&gt;&lt;/blockquote&gt;'''1894 January 31, Wednesday''', Dermot, Earl of Mayo and Geraldine, Countess of Mayo hosted [[Social Victorians/Timeline/1894#Also 31 January 1894, Wednesday|the Kildare Hunt Ball]].

'''1894 October 10''', Lady Susan Georgiana Ramsay Bourke and Surgn.-Lt.-Col. William Hamilton Broun married.&lt;ref name=&quot;:3&quot; /&gt;

'''1894 October 22''', Robert Bourke, 1st Baron Connemara and Gertrude Lawrence Knight Walsh married.&lt;ref name=&quot;:4&quot;&gt;&quot;Gertrude Lawrence Knight Walsh.&quot; {{Cite web|url=https://www.thepeerage.com/p23213.htm#i232125|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p23213.htm#i232125.&lt;/ref&gt;

'''1895 April 27, Saturday''', Norah Mary Madeline Bourke and Mr. Henry Lindsay married.&lt;ref&gt;&quot;Mr. Henry E. A. Lindsay to Miss Norah M. M. Bourke.&quot; ''Gentlewoman'' 11 May 1895 Saturday: 97 [of 133], Col. 1c–2a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18950511/437/0097.&lt;/ref&gt;

'''1897 July 2''', [[Social Victorians/People/Bourke|Algernon Bourke]] and Guendoline Sloane-Stanley [[Social Victorians/People/Bourke|Bourke]] attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House.

'''1904 September 15, Thursday''', according to what was at the time called the ''Irish Daily Independent and Nation'', [[Social Victorians/People/Bourke|Algernon Bourke]] was living in Venice and not in the UK at this point:&lt;blockquote&gt;Algernon Bourke, who usually lives in Venice, has spent some time in England during the present summer, and has now gone on a fishing expedition to Sweden, accompanied by his brother, Lord Mayo. Lady Mayo has been staying meanwhile in Ireland, and has had a visit from her mother, Lady Maria Ponsonby, who is a sister of Lend Obventry.&lt;ref&gt;&quot;Society Notes.&quot; ''Irish Independent'' 15 September 1904, Thursday: 4 [of 8], Col. 5b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001986/19040915/131/0004. Print title: ''Irish Daily Independent and Nation'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;'''1908 August 5''', Emma Mary Augusta Hatch Bourke and Edward Hyde Villiers, 5th Earl of Clarendon married.&lt;ref name=&quot;:5&quot; /&gt;

'''1909 May 22, Saturday''', [[Social Victorians/People/Bourke|Algernon Bourke]] appears to have been living in Pisa. A columnist for the ''Queen'' reported on the Royal School of Art Needlework:&lt;blockquote&gt;Lady Leconfield [?] was there, also her sister-in-law, the Dowager Lady Mayo, only just back from her winter on the Continent, when she spent most of the time at Pisa, where her son Mr Algernon Bourke has also been staying. The latter is a great connoisseur as regards [art?] notably in what is really good in the way of old Italian sculpture and carving. He and his handsome wife have a place near to Putney, and this winter again Mr Bourke, as the result of his Italian travels, has been sending home such relics of the old Italian palace gardens as as stone and marble carved vases, garden seats, and what-not of the kind — not all for himself and his own gardens by any means, I fancy; but his friends, relying on his knowledge in such matters, get him when abroad to choose for [them?] the adornment of their English terraces and gardens.&lt;ref&gt;&quot;My Social Diary.&quot; The ''Queen'' 22 May 1909, Saturday: 31 [of 86], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19090522/203/0031. Print p. 871.&lt;/ref&gt;&lt;/blockquote&gt;

== Demographics ==
* Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
===Residences===
* London: 20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt;
* Ireland: Palmerstown House (built in 1872 by the 7th Earl in honor of his father after his assassination), Palmerstown, County Galway&lt;ref name=&quot;:6&quot; /&gt;
* Ireland: 1873: Palmerston House, Straffan, Co. Kildare&lt;ref&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
==Family==

* Robert Bourke, 5th Earl of Mayo (12 January 1797 – 12 August 1867)&lt;ref&gt;&quot;Robert Bourke, 5th Earl of Mayo.&quot; {{Cite web|url=https://www.thepeerage.com/p4710.htm#i47094|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p4710.htm#i47094.&lt;/ref&gt;
* Anne Charlotte Jocelyn ( – 26 January 1867)&lt;ref&gt;&quot;Anne Charlotte Jocelyn.&quot; {{Cite web|url=https://www.thepeerage.com/p4710.htm#i47095|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p4710.htm#i47095.&lt;/ref&gt;
*# '''Richard Southwell Bourke, 6th Earl of Mayo''' (21 February 1822 – 8 February 1872)
*# Lt.-Gen. John Jocelyn Bourke (5 October 1823 – 25 September 1904)
*# '''Robert Bourke, 1st and last Baron Connemara''' (11 June 1827 – 3 September 1902)
*# Rev. Hon. George Wingfield Bourke (16 February 1829 – 9 October 1903)
*# Hon. Charles Fowler Bourke (5 September 1832 – 4 April 1899)
*# '''Major Hon. Edward Roden Bourke''' (13 December 1835 – 7 June 1907)
*# Hon. Henry Lorton Bourke (26 September 1840 – 30 January 1911)


* Richard Southwell Bourke, 6th Earl of Mayo (21 February 1822 – 8 February 1872)&lt;ref&gt;&quot;Richard Southwell Bourke, 6th Earl of Mayo.&quot; {{Cite web|url=https://www.thepeerage.com/p2575.htm#i25748|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
* Hon. Blanche Julia Wyndham (21 November 1826 – 31 January 1918)&lt;ref&gt;&quot;Hon. Blanche Julia Wyndham.&quot; {{Cite web|url=https://www.thepeerage.com/p2963.htm#i29627|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
# Lady Eva Constance Aline Bourke ( – 19 January 1940)&lt;ref&gt;&quot;Lady Eva Constance Aline Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p2575.htm#i25747|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
# unknown daughter Bourke
# Dermot Robert Wyndham Bourke, 7th Earl of Mayo (2 July 1851 – 31 December 1927)
# Captain Hon. Sir Maurice Archibald Bourke (22 December 1853 – 16 September 1900)
# '''Hon. Algernon Henry Bourke''' (31 December 1854 – 7 April 1922)
# Lady Florence Blanche Bourke (16 August 1861 – 1953)
# Hon. Terence Theobald Bourke (2 April 1865 – 13 May 1923)


* Dermot Robert Wyndham Bourke, 7th Earl of Mayo (2 July 1851 – 31 December 1927)&lt;ref&gt;&quot;Dermot Robert Wyndham Bourke, 7th Earl of Mayo.&quot; ''The Peerage: A Genealogical Survey of the Peerage of Britain as well as the Royal Families of Europe''. Person page 14031, Person 140310. https://www.thepeerage.com/p14031.htm#i140310.&lt;/ref&gt;
* Geraldine Sarah Ponsonby ( – 29 November 1944)&lt;ref&gt;&quot;Geraldine Sarah Ponsonby.&quot; ''The Peerage: A Genealogical Survey of the Peerage of Britain as well as the Royal Families of Europe''. Person page, 14031, Person 140309. https://www.thepeerage.com/p14031.htm#i140309.&lt;/ref&gt;


* Robert Bourke, 1st and last Baron Connemara (11 June 1827 – 3 September 1902)&lt;ref name=&quot;:2&quot; /&gt;
* Lady Susan Georgiana Ramsay ( – 22 January 1898)&lt;ref name=&quot;:3&quot; /&gt; [she remarried as well]
* Gertrude Lawrence Knight Walsh (baptised 13 August 1833 – 23 November 1898)&lt;ref name=&quot;:4&quot; /&gt; [he was her 2nd husband as well]


* Emma Mary Augusta Hatch (1855 – 9 March 1935)&lt;ref name=&quot;:5&quot; /&gt;
* Major Hon. Edward Roden Bourke (13 December 1835 – 7 June 1907)&lt;ref&gt;&quot;Major Hon. Edward Roden Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p2096.htm#i20954|title=Person Page|website=www.thepeerage.com|access-date=2021-08-27}} https://www.thepeerage.com/p2096.htm#i20954.&lt;/ref&gt;
*# Norah Mary Madeline Bourke ( – 20 June 1948)
*# Madeline Emmie Louisa Bourke ( – 5 August 1961)
*# Cecil Richard Donoughmore Bourke (29 Sep 1875 – 30 November 1884)
*# Anne Kathleen Julia Bourke (c. 1878 – 16 March 1935)
*# Lt.-Col. Nigel Edward Jocelyn Bourke (21 August 1886 – 27 September 1970)
* Edward Hyde Villiers, [[Social Victorians/People/Villiers|5th Earl of Clarendon]]


* Hon. Algernon Henry Bourke (31 December 1854 – 7 April 1922)&lt;ref&gt;&quot;Hon. Algernon Henry Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p29657.htm#i296561|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
* Guendoline Irene Emily Sloane-Stanley Bourke (c. 1869 – 30 December 1967)&lt;ref name=&quot;:1&quot; /&gt;
# Daphne Marjory Bourke (5 April 1895 – 22 May 1962)

==Biographical Materials==

==Questions and Notes==
==Footnotes==
{{reflist}}</text>
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    <title>Category:Media reform to improve democracy</title>
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      <text bytes="5408" sha1="318iyyxb5u5kq2ubylsjjis72jh8ar0" xml:space="preserve">A number of seemingly credible sources are describing an increase in political polarization worldwide. [[w:Maria Ressa|Maria Ressa]] describes how [[w:Rodrigo Duterte|Rodrigo Duterte]], former President of the [[w:Philippines|Philippines]] &quot;started ... with five hundred volunteers&lt;ref&gt;Ressa (2022, pp. 147-8).&lt;/ref&gt; (1) creating “sock puppets,” or fake accounts that attack or praise; (2) “mass reporting,” or organizing to negatively impact a targeted account; and (3) “astroturfing,” or fake posts or lies designed to look like grassroots support or interest.&lt;ref&gt;Ressa (2022, pp. 152-3).&lt;/ref&gt; These actions tricked the algorithms of social media companies like Facebook and Twitter into amplifying fraudulent messages including incitements to violence and criminal prosecutions based on trumped up charges. The results easily overwhelmed honest media. [[w:Leila de Lima|Leila de Lima]], a Senator and former Secretary of Justice of the Philippines, spent years  in pretrial detention before the charges were dropped for lack of evidence.&lt;ref&gt;Ressa (2022, p. 158ff) and Wikipedia, &quot;[[w:Leila de Lima|Leila de Lima]]&quot;, accessed 2024-07-22.&lt;/ref&gt; Ressa's news organization, [[w:Rappler|Rappler]].com, was ordered to close. Ressa herself was convicted on questionable charges. Both continued operating while the legal procedures against them were appealed.&lt;ref&gt;Ressa (2022, pp. 152-3) and Wikipedia, &quot;[[w:Maria Ressa|Maria Ressa]]&quot;, accessed 2024-07-22.&lt;/ref&gt; Ressa says similar procedures are making major contributions to the rise of fascism and far-right nationalist populists in the US, Europe, Turkey, India, Russia, and elsewhere.&lt;ref&gt;Ressa (2022, pp. 152-3).&lt;/ref&gt; [[w:H. R. McMaster|H. R. McMaster]], former President Trump's second National Security advisor, said that &quot;The internet and social media thus provided [Russia] with a low-cost, easy way to divide and weaken America from within.&quot;&lt;ref&gt;McMaster (2020, pp. 47-48).&lt;/ref&gt; The [[w:2021 Facebook leak|2021 Facebook leak]] documented how executives of [[w:Facebook|Facebook]] and [[w:Meta Platforms|Meta]] knowingly prioritized profits over action to limit incitements to violence, even facilitating the [[w:Rohingya genocide|Rohingya genocide]] in [[w:Myanmar|Myanmar]], because doing otherwise would have reduced their revenue. 

This &quot;Category:Media reform to improve democracy&quot; include videos of interviews with experts and activists working this issue along with 29:00 mm:ss audio files submitted to a ''Media &amp; Democracy'' series syndicated on the [[w:List of Pacifica Radio stations and affiliates|Pacifica radio network]]&lt;ref&gt;&lt;!--Media &amp; Democracy on Audioport--&gt;{{cite Q|Q127839818}}&lt;/ref&gt; plus text and space for a moderated discussion. 

The 2024-09-11 episode of Sprouts:Radio from the Grassroots&lt;ref&gt;&lt;!--Sprouts: Radio From the Grassroots--&gt;{{cite Q|Q98781702}}&lt;/ref&gt; [[Media &amp; Democracy on Sprouts|featured excerpts from the interviews in this series]]. The Wikiversity article on this episode includes the 29:00 mm:ss podcast inviting a discussion of issues discussed in that podcast. 

== Table of episodes == 

{| class=&quot;wikitable sortable&quot;
|+ Episodes of &quot;Media &amp; Democracy&quot; for the [[w:List of Pacifica Radio stations and affiliates|Pacifica Radio Network]]
|-
! colspan=3 | Date !! 
|- 
! recorded !! broadcasted on [[w:KKFI|KKFI]] !! released to Pacifica !! Episode 
|-
| 2024-12-20 || 2024-12-31 || 2024-01-04 || [[HR 9495, the nonprofit-killer bill, per Michael Novick]]
|- 
| 2024-12-13 || 2024-12-24 || 2024-12-21 || [[Information is a public good per communications prof Pickard]]
|-
| 2024-12-02 || 2024-12-10 || 2024-12-07 || [[Media literacy for the Arab World per Ahmed Al-Rawi]]
|-
| 2024-11-21 || 2024-11-26 || 2024-11-23 || [[Thom Hartmann on The Hidden History of the American Dream]]
|-
| 2024-10-25 || 2024-11-05 || 2024-11-09 || [[Legal concerns of Wikimedia Europe]] 
|-
| 2024-10-26 || 2024-20-19 || 2024-10-27 || [[Project 2025 per Professor Brooks]]
|-
| 2024-10-01 || 2024-10-01 || 2024-10-12 || [[Jacob Ware on far-right terrorism in the US]]
|-
| 2024-09-13 || 2024-09-17 || 2024-09-29 || [[Dis- and misinformation and their threats to democracy]]
|- 
| 2024-09-11 || 2024-11-12 || 2024-09-14 || [[22nd Century Initiative]]
|- 
| 2024-08-22|| 2024-08-27 || 2024-08-31 || [[Global Project Against Hate &amp; Extremism (GPAHE)]]
|-
| 2024-08-19 || 2024-08-20 || 2024-08-24 || [[Facebook whistleblower Frances Haugen says]]
|-
| 2024-08-13 || 2024-08-13 || 2024-08-17 || [[Legal concerns of Free Press including Section 230]]
|-
| 2024-08-02 || 2024-08-06 || 2024-08-10 || [[How psychological and interpersonal processes are influenced by human-computer interactions]]
|-
| 2024-07-30 || 2024-07-30 || 2024-08-03 || [[Dean Baker on Internet companies threatening democracy internationally and how to fix that]]
|-
| 2021-04-29 || 2021-04-29 || 2021-05-16 || [[Media reform per Freepress.net]]
|- 
| 2021-02-23 || 2021-02-23 || 2021-03-17 ||[[Unrigging the media and the economy]]
|}

== Notes ==
{{reflist}}

== Bibliography == 

* &lt;!-- H. R. McMaster (2020) Battlegrounds: The Fight to Defend the Free World--&gt;{{cite Q|Q104774898}}
* &lt;!--Maria Ressa (2022) How to Stand Up To a Dictator--&gt;{{cite Q|Q117559286}}

[[Category:Interdisciplinary studies]]

[[Category:Political science]]
[[Category:Economics]]
[[Category:Freedom and abundance]]
[[Category:Videoconferences on media and democracy]]</text>
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    <title>C language in plain view</title>
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      <text bytes="9878" sha1="rswajv9w5bbw37ziccz0yiej1gphst3" xml:space="preserve">=== Introduction ===
* Overview ([[Media:C01.Intro1.Overview.1.A.20170925.pdf |A.pdf]], [[Media:C01.Intro1.Overview.1.B.20170901.pdf |B.pdf]], [[Media:C01.Intro1.Overview.1.C.20170904.pdf |C.pdf]])
* Number System ([[Media:C01.Intro2.Number.1.A.20171023.pdf |A.pdf]], [[Media:C01.Intro2.Number.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro2.Number.1.C.20170914.pdf |C.pdf]])
* Memory System ([[Media:C01.Intro2.Memory.1.A.20170907.pdf |A.pdf]], [[Media:C01.Intro3.Memory.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro3.Memory.1.C.20170914.pdf |C.pdf]])

=== Handling Repetition ===
* Control ([[Media:C02.Repeat1.Control.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat1.Control.1.B.20170918.pdf |B.pdf]], [[Media:C02.Repeat1.Control.1.C.20170926.pdf |C.pdf]])
* Loop ([[Media:C02.Repeat2.Loop.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat2.Loop.1.B.20170918.pdf |B.pdf]])

=== Handling a Big Work ===
* Function Overview ([[Media:C03.Func1.Overview.1.A.20171030.pdf |A.pdf]], [[Media:C03.Func1.Oerview.1.B.20161022.pdf |B.pdf]])
* Functions &amp; Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]])
* Functions &amp; Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]])
* Functions &amp; Recursions ([[Media:C03.Func4.Recursion.1.A.20161214.pdf |A.pdf]], [[Media:C03.Func4.Recursion.1.B.20161214.pdf |B.pdf]])

=== Handling Series of Data ===

==== Background ==== 
* Background ([[Media:C04.Series0.Background.1.A.20180727.pdf |A.pdf]])
 
==== Basics ====
* Pointers ([[Media:C04.S1.Pointer.1A.20240524.pdf |A.pdf]], [[Media:C04.Series2.Pointer.1.B.20161115.pdf |B.pdf]])
* Arrays ([[Media:C04.S2.Array.1A.20240514.pdf |A.pdf]], [[Media:C04.Series1.Array.1.B.20161115.pdf |B.pdf]])
* Array Pointers ([[Media:C04.S3.ArrayPointer.1A.20240208.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]])
* Multi-dimensional Arrays ([[Media:C04.Series4.MultiDim.1.A.20221130.pdf |A.pdf]], [[Media:C04.Series4.MultiDim.1.B.1111.pdf |B.pdf]])
* Array Access Methods ([[Media:C04.Series4.ArrayAccess.1.A.20190511.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]])
* Structures ([[Media:C04.Series3.Structure.1.A.20171204.pdf |A.pdf]], [[Media:C04.Series2.Structure.1.B.20161130.pdf |B.pdf]])

==== Examples ==== 
* Spreadsheet Example Programs
:: Example 1 ([[Media:C04.Series7.Example.1.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.1.C.20171213.pdf |C.pdf]])
:: Example 2 ([[Media:C04.Series7.Example.2.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.2.C.20171213.pdf |C.pdf]])
:: Example 3 ([[Media:C04.Series7.Example.3.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.3.C.20171213.pdf |C.pdf]])
:: Bubble Sort ([[Media:C04.Series7.BubbleSort.1.A.20171211.pdf |A.pdf]])

==== Applications ==== 
* Address-of and de-reference operators ([[Media:C04.SA0.PtrOperator.1A.20241223.pdf |A.pdf]])
* Applications of Pointers ([[Media:C04.SA1.AppPointer.1A.20241121.pdf |A.pdf]])
* Applications of Arrays ([[Media:C04.SA2.AppArray.1A.20240715.pdf |A.pdf]])
* Applications of Array Pointers ([[Media:C04.SA3.AppArrayPointer.1A.20240210.pdf |A.pdf]])
* Applications of Multi-dimensional Arrays ([[Media:C04.Series4App.MultiDim.1.A.20210719.pdf |A.pdf]])
* Applications of Array Access Methods ([[Media:C04.Series9.AppArrAcess.1.A.20190511.pdf |A.pdf]])
* Applications of Structures ([[Media:C04.Series6.AppStruct.1.A.20190423.pdf |A.pdf]])

=== Handling Various Kinds of Data ===
* Types ([[Media:C05.Data1.Type.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data1.Type.1.B.20161212.pdf |B.pdf]])
* Typecasts ([[Media:C05.Data2.TypeCast.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data2.TypeCast.1.B.20161216.pdf |A.pdf]])
* Operators ([[Media:C05.Data3.Operators.1.A.20161219.pdf |A.pdf]], [[Media:C05.Data3.Operators.1.B.20161216.pdf |B.pdf]])
* Files ([[Media:C05.Data4.File.1.A.20161124.pdf |A.pdf]], [[Media:C05.Data4.File.1.B.20161212.pdf |B.pdf]])

=== Handling Low Level Operations ===
* Bitwise Operations ([[Media:BitOp.1.B.20161214.pdf |A.pdf]], [[Media:BitOp.1.B.20161203.pdf |B.pdf]])
* Bit Field ([[Media:BitField.1.A.20161214.pdf |A.pdf]], [[Media:BitField.1.B.20161202.pdf |B.pdf]])
* Union ([[Media:Union.1.A.20161221.pdf |A.pdf]], [[Media:Union.1.B.20161111.pdf |B.pdf]])
* Accessing IO Registers ([[Media:IO.1.A.20141215.pdf |A.pdf]], [[Media:IO.1.B.20161217.pdf |B.pdf]])

=== Declarations ===
* Type Specifiers and Qualifiers ([[Media:C07.Spec1.Type.1.A.20171004.pdf |pdf]])
* Storage Class Specifiers ([[Media:C07.Spec2.Storage.1.A.20171009.pdf |pdf]])
* Scope 


=== Class Notes ===

* TOC ([[Media:TOC.20171007.pdf |TOC.pdf]])
* Day01 ([[Media:Day01.A.20171007.pdf |A.pdf]], [[Media:Day01.B.20171209.pdf |B.pdf]], [[Media:Day01.C.20171211.pdf |C.pdf]]) ...... Introduction (1) Standard Library
* Day02 ([[Media:Day02.A.20171007.pdf |A.pdf]], [[Media:Day02.B.20171209.pdf |B.pdf]], [[Media:Day02.C.20171209.pdf |C.pdf]]) ...... Introduction (2) Basic Elements
* Day03 ([[Media:Day03.A.20171007.pdf |A.pdf]], [[Media:Day03.B.20170908.pdf |B.pdf]], [[Media:Day03.C.20171209.pdf |C.pdf]]) ...... Introduction (3) Numbers
* Day04 ([[Media:Day04.A.20171007.pdf |A.pdf]], [[Media:Day04.B.20170915.pdf |B.pdf]], [[Media:Day04.C.20171209.pdf |C.pdf]]) ...... Structured Programming (1) Flowcharts
* Day05 ([[Media:Day05.A.20171007.pdf |A.pdf]], [[Media:Day05.B.20170915.pdf |B.pdf]], [[Media:Day05.C.20171209.pdf |C.pdf]]) ...... Structured Programming (2) Conditions and Loops
* Day06 ([[Media:Day06.A.20171007.pdf |A.pdf]], [[Media:Day06.B.20170923.pdf |B.pdf]], [[Media:Day06.C.20171209.pdf |C.pdf]]) ...... Program Control
* Day07 ([[Media:Day07.A.20171007.pdf |A.pdf]], [[Media:Day07.B.20170926.pdf |B.pdf]], [[Media:Day07.C.20171209.pdf |C.pdf]]) ...... Function (1) Definitions
* Day08 ([[Media:Day08.A.20171028.pdf |A.pdf]], [[Media:Day08.B.20171016.pdf |B.pdf]], [[Media:Day08.C.20171209.pdf |C.pdf]]) ...... Function (2) Storage Class and Scope
* Day09 ([[Media:Day09.A.20171007.pdf |A.pdf]], [[Media:Day09.B.20171017.pdf |B.pdf]], [[Media:Day09.C.20171209.pdf |C.pdf]]) ...... Function (3) Recursion
* Day10 ([[Media:Day10.A.20171209.pdf |A.pdf]], [[Media:Day10.B.20171017.pdf |B.pdf]], [[Media:Day10.C.20171209.pdf |C.pdf]]) ...... Arrays (1) Definitions
* Day11 ([[Media:Day11.A.20171024.pdf |A.pdf]], [[Media:Day11.B.20171017.pdf |B.pdf]], [[Media:Day11.C.20171212.pdf |C.pdf]]) ...... Arrays (2) Applications
* Day12 ([[Media:Day12.A.20171024.pdf |A.pdf]], [[Media:Day12.B.20171020.pdf |B.pdf]], [[Media:Day12.C.20171209.pdf |C.pdf]]) ...... Pointers (1) Definitions
* Day13 ([[Media:Day13.A.20171025.pdf |A.pdf]], [[Media:Day13.B.20171024.pdf |B.pdf]], [[Media:Day13.C.20171209.pdf |C.pdf]]) ...... Pointers (2) Applications
* Day14 ([[Media:Day14.A.20171226.pdf |A.pdf]], [[Media:Day14.B.20171101.pdf |B.pdf]], [[Media:Day14.C.20171209.pdf |C.pdf]]) ...... C String (1) 
* Day15 ([[Media:Day15.A.20171209.pdf |A.pdf]], [[Media:Day15.B.20171124.pdf |B.pdf]], [[Media:Day15.C.20171209.pdf |C.pdf]]) ...... C String (2)
* Day16 ([[Media:Day16.A.20171208.pdf |A.pdf]], [[Media:Day16.B.20171114.pdf |B.pdf]], [[Media:Day16.C.20171209.pdf |C.pdf]]) ...... C Formatted IO
* Day17 ([[Media:Day17.A.20171031.pdf |A.pdf]], [[Media:Day17.B.20171111.pdf |B.pdf]], [[Media:Day17.C.20171209.pdf |C.pdf]]) ...... Structure (1) Definitions
* Day18 ([[Media:Day18.A.20171206.pdf |A.pdf]], [[Media:Day18.B.20171128.pdf |B.pdf]], [[Media:Day18.C.20171212.pdf |C.pdf]]) ...... Structure (2) Applications
* Day19 ([[Media:Day19.A.20171205.pdf |A.pdf]], [[Media:Day19.B.20171121.pdf |B.pdf]], [[Media:Day19.C.20171209.pdf |C.pdf]]) ...... Union, Bitwise Operators, Enum
* Day20 ([[Media:Day20.A.20171205.pdf |A.pdf]], [[Media:Day20.B.20171201.pdf |B.pdf]], [[Media:Day20.C.20171212.pdf |C.pdf]]) ...... Linked List 
* Day21 ([[Media:Day21.A.20171206.pdf |A.pdf]], [[Media:Day21.B.20171208.pdf |B.pdf]], [[Media:Day21.C.20171212.pdf |C.pdf]]) ...... File Processing
* Day22 ([[Media:Day22.A.20171212.pdf |A.pdf]], [[Media:Day22.B.20171213.pdf |B.pdf]], [[Media:Day22.C.20171212.pdf |C.pdf]]) ...... Preprocessing


&lt;!----------------------------------------------------------------------&gt;
&lt;/br&gt;
See also https://cprogramex.wordpress.com/

== '''Old Materials '''==

until 201201
* Intro.Overview.1.A ([[Media:C.Intro.Overview.1.A.20120107.pdf |pdf]])
* Intro.Memory.1.A ([[Media:C.Intro.Memory.1.A.20120107.pdf |pdf]])
* Intro.Number.1.A ([[Media:C.Intro.Number.1.A.20120107.pdf |pdf]])
* Repeat.Control.1.A ([[Media:C.Repeat.Control.1.A.20120109.pdf |pdf]])
* Repeat.Loop.1.A ([[Media:C.Repeat.Loop.1.A.20120113.pdf |pdf]])
* Work.Function.1.A ([[Media:C.Work.Function.1.A.20120117.pdf |pdf]])
* Work.Scope.1.A ([[Media:C.Work.Scope.1.A.20120117.pdf |pdf]])
* Series.Array.1.A ([[Media:Series.Array.1.A.20110718.pdf |pdf]])
* Series.Pointer.1.A ([[Media:Series.Pointer.1.A.20110719.pdf |pdf]])
* Series.Structure.1.A ([[Media:Series.Structure.1.A.20110805.pdf |pdf]])
* Data.Type.1.A ([[Media:C05.Data2.TypeCast.1.A.20130813.pdf |pdf]])
* Data.TypeCast.1.A ([[Media:Data.TypeCast.1.A.pdf |pdf]])
* Data.Operators.1.A ([[Media:Data.Operators.1.A.20110712.pdf |pdf]])
 
&lt;br&gt;

until 201107
* Intro.1.A ([[Media:Intro.1.A.pdf |pdf]])
* Control.1.A ([[Media:Control.1.A.20110706.pdf |pdf]])
* Iteration.1.A ([[Media:Iteration.1.A.pdf |pdf]])
* Function.1.A ([[Media:Function.1.A.20110705.pdf |pdf]])
* Variable.1.A ([[Media:Variable.1.A.20110708.pdf |pdf]])
* Operators.1.A ([[Media:Operators.1.A.20110712.pdf |pdf]])
* Pointer.1.A ([[Media:Pointer.1.A.pdf |pdf]])
* Pointer.2.A ([[Media:Pointer.2.A.pdf |pdf]])
* Array.1.A ([[Media:Array.1.A.pdf |pdf]])
* Type.1.A ([[Media:Type.1.A.pdf |pdf]])
* Structure.1.A ([[Media:Structure.1.A.pdf |pdf]])


go to [ [[C programming in plain view]] ]

[[Category:C programming language]]

&lt;/br&gt;</text>
      <sha1>rswajv9w5bbw37ziccz0yiej1gphst3</sha1>
    </revision>
    <revision>
      <id>2693110</id>
      <parentid>2693020</parentid>
      <timestamp>2024-12-24T10:27:36Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Applications */</comment>
      <origin>2693110</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="9878" sha1="13l1n7mfiw70u6z5zp013j68uivvyjy" xml:space="preserve">=== Introduction ===
* Overview ([[Media:C01.Intro1.Overview.1.A.20170925.pdf |A.pdf]], [[Media:C01.Intro1.Overview.1.B.20170901.pdf |B.pdf]], [[Media:C01.Intro1.Overview.1.C.20170904.pdf |C.pdf]])
* Number System ([[Media:C01.Intro2.Number.1.A.20171023.pdf |A.pdf]], [[Media:C01.Intro2.Number.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro2.Number.1.C.20170914.pdf |C.pdf]])
* Memory System ([[Media:C01.Intro2.Memory.1.A.20170907.pdf |A.pdf]], [[Media:C01.Intro3.Memory.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro3.Memory.1.C.20170914.pdf |C.pdf]])

=== Handling Repetition ===
* Control ([[Media:C02.Repeat1.Control.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat1.Control.1.B.20170918.pdf |B.pdf]], [[Media:C02.Repeat1.Control.1.C.20170926.pdf |C.pdf]])
* Loop ([[Media:C02.Repeat2.Loop.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat2.Loop.1.B.20170918.pdf |B.pdf]])

=== Handling a Big Work ===
* Function Overview ([[Media:C03.Func1.Overview.1.A.20171030.pdf |A.pdf]], [[Media:C03.Func1.Oerview.1.B.20161022.pdf |B.pdf]])
* Functions &amp; Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]])
* Functions &amp; Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]])
* Functions &amp; Recursions ([[Media:C03.Func4.Recursion.1.A.20161214.pdf |A.pdf]], [[Media:C03.Func4.Recursion.1.B.20161214.pdf |B.pdf]])

=== Handling Series of Data ===

==== Background ==== 
* Background ([[Media:C04.Series0.Background.1.A.20180727.pdf |A.pdf]])
 
==== Basics ====
* Pointers ([[Media:C04.S1.Pointer.1A.20240524.pdf |A.pdf]], [[Media:C04.Series2.Pointer.1.B.20161115.pdf |B.pdf]])
* Arrays ([[Media:C04.S2.Array.1A.20240514.pdf |A.pdf]], [[Media:C04.Series1.Array.1.B.20161115.pdf |B.pdf]])
* Array Pointers ([[Media:C04.S3.ArrayPointer.1A.20240208.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]])
* Multi-dimensional Arrays ([[Media:C04.Series4.MultiDim.1.A.20221130.pdf |A.pdf]], [[Media:C04.Series4.MultiDim.1.B.1111.pdf |B.pdf]])
* Array Access Methods ([[Media:C04.Series4.ArrayAccess.1.A.20190511.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]])
* Structures ([[Media:C04.Series3.Structure.1.A.20171204.pdf |A.pdf]], [[Media:C04.Series2.Structure.1.B.20161130.pdf |B.pdf]])

==== Examples ==== 
* Spreadsheet Example Programs
:: Example 1 ([[Media:C04.Series7.Example.1.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.1.C.20171213.pdf |C.pdf]])
:: Example 2 ([[Media:C04.Series7.Example.2.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.2.C.20171213.pdf |C.pdf]])
:: Example 3 ([[Media:C04.Series7.Example.3.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.3.C.20171213.pdf |C.pdf]])
:: Bubble Sort ([[Media:C04.Series7.BubbleSort.1.A.20171211.pdf |A.pdf]])

==== Applications ==== 
* Address-of and de-reference operators ([[Media:C04.SA0.PtrOperator.1A.20241224.pdf |A.pdf]])
* Applications of Pointers ([[Media:C04.SA1.AppPointer.1A.20241121.pdf |A.pdf]])
* Applications of Arrays ([[Media:C04.SA2.AppArray.1A.20240715.pdf |A.pdf]])
* Applications of Array Pointers ([[Media:C04.SA3.AppArrayPointer.1A.20240210.pdf |A.pdf]])
* Applications of Multi-dimensional Arrays ([[Media:C04.Series4App.MultiDim.1.A.20210719.pdf |A.pdf]])
* Applications of Array Access Methods ([[Media:C04.Series9.AppArrAcess.1.A.20190511.pdf |A.pdf]])
* Applications of Structures ([[Media:C04.Series6.AppStruct.1.A.20190423.pdf |A.pdf]])

=== Handling Various Kinds of Data ===
* Types ([[Media:C05.Data1.Type.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data1.Type.1.B.20161212.pdf |B.pdf]])
* Typecasts ([[Media:C05.Data2.TypeCast.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data2.TypeCast.1.B.20161216.pdf |A.pdf]])
* Operators ([[Media:C05.Data3.Operators.1.A.20161219.pdf |A.pdf]], [[Media:C05.Data3.Operators.1.B.20161216.pdf |B.pdf]])
* Files ([[Media:C05.Data4.File.1.A.20161124.pdf |A.pdf]], [[Media:C05.Data4.File.1.B.20161212.pdf |B.pdf]])

=== Handling Low Level Operations ===
* Bitwise Operations ([[Media:BitOp.1.B.20161214.pdf |A.pdf]], [[Media:BitOp.1.B.20161203.pdf |B.pdf]])
* Bit Field ([[Media:BitField.1.A.20161214.pdf |A.pdf]], [[Media:BitField.1.B.20161202.pdf |B.pdf]])
* Union ([[Media:Union.1.A.20161221.pdf |A.pdf]], [[Media:Union.1.B.20161111.pdf |B.pdf]])
* Accessing IO Registers ([[Media:IO.1.A.20141215.pdf |A.pdf]], [[Media:IO.1.B.20161217.pdf |B.pdf]])

=== Declarations ===
* Type Specifiers and Qualifiers ([[Media:C07.Spec1.Type.1.A.20171004.pdf |pdf]])
* Storage Class Specifiers ([[Media:C07.Spec2.Storage.1.A.20171009.pdf |pdf]])
* Scope 


=== Class Notes ===

* TOC ([[Media:TOC.20171007.pdf |TOC.pdf]])
* Day01 ([[Media:Day01.A.20171007.pdf |A.pdf]], [[Media:Day01.B.20171209.pdf |B.pdf]], [[Media:Day01.C.20171211.pdf |C.pdf]]) ...... Introduction (1) Standard Library
* Day02 ([[Media:Day02.A.20171007.pdf |A.pdf]], [[Media:Day02.B.20171209.pdf |B.pdf]], [[Media:Day02.C.20171209.pdf |C.pdf]]) ...... Introduction (2) Basic Elements
* Day03 ([[Media:Day03.A.20171007.pdf |A.pdf]], [[Media:Day03.B.20170908.pdf |B.pdf]], [[Media:Day03.C.20171209.pdf |C.pdf]]) ...... Introduction (3) Numbers
* Day04 ([[Media:Day04.A.20171007.pdf |A.pdf]], [[Media:Day04.B.20170915.pdf |B.pdf]], [[Media:Day04.C.20171209.pdf |C.pdf]]) ...... Structured Programming (1) Flowcharts
* Day05 ([[Media:Day05.A.20171007.pdf |A.pdf]], [[Media:Day05.B.20170915.pdf |B.pdf]], [[Media:Day05.C.20171209.pdf |C.pdf]]) ...... Structured Programming (2) Conditions and Loops
* Day06 ([[Media:Day06.A.20171007.pdf |A.pdf]], [[Media:Day06.B.20170923.pdf |B.pdf]], [[Media:Day06.C.20171209.pdf |C.pdf]]) ...... Program Control
* Day07 ([[Media:Day07.A.20171007.pdf |A.pdf]], [[Media:Day07.B.20170926.pdf |B.pdf]], [[Media:Day07.C.20171209.pdf |C.pdf]]) ...... Function (1) Definitions
* Day08 ([[Media:Day08.A.20171028.pdf |A.pdf]], [[Media:Day08.B.20171016.pdf |B.pdf]], [[Media:Day08.C.20171209.pdf |C.pdf]]) ...... Function (2) Storage Class and Scope
* Day09 ([[Media:Day09.A.20171007.pdf |A.pdf]], [[Media:Day09.B.20171017.pdf |B.pdf]], [[Media:Day09.C.20171209.pdf |C.pdf]]) ...... Function (3) Recursion
* Day10 ([[Media:Day10.A.20171209.pdf |A.pdf]], [[Media:Day10.B.20171017.pdf |B.pdf]], [[Media:Day10.C.20171209.pdf |C.pdf]]) ...... Arrays (1) Definitions
* Day11 ([[Media:Day11.A.20171024.pdf |A.pdf]], [[Media:Day11.B.20171017.pdf |B.pdf]], [[Media:Day11.C.20171212.pdf |C.pdf]]) ...... Arrays (2) Applications
* Day12 ([[Media:Day12.A.20171024.pdf |A.pdf]], [[Media:Day12.B.20171020.pdf |B.pdf]], [[Media:Day12.C.20171209.pdf |C.pdf]]) ...... Pointers (1) Definitions
* Day13 ([[Media:Day13.A.20171025.pdf |A.pdf]], [[Media:Day13.B.20171024.pdf |B.pdf]], [[Media:Day13.C.20171209.pdf |C.pdf]]) ...... Pointers (2) Applications
* Day14 ([[Media:Day14.A.20171226.pdf |A.pdf]], [[Media:Day14.B.20171101.pdf |B.pdf]], [[Media:Day14.C.20171209.pdf |C.pdf]]) ...... C String (1) 
* Day15 ([[Media:Day15.A.20171209.pdf |A.pdf]], [[Media:Day15.B.20171124.pdf |B.pdf]], [[Media:Day15.C.20171209.pdf |C.pdf]]) ...... C String (2)
* Day16 ([[Media:Day16.A.20171208.pdf |A.pdf]], [[Media:Day16.B.20171114.pdf |B.pdf]], [[Media:Day16.C.20171209.pdf |C.pdf]]) ...... C Formatted IO
* Day17 ([[Media:Day17.A.20171031.pdf |A.pdf]], [[Media:Day17.B.20171111.pdf |B.pdf]], [[Media:Day17.C.20171209.pdf |C.pdf]]) ...... Structure (1) Definitions
* Day18 ([[Media:Day18.A.20171206.pdf |A.pdf]], [[Media:Day18.B.20171128.pdf |B.pdf]], [[Media:Day18.C.20171212.pdf |C.pdf]]) ...... Structure (2) Applications
* Day19 ([[Media:Day19.A.20171205.pdf |A.pdf]], [[Media:Day19.B.20171121.pdf |B.pdf]], [[Media:Day19.C.20171209.pdf |C.pdf]]) ...... Union, Bitwise Operators, Enum
* Day20 ([[Media:Day20.A.20171205.pdf |A.pdf]], [[Media:Day20.B.20171201.pdf |B.pdf]], [[Media:Day20.C.20171212.pdf |C.pdf]]) ...... Linked List 
* Day21 ([[Media:Day21.A.20171206.pdf |A.pdf]], [[Media:Day21.B.20171208.pdf |B.pdf]], [[Media:Day21.C.20171212.pdf |C.pdf]]) ...... File Processing
* Day22 ([[Media:Day22.A.20171212.pdf |A.pdf]], [[Media:Day22.B.20171213.pdf |B.pdf]], [[Media:Day22.C.20171212.pdf |C.pdf]]) ...... Preprocessing


&lt;!----------------------------------------------------------------------&gt;
&lt;/br&gt;
See also https://cprogramex.wordpress.com/

== '''Old Materials '''==

until 201201
* Intro.Overview.1.A ([[Media:C.Intro.Overview.1.A.20120107.pdf |pdf]])
* Intro.Memory.1.A ([[Media:C.Intro.Memory.1.A.20120107.pdf |pdf]])
* Intro.Number.1.A ([[Media:C.Intro.Number.1.A.20120107.pdf |pdf]])
* Repeat.Control.1.A ([[Media:C.Repeat.Control.1.A.20120109.pdf |pdf]])
* Repeat.Loop.1.A ([[Media:C.Repeat.Loop.1.A.20120113.pdf |pdf]])
* Work.Function.1.A ([[Media:C.Work.Function.1.A.20120117.pdf |pdf]])
* Work.Scope.1.A ([[Media:C.Work.Scope.1.A.20120117.pdf |pdf]])
* Series.Array.1.A ([[Media:Series.Array.1.A.20110718.pdf |pdf]])
* Series.Pointer.1.A ([[Media:Series.Pointer.1.A.20110719.pdf |pdf]])
* Series.Structure.1.A ([[Media:Series.Structure.1.A.20110805.pdf |pdf]])
* Data.Type.1.A ([[Media:C05.Data2.TypeCast.1.A.20130813.pdf |pdf]])
* Data.TypeCast.1.A ([[Media:Data.TypeCast.1.A.pdf |pdf]])
* Data.Operators.1.A ([[Media:Data.Operators.1.A.20110712.pdf |pdf]])
 
&lt;br&gt;

until 201107
* Intro.1.A ([[Media:Intro.1.A.pdf |pdf]])
* Control.1.A ([[Media:Control.1.A.20110706.pdf |pdf]])
* Iteration.1.A ([[Media:Iteration.1.A.pdf |pdf]])
* Function.1.A ([[Media:Function.1.A.20110705.pdf |pdf]])
* Variable.1.A ([[Media:Variable.1.A.20110708.pdf |pdf]])
* Operators.1.A ([[Media:Operators.1.A.20110712.pdf |pdf]])
* Pointer.1.A ([[Media:Pointer.1.A.pdf |pdf]])
* Pointer.2.A ([[Media:Pointer.2.A.pdf |pdf]])
* Array.1.A ([[Media:Array.1.A.pdf |pdf]])
* Type.1.A ([[Media:Type.1.A.pdf |pdf]])
* Structure.1.A ([[Media:Structure.1.A.pdf |pdf]])


go to [ [[C programming in plain view]] ]

[[Category:C programming language]]

&lt;/br&gt;</text>
      <sha1>13l1n7mfiw70u6z5zp013j68uivvyjy</sha1>
    </revision>
  </page>
  <page>
    <title>Workings of gcc and ld in plain view</title>
    <ns>0</ns>
    <id>285384</id>
    <revision>
      <id>2693033</id>
      <parentid>2692992</parentid>
      <timestamp>2024-12-23T15:55:24Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Integer Arithmetic */</comment>
      <origin>2693033</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3547" sha1="feivxuxayx45ge5ul6xuws6vu2j0ca8" xml:space="preserve">=== 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.20241204.pdf |pdf]])
* Overflow Flag ([[Media:gcc.3.Overflow.20241205.pdf |pdf]])
* Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]])
* Borrow ([[Media:Borrow.20241223.pdf |pdf]])

==== Floating point Arithmetic ====
&lt;/br&gt;

=== Workings of the GNU Linker for IA-32 ===

==== Linking Libraries ====

* Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]])
* Shared Libraries ([[Media:LIB.2A.Shared.20241223.pdf |pdf]])

==== Dynamic Linking - Directories and Symbolic Links ====

* Shared Library Names ([[Media:DIR.1A.Names.20241223.pdf |pdf]])
* Managing Shared Libraries ([[Media:DIR.2A.Manage.20241223.pdf |pdf]])

==== Dynamic Loading - API Functions ====

* DL API ([[Media:API.1A.Functions.20241223.pdf |pdf]])

==== Library Search Path ====

* Using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]])

* 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]], [[Media:LNK.5C.StaticLinking.20241128.pdf |C.pdf]])

* Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]], [[Media:LNK.6C.DynamicLinking.20241128.pdf |C.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]])


&lt;/br&gt;
go to [ [[C programming in plain view]] ]

[[Category:C programming language]]</text>
      <sha1>feivxuxayx45ge5ul6xuws6vu2j0ca8</sha1>
    </revision>
    <revision>
      <id>2693080</id>
      <parentid>2693033</parentid>
      <timestamp>2024-12-24T00:25:27Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Linking Libraries */</comment>
      <origin>2693080</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3547" sha1="18cyf28k083ie6nnqce9bsw2v04nsir" xml:space="preserve">=== 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.20241204.pdf |pdf]])
* Overflow Flag ([[Media:gcc.3.Overflow.20241205.pdf |pdf]])
* Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]])
* Borrow ([[Media:Borrow.20241223.pdf |pdf]])

==== Floating point Arithmetic ====
&lt;/br&gt;

=== Workings of the GNU Linker for IA-32 ===

==== Linking Libraries ====

* Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]])
* Shared Libraries ([[Media:LIB.2A.Shared.20241224.pdf |pdf]])

==== Dynamic Linking - Directories and Symbolic Links ====

* Shared Library Names ([[Media:DIR.1A.Names.20241223.pdf |pdf]])
* Managing Shared Libraries ([[Media:DIR.2A.Manage.20241223.pdf |pdf]])

==== Dynamic Loading - API Functions ====

* DL API ([[Media:API.1A.Functions.20241223.pdf |pdf]])

==== Library Search Path ====

* Using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]])

* 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]], [[Media:LNK.5C.StaticLinking.20241128.pdf |C.pdf]])

* Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]], [[Media:LNK.6C.DynamicLinking.20241128.pdf |C.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]])


&lt;/br&gt;
go to [ [[C programming in plain view]] ]

[[Category:C programming language]]</text>
      <sha1>18cyf28k083ie6nnqce9bsw2v04nsir</sha1>
    </revision>
    <revision>
      <id>2693082</id>
      <parentid>2693080</parentid>
      <timestamp>2024-12-24T03:01:16Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Dynamic Linking - Directories and Symbolic Links */</comment>
      <origin>2693082</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3547" sha1="kpn2490bovdgpn7et4xkdac8elyro3c" xml:space="preserve">=== 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.20241204.pdf |pdf]])
* Overflow Flag ([[Media:gcc.3.Overflow.20241205.pdf |pdf]])
* Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]])
* Borrow ([[Media:Borrow.20241223.pdf |pdf]])

==== Floating point Arithmetic ====
&lt;/br&gt;

=== Workings of the GNU Linker for IA-32 ===

==== Linking Libraries ====

* Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]])
* Shared Libraries ([[Media:LIB.2A.Shared.20241224.pdf |pdf]])

==== Dynamic Linking - Directories and Symbolic Links ====

* Shared Library Names ([[Media:DIR.1A.Names.20241224.pdf |pdf]])
* Managing Shared Libraries ([[Media:DIR.2A.Manage.20241223.pdf |pdf]])

==== Dynamic Loading - API Functions ====

* DL API ([[Media:API.1A.Functions.20241223.pdf |pdf]])

==== Library Search Path ====

* Using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]])

* 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]], [[Media:LNK.5C.StaticLinking.20241128.pdf |C.pdf]])

* Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]], [[Media:LNK.6C.DynamicLinking.20241128.pdf |C.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]])


&lt;/br&gt;
go to [ [[C programming in plain view]] ]

[[Category:C programming language]]</text>
      <sha1>kpn2490bovdgpn7et4xkdac8elyro3c</sha1>
    </revision>
    <revision>
      <id>2693086</id>
      <parentid>2693082</parentid>
      <timestamp>2024-12-24T03:27:11Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Dynamic Linking - Directories and Symbolic Links */</comment>
      <origin>2693086</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3547" sha1="0wiu8ufklh1z4mcqxc4qr8tyr3v7sf8" xml:space="preserve">=== 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.20241204.pdf |pdf]])
* Overflow Flag ([[Media:gcc.3.Overflow.20241205.pdf |pdf]])
* Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]])
* Borrow ([[Media:Borrow.20241223.pdf |pdf]])

==== Floating point Arithmetic ====
&lt;/br&gt;

=== Workings of the GNU Linker for IA-32 ===

==== Linking Libraries ====

* Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]])
* Shared Libraries ([[Media:LIB.2A.Shared.20241224.pdf |pdf]])

==== Dynamic Linking - Directories and Symbolic Links ====

* Shared Library Names ([[Media:DIR.1A.Names.20241224.pdf |pdf]])
* Managing Shared Libraries ([[Media:DIR.2A.Manage.20241224.pdf |pdf]])

==== Dynamic Loading - API Functions ====

* DL API ([[Media:API.1A.Functions.20241223.pdf |pdf]])

==== Library Search Path ====

* Using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]])

* 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]], [[Media:LNK.5C.StaticLinking.20241128.pdf |C.pdf]])

* Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]], [[Media:LNK.6C.DynamicLinking.20241128.pdf |C.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]])


&lt;/br&gt;
go to [ [[C programming in plain view]] ]

[[Category:C programming language]]</text>
      <sha1>0wiu8ufklh1z4mcqxc4qr8tyr3v7sf8</sha1>
    </revision>
  </page>
  <page>
    <title>Social Victorians/Terminology</title>
    <ns>0</ns>
    <id>285723</id>
    <revision>
      <id>2693041</id>
      <parentid>2692796</parentid>
      <timestamp>2024-12-23T19:52:21Z</timestamp>
      <contributor>
        <username>Scogdill</username>
        <id>1331941</id>
      </contributor>
      <comment>/* Hoops */</comment>
      <origin>2693041</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="113655" sha1="8jw5h9jy5gtl1b5d7q07houq253sr8w" xml:space="preserve">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 &quot;Short skirt or flared flounce layered at the waist of a jacket, blouse or dress&quot; [translation by Google Translate].&lt;ref&gt;{{Cite journal|date=2021-07-02|title=péplum|url=https://fr.wiktionary.org/w/index.php?title=p%C3%A9plum&amp;oldid=29547727|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/p%C3%A9plum.&lt;/ref&gt; The ''Oxford English Dictionary'' has a fuller definition, although, it focuses on women's clothing because the sense is written for the present day:&lt;blockquote&gt;''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.&lt;ref name=&quot;:5&quot;&gt;“peplum, n.”. ''Oxford English Dictionary'', Oxford University Press, September 2023, &lt;https://doi.org/10.1093/OED/1832614702&gt;.&lt;/ref&gt;&lt;/blockquote&gt;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.&lt;ref name=&quot;:5&quot; /&gt;

=== Revers ===
According to the ''Oxford English Dictionary'', ''revers'' are the &quot;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.&quot;&lt;ref&gt;&quot;revers, n.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/164777. Accessed 17 April 2023.&lt;/ref&gt; The term is French and was used this way in the 19th century (according to the ''Wiktionnaire'').&lt;ref&gt;{{Cite journal|date=2023-03-07|title=revers|url=https://fr.wiktionary.org/w/index.php?title=revers&amp;oldid=31706560|journal=Wiktionnaire|language=fr}} https://fr.wiktionary.org/wiki/revers.&lt;/ref&gt;

== 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''' &quot;at the foot of the Buckingham tomb in Henry VII's Chapel at Westminster Abbey.&quot;&lt;ref&gt;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.&lt;/ref&gt;{{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.&lt;ref&gt;{{Cite journal|date=2023-04-25|title=Cavalier poet|url=https://en.wikipedia.org/w/index.php?title=Cavalier_poet&amp;oldid=1151690299|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Cavalier_poet.&lt;/ref&gt;

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 &quot;Tight-fitting breeches, worn by men in the 18th and early 19th centuries, and still forming part of court-dress.&quot;&lt;ref&gt;“Tights, N.” ''Oxford English Dictionary'', Oxford UP, July 2023, https://doi.org/10.1093/OED/2693287467.&lt;/ref&gt; 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.&lt;ref&gt;{{Cite journal|date=2021-06-26|title=Collerette (costume)|url=https://fr.wikipedia.org/w/index.php?title=Collerette_(costume)&amp;oldid=184136746|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Collerette_(costume)#Au+xixe+siècle+:+la+Chérusque.&lt;/ref&gt;

=== Corsage ===
According to the ''Oxford English Dictionary'', the corsage is the &quot;'body' of a woman's dress; a bodice.&quot;&lt;ref&gt;&quot;corsage, n.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/42056. Accessed 7 February 2023.&lt;/ref&gt; 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 &quot;a bouquet worn on the bodice&quot; is, according to the ''OED'', American.

=== Décolletage ===

=== Girdle ===

=== Mancheron ===
According to the ''Oxford English Dictionary'', a ''mancheron'' is a &quot;historical&quot; word for &quot;A piece of trimming on the upper part of a sleeve on a woman's dress.&quot;&lt;ref&gt;&quot;mancheron, n.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/113251. Accessed 17 April 2023.&lt;/ref&gt; At the present, in French, a ''mancheron'' is a cap sleeve &quot;cut directly on the bodice.&quot;&lt;ref&gt;{{Cite journal|date=2022-11-28|title=Manche (vêtement)|url=https://fr.wikipedia.org/w/index.php?title=Manche_(v%C3%AAtement)&amp;oldid=199054843|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Manche_(v%C3%AAtement).&lt;/ref&gt;

=== Petticoat ===

According to the ''O.E.D.'', a petticoat is a &lt;blockquote&gt;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''.&lt;ref&gt;“petticoat, n., sense 2.b”.  ''Oxford English Dictionary'', Oxford University Press,  September 2023, &lt;https://doi.org/10.1093/OED/1021034245&gt;&lt;/ref&gt; &lt;/blockquote&gt;This sense is, according to the ''O.E.D.'', &quot;The usual sense between the 17th and 19th centuries.&quot; 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 &quot;An ornamental covering for the chest (often covered with jewels) worn by women under the lacing of the bodice,&quot;&lt;ref&gt;“stomacher, n.¹, sense 3.a”. ''Oxford English Dictionary'', Oxford University Press, September 2023, &lt;https://doi.org/10.1093/OED/1169498955&gt;&lt;/ref&gt; 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,&lt;blockquote&gt;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&lt;ref name=&quot;:2&quot;&gt;{{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/.&lt;/ref&gt;
&lt;/blockquote&gt;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?''']

=== Foundation Garments ===
Unlike undergarments, Victorian women's foundation garments created the distinctive silhouette. Victorian undergarments included the chemise, the bloomers, the corset cover — articles that are not structural. 

The corset was an important element of the understructure of foundation garments — 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 &quot;look&quot; 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.

=== Hoops ===
'''This section is under construction right now'''.

''Hoops'' is a mid-19th-century term for a cage-like structure worn under a skirt to hold it away from the body. '''Striking''' for how long they lasted and '''the ways''' they evolved, hoops were the foundation undergarment for the bottom half of a woman's body, for a skirt and petticoat.

Women wore this cage-like structure from the '''15th century''' through the late 19th century. The 16th-century Katherine of Aragon is credited with making it fashionable outside Spain.

The cage caused the silhouette of skirts to change shape over time and enabled the extreme distortions of 17th-and-18th-century panniers and the late 19th-century bustle. Early hoops circled the body in a bell, cone or drum shape, then were moved to the sides with panniers, then ballooned around the body like the top half of a sphere, and finally were pulled to the rear with a bustle.

That is, the distorted shapes of high fashion were made possible by hoops. High fashion demanded these shapes, which disguised women's bodies, especially below the waist, while [[Social Victorians/Terminology#Corsets|corsets]] did their work above it. 

Besides the shape, the structure used to construct hoops evolved — from cane and wood to whalebone, then steel '''bands''' and wire. Add fabric structural stuff: tabs, wires inserted into casings in a linen, muslin or, later, crinoline underskirt

[[File:Pedro García de Benabarre St John Retable Detail.jpg|thumb|alt=Old oil painting of a woman wearing a dress from the 1400s holding the decapitated head of a man with a halo before a table of people at a dinner party|Pedro García de Benabarre, Detail from St. John Altarpiece, c. 1470, Showing Visible Hoops]]
[[File:Alonso Sánchez Coello 011.jpg|thumb|alt=Old painting of a princess wearing a richly jeweled outfit|Infanta Isabel Clara Eugenia Wearing a Vertugado, or Spanish Farthingale]]
==== 15th Century ====
Hoops first appeared in Spain in the 15th century and influenced European fashion for '''many years'''.

A detail (right) from Pedro García de Benabarre's c. 1470 larger altarpiece painting shows women wearing a style of hoops that predates the farthingale but marks the beginning point of the development of that fashion. Salome (holding John the Baptist's head) is wearing a dress with what looks like visible wooden hoops attached to the outside of the skirt, which also appears to have padding at the hips underneath it.

De Benabarre was &quot;active in Aragon and in Catalonia, between 1445–1496,&quot;&lt;ref&gt;{{Cite web|url=https://www.mfab.hu/artworks/10528/|title=Saint Peter|website=Museum of Fine Arts, Budapest|language=en-US|access-date=2024-12-11}} https://www.mfab.hu/artworks/10528/.&lt;/ref&gt; so perhaps he saw the styles worn by people like Katharine of Aragon.

==== 16th Century ====
Styles in personal adornment and architectural decoration: The &quot;Golden Age&quot; in '''England''', the Elizabethan Age.
[[File:Queen Elizabeth I ('The Ditchley portrait') by Marcus Gheeraerts the YoungerFXD.jpg|thumb|alt=Old oil painting of a queen in a white dress with shoulders and hips exaggerated by her dress|Queen Elizabeth I in a French Cartwheel Farthingale]]
In the 16th century, the garment we call ''hoops'' was called a farthingale.&lt;blockquote&gt;''&quot;FARTHINGALE:  Renaissance (1450-1550 C.E. to Elizabethan (1550-1625 C.E.). Linen underskirt with '''wire supports''' which, when shaped, produced a variety of dome, bell, and oblong shapes.&quot;&lt;ref name=&quot;:7&quot; /&gt;''{{rp|105}} ['''our emphasis''']&lt;/blockquote&gt;''Vertugadin'' is a French term for ''farthingale'' — &quot;un élément essentiel de la mode Tudor en Angleterre [an essential element of Tudor fashion in England].&quot;&lt;ref name=&quot;:0&quot;&gt;{{Cite journal|date=2022-03-12|title=Vertugadin|url=https://fr.wikipedia.org/w/index.php?title=Vertugadin&amp;oldid=191825729|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Vertugadin.&lt;/ref&gt; ''Farthingale'' is the term in English; in French, it's ''vertugadin'', and in Spanish ''vertugado''. The hoops in the Pedro García de Benabarre painting (above right) predate what would technically be a vertugado.&lt;p&gt;
Blanche Payne says,&lt;blockquote&gt;Katherine of Aragon is reputed to have introduced the Spanish farthingale ... into England early in the century. The result was to convert the columnar skirt of the fifteenth century into the cone shape of the sixteenth. ...&lt;p&gt;
Spanish influence had introduced the hoop-supported skirt, smooth in contour, '''which was quite generally worn'''.&lt;ref name=&quot;:11&quot; /&gt;{{rp|291}} ['''our emphasis''']&lt;/blockquote&gt;

In fact, &quot;The Spanish princess Catherine of Aragon brought the fashion to England for her marriage to Prince Arthur, eldest son of Henry VII in 1501 [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].&quot;&lt;ref name=&quot;:0&quot; /&gt; Catherine of Aragon, of course, married Henry VIII after Arthur's death.

The vertugado was &quot;quite generally worn&quot; among the ruling and culturally elite classes in Spain, and not by working-class women, which was enforced by sumptuary laws.

By the end of the 16th century the French and Spanish farthingales were not identical.

The Spanish vertugado shaped the skirt into an A-line with a graduated series of hoops sewn to an undergarment. Alonso Sánchez Coello's c. 1584&lt;ref name=&quot;:11&quot; /&gt;{{rp|316}} portrait (right) shows infanta Isabel Clara Eugenia wearing a vertugado, with its &quot;typically Spanish smooth cone-shaped contour.&quot;&lt;ref name=&quot;:11&quot; /&gt;{{rp|315–316}}

The French vertugadin was a flattish &quot;cartwheel&quot; '''in which a''' 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 it into a kind of drum. Marcus Gheeraerts the Younger's portrait (right) of Queen Elizabeth I shows an English queen wearing a French drum-shaped farthingale. The skirt over a cartwheel farthingale did not touch the floor in front, so the dress flowed and the women's feet would show as they walked. Interestingly, shoes often appear in portraits of women wearing the vertugadin, as Elizabeth's do in Gheeraerts' image. 

The shoes do not show in the portraits of women wearing the Spanish vertugado. The round hoops stayed in place in front, giving their feet enough room to take steps.

By the end of the 16th century France had become the arbiter of fashion for the western world, which it still is.

==== 17th Century ====
The 17th century encompassed movements in the arts and architecture as well as styling for personal adornment and the decoration of home. The Cavalier style, for example, was a style of men's dress but at base it was a political movement in support of England's King Charles II. The Baroque style centered on the courts of Europe. The speed with which fashion trends changed began to accelerate in the 17th century, making fashion more expensive and more difficult to keep up.

Hoops disappeared from high fashion for about a century, reappearing flattened and widened as panniers and shifted to the back as bustles. Without structures like hoops, dresses draped loosely to the floor, shaped to some degree by padding, like bum rolls. And what had been starched and stiff in the 16th century became looser and flatter in the 17th.

People associate bustles with late-19th-century styles, but in fact the bustle existed in the 17th century, sometimes as padding rather than a structural cage. Panniers are associated with 18th-century styles, but they first began in the 17th century as well.

Payne says, &quot;The bustle was a continuation of the 1690 mode.&quot;&lt;ref name=&quot;:11&quot; /&gt;{{rp|411}}

Generally, panniers were a kind of undergarment worn in the 17th and 18th centuries. Their design evolved during the century. Made of hoops of wood, they were &quot;baskets&quot; or cages worn on either side of the waist to broaden the skirts to the sides.

This is a contemporary reproduction of a foundation for panniers, giving an idea of what they may have looked like. Almost no examples of panniers survive. The hoops are wooden, connected with fabric strips or ribbons. This structure is not for the extremely wide panniers, so it probably represents panniers predating the 1740s and certainly before Marie Antoinette exaggerated the width of panniers in court dress. The original panniers would not have been red, but in this reconstruction, the contrasting red makes the structure easier to see.[[File:Panniers 1.jpg|thumb|alt=Photograph of the wooden and fabric skeleton of an 18th-century women's foundation garment|Wooden and Fabric Structure for 18th-century Panniers|center]]
==== 18th Century ====

Styles in personal adornment and architectural decoration: Rococo, post French Revolution, Empire

By the 18th century, the farthingale was called hoops, which were at this point made of wood.

Images:

* Hoop petticoat and corset England 1750-1780 LACMA.jpg

[[File:Hoop petticoat and corset England 1750-1780 LACMA.jpg|center|thumb|Hoops as Panniers, 1750–1780]]

* '''Johanna Gabriele of Habsburg Lorraine1 copy.jpg'''

* [[File:Johanna Gabriele of Habsburg Lorraine1 copy.jpg|center|thumb|Martin van Meytens, Johanna Gabriele of Habsburg Lorraine, c. 1760]]
*
* 1789, extreme panniers, hat, Goya: Maria Luisa de Parma con tontillo.jpg
* [[File:Maria Luisa de Parma con tontillo.jpg|center|thumb|1789, extreme panniers, hat, Goya]]&lt;br /&gt;

Blanche Payne outlines the evolution of hoops, and thus the shape of the skirt, in the 18th century:&lt;blockquote&gt;SKIRT FASHIONS. Since skirts experienced the greatest alterations, a brief summary of the successive silhouettes should help to place individual costumes in their proper niches. Six basic forms appeared during the century, in the following order:

# The bustle was a continuation of the 1690 mode.
# The bell or dome shape resulted from the reintroduction of hoops; in England by 1710, in France by 1720.
# The ellipse, the second phase of the hoop skirt, was achieved by broadening the support from side to side and compressing it from front to back. It had a long run of popularity, from 1740 to 1770, the extreme width being retained in court costumes. In France it persisted until the revolution, except that skirts were allowed to curve outward in [the] back again. English court costume [411/413] followed this fashion well into the nineteenth century.
# The dairy maid, or polonaise, style could be achieved either by pulling the lower part of the overskirt through its own pocket holes, thus creating a bouffant effect, or by planned control of the overskirt, through the cut or by means of draw cords, ribbons, or loops and buttons, which were used to form the three great ‘poufs’ known as the polonaise .... These diversions appeared in the late sixties and became prevalent in the seventies. They were much like the familiar styles of our own [American] Revolutionary War period.
# The return of the bustle in the 1780s.
# The tubular form, drawn from classic art, in the 1790s.&lt;ref name=&quot;:11&quot; /&gt;{{rp|411, 413}}
&lt;/blockquote&gt;While we think of the bustle as a 19th-century look, it can be found in the 18th century, as Payne says.&lt;p&gt;
The Polonaise was a late-Georgian or late-18th-century style, dating in written English, according to the ''Oxford English Dictionary'', from 1773:&lt;blockquote&gt;A woman's dress consisting of a tight, unboned bodice and a skirt open from the waist downwards to reveal a decorative underskirt. Now historical.&lt;ref name=&quot;:13&quot;&gt;“Polonaise, N. &amp; Adj.” ''Oxford English Dictionary'', Oxford UP, September 2024, https://doi.org/10.1093/OED/2555138986.&lt;/ref&gt;&lt;/blockquote&gt;Even though it looks ''à la français'', the term itself does not appear as a term used to describe clothing by the French, either now or in the past.&lt;p&gt;
Payne says,&lt;blockquote&gt;The dairy maid, or polonaise, style could be achieved either by pulling the lower part of the overskirt through its own pocket holes, thus creating a bouffant effect, or by planned control of the overskirt, through the cut or by means of draw cords, ribbons, or loops and buttons, [or, later, buckles] which were used to form the three great ‘poufs’ known as the polonaise .... These diversions appeared in the late sixties and became prevalent in the seventies. They were much like the familiar styles of our own [American] Revolutionary War period.&lt;ref name=&quot;:11&quot; /&gt;{{rp|413}}&lt;/blockquote&gt;

==== 19th Century ====
Possible images:

* File:Crinoline era3.gif
[[File:Crinoline era3.gif|center|thumb|Crinoline era3.gif]]
* Crinoline (6795291959).jpg
[[File:Crinoline (6795291959).jpg|center|thumb|Augusta Congreve, side entrance of Clonbrock House, Ahascragh, Co. Galway.  31 January 1866]]
* Elisabeth Franziska wearing a crinoline and feathered hat.jpg
[[File:Elisabeth Franziska wearing a crinoline and feathered hat.jpg|center|thumb|Archduchess Elisabeth Franziska (1831-1903) wearing a crinoline and feathered hat, 1860s]]
*HM Queen Victoria. Photograph by C. Clifford of Madrid, 1861 Wellcome V0027547.jpg
*Queen Victoria at Windsor Castle, in evening dress, with diadem &amp; jewels. The Regalportrait photographed from live by C.Clifford of Madrid. 14 November 1861. Carte de visite[[File:Her Majesty the Queen Victoria.JPG|center|thumb|Queen Victoria at Windsor Castle, in evening dress, with diadem &amp; jewels. The Regalportrait photographed from live by C.Clifford of Madrid. 14 November 1861]]
* Her Majesty the Queen Victoria.JPG

* Queen Victoria photographed by Mayall.JPG
[[File:Queen Victoria photographed by Mayall.JPG|center|thumb|Queen Victoria photographed by Mayall, 1860s, carte de visite]]
*
* File:The Secret of England's Greatness' (Queen Victoria presenting a Bible in the Audience Chamber at Windsor) by Thomas Jones Barker.jpg
[[File:The Secret of England's Greatness' (Queen Victoria presenting a Bible in the Audience Chamber at Windsor) by Thomas Jones Barker.jpg|center|thumb|The Secret of England's Greatness' (Queen Victoria presenting a Bible in the Audience Chamber at Windsor) by Thomas Jones Barker, c. 1863]]
* Bustle: Princess Victoria Mary of Teck.jpg
[[File:Princess Victoria Mary of Teck.jpg|center|thumb|Princess Victoria Mary of Teck, 1886. Bustle]]
* Development of the full-cage hoop to flatter in front, with fabric going to the back: Queen Emma of Hawaii, photograph by John &amp; Charles Watkins, The Royal Collection Trust.jpg
[[File:Queen Emma of Hawaii, photograph by John &amp; Charles Watkins, The Royal Collection Trust (crop).jpg|center|thumb|Queen Emma of Hawaii, photograph by John &amp; Charles Watkins, The Royal Collection Trust, 1865]]
* Miss Victoria Stuart-Wortley, later Victoria, Lady Welby (1837-1912) 1859.jpg

[[File:Cutaway sketch of crinoline.gif|thumb|Cutaway sketch of crinoline]]
[[File:Paris voulant englober la banlieue.JPG|thumb|Paris voulant englober la banlieue]]
[[File:Vrouw moet haar hoepelrok uitdoen om de tram te betreden New Omnibus Regulation. Werry sorry'm, but yer l'av to leave yer Krinerline outside (Vide Punch) (titel op object), RP-F-F10723.jpg|thumb|Vrouw moet haar hoepelrok uitdoen om de tram te betreden New Omnibus Regulation. Werry sorry'm, but yer l'av to leave yer Krinerline outside (Vide Punch) (titel op object), RP-F-F10723]]
Styles in personal adornment and architectural decoration: Romantic, Victorian (at least in '''the UK'''), &quot;New Woman,&quot; [[Social Victorians/Terminology#Traditional vs Progressive Style|Traditional vs Progressive Style]], Crinoline 

In the 19th century, the hoops were made of wire and became lighter. By the 1860s, hoops caused skirts to be huge and round.

By the 19th century, fashion had begun to move down the social classes so that hoops (and, for example, top hats) were worn by the middle and sometimes working classes.

'''''1880s'''''


Laura Ingalls Wilder wrote about the hoops her fictionalized self wore the century before. In ''These Happy Golden Years'' (1943), she gives a detailed description of the clothing under her dress:&lt;blockquote&gt;
“Then carefully over her under-petticoats she put on her hoops. She liked these new hoops. They were the very latest style in the East, and these were the first of the kind that Miss Bell had got. Instead of wires, there were wide tapes across the front, almost to her knees, holding the petticoats so that her dress would lie flat. These tapes held the wire bustle in place at the back, and it was an adjustable bustle. Short lengths of tape were fastened either end of it; these could be buckled together underneath the bustle to puff it out, either large or small. Or they could be buckled together in front, drawing the bustle down close in back so that a dress rounded smoothly over it. Laura did not like a large bustle, so she buckled the tapes in front.

&quot;Then carefully over all she buttoned her best petticoat, and over all the starched petticoats she put on the underskirt of her new dress. It was of brown cambric, fitting smoothly around the top over the bustle, and gored to flare smoothly down over the hoops. At the bottom, just missing the floor, was a twelve-inch-wide flounce of the brown poplin, bound with an inch-wide band of plain brown silk. The poplin was not plain poplin, but striped with an openwork silk stripe.

&quot;Then over this underskirt and her starched white corset-cover, Laura put on the polonaise. Its smooth, long sleeves fitted her arms perfectly to the wrists, where a band of the plain silk ended them. The neck was high with a smooth band of the plain silk around the throat. The polonaise fitted tightly and buttoned all down the front with small round buttons covered with the plain brown silk. Below the smooth hips it flared and rippled down and covered the top of the flounce on the underskirt. A band of the plain silk finished the polonaise at the bottom.&quot;&lt;ref&gt;Wilder, Laura Ingalls. ''These Happy Golden Years.'' Harper &amp; Row, Publishers, 1943. Pp. 161–163.&lt;/ref&gt;&lt;/blockquote&gt;
When a 20th-century Laura Ingalls Wilder calls her character's late-19th-century dress a polonaise, she is probably referring to the &quot;tight, unboned bodice&quot;&lt;ref name=&quot;:13&quot; /&gt; and perhaps the simple, modest look of a dairy maid. 

In Wilder's 1941 ''Little Town on the Prairie'', she provides an interesting story about how the wind could affect hoops:&lt;blockquote&gt;“Well,” Laura began; then she stopped and spun round and round, for the strong wind blowing against her always made the wires of her hoop skirt creep slowly upward under her skirts until they bunched around her knees. Then she must whirl around and around until the wires shook loose and spiraled down to the bottom of her skirts where they should be.

“As she and Carrie hurried on she began again. “I think it was silly, the way they dressed when Ma was a girl, don’t you? Drat this wind!” she exclaimed as the hoops began creeping upward again.

“Quietly Carrie stood by while Laura whirled. “I’m glad I’m not old enough to have to wear hoops,” she said. “They’d make me dizzy.”

“They are rather a nuisance,” Laura admitted. “But they are stylish, and when you’re my age you’ll want to be in style.”&lt;ref&gt;Wilder, Laura Ingalls. ''Little Town on the Prairie.'' Harper and Row, 1941. Pp. 272–273.&lt;/ref&gt;&lt;/blockquote&gt;This moment is set in 1883.&lt;ref&gt;Hill, Pamela Smith, ed. ''Pioneer Girl: The Annotated Autobiography''.&lt;/ref&gt; The 16-year-old Laura makes the comment that she wants to be in style, but she lives on the prairie, far from a large city, and would not necessarily wear the latest Parisian style. This description of the way the wind could make hoops creep — and the solution of spinning to get the hoops to go back down — is very unusual. It must have been happening to other women wearing hoops at the time, but no other writer addresses this.

== '''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 ===
Images

* Smooth bodice, fabric draped to the back, bustle, laters: Victoria Hesse NPG 95941 crop.jpg


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 &quot;high style&quot; in a gown by Worth with &quot;the idiosyncrasies of the [1890s] full blown&quot;:&lt;blockquote&gt;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.&lt;ref name=&quot;:11&quot;&gt;Payne, Blanche. ''History of Costume from the Ancient Egyptians to the Twentieth Century''. Harper &amp; Row, 1965.&lt;/ref&gt;{{rp|530}}&lt;/blockquote&gt;

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 — &quot;recording for posterity the aesthetic craze as regards dress&quot; — deliberately contrasts what he calls the &quot;folly&quot; of the Artistic Dress movement and the look of the traditional corseted waist.&lt;ref&gt;Frith, William Powell. ''My Autobiography and Reminiscences''. 1887.&lt;/ref&gt; Frith considered the Artistic Movement and Artistic Dress &quot;ephemeral,&quot; 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 &quot;craze&quot; 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 &quot;bones&quot;) 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'''&lt;ref&gt;Calvert, Robyne Erica. ''Fashioning the Artist: Artistic Dress in Victorian Britain 1848-1900''. Ph.D. thesis, University of Glasgow, 2012. &lt;nowiki&gt;https://theses.gla.ac.uk/3279/&lt;/nowiki&gt;&lt;/ref&gt;] 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, &quot;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.&quot;&lt;ref&gt;Mitchell, Rebecca N. &quot;The Victorian Fancy Dress Ball, 1870–1900.&quot; ''Fashion Theory'' 2017 (21: 3): 291–315. DOI: 10.1080/1362704X.2016.1172817.&lt;/ref&gt; (294)

* historical dress: beautiful clothing.

* the range at the ball, from Minnie Paget to Gwladys
* &quot;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 ...&quot;

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. &quot;Every cap, bow, streamer, ruffle, fringe, bustle, glove,&quot; that is, the trim and decorations on their garments, their jewelry and accessories — which Davidoff calls &quot;elaborations&quot;&lt;ref name=&quot;:1&quot;&gt;Davidoff, Leonore. ''The Best Circles: Society Etiquette and the Season''. Intro., Victoria Glendinning. The Cressett Library (Century Hutchinson), 1986 (orig 1973).&lt;/ref&gt;{{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.&lt;ref&gt;&quot;cinquecento, n.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/33143. Accessed 7 February 2023.&lt;/ref&gt; 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.&lt;ref&gt;&quot;creve, v.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/44339. Accessed 8 February 2023.&lt;/ref&gt; ['''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 &quot;Elastic cord or string, usually woven with india-rubber,&quot;&lt;ref name=&quot;:6&quot;&gt;“elastic, adj. &amp; n.”.  ''Oxford English Dictionary'', Oxford University Press,  September 2023, &lt;https://doi.org/10.1093/OED/1199670313&gt;.&lt;/ref&gt; the ''Oxford English Dictionary'' has usage examples beginning in 1847. The example for 1886 is vivid: &quot;The thorough-going prim man will always place a circle of elastic round his hair previous to putting on his college cap.&quot;&lt;ref name=&quot;:6&quot; /&gt;

== 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.”&lt;ref name=&quot;:1&quot; /&gt;{{rp|93}}

Looking at these elaborations as meaningful rather than dismissing them as failed attempts at &quot;historical accuracy&quot; 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,&lt;blockquote&gt;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.&lt;ref&gt;Gormally, Mary Frances. Review essay of ''The House of Worth: Portrait of an Archive'', by Amy de la Haye and Valerie D. Mendes (V&amp;A Publishing, 2014). ''Fashion Theory'' 2017 (21, 1): 109–126. DOI: 10.1080/1362704X.2016.1179400.&lt;/ref&gt; (117)&lt;/blockquote&gt;

[[File:Aglets from Spanish portraits - collage by shakko.jpg|thumb|alt=A collage of 12 different ornaments typically worn by elite people from Spain in the 1500s and later|Aglets — Detail from Spanish Portraits]]
=== Aglet, Aiglet ===
Historically, an aglet is a &quot;point or metal piece that capped a string [or ribbon] used to attach two pieces of the garment together, i.e., sleeve and bodice.&quot;&lt;ref name=&quot;:7&quot; /&gt;{{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).

Alonso Sánchez Coello's c. 1584 (316) portrait (above right, in the [[Social Victorians/Terminology#16th Century|Hoops section]]) shows infanta Isabel Clara Eugenia wearing a vertugado, with its &quot;typically Spanish smooth cone-shaped contour,&quot; with &quot;handsome aiglets cascad[ing] down center front.&quot;&lt;ref name=&quot;:11&quot; /&gt; (315)

=== Frou-frou ===
In French, ''frou-frou'' or, spelled as ''froufrou'', is the sound of the rustling of silk or sometimes of fabrics in general.&lt;ref&gt;{{Cite journal|date=2023-07-25|title=frou-frou|url=https://fr.wiktionary.org/w/index.php?title=frou-frou&amp;oldid=32508509|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/frou-frou.&lt;/ref&gt; The first use the French ''Wiktionnaire'' lists is Honoré Balzac, ''La Cousine Bette'', 1846.&lt;ref&gt;{{Cite journal|date=2023-06-03|title=froufrou|url=https://fr.wiktionary.org/w/index.php?title=froufrou&amp;oldid=32330124|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/froufrou.&lt;/ref&gt;

''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 &quot;kind of women's hairstyle&quot;:&lt;blockquote&gt;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)&lt;/blockquote&gt;''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 &quot;small, scalelike glittering disks.&quot;&lt;ref name=&quot;:7&quot; /&gt;(216) The French ''Wiktionnaire'' defines ''paillette'' as &quot;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.]&quot;&lt;ref name=&quot;:8&quot;&gt;{{Cite journal|date=2024-03-18|title=paillette|url=https://fr.wiktionary.org/w/index.php?title=paillette&amp;oldid=33809572|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/paillette.&lt;/ref&gt;

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.&lt;ref&gt;“Sequin, N.” ''Oxford English Dictionary'', Oxford UP, September 2023,  https://doi.org/10.1093/OED/4074851670.&lt;/ref&gt; The first instance of ''spangle'' as &quot;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&quot; is from c. 1420.&lt;ref&gt;“Spangle, N. (1).” ''Oxford English Dictionary'', Oxford UP, July 2023,  https://doi.org/10.1093/OED/4727197141.&lt;/ref&gt; The first use of ''paillette'' listed in the French ''Wiktionnaire'' is in Jules Verne in 1873 to describe colored spots on icy walls.&lt;ref name=&quot;:8&quot; /&gt;

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:&lt;blockquote&gt;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.&lt;ref name=&quot;:9&quot; /&gt;{{rp|6–7}}&lt;/blockquote&gt;

==== 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.)&lt;blockquote&gt;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) — &quot;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.&quot; 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&quot; 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 &quot;tissue&quot; 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 &quot;gold wire&quot; 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, &amp;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. &quot;Gold and silver,&quot; says Dr Birdwood in his ''Handbook to the British-Indian Section, Paris Exhibition'', 1878, &quot;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.&quot;

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 &quot;orris,&quot; 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, &amp;c., and the remainder is worked up in the gold lace trade.&lt;ref&gt;William Chandler Roberts-Austen and H. Bauerman [W.C.R. — H.B.]. &quot;Gold and Silver Lace.&quot; In &quot;Gold.&quot; ''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.&lt;/ref&gt;&lt;/blockquote&gt;

==== Honiton Lace ====

Kate Stradsin says,&lt;blockquote&gt;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.&lt;ref&gt;Strasdin, Kate. &quot;Rediscovering Queen Alexandra’s Wardrobe: The Challenges and Rewards of Object-Based Research.&quot; ''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 &quot;Margaret Tomlinson, ''Three Generations in the Honiton Lace Trade: A Family History'', self-published, 1983.&quot;&lt;/ref&gt;&lt;/blockquote&gt;

[[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 &quot;''exubérance''&quot; in passementerie in French design, including the development and widespread use of the Jacquard loom.&lt;ref&gt;{{Cite journal|date=2023-06-10|title=Passementerie|url=https://fr.wikipedia.org/w/index.php?title=Passementerie&amp;oldid=205068926|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Passementerie.&lt;/ref&gt;

==== 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,&lt;ref name=&quot;:7&quot;&gt;Lewandowski, Elizabeth J. ''The Complete Costume Dictionary''. Scarecrow Press, 2011.&lt;/ref&gt;{{rp|233}} so Alençon point is &quot;a two thread [needlepoint] lace.&quot;&lt;ref name=&quot;:7&quot; /&gt;{{rp|7}} Alençon lace has a &quot;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.&quot;&lt;ref name=&quot;:7&quot; /&gt;{{rp|7}}

The sample of point d'Alençon lace (right), from 1750–1775, shows the linen mesh that the lace was constructed on.&lt;ref&gt;{{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.&lt;/ref&gt; 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:&lt;blockquote&gt;La '''brocatelle''' est un type de tissu datant du &lt;abbr&gt;xvi&lt;sup&gt;e&lt;/sup&gt;&lt;/abbr&gt; 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.&lt;ref&gt;{{Cite journal|date=2023-06-01|title=Brocatelle|url=https://fr.wikipedia.org/w/index.php?title=Brocatelle&amp;oldid=204796410|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Brocatelle.&lt;/ref&gt;&lt;/blockquote&gt;Which translates to this:&lt;blockquote&gt;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.&lt;/blockquote&gt;The ''Oxford English Dictionary'' says, brocatelle is an &quot;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&quot; between the late 17th century and 1888, the last time this definition was revised.&lt;ref&gt;&quot;brocatelle, n.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/23550. Accessed 4 July 2023.&lt;/ref&gt;

=== 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 &quot;often borrowed [from the French] as a term for all crapy fabrics other than ordinary black mourning crape,&quot;&lt;ref&gt;&quot;crêpe, n.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/44242. Accessed 10 February 2023.&lt;/ref&gt; with usage examples ranging from 1797 to the mid 20th century. Crêpe de chine, it says is &quot;a white or other coloured crape made of raw silk.&quot;

=== 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 &quot;kind of silk gauze&quot; was used in the 19th-century UK and US.&lt;ref&gt;&quot;lisse, n.1.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/108978. Accessed 4 July 2023.&lt;/ref&gt;

=== Satin ===
The pre-1927 ''History of Feminine Fashion'', probably commissioned by Charles Frederick Worth's sons, describes Worth's &quot;insistence on new fabrics, new trimmings, new materials of every description&quot; at the beginning of his career in the mid 19th century:&lt;blockquote&gt;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.&lt;ref name=&quot;:9&quot;&gt;[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.]&lt;/ref&gt;{{rp|6 in printed, 26 in digital book}}&lt;/blockquote&gt;

=== Selesia ===
According to the ''Oxford English Dictionary'', ''silesia'' is &quot;A fine linen or cotton fabric originally manufactured in Silesia in what is now Germany (''Schlesien'').&lt;ref&gt;&quot;Silesia, n.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/179664. Accessed 9 February 2023.&lt;/ref&gt; 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'' — &quot;Of textile fabrics or materials: Thin or flimsy in texture; having little substance or body.&quot;&lt;ref&gt;&quot;sleazy, adj.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/181563. Accessed 9 February 2023.&lt;/ref&gt; — may be related.

=== Shot Fabric ===
According to the ''Oxford English Dictionary'', &quot;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.&quot;&lt;ref&gt;“Shot, ''Adj.''”  ''Oxford English Dictionary'', Oxford UP,  July 2023,  https://doi.org/10.1093/OED/2977164390.&lt;/ref&gt; 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 &quot;rich kind of cloth, often interwoven with gold or silver&quot; or &quot;various rich or fine fabrics of delicate or gauzy texture.&quot;&lt;ref&gt;“Tissue, N.” ''Oxford English Dictionary'', Oxford UP, March 2024, https://doi.org/10.1093/OED/5896731814.&lt;/ref&gt;

== 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.)&lt;blockquote&gt;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 &lt;small&gt;B&lt;/small&gt;.&lt;small&gt;C&lt;/small&gt;. 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 &quot;genre&quot; 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, &amp;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''.&lt;ref&gt;J. H. Pollen [J.H.P.]. &quot;Fan.&quot; ''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.&lt;/ref&gt;&lt;/blockquote&gt;

== 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: &quot;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.&quot;&lt;ref&gt;Holt, Ardern. &quot;Fancy Dress a la Mode.&quot; 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.&lt;/ref&gt; 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 &amp; 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 &amp; Freebody, 1882. Illustr., Lillian Young. (HathiTrust has this.) Later editions: 4th ed — 1884; 1887 (HathiTrust); 6th ed. — 1896 (HathiTrust)


As Leonore Davidoff says, &quot;Every cap, bow, streamer, ruffle, fringe, bustle, glove and other elaboration symbolised some status category for the female wearer.&quot;&lt;ref name=&quot;:1&quot; /&gt;{{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 &quot;Victorian&quot; to our eyes is the line of the silhouette caused by the foundation undergarments as well as the many &quot;elaborations&quot;&lt;ref name=&quot;:1&quot; /&gt;{{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 &quot;France. Feather or plume from an egret or heron.&quot;&lt;ref name=&quot;:7&quot; /&gt;(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&lt;blockquote&gt;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.&lt;p&gt;
White veils or lace lappets must be worn with the feathers. The veils should not be longer than 45 inches.&lt;ref&gt;{{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/.&lt;/ref&gt;&lt;/blockquote&gt;[[Social Victorians/Victorian Things#Ostrich Feathers and Prince of Wales's Feathers|This fashion was imported from France]] in the mid 1770s.&lt;ref&gt;&quot;Abstract&quot; for Blackwell, Caitlin. &quot;'&lt;nowiki/&gt;''The Feather'd Fair in a Fright''': The Emblem of the Feather in Graphic Satire of 1776.&quot; ''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).&lt;/ref&gt;

Separately, a secondary heraldic emblem of the Prince of Wales has been a specific arrangement of 3 ostrich feathers in a gold coronet&lt;ref&gt;{{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&amp;oldid=1120556015|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Prince_of_Wales's_feathers.&lt;/ref&gt; since King Edward III (1312–1377&lt;ref&gt;{{Cite journal|date=2022-12-14|title=Edward III of England|url=https://en.wikipedia.org/w/index.php?title=Edward_III_of_England&amp;oldid=1127343221|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Edward_III_of_England.&lt;/ref&gt;).

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 &quot;Daisy&quot; 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. &quot;'''The Feather'd Fair in a Fright'&lt;nowiki/&gt;'': The Emblem of the Feather in Graphic Satire of 1776.&quot; 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.
* &quot;Prince of Wales's feathers.&quot; ''Wikipedia'' https://en.wikipedia.org/wiki/Prince_of_Wales%27s_feathers (accessed November 2022). ['''Add women to this page''']
* Simpson, William. &quot;On the Origin of the Prince of Wales' Feathers.&quot; ''Fraser's magazine'' 617 (1881): 637-649. Hathi Trust https://babel.hathitrust.org/cgi/pt?id=chi.79253140&amp;view=1up&amp;seq=643&amp;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 &quot;Last Knight&quot; 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 &quot;the most prestigious and historic order of chivalry in the world&quot; because of its long history and strict limitations on membership.&lt;ref name=&quot;:10&quot;&gt;{{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&amp;oldid=980340875|journal=Wikipedia|language=en}}&lt;/ref&gt; 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,&lt;ref name=&quot;:12&quot;&gt;Thompson, R[obert]. H[ugh]. &quot;The Golden Fleece in Britain.&quot; Publication of the ''British Numismatic Society''. 2009 https://www.britnumsoc.org/publications/Digital%20BNJ/pdfs/2009_BNJ_79_8.pdf (accessed January 2023).&lt;/ref&gt; the first Protestant to be admitted to the order.&lt;ref name=&quot;:10&quot; /&gt; 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.&lt;ref name=&quot;:10&quot; /&gt;

[[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 &quot;turn of the XV and XVI centuries.&quot;&lt;ref&gt;{{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.&lt;/ref&gt; 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.&lt;ref&gt;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.&lt;/ref&gt;

=== 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 &quot;the rough parts&quot; and the parts that are not the right stone.&lt;ref&gt;&quot;cabochon, n.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/25778. Accessed 7 February 2023.&lt;/ref&gt; 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 &quot;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.&quot;&lt;ref&gt;&quot;baldric, n.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/14849. Accessed 17 May 2023.&lt;/ref&gt; This sense has been in existence since c. 1300.

=== Cuirass ===
According to the ''Oxford English Dictionary'', the primary sense of ''cuirass'' is &quot;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 ....&quot;&lt;ref&gt;&quot;cuirass, n.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/45604. Accessed 17 May 2023.&lt;/ref&gt;

[[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 &quot;the Restoration of the Monarchy in 1660.&quot;&lt;ref name=&quot;:3&quot;&gt;Joll, Christopher. &quot;Tales of the Household Cavalry, No. 1. Roles.&quot; 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.&lt;/ref&gt;{{rp|1}} Regimental Historian Christopher Joll says, &quot;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.&quot;&lt;ref name=&quot;:3&quot; /&gt;{{rp|1–2}} The 1st and 2nd Life Guards were formed from &quot;the Troops of Horse and Horse Grenadier Guards ... in 1788.&quot;&lt;ref name=&quot;:3&quot; /&gt;{{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.&lt;ref name=&quot;:3&quot; /&gt;{{rp|3}} Besides arresting the Cato Steet conspirators in 1820 &quot;and guarding their subsequent execution,&quot; the Household Cavalry contributed to the &quot;the expedition to rescue General Gordon, who was trapped in Khartoum by The Mahdi and his army of insurgents&quot; in 1884.&lt;ref name=&quot;:3&quot; /&gt;{{rp|3}} In 1887 they &quot;were involved ... in the suppression of rioters in Trafalgar Square on Bloody Sunday.&quot;&lt;ref name=&quot;:3&quot; /&gt;{{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 &quot;scarlet tunics, ... full blue breeches, scarlet hose and shoes, lappet wigs&quot; as well as items associated with weapons and armor.&lt;ref name=&quot;:14&quot;&gt;“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.&lt;/ref&gt;{{rp|p. 34, Col. 2a}}

Founded in England in 1656 as Foot Guards, this infantry regiment &quot;was granted the 'Grenadier' designation by a Royal Proclamation&quot; at the end of the Napoleonic Wars.&lt;ref&gt;{{Cite journal|date=2023-04-22|title=Grenadier Guards|url=https://en.wikipedia.org/w/index.php?title=Grenadier_Guards&amp;oldid=1151238350|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Grenadier_Guards.&lt;/ref&gt; 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.&lt;ref&gt;{{Cite journal|date=2022-07-24|title=Lord Wentworth's Regiment|url=https://en.wikipedia.org/w/index.php?title=Lord_Wentworth%27s_Regiment&amp;oldid=1100069077|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Lord_Wentworth%27s_Regiment.&lt;/ref&gt;

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.&lt;ref&gt;{{Cite journal|date=2023-04-22|title=Cavalier|url=https://en.wikipedia.org/w/index.php?title=Cavalier&amp;oldid=1151166569|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Cavalier.&lt;/ref&gt;

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,&lt;blockquote&gt;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.&lt;ref&gt;{{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/.&lt;/ref&gt;&lt;/blockquote&gt;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:&lt;blockquote&gt;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.&lt;ref&gt;{{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/.&lt;/ref&gt;&lt;/blockquote&gt;

==== 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.&lt;ref name=&quot;:14&quot; /&gt;{{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.&lt;ref name=&quot;:4&quot;&gt;{{Cite journal|date=2023-09-30|title=Battle of Waterloo|url=https://en.wikipedia.org/w/index.php?title=Battle_of_Waterloo&amp;oldid=1177893566|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Battle_of_Waterloo.&lt;/ref&gt; The 1st Life Guards were on &quot;the extreme right&quot; of a French countercharge and &quot;kept their cohesion and consequently suffered significantly fewer casualties.&quot;&lt;ref name=&quot;:4&quot; /&gt;

== Photography ==

== Footnotes ==
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{{professional responsibility}}

[[w:Natural_law|Natural law]] is a probable source of most [[w:List_of_ancient_legal_codes|Ancient legal codes]].  Revealed law includes for example the [[w:Noahide covenant|Noahide covenant]] and its derivative [[w:Mosaic law|Mosaic law]], which were the first to introduce the concept of [[w:Equal_justice_under_law|equal justice under law]] or [[w:Equality_before_the_law|equality before the law]], a concept later expressed in [[w:Pericles_funeral_oration|Pericles funeral oration]] and engraved on the West Pediment, above the front entrance of the [[w:United_States_Supreme_Court_building|United States Supreme Court building]].  According to Aristotle's Nicomachean [[w:Ethics (Aristotle)|Ethics]] and [[w:Politics (Aristotle)|Politics]], [[w:Justice_(virtue)|Justice]] is the chief [[w:Cardinal_virtue|cardinal virtue]], and as such deeply rooted in our human nature as social or political animals.  Promoting this [[w:Rule_of_law|rule of law]] he states &quot;It is more proper that law should govern than any one of the citizens: upon the same principle, if it is advantageous to place the supreme power in some particular persons, they should be appointed to be only guardians, and the servants of the laws.&quot;&lt;ref&gt;Aristotle Politics [[s:Politics_(Ellis)/Book_3#CHAPTER_XVI|Book 3 chapter 16]]&lt;/ref&gt; As opposed to the [[w:Divine_right_of_kings|divine right of kings]].  [[wikipedia:Ancient_Egypt#Legal_system|Ancient_Egypt#Legal_system]], [[w:Code_of_Ur-Nammu|Code of Ur-Nammu]], [[w:Code of Hammurabi|Code of Hammurabi]], [[w:Laws of Solon|Laws of Solon]], [[w:Draconian constitution|Draconian constitution]], [[w:Twelve Tables|Law of the Twelve Tables]], [[w:Magna Carta|Magna Carta]], [[w:Common law|Common law]], [[w:List of Latin legal terms|List of Latin legal terms]]. 
[https://www.sefaria.org/sheets/326346?lang=bi Equal Justice under law - Noachide Covenant Source Sheet]

[[w:Rechtsstaat|Rechtsstaat]], constitutional state, [[w:Rule_according_to_higher_law|Rule according to higher law]]

[[w:Corpus Juris Civilis|Corpus Juris Civilis]] ([[w:Code of Justinian|Code of Justinian]] compiles imperial constitutions, [[w:Digest (Roman law)|Digest]] and Pandects, [[w:Institutes (Justinian)|Institutes]] is student textbook), used both the ''[[w:Codex_Theodosianus|Codex Theodosianus]]'' and the fourth-century collections embodied in the ''[[w:Codex_Gregorianus|Codex Gregorianus]]'' and ''[[w:Codex_Hermogenianus|Codex Hermogenianus]]'', which provided the model for division into books that were themselves divided into titles.  Revised into Greek, as [[w:Basilika|Basilika]] ''([[Greek language|Greek]]: τὰ βασιλικά, 'imperial laws'), through the 15th century continued to form the basis of the Eastern Roman empire's laws, for local legal codes in the Balkans during the following Ottoman period, adjacent to [[w:Ottoman_law|Ottoman law]], and later formed the basis of the [[w:Judiciary_of_Greece|legal code of Modern Greece]].  Never became well established in the Western Empire, and was only r''ecovered in the Middle Ages, being &quot;received&quot; or imitated as [[w:Private_law|private law]].  Its [[w:Public_law|public law]] content was quarried for arguments by both secular and ecclesiastical authorities. This recovered Roman law, in turn, became the foundation of law in all [[w:Civil_law_(legal_system)|civil law]] jurisdictions. The provisions of the ''Corpus Juris Civilis'' also influenced the [[w:Canon_law_(Catholic_Church)|canon law]] of the Catholic Church: it was said that ''ecclesia vivit lege romana'' – the church lives by Roman law.&lt;ref&gt;Cf. ''[[Lex Ripuaria]]'', tit. 58, c. 1: &quot;Episcopus archidiaconum jubeat, ut ei tabulas secundum legem romanam, qua ecclesia vivit, scribere faciat&quot;. ([https://books.google.com/books?id=7I8GAAAAQAAJ&amp;pg=PA169&amp;dq=%22secundum+legem+romanam+qua+ecclesia+vivit])&lt;/ref&gt; Its influence on [[w:Common_law|common law]] legal systems, although some basic concepts survived through [[w:Norman_law|Norman law]] – such as the contrast, especially in the ''Institutes'', between &quot;law&quot; (statute) and custom. The Corpus continues to have a major influence on [[public international law]]. Its four parts thus constitute the foundation documents of the [[w:Western_legal_tradition|Western legal tradition]].

1660's [[w:Clarendon_Code|Clarendon Code]] rejected the [[w:Solemn_League_and_Covenant_of_1643|Solemn League and Covenant of 1643]] and the [[w:Long_Parliament|Long Parliament]], [[w:English_Bill_of_Rights_of_1689|English Bill of Rights of 1689]], [[w:Acts_of_Union_1707|Acts of Union 1707]], [[w:Constitution_of_the_United_Kingdom|Constitution of the United Kingdom]], [[:fr:Constitution_française_de_1791|Constitution française de 1791]] 

[[w:Virginia_Bill_of_Rights|Virginia Bill of Rights]], [[w:US_Bill_of_Rights|US Bill of Rights]]

[[s:Washington State Constitution]], [[w:Washington State Constitution]], [[w:Constitution of Oregon|Constitution of Oregon]] - [[wikisource:Oregon_Constitution|s:Oregon Constitution]], [[w:Constitution of California|Constitution of California]] - [[s:Constitution of California]],  [[w:Law_of_California|Law of California]].

[[w:William_Blackstone|William Blackstone]]'s [[w:Commentaries_on_the_Laws_of_England|Commentaries on the Laws of England]]. 

[[w:Hugo_Grotius|Hugo Grotius]]'s : ''[[w:De_jure_belli_ac_pacis|De jure belli ac pacis]]'' (''On the Law of War and Peace''), and the ''[[w:Mare_Liberum|Mare Liberum]]'' 

[[w:Model_Penal_Code|Model Penal Code]] - ALI, [[w:Legal_terminology_textbook|legal terminology textbook]], [[w:Template:Rights|Template:Rights]] 

{{Wikisource|Commentaries on the Laws of England|''Commentaries on the Laws of England''}}

== Forum and Jurisdiction ==
[[w:choice of law|choice of law]], [[w:conflict of laws|conflict of laws]]:  [[w:lex causae|lex causae]] should be determined by the [[w:locus in quo|locus in quo]] &quot;place in which&quot;.   [[w:Lex loci|Lex loci]], Lex loci delictus

[[w:Characterisation (law)|Characterisation]]

[[w:Incidental question|Incidental question]]

[[w:Renvoi|Renvoi]]

[[w:Enforcement of foreign judgments|Enforcement of foreign judgments]], [[w:Dépeçage|Dépeçage]]

[[w:private-law|private-law]]

Although the [[w:Multnomah County Circuit Court|Multnomah County Circuit Court]] has personal and territorial jurisdication, it does not have [[w:Subject_matter_jurisdiction|subject matter jurisdiction]], therefore is a [[w:forum non conveniens|forum non conveniens]]

[[w:American Bar Association Model Rules of Professional Conduct|American Bar Association Model Rules of Professional Conduct]]

[[w:Law school|Law school]], [[w:American Bar Association|American Bar Association]], [[w:Oregon State Bar|Oregon State Bar]]

=== International Law ===
'''''[[w:Erga_omnes|Erga omnes]]''''' [[w:Rights|rights]] or [[w:Obligations|obligations]] are owed toward all. ''Erga omnes'' is a Latin phrase which means &quot;towards all&quot; or &quot;towards everyone&quot;. For instance, a [[w:Property_right|property right]] is an ''erga omnes'' entitlement.

An {{lang|la|erga omnes}} obligation exists because of the universal and undeniable interest in the perpetuation of critical rights and the prevention of their breach. Consequently, any state has the right to invoke [[state responsibility]]&lt;ref name=&quot;Hathaway Mills Poston 2023 k590&quot;&gt;{{cite journal|last=Hathaway|first=Oona A.|last2=Mills|first2=Maggie|last3=Poston|first3=Thomas M.|date=2023-11-08|title=War Reparations: The Case for Countermeasures|url=https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4548945|journal=Stanford Law Review|volume=76|issue=5|access-date=2023-12-07}}&lt;/ref&gt; in order to hold the responsible state legally liable and required to pay reparations. {{lang|la|Erga omnes}} obligations attach when there is a serious breach of peremptory norms of international law like those against [[piracy]], [[genocide]] and [[War of aggression|wars of aggression]].&lt;ref name=&quot;Hook Diamond 2023 w500&quot;&gt;{{cite web|url=https://www.atlanticcouncil.org/in-depth-research-reports/issue-brief/the-case-for-seizing-russian-assets-of-aggression/|title=The case for seizing Putin regime assets|last=Hook|first=Kristina|last2=Diamond|first2=Yonah|date=2023-08-23|website=Atlantic Council|access-date=2023-12-07}}&lt;/ref&gt;&lt;ref name=&quot;UN p799&quot;&gt;{{cite web|url=https://legal.un.org/legislativeseries/pdfs/chapters/book25/english/book25_part2_ch3.pdf|title=Serious Breaches of Obligations under Peremptory Norms of General International Law|date=2001|website=United Nations|access-date=25 December 2023}}&lt;/ref&gt; The concept was recognized in the [[International Court of Justice]]'s decision in the ''[[Case Concerning Barcelona Traction, Light, and Power Company, Ltd|Barcelona Traction]]'' case&lt;ref&gt;{{Cite journal|last=Simma|first=Bruno|author-link=Bruno Simma|last2=Paulus|first2=Andreas L.|author-link2=Andreas Paulus|year=1998|title=The 'International Community': Facing the Challenge of Globalization|journal=[[European Journal of International Law]]|language=en|volume=9|issue=2|pages=266–277|doi=10.1093/ejil/9.2.266|issn=0938-5428|doi-access=free}}&lt;/ref&gt; [(''Belgium v Spain'') (Second Phase) ICJ Rep 1970 3 at paragraph 33]:  &quot;''an essential distinction should be drawn between the obligations of a State towards the international community as a whole, and those arising [[w:Bilateral_treaty|vis-à-vis another State]] in the field of [[w:Diplomatic_protection|diplomatic protection]]. By their very nature, the former are the concern of all States..&quot;.''

[[w:Jus_cogens|Jus cogens]] ([[Latin]] for &quot;compelling law&quot;) is a ''peremptory norm'' &lt;ref&gt;{{Cite web|url=http://oxforddictionaries.com/definition/jus+cogens|title=Jus cogens &amp;#124; Definition of jus cogens in English by Oxford Dictionaries|archive-url=https://web.archive.org/web/20110717135623/http://oxforddictionaries.com/definition/jus+cogens|archive-date=July 17, 2011|url-status=dead}}&lt;/ref&gt;, a fundamental principle of [[international law]] that is accepted by the international community of [[Sovereign state|states]] as a [[Norm (sociology)|norm]] from which no [[derogation]] is permitted.  There is no universal agreement, but generally accepted that ''jus cogens'' bans [[genocide]], maritime [[piracy]], enslaving in general (i.e. [[slavery]] as well as [[History of slavery|slave trade]]), [[War of aggression|wars of aggression and territorial aggrandizement]], and generally as well [[torture]], and [[refoulement]].&lt;ref&gt;M. Cherif Bassiouni. (Autumn 1996) &quot;International Crimes: 'Jus Cogens' and 'Obligatio Erga Omnes{{'&quot;}}. ''Law and Contemporary Problems''. Vol. 59, No. 4, p. 68.&lt;/ref&gt;

The [[w:Vienna_Convention_on_the_Law_of_Treaties|Vienna Convention on the Law of Treaties]] has 115 signatories, excluding U.S.  [[w:Multilateral_treaty|Multilateral treaty]].

[[w:Customary_international_law|Customary international law]] is an aspect of [[international law]] involving the principle of custom. Along with [[Sources of international law#General principles of law|general principles of law]] and treaties, custom is considered by the [[International Court of Justice]], [[Jurist|jurists]], the [[United Nations]], and its [[member states]] to be among the primary [[sources of international law]].  Rule becomes customary international if both (1) There is a [[Sources of international law#State practice|state practice]] that &quot;appears to be sufficiently widespread, representative as well as consistent&quot; showing that a significant number of states have used and relied on the rule in question and the concept has not been rejected by a significant number of states,&lt;ref name=&quot;Wood Law 2014 h359&quot;&gt;{{cite web|url=https://digitallibrary.un.org/record/774305|title=Second report on identification of customary international law by Michael Wood, Special Rapporteur|last=Wood|first=Michael C.|date=2014-05-22|publisher=UN|access-date=2023-12-13}}&lt;/ref&gt;&lt;ref name=&quot;Legal g698&quot;&gt;{{cite web|url=https://internationallaw.uslegal.com/sources-of-international-law/customary-international-law/|title=Customary International Law – International Law|website=USLegal|access-date=2023-12-11}}&lt;/ref&gt; (2) states were motivated by a belief that they were legally compelled to accept the legitimacy of the rule in question because customary international law obligated them to do so {{lang|la|([[Opinio juris sive necessitatis|opinio juris]])}}.&lt;ref name=&quot;Wood Law 2014 h359&quot; /&gt;

In [[w:International_courts|international courts]], legal submissions by [[w:Intervention_(law)|intervenors]] are called '''[[w:Amicus_curiae|amicus curiae]] observations'''.

'''''[[w:Dedimus_potestatem|dedimus potestatem]]''''' (Latin for &quot;we have given the power&quot;) is a [[w:Writ|writ]] whereby commission is given to one or more private persons for the expedition of some act normally performed by a judge

== Criminal Procedure ==
[[w:Arraignment|Arraignment]] on charges, [[w:Pleading|Pleadings]]. An [[w:Allegation|allegation]] is a claim of an unproven fact by a [[w:Party_(law)|party]] in a pleading, charge, or defense.

[[w:Defense (legal)|Legal Defense]]

A [[w:Demurrer|Demurrer pleading]] is an objection to the charging information, insufficiency of allegations.  &quot;So what?&quot;  

[[w:affirmative defense|Affirmative defense]]s claim [[w:justification (jurisprudence)|justification]], [[w:necessity (criminal law)|necessity]], [[w:Defence of property|defense of property]], [[w:self-defense|self-defense]], [[w:Lesser_of_two_evils_principle|choice of evils]].  Else a [[w:mistake of law|mistake of law]] that a reasonable person might make.

===[[w:United States criminal procedure|Criminal procedure in the United States]]===
[[#Searches and Seizures|#4th: No Unlawful Searches and Seizures]]

[[#Due Process of Law, Indictments by Grand Jury, Prohibited Double Jeopardy, compulsory Self-incrimination, Takings|#5th:  Due Process of Law, Indictments by Grand Jury, no Double Jeopardy, no compulsory Self-incrimination, no Takings]]

[[#Trial by Jury, Speedy and Public, with Assistance of Counsel|#6th: Speedy and Public Trial by Jury of Vicinage, with Confrontation, Compulsory process, and Assistance of Counsel]]

[[#Cruel and Unusual Punishment prohibited|#8th: Cruel and Unusual Punishment prohibited]]

SCOTUS has [[w:Incorporation of the Bill of Rights|incorporated and applied]] the above protections of these 4th, 5th, 6th, and 8th amendments to the states through the [[w:Fourteenth Amendment to the United States Constitution#Due%20Process%20Clause|Due Process Clause of the Fourteenth Amendment]].

[[w:Template:Evidence law]]

[[w:Federal_Rules_of_Evidence|Federal Rules of Evidence]] also adopted by many states:  [https://www.oregonlegislature.gov/bills_laws/ors/ors040.html ORS 40 - Oregon Rules of Evidence in both civil and criminal procedure] has approximately same rule numbers as the FRE, with some additions. [https://casetext.com/statute/california-codes/california-evidence-code California Evidence Code] uses a slightly different numbering scheme.

[[w:Judicial notice]]  FRE 201 covers judicial notice of adjudicative facts, which are those concerning the parties to a proceeding, but not of legislative facts, which are general.

FRE 201(b) permits judges to take judicial notice of two categories of facts:

# Those that are &quot;generally known within the territorial jurisdiction of the trial court&quot; (e.g. locations of streets within the court's jurisdiction) or
# Those that are &quot;capable of accurate and ready determination by resort to sources whose accuracy cannot reasonably be questioned&quot; (e.g. the day of the week on a certain date).

FRE 201(c) notes that judicial notice may be permissive or mandatory.

[[w:Federal_Rules_of_Criminal_Procedure|Federal Rules of Criminal Procedure]]

[https://www.courts.oregon.gov/rules/UTCR/2023_UTCR.pdf Oregon Uniform Trial Court Rules]

[https://www.oregonlegislature.gov/bills_laws/ors/ors135.html ORS 135 Criminal Procedure] 

[[w:preliminary hearing|preliminary hearing]]  

=== [[w:Pretrial motion|Pre-trial motion]] practice ===
[[w:Motion_to_compel|Motions to compel]], usually related to [[w:Discovery_(law)|discovery]].   

Motion to suppress evidence obtained by unlawful means, such as an arrest without probable cause.

&quot;Criminal Law in Oregon&quot; by OSB (2022 Vol. 1):

12.1-1  a) &quot;providing the accused with sufficient information to make an informed plea;  (4) avoiding unnecessary and repetitious trials by '''exposing latent procedural or constitutional issues and providing remedies''' for them before trial. (5) reducing interruptions and complications of trials by '''identifying issues collateral to guilt or innocence and determining them before trial''' ..&quot; may be needed to identify and preserve issues for subsequent review on appeal or to meet the the exhaustion requirements for federal habeas corpus relief.

[https://www.courts.oregon.gov/rules/UTCR/2024_UTCR.pdf Oregon Uniform Trial Court Rules (UTCR)]

UTCR 2.010 Form of Documents

UTCR 2.030 Matters under Advisement

UTCR 4.010 Time for Filing

UTCR 4.050 Oral Argument

UTCR 4.060 Motion to Suppress Evidence

[https://www.courts.oregon.gov/rules/Documents/Multnomah_SLR_2024.pdf Supplemental Local Rules (SLR) for Multnomah County Circuit]

A &quot;'''motion for [[w:Summary_judgment|summary judgment]]'''&quot; asks the court to decide that the available evidence, even if taken in the light most favorable to the non-moving party, supports a ruling in favor of the moving party. This motion is usually only made when sufficient time for discovering all evidence has expired. For summary judgment to be granted in most jurisdictions, a two-part standard must be satisfied: (i) no genuine issue of material fact can be in dispute between the parties, and (ii) the moving party must be entitled to judgment as a matter of law.   It is a [[w:Dispositive_motion|dispositive motion]].

Judgement as a matter of law (JMOL) replaces JNOV (Judgement [[w:Non_obstante_veredicto|non obstante veredicto]]).

A &quot;'''motion for a [[w:Directed_verdict|directed verdict]]'''&quot; asks the court to rule that the plaintiff or prosecutor has not proven the case, and there is no need for the defense to attempt to present evidence. This motion is made after the plaintiff has rested its case, and prior to the defense presenting any evidence.

=== Capacity to litigate, [[w:Competence_(law)|Competence]], and [[w:Insanity_defense|Insanity]] defense ===
[https://www.theatlantic.com/magazine/archive/2019/04/mind-fixers-anne-harrington/583228/ Psychiatry's Incurable Hubris], [https://www.counterpunch.org/2021/08/06/pathologizing-dissent/ Pathologizing Dissent]

[[w:User:Jaredscribe/Psychodynamic theory|User:Jaredscribe/Psychodynamic theory]]

[[w:User:Jaredscribe/Psycholysis|User:Jaredscribe/Psycholysis]]

[https://caselaw.nationalarchives.gov.uk/ewcop/2023/40 &lt;nowiki&gt;A NHS Trust v ST &amp; Ors [2023] EWCOP 40&lt;/nowiki&gt;]

[https://www.courtofprotectionhub.uk/cases/a-nhs-trust-v-st-ors-2023-ewcop-40 Case summary Judge Roberts]:  ''&lt;nowiki/&gt;'The question which I must answer in the light of this evidence is whether ST is thereby rendered unable to make a decision in relation to her medical care because of an impairment of, or disturbance in the functioning of, her mind or brain.'''

She is satisfied it is the case here because, broadly, of the trauma suffered by ST by admission to, and long stay in hospital, and her fear of dying. Given the decision ST lacked capacity to decide on her medical treatment, it followed she also lacked litigation capacity.

=== Trial and Argumentation===
Must be [[w:concurrence|concurrence]] between [[w:Actus reus|Actus reus]] and [[w:mens rea|mens rea]], except where there is [[w:strict liability|strict liability]].  [[w:inchoate offense|inchoate offense]].

[[w:Witness|Witness]], [[w:direct examination|direct examination]], [[w:cross-examination|cross-examination]], impeachment and rehabilitation of witnesses.
[[w:Objection_(argument)|Objection_]], [[w:argument map|argument map]]  Toulmin

[[w:falsus in uno, falsus in omnibus|falsus in uno]]

=== Role of the Prosecutor ===
The [[w:District_Attorney|District Attorney]] is the chief [[w:Prosecutor|prosecutor]] in most American [[w:Jurisdiction|jurisdiction]]&lt;nowiki/&gt;s.  A [[w:Private_attorney_general|Private attorney general]]  or '''public interest lawyer''' can bring a lawsuit in the [[w:Public_interest|public interest]], often as a [[w:Class_action|class action]].  [[w:Cause_lawyer|Cause lawyer]]. '''''[[w:Qui_tam|Qui tam]] pro domino rege quam pro se ipso in hac parte sequitur''''', meaning &quot;[he] who sues in this matter for the king as well as for himself.&quot;  fell into disuse in [[England and Wales]] following the [[Common Informers Act 1951]] but remains current in the [[United States]] under the [[False Claims Act]], {{UnitedStatesCode|31|3729}} ''et seq.'', which allows a private individual, or &quot;[[whistleblower]]&quot; (or [[Relator (law)|relator]]), with knowledge of past or present [[fraud]] committed against the [[Federal government of the United States|federal government]] to bring suit on its behalf.


Don't do [[w:Prosecutorial_misconduct|Prosecutorial misconduct]].

[[w:American_Bar_Association|American Bar Association]] [https://www.americanbar.org/groups/criminal_justice/standards/ProsecutionFunctionFourthEdition/ Criminal Justice Standards for the Prosecution Function (2017) 4th ed.] 

3-1.2 (a) The prosecutor is an administrator of justice, a zealous advocate, and an officer of the court. The prosecutor’s office should exercise sound discretion and independent judgment in the performance of the prosecution function.

(b) The primary duty of the prosecutor is to seek justice within the bounds of the law, not merely to convict. The prosecutor serves the public interest and should act with integrity and balanced judgment to increase public safety both by pursuing appropriate criminal charges of appropriate severity, and by exercising discretion to not pursue criminal charges in appropriate circumstances. The prosecutor should seek to protect the innocent and convict the guilty, consider the interests of victims and witnesses, and respect the constitutional and legal rights of all persons, including suspects and defendants.

(e) The prosecutor should be knowledgeable about, consider, and where appropriate develop or assist in developing alternatives to prosecution or conviction that may be applicable in individual cases or classes of cases. The prosecutor’s office should be available to assist community efforts addressing problems that lead to, or result from, criminal activity or perceived flaws in the criminal justice system.

(f) The prosecutor is not merely a case-processor but also a problem-solver responsible for considering broad goals of the criminal justice system. The prosecutor should seek to reform and improve the administration of criminal justice, and when inadequacies or injustices in the substantive or procedural law come to the prosecutor's attention, the prosecutor should stimulate and support efforts for remedial action. The prosecutor should provide service to the community, including involvement in public service and Bar activities, public education[...]


3-2.1(c) ''If a particular matter requires the appointment of a [[w:Special_prosecutor|special prosecutor]] from outside the office, adequate funding for this purpose should be made available. Such special prosecutors should know and are governed by applicable conflict of interest standards for prosecutors. A private attorney who is paid by, or who has an attorney-client relationship with, an individual or entity that is a victim of the charged crime, or who has a personal or financial interest in the prosecution of particular charges, or who has demonstrated any impermissible bias relevant to the particular matter, should not be permitted to serve as prosecutor in that matter.''

=== Role of the Defense Attorney ===
[https://www.osbar.org/_docs/rulesregs/orpc.pdf Oregon rules of professional conduct]

[https://www.osbar.org/surveys_research/idtf/annot1.html OSBAR general standards for representation]

[https://www.osbar.org/ethics/ethicsops.html OSBAR ethics opinions]

=== Israel ancient and modern ===
[[w:Sanhedrin|Sanhedrin]] - criminal procedure, capital offenses

[[w:Makkot|Makkot]] - lashes and other punishments

[[w:Shevuot|Shevuot]] - oaths and consequences

== Criminal Law ==
[[w:Template:Criminal law]]

[[w:Criminal law in the United States|Criminal law in the United States]]

[https://docs.google.com/document/d/1CGK_IrUtycQ0lJSxNGcwwhAUdbBN0bbDnxJJlmJvtOM/edit Excerpts from Oregon Criminal Law and Procedure]

'''Multiplicity''', also known as ''allied offenses of similar import'', is the situation where two or more allegations allege the same offense, or a situation where one defined offense necessarily includes another. Accounts may also be multiplicious if two or more describe substantially the same misconduct in different ways. For example, assault and disorderly conduct may be multiplicious if facts and evidence presented at trial prove that the disorderly conduct consists solely of the assault. That is to say, if all the elements contained in one are all in another they are allied offenses of similar import.  [[w:Motion_(legal)#To_dismiss|Motion_(legal)#To_dismiss]]. 

== [[w:Torts|Torts]], [[w:Contracts|Contracts]], and Damages ==
[[w:Seder_Nezikin|Seder Nezikin]]: [[w:Bava_Kamma|Bava Kamma]], [[w:Bava_Metzia|Bava Metzia]], [[w:Bava_Batra|Bava Batra]]

[[w:Inter_partes|Inter partes]], [[w:In_rem|in rem]], [[w:Ex_parte|ex parte]], [[w:In_personam|In_personam]], [[w:Quasi_in_rem|quasi in rem]]

[[w:Privity_of_contract|Privity of contract]]

[[w:Joint_and_several_liability|Joint and several liability]]

[[w:Party_(law)|Party (law)]]

* [[w:Plaintiff|plaintiff]] (person filing a civil [[w:Complaint|complaint]]), [[w:Allegation|alleges]] facts sufficient to establish all the elements of the [[Cause of action|claim]] and thus states a [[cause of action]]. The plaintiff must then carry the [[Legal burden of proof|burden of proof]] and the [[Legal burden of proof|burden of persuasion]] in order to succeed in the [[lawsuit]].
* [[w:Defendant|defendant]] (person sued or charged with a crime).  A [[w:Counter-claim|counter-claim]] asserts that the party (usually a defendant) is entitled to offset the damages awarded to plaintiff by the proportionate share of any responsibility, liability, or fault assigned to the plaintiff by the jury.  
* [[w:Petitioner|petitioner]] (files a petition asking for a court ruling),
* [[w:Respondent|respondent]] (usually in opposition to a petition or an appeal),
* [applicant]] (files an application which may require a ruling on it)
* cross-complainant (a defendant who sues someone else in the same lawsuit).  [[w:Contribution_claim_(legal)|Contribution claim (legal)]] asserts the party (usually a defendant) is entitled to &quot;contribution&quot; from a third party for any money damages awarded to the plaintiff.
* cross-defendant (a person sued by a cross-complainant).  A [[w:Cross-claim|cross-claim]] is asserted by a defendant against other defendants.
* '''[[w:Intervention_(law)|Intervenor]]''' joins ongoing litigation, either as a matter of right or at the discretion of the court, without the permission of the original litigants, on the basis that a [[w:Judgment_(law)|judgment]] may affect the rights of nonparties, who ideally should have the right to be heard.
* [[w:Amicus_curiae|Amicus curiae]]

=== [[w:Civil procedure in the United States]] ===
[[w:Template:US fed civ pro]]

[[w:Civil_discovery_under_United_States_federal_law|Civil discovery under United States federal law]]: methods such as [[interrogatories]], [[Request for production|requests for production of documents]], [[Request for admissions|requests for admissions]] and [[Deposition (law)|depositions]].  Discovery can be obtained from nonparties using [[w:Subpoena_ad_testificandum|subpoena ad testificandum]] or for documents, [[w:Subpoena_duces_tecum|subpoena duces tecum]].

[https://www.oregonlegislature.gov/bills_laws/SiteAssets/ORCP.html Oregon Rules of Civil Procedure] [https://www.oregonlegislature.gov/bills_laws/Pages/orcp.aspx ORCP]

[[w:Harmless error|Harmless error]]

[[w:Stipulated agreement|Stipulated agreement]]

[[w:Ex parte|Ex parte]] non-docketed matters.

== Appeals ==
[[w:Declaratory judgment|Declaratory judgement]].

Article III [[w:Case or Controversy Clause|Case or Controversy Clause]] restricts court's ability to issue [[w:Advisory opinion|Advisory Opinion|]]s, or hearing cases that are either [[w:Ripeness|unripe]] or [[w:Mootness|moot]].  Parties must have [[w:Standing (law)|Standing]].
[[w:Chilling_effect|Chilling_effect]] argument is a rare exception.  In [[w:Roe v. Wade|Roe v. Wade]], for instance, the Court applied the mootness exception for cases &quot;capable of repetition, yet evading review.&quot;

== Constitutional Law and the Supremes ==

=== US Constitutional Law ===
[[w:Template:US Constitution]]

[[w:Template:United_States_constitutional_law|Template:United_States_constitutional_law]], [[w:Template:SCOTUS_horizontal|Template:SCOTUS horizontal]]
[[w:Lists_of_landmark_court_decisions|Lists of landmark court decisions]]

=== Judicial review ===
[[w:Horayot|Horayot]] - appeals and judicial review
[[w:Judicial_review_in_the_United_States|Judicial review in the United States]] began with [[w:Marbury_v._Madison|Marbury v. Madison]] (1803).  Court has no original jurisdiction to issue [[w:Writ_of_mandamus|writ of mandamus]], court invalidated Section 13 of the [[w:Judiciary_Act_of_1789|Judiciary Act of 1789]].  The second decision was [[w:Dred_Scott_v._Sandford|Dred Scott v. Sandford]] invalidating the [[w:Missouri_Compromise|Missouri Compromise]]. In 1865, after the Union's victory, the Court's ruling in ''Dred Scott'' was superseded by the passage of the [[w:Thirteenth_Amendment_to_the_U.S._Constitution|Thirteenth Amendment to the U.S. Constitution]], which abolished slavery, and the [[w:Fourteenth_Amendment_to_the_U.S._Constitution|Fourteenth Amendment]].   During the United States election of 1860, abolitionists formed the new Republican Party, which rejected the ruling as being corrupted by partisanship and non-binding because the court had no jurisdiction. Their Presidential nominee, Abraham Lincoln, stated he would not permit slavery anywhere in the country except where it already existed, which directly contradicted the court's ruling.

[[w:McCulloch_v._Maryland|McCulloch v. Maryland]]

[[w:Judicial_review|Judicial_review]], [[:he:ביקורת_שיפוטית]], [[w:Constitutional_review|constitutional review]], [[:he:חוקתיות]]

[[w:Reasonableness]], [[:he:עילת_הסבירות]]

=== Freedoms of Speech, Press, Assembly ===
[[w:First_Amendment_to_the_United_States_Constitution|First Amendment to the United States Constitution]], first of the ten that constitute the [[w:United_States_Bill_of_Rights|Bill of Rights]]:   ''&quot;Congress shall make no law respecting an [[w:Establishment_of_religion|establishment of religion]], or prohibiting [[w:Free_exercise_clause|the free exercise thereof]]; or abridging the [[w:Freedom_of_speech_in_the_United_States|freedom of speech]], or [[w:Freedom_of_the_press_in_the_United_States|of the press]]; or the right of the people [[w:Freedom_of_Assembly|peaceably to assemble]], and [[w:Right_to_petition_in_the_United_States|to petition the Government for a redress]] of grievances&quot;''

==== [[w:Public_forum|Public forum]]&lt;nowiki/&gt;s, [https://constitution.congress.gov/browse/essay/amdt1-7-7-1/ALDE_00013542/#ALDF_00025595 #1.7.7.1 - the Public Forum] ====

In ''[[w:Hague_v._CIO|Hague v. CIO]]'', the Court reconsidered the issue. [[w:Justice_Owen_Roberts|Justice Owen Roberts]] wrote in ''Hague'':&lt;blockquote&gt;Wherever the title of streets and parks may rest, they have immemorially been held in trust for the use of the public and, time out of mind, have been used for purposes of assembly, communicating thoughts between citizens, and discussing public questions. Such use of the streets and public places has from ancient times, been a part of the privileges, immunities, rights, and liberties of citizens.4&lt;/blockquote&gt;In ''[[w:U.S._Postal_Service_v._Greenburgh_Civic_Associations|U.S. Postal Service v. Greenburgh Civic Associations]]'', the Court stated: &lt;q&gt;''[T]he First Amendment does not guarantee access to property simply because it is owned or controlled by the government,''&lt;/q&gt;15 while in ''[[w:Grayned_v._City_of_Rockford|Grayned v. City of Rockford]]'', the Court stated: &lt;q&gt;'''''The crucial question is whether the manner of expression is basically compatible with the normal activity of a particular place at a particular time'''.''&lt;/q&gt;16 Thus, by the nature of the use to which the property is put or by tradition, some sites are simply not as open for expression as streets and parks are.17 But if government does open non-traditional forums for expressive activities, it '''may not [[w:Viewpoint_discrimination|discriminate on the basis of content or viewpoint]]''' in according access.18

Speech in public forums is '''subject to time, place, and manner regulations''' that take into account such matters as control of traffic in the streets, the scheduling of two meetings or demonstrations at the same time and place, the preventing of blockages of building entrances, and the like.19 Such regulations are closely scrutinized in order to protect free expression, and, to be valid, must be justified without reference to the content or subject matter of speech,20 must serve a significant governmental interest,21 and must leave open ample alternative channels for communication of the information.22 The Court has written in [[w:Ward_v._Rock_Against_Racism|''Ward v. Rock Against Racism'' (1989)]] &lt;blockquote&gt;must be [[w:Narrow_tailoring|narrowly tailored]] to serve the government’s legitimate, content-neutral interests but that it need not be the least restrictive or least intrusive means of doing so. Rather, the requirement of narrow tailoring is satisfied. . .[s]o long as the means chosen are not substantially broader than necessary to achieve the government’s interest. . ..23&lt;/blockquote&gt;A content-neutral time, place, and manner regulation of the use of a public forum must also &lt;q&gt;'''''contain adequate standards to guide the official’s decision and render it subject to effective judicial review.'''''&lt;/q&gt;24

Unlike a content-based licensing scheme, however, it need not &lt;q&gt;adhere to the procedural requirements set forth in ''Freedman''.&lt;/q&gt;25 In ''[[w:Freedman_v._Maryland|Freedman v. Maryland]]'', the Court had set forth certain requirements, including that the &lt;q&gt;burden of proving that the film [or other speech] is unprotected expression must rest on the censor,&lt;/q&gt; and that the censor must, ''&lt;q&gt;'''within a specified brief period, either issue a license or go to court to restrain showing the film. Any restraint imposed in advance of a final judicial determination on the merits must similarly be limited to preservation of the status quo for the shortest fixed period compatible with sound judicial resolution.'''&lt;/q&gt;2''6

A corollary to the rule forbidding regulation based on content is the principle—a merging of free expression and equal protection standards—that government may not discriminate between different kinds of messages in affording access.27 In order to ensure against covert forms of discrimination against expression and between different kinds of content, the Court has insisted that licensing systems be constructed as free as possible of the opportunity for arbitrary administration.28 The Court has also applied its general strictures against prior restraints in the contexts of permit systems and judicial restraint of expression.29

It appears that the government may not deny access to the public forum for demonstrators on the ground that the past meetings of these demonstrators resulted in violence,30 and may not vary a demonstration licensing fee based on an estimate of the amount of hostility likely to be engendered.31 The Court has also suggested that the '''government cannot effectuate a &lt;q&gt;heckler’s veto,&lt;/q&gt;''' the governmental termination of a speech or demonstration because of hostile crowd reaction.32

The Court has defined three categories of public property for public forum analysis.33 First, there is the '''&lt;big&gt;traditional public forum&lt;/big&gt;—places such as streets and parks''' that have traditionally been used for public assembly and debate.34 In such a forum, the government &lt;q&gt;'''may impose reasonable time, place, and manner restrictions on private speech, but restrictions based on content must satisfy strict scrutiny, and those based on viewpoint are prohibited.'''&lt;/q&gt;35 Second, there is the designated public forum, where the government opens property for communicative activity and thereby creates a public forum.36 Such a forum may be limited—hence the expression '''&lt;q&gt;&lt;big&gt;limited public forum&lt;/big&gt;&lt;/q&gt;—for &lt;q&gt;use by certain groups,&lt;/q&gt;''' &lt;q&gt;for example, ''[[w:Widmar_v._Vincent|Widmar v. Vincent]]'' (student groups), or for discussion of certain subjects, for example, ''[[w:City_of_Madison_Joint_School_District_v._Wisconsin_PERC|City of Madison Joint School District v. Wisconsin PERC]]'' (school board business),&lt;/q&gt;'''37 but, within the framework of such legitimate limitations, &lt;q&gt;a content-based prohibition must be narrowly drawn to effectuate a compelling state interest.&lt;/q&gt;'''38 Third, in a '''&lt;q&gt;&lt;big&gt;nonpublic forum,&lt;/big&gt;&lt;/q&gt; or &lt;q&gt;a space that ‘is not by tradition or designation a forum for public communication,’&lt;/q&gt;39 the government &lt;q&gt;may reserve the forum for its intended purposes, communicative or otherwise, as long as the regulation on speech is reasonable and not an effort to suppress expression merely because public officials oppose the speaker’s view.&lt;/q&gt;4'''0

[https://constitution.congress.gov/browse/essay/amdt1-7-7-2/ALDE_00013543/ #1.7.7.2 - Public and Non Public Forums]
Streets, parks, and sidewalks are considered open to public discourse by tradition and are designated as ''traditional public forums''. The government creates a ''designated public forum'' when it intentionally opens a nontraditional forum for public discourse''. Limited public forums'', such as municipal meeting rooms, are nonpublic forums that have been specifically designated by the government as open to certain groups or topics. Traditional public forums cannot be changed to nonpublic forums by governments

==== Content restrictions ====
{{further|Censorship in the United States}}
From the late 1800s to the mid-1900s, various laws restricted speech in ways that are today not allowed, mainly due to societal norms. The government of New York State to create the [[New York Society for the Suppression of Vice]], in 1873, and inspired the creation of the [[Watch and Ward Society]] in Boston in 1878.  City and state governments monitored newspapers, [[Book censorship in the United States|books]], theater, comedy acts, and films for offensive content, and enforced laws with arrests, impoundment of materials, and fines. The [[Comstock laws]] passed by Congress (and related state laws) prohibited sending materials through the U.S. mail that included pornography; information about contraception, abortion, and sex toys; and personal letters mentioning sexual activities. [[Film censorship in the United States|Regulation of American film]] by state and local governments was supplemented by the [[Motion Picture Production Code]] from to 1930 to 1968, in an industry effort to preempt federal regulation. The similar industry-backed [[Comics Code Authority]] lasted from 1954 to 2011.

Some laws were motivated not by morality, but concerns over national security. The [[Office of Censorship]] suppressed communication of information of military importance during [[World War II]], including by journalists and all correspondence going into or out of the United States. [[McCarthyism]] from the 1940s to the 1950s resulted in the suppression of advocacy of [[Communism]], and the [[Hollywood blacklist]].  This included some prosecutions under the [[Smith Act]] of 1940.

As a result of the jurisprudence of the [[Warren Court]] in the mid-to-late 20th century, the Court has moved towards a baseline default rule under which freedom of speech is generally presumed to be protected, unless a specific exception applies. Therefore, apart from certain narrow exceptions, the government normally cannot regulate the ''content'' of speech. In 1971, in ''[[Cohen v. California]]'', Justice [[John Marshall Harlan II]], citing ''[[Whitney v. California]]'', emphasized that the [[First Amendment to the United States Constitution|First Amendment]] operates to protect the inviolability of ''&quot;a [[marketplace of ideas]]&quot;'', while Associate Justice [[Thurgood Marshall]] cogently explained in 1972 that:{{blockquote|[A]bove all else, the First Amendment means that government has no power to restrict expression because of its message, its ideas, its subject matter, or its content. [Citations.] To permit the continued building of our politics and culture, and to assure self-fulfillment for each individual, our people are guaranteed the right to express any thought, free from government censorship. The essence of this forbidden censorship is content control. Any restriction on expressive activity because of its content would completely undercut the 'profound national commitment to the principle that debate on public issues should be uninhibited, robust, and wide-open.' [Citation.]&lt;ref&gt;''[[Police Dept. of Chicago v. Mosley]]'', {{ussc|408|92|1972}}.&lt;/ref&gt;}}In ''[[w:Legal_Services_Corp._v._Velazquez|Legal Services Corp. v. Velazquez]]'' in 2001. In this case, the Court held that government subsidies cannot be used to discriminate against a specific instance of viewpoint advocacy.

The Court pointed out in ''[[w:Snyder_v._Phelps|Snyder v. Phelps]]'' (2011) that one way to ascertain whether a restriction is content-based versus content-neutral is to consider if the speaker had delivered a ''different'' message under exactly the same circumstances.

==== Treason ====
[[w:Alien_and_Sedition_Acts|Alien and Sedition Acts]] prohibited the publication of &lt;blockquote&gt;&quot;false, scandalous, and malicious writings against the government of the United States, or either house of the Congress of the United States, or the President of the United States, with intent to defame ... or to bring them ... into contempt or disrepute; or to excite against them ... hatred of the good people of the United States, or to stir up sedition within the United States, or to excite any unlawful combinations therein, for opposing or resisting any law of the United States, or any act of the President of the United States&quot;.&lt;/blockquote&gt;

The law did allow truth as a defense and required proof of malicious intent.

The [[Federalist Party (United States)|Federalists]] under President [[John Adams]] aggressively used the law against their rivals, the [[Democratic-Republican Party|Democratic-Republicans]]. The Alien and Sedition Acts were a major political issue in the [[1800 United States presidential election|1800 election]], and after he was elected President, [[Thomas Jefferson]] pardoned those who had been convicted under the Act. The Act expired and the [[Supreme Court of the United States|Supreme Court]] never ruled on its constitutionality.

In ''[[w:New_York_Times_v._Sullivan|New York Times v. Sullivan]]'', the Court declared &quot;'''''Although the Sedition Act was never tested in this Court, the attack upon its validity has carried the day in the court of history.&quot;''''' 376 U.S. 254, 276 (1964).

See also: [[w:Espionage_Act_of_1917|Espionage Act of 1917]] and [[w:Sedition_Act_of_1918|Sedition Act of 1918]]

[[w:Force_v._Facebook_Inc.|Force v. Facebook]], [[w:Twitter,_Inc._v._Taamneh|Twitter v. Taamneh]] (new articles contributed) Re: [[w:Section_230|Section 230]]

==== Incitement and Imminent Lawless Action ====
Schenk vs.  &quot;[[w:Clear_and_present_danger|clear and present danger]]&quot;

[[w:Brandenburg_vs._Ohio|Brandenburg vs. Ohio]]:  &quot;[[w:Imminent_lawless_action|Imminent lawless action]]&quot;

The Skokie case.

[[w:Hess_v._Indiana|Hess v. Indiana]]

==== Obscenity, Slander, Libel, Fraud ====
Categories of speech that are given lesser or no protection by the First Amendment include [[United States obscenity law|obscenity]] (as determined by the [[Miller test]]), [[fraud]], [[Child pornography laws in the United States|child pornography]], speech integral to illegal conduct,&lt;ref&gt;{{cite journal|last1=Volokh|first1=Eugene|date=2016|title=The 'Speech Integral to Criminal Conduct' Exception|url=http://www2.law.ucla.edu/volokh/integral.pdf|journal=Cornell Law Review|volume=101|page=981|access-date=6 August 2017|author-link1=Eugene Volokh}}&lt;/ref&gt; speech that incites [[imminent lawless action]], and regulation of commercial speech such as [[advertising]].&lt;ref&gt;{{cite court|litigants=United States v. Alvarez|vol=132|reporter=S. Ct.|opinion=2537|court=Supreme Court of the United States|date=2012|url=https://scholar.google.com/scholar_case?q=United+States+v.+Alvarez&amp;hl=en&amp;as_sdt=800003&amp;as_ylo=2012&amp;as_yhi=2012&amp;case=2853347803518998660&amp;scilh=0}}&lt;/ref&gt;&lt;ref&gt;{{cite court|litigants=Sorrell v. IMS Health, Inc.|vol=131|reporter=S. Ct.|opinion=2653|court=Supreme Court of the United States|date=2011|url=https://scholar.google.com/scholar_case?case=838098438403992670&amp;hl=en&amp;as_sdt=6&amp;as_vis=1&amp;oi=scholarr}}&lt;/ref&gt;  Within these limited areas, other limitations on free speech balance rights to free speech and other rights, such as rights for authors over their works ([[copyright]]), protection from imminent or potential violence against particular persons, restrictions on the use of untruths to harm others ([[slander]] and [[libel]]), and communications while a person is in prison. When a speech restriction is challenged in court, it is presumed invalid and the government bears the burden of convincing the court that the restriction is constitutional.&lt;ref&gt;{{cite court|litigants=Ashcroft v. American Civil Liberties Union|vol=542|reporter=U.S.|opinion=656|pinpoint=660|court=Supreme Court of the United States|date=2004|url=https://www.law.cornell.edu/supct/html/03-218.ZO.html}}&lt;/ref&gt;

=== Freedom From Religious Establishment and of Free Exercise Thereof ===
''&quot;.. no law respecting an [[w:Establishment_of_religion|establishment of religion]], or prohibiting [[w:Free_exercise_clause|the free exercise thereof]];&quot;''

[[w:TWA_v._Hardison|TWA v. Hardison]] (new draft) [[w:Groff_v._DeJoy|Groff v. DeJoy]]

=== Searches and Seizures ===
[[w:Eduyot|Eduyot]] - witnesses, evidence, testimonies

[[w:Fourth_Amendment_to_the_United_States_Constitution|Fourth Amendment]]:  &quot;''The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable [[Search and seizure|searches and seizures]], shall not be violates, and no [[Warrant (law)|warrants]] shall issue but upon [[probable cause]], supported by oath or affirmation, and particularly describing the place to be searched and the persons or things to be seized.&quot;''

Historical background: [http://Constitution.congress.gov/browse/essay/amdt4-2/ALDE&amp;#x20;00013706/ constitution.congress.gov/browse/essay/amdt4-2/ALDE_00013706/]

[[w:Search_incident_to_a_lawful_arrest|Search incident to a lawful arrest]] (SITA) or the '''''Chimel'' rule''' (from ''[[Chimel v. California]]''), is a U.S. legal principle that allows [[Law enforcement in the United States|police]] to perform a [[Warrantless searches in the United States|warrantless search]] of an [[Arrest|arrested]] person, and the area within the arrestee’s immediate control, in the interest of officer safety, the prevention of escape, and the preservation of [[evidence]].&lt;ref name=&quot;Riley&quot;&gt;{{cite court|litigants=Riley v. California|vol=573|reporter=U.S.|court=United States Supreme Court|date=2014|url=https://www.supremecourt.gov/opinions/13pdf/13-132_8l9c.pdf|access-date=2014-06-25}}&lt;/ref&gt; In most cases, a [[search warrant]] is required.

''[[Katz v. United States]]'' (1967) extended its protections on intrusions on privacy.  Exceptions for [[Consent search|consent searches]], [[Motor vehicle exception|motor vehicle searches]], [[Plain view doctrine|evidence in plain view]], [[Exigent circumstance in United States law|exigent circumstances]], [[Border search exception|border searches]], and other situations.

The [[exclusionary rule]] is one way the amendment is enforced. Established in ''[[Weeks v. United States]]'' (1914), this rule holds that [[evidence]] obtained as a result of a Fourth Amendment violation is generally [[Admissible evidence|inadmissible]] at criminal trials. Evidence discovered as a later result of an illegal search may also be inadmissible as &quot;[[fruit of the poisonous tree]]&quot;. The exception is if it [[Inevitable discovery|inevitably would have been discovered by legal means]].

=== Due Process of Law, Indictments by Grand Jury, Prohibited Double Jeopardy, compulsory Self-incrimination, Takings ===
[[w:Fifth_Amendment_to_the_United_States_Constitution|Fifth Amendment to the US Constitution]]: ''&quot;No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.&quot;''  

==== the [[Grand juries in the United States#Grand Jury Clause|Grand Jury Clause]] and the [[Double Jeopardy Clause]] ====

==== The [[Self-incrimination#United States law|Self Incrimination Clause]] ====
''[[Miranda v. Arizona]]'', the Supreme Court held that the Self-Incrimination Clause requires the police to issue a [[Miranda warning|''Miranda'' warning]]

==== The [[Due Process Clause]] ====
The Fifth Amendment's [[Due Process Clause]] applies to the federal government, while the Fourteenth Amendment's Due Process Clause applies to state governments (and by extension, [[local governments]]). The Supreme Court has interpreted the Fifth Amendment's Due Process Clause to provide two main protections: [[procedural due process]], which requires government officials to follow fair procedures before depriving a person of life, liberty, or property, and [[substantive due process]], which protects certain [[Fundamental rights in the United States|fundamental rights]] from government interference. The Supreme Court has also held that the Due Process Clause contains a [[Vagueness doctrine|prohibition against vague laws]] and an implied equal protection requirement similar to the Fourteenth Amendment's [[Equal Protection Clause]]

==== the [[User:Jaredscribe/Comparative law#Takings Clause|Takings Clause]]. ====

=== Trial by Jury, Speedy and Public, with Assistance of Counsel ===
the [[w:Sixth Amendment to the United States Constitution|Sixth Amendment to the United States Constitution]]: ''&quot;In all [[w:Criminal_prosecutions|criminal prosecution]]&lt;nowiki/&gt;s, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence.&quot;''

[[w:Speedy_Trial_clause|Speedy Trial clause]]

[[w:public trial|public trial]] &quot;Justice is not a cloistered virtue&quot;.  [[w:Secret trial|Secret trials]] violate the [[w:open court principle]] 

[[w:Juries_in_the_United_States|Juries in the United States]] conviction requires unanimous verdict [[w:Ramos_v._Louisiana_(2020)|''Ramos v. Louisiana'' (2020)]]

[[w:Vicinage_Clause|Vicinage Clause]]

[[w:Notice|Notice]] of the nature and cause of accusations. 

The [[w:Confrontation_Clause|Confrontation Clause]] gives criminal defendants the right to confront and cross-examine witnesses

The [[w:Compulsory_Process_Clause|Compulsory Process Clause]] gives power to [[w:Subpoena_ad_testificandum|subpoena ad testificandum]] or [[w:Subpoena_duces_tecum|subpoena duces tecum]].

[[w:Assistance of Counsel Clause|Assistance of Counsel Clause]] of the requires courts provide a [[w:public defender|public defender]] to indigents, decided the court in [[w:Gideon v. Wainwright|Gideon v. Wainwright]].  [[w:Ineffective assistance of counsel|Ineffective assistance of counsel]] contemplated in [[w:Strickland v. Washington|Strickland v. Washington]].  The high court in [[w:Farretta v. California|Farretta v. California]] guarantees right to represent [[w:pro se|pro se]].   [[w:Star chamber|Star chamber]] of palace of Westminster had denied rights by imposing representation.

SCOTUS has [[w:Incorporation of the Bill of Rights|incorporated and applied]] the protections of this amendment to the states through the [[w:Fourteenth Amendment to the United States Constitution#Due%20Process%20Clause|Due Process Clause of the Fourteenth Amendment]].

=== Cruel and Unusual Punishment Prohibited ===
[[w:Martin_v._Boise|Martin v. Boise]] precedent overturned in [[w:City_of_Grants_Pass_v._Johnson|City of Grants Pass v. Jones]], holds that criminalizing houselessness does not violate 8th Ammendment prohibition on cruel and unusual punishment.

==== US Incorporation of Rights Doctrine ====
14th Amendment equal protection clause due process clause

Incorporation of the Bill of rights to [[Incorporation of the Bill of Rights|apply to state and local governments]], via the [[Due Process Clause]] (or [[w:Equal_Protection_clause|Equal Protection clause]]) of the [[Fourteenth Amendment to the United States Constitution|Fourteenth Amendment]].

'''4th incorporated in ''[[Mapp v. Ohio]]'' (1961)''' 

'''1st [[w:Establishment_Clause|non-establishment of religion]] incorporated''' in [[w:Gitlow_v._New_York|'''''Gitlow v. New York''''', 268 U.S. 652 (1925)]]
[[w:De_Jonge_v._Oregon|'''''De Jonge v. Oregon''''', 299 U.S. 353 (1937)]]
''See [[w:Everson_v._Board_of_Education|Everson v. Board of Education]]'', {{ussc|330|1|1947}}.&lt;ref&gt;Justice [[Clarence Thomas|Thomas]], in a concurring opinion in ''[[Elk Grove Unified School District v. Newdow]]'', expressed his view that ''Everson'' was wrongly decided and that incorporation of the Establishment Clause is not justified under the Constitution. See {{cite book|url=https://archive.org/details/libertyofconscie0000nuss|title=Liberty of conscience: in defense of America's tradition of religious equality|last=Nussbaum|first=Martha Craven|publisher=Basic Books|year=2008|isbn=978-0-465-05164-9|pages=[https://archive.org/details/libertyofconscie0000nuss/page/105 105] et seq. and Chapter 4|author-link=Martha Craven Nussbaum|url-access=registration}} {{cite journal|author=Richard F. Duncan|date=2007|title=JUSTICE THOMAS AND PARTIAL INCORPORATION OF THE ESTABLISHMENT CLAUSE: HEREIN OF STRUCTURAL LIMITATIONS, LIBERTY INTERESTS, AND TAKING INCORPORATION SERIOUSLY|url=http://law.unl.edu/sites/unl.edu.college-of-law.law/files/facstaff/faculty/resident/docs/Thomas_ArticleDuncan2010.pdf|journal=Regent University Law Review|volume=20|pages=37–56|archive-url=https://web.archive.org/web/20130115120648/http://law.unl.edu/sites/unl.edu.college-of-law.law/files/facstaff/faculty/resident/docs/Thomas_ArticleDuncan2010.pdf|archive-date=2013-01-15|url-status=dead}}&lt;/ref&gt;

'''1st [[w:Free_Exercise_Clause|free exercise of religion]] incorporated''' in ''[[w:Cantwell_v._Connecticut|Cantwell v. Connecticut]]'', {{ussc|310|296|1940}}. [[w:Template:USSC]]

=== US Civil Rights Law ===
[[w:Civil_Rights_Act_of_1964|US Civil Rights Act of 1964]]

=== Israel Basic Laws ===
[[w:Basic_Laws_of_Israel|Basic_Laws_of_Israel]],  [[w:Basic_Law:_Human_Dignity_and_Liberty|Basic_Law:_Human_Dignity_and_Liberty]], [[:he:חוק_יסוד:_כבוד_האדם_וחירותו]]

[[w:2023_Israeli_judicial_reform|2023 Israeli judicial reform]], [[:he:רפורמת_לוין]], 

==Notes and References==


This research project is developed from [[w:User:Jaredscribe/Law]]</text>
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  <page>
    <title>Exploring Existential Concerns</title>
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      <contributor>
        <username>Lbeaumont</username>
        <id>278565</id>
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      <comment>/* Significance */ Linked to What Ought we do?</comment>
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      <text bytes="2420" sha1="8dc2gvdtgamna0l7xa7pgvq3itvzwrj" xml:space="preserve">''—Do I Even Matter?''
[[File:Night sky from Tony Grove Lake, United States.jpg|thumb|300px| We often [[Cherishing awe|wonder in awe]] what more there might be.]]
{{TOC right | limit|limit=2}}
Although a discussion of [[w:Existentialism|existential philosophy]] is well beyond the scope of this course, everyone has important questions and legitimate concerns about their very existence.&lt;ref&gt;These materials are adapted from the [https://www.emotionalcompetency.com/existential.htm EmotionalCompetency.com] website, with permission of the author. &lt;/ref&gt; Focusing excessive attention on these concerns can provoke fear, anxiety, guilt, and shame, especially if you feel helpless or overwhelmed.

Strive for an accurate optimism while remaining curious. Keep in mind [[what you can change and what you cannot]].

Here are some typical existential concerns:

== Survival ==

* How long will I live?
* Will I be healthy?
* What will the future bring?
* How will I die?
* What will happen to me and others I care about after death?

== Success ==

* Who am I?
* Am I doing OK?
* Am I doing enough?
* Am I doing the best I can?
* Have I made good choices?
* What could have happened if I made different choices?
* Am I competent?
* What is my stature?
* What are my goals, values, and beliefs?
* Am I living honorably?
* Am I living life to the fullest?

== Significance ==

* Who are we?
* What can we know?
* Do I even matter?
* Who cares about me?
* Who do I care about?
* What is my legacy?
* What is my significance in the world?
* What is a good life?
* [[/What Ought We Do?/|What ought we do?]]
* Am I wasting my life?
* Am I worthy?
* Have I struck a good balance between caring for myself and empathy for others?
* How does my life have meaning for me and others?

{{CourseCat}}

== Assignment ==

# Select any question or concern, listed above or from any other source, that you are interested in or concerned about.
# [[Reflective thinking|Reflect]] on the question privately, engage a trusted friend in [[Practicing Dialogue|dialogue]] on the question, or practice [[Socratic Methods]] to explore the question.
# [[Living Wisely/Take Care|Take care]] of yourself. Know that “And whether or not it is clear to you, no doubt the universe is unfolding as it should” ~ from the poem [[w:Desiderata|Desiderata]]

[[Category:Applied Wisdom]]

[[Category:Humanities]]

[[Category:Theology]]

[[Category:Philosophy]]</text>
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      <text bytes="2497" sha1="fd9qlr42shdf2ilmc7bwgumjfjr8kd0" xml:space="preserve">''—Do I Even Matter?''
[[File:Night sky from Tony Grove Lake, United States.jpg|thumb|300px| We often [[Cherishing awe|wonder in awe]] what more there might be.]]
{{TOC right | limit|limit=2}}
Although a discussion of [[w:Existentialism|existential philosophy]] is well beyond the scope of this course, everyone has important questions and legitimate concerns about their very existence.&lt;ref&gt;These materials are adapted from the [https://www.emotionalcompetency.com/existential.htm EmotionalCompetency.com] website, with permission of the author. &lt;/ref&gt; Focusing excessive attention on these concerns can provoke fear, anxiety, guilt, and shame, especially if you feel helpless or overwhelmed.

Strive for an accurate optimism while remaining curious. Keep in mind [[what you can change and what you cannot]].

Here are some typical existential concerns:

== Survival ==

* How long will I live?
* Will I be healthy?
* What will the future bring?
* How will I die?
* What will happen to me and others I care about after death?

== Success ==

* [[True Self|Who am I?]]
* Am I doing OK?
* Am I doing enough?
* Am I doing the best I can?
* Have I made good choices?
* What could have happened if I made different choices?
* Am I competent?
* What is my stature?
* [[Clarifying values|What are my goals, values, and beliefs?]]
* Am I living honorably?
* [[What Matters|Am I living life to the fullest?]]

== Significance ==

* Who are we?
* [[Knowing How You Know|What can we know?]]
* Do I even matter?
* Who cares about me?
* Who do I care about?
* What is my legacy?
* What is my significance in the world?
* What is a good life?
* [[/What Ought We Do?/|What ought we do?]]
* Am I wasting my life?
* Am I worthy?
* Have I struck a good balance between caring for myself and empathy for others?
* How does my life have meaning for me and others?

== Assignment ==

# Select any question or concern, listed above or from any other source, that you are interested in or concerned about.
# [[Reflective thinking|Reflect]] on the question privately, engage a trusted friend in [[Practicing Dialogue|dialogue]] on the question, or practice [[Socratic Methods]] to explore the question.
# [[Living Wisely/Take Care|Take care]] of yourself. Know that “And whether or not it is clear to you, no doubt the universe is unfolding as it should” ~ from the poem [[w:Desiderata|Desiderata]]

{{CourseCat}}
[[Category:Applied Wisdom]]

[[Category:Humanities]]

[[Category:Theology]]

[[Category:Philosophy]]</text>
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      <text bytes="2526" sha1="f6pwy10cytkhns1bloyo9kqzp1v3kxm" xml:space="preserve">''—Do I Even Matter?''
[[File:Night sky from Tony Grove Lake, United States.jpg|thumb|300px| We often [[Cherishing awe|wonder in awe]] what more there might be.]]
{{TOC right | limit|limit=2}}
Although a discussion of [[w:Existentialism|existential philosophy]] is well beyond the scope of this course, everyone has important questions and legitimate concerns about their very existence.&lt;ref&gt;These materials are adapted from the [https://www.emotionalcompetency.com/existential.htm EmotionalCompetency.com] website, with permission of the author. &lt;/ref&gt; Focusing excessive attention on these concerns can provoke fear, anxiety, guilt, and shame, especially if you feel helpless or overwhelmed.

Strive for an accurate optimism while remaining curious. Keep in mind [[what you can change and what you cannot]].

Here are some typical existential concerns:

== Survival ==

* How long will I live?
* Will I be healthy?
* What will the future bring?
* How will I die?
* What will happen to me and others I care about after death?

== Success ==

* [[True Self|Who am I?]]
* Am I doing OK?
* [[Doing Good|Am I doing enough?]]
* Am I doing the best I can?
* Have I made good choices?
* What could have happened if I made different choices?
* Am I competent?
* What is my stature?
* [[Clarifying values|What are my goals, values, and beliefs?]]
* Am I living honorably?
* [[What Matters|Am I living life to the fullest?]]

== Significance ==

* Who are we?
* [[Knowing How You Know|What can we know?]]
* Do I even matter?
* Who cares about me?
* Who do I care about?
* What is my legacy?
* What is my significance in the world?
* [[Stoic joy|What is a good life?]]
* [[/What Ought We Do?/|What ought we do?]]
* Am I wasting my life?
* Am I worthy?
* Have I struck a good balance between caring for myself and empathy for others?
* How does my life have meaning for me and others?

== Assignment ==

# Select any question or concern, listed above or from any other source, that you are interested in or concerned about.
# [[Reflective thinking|Reflect]] on the question privately, engage a trusted friend in [[Practicing Dialogue|dialogue]] on the question, or practice [[Socratic Methods]] to explore the question.
# [[Living Wisely/Take Care|Take care]] of yourself. Know that “And whether or not it is clear to you, no doubt the universe is unfolding as it should” ~ from the poem [[w:Desiderata|Desiderata]]

{{CourseCat}}
[[Category:Applied Wisdom]]

[[Category:Humanities]]

[[Category:Theology]]

[[Category:Philosophy]]</text>
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    <title>The Idea Incubator/The Wisdom Playground</title>
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      <text bytes="8810" sha1="oaq28qnfme3sfnzbxd17duvf0skiv1h" xml:space="preserve">—A Sanctuary for Intellectual and Emotional Growth
[[File:Wisdom_playground.jpg|thumb|300px|A Wisdom Playground]]
{{TOC right | limit|limit=2}}
In an age where the fast pace of life often overshadows the pursuit of deeper understanding and reflection, the concept of a ''Wisdom Playground'' emerges as a sanctuary for intellectual and emotional growth.&lt;ref&gt;[[w:ChatGPT|ChatGPT]] generated this text responding to the prompt: “Write an essay describing a wisdom playground”.&lt;/ref&gt;&lt;sup&gt;,&lt;/sup&gt;&lt;ref&gt;This text appeared earlier as a [https://lelandbeaumont.substack.com/p/the-wisdom-playground substack article] and is used here with permission of the author. &lt;/ref&gt; This imaginative space is designed to cultivate [[wisdom]] through play, interaction, and contemplation, providing a holistic environment where individuals of all ages can explore and develop their inner wisdom.


== The Concept of a Wisdom Playground ==
A Wisdom Playground is more than just a physical space; it is an ecosystem where various elements converge to foster the development of wisdom. This environment integrates elements of nature, art, philosophy, and technology, creating a harmonious blend that stimulates the mind, nurtures the soul, and invigorates the body. The goal is to provide a setting where people can engage in activities that promote reflection, empathy, critical thinking, and emotional intelligence.

== Elements of the Wisdom Playground ==

# '''Nature and Serenity''': The Wisdom Playground is designed with ample green spaces, gardens, and water features. These natural elements are essential in providing a serene environment that encourages contemplation and mindfulness. Walking paths, meditation gardens, and quiet nooks allow individuals to connect with nature and find peace amidst the chaos of daily life.
# '''Interactive Art Installations''': Art plays a crucial role in the Wisdom Playground. Interactive installations that respond to touch, sound, and movement invite participants to engage with art in a personal and meaningful way. These installations challenge individuals to think creatively and see the world from different perspectives.
# '''Philosophical Zones''': Dedicated areas within the playground are designed for philosophical exploration. These zones feature thought-provoking sculptures, murals, and quotes from great thinkers throughout history. Workshops and discussion circles are regularly held to facilitate [[Practicing Dialogue|dialogues]] on philosophical topics, encouraging participants to ponder life’s big questions and develop their own understanding.
# '''Technology and Innovation Hubs''': While the Wisdom Playground emphasizes natural and artistic elements, it also embraces technology as a tool for learning and growth. Interactive digital displays, virtual reality experiences, and augmented reality installations provide immersive experiences that broaden horizons and stimulate intellectual curiosity.
# '''Storytelling Corners''': Storytelling is a powerful medium for sharing wisdom across generations. Cozy corners with comfortable seating and storytelling sessions offer a space for people to share their experiences, listen to others, and learn valuable life lessons. These sessions can be intergenerational, allowing wisdom to flow from the older to the younger and vice versa.
# '''Play and Movement Areas''': Physical activity is integral to holistic well-being. Play areas with equipment that encourages physical movement, teamwork, and [[Solving Problems|problem-solving]] are essential components of the Wisdom Playground. These areas are designed not only for children but for adults as well, promoting the idea that [[Playing|play]] is a lifelong activity crucial for maintaining a healthy mind and body.

== The Impact of a Wisdom Playground ==
The creation of a Wisdom Playground has far-reaching impacts on individuals and the community. For children, it provides an environment that nurtures curiosity, creativity, and [[Emotional Competency|emotional intelligence]] from a young age. For adults, it offers a refuge from the stresses of modern life, a place to reconnect with their inner selves, and an opportunity to engage in lifelong learning.

Communities with access to such a playground are likely to see enhanced social cohesion, as the space fosters interactions between people of different ages, backgrounds, and perspectives. The Wisdom Playground becomes a hub for [[Creating Communities|community activities]], cultural events, and educational programs, strengthening the fabric of the community.

Moreover, by prioritizing the development of wisdom, such playgrounds contribute to the creation of a more thoughtful, empathetic, and enlightened society. Individuals who frequent the Wisdom Playground are better equipped to navigate the complexities of life, make informed decisions, and contribute positively to the world around them.

== Conclusion ==
In conclusion, the Wisdom Playground represents a visionary approach to personal and communal growth. By integrating nature, art, philosophy, and technology, it creates a nurturing environment that fosters the development of wisdom in its many forms. This sanctuary for intellectual and emotional growth has the potential to transform individuals and communities, making it an invaluable asset in our pursuit of a more enlightened and harmonious world.

== Prototypes ==
Several existing venues hold the potential to be transformed into Wisdom Playgrounds. These include:

# [[w:Esalen_Institute|The Esalen Institute]] is a non-profit American retreat center and intentional community in Big Sur, California, which focuses on humanistic alternative education.
# [[w:Canyon_Ranch|Canyon ranch]] operates several wellness resorts.  
# The [[w:Omega_Institute_for_Holistic_Studies|Omega Institute for Holistic Studies]] is a non-profit educational retreat center located in Rhinebeck, New York.  The institute's stated mission is to &quot;provide hope and healing for individuals and society through innovative educational experiences that awaken the best in the human spirit&quot;.
# The [[w:Santa_Fe_Institute|Santa Fe Institute]] (SFI) is an independent, nonprofit theoretical research institute located in Santa Fe, New Mexico, United States and dedicated to the multidisciplinary study of the fundamental principles of complex adaptive systems, including physical, computational, biological, and social systems.
# [[w:Braver_Angels|Braver Angels]] is a nonprofit dedicated to political depolarization. The organization runs workshops, debates, and other events where &quot;red&quot; (conservative) and &quot;blue&quot; (liberal) participants attempt to better understand one another's positions and discover their shared values.
# A [[w:Salon_(gathering)|salon]] is a gathering of people held by a host created either to please or to educate the guests. 
# Existing parks, playgrounds, libraries, book stores, universities, museums, schools, pubs, community centers, health spas, fitness centers, yoga studios, open spaces, your [[w:Third_place|third place]], and on-line forums could also be transformed into Wisdom Playgrounds that are local and accessible to a large population.

== Wisdom Playground Rules ==
[[File:Wisdom_Playground_Rules.jpg|thumb|300px|Wisdom Playground Rules]]
Like any well-run playground each wisdom playground needs a set of rules.

Here is a proposal:

# [[Living Wisely/Take Care|Stay safe]];
# [[Playing|Have fun]];
# Stay curious;
# [[Knowing Someone/Asking Better Questions|Ask questions]];
# [[Social Skills/The Power of Active Listening|Listen]];
# Practice [[Emotional Competency|emotional competency]];
# Focus on [[What Matters|what matters]];
# Practice [[Practicing Dialogue|dialogue]];
# [[Living Wisely/Seeking Real Good|Seek real good]];
# [[Finding Common Ground|Find common ground]];
# Expect [[intellectual honesty]];
# [[Possibilities/Curriculum|Create possibilities]];
# [[Cherishing awe|Cherish awe]];
# [[Transcending Conflict|Transcend conflict]];
# [[Coming Together|Come together]];
# [[Doing Good|Do good]];
# Adopt a [[Global Perspective|global perspective]];
# Evolve toward [[Evolving Governments/Good Government|good government]];
# [[Assessing Human Rights/Beyond Olympic Gold|Advance human rights, worldwide]];
# [[Living Wisely|Live wisely]].

[[Practicing Dialogue|Skillful dialogue]] on [[Knowing Someone/Conversation Topics|important topics]] are at the core of each wisdom playground. Consider beginning by exploring the question “[[Exploring Existential Concerns/What Ought We Do?|What ought we do?]]”.  

Adopting these rules can transform many ordinary spaces such as neighborhoods, coffee shops, pubs, parks, libraries, classrooms, and museums into wisdom playgrounds.

==Notes==

{{CourseCat}}
[[Category:Creating Communities]]</text>
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    <title>Global Project Against Hate &amp; Extremism (GPAHE)</title>
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      <text bytes="6820" sha1="034nydkhxyoyz3qu28qjbllnakm7vuv" xml:space="preserve">:''This is a discussion of an interview on 2024-08-22 with Heidi Beirich,&lt;ref name=Beirich&gt;&lt;!-- Heidi Beirich--&gt;{{cite Q|Q128844587}}&lt;/ref&gt; a co-founder and Chief Strategy Officer of Global Project Against Hate &amp; Extremism (GPAHE).&lt;ref name=GPAHE&gt;&lt;!-- GPAHE--&gt;{{cite Q|Q125952435}}&lt;/ref&gt; After the interview, at most 29 minutes from it was broadcasted the following Tuesday as Radio Active Magazine&lt;ref&gt;&lt;!-- Radio Active Magazine--&gt;{{cite Q|Q57451712}}&lt;/ref&gt; on [[w:KKFI|KKFI]], followed a few days later by a 29:00 mm:ss audio file prepared for distribution as the &quot;Media &amp; Democracy&quot; show&lt;ref&gt;&lt;!--Media &amp; Democracy--&gt;{{cite Q|Q127839818}}&lt;/ref&gt; syndicated for the [[w:Pacifica Foundation|Pacifica Radio]]&lt;ref&gt;&lt;!--Pacifica Radio Network--&gt;{{cite Q|Q2045587}}&lt;/ref&gt; Network of [[w:List of Pacifica Radio stations and affiliates|over 200 community radio stations]].''&lt;ref&gt;&lt;!--list of Pacifica Radio stations and affiliates--&gt;{{cite Q|Q6593294}}&lt;/ref&gt;

:''It is posted here to invite others to contribute other perspectives, subject to the Wikimedia rules of [[w:Wikipedia:Neutral point of view|writing from a neutral point of view]] [[w:Wikipedia:Citing sources|citing credible sources]]&lt;ref name=NPOV&gt;The rules of writing from a neutral point of view citing credible sources may not be enforced on other parts of Wikiversity. However, they can facilitate dialog between people with dramatically different beliefs.&lt;/ref&gt; and treating others with respect.&lt;ref name=AGF&gt;[[Wikiversity:Assume good faith|Wikiversity asks contributors to assume good faith]], similar to Wikipedia. The rule in [[w:Wikinews|Wikinews]] is different: Contributors there are asked to [[Wikinews:Never assume|&quot;Don't assume things; be skeptical about everything.&quot;]] That's wise. However, we should still treat others with respect while being skeptical.&lt;/ref&gt;'' 
[[File:Heidi Beirich discusses the Global Project Against Hate &amp; Extremism.webm|thumb|Heidi Beirich discusses the Global Project Against Hate &amp; Extremism (GPAHE).]]
[[File:Heidi Beirich discusses the Global Project Against Hate and Extremism.ogg|thumb|29:00 mm:ss extract from an interview conducted 2021-08-22 with Heidi Beirich regarding the Global Project Against Hate and Extremism]]

Heidi Beirich,&lt;ref name=Beirich/&gt; co-founder and Chief Strategy Officer of Global Project Against Hate &amp; Extremism (GPAHE)&lt;ref name=GPAHE/&gt; discusses their work. This includes what they and others are doing to reduce political polarization and violence and what individuals and governments can do to combat these threats.

Beirich has authored multiple publications on issues related to hate and extremism. This includes co-editing (2008) ''Neo-Confederacy: A Critical Introduction'' (University of Texas Press)&lt;ref&gt;Hague et al.(2008).&lt;/ref&gt; and testifying on &quot;Alarming Incidents of White Supremacy in the Military – How to Stop It?&quot; 2020-02-11 before the Military Personnel Subcommittee of the Armed Services Committee of the US House of Representatives.&lt;ref&gt;Beirich (2020).&lt;/ref&gt;

She said that many teenagers, especially teenage males with difficult home lives, get recruited online into a violent extremist ideology. Some are encouraged to become a &quot;lone wolf&quot; extremist like [[w:Timothy McVeigh|Timothy McVeigh]], who committed the [[w:Oklahoma City bombing|Oklahoma City bombing]] 1995-04-19. She mentioned the neo-Nazi [[w:Atomwaffen Division|Atomwaffen Division]], which has been connected to multiple murders.

In addition to teenagers, many current military and law enforcement personnel are recruited into neo-Nazi groups. Veterans are often recruited as they are leaving the military; this is a particularly vulnerable time for many. 

She said the military should be doing more. [[w:Lloyd Austin|Lloyd Austin]], the current US Secretary of Defense, became aware of this as a Lt. Col. and wanted to do something about it at Secretary of Defense. However, Republicans in the US Congress have explicitly zeroed out his budget to prevent him from doing anything to minimize the problem with violent extremists in the US military.&lt;ref&gt;That Person Called Morgan (2024); Donnelly (2022).&lt;/ref&gt; 

When asked what concerned parents or community members should do to minimize the risks of teenagers in their community involving themselves in extremist violence, she recommended PERIL, the Polarization and Extremism Research &amp; Innovation Lab,&lt;ref&gt;&lt;!--Polarization and Extremism Research &amp; Innovation Lab (PERIL)--&gt;{{cite Q|Q129673094}}&lt;/ref&gt; headed by Professor Cynthia Miller-Idriss&lt;ref&gt;&lt;!--Cynthia Miller-Idriss--&gt;{{cite Q|Q110463618}}&lt;/ref&gt; at [[w:American University|American University]]: They are &quot;Equipping communities with tools for change&quot;, including resources for, parents &amp; caregivers, government and policymakers, faith leaders &amp; small businesses, educators &amp; mental health counselors, community members, and victims &amp; survivors. 

== Beirich == 

Heidi Beirich earned a doctorate in political science from [[w:Purdue University|Purdue]] and worked for the [[w:Southern Poverty Law Center|Southern Poverty Law Center]] from 1999 until she left to found the Global Project Against Hate &amp; Extremism&lt;ref name=GPAHE/&gt; in 2020.

She is interviewed by Karl Brooks&lt;ref&gt;&lt;!--Karl Brooks--&gt;{{cite Q|Q128214400}}&lt;/ref&gt; and Spencer Graves.&lt;ref&gt;&lt;!--Spencer Graves--&gt;{{cite Q|Q56452480}}&lt;/ref&gt; 

== The threat == 

Internet company executives have knowingly increased political polarization and violence including the [[w:Rohingya genocide|Rohingya genocide]] in [[w:Myanmar|Myanmar]], because doing otherwise might have reduced their profits. Documentation of this is summarized in [[:Category:Media reform to improve democracy]].

==Discussion == 

:''[Interested readers are invite to comment here, subject to the Wikimedia rules of [[w:Wikipedia:Neutral point of view|writing from a neutral point of view]] [[w:Wikipedia:Citing sources|citing credible sources]]&lt;ref name=NPOV/&gt; and treating others with respect.&lt;ref name=AGF/&gt;]''

== Notes ==
{{reflist}}

== Bibliography == 

* &lt;!-- Beirich (2020-02-11) &quot;Alarming Incidents of White Supremacy in the Military – How to Stop It?&quot;, testimony before the Military Personnel Subcommittee of the Armed Services Committee of the US House of Representatives.--&gt;{{cite Q|Q129350693}}
* &lt;!--John M. Donnelly (2022-12-14) Final NDAA removes most House provisions on hate groups, Roll Call--&gt;{{cite Q|Q130545466}}
* &lt;!--Hague, Beirich and Sebasta, eds. (2008) Neo-Confederacy: A Critical Introduction (University of Texas Press)--&gt;{{cite Q|Q129348759|editor=Euan Hague, Heidi Beirich, and Edward H. Sebesta}}
* &lt;!--That person called Morgan (2024-01-30) Foreign Policy Analysis Paper: Countering Extremism Activity Working Group (CEAWG), Medium--&gt;{{cite Q|Q130545443}}

[[Category:Freedom and abundance]]
[[Category:Media reform to improve democracy]]</text>
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      <text bytes="616" sha1="9v5qoacjbzs07cxzuyl0tvyj8l1zrup" xml:space="preserve">* [[User:Atcovi/Health Psychology/Chapter 1 - What is Health?]]
* [[User:Atcovi/Health Psychology/Chapter 5 - Diverse Understandings of Stress]]
* [[User:Atcovi/Health Psychology/Chapter 6 - Coping and Social Support]]
* [[User:Atcovi/Health Psychology/Chapter 7 -Why Don’t We Do What We Need to?|User:Atcovi/Health Psychology/Chapter 7 - Why Don’t We Do What We Need to?]]
* [[User:Atcovi/Health Psychology/Chapter 8 - Health Behaviors]]
* [[User:Atcovi/Health Psychology/Illness Cognitions, Adherence, and Patient–Practitioner Interactions: Introduction]]

[[Category:Psychology]]

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      <text bytes="628" sha1="ce84yvgmtxaq39ddzfu2d1mng31n1kv" xml:space="preserve">* [[User:Atcovi/Health Psychology/Chapter 1 - What is Health?]]
* [[User:Atcovi/Health Psychology/Chapter 5 - Diverse Understandings of Stress]]
* [[User:Atcovi/Health Psychology/Chapter 6 - Coping and Social Support]]
* [[User:Atcovi/Health Psychology/Chapter 7 -Why Don’t We Do What We Need to?|User:Atcovi/Health Psychology/Chapter 7 - Why Don’t We Do What We Need to?]]
* [[User:Atcovi/Health Psychology/Chapter 8 - Health Behaviors]]
* [[User:Atcovi/Health Psychology/Chapter 9 - Illness Cognitions, Adherence, and Patient–Practitioner Interactions: Introduction]]

[[Category:Psychology]]

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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/leveled praetor sword|leveled praetor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 10
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 4, 24, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 2|nameless 2]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
      <sha1>i1p3qxcsefkzcgffknmbdnjyugroivs</sha1>
    </revision>
    <revision>
      <id>2693018</id>
      <parentid>2693005</parentid>
      <timestamp>2024-12-23T14:11:12Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693018</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="33462" sha1="eyznuc2u85owh64nuymg27w0c2znz9d" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/leveled praetor sword|leveled praetor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 10
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 4, 24, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 2|nameless 2]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
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    </revision>
    <revision>
      <id>2693068</id>
      <parentid>2693018</parentid>
      <timestamp>2024-12-23T22:34:59Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
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      <text bytes="33786" sha1="9trskylzjs9fwm7w6g7ce3ukcgujn63" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater twin mentor|greater twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 10
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 4, 24, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
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    </revision>
    <revision>
      <id>2693073</id>
      <parentid>2693068</parentid>
      <timestamp>2024-12-23T23:23:06Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
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      <text bytes="33650" sha1="hpnhl3lv5fr5t43l87po7fo9suc9lzj" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater twin mentor|greater twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
      <sha1>hpnhl3lv5fr5t43l87po7fo9suc9lzj</sha1>
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  <page>
    <title>Boolf prop/3-ary/twin mentor</title>
    <ns>0</ns>
    <id>317256</id>
    <revision>
      <id>2693052</id>
      <parentid>2692107</parentid>
      <timestamp>2024-12-23T21:53:22Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693052</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="14138" sha1="dy42q1pnowf55jwec4bx27xgnhhd6ya" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 87183322370842425795587566660030343945541236792690890543826997033971843334915.svg|thumb|500px|The values 0, 1, 8, 9... form the block of [[Boolf prop/3-ary/great patron|great patron]] 0.]]

&lt;source lang=&quot;python&quot;&gt;
val = tuple(boolf.twin(3) ^ boolf.mentor(3)).zhe
&lt;/source&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| nameless 2
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| 0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 40, 72, 96]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_79228167236630821562700791809.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| 232
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 41, 73, 97]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_158456334473261643125401583618.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| 191
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 42, 74, 98]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_316912668946523286250803167236.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| 87
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 43, 75, 99]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_633825337893046572501606334472.svg|420px]]
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[[Category:Boolf prop/3-ary|nameless 2]]</text>
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    <revision>
      <id>2693054</id>
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        <id>137431</id>
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[[File:Set of 3-ary Boolean functions 87183322370842425795587566660030343945541236792690890543826997033971843334915.svg|thumb|500px|The values 0, 1, 8, 9... form the block of [[Boolf prop/3-ary/great patron|great patron]] 0.]]

&lt;source lang=&quot;python&quot;&gt;
val = (boolf.twin(3) ^ boolf.mentor(3)).zhe
&lt;/source&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;
&lt;/div&gt;

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[[Category:Boolf prop/3-ary|nameless 2]]</text>
      <sha1>374rzqx9kfzbjhymt41ocokjknnm2ao</sha1>
    </revision>
    <revision>
      <id>2693060</id>
      <parentid>2693054</parentid>
      <timestamp>2024-12-23T22:26:35Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <minor />
      <comment>Watchduck moved page [[Boolf prop/3-ary/nameless 2]] to [[Boolf prop/3-ary/twin mentor]]</comment>
      <origin>2693054</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="14133" sha1="374rzqx9kfzbjhymt41ocokjknnm2ao" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 87183322370842425795587566660030343945541236792690890543826997033971843334915.svg|thumb|500px|The values 0, 1, 8, 9... form the block of [[Boolf prop/3-ary/great patron|great patron]] 0.]]

&lt;source lang=&quot;python&quot;&gt;
val = (boolf.twin(3) ^ boolf.mentor(3)).zhe
&lt;/source&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;
&lt;/div&gt;

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[[Category:Boolf prop/3-ary|nameless 2]]</text>
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  </page>
  <page>
    <title>Boolf prop/3-ary/great patron</title>
    <ns>0</ns>
    <id>317258</id>
    <revision>
      <id>2693006</id>
      <parentid>2692110</parentid>
      <timestamp>2024-12-23T13:16:50Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
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&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;
&lt;/div&gt;

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!class=&quot;prop&quot;| patron tiling and slatting
!class=&quot;prop&quot;| patron symmetry perm
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|}

[[Category:Boolf prop/3-ary|great patron]]</text>
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      <contributor>
        <username>Bert Niehaus</username>
        <id>2387134</id>
      </contributor>
      <comment>/* Relation to Homology Theory */</comment>
      <origin>2693108</origin>
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      <text bytes="9612" sha1="3eaqfm06njpyw4bt2dibcwc78e8j91t" xml:space="preserve">== Introduction ==
'''Chain''' and '''cycle''' are mathematical objects studied in [[Complex Analysis|Complex Analysis]] but also appear as special cases in [[w:en:Algebraic topology|Algebraic topology]]. A chain generalizes a [[w:en:Path (topology)|curve]], and a cycle generalizes a closed curve. They are primarily used in integration in complex analysis.

== Definitions ==
=== Chain ===
A chain on a set &lt;math&gt;G \subset \mathbb{C}&lt;/math&gt; is defined as a finite integer linear combination of paths &lt;math&gt;\gamma_1,\ldots, \gamma_k&lt;/math&gt;:
&lt;math&gt;\Gamma := \sum_{i=1}^k n_i\gamma_i \quad n_i \in \mathbb{Z}&lt;/math&gt;.
&lt;math&gt;\gamma_1,\ldots, \gamma_k&lt;/math&gt; are generally continuous [[w:en:Curve|Curve]] in &lt;math&gt;G&lt;/math&gt;.

=== Integration over a chain ===
Let &lt;math&gt;f:G \to \mathbb{C}&lt;/math&gt; be integrable, and let &lt;math&gt;\Gamma&lt;/math&gt; be a chain of piecewise continuously differentiable paths (paths of integration) &lt;math&gt;\gamma_1,\ldots, \gamma_k&lt;/math&gt; in &lt;math&gt;G \subset \mathbb{C}&lt;/math&gt;. The integral over the chain &lt;math&gt;\Gamma&lt;/math&gt; is defined by:
:&lt;math&gt;\int_\Gamma f(z) \, dz := \sum_{i = 1}^k n_i \int_{\gamma_i} f(z) \, dz&lt;/math&gt;

=== Definition: Cycle ===
'''Version 1:''' A cycle is a chain &lt;math&gt;\Gamma := \sum_{i=1}^k n_i\gamma_i&lt;/math&gt;, where every point &lt;math&gt;a \in \mathbb{C}&lt;/math&gt; appears as the starting point as many times as it appears as the endpoint of the curves &lt;math&gt;\gamma_i&lt;/math&gt;, taking multiplicities &lt;math&gt;n_i&lt;/math&gt; into account.

'''Version 2:''' A cycle is a chain &lt;math&gt;\Gamma := \sum_{i=1}^k n_i\gamma_i&lt;/math&gt; consisting of closed paths &lt;math&gt;\gamma_1, \ldots, \gamma_k&lt;/math&gt;.

=== Connection Between Version 1 and Version 2 ===
Version 2 is essential for complex analysis. Based on the properties of Version 1, any cycle &lt;math&gt;\Gamma := \sum_{i=1}^k n_i\gamma_i&lt;/math&gt; can be transformed into a chain &lt;math&gt;\hat{\Gamma} := \sum_{i=1}^m \hat{n}_i \hat{\gamma}_i&lt;/math&gt; of closed paths &lt;math&gt;\hat{\gamma}_1, \ldots, \hat{\gamma}_m&lt;/math&gt;.
If the paths &lt;math&gt;\gamma_1, \ldots, \gamma_k&lt;/math&gt; are piecewise continuously differentiable, then the closed paths &lt;math&gt;\hat{\gamma}1, \ldots, \hat{\gamma}m&lt;/math&gt; are also continuously differentiable. For all holomorphic functions &lt;math&gt;f:G \to \mathbb{C}&lt;/math&gt;, it holds that:
&lt;math&gt;\int\Gamma f(z) , dz = \int{\hat{\Gamma}} f(z) , dz&lt;/math&gt;.

=== Trace of a path ===
The '''trace''' of a path &lt;math&gt;\gamma : [a,b] \to G&lt;/math&gt; is defined as:
&lt;math&gt;\operatorname{Trace}(\gamma_i) := \operatorname{Image}(\gamma) := { \gamma(t) ,| , t \in [a,b] }&lt;/math&gt;.

=== Trace of a cycle/chain ===
The trace of a chain &lt;math&gt;\Gamma&lt;/math&gt; is the union of the [[w:en:Image (mathematics)|Image (mathematics)]] of its individual curves, i.e.:
&lt;math&gt;\operatorname{Trace}(\Gamma) := \bigcup_{i=1}^N\operatorname{Image}(\gamma_i)&lt;/math&gt;.
If &lt;math&gt;\operatorname{Trace}(\Gamma) \subset \mathbb{C}&lt;/math&gt; is a subset of &lt;math&gt;G \subset \mathbb{C}&lt;/math&gt;, then &lt;math&gt;\Gamma&lt;/math&gt; is called a cycle '''in''' &lt;math&gt;G&lt;/math&gt; if and only if the trace &lt;math&gt;\operatorname{Trace}(\Gamma) \subseteq G&lt;/math&gt; lies in &lt;math&gt;G&lt;/math&gt;.

=== Winding number ===
The '''[[w:en:Winding number|Winding number]]''' is defined analogously to that of a closed curve but uses the integral defined above. For &lt;math&gt;z \not\in \operatorname{Trace}(\Gamma)&lt;/math&gt;, it is given by:
&lt;math&gt;n(\Gamma , z) := \frac{1}{2\pi \mathrm{i}} \int_\Gamma \frac{\mathrm{d}\zeta}{\zeta - z} \in \mathbb{Z}&lt;/math&gt;.

=== Interior points of a cycle ===
The '''interior''' of a cycle consists of all points for which the winding number is non-zero:
&lt;math&gt;\operatorname{Int}(\Gamma):={z\in\mathbb{C}\setminus\operatorname{Trace}(\Gamma) : n(\Gamma , z) \neq 0}&lt;/math&gt;.

=== Exterior points of a cycle ===
Analogously, the '''exterior''' is the set of points for which the winding number is zero:
&lt;math&gt;\operatorname{Ext}(\Gamma):={z\in\mathbb{C}\setminus\operatorname{Trace}(\Gamma) : n(\Gamma , z) = 0}&lt;/math&gt;.

=== zero-homologous cycle ===
A cycle is called '''null-homologous''' for a set &lt;math&gt;G\subseteq\mathbb{C}&lt;/math&gt; if and only if the interior &lt;math&gt;\operatorname{Int}(\Gamma)&lt;/math&gt; lies entirely within &lt;math&gt;G&lt;/math&gt;. This is equivalent to the winding number vanishing for all points in &lt;math&gt;\mathbb{C} \setminus G&lt;/math&gt;.

=== Homologous cycles ===
Two cycles &lt;math&gt;\Gamma_1&lt;/math&gt;, &lt;math&gt;\Gamma_2&lt;/math&gt; are called '''homologous''' in &lt;math&gt;G\subseteq\mathbb{C}&lt;/math&gt; if and only if their formal difference &lt;math&gt;\Gamma_1-\Gamma_2&lt;/math&gt; is null-homologous in &lt;math&gt;G&lt;/math&gt;.

== Integral Theorems ==
Chains and cycles are important in complex analysis because, as mentioned, they generalize curve integrals. In particular, the integral over a cycle generalizes the closed curve integral. The [[w:en:Cauchy's integral theorem|Cauchy's integral theorem]], the [[w:en:Cauchy's integral formula|Cauchy's integral formula]], and the [[w:en:Residue theorem|Residue theorem]] can be proven for cycles.

== Relation to Homology Theory ==
To indicate that chains and cycles are special cases of objects in [[w:en:Homology (mathematics)|Homology (mathematics)]] of algebraic topology, they are sometimes referred to as 1-chains and 1-cycles.&lt;ref&gt;[[w:en:Otto Forster|Otto Forster]]: ''Riemann surfaces'', Springer 1977; English edition: ''Lectures on Riemann surfaces'', Graduate Texts in Mathematics, Springer-Verlag, 1991, ISBN 3-540-90617-7, Chapter 20&lt;/ref&gt;. In algebraic topology, the term 1-cycle or p-cycle is commonly used instead of cycle.&lt;ref&gt;{{Literature| Author=Wolfgang Lück| Title=Algebraic Topology: Homology and Manifolds| Publisher=Vieweg| Year=2005}}&lt;/ref&gt;. 

=== Embedding in Homology Theory ===
The terms chain and cycle are special cases of [[w:en:Mathematical object|Mathematical object]] in [[w:en:Topology (mathematics)|topology]]. In [[w:en:Algebraic topology|Algebraic topology]], one considers [[w:en:Chain complex|complexes of p-chains]] and constructs [[w:en:Homology (mathematics)|Homology (mathematics)]] from them. These groups are [[w:en:Invariant (mathematics)|Invariant (mathematics)]] in topology. A very important [[w:en:Homology (mathematics)|Homology (mathematics)]] is that of [[w:en:Singular homology|Singular homology]].

=== 1-Chain of the Singular Complex ===
A chain, as defined here, is a 1-chain of the [[w:en:Singular homology|Singular homology]], which is a specific chain complex. The operator defined in the section on cycles, &lt;math&gt;\partial \colon C_1(X) \to \operatorname{Div}(X)&lt;/math&gt;, is the first [[w:en:Boundary operator|boundary operator]] of the singular complex. The group of divisors is therefore identical to the group of 0-chains. The group of cycles, defined as the kernel of the boundary operator &lt;math&gt;\partial&lt;/math&gt;, is a 1-[[w:en:Chain complex|Chain complex]] in the sense of the singular complex.

=== Algebraic Topology ===
In algebraic topology, one considers both the kernel of the boundary operator and the image of this operator, constructing a corresponding homology group from these two sets. In the case of the singular complex, one obtains [[w:en:Singular homology|Singular homology]]. In this context, the previously defined terms homologous chain and null-homologous chain take on a more abstract meaning.

== See also ==

*[[w:en:Global Cauchy Integral Theorem]]

*[[w:en:Stokes' theorem|Stokes' theorem]]

*[[w:en:Smooth function|smooth function]]

== References ==

{{Literature
| Author=Wolfgang Fischer, Ingo Lieb
| Title=Complex Analysis
| Edition=8th
| Publisher=Vieweg
| Location=Braunschweig
| Year=2003
| ISBN=3-528-77247-6
}}

[[w:en:Otto Forster|Otto Forster]]: ''Riemann surfaces'', Springer 1977; English edition: ''Lectures on Riemann surfaces'', Graduate Texts in Mathematics, Springer-Verlag, 1991, ISBN 3-540-90617-7, Chapter 20


== Notes ==
&lt;references /&gt;

[[Category:Complex analysis]]

== Page Information ==
You can display this page as 
'''[https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/cycle&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=cycle&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]'''

=== Wiki2Reveal ===
The'''[https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/cycle&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=cycle&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]'''  were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' 
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&lt;!--
* Contents of the page are based on:
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* Date: 12/17/2024

&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Zyklus&quot; srclang=&quot;de&quot; date=&quot;12/17/2024&quot; time=&quot;08:50&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Kurs:Funktionentheorie/Zyklus]]
&lt;/noinclude&gt;

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      <contributor>
        <username>Bert Niehaus</username>
        <id>2387134</id>
      </contributor>
      <comment>/* Relation to Homology Theory */ Book titles should not be translated</comment>
      <origin>2693109</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="9584" sha1="6sh66c6z8j289llehfcmp0m2vm6ilgl" xml:space="preserve">== Introduction ==
'''Chain''' and '''cycle''' are mathematical objects studied in [[Complex Analysis|Complex Analysis]] but also appear as special cases in [[w:en:Algebraic topology|Algebraic topology]]. A chain generalizes a [[w:en:Path (topology)|curve]], and a cycle generalizes a closed curve. They are primarily used in integration in complex analysis.

== Definitions ==
=== Chain ===
A chain on a set &lt;math&gt;G \subset \mathbb{C}&lt;/math&gt; is defined as a finite integer linear combination of paths &lt;math&gt;\gamma_1,\ldots, \gamma_k&lt;/math&gt;:
&lt;math&gt;\Gamma := \sum_{i=1}^k n_i\gamma_i \quad n_i \in \mathbb{Z}&lt;/math&gt;.
&lt;math&gt;\gamma_1,\ldots, \gamma_k&lt;/math&gt; are generally continuous [[w:en:Curve|Curve]] in &lt;math&gt;G&lt;/math&gt;.

=== Integration over a chain ===
Let &lt;math&gt;f:G \to \mathbb{C}&lt;/math&gt; be integrable, and let &lt;math&gt;\Gamma&lt;/math&gt; be a chain of piecewise continuously differentiable paths (paths of integration) &lt;math&gt;\gamma_1,\ldots, \gamma_k&lt;/math&gt; in &lt;math&gt;G \subset \mathbb{C}&lt;/math&gt;. The integral over the chain &lt;math&gt;\Gamma&lt;/math&gt; is defined by:
:&lt;math&gt;\int_\Gamma f(z) \, dz := \sum_{i = 1}^k n_i \int_{\gamma_i} f(z) \, dz&lt;/math&gt;

=== Definition: Cycle ===
'''Version 1:''' A cycle is a chain &lt;math&gt;\Gamma := \sum_{i=1}^k n_i\gamma_i&lt;/math&gt;, where every point &lt;math&gt;a \in \mathbb{C}&lt;/math&gt; appears as the starting point as many times as it appears as the endpoint of the curves &lt;math&gt;\gamma_i&lt;/math&gt;, taking multiplicities &lt;math&gt;n_i&lt;/math&gt; into account.

'''Version 2:''' A cycle is a chain &lt;math&gt;\Gamma := \sum_{i=1}^k n_i\gamma_i&lt;/math&gt; consisting of closed paths &lt;math&gt;\gamma_1, \ldots, \gamma_k&lt;/math&gt;.

=== Connection Between Version 1 and Version 2 ===
Version 2 is essential for complex analysis. Based on the properties of Version 1, any cycle &lt;math&gt;\Gamma := \sum_{i=1}^k n_i\gamma_i&lt;/math&gt; can be transformed into a chain &lt;math&gt;\hat{\Gamma} := \sum_{i=1}^m \hat{n}_i \hat{\gamma}_i&lt;/math&gt; of closed paths &lt;math&gt;\hat{\gamma}_1, \ldots, \hat{\gamma}_m&lt;/math&gt;.
If the paths &lt;math&gt;\gamma_1, \ldots, \gamma_k&lt;/math&gt; are piecewise continuously differentiable, then the closed paths &lt;math&gt;\hat{\gamma}1, \ldots, \hat{\gamma}m&lt;/math&gt; are also continuously differentiable. For all holomorphic functions &lt;math&gt;f:G \to \mathbb{C}&lt;/math&gt;, it holds that:
&lt;math&gt;\int\Gamma f(z) , dz = \int{\hat{\Gamma}} f(z) , dz&lt;/math&gt;.

=== Trace of a path ===
The '''trace''' of a path &lt;math&gt;\gamma : [a,b] \to G&lt;/math&gt; is defined as:
&lt;math&gt;\operatorname{Trace}(\gamma_i) := \operatorname{Image}(\gamma) := { \gamma(t) ,| , t \in [a,b] }&lt;/math&gt;.

=== Trace of a cycle/chain ===
The trace of a chain &lt;math&gt;\Gamma&lt;/math&gt; is the union of the [[w:en:Image (mathematics)|Image (mathematics)]] of its individual curves, i.e.:
&lt;math&gt;\operatorname{Trace}(\Gamma) := \bigcup_{i=1}^N\operatorname{Image}(\gamma_i)&lt;/math&gt;.
If &lt;math&gt;\operatorname{Trace}(\Gamma) \subset \mathbb{C}&lt;/math&gt; is a subset of &lt;math&gt;G \subset \mathbb{C}&lt;/math&gt;, then &lt;math&gt;\Gamma&lt;/math&gt; is called a cycle '''in''' &lt;math&gt;G&lt;/math&gt; if and only if the trace &lt;math&gt;\operatorname{Trace}(\Gamma) \subseteq G&lt;/math&gt; lies in &lt;math&gt;G&lt;/math&gt;.

=== Winding number ===
The '''[[w:en:Winding number|Winding number]]''' is defined analogously to that of a closed curve but uses the integral defined above. For &lt;math&gt;z \not\in \operatorname{Trace}(\Gamma)&lt;/math&gt;, it is given by:
&lt;math&gt;n(\Gamma , z) := \frac{1}{2\pi \mathrm{i}} \int_\Gamma \frac{\mathrm{d}\zeta}{\zeta - z} \in \mathbb{Z}&lt;/math&gt;.

=== Interior points of a cycle ===
The '''interior''' of a cycle consists of all points for which the winding number is non-zero:
&lt;math&gt;\operatorname{Int}(\Gamma):={z\in\mathbb{C}\setminus\operatorname{Trace}(\Gamma) : n(\Gamma , z) \neq 0}&lt;/math&gt;.

=== Exterior points of a cycle ===
Analogously, the '''exterior''' is the set of points for which the winding number is zero:
&lt;math&gt;\operatorname{Ext}(\Gamma):={z\in\mathbb{C}\setminus\operatorname{Trace}(\Gamma) : n(\Gamma , z) = 0}&lt;/math&gt;.

=== zero-homologous cycle ===
A cycle is called '''null-homologous''' for a set &lt;math&gt;G\subseteq\mathbb{C}&lt;/math&gt; if and only if the interior &lt;math&gt;\operatorname{Int}(\Gamma)&lt;/math&gt; lies entirely within &lt;math&gt;G&lt;/math&gt;. This is equivalent to the winding number vanishing for all points in &lt;math&gt;\mathbb{C} \setminus G&lt;/math&gt;.

=== Homologous cycles ===
Two cycles &lt;math&gt;\Gamma_1&lt;/math&gt;, &lt;math&gt;\Gamma_2&lt;/math&gt; are called '''homologous''' in &lt;math&gt;G\subseteq\mathbb{C}&lt;/math&gt; if and only if their formal difference &lt;math&gt;\Gamma_1-\Gamma_2&lt;/math&gt; is null-homologous in &lt;math&gt;G&lt;/math&gt;.

== Integral Theorems ==
Chains and cycles are important in complex analysis because, as mentioned, they generalize curve integrals. In particular, the integral over a cycle generalizes the closed curve integral. The [[w:en:Cauchy's integral theorem|Cauchy's integral theorem]], the [[w:en:Cauchy's integral formula|Cauchy's integral formula]], and the [[w:en:Residue theorem|Residue theorem]] can be proven for cycles.

== Relation to Homology Theory ==
To indicate that chains and cycles are special cases of objects in [[w:en:Homology (mathematics)|Homology (mathematics)]] of algebraic topology, they are sometimes referred to as 1-chains and 1-cycles.&lt;ref&gt;[[w:en:Otto Forster|Otto Forster]]: ''Riemann surfaces'', Springer 1977; English edition: ''Lectures on Riemann surfaces'', Graduate Texts in Mathematics, Springer-Verlag, 1991, ISBN 3-540-90617-7, Chapter 20&lt;/ref&gt;. In algebraic topology, the term 1-cycle or p-cycle is commonly used instead of cycle.&lt;ref&gt;Wolfgang Lück: Algebraische Topologie : Homologie und Mannigfaltigkeiten. Vieweg, 2005&lt;/ref&gt;. 


=== Embedding in Homology Theory ===
The terms chain and cycle are special cases of [[w:en:Mathematical object|Mathematical object]] in [[w:en:Topology (mathematics)|topology]]. In [[w:en:Algebraic topology|Algebraic topology]], one considers [[w:en:Chain complex|complexes of p-chains]] and constructs [[w:en:Homology (mathematics)|Homology (mathematics)]] from them. These groups are [[w:en:Invariant (mathematics)|Invariant (mathematics)]] in topology. A very important [[w:en:Homology (mathematics)|Homology (mathematics)]] is that of [[w:en:Singular homology|Singular homology]].

=== 1-Chain of the Singular Complex ===
A chain, as defined here, is a 1-chain of the [[w:en:Singular homology|Singular homology]], which is a specific chain complex. The operator defined in the section on cycles, &lt;math&gt;\partial \colon C_1(X) \to \operatorname{Div}(X)&lt;/math&gt;, is the first [[w:en:Boundary operator|boundary operator]] of the singular complex. The group of divisors is therefore identical to the group of 0-chains. The group of cycles, defined as the kernel of the boundary operator &lt;math&gt;\partial&lt;/math&gt;, is a 1-[[w:en:Chain complex|Chain complex]] in the sense of the singular complex.

=== Algebraic Topology ===
In algebraic topology, one considers both the kernel of the boundary operator and the image of this operator, constructing a corresponding homology group from these two sets. In the case of the singular complex, one obtains [[w:en:Singular homology|Singular homology]]. In this context, the previously defined terms homologous chain and null-homologous chain take on a more abstract meaning.

== See also ==

*[[w:en:Global Cauchy Integral Theorem]]

*[[w:en:Stokes' theorem|Stokes' theorem]]

*[[w:en:Smooth function|smooth function]]

== References ==

{{Literature
| Author=Wolfgang Fischer, Ingo Lieb
| Title=Complex Analysis
| Edition=8th
| Publisher=Vieweg
| Location=Braunschweig
| Year=2003
| ISBN=3-528-77247-6
}}

[[w:en:Otto Forster|Otto Forster]]: ''Riemann surfaces'', Springer 1977; English edition: ''Lectures on Riemann surfaces'', Graduate Texts in Mathematics, Springer-Verlag, 1991, ISBN 3-540-90617-7, Chapter 20


== Notes ==
&lt;references /&gt;

[[Category:Complex analysis]]

== Page Information ==
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=== Wiki2Reveal ===
The'''[https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/cycle&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=cycle&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]'''  were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' 
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&lt;!--
* Contents of the page are based on:
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=== Translation and Version Control ===

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Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/Zyklus|Kurs:Funktionentheorie/Zyklus]] - URL:
https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Zyklus
* Date: 12/17/2024

&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Zyklus&quot; srclang=&quot;de&quot; date=&quot;12/17/2024&quot; time=&quot;08:50&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Kurs:Funktionentheorie/Zyklus]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
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      <minor />
      <comment>Watchduck moved page [[Boolf prop/3-ary/leveled praetor sword]] to [[Boolf prop/3-ary/greater twin mentor]]</comment>
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&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;
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[[Category:Boolf prop/3-ary|leveled praetor sword]]</text>
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&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;
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[[Category:Boolf prop/3-ary|greater twin mentor]]</text>
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      <text bytes="252" sha1="ebs6i9btu2r083gid78z4cpms549zc3" xml:space="preserve">== Summary ==
{{Information
|Description=Borrows (20241217 - 20241216)
|Source={{own|Young1lim}}
|Date=2024-12-17
|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}}</text>
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    <title>Complex Analysis/Cauchy Integral Theorem</title>
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      <text bytes="7933" sha1="d8yzrkegv913efcym9nfzgnfvhcmctk" xml:space="preserve">==Introduction==
The Cauchy integral theorem is one of the central results of [[w:en:Complex Analysis|Complex Analysis]]. It exists in various versions, and in this article, we aim to present a basic one for convex regions and a relatively general one for [[w:en:Homology (mathematics)|nullhomologous cycles]].
==For Convex Regions==
=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a convex region, and let &lt;math&gt;\gamma&lt;/math&gt; be a closed 
[[Complex Analysis/rectifiable curve|rectifiable curve]] 
[[Complex Analysis/Trace|Trace of Curve]] in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof 1: Primitive of &lt;math&gt;f&lt;/math&gt; ===
First, we observe that &lt;math&gt;f&lt;/math&gt; has a primitive in &lt;math&gt;G&lt;/math&gt;. Fix a point &lt;math&gt;z_0 \in G&lt;/math&gt;. For any point &lt;math&gt;z \in G&lt;/math&gt;, let &lt;math&gt;[z_0, z]&lt;/math&gt; denote the straight-line segment connecting &lt;math&gt;z_0&lt;/math&gt; and &lt;math&gt;z&lt;/math&gt;.

== Proof 2: Definition of the Primitive ==
Define &lt;math&gt;F \colon G \to \mathbb{C}&lt;/math&gt; by:
:&lt;math&gt;F(z) := \int_{[z_0, z]} f(\zeta), d\zeta&lt;/math&gt;.
Due to the convexity of &lt;math&gt;G&lt;/math&gt;, the triangle &lt;math&gt;D&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w&lt;/math&gt; lies entirely within &lt;math&gt;G&lt;/math&gt; for &lt;math&gt;z, w \in G&lt;/math&gt;.

=== Proof 3: Application of Goursat’s Lemma ===
By [[Complex Analysis/Goursat's Lemma|Goursat's Lemma]] for the boundary &lt;math&gt;\partial \Delta&lt;/math&gt; of a triangle &lt;math&gt;\Delta&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w \in \mathbb{C}&lt;/math&gt;, we have:
:&lt;math&gt; \begin{array}{rl}   0         &amp;= \int_{\partial \Delta} f(z)\, dz \\     &amp;=  \int_{[z_{0},z]} f(\zeta)\, d\zeta - \int_{[z_{0},w]} f(\zeta)\, d\zeta + \int_{[z,w]} f(\zeta)\, d\zeta \\    &amp; = F(z) - F(w) + \int_{[z,w]} f(\zeta)\, d\zeta      \end{array} &lt;/math&gt;

=== Proof 4: Conclusion Using Goursat's Lemma ===
This leads to:
:&lt;math&gt;\begin{array}{rl}  F(z) - F(w) &amp;= \int_{[w,z]} f(\zeta)\,d\zeta\\              &amp;= \int_0^1 f\bigl(w + t(z-w)\bigr)\cdot (z-w)\, dt\\     &amp;= \underbrace{\int_0^1 f\bigl(w+t(z-w)\bigr)\, dt}_{A(z):=} \cdot (z-w)  \end{array}&lt;/math&gt;
Thus, we have:
:&lt;math&gt;A(z)=\frac{F(z) - F(w)}{(z-w)}&lt;/math&gt;
=== Proof 5: Limit Process ===
Since &lt;math&gt;A&lt;/math&gt; is continuous in &lt;math&gt;w&lt;/math&gt;, taking the limit as &lt;math&gt;z \to w&lt;/math&gt; gives:
:&lt;math&gt;A(w) = \lim_{z \to w} A(z) = \lim_{z \to w} \frac{F(z) - F(w)}{(z-w)} = F'(w).&lt;/math&gt;

=== Proof 5: Differentiability of &lt;math&gt;F&lt;/math&gt; ===
Therefore, &lt;math&gt;A \colon G \to \mathbb{C}&lt;/math&gt; is continuous, and &lt;math&gt;F&lt;/math&gt; is differentiable in &lt;math&gt;w \in G&lt;/math&gt;, with:

&lt;center&gt;&lt;math&gt;F'(w) = A(w) = f(w).&lt;/math&gt;&lt;/center&gt;  
Since &lt;math&gt;w \in G&lt;/math&gt; was arbitrary, we conclude &lt;math&gt;F' = f&lt;/math&gt;, proving that &lt;math&gt;f&lt;/math&gt; has a primitive.
=== Proof 6: Path Integration ===
Now, let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be a piecewise continuously differentiable, closed curve. Then:

&lt;center&gt;&lt;math&gt;  
\begin{array}{rl}  
  \int_\gamma f(z)\, dz &amp;= \int_a^b f(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b F'(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b (F \circ \gamma)'(t)\, dt \\  
                        &amp;= F(\gamma(b)) - F(\gamma(a)) = 0.  
\end{array}  
&lt;/math&gt;&lt;/center&gt;
=== Proof 7: ===
Let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be an arbitrary integration path in &lt;math&gt;G&lt;/math&gt;, and let &lt;math&gt;\epsilon &gt; 0&lt;/math&gt;. As shown [[Complex Analysis/Curve Integral #Approximation by polygonal paths|here]], we choose a polygonal path &lt;math&gt;\hat{\gamma} \colon [a, b] \to \mathbb{C}&lt;/math&gt; such that &lt;math&gt;\hat{\gamma}(a) = \gamma(a)&lt;/math&gt;, &lt;math&gt;\hat{\gamma}(b) = \gamma(b)&lt;/math&gt;, and
:&lt;math&gt;\left|\int_{\hat{\gamma}} f(z), dz - \int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
Since polygonal paths are piecewise continuously differentiable, the above result implies &lt;math&gt;\int_{\hat{\gamma}} f(z), dz = 0&lt;/math&gt;. Consequently,
:&lt;math&gt;\left|\int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
As &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; was arbitrary, the claim follows.

== For Cycles in Arbitrary Open Sets ==
In arbitrary open sets, one must ensure that cycles do not enclose singularities or poles in the complement of the domain. Enclosing such singularities may contribute a non-zero value to the integral (e.g., the function &lt;math&gt;f(z) = \frac{1}{z}&lt;/math&gt; and &lt;math&gt;\gamma(t) := e^{it}&lt;/math&gt; in a domain &lt;math&gt;G = \mathbb{C}\setminus \{0\}&lt;/math&gt; . Even though &lt;math&gt;f&lt;/math&gt; is holomorphic in &lt;math&gt;G&lt;/math&gt;, the integral is not zero but &lt;math&gt;2\pi i&lt;/math&gt; (see [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous cycle]]).

=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be open, and let &lt;math&gt;\Gamma&lt;/math&gt; be a [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous]] cycle in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\Gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof ===
Let &lt;math&gt;w \in G \setminus \text{trace}(\Gamma)&lt;/math&gt;, and define &lt;math&gt;g \colon G \to \mathbb{C}&lt;/math&gt; by

&lt;center&gt;&lt;math&gt;g(z) := (z-w) \cdot f(z).&lt;/math&gt;&lt;/center&gt;  
Then, &lt;math&gt;g&lt;/math&gt; is holomorphic, and by the [[w:en:Cauchy integral formula#For cycles in arbitrary open sets|global integral formula]], we have:  
:&lt;math&gt;  
\int_\Gamma f(z)\, dz = \int_{\Gamma} \frac{g(z)}{z-w}\, dz = 2\pi i \cdot n(\Gamma, w) \cdot g(w) = 0.  
&lt;/math&gt;
== See Also ==

*[[w:en:Complex Analysis|Complex Analysis]]

*[[w:en:Cauchy's integral theorem|Cauchy integral theorem for disks]]
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=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Integralsatz von Cauchy Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Integralsatz von Cauchy|Integralsatz von Cauchy]] - URL: https://de.wikiversity.org/wiki/Integralsatz von Cauchy
* Date: 12/18/2024

&lt;span type=&quot;translate&quot; src=&quot;Integralsatz von Cauchy&quot; srclang=&quot;de&quot; date=&quot;12/18/2024&quot; time=&quot;09:15&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Integralsatz von Cauchy]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
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      <text bytes="7912" sha1="f9yrg8bf16drwl61k68w99onnemovix" xml:space="preserve">==Introduction==
The Cauchy integral theorem is one of the central results of [[Complex Analysis]]. It exists in various versions, and in this article, we aim to present a basic one for convex regions and a relatively general one for [[w:en:Homology (mathematics)|nullhomologous cycles]].

==For Convex Regions==
=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a convex region, and let &lt;math&gt;\gamma&lt;/math&gt; be a closed 
[[Complex Analysis/rectifiable curve|rectifiable curve]] 
[[Complex Analysis/Trace|Trace of Curve]] in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof 1: Primitive of &lt;math&gt;f&lt;/math&gt; ===
First, we observe that &lt;math&gt;f&lt;/math&gt; has a primitive in &lt;math&gt;G&lt;/math&gt;. Fix a point &lt;math&gt;z_0 \in G&lt;/math&gt;. For any point &lt;math&gt;z \in G&lt;/math&gt;, let &lt;math&gt;[z_0, z]&lt;/math&gt; denote the straight-line segment connecting &lt;math&gt;z_0&lt;/math&gt; and &lt;math&gt;z&lt;/math&gt;.

== Proof 2: Definition of the Primitive ==
Define &lt;math&gt;F \colon G \to \mathbb{C}&lt;/math&gt; by:
:&lt;math&gt;F(z) := \int_{[z_0, z]} f(\zeta), d\zeta&lt;/math&gt;.
Due to the convexity of &lt;math&gt;G&lt;/math&gt;, the triangle &lt;math&gt;D&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w&lt;/math&gt; lies entirely within &lt;math&gt;G&lt;/math&gt; for &lt;math&gt;z, w \in G&lt;/math&gt;.

=== Proof 3: Application of Goursat’s Lemma ===
By [[Complex Analysis/Goursat's Lemma|Goursat's Lemma]] for the boundary &lt;math&gt;\partial \Delta&lt;/math&gt; of a triangle &lt;math&gt;\Delta&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w \in \mathbb{C}&lt;/math&gt;, we have:
:&lt;math&gt; \begin{array}{rl}   0         &amp;= \int_{\partial \Delta} f(z)\, dz \\     &amp;=  \int_{[z_{0},z]} f(\zeta)\, d\zeta - \int_{[z_{0},w]} f(\zeta)\, d\zeta + \int_{[z,w]} f(\zeta)\, d\zeta \\    &amp; = F(z) - F(w) + \int_{[z,w]} f(\zeta)\, d\zeta      \end{array} &lt;/math&gt;

=== Proof 4: Conclusion Using Goursat's Lemma ===
This leads to:
:&lt;math&gt;\begin{array}{rl}  F(z) - F(w) &amp;= \int_{[w,z]} f(\zeta)\,d\zeta\\              &amp;= \int_0^1 f\bigl(w + t(z-w)\bigr)\cdot (z-w)\, dt\\     &amp;= \underbrace{\int_0^1 f\bigl(w+t(z-w)\bigr)\, dt}_{A(z):=} \cdot (z-w)  \end{array}&lt;/math&gt;
Thus, we have:
:&lt;math&gt;A(z)=\frac{F(z) - F(w)}{(z-w)}&lt;/math&gt;
=== Proof 5: Limit Process ===
Since &lt;math&gt;A&lt;/math&gt; is continuous in &lt;math&gt;w&lt;/math&gt;, taking the limit as &lt;math&gt;z \to w&lt;/math&gt; gives:
:&lt;math&gt;A(w) = \lim_{z \to w} A(z) = \lim_{z \to w} \frac{F(z) - F(w)}{(z-w)} = F'(w).&lt;/math&gt;

=== Proof 5: Differentiability of &lt;math&gt;F&lt;/math&gt; ===
Therefore, &lt;math&gt;A \colon G \to \mathbb{C}&lt;/math&gt; is continuous, and &lt;math&gt;F&lt;/math&gt; is differentiable in &lt;math&gt;w \in G&lt;/math&gt;, with:

&lt;center&gt;&lt;math&gt;F'(w) = A(w) = f(w).&lt;/math&gt;&lt;/center&gt;  
Since &lt;math&gt;w \in G&lt;/math&gt; was arbitrary, we conclude &lt;math&gt;F' = f&lt;/math&gt;, proving that &lt;math&gt;f&lt;/math&gt; has a primitive.
=== Proof 6: Path Integration ===
Now, let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be a piecewise continuously differentiable, closed curve. Then:

&lt;center&gt;&lt;math&gt;  
\begin{array}{rl}  
  \int_\gamma f(z)\, dz &amp;= \int_a^b f(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b F'(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b (F \circ \gamma)'(t)\, dt \\  
                        &amp;= F(\gamma(b)) - F(\gamma(a)) = 0.  
\end{array}  
&lt;/math&gt;&lt;/center&gt;
=== Proof 7: ===
Let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be an arbitrary integration path in &lt;math&gt;G&lt;/math&gt;, and let &lt;math&gt;\epsilon &gt; 0&lt;/math&gt;. As shown [[Complex Analysis/Curve Integral #Approximation by polygonal paths|here]], we choose a polygonal path &lt;math&gt;\hat{\gamma} \colon [a, b] \to \mathbb{C}&lt;/math&gt; such that &lt;math&gt;\hat{\gamma}(a) = \gamma(a)&lt;/math&gt;, &lt;math&gt;\hat{\gamma}(b) = \gamma(b)&lt;/math&gt;, and
:&lt;math&gt;\left|\int_{\hat{\gamma}} f(z), dz - \int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
Since polygonal paths are piecewise continuously differentiable, the above result implies &lt;math&gt;\int_{\hat{\gamma}} f(z), dz = 0&lt;/math&gt;. Consequently,
:&lt;math&gt;\left|\int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
As &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; was arbitrary, the claim follows.

== For Cycles in Arbitrary Open Sets ==
In arbitrary open sets, one must ensure that cycles do not enclose singularities or poles in the complement of the domain. Enclosing such singularities may contribute a non-zero value to the integral (e.g., the function &lt;math&gt;f(z) = \frac{1}{z}&lt;/math&gt; and &lt;math&gt;\gamma(t) := e^{it}&lt;/math&gt; in a domain &lt;math&gt;G = \mathbb{C}\setminus \{0\}&lt;/math&gt; . Even though &lt;math&gt;f&lt;/math&gt; is holomorphic in &lt;math&gt;G&lt;/math&gt;, the integral is not zero but &lt;math&gt;2\pi i&lt;/math&gt; (see [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous cycle]]).

=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be open, and let &lt;math&gt;\Gamma&lt;/math&gt; be a [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous]] cycle in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\Gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof ===
Let &lt;math&gt;w \in G \setminus \text{trace}(\Gamma)&lt;/math&gt;, and define &lt;math&gt;g \colon G \to \mathbb{C}&lt;/math&gt; by

&lt;center&gt;&lt;math&gt;g(z) := (z-w) \cdot f(z).&lt;/math&gt;&lt;/center&gt;  
Then, &lt;math&gt;g&lt;/math&gt; is holomorphic, and by the [[w:en:Cauchy integral formula#For cycles in arbitrary open sets|global integral formula]], we have:  
:&lt;math&gt;  
\int_\Gamma f(z)\, dz = \int_{\Gamma} \frac{g(z)}{z-w}\, dz = 2\pi i \cdot n(\Gamma, w) \cdot g(w) = 0.  
&lt;/math&gt;
== See Also ==

*[[w:en:Complex Analysis|Complex Analysis]]

*[[w:en:Cauchy's integral theorem|Cauchy integral theorem for disks]]
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=== Translation and Version Control ===

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* Source: [[v:de:Integralsatz von Cauchy|Integralsatz von Cauchy]] - URL: https://de.wikiversity.org/wiki/Integralsatz von Cauchy
* Date: 12/18/2024

&lt;span type=&quot;translate&quot; src=&quot;Integralsatz von Cauchy&quot; srclang=&quot;de&quot; date=&quot;12/18/2024&quot; time=&quot;09:15&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Integralsatz von Cauchy]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
      <sha1>f9yrg8bf16drwl61k68w99onnemovix</sha1>
    </revision>
    <revision>
      <id>2693103</id>
      <parentid>2693102</parentid>
      <timestamp>2024-12-24T09:41:31Z</timestamp>
      <contributor>
        <username>Bert Niehaus</username>
        <id>2387134</id>
      </contributor>
      <minor />
      <comment>Bert Niehaus moved page [[Complex Analysis Cauchy Integral Theorem]] to [[Complex Analysis/Cauchy Integral Theorem]] without leaving a redirect: Slash was removed in link - that moved learning resource out of Complex Analysis</comment>
      <origin>2693102</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="7912" sha1="f9yrg8bf16drwl61k68w99onnemovix" xml:space="preserve">==Introduction==
The Cauchy integral theorem is one of the central results of [[Complex Analysis]]. It exists in various versions, and in this article, we aim to present a basic one for convex regions and a relatively general one for [[w:en:Homology (mathematics)|nullhomologous cycles]].

==For Convex Regions==
=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a convex region, and let &lt;math&gt;\gamma&lt;/math&gt; be a closed 
[[Complex Analysis/rectifiable curve|rectifiable curve]] 
[[Complex Analysis/Trace|Trace of Curve]] in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof 1: Primitive of &lt;math&gt;f&lt;/math&gt; ===
First, we observe that &lt;math&gt;f&lt;/math&gt; has a primitive in &lt;math&gt;G&lt;/math&gt;. Fix a point &lt;math&gt;z_0 \in G&lt;/math&gt;. For any point &lt;math&gt;z \in G&lt;/math&gt;, let &lt;math&gt;[z_0, z]&lt;/math&gt; denote the straight-line segment connecting &lt;math&gt;z_0&lt;/math&gt; and &lt;math&gt;z&lt;/math&gt;.

== Proof 2: Definition of the Primitive ==
Define &lt;math&gt;F \colon G \to \mathbb{C}&lt;/math&gt; by:
:&lt;math&gt;F(z) := \int_{[z_0, z]} f(\zeta), d\zeta&lt;/math&gt;.
Due to the convexity of &lt;math&gt;G&lt;/math&gt;, the triangle &lt;math&gt;D&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w&lt;/math&gt; lies entirely within &lt;math&gt;G&lt;/math&gt; for &lt;math&gt;z, w \in G&lt;/math&gt;.

=== Proof 3: Application of Goursat’s Lemma ===
By [[Complex Analysis/Goursat's Lemma|Goursat's Lemma]] for the boundary &lt;math&gt;\partial \Delta&lt;/math&gt; of a triangle &lt;math&gt;\Delta&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w \in \mathbb{C}&lt;/math&gt;, we have:
:&lt;math&gt; \begin{array}{rl}   0         &amp;= \int_{\partial \Delta} f(z)\, dz \\     &amp;=  \int_{[z_{0},z]} f(\zeta)\, d\zeta - \int_{[z_{0},w]} f(\zeta)\, d\zeta + \int_{[z,w]} f(\zeta)\, d\zeta \\    &amp; = F(z) - F(w) + \int_{[z,w]} f(\zeta)\, d\zeta      \end{array} &lt;/math&gt;

=== Proof 4: Conclusion Using Goursat's Lemma ===
This leads to:
:&lt;math&gt;\begin{array}{rl}  F(z) - F(w) &amp;= \int_{[w,z]} f(\zeta)\,d\zeta\\              &amp;= \int_0^1 f\bigl(w + t(z-w)\bigr)\cdot (z-w)\, dt\\     &amp;= \underbrace{\int_0^1 f\bigl(w+t(z-w)\bigr)\, dt}_{A(z):=} \cdot (z-w)  \end{array}&lt;/math&gt;
Thus, we have:
:&lt;math&gt;A(z)=\frac{F(z) - F(w)}{(z-w)}&lt;/math&gt;
=== Proof 5: Limit Process ===
Since &lt;math&gt;A&lt;/math&gt; is continuous in &lt;math&gt;w&lt;/math&gt;, taking the limit as &lt;math&gt;z \to w&lt;/math&gt; gives:
:&lt;math&gt;A(w) = \lim_{z \to w} A(z) = \lim_{z \to w} \frac{F(z) - F(w)}{(z-w)} = F'(w).&lt;/math&gt;

=== Proof 5: Differentiability of &lt;math&gt;F&lt;/math&gt; ===
Therefore, &lt;math&gt;A \colon G \to \mathbb{C}&lt;/math&gt; is continuous, and &lt;math&gt;F&lt;/math&gt; is differentiable in &lt;math&gt;w \in G&lt;/math&gt;, with:

&lt;center&gt;&lt;math&gt;F'(w) = A(w) = f(w).&lt;/math&gt;&lt;/center&gt;  
Since &lt;math&gt;w \in G&lt;/math&gt; was arbitrary, we conclude &lt;math&gt;F' = f&lt;/math&gt;, proving that &lt;math&gt;f&lt;/math&gt; has a primitive.
=== Proof 6: Path Integration ===
Now, let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be a piecewise continuously differentiable, closed curve. Then:

&lt;center&gt;&lt;math&gt;  
\begin{array}{rl}  
  \int_\gamma f(z)\, dz &amp;= \int_a^b f(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b F'(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b (F \circ \gamma)'(t)\, dt \\  
                        &amp;= F(\gamma(b)) - F(\gamma(a)) = 0.  
\end{array}  
&lt;/math&gt;&lt;/center&gt;
=== Proof 7: ===
Let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be an arbitrary integration path in &lt;math&gt;G&lt;/math&gt;, and let &lt;math&gt;\epsilon &gt; 0&lt;/math&gt;. As shown [[Complex Analysis/Curve Integral #Approximation by polygonal paths|here]], we choose a polygonal path &lt;math&gt;\hat{\gamma} \colon [a, b] \to \mathbb{C}&lt;/math&gt; such that &lt;math&gt;\hat{\gamma}(a) = \gamma(a)&lt;/math&gt;, &lt;math&gt;\hat{\gamma}(b) = \gamma(b)&lt;/math&gt;, and
:&lt;math&gt;\left|\int_{\hat{\gamma}} f(z), dz - \int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
Since polygonal paths are piecewise continuously differentiable, the above result implies &lt;math&gt;\int_{\hat{\gamma}} f(z), dz = 0&lt;/math&gt;. Consequently,
:&lt;math&gt;\left|\int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
As &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; was arbitrary, the claim follows.

== For Cycles in Arbitrary Open Sets ==
In arbitrary open sets, one must ensure that cycles do not enclose singularities or poles in the complement of the domain. Enclosing such singularities may contribute a non-zero value to the integral (e.g., the function &lt;math&gt;f(z) = \frac{1}{z}&lt;/math&gt; and &lt;math&gt;\gamma(t) := e^{it}&lt;/math&gt; in a domain &lt;math&gt;G = \mathbb{C}\setminus \{0\}&lt;/math&gt; . Even though &lt;math&gt;f&lt;/math&gt; is holomorphic in &lt;math&gt;G&lt;/math&gt;, the integral is not zero but &lt;math&gt;2\pi i&lt;/math&gt; (see [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous cycle]]).

=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be open, and let &lt;math&gt;\Gamma&lt;/math&gt; be a [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous]] cycle in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\Gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof ===
Let &lt;math&gt;w \in G \setminus \text{trace}(\Gamma)&lt;/math&gt;, and define &lt;math&gt;g \colon G \to \mathbb{C}&lt;/math&gt; by

&lt;center&gt;&lt;math&gt;g(z) := (z-w) \cdot f(z).&lt;/math&gt;&lt;/center&gt;  
Then, &lt;math&gt;g&lt;/math&gt; is holomorphic, and by the [[w:en:Cauchy integral formula#For cycles in arbitrary open sets|global integral formula]], we have:  
:&lt;math&gt;  
\int_\Gamma f(z)\, dz = \int_{\Gamma} \frac{g(z)}{z-w}\, dz = 2\pi i \cdot n(\Gamma, w) \cdot g(w) = 0.  
&lt;/math&gt;
== See Also ==

*[[w:en:Complex Analysis|Complex Analysis]]

*[[w:en:Cauchy's integral theorem|Cauchy integral theorem for disks]]
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=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Integralsatz von Cauchy Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Integralsatz von Cauchy|Integralsatz von Cauchy]] - URL: https://de.wikiversity.org/wiki/Integralsatz von Cauchy
* Date: 12/18/2024

&lt;span type=&quot;translate&quot; src=&quot;Integralsatz von Cauchy&quot; srclang=&quot;de&quot; date=&quot;12/18/2024&quot; time=&quot;09:15&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Integralsatz von Cauchy]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
      <sha1>f9yrg8bf16drwl61k68w99onnemovix</sha1>
    </revision>
    <revision>
      <id>2693104</id>
      <parentid>2693103</parentid>
      <timestamp>2024-12-24T09:43:58Z</timestamp>
      <contributor>
        <username>Bert Niehaus</username>
        <id>2387134</id>
      </contributor>
      <comment>/* Page Information */</comment>
      <origin>2693104</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="7967" sha1="149hrshjoeezyfsb08rsommbdu7u7a2" xml:space="preserve">==Introduction==
The Cauchy integral theorem is one of the central results of [[Complex Analysis]]. It exists in various versions, and in this article, we aim to present a basic one for convex regions and a relatively general one for [[w:en:Homology (mathematics)|nullhomologous cycles]].

==For Convex Regions==
=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a convex region, and let &lt;math&gt;\gamma&lt;/math&gt; be a closed 
[[Complex Analysis/rectifiable curve|rectifiable curve]] 
[[Complex Analysis/Trace|Trace of Curve]] in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof 1: Primitive of &lt;math&gt;f&lt;/math&gt; ===
First, we observe that &lt;math&gt;f&lt;/math&gt; has a primitive in &lt;math&gt;G&lt;/math&gt;. Fix a point &lt;math&gt;z_0 \in G&lt;/math&gt;. For any point &lt;math&gt;z \in G&lt;/math&gt;, let &lt;math&gt;[z_0, z]&lt;/math&gt; denote the straight-line segment connecting &lt;math&gt;z_0&lt;/math&gt; and &lt;math&gt;z&lt;/math&gt;.

== Proof 2: Definition of the Primitive ==
Define &lt;math&gt;F \colon G \to \mathbb{C}&lt;/math&gt; by:
:&lt;math&gt;F(z) := \int_{[z_0, z]} f(\zeta), d\zeta&lt;/math&gt;.
Due to the convexity of &lt;math&gt;G&lt;/math&gt;, the triangle &lt;math&gt;D&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w&lt;/math&gt; lies entirely within &lt;math&gt;G&lt;/math&gt; for &lt;math&gt;z, w \in G&lt;/math&gt;.

=== Proof 3: Application of Goursat’s Lemma ===
By [[Complex Analysis/Goursat's Lemma|Goursat's Lemma]] for the boundary &lt;math&gt;\partial \Delta&lt;/math&gt; of a triangle &lt;math&gt;\Delta&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w \in \mathbb{C}&lt;/math&gt;, we have:
:&lt;math&gt; \begin{array}{rl}   0         &amp;= \int_{\partial \Delta} f(z)\, dz \\     &amp;=  \int_{[z_{0},z]} f(\zeta)\, d\zeta - \int_{[z_{0},w]} f(\zeta)\, d\zeta + \int_{[z,w]} f(\zeta)\, d\zeta \\    &amp; = F(z) - F(w) + \int_{[z,w]} f(\zeta)\, d\zeta      \end{array} &lt;/math&gt;

=== Proof 4: Conclusion Using Goursat's Lemma ===
This leads to:
:&lt;math&gt;\begin{array}{rl}  F(z) - F(w) &amp;= \int_{[w,z]} f(\zeta)\,d\zeta\\              &amp;= \int_0^1 f\bigl(w + t(z-w)\bigr)\cdot (z-w)\, dt\\     &amp;= \underbrace{\int_0^1 f\bigl(w+t(z-w)\bigr)\, dt}_{A(z):=} \cdot (z-w)  \end{array}&lt;/math&gt;
Thus, we have:
:&lt;math&gt;A(z)=\frac{F(z) - F(w)}{(z-w)}&lt;/math&gt;
=== Proof 5: Limit Process ===
Since &lt;math&gt;A&lt;/math&gt; is continuous in &lt;math&gt;w&lt;/math&gt;, taking the limit as &lt;math&gt;z \to w&lt;/math&gt; gives:
:&lt;math&gt;A(w) = \lim_{z \to w} A(z) = \lim_{z \to w} \frac{F(z) - F(w)}{(z-w)} = F'(w).&lt;/math&gt;

=== Proof 5: Differentiability of &lt;math&gt;F&lt;/math&gt; ===
Therefore, &lt;math&gt;A \colon G \to \mathbb{C}&lt;/math&gt; is continuous, and &lt;math&gt;F&lt;/math&gt; is differentiable in &lt;math&gt;w \in G&lt;/math&gt;, with:

&lt;center&gt;&lt;math&gt;F'(w) = A(w) = f(w).&lt;/math&gt;&lt;/center&gt;  
Since &lt;math&gt;w \in G&lt;/math&gt; was arbitrary, we conclude &lt;math&gt;F' = f&lt;/math&gt;, proving that &lt;math&gt;f&lt;/math&gt; has a primitive.
=== Proof 6: Path Integration ===
Now, let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be a piecewise continuously differentiable, closed curve. Then:

&lt;center&gt;&lt;math&gt;  
\begin{array}{rl}  
  \int_\gamma f(z)\, dz &amp;= \int_a^b f(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b F'(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b (F \circ \gamma)'(t)\, dt \\  
                        &amp;= F(\gamma(b)) - F(\gamma(a)) = 0.  
\end{array}  
&lt;/math&gt;&lt;/center&gt;
=== Proof 7: ===
Let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be an arbitrary integration path in &lt;math&gt;G&lt;/math&gt;, and let &lt;math&gt;\epsilon &gt; 0&lt;/math&gt;. As shown [[Complex Analysis/Curve Integral #Approximation by polygonal paths|here]], we choose a polygonal path &lt;math&gt;\hat{\gamma} \colon [a, b] \to \mathbb{C}&lt;/math&gt; such that &lt;math&gt;\hat{\gamma}(a) = \gamma(a)&lt;/math&gt;, &lt;math&gt;\hat{\gamma}(b) = \gamma(b)&lt;/math&gt;, and
:&lt;math&gt;\left|\int_{\hat{\gamma}} f(z), dz - \int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
Since polygonal paths are piecewise continuously differentiable, the above result implies &lt;math&gt;\int_{\hat{\gamma}} f(z), dz = 0&lt;/math&gt;. Consequently,
:&lt;math&gt;\left|\int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
As &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; was arbitrary, the claim follows.

== For Cycles in Arbitrary Open Sets ==
In arbitrary open sets, one must ensure that cycles do not enclose singularities or poles in the complement of the domain. Enclosing such singularities may contribute a non-zero value to the integral (e.g., the function &lt;math&gt;f(z) = \frac{1}{z}&lt;/math&gt; and &lt;math&gt;\gamma(t) := e^{it}&lt;/math&gt; in a domain &lt;math&gt;G = \mathbb{C}\setminus \{0\}&lt;/math&gt; . Even though &lt;math&gt;f&lt;/math&gt; is holomorphic in &lt;math&gt;G&lt;/math&gt;, the integral is not zero but &lt;math&gt;2\pi i&lt;/math&gt; (see [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous cycle]]).

=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be open, and let &lt;math&gt;\Gamma&lt;/math&gt; be a [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous]] cycle in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\Gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof ===
Let &lt;math&gt;w \in G \setminus \text{trace}(\Gamma)&lt;/math&gt;, and define &lt;math&gt;g \colon G \to \mathbb{C}&lt;/math&gt; by

&lt;center&gt;&lt;math&gt;g(z) := (z-w) \cdot f(z).&lt;/math&gt;&lt;/center&gt;  
Then, &lt;math&gt;g&lt;/math&gt; is holomorphic, and by the [[w:en:Cauchy integral formula#For cycles in arbitrary open sets|global integral formula]], we have:  
:&lt;math&gt;  
\int_\Gamma f(z)\, dz = \int_{\Gamma} \frac{g(z)}{z-w}\, dz = 2\pi i \cdot n(\Gamma, w) \cdot g(w) = 0.  
&lt;/math&gt;
== See Also ==

*[[w:en:Complex Analysis|Complex Analysis]]

*[[w:en:Cauchy's integral theorem|Cauchy integral theorem for disks]]

== Page Information ==
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* Date: 12/18/2024

&lt;span type=&quot;translate&quot; src=&quot;Integralsatz von Cauchy&quot; srclang=&quot;de&quot; date=&quot;12/18/2024&quot; time=&quot;09:15&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Integralsatz von Cauchy]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
      <sha1>149hrshjoeezyfsb08rsommbdu7u7a2</sha1>
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    <revision>
      <id>2693106</id>
      <parentid>2693104</parentid>
      <timestamp>2024-12-24T09:48:15Z</timestamp>
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      <text bytes="7967" sha1="srb9kifhq0q17h9ahfr7dz6so0fo92f" xml:space="preserve">==Introduction==
The Cauchy integral theorem is one of the central results of [[Complex Analysis]]. It exists in various versions, and in this article, we aim to present a basic one for convex regions and a relatively general one for [[w:en:Homology (mathematics)|nullhomologous cycles]].

==For Convex Regions==
=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a convex region, and let &lt;math&gt;\gamma&lt;/math&gt; be a closed 
[[Complex Analysis/rectifiable curve|rectifiable curve]] 
[[Complex Analysis/Trace|Trace of Curve]] in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof 1: Primitive of &lt;math&gt;f&lt;/math&gt; ===
First, we observe that &lt;math&gt;f&lt;/math&gt; has a primitive in &lt;math&gt;G&lt;/math&gt;. Fix a point &lt;math&gt;z_0 \in G&lt;/math&gt;. For any point &lt;math&gt;z \in G&lt;/math&gt;, let &lt;math&gt;[z_0, z]&lt;/math&gt; denote the straight-line segment connecting &lt;math&gt;z_0&lt;/math&gt; and &lt;math&gt;z&lt;/math&gt;.

== Proof 2: Definition of the Primitive ==
Define &lt;math&gt;F \colon G \to \mathbb{C}&lt;/math&gt; by:
:&lt;math&gt;F(z) := \int_{[z_0, z]} f(\zeta), d\zeta&lt;/math&gt;.
Due to the convexity of &lt;math&gt;G&lt;/math&gt;, the triangle &lt;math&gt;D&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w&lt;/math&gt; lies entirely within &lt;math&gt;G&lt;/math&gt; for &lt;math&gt;z, w \in G&lt;/math&gt;.

=== Proof 3: Application of Goursat’s Lemma ===
By [[Complex Analysis/Goursat's Lemma|Goursat's Lemma]] for the boundary &lt;math&gt;\partial \Delta&lt;/math&gt; of a triangle &lt;math&gt;\Delta&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w \in \mathbb{C}&lt;/math&gt;, we have:
:&lt;math&gt; \begin{array}{rl}   0         &amp;= \int_{\partial \Delta} f(z)\, dz \\     &amp;=  \int_{[z_{0},z]} f(\zeta)\, d\zeta - \int_{[z_{0},w]} f(\zeta)\, d\zeta + \int_{[z,w]} f(\zeta)\, d\zeta \\    &amp; = F(z) - F(w) + \int_{[z,w]} f(\zeta)\, d\zeta      \end{array} &lt;/math&gt;

=== Proof 4: Conclusion Using Goursat's Lemma ===
This leads to:
:&lt;math&gt;\begin{array}{rl}  F(z) - F(w) &amp;= \int_{[w,z]} f(\zeta)\,d\zeta\\              &amp;= \int_0^1 f\bigl(w + t(z-w)\bigr)\cdot (z-w)\, dt\\     &amp;= \underbrace{\int_0^1 f\bigl(w+t(z-w)\bigr)\, dt}_{A(z):=} \cdot (z-w)  \end{array}&lt;/math&gt;
Thus, we have:
:&lt;math&gt;A(z)=\frac{F(z) - F(w)}{(z-w)}&lt;/math&gt;
=== Proof 5: Limit Process ===
Since &lt;math&gt;A&lt;/math&gt; is continuous in &lt;math&gt;w&lt;/math&gt;, taking the limit as &lt;math&gt;z \to w&lt;/math&gt; gives:
:&lt;math&gt;A(w) = \lim_{z \to w} A(z) = \lim_{z \to w} \frac{F(z) - F(w)}{(z-w)} = F'(w).&lt;/math&gt;

=== Proof 5: Differentiability of &lt;math&gt;F&lt;/math&gt; ===
Therefore, &lt;math&gt;A \colon G \to \mathbb{C}&lt;/math&gt; is continuous, and &lt;math&gt;F&lt;/math&gt; is differentiable in &lt;math&gt;w \in G&lt;/math&gt;, with:

&lt;center&gt;&lt;math&gt;F'(w) = A(w) = f(w).&lt;/math&gt;&lt;/center&gt;  
Since &lt;math&gt;w \in G&lt;/math&gt; was arbitrary, we conclude &lt;math&gt;F' = f&lt;/math&gt;, proving that &lt;math&gt;f&lt;/math&gt; has a primitive.
=== Proof 6: Path Integration ===
Now, let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be a piecewise continuously differentiable, closed curve. Then:

&lt;center&gt;&lt;math&gt;  
\begin{array}{rl}  
  \int_\gamma f(z)\, dz &amp;= \int_a^b f(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b F'(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b (F \circ \gamma)'(t)\, dt \\  
                        &amp;= F(\gamma(b)) - F(\gamma(a)) = 0.  
\end{array}  
&lt;/math&gt;&lt;/center&gt;
=== Proof 7: ===
Let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be an arbitrary integration path in &lt;math&gt;G&lt;/math&gt;, and let &lt;math&gt;\epsilon &gt; 0&lt;/math&gt;. As shown [[Complex Analysis/Curve Integral #Approximation by polygonal paths|here]], we choose a polygonal path &lt;math&gt;\hat{\gamma} \colon [a, b] \to \mathbb{C}&lt;/math&gt; such that &lt;math&gt;\hat{\gamma}(a) = \gamma(a)&lt;/math&gt;, &lt;math&gt;\hat{\gamma}(b) = \gamma(b)&lt;/math&gt;, and
:&lt;math&gt;\left|\int_{\hat{\gamma}} f(z), dz - \int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
Since polygonal paths are piecewise continuously differentiable, the above result implies &lt;math&gt;\int_{\hat{\gamma}} f(z), dz = 0&lt;/math&gt;. Consequently,
:&lt;math&gt;\left|\int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
As &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; was arbitrary, the claim follows.

== For Cycles in Arbitrary Open Sets ==
In arbitrary open sets, one must ensure that cycles do not enclose singularities or poles in the complement of the domain. Enclosing such singularities may contribute a non-zero value to the integral (e.g., the function &lt;math&gt;f(z) = \frac{1}{z}&lt;/math&gt; and &lt;math&gt;\gamma(t) := e^{it}&lt;/math&gt; in a domain &lt;math&gt;G = \mathbb{C}\setminus \{0\}&lt;/math&gt; . Even though &lt;math&gt;f&lt;/math&gt; is holomorphic in &lt;math&gt;G&lt;/math&gt;, the integral is not zero but &lt;math&gt;2\pi i&lt;/math&gt; (see [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous cycle]]).

=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be open, and let &lt;math&gt;\Gamma&lt;/math&gt; be a [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous]] cycle in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\Gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof ===
Let &lt;math&gt;w \in G \setminus \text{trace}(\Gamma)&lt;/math&gt;, and define &lt;math&gt;g \colon G \to \mathbb{C}&lt;/math&gt; by

&lt;center&gt;&lt;math&gt;g(z) := (z-w) \cdot f(z).&lt;/math&gt;&lt;/center&gt;  
Then, &lt;math&gt;g&lt;/math&gt; is holomorphic, and by the [[w:en:Cauchy integral formula#For cycles in arbitrary open sets|global integral formula]], we have:  
:&lt;math&gt;  
\int_\Gamma f(z)\, dz = \int_{\Gamma} \frac{g(z)}{z-w}\, dz = 2\pi i \cdot n(\Gamma, w) \cdot g(w) = 0.  
&lt;/math&gt;
== See Also ==

*[[w:en:Complex Analysis|Complex Analysis]]

*[[w:en:Cauchy's integral theorem|Cauchy integral theorem for disks]]

== Page Information ==
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* Date: 12/18/2024

&lt;span type=&quot;translate&quot; src=&quot;Integralsatz von Cauchy&quot; srclang=&quot;de&quot; date=&quot;12/18/2024&quot; time=&quot;09:15&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Integralsatz von Cauchy]]
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[[Category:Wiki2Reveal]]</text>
      <sha1>srb9kifhq0q17h9ahfr7dz6so0fo92f</sha1>
    </revision>
    <revision>
      <id>2693107</id>
      <parentid>2693106</parentid>
      <timestamp>2024-12-24T09:57:22Z</timestamp>
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      <text bytes="7987" sha1="jre0jj8xsbe6iemctmr5bhl5zvtju15" xml:space="preserve">==Introduction==
The Cauchy integral theorem is one of the central results of [[Complex Analysis]]. It exists in various versions, and in this article, we aim to present a basic one for convex regions and a relatively general one for [[w:en:Homology (mathematics)|nullhomologous cycles]].

==For Convex Regions==
=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a convex region, and let &lt;math&gt;\gamma&lt;/math&gt; be a closed 
[[Complex Analysis/rectifiable curve|rectifiable curve]] 
[[Complex Analysis/Trace|Trace of Curve]] in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof 1:  Antiderivatives of f ===
First, we observe that &lt;math&gt;f&lt;/math&gt; has a  antiderivative in &lt;math&gt;G&lt;/math&gt;. Fix a point &lt;math&gt;z_0 \in G&lt;/math&gt;. For any point &lt;math&gt;z \in G&lt;/math&gt;, let &lt;math&gt;[z_0, z]&lt;/math&gt; denote the straight-line segment connecting &lt;math&gt;z_0&lt;/math&gt; and &lt;math&gt;z&lt;/math&gt; as path.

== Proof 2: Definition of the Antiderivative ==
Define &lt;math&gt;F \colon G \to \mathbb{C}&lt;/math&gt; by:
:&lt;math&gt;F(z) := \int_{[z_0, z]} f(\zeta), d\zeta&lt;/math&gt;.
Due to the convexity of &lt;math&gt;G&lt;/math&gt;, the triangle &lt;math&gt;D&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w&lt;/math&gt; lies entirely within &lt;math&gt;G&lt;/math&gt; for &lt;math&gt;z, w \in G&lt;/math&gt;.

=== Proof 3: Application of Goursat’s Lemma ===
By [[Complex Analysis/Goursat's Lemma|Goursat's Lemma]] for the boundary &lt;math&gt;\partial \Delta&lt;/math&gt; of a triangle &lt;math&gt;\Delta&lt;/math&gt; with vertices &lt;math&gt;z_0, z, w \in \mathbb{C}&lt;/math&gt;, we have:
:&lt;math&gt; \begin{array}{rl}   0         &amp;= \int_{\partial \Delta} f(z)\, dz \\     &amp;=  \int_{[z_{0},z]} f(\zeta)\, d\zeta - \int_{[z_{0},w]} f(\zeta)\, d\zeta + \int_{[z,w]} f(\zeta)\, d\zeta \\    &amp; = F(z) - F(w) + \int_{[z,w]} f(\zeta)\, d\zeta      \end{array} &lt;/math&gt;

=== Proof 4: Conclusion Using Goursat's Lemma ===
This leads to:
:&lt;math&gt;\begin{array}{rl}  F(z) - F(w) &amp;= \int_{[w,z]} f(\zeta)\,d\zeta\\              &amp;= \int_0^1 f\bigl(w + t(z-w)\bigr)\cdot (z-w)\, dt\\     &amp;= \underbrace{\int_0^1 f\bigl(w+t(z-w)\bigr)\, dt}_{A(z):=} \cdot (z-w)  \end{array}&lt;/math&gt;
Thus, we have:
:&lt;math&gt;A(z)=\frac{F(z) - F(w)}{(z-w)}&lt;/math&gt;
=== Proof 5: Limit Process ===
Since &lt;math&gt;A&lt;/math&gt; is continuous in &lt;math&gt;w&lt;/math&gt;, taking the limit as &lt;math&gt;z \to w&lt;/math&gt; gives:
:&lt;math&gt;A(w) = \lim_{z \to w} A(z) = \lim_{z \to w} \frac{F(z) - F(w)}{(z-w)} = F'(w).&lt;/math&gt;

=== Proof 5: Differentiability of &lt;math&gt;F&lt;/math&gt; ===
Therefore, &lt;math&gt;A \colon G \to \mathbb{C}&lt;/math&gt; is continuous, and &lt;math&gt;F&lt;/math&gt; is differentiable in &lt;math&gt;w \in G&lt;/math&gt;, with:

&lt;center&gt;&lt;math&gt;F'(w) = A(w) = f(w).&lt;/math&gt;&lt;/center&gt;  
Since &lt;math&gt;w \in G&lt;/math&gt; was arbitrary, we conclude &lt;math&gt;F' = f&lt;/math&gt;, proving that &lt;math&gt;f&lt;/math&gt; has a  antiderivative.

=== Proof 6: Path Integration ===
Now, let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be a piecewise continuously differentiable, closed curve. Then:

&lt;center&gt;&lt;math&gt;  
\begin{array}{rl}  
  \int_\gamma f(z)\, dz &amp;= \int_a^b f(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b F'(\gamma(t)) \gamma'(t)\, dt \\  
                        &amp;= \int_a^b (F \circ \gamma)'(t)\, dt \\  
                        &amp;= F(\gamma(b)) - F(\gamma(a)) = 0.  
\end{array}  
&lt;/math&gt;&lt;/center&gt;
=== Proof 7: ===
Let &lt;math&gt;\gamma \colon [a, b] \to G&lt;/math&gt; be an arbitrary integration path in &lt;math&gt;G&lt;/math&gt;, and let &lt;math&gt;\epsilon &gt; 0&lt;/math&gt;. As shown [[Complex Analysis/Curve Integral #Approximation by polygonal paths|here]], we choose a polygonal path &lt;math&gt;\hat{\gamma} \colon [a, b] \to \mathbb{C}&lt;/math&gt; such that &lt;math&gt;\hat{\gamma}(a) = \gamma(a)&lt;/math&gt;, &lt;math&gt;\hat{\gamma}(b) = \gamma(b)&lt;/math&gt;, and
:&lt;math&gt;\left|\int_{\hat{\gamma}} f(z), dz - \int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
Since polygonal paths are piecewise continuously differentiable, the above result implies &lt;math&gt;\int_{\hat{\gamma}} f(z), dz = 0&lt;/math&gt;. Consequently,
:&lt;math&gt;\left|\int_{\gamma} f(z), dz\right| &lt; \epsilon.&lt;/math&gt;
As &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; was arbitrary, the claim follows.

== For Cycles in Arbitrary Open Sets ==
In arbitrary open sets, one must ensure that cycles do not enclose singularities or poles in the complement of the domain. Enclosing such singularities may contribute a non-zero value to the integral (e.g., the function &lt;math&gt;f(z) = \frac{1}{z}&lt;/math&gt; and &lt;math&gt;\gamma(t) := e^{it}&lt;/math&gt; in a domain &lt;math&gt;G = \mathbb{C}\setminus \{0\}&lt;/math&gt; . Even though &lt;math&gt;f&lt;/math&gt; is holomorphic in &lt;math&gt;G&lt;/math&gt;, the integral is not zero but &lt;math&gt;2\pi i&lt;/math&gt; (see [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous cycle]]).

=== Statement ===
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be open, and let &lt;math&gt;\Gamma&lt;/math&gt; be a [[w:en:Homology (mathematics)#Nullhomologous cycle|nullhomologous]] cycle in &lt;math&gt;G&lt;/math&gt;. Then, for every holomorphic function &lt;math&gt;f \colon G \to \mathbb{C}&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;\int_\Gamma f(z)\, dz = 0&lt;/math&gt;&lt;/center&gt;
=== Proof ===
Let &lt;math&gt;w \in G \setminus \text{trace}(\Gamma)&lt;/math&gt;, and define &lt;math&gt;g \colon G \to \mathbb{C}&lt;/math&gt; by

&lt;center&gt;&lt;math&gt;g(z) := (z-w) \cdot f(z).&lt;/math&gt;&lt;/center&gt;  
Then, &lt;math&gt;g&lt;/math&gt; is holomorphic, and by the [[w:en:Cauchy integral formula#For cycles in arbitrary open sets|global integral formula]], we have:  
:&lt;math&gt;  
\int_\Gamma f(z)\, dz = \int_{\Gamma} \frac{g(z)}{z-w}\, dz = 2\pi i \cdot n(\Gamma, w) \cdot g(w) = 0.  
&lt;/math&gt;
== See Also ==

*[[w:en:Complex Analysis|Complex Analysis]]

*[[w:en:Cauchy's integral theorem|Cauchy integral theorem for disks]]

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=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Integralsatz von Cauchy Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Integralsatz von Cauchy|Integralsatz von Cauchy]] - URL: https://de.wikiversity.org/wiki/Integralsatz_von_Cauchy
* Date: 12/18/2024

&lt;span type=&quot;translate&quot; src=&quot;Integralsatz von Cauchy&quot; srclang=&quot;de&quot; date=&quot;12/18/2024&quot; time=&quot;09:15&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Integralsatz von Cauchy]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
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    <title>Boolf prop/3-ary/nameless 4</title>
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      <timestamp>2024-12-23T23:39:16Z</timestamp>
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      <text bytes="5304" sha1="aabttw3g5o9rffj9t58iamkjrzfxhlg" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 1809251421294659332139685398512665750726255159685711951796174474417100816385.svg|thumb|500px|The twins have the transposed pattern of [[Boolf prop/3-ary/nameless 1|nameless 1]]]]

&lt;source lang=&quot;python&quot;&gt;
val = boolf.quaestor(3) ^ boolf.consul(3)
&lt;/source&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| nameless 4
!class=&quot;block&quot;| block
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|class=&quot;size&quot;| 16
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 29, 33, 60, 71, 90, 102, 123, 132, 153, 165, 184, 195, 222, 226, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57896044733237871097417045490205538760474164395213398111671384344995827810305.svg|420px]]
|-
|class=&quot;size&quot;| 16
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|-
|class=&quot;size&quot;| 16
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 31, 35, 62, 69, 88, 100, 121, 134, 155, 167, 186, 193, 220, 224, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14474011183309467774446211280426351952526512916562604391779217547965954523140.svg|420px]]
|-
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|-
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|-
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|-
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|-
|class=&quot;size&quot;| 16
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 26, 38, 59, 64, 93, 97, 124, 131, 158, 162, 191, 196, 217, 229, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_452313711512184424103090603022120544737747767387152777146909167455213453440.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 11
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[8, 21, 41, 52, 79, 82, 110, 115, 140, 145, 173, 176, 203, 214, 234, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_226184031303361284863412941307989648842752207751176135687412462083400270080.svg|420px]]
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|class=&quot;size&quot;| 16
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|-
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[11, 22, 42, 55, 76, 81, 109, 112, 143, 146, 174, 179, 200, 213, 233, 244]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28283356542313373798311729864485873022686041594398287226769861131519395840.svg|420px]]
|-
|class=&quot;size&quot;| 16
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[12, 17, 45, 48, 75, 86, 106, 119, 136, 149, 169, 180, 207, 210, 238, 243]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14576488286272863347581805008971331325909835609498165357011196770267566080.svg|420px]]
|-
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|-
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[[Category:Boolf prop/3-ary|nameless 4]]</text>
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      <parentid>2692704</parentid>
      <timestamp>2024-12-23T23:36:54Z</timestamp>
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      <text bytes="2545" sha1="jbpfen8hb1qshc2okaffaz17sksllh6" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;source lang=&quot;python&quot;&gt;
val = boolf.reverse.twin(3).reverse.lictor(3)
&lt;/source&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| nameless 5
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 64
|class=&quot;prop&quot;| 0
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|-
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|-
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|}

[[Category:Boolf prop/3-ary|nameless 5]]</text>
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    <title>File talk:Nm1.s11.mtg25.djvu</title>
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      <contributor>
        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <comment>Reset talk page with [[:w:simple:User:DannyS712/Reset talk|reset talk]] (version 1.1)</comment>
      <origin>2692999</origin>
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      <text bytes="15" sha1="6ujz0t3lkt6jsf7d1r360l6l7wj3njb" xml:space="preserve">{{Talk header}}</text>
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    <title>User talk:180.244.208.121</title>
    <ns>3</ns>
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    <revision>
      <id>2693000</id>
      <timestamp>2024-12-23T12:12:35Z</timestamp>
      <contributor>
        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <comment>New resource with &quot;==December 2024== {{subst:uw-vandalism1}} ~~~~&quot;</comment>
      <origin>2693000</origin>
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      <text bytes="510" sha1="ik996a2myj7baq27c3s3ihkwsldto0b" xml:space="preserve">==December 2024==
[[File:Information.svg|25px|alt=Information icon]] Hello, I’m letting you know that one or more of your recent contributions have been reverted because they did not appear constructive. If you would like to experiment, please use the [[Wikiversity:Sandbox|sandbox]] or ask for assistance at the [[Wikiversity:Colloquium|Colloquium]]. Thank you. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 12:12, 23 December 2024 (UTC)</text>
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  <page>
    <title>Boolf prop/3-ary/symmetry perm</title>
    <ns>0</ns>
    <id>317436</id>
    <revision>
      <id>2693002</id>
      <timestamp>2024-12-23T12:37:42Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
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      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; &lt;/div&gt;  {| class=&quot;wikitable sortable boolf-blocks&quot; !class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt; !cl...&quot;</comment>
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      <text bytes="2421" sha1="kx9v7da749psnvdkuwclfn7rlme4gtk" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| symmetry perm
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{1, 2, 4}, {3, 5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 1, 22, 23, 104, 105, 126, 127, 128, 129, 150, 151, 232, 233, 254, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_86844087633226186939369601060787799465383022669001262447603868028627564101635.svg|420px]]
|-
|class=&quot;size&quot;| 48
|class=&quot;prop&quot;| {{2, 4}, {3, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[2, 3, 20, 21, 40, 41, 42, 43, 60, 61, 62, 63, 64, 65, 66, 67, 84, 85, 86, 87, 106, 107, 124, 125, 130, 131, 148, 149, 168, 169, 170, 171, 188, 189, 190, 191, 192, 193, 194, 195, 212, 213, 214, 215, 234, 235, 252, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_21711099553051678502165595788621210661963813463085113715380771866465159610380.svg|420px]]
|-
|class=&quot;size&quot;| 48
|class=&quot;prop&quot;| {{1, 4}, {3, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[4, 5, 18, 19, 32, 33, 36, 37, 50, 51, 54, 55, 72, 73, 76, 77, 90, 91, 94, 95, 108, 109, 122, 123, 132, 133, 146, 147, 160, 161, 164, 165, 178, 179, 182, 183, 200, 201, 204, 205, 218, 219, 222, 223, 236, 237, 250, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5428085488307632061787149478125856477491231219014946446051078008848536830000.svg|420px]]
|-
|class=&quot;size&quot;| 48
|class=&quot;prop&quot;| {{1, 2}, {5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[6, 7, 8, 9, 14, 15, 16, 17, 24, 25, 30, 31, 96, 97, 102, 103, 110, 111, 112, 113, 118, 119, 120, 121, 134, 135, 136, 137, 142, 143, 144, 145, 152, 153, 158, 159, 224, 225, 230, 231, 238, 239, 240, 241, 246, 247, 248, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1702804115869767992010662927522266843237938497567113536663625660513061684160.svg|420px]]
|-
|class=&quot;size&quot;| 96
|class=&quot;prop&quot;| {}
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_106012446860929928237975753630774405193978816972127893758240443458807413760.svg|420px]]
|}

[[Category:Boolf prop/3-ary|symmetry perm]]</text>
      <sha1>kx9v7da749psnvdkuwclfn7rlme4gtk</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/symmetry neg</title>
    <ns>0</ns>
    <id>317437</id>
    <revision>
      <id>2693003</id>
      <timestamp>2024-12-23T12:43:28Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;10&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span clas...&quot;</comment>
      <origin>2693003</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3330" sha1="cxofl8vcqmpoq4oe136acdcu2miyrbv" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;10&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| symmetry neg
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| &lt;nowiki&gt;{{0, 1, 2, 3, 4, 5, 6, 7}}&lt;/nowiki&gt;
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57896044618658097711785492504343953926634992332820282019728792003956564819969.svg|420px]]
|-
|class=&quot;size&quot;| 184
|class=&quot;prop&quot;| {}
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_47758921764525901261551430907217716309817200892775286220327341333423315315094.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| {{0, 4}, {1, 5}, {2, 6}, {3, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[3, 5, 10, 12, 17, 34, 48, 63, 68, 80, 95, 119, 136, 160, 175, 187, 192, 207, 221, 238, 243, 245, 250, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_9117372569392856764669015109861959849500382286899122289979294063395260732456.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 3}, {1, 2}, {4, 7}, {5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 9, 96, 111, 144, 159, 246, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1017703909312349373839979361158694184527283310552997901882537932975729803840.svg|420px]]
|-
|class=&quot;size&quot;| 6
|class=&quot;prop&quot;| {{0, 2, 4, 6}, {1, 3, 5, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[15, 51, 85, 170, 204, 240]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1766847064804095338292937922828216753893183071823361306064178494985764864.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 5}, {1, 4}, {2, 7}, {3, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 33, 72, 123, 132, 183, 222, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_220862623083964841117825181273752891404574814892778593448892297302507520.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 6}, {1, 7}, {2, 4}, {3, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 40, 65, 125, 130, 190, 215, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_55214023430471913853505242527422408066944382012676641618461839930163200.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 7}, {1, 6}, {2, 5}, {3, 4}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[24, 36, 66, 126, 129, 189, 219, 231]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3451715671729414988927884610456227198687578716693276844744939656970240.svg|420px]]
|-
|class=&quot;size&quot;| 6
|class=&quot;prop&quot;| {{0, 3, 4, 7}, {1, 2, 5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[60, 90, 102, 153, 165, 195]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_50216813929872916486816856452299552604448852053559498244096.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 3, 5, 6}, {1, 2, 4, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[105, 150]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1427247692706000445877493272790343030885318656.svg|420px]]
|}

[[Category:Boolf prop/3-ary|symmetry neg]]</text>
      <sha1>cxofl8vcqmpoq4oe136acdcu2miyrbv</sha1>
    </revision>
    <revision>
      <id>2693072</id>
      <parentid>2693003</parentid>
      <timestamp>2024-12-23T23:16:05Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693072</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4545" sha1="536r63x561ytqzgxsbkzkaw3wj2owa2" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| symmetry neg
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| &lt;nowiki&gt;{{0, 1, 2, 3, 4, 5, 6, 7}}&lt;/nowiki&gt;
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57896044618658097711785492504343953926634992332820282019728792003956564819969.svg|420px]]
|-
|class=&quot;size&quot;| 184
|class=&quot;prop&quot;| {}
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_47758921764525901261551430907217716309817200892775286220327341333423315315094.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 1}, {2, 3}, {4, 5}, {6, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 12, 48, 63, 192, 207, 243, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7251140353850694982956619829190887723939603004798329462225855145563696140296.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 2}, {1, 3}, {4, 6}, {5, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 10, 80, 95, 160, 175, 245, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1865790500405973852040010052731675649071549611688552189837639037244453946400.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 3}, {1, 2}, {4, 7}, {5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 9, 96, 111, 144, 159, 246, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1017703909312349373839979361158694184527283310552997901882537932975729803840.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 1, 2, 3}, {4, 5, 6, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[15, 240]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1766847064778384329583297500742918515827483896875618958121606201292652544.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 4}, {1, 5}, {2, 6}, {3, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[17, 34, 68, 119, 136, 187, 221, 238]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_441715136187929672385227939396476489229670412240637915799880587110645760.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 5}, {1, 4}, {2, 7}, {3, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 33, 72, 123, 132, 183, 222, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_220862623083964841117825181273752891404574814892778593448892297302507520.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 6}, {1, 7}, {2, 4}, {3, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 40, 65, 125, 130, 190, 215, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_55214023430471913853505242527422408066944382012676641618461839930163200.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 7}, {1, 6}, {2, 5}, {3, 4}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[24, 36, 66, 126, 129, 189, 219, 231]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3451715671729414988927884610456227198687578716693276844744939656970240.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 1, 4, 5}, {2, 3, 6, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[51, 204]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_25711008708143844408671393477458601640355247902776485178507264.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 1, 6, 7}, {2, 3, 4, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[60, 195]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_50216813883093446110686315385661331328819996477216882950144.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 2, 4, 6}, {1, 3, 5, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[85, 170]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1496577676626844588240573307387100039795808514605056.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 2, 5, 7}, {1, 3, 4, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[90, 165]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_46768052394588893382519152586960342009264740499456.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 3, 4, 7}, {1, 2, 5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[102, 153]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_11417981541647684119068688668513567077874794496.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 3, 5, 6}, {1, 2, 4, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[105, 150]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1427247692706000445877493272790343030885318656.svg|420px]]
|}

[[Category:Boolf prop/3-ary|symmetry neg]]</text>
      <sha1>536r63x561ytqzgxsbkzkaw3wj2owa2</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/symmetry negperm</title>
    <ns>0</ns>
    <id>317438</id>
    <revision>
      <id>2693004</id>
      <timestamp>2024-12-23T12:48:43Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;37&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span cl...&quot;</comment>
      <origin>2693004</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10381" sha1="ouh7afnegcuuahx97952g5lqx1dcy58" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;37&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| symmetry negperm
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| &lt;nowiki&gt;{{0, 1, 2, 3, 4, 5, 6, 7}}&lt;/nowiki&gt;
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57896044618658097711785492504343953926634992332820282019728792003956564819969.svg|420px]]
|-
|class=&quot;size&quot;| 10
|class=&quot;prop&quot;| {{1, 2, 4}, {3, 5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 22, 23, 104, 127, 128, 151, 232, 233, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28948043014568089227584108556442418290289689010162991391809692814918635487234.svg|420px]]
|-
|class=&quot;size&quot;| 10
|class=&quot;prop&quot;| {{0, 3, 5}, {2, 4, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 41, 43, 64, 107, 148, 191, 212, 214, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14474011154697434522231348114622785059150966457138099831020219840919062446084.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 1}, {2, 3, 4, 5}, {6, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 63, 192, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7237005577332262220250288298429675004665163464810201668577677816995459891208.svg|420px]]
|-
|class=&quot;size&quot;| 10
|class=&quot;prop&quot;| {{0, 3, 6}, {1, 4, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 32, 73, 77, 109, 146, 178, 182, 223, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3618502802146104440568426284903773894553320104014902271820719959398668042256.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 2}, {1, 3, 4, 6}, {5, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 95, 160, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1809251394333065553493296642222250197538246428643932727089939938576347168800.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 3}, {1, 2}, {4, 7}, {5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 9, 96, 111, 144, 159, 246, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1017703909312349373839979361158694184527283310552997901882537932975729803840.svg|420px]]
|-
|class=&quot;size&quot;| 20
|class=&quot;prop&quot;| {{1, 2}, {5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[7, 14, 25, 30, 31, 103, 110, 112, 118, 120, 135, 137, 143, 145, 152, 224, 225, 230, 241, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_455848349029249856125356997887448767814949010072298716348459625578976264320.svg|420px]]
|-
|class=&quot;size&quot;| 10
|class=&quot;prop&quot;| {{0, 5, 6}, {1, 2, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[8, 16, 97, 113, 121, 134, 142, 158, 239, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_227039847824022386351453729210846035583597366639028516312833539803933901056.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 2, 5, 7}, {1, 3}, {4, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[10, 80, 175, 245]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_56539106072908298546713410509425451533303183044619462747699098668106777600.svg|420px]]
|-
|class=&quot;size&quot;| 20
|class=&quot;prop&quot;| {{0, 3}, {4, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[11, 13, 38, 45, 47, 70, 75, 79, 98, 100, 155, 157, 176, 180, 185, 208, 210, 217, 242, 244]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_35336941508249150676099965011626218374513661845577735998606324468872652800.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 1, 6, 7}, {2, 3}, {4, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[12, 48, 207, 243]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14134776518432762706331530761212719274439539988127793648177328568236249088.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 1, 2, 3}, {4, 5, 6, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[15, 240]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1766847064778384329583297500742918515827483896875618958121606201292652544.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 4}, {1, 2, 5, 6}, {3, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[17, 119, 136, 238]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_441711766194596082395824375185816741907416732358009299881807613125591040.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 5}, {1, 4}, {2, 7}, {3, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 33, 72, 123, 132, 183, 222, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_220862623083964841117825181273752891404574814892778593448892297302507520.svg|420px]]
|-
|class=&quot;size&quot;| 20
|class=&quot;prop&quot;| {{1, 4}, {3, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[19, 37, 50, 54, 55, 76, 91, 94, 108, 122, 133, 147, 161, 164, 179, 200, 201, 205, 218, 236]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_110428362854058527143041622753345056525811869264963134331542723092807680.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{0, 6}, {1, 7}, {2, 4}, {3, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 40, 65, 125, 130, 190, 215, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_55214023430471913853505242527422408066944382012676641618461839930163200.svg|420px]]
|-
|class=&quot;size&quot;| 20
|class=&quot;prop&quot;| {{2, 4}, {3, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[21, 42, 61, 62, 67, 84, 86, 87, 106, 124, 131, 149, 168, 169, 171, 188, 193, 194, 213, 234]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_27606998551236768652773731765342729239292619202521134638066832467034112.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 1, 2, 5, 6, 7}, {3, 4}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[24, 231]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3450873173395281893717377931138512726225554486085193277581262128676864.svg|420px]]
|-
|class=&quot;size&quot;| 20
|class=&quot;prop&quot;| {{0, 5}, {2, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[26, 35, 49, 57, 59, 74, 82, 88, 99, 115, 140, 156, 167, 173, 181, 196, 198, 206, 220, 229]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_864403393361723436973689966636962766192783611141094693394810687979520.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 1}, {2, 5}, {3, 4}, {6, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[27, 39, 216, 228]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_431464458966078793901370159419997761210513205856049708809461964996608.svg|420px]]
|-
|class=&quot;size&quot;| 20
|class=&quot;prop&quot;| {{0, 6}, {1, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[28, 44, 52, 56, 69, 81, 89, 93, 101, 117, 138, 154, 162, 166, 174, 186, 199, 203, 211, 227]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_215682878005391240730100963307682294727932948312544431907445158182912.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 2}, {1, 6}, {3, 4}, {5, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[29, 71, 184, 226]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_107839786668627079107321914569812256246982982639461372991804738109440.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 3, 4, 7}, {1, 5}, {2, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[34, 68, 187, 221]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3369993333589989403564210659747322253679882628615918072973985054720.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 1, 3, 4, 6, 7}, {2, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[36, 219]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_842498333348457493583344221469363458551160763204392890103207297024.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 7}, {1, 3}, {2, 5}, {4, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[46, 116, 139, 209]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_822752278660603021078181489649206084201098166069368502983065600.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 1, 4, 5}, {2, 3, 6, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[51, 204]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_25711008708143844408671393477458601640355247902776485178507264.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 4}, {1, 6}, {2, 5}, {3, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[53, 83, 172, 202]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_6427752183022271808675226722326943494566113789566103689625600.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 7}, {1, 5}, {2, 6}, {3, 4}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[58, 92, 163, 197]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_200867255544065797541392484888279755737163068131572312965120.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 1, 6, 7}, {2, 3, 4, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[60, 195]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_50216813883093446110686315385661331328819996477216882950144.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 2, 3, 4, 5, 7}, {1, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[66, 189]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_784637716923335095479473677900958302086581406852842520576.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| {{0, 7}, {1, 6}, {2, 3}, {4, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[78, 114, 141, 177]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_191561942611023700465378893720922154705449078071754752.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 2, 4, 6}, {1, 3, 5, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[85, 170]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1496577676626844588240573307387100039795808514605056.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 2, 5, 7}, {1, 3, 4, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[90, 165]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_46768052394588893382519152586960342009264740499456.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 3, 4, 7}, {1, 2, 5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[102, 153]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_11417981541647684119068688668513567077874794496.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 3, 5, 6}, {1, 2, 4, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[105, 150]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1427247692706000445877493272790343030885318656.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 7}, {1, 2, 3, 4, 5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[126, 129]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_765635325572111542792592866721478475776.svg|420px]]
|}

[[Category:Boolf prop/3-ary|symmetry negperm]]</text>
      <sha1>ouh7afnegcuuahx97952g5lqx1dcy58</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/patron symmetry neg</title>
    <ns>0</ns>
    <id>317439</id>
    <revision>
      <id>2693007</id>
      <timestamp>2024-12-23T13:25:27Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt; &lt;/div&gt;  {| class=&quot;wikitable sortable boolf-blocks&quot; !class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt; !class=&quot;prop&quot;| patron symmetry neg !class=&quot;block&quot;| block |- |cla...&quot;</comment>
      <origin>2693007</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2296" sha1="n5ab5pt8a672vncpoq4olds91hl76yi" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| patron symmetry neg
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;nowiki&gt;{{0, 1, 2, 3, 4, 5, 6, 7}}&lt;/nowiki&gt;
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 30, 40, 54, 72, 86, 96, 126, 128, 158, 168, 182, 200, 214, 224, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28948022336315325202904699959177005221122795925822929966558420718528929726465.svg|420px]]
|-
|class=&quot;size&quot;| 176
|class=&quot;prop&quot;| {}
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_86130107107387453332624428550059207133746272043197880897550878435910024423870.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{0, 3}, {1, 2}, {4, 7}, {5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 24, 46, 48, 78, 80, 102, 120, 134, 152, 174, 176, 206, 208, 230, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_452314574020367306188553621987165297295031963802388352215619825219179380800.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{0, 7}, {1, 6}, {2, 5}, {3, 4}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[9, 23, 33, 63, 65, 95, 105, 119, 137, 151, 161, 191, 193, 223, 233, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_226170241264300124582311188332885521448566010148067096101156585590036103680.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{0, 6}, {1, 7}, {2, 4}, {3, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[10, 20, 34, 60, 66, 92, 106, 116, 138, 148, 162, 188, 194, 220, 234, 244]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28297161706838003726123292056778560072686043379682147634683187706662487040.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{0, 5}, {1, 4}, {2, 7}, {3, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[12, 18, 36, 58, 68, 90, 108, 114, 140, 146, 164, 186, 196, 218, 236, 242]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7177816621911453544868397074866119584632679289615579396825254958297518080.svg|420px]]
|}

[[Category:Boolf prop/3-ary|patron symmetry neg]]</text>
      <sha1>n5ab5pt8a672vncpoq4olds91hl76yi</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/patron symmetry negperm</title>
    <ns>0</ns>
    <id>317440</id>
    <revision>
      <id>2693008</id>
      <timestamp>2024-12-23T13:29:12Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; &lt;/div&gt;  {| class=&quot;wikitable sortable boolf-blocks&quot; !class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt; !class=&quot;prop&quot;| patron symmetry negperm !class=&quot;block&quot;| block |-...&quot;</comment>
      <origin>2693008</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4558" sha1="95zq2i8d6j8ui1a8e6d6zkcckdqjjkr" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| patron symmetry negperm
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;nowiki&gt;{{0, 1, 2, 3, 4, 5, 6, 7}}&lt;/nowiki&gt;
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 30, 40, 54, 72, 86, 96, 126, 128, 158, 168, 182, 200, 214, 224, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28948022336315325202904699959177005221122795925822929966558420718528929726465.svg|420px]]
|-
|class=&quot;size&quot;| 32
|class=&quot;prop&quot;| {{1, 2, 4}, {3, 5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[1, 8, 22, 31, 32, 41, 55, 62, 64, 73, 87, 94, 97, 104, 118, 127, 129, 136, 150, 159, 160, 169, 183, 190, 192, 201, 215, 222, 225, 232, 246, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_58009129793262800468100555512520453202969874856719893481167419729852877504770.svg|420px]]
|-
|class=&quot;size&quot;| 32
|class=&quot;prop&quot;| {{2, 4}, {3, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[2, 3, 28, 29, 42, 43, 52, 53, 74, 75, 84, 85, 98, 99, 124, 125, 130, 131, 156, 157, 170, 171, 180, 181, 202, 203, 212, 213, 226, 227, 252, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_21711017055535911985676224782151989008715061916228543421554093693005209796620.svg|420px]]
|-
|class=&quot;size&quot;| 32
|class=&quot;prop&quot;| {{1, 4}, {3, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[4, 5, 26, 27, 44, 45, 50, 51, 76, 77, 82, 83, 100, 101, 122, 123, 132, 133, 154, 155, 172, 173, 178, 179, 204, 205, 210, 211, 228, 229, 250, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5427755477081650330409855446614937623670625366502519641929636039685352456240.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{0, 3}, {1, 2}, {4, 7}, {5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 24, 46, 48, 78, 80, 102, 120, 134, 152, 174, 176, 206, 208, 230, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_452314574020367306188553621987165297295031963802388352215619825219179380800.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{0, 5, 6}, {1, 2, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 25, 47, 49, 79, 81, 103, 121, 135, 153, 175, 177, 207, 209, 231, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_904629148040734612377107243974330594590063927604776704431239650438358761600.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{0, 7}, {1, 2, 3, 4, 5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[9, 23, 33, 63, 65, 95, 105, 119, 137, 151, 161, 191, 193, 223, 233, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_226170241264300124582311188332885521448566010148067096101156585590036103680.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{0, 6}, {1, 7}, {2, 4}, {3, 5}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[10, 20, 34, 60, 66, 92, 106, 116, 138, 148, 162, 188, 194, 220, 234, 244]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28297161706838003726123292056778560072686043379682147634683187706662487040.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{0, 3, 5}, {2, 4, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[11, 21, 35, 61, 67, 93, 107, 117, 139, 149, 163, 189, 195, 221, 235, 245]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_56594323413676007452246584113557120145372086759364295269366375413324974080.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{0, 5}, {1, 4}, {2, 7}, {3, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[12, 18, 36, 58, 68, 90, 108, 114, 140, 146, 164, 186, 196, 218, 236, 242]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7177816621911453544868397074866119584632679289615579396825254958297518080.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{0, 3, 6}, {1, 4, 7}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[13, 19, 37, 59, 69, 91, 109, 115, 141, 147, 165, 187, 197, 219, 237, 243]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14355633243822907089736794149732239169265358579231158793650509916595036160.svg|420px]]
|-
|class=&quot;size&quot;| 32
|class=&quot;prop&quot;| {{1, 2}, {5, 6}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[14, 15, 16, 17, 38, 39, 56, 57, 70, 71, 88, 89, 110, 111, 112, 113, 142, 143, 144, 145, 166, 167, 184, 185, 198, 199, 216, 217, 238, 239, 240, 241]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_6625676808857021518702186534207344486008530803552194405472437598305894400.svg|420px]]
|}

[[Category:Boolf prop/3-ary|patron symmetry negperm]]</text>
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  <page>
    <title>Boolf prop/3-ary/noble symmetry perm</title>
    <ns>0</ns>
    <id>317441</id>
    <revision>
      <id>2693009</id>
      <timestamp>2024-12-23T13:36:19Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;20&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; &lt;/div&gt;  {| class=&quot;wikitable sortable boolf-blocks&quot; !class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt; !class=&quot;prop&quot;| noble symmetry perm !class=&quot;block&quot;| block |- |cla...&quot;</comment>
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      <text bytes="6772" sha1="lemtrzp434nzbh5nppiplfg9lk401y0" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| noble symmetry perm
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{1, 2, 4, 8}, {3, 5, 6, 9, 10, 12}, {7, 11, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 23, 104, 127, 128, 151, 232, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57896051520404444502349279939102670699556280274355188060900978491848466104321.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{1, 2, 4}, {3, 5, 6}, {9, 10, 12}, {11, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 22, 105, 126, 129, 150, 233, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28948036112821742437020321121685128765826742394646074386702889536779097997314.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{2, 4}, {3, 5}, {10, 12}, {11, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 21, 41, 62, 65, 86, 106, 125, 130, 149, 169, 190, 193, 214, 234, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14474038761676239677242141814693500753984313642843682837967548954426447233028.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{1, 2, 4, 8}, {3, 5, 10, 12}, {6, 9}, {7, 11, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 20, 107, 124, 131, 148, 235, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7237060791303036538483486041090249271699696886003920377937723838469099225096.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{1, 4}, {3, 6}, {9, 12}, {11, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 19, 33, 54, 73, 94, 108, 123, 132, 147, 161, 182, 201, 222, 236, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3618613223347669636677070689349243650012998078020072141269552992280417665040.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{1, 2, 4, 8}, {3, 6, 9, 12}, {5, 10}, {7, 11, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 18, 109, 122, 133, 146, 237, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1809472250216162851534494552948430638896969370870587219532436776714573709344.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{1, 2, 4, 8}, {3, 12}, {5, 6, 9, 10}, {7, 11, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 17, 110, 121, 134, 145, 238, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_905067408932727372829044144755604633003756924426665009843027695712965099584.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{1, 2}, {5, 6}, {9, 10}, {13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 9, 16, 30, 97, 111, 118, 120, 135, 137, 144, 158, 225, 239, 246, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_566274538181365511932726438687533486222273157099220818899684608590326334080.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{1, 2}, {4, 8}, {5, 6, 9, 10}, {7, 11}, {13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[8, 14, 25, 31, 96, 102, 113, 119, 136, 142, 153, 159, 224, 230, 241, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_229691870817723327637415329194734525839926399315998755379116121550110081280.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{2, 8}, {3, 9}, {6, 12}, {7, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[10, 29, 47, 56, 71, 80, 98, 117, 138, 157, 175, 184, 199, 208, 226, 245]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_56539213913107146782144949019704587737917683867982002403353289010976916480.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{1, 2}, {4, 8}, {5, 10}, {6, 9}, {7, 11}, {13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[11, 13, 26, 28, 99, 101, 114, 116, 139, 141, 154, 156, 227, 229, 242, 244]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_35338019693434372617257736809645151009794533424115220420415194056045373440.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{1, 8}, {3, 10}, {5, 12}, {7, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[12, 27, 39, 48, 79, 88, 100, 115, 140, 155, 167, 176, 207, 216, 228, 243]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14135207982891728785221400220559155644628841262829597032853507922194337792.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{1, 2, 8}, {3, 9, 10}, {5, 6, 12}, {7, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[15, 24, 103, 112, 143, 152, 231, 240]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1770297937951779611477014884394198171982016725228952541797234659660169216.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{1, 4}, {2, 8}, {3, 6, 9, 12}, {7, 13}, {11, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[32, 37, 50, 55, 72, 77, 90, 95, 160, 165, 178, 183, 200, 205, 218, 223]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_13901275529217652327245970153994796988196477533108020402745025495040.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{4, 8}, {5, 9}, {6, 10}, {7, 11}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[34, 44, 53, 59, 68, 74, 83, 93, 162, 172, 181, 187, 196, 202, 211, 221]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3373290870893507601034959821752118419834948812535356919119284797440.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{1, 4}, {2, 8}, {3, 12}, {6, 9}, {7, 13}, {11, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[35, 38, 49, 52, 75, 78, 89, 92, 163, 166, 177, 180, 203, 206, 217, 220]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1895736949574940170573955532367379596523916439416560905111658823680.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{1, 4, 8}, {3, 6, 10}, {5, 9, 12}, {7, 11, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[36, 51, 76, 91, 164, 179, 204, 219]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_842524044357931908582212034586466781927809552141067837108519960576.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{1, 8}, {2, 4}, {3, 5, 10, 12}, {7, 14}, {11, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[40, 43, 60, 63, 64, 67, 84, 87, 168, 171, 188, 191, 192, 195, 212, 215]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_59238224088352129452486105152124518892717258952081606738068897792.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| {{2, 4, 8}, {3, 5, 9}, {6, 10, 12}, {7, 11, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[42, 61, 66, 85, 170, 189, 194, 213]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_13164062351615803384974531127678415344793240523417466831544254464.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| {{1, 8}, {2, 4}, {3, 12}, {5, 10}, {7, 14}, {11, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[45, 46, 57, 58, 69, 70, 81, 82, 173, 174, 185, 186, 197, 198, 209, 210]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_2468859584903895971950156682139742058335821949700628238647164928.svg|420px]]
|}

[[Category:Boolf prop/3-ary|noble symmetry perm]]</text>
      <sha1>lemtrzp434nzbh5nppiplfg9lk401y0</sha1>
    </revision>
  </page>
  <page>
    <title>Exploring Existential Concerns/What Ought We Do?</title>
    <ns>0</ns>
    <id>317442</id>
    <revision>
      <id>2693011</id>
      <timestamp>2024-12-23T13:38:20Z</timestamp>
      <contributor>
        <username>Lbeaumont</username>
        <id>278565</id>
      </contributor>
      <comment>Created the essay</comment>
      <origin>2693011</origin>
      <model>wikitext</model>
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      <text bytes="4203" sha1="dvlv2sxbj7m29cy6vzocsxyn6voavbd" xml:space="preserve">Let us pause to consider a question both intimate and vast: ''What ought we do?''&lt;ref&gt;This text first appeared in the public domain article [https://lelandbeaumont.substack.com/p/what-ought-we-do What Ought We Do?]&lt;/ref&gt;
[[File:Earth Rise as Seen From Lunar Surface (5052124921).jpg|thumb|We all live on this one beautiful planet.]]

In the smallest, most immediate sense, the answer starts with the mundane: getting out of bed, taking a shower, eating breakfast, and moving into the rhythms of the day. The tasks are familiar—getting the kids off to school, heading to work, and planning dinner. The chores persist too: laundry to fold, dishes to wash, trash to take out. There is, perhaps, a lawn waiting to be mowed.

As the holidays approach, those rhythms take on a festive hue. The to-do list stretches to include shopping for food, decorating the house, sending cards, and buying gifts. These acts, though seemingly small, tether us to a shared tradition and a broader sense of purpose.

Yet, even amid this busyness, there is room for stillness. In those quiet moments—while journaling, [[Guided Meditations|meditating]], practicing yoga, or simply breathing deeply—we might pause and ask ourselves [[What Matters|what truly matters]]. What do we care for? Whom do we care for? Perhaps it starts with [[Living Wisely/Take Care|taking care]] and giving care.

From there, the scope widens. Our thoughts turn outward to family, friends, neighbors, and our [[Creating Communities|communities]]. The timeframe stretches too—from the immediate to the weekly, monthly, yearly, and even the arc of a lifetime. We think about how to care for ourselves better: eating well, exercising more, tending to our physical and mental health. We think about how to care for others: making time for loved ones, offering support, and building connections.

Perhaps this season prompts us to consider not just resolutions but transformations. What kind of person do we want to become? [[Clarifying values|What values do we hold dear]]? How might we embody [[Virtues/Compassion|compassion]], practice [[Virtues|virtue]], or [[Living the Golden Rule|live the golden rule]]? Self-improvement, we realize, is not just for our benefit; it is a gift to those around us.

The scope of concern expands further still. Beyond friends and family, we think of those we may never meet: neighbors we’ve yet to know, strangers in distant places, people across the globe. We recognize that our actions ripple outward—influencing [[Creating Communities|communities]], nations, and the world. Citizenship asks more of us than paying taxes and voting; it invites us to engage actively, to care deeply, and to envision a future where all can thrive.

“What ought we do?” is not a question we answer once but one we carry with us, a companion to our days and years. It invites reflection on our interconnectedness and our shared humanity. It challenges us to think beyond ourselves, to consider the needs of others, and to act with both urgency and foresight.

To [[Living Wisely/Seeking Real Good|seek real good]] is a lifelong endeavor. It is a quest to understand what is true, to discern what is just, and to align our actions with those ideals. It asks us to [[Seeking True Beliefs|explore our beliefs]], [[Exploring Worldviews/Aligning worldviews|refine our worldview]], and strive for harmony between our aspirations and reality. It is about [[Finding Common Ground|finding common ground]] and working together to [[Level 5 Research Center|build a better world]].

We begin to see the [[Moral Reasoning|ethical imperative]]: to promote flourishing and minimize harm, to act with empathy and integrity, to commit ourselves to [[Virtues/Justice|justice]]. This is not easy work, but it is essential. It calls us to address the [[grand challenges]] of our time—climate change, inequality, [[w:human_rights|human rights]]—and to [[Envisioning Our Future|imagine a future]] that is better for all.

What [[w:Is–ought_problem|ought]] we do? We ought to ''seek real good''. And in doing so, perhaps we can take small but meaningful steps toward peace on Earth and goodwill toward all.

&lt;references /&gt;

{{CourseCat}}</text>
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    </revision>
    <revision>
      <id>2693026</id>
      <parentid>2693011</parentid>
      <timestamp>2024-12-23T14:51:49Z</timestamp>
      <contributor>
        <username>Lbeaumont</username>
        <id>278565</id>
      </contributor>
      <comment>Added assignment</comment>
      <origin>2693026</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4345" sha1="jrq3k0ybujlx0hqxabm4hnimo16gusb" xml:space="preserve">It is intriguing to pause and consider a question both intimate and vast: ''What ought we do?''&lt;ref&gt;This text is adapted from the public domain article [https://lelandbeaumont.substack.com/p/what-ought-we-do What Ought We Do?]&lt;/ref&gt;
[[File:Earth Rise as Seen From Lunar Surface (5052124921).jpg|thumb|We all live on this one beautiful planet.]]

In the smallest, most immediate sense, the answer starts with the mundane: getting out of bed, taking a shower, eating breakfast, and moving into the rhythms of the day. The tasks are familiar—getting the kids off to school, heading to work, and planning dinner. The chores persist too: laundry to fold, dishes to wash, trash to take out. There is, perhaps, a lawn waiting to be mowed.

As the holidays approach, those rhythms take on a festive hue. The to-do list stretches to include shopping for food, decorating the house, sending cards, and buying gifts. These acts, though seemingly small, tether us to a shared tradition and a broader sense of purpose.

Yet, even amid this busyness, there is room for stillness. In those quiet moments—while journaling, [[Guided Meditations|meditating]], practicing yoga, or simply breathing deeply—we might pause and ask ourselves [[What Matters|what truly matters]]. What do we care for? Whom do we care for? Perhaps it starts with [[Living Wisely/Take Care|taking care]] and giving care.

From there, the scope widens. Our thoughts turn outward to family, friends, neighbors, and our [[Creating Communities|communities]]. The timeframe stretches too—from the immediate to the weekly, monthly, yearly, and even the arc of a lifetime. We think about how to care for ourselves better: eating well, exercising more, tending to our physical and mental health. We think about how to care for others: making time for loved ones, offering support, and building connections.

Perhaps this season prompts us to consider not just resolutions but transformations. What kind of person do we want to become? [[Clarifying values|What values do we hold dear]]? How might we embody [[Virtues/Compassion|compassion]], practice [[Virtues|virtue]], or [[Living the Golden Rule|live the golden rule]]? Self-improvement, we realize, is not just for our benefit; it is a gift to those around us.

The scope of concern expands further still. Beyond friends and family, we think of those we may never meet: neighbors we’ve yet to know, strangers in distant places, people across the globe. We recognize that our actions ripple outward—influencing [[Creating Communities|communities]], nations, and the world. Citizenship asks more of us than paying taxes and voting; it invites us to engage actively, to care deeply, and to envision a future where all can thrive.

“What ought we do?” is not a question we answer once but one we carry with us, a companion to our days and years. It invites reflection on our interconnectedness and our shared humanity. It challenges us to think beyond ourselves, to consider the needs of others, and to act with both urgency and foresight.

To [[Living Wisely/Seeking Real Good|seek real good]] is a lifelong endeavor. It is a quest to understand what is true, to discern what is just, and to align our actions with those ideals. It asks us to [[Seeking True Beliefs|explore our beliefs]], [[Exploring Worldviews/Aligning worldviews|refine our worldview]], and strive for harmony between our aspirations and reality. It is about [[Finding Common Ground|finding common ground]] and working together to [[Level 5 Research Center|build a better world]].

We begin to see the [[Moral Reasoning|ethical imperative]]: to promote flourishing and minimize harm, to act with empathy and integrity, to commit ourselves to [[Virtues/Justice|justice]]. This is not easy work, but it is essential. It calls us to address the [[grand challenges]] of our time—climate change, inequality, [[w:human_rights|human rights]]—and to [[Envisioning Our Future|imagine a future]] that is better for all.

What [[w:Is–ought_problem|ought]] we do? We ought to ''seek real good''. And in doing so, perhaps we can take small but meaningful steps toward peace on Earth and goodwill toward all.

=== Assignment: ===
1.     Use this planning grid to record your plans over various timeframes and expanding circles of concern.&lt;references /&gt;

{{CourseCat}}</text>
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    <revision>
      <id>2693028</id>
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      <timestamp>2024-12-23T14:53:26Z</timestamp>
      <contributor>
        <username>Lbeaumont</username>
        <id>278565</id>
      </contributor>
      <comment>/* Assignment: */ Added the assignment</comment>
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      <text bytes="4358" sha1="mxao0i12dq4aal6xzggpjdgnx5fmnr5" xml:space="preserve">It is intriguing to pause and consider a question both intimate and vast: ''What ought we do?''&lt;ref&gt;This text is adapted from the public domain article [https://lelandbeaumont.substack.com/p/what-ought-we-do What Ought We Do?]&lt;/ref&gt;
[[File:Earth Rise as Seen From Lunar Surface (5052124921).jpg|thumb|We all live on this one beautiful planet.]]

In the smallest, most immediate sense, the answer starts with the mundane: getting out of bed, taking a shower, eating breakfast, and moving into the rhythms of the day. The tasks are familiar—getting the kids off to school, heading to work, and planning dinner. The chores persist too: laundry to fold, dishes to wash, trash to take out. There is, perhaps, a lawn waiting to be mowed.

As the holidays approach, those rhythms take on a festive hue. The to-do list stretches to include shopping for food, decorating the house, sending cards, and buying gifts. These acts, though seemingly small, tether us to a shared tradition and a broader sense of purpose.

Yet, even amid this busyness, there is room for stillness. In those quiet moments—while journaling, [[Guided Meditations|meditating]], practicing yoga, or simply breathing deeply—we might pause and ask ourselves [[What Matters|what truly matters]]. What do we care for? Whom do we care for? Perhaps it starts with [[Living Wisely/Take Care|taking care]] and giving care.

From there, the scope widens. Our thoughts turn outward to family, friends, neighbors, and our [[Creating Communities|communities]]. The timeframe stretches too—from the immediate to the weekly, monthly, yearly, and even the arc of a lifetime. We think about how to care for ourselves better: eating well, exercising more, tending to our physical and mental health. We think about how to care for others: making time for loved ones, offering support, and building connections.

Perhaps this season prompts us to consider not just resolutions but transformations. What kind of person do we want to become? [[Clarifying values|What values do we hold dear]]? How might we embody [[Virtues/Compassion|compassion]], practice [[Virtues|virtue]], or [[Living the Golden Rule|live the golden rule]]? Self-improvement, we realize, is not just for our benefit; it is a gift to those around us.

The scope of concern expands further still. Beyond friends and family, we think of those we may never meet: neighbors we’ve yet to know, strangers in distant places, people across the globe. We recognize that our actions ripple outward—influencing [[Creating Communities|communities]], nations, and the world. Citizenship asks more of us than paying taxes and voting; it invites us to engage actively, to care deeply, and to envision a future where all can thrive.

“What ought we do?” is not a question we answer once but one we carry with us, a companion to our days and years. It invites reflection on our interconnectedness and our shared humanity. It challenges us to think beyond ourselves, to consider the needs of others, and to act with both urgency and foresight.

To [[Living Wisely/Seeking Real Good|seek real good]] is a lifelong endeavor. It is a quest to understand what is true, to discern what is just, and to align our actions with those ideals. It asks us to [[Seeking True Beliefs|explore our beliefs]], [[Exploring Worldviews/Aligning worldviews|refine our worldview]], and strive for harmony between our aspirations and reality. It is about [[Finding Common Ground|finding common ground]] and working together to [[Level 5 Research Center|build a better world]].

We begin to see the [[Moral Reasoning|ethical imperative]]: to promote flourishing and minimize harm, to act with empathy and integrity, to commit ourselves to [[Virtues/Justice|justice]]. This is not easy work, but it is essential. It calls us to address the [[grand challenges]] of our time—climate change, inequality, [[w:human_rights|human rights]]—and to [[Envisioning Our Future|imagine a future]] that is better for all.

What [[w:Is–ought_problem|ought]] we do? We ought to ''seek real good''. And in doing so, perhaps we can take small but meaningful steps toward peace on Earth and goodwill toward all.

=== Assignment: ===
# Use this [[/Planning Grid/|planning grid]] to record your plans over various timeframes and expanding circles of concern.&lt;references /&gt;

{{CourseCat}}</text>
      <sha1>mxao0i12dq4aal6xzggpjdgnx5fmnr5</sha1>
    </revision>
    <revision>
      <id>2693029</id>
      <parentid>2693028</parentid>
      <timestamp>2024-12-23T14:54:56Z</timestamp>
      <contributor>
        <username>Lbeaumont</username>
        <id>278565</id>
      </contributor>
      <comment>Improved reference</comment>
      <origin>2693029</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4360" sha1="i5q7cp8j7b4esv1navans1nb1z7dona" xml:space="preserve">It is intriguing to pause and consider a question both intimate and vast: ''What ought we do?''&lt;ref&gt;This text is adapted from the public domain article [https://lelandbeaumont.substack.com/p/what-ought-we-do What Ought We Do?]&lt;/ref&gt;
[[File:Earth Rise as Seen From Lunar Surface (5052124921).jpg|thumb|We all live on this one beautiful planet.]]

In the smallest, most immediate sense, the answer starts with the mundane: getting out of bed, taking a shower, eating breakfast, and moving into the rhythms of the day. The tasks are familiar—getting the kids off to school, heading to work, and planning dinner. The chores persist too: laundry to fold, dishes to wash, trash to take out. There is, perhaps, a lawn waiting to be mowed.

As the holidays approach, those rhythms take on a festive hue. The to-do list stretches to include shopping for food, decorating the house, sending cards, and buying gifts. These acts, though seemingly small, tether us to a shared tradition and a broader sense of purpose.

Yet, even amid this busyness, there is room for stillness. In those quiet moments—while journaling, [[Guided Meditations|meditating]], practicing yoga, or simply breathing deeply—we might pause and ask ourselves [[What Matters|what truly matters]]. What do we care for? Whom do we care for? Perhaps it starts with [[Living Wisely/Take Care|taking care]] and giving care.

From there, the scope widens. Our thoughts turn outward to family, friends, neighbors, and our [[Creating Communities|communities]]. The timeframe stretches too—from the immediate to the weekly, monthly, yearly, and even the arc of a lifetime. We think about how to care for ourselves better: eating well, exercising more, tending to our physical and mental health. We think about how to care for others: making time for loved ones, offering support, and building connections.

Perhaps this season prompts us to consider not just resolutions but transformations. What kind of person do we want to become? [[Clarifying values|What values do we hold dear]]? How might we embody [[Virtues/Compassion|compassion]], practice [[Virtues|virtue]], or [[Living the Golden Rule|live the golden rule]]? Self-improvement, we realize, is not just for our benefit; it is a gift to those around us.

The scope of concern expands further still. Beyond friends and family, we think of those we may never meet: neighbors we’ve yet to know, strangers in distant places, people across the globe. We recognize that our actions ripple outward—influencing [[Creating Communities|communities]], nations, and the world. Citizenship asks more of us than paying taxes and voting; it invites us to engage actively, to care deeply, and to envision a future where all can thrive.

“What ought we do?” is not a question we answer once but one we carry with us, a companion to our days and years. It invites reflection on our interconnectedness and our shared humanity. It challenges us to think beyond ourselves, to consider the needs of others, and to act with both urgency and foresight.

To [[Living Wisely/Seeking Real Good|seek real good]] is a lifelong endeavor. It is a quest to understand what is true, to discern what is just, and to align our actions with those ideals. It asks us to [[Seeking True Beliefs|explore our beliefs]], [[Exploring Worldviews/Aligning worldviews|refine our worldview]], and strive for harmony between our aspirations and reality. It is about [[Finding Common Ground|finding common ground]] and working together to [[Level 5 Research Center|build a better world]].

We begin to see the [[Moral Reasoning|ethical imperative]]: to promote flourishing and minimize harm, to act with empathy and integrity, to commit ourselves to [[Virtues/Justice|justice]]. This is not easy work, but it is essential. It calls us to address the [[grand challenges]] of our time—climate change, inequality, [[w:human_rights|human rights]]—and to [[Envisioning Our Future|imagine a future]] that is better for all.

What [[w:Is–ought_problem|ought]] we do? We ought to ''seek real good''. And in doing so, perhaps we can take small but meaningful steps toward peace on Earth and goodwill toward all.

=== Assignment: ===
# Use this [[/Planning Grid/|planning grid]] to record your plans over various timeframes and expanding circles of concern.

&lt;references /&gt;

{{CourseCat}}</text>
      <sha1>i5q7cp8j7b4esv1navans1nb1z7dona</sha1>
    </revision>
  </page>
  <page>
    <title>Category:Exploring Existential Concerns</title>
    <ns>14</ns>
    <id>317443</id>
    <revision>
      <id>2693012</id>
      <timestamp>2024-12-23T13:39:40Z</timestamp>
      <contributor>
        <username>Lbeaumont</username>
        <id>278565</id>
      </contributor>
      <comment>New resource with &quot;Everyone has important questions and legitimate concerns about their very existence. These are our Existential Concerns.&quot;</comment>
      <origin>2693012</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="120" sha1="1v2furuh0g2839e5b2c3bf1bj2mm0yd" xml:space="preserve">Everyone has important questions and legitimate concerns about their very existence. These are our Existential Concerns.</text>
      <sha1>1v2furuh0g2839e5b2c3bf1bj2mm0yd</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/noble symmetry negperm</title>
    <ns>0</ns>
    <id>317444</id>
    <revision>
      <id>2693016</id>
      <timestamp>2024-12-23T13:49:47Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;66&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; &lt;/div&gt;  {| class=&quot;wikitable sortable boo...&quot;</comment>
      <origin>2693016</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="17547" sha1="os1er20gm12e8hqtk8kspf75q89p7eq" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;66&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| noble symmetry negperm
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| &lt;nowiki&gt;{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}}&lt;/nowiki&gt;
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1.svg|420px]]
|-
|class=&quot;size&quot;| 6
|class=&quot;prop&quot;| {{1, 2, 4}, {3, 5, 6}, {9, 10, 12}, {11, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 22, 105, 129, 150, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28948022309329048855892746252173404211690766900697895430063935559872708345858.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{2, 4}, {3, 5}, {10, 12}, {11, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 21, 41, 62, 65, 86, 106, 125, 149, 190, 193, 234]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_27606985387176378628643644194450621224363588500354594809182059193434116.svg|420px]]
|-
|class=&quot;size&quot;| 6
|class=&quot;prop&quot;| {{1, 2, 4, 8}, {3, 5, 10, 12}, {6, 9}, {7, 11, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 124, 131, 148, 235, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7237060791303036538483486041090249271699696723744643548724360446891087888392.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{1, 4}, {3, 6}, {9, 12}, {11, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 19, 33, 54, 73, 94, 108, 123, 147, 161, 222, 236]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_110434681535315808258907683731884796175116049982818482047251050435969040.svg|420px]]
|-
|class=&quot;size&quot;| 6
|class=&quot;prop&quot;| {{1, 2, 4, 8}, {3, 6, 9, 12}, {5, 10}, {7, 11, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 122, 133, 146, 237, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1809472250216162851534494552948430638896968721833479902678983210402532294688.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| {{0, 3, 12, 15}, {1, 2, 4, 7, 8, 11, 13, 14}, {5, 6, 9, 10}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_64.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{1, 2}, {5, 6}, {9, 10}, {13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 9, 16, 30, 97, 111, 118, 120, 135, 137, 246, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_565391060729082985466655200237734142847173807702431420442135440006970409600.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 12}, {1, 2, 13, 14}, {3, 15}, {4, 8}, {5, 6, 9, 10}, {7, 11}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[8, 14]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_16640.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{2, 8}, {3, 9}, {6, 12}, {7, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[10, 29, 47, 56, 71, 80, 98, 117, 157, 184, 199, 226]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_107839787472096101236999740045459831436156131478119467399875559162880.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 3}, {1, 2}, {4, 7, 8, 11}, {5, 10}, {6, 9}, {12, 15}, {13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[11, 13]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_10240.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{1, 8}, {3, 10}, {5, 12}, {7, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[12, 27, 39, 48, 79, 88, 100, 115, 155, 167, 216, 228]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_431464458966078794088488040924519966996421558563078308249111204204544.svg|420px]]
|-
|class=&quot;size&quot;| 6
|class=&quot;prop&quot;| {{1, 2, 8}, {3, 9, 10}, {5, 6, 12}, {7, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[15, 24, 103, 143, 152, 240]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1766847064778384329583297506463059659250598873884332520891122901219049472.svg|420px]]
|-
|class=&quot;size&quot;| 6
|class=&quot;prop&quot;| {{1, 2, 4, 8}, {3, 12}, {5, 6, 9, 10}, {7, 11, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[17, 110, 134, 145, 238, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_905067408932727372829044144755604633001098468435095178097220081592404410368.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| {{0, 5, 10, 15}, {1, 2, 4, 7, 8, 11, 13, 14}, {3, 6, 9, 12}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_262144.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| {{0, 6, 9, 15}, {1, 2, 4, 7, 8, 11, 13, 14}, {3, 5, 10, 12}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1048576.svg|420px]]
|-
|class=&quot;size&quot;| 6
|class=&quot;prop&quot;| {{1, 2, 4, 8}, {3, 5, 6, 9, 10, 12}, {7, 11, 13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[23, 104, 128, 151, 232, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57896051520404444502349279939102670699386139090894718829169291188132581998592.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{1, 2}, {4, 8}, {5, 6, 9, 10}, {7, 11}, {13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[25, 31, 113, 119, 136, 142, 153, 159, 224, 230, 241, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_229691870817723327637415329194734525839926394166168191951934177969753292800.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{1, 2}, {4, 8}, {5, 10}, {6, 9}, {7, 11}, {13, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[26, 28, 114, 116, 139, 141, 154, 156, 227, 229, 242, 244]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_35338019693434372617257736809645151009794530254988719849841690314287349760.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 10}, {1, 4, 11, 14}, {2, 8}, {3, 6, 9, 12}, {5, 15}, {7, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[32, 50]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1125904201809920.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{4, 8}, {5, 9}, {6, 10}, {7, 11}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[34, 44, 53, 59, 68, 74, 83, 93, 172, 181, 202, 211]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3297436869890425437850391308553722017664195711767561293550059520.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 5}, {1, 4}, {2, 7, 8, 13}, {3, 12}, {6, 9}, {10, 15}, {11, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[35, 49]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_562984313159680.svg|420px]]
|-
|class=&quot;size&quot;| 6
|class=&quot;prop&quot;| {{1, 4, 8}, {3, 6, 10}, {5, 9, 12}, {7, 11, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[36, 51, 91, 164, 179, 204]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_25711009474414998867813117103323376648713378811221159708721152.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{1, 4}, {2, 8}, {3, 6, 9, 12}, {7, 13}, {11, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[37, 55, 77, 95, 160, 165, 178, 183, 200, 205, 218, 223]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_13901275529217652327245970153994796988195239588346367413696279347200.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{1, 4}, {2, 8}, {3, 12}, {6, 9}, {7, 13}, {11, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[38, 52, 78, 92, 163, 166, 177, 180, 203, 206, 217, 220]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1895736949574940170573955532367379596523297431617985789032734392320.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 6}, {1, 7, 8, 14}, {2, 4}, {3, 5, 10, 12}, {9, 15}, {11, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[40, 60]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1152922604118474752.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| {{0, 14}, {1, 15}, {2, 4, 6, 8, 10, 12}, {3, 5, 7, 9, 11, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[42]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_4398046511104.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{1, 8}, {2, 4}, {3, 5, 10, 12}, {7, 14}, {11, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[43, 63, 67, 87, 168, 171, 188, 191, 192, 195, 212, 215]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_59238224088352129452486105152124518892697916119368105993445572608.svg|420px]]
|-
|class=&quot;size&quot;| 2
|class=&quot;prop&quot;| {{0, 9}, {1, 8}, {2, 4, 11, 13}, {3, 12}, {5, 10}, {6, 15}, {7, 14}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[45, 57]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_144150372447944704.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| {{1, 8}, {2, 4}, {3, 12}, {5, 10}, {7, 14}, {11, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[46, 58, 70, 82, 173, 174, 185, 186, 197, 198, 209, 210]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_2468859584903895971950156682139742058333403507621438249144156160.svg|420px]]
|-
|class=&quot;size&quot;| 6
|class=&quot;prop&quot;| {{2, 4, 8}, {3, 5, 9}, {6, 10, 12}, {7, 11, 13}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[61, 66, 85, 170, 194, 213]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_13164061566978086461639435648204737443834938510623031875493429248.svg|420px]]
|-
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[[Category:Boolf prop/3-ary|noble symmetry negperm]]</text>
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  </page>
  <page>
    <title>Boolf prop/3-ary/noble symmetry neg</title>
    <ns>0</ns>
    <id>317445</id>
    <revision>
      <id>2693019</id>
      <timestamp>2024-12-23T14:13:42Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt; &lt;/div&gt;  {| class=&quot;wikitable sortable boolf...&quot;</comment>
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      <text bytes="4268" sha1="dynid63us1j70po8bys46446yp3uywm" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| noble symmetry neg
!class=&quot;block&quot;| block
|-
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|-
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|-
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|-
|class=&quot;size&quot;| 2
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[64, 84]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_19342831560578140504850432.svg|420px]]
|-
|class=&quot;size&quot;| 2
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[72, 90]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1237944761651863144544337920.svg|420px]]
|-
|class=&quot;size&quot;| 1
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|-
|class=&quot;size&quot;| 4
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[107, 109, 121, 127]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_172800450748423209544311875726496235520.svg|420px]]
|-
|class=&quot;size&quot;| 1
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[112]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5192296858534827628530496329220096.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| {{0, 7}, {1, 6}, {2, 5}, {3, 4}, {8, 15}, {9, 14}, {10, 13}, {11, 12}}
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[126]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_85070591730234615865843651857942052864.svg|420px]]
|}

[[Category:Boolf prop/3-ary|noble symmetry neg]]</text>
      <sha1>dynid63us1j70po8bys46446yp3uywm</sha1>
    </revision>
  </page>
  <page>
    <title>File:Laurent.5.Permutation.6B.20241223.pdf</title>
    <ns>6</ns>
    <id>317446</id>
    <revision>
      <id>2693023</id>
      <timestamp>2024-12-23T14:31:48Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=Laurent.5: Permutations 6B (20241223 - 20241216)
|Source={{own|Young1lim}}
|Date=2024-12-23
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}</comment>
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      <text bytes="271" sha1="fhwghi52y9p350i2my17l8zny9v1z6q" xml:space="preserve">== Summary ==
{{Information
|Description=Laurent.5: Permutations 6B (20241223 - 20241216)
|Source={{own|Young1lim}}
|Date=2024-12-23
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
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== Licensing ==
{{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}</text>
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    <title>File:C04.SA0.PtrOperator.1A.20241223.pdf</title>
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        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=C04.SA0: Address-of and de-reference operators 1A (20241223 - 20241219) 
|Source={{own|Young1lim}}
|Date=2024-12-23
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
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      <text bytes="294" sha1="04g4jzpxv6fc2xtulun3kbjhtcyjprl" xml:space="preserve">== Summary ==
{{Information
|Description=C04.SA0: Address-of and de-reference operators 1A (20241223 - 20241219) 
|Source={{own|Young1lim}}
|Date=2024-12-23
|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}}</text>
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  <page>
    <title>File:VLSI.Arith.5A.CSkip.20241223.pdf</title>
    <ns>6</ns>
    <id>317448</id>
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      <timestamp>2024-12-23T14:32:48Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=VLSI.Arith: Carry Skip Adders 1A (20241223 - 20241219)
|Source={{own|Young1lim}}
|Date=2024-12-23
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}</comment>
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      <text bytes="277" sha1="fq06iv1tp9yw5tnuc9z8ospbsvpopyn" xml:space="preserve">== Summary ==
{{Information
|Description=VLSI.Arith: Carry Skip Adders 1A (20241223 - 20241219)
|Source={{own|Young1lim}}
|Date=2024-12-23
|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}}</text>
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  </page>
  <page>
    <title>Exploring Existential Concerns/What Ought We Do?/Planning Grid</title>
    <ns>0</ns>
    <id>317449</id>
    <revision>
      <id>2693027</id>
      <timestamp>2024-12-23T14:53:03Z</timestamp>
      <contributor>
        <username>Lbeaumont</username>
        <id>278565</id>
      </contributor>
      <comment>Created the resource</comment>
      <origin>2693027</origin>
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      <text bytes="507" sha1="3s4wzi4bahopej869e0y3ho41t4kq5q" xml:space="preserve">Consider the question [[Exploring Existential Concerns/What Ought We Do?|What ought we do?]] and use this grid to record your plans over various timeframes and expanding circles of concern. 
{| class=&quot;wikitable&quot;
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Please print out this form for your own use, rather than editing this form.</text>
      <sha1>3s4wzi4bahopej869e0y3ho41t4kq5q</sha1>
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    <revision>
      <id>2693030</id>
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      <timestamp>2024-12-23T15:06:16Z</timestamp>
      <contributor>
        <username>Lbeaumont</username>
        <id>278565</id>
      </contributor>
      <comment>Focus</comment>
      <origin>2693030</origin>
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      <format>text/x-wiki</format>
      <text bytes="716" sha1="0nc85jrte4mij5jbct2dyw7kne2qfbu" xml:space="preserve">Consider the question [[Exploring Existential Concerns/What Ought We Do?|What ought we do?]] and use this grid to record your plans over various timeframes and expanding circles of concern. 
{| class=&quot;wikitable&quot;
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|Today
|This Week
|This Month
|This Year
|Before I Die
|-
|For me
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Are you focusing on [[What Matters|what matters]]? Are you satisfied with how you are [[w:Time_management#The_Eisenhower_Method|distributing your time]] among the first few rows and columns, and the last few?

Please print out this form for your own use, rather than editing this form.</text>
      <sha1>0nc85jrte4mij5jbct2dyw7kne2qfbu</sha1>
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  </page>
  <page>
    <title>File:Borrow.20241223.pdf</title>
    <ns>6</ns>
    <id>317450</id>
    <revision>
      <id>2693035</id>
      <timestamp>2024-12-23T15:57:05Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=Borrows (20241223 - 20241217)
|Source={{own|Young1lim}}
|Date=2024-12-23
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}</comment>
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      <format>text/x-wiki</format>
      <text bytes="251" sha1="o3yva1ly9cqyzzwnwj3owp6b3oc11er" xml:space="preserve">== Summary ==
{{Information
|Description=Borrows (20241223 - 20241217)
|Source={{own|Young1lim}}
|Date=2024-12-23
|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}}</text>
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  <page>
    <title>HR 9495, the nonprofit-killer bill, per Michael Novick</title>
    <ns>0</ns>
    <id>317451</id>
    <revision>
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      <contributor>
        <username>DavidMCEddy</username>
        <id>218607</id>
      </contributor>
      <comment>create</comment>
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      <text bytes="21928" sha1="8426lqdwb1z2m6ti3gir9n418eowbg9" xml:space="preserve">:''This is a discussion of a Zoom interview recorded 2024-12-20 with Michael Novick, former interim general manager for KPFK, the second station in the Pacifica Radio Network, about HR 9495, which has been called the &quot;nonprofit-killer bill, by its opponents. A 29:00 mm:ss podcast excerpted from the companion video will be posted here after it is released to the fortnightly &quot;Media &amp; Democracy&quot; show&lt;ref name=M&amp;D&gt;&lt;!--Media &amp; Democracy--&gt;{{cite Q|Q127839818}}&lt;/ref&gt; syndicated for the [[w:Pacifica Foundation|Pacifica Radio]]&lt;ref&gt;&lt;!--Pacifica Radio Network--&gt;{{cite Q|Q2045587}}&lt;/ref&gt; Network of [[w:List of Pacifica Radio stations and affiliates|over 200 community radio stations]].&lt;ref&gt;&lt;!--list of Pacifica Radio stations and affiliates--&gt;{{cite Q|Q6593294}}&lt;/ref&gt; 

:''It is posted here to invite others to contribute other perspectives, subject to the Wikimedia rules of [[w:Wikipedia:Neutral point of view|writing from a neutral point of view]] while [[w:Wikipedia:Citing sources|citing credible sources]]&lt;ref name=NPOV&gt;The rules of writing from a neutral point of view citing credible sources may not be enforced on other parts of Wikiversity. However, they can facilitate dialog between people with dramatically different beliefs&lt;/ref&gt; and treating others with respect.&lt;ref name=AGF&gt;[[Wikiversity:Assume good faith|Wikiversity asks contributors to assume good faith]], similar to Wikipedia. The rule in [[w:Wikinews|Wikinews]] is different: Contributors there are asked to [[Wikinews:Never assume|&quot;Don't assume things; be skeptical about everything.&quot;]] That's wise. However, we should still treat others with respect while being skeptical.&lt;/ref&gt;'' 

::[Video of the interview coming soon.] 
&lt;!--[[File: ... .webm|thumb|HR 9495, the nonprofit-killer bill, per Michael Novick]]--&gt;
&lt;!--[[File: ... .ogg|thumb|29:00 mm:ss extract from interview recorded 2024-12-20 with Michael Novick regarding, HR 9495, the nonprofit-killer bill.]]--&gt;

Michael Novick discussed HR 9495, the “Stop Terror Financing and Tax Penalties on American Hostages Act”, which passed the House November 21. Its opponents have called it the “nonprofit-killer” bill, because it would give the Secretary of Treasury the authority to designate any nonprofit as a suspected “Terrorist Supporting Organization&quot; and remove their tax-exempt status unless they convince the Secretary of Treasury that they do not support terrorists.&lt;ref name=HR9495&gt;US House (2024).&lt;/ref&gt; Mother Jones reported, 'In the bill’s original iteration, it was popular among both Republicans and Democrats, who saw it as an appealing way to police Palestinian rights organizations after protests last year. An earlier version, in April, passed the House easily, with only 11 votes against the bill. It didn’t make it through the Senate ... One of those early no votes was Rep. Rashida Tlaib (D-Mich.), who said on the House floor [November 21], “... This is a dangerous and an unconstitutional bill that would allow unchecked power to target nonprofit organizations as political enemies and shut them down without due process.”'&lt;ref&gt;Hurwitz (2024).&lt;/ref&gt; 

Beth Gazley, Professor of Nonprofit Management and Policy at Indiana University,&lt;ref&gt;&lt;!--Beth Gazley--&gt;{{cite Q|Q131542978}}&lt;/ref&gt; said, &quot;I believe that this is part of a strategy to preempt opposition to Republican policies and encourage self-censorship. It’s a way for the GOP to try to restrict what activists and nonprofit organizations can say or do. And, essentially, it’s a threat to political opponents of President-elect Donald Trump.&quot; On November 21, only 15 Democrats supported it and one Republican opposed it. Rep. [[w:Jamie Raskin|Jamie Raskin]] (D-MD) called the bill “a werewolf in sheep’s clothing.&quot; ... An earlier version of this legislation was introduced in December 2023 and passed in the House in April 2024. Based on the timing, it was widely interpreted as an attempt to quell widespread protests by students and other people who were expressing their solidarity with Palestinians and their objections to Israel’s military operations in Gaza. But this legislation could easily do far more than that, because it does not distinguish between foreign and domestic terrorism – whether it’s real or imagined.&lt;ref name=Gazley&gt;Gazley (2024).&lt;/ref&gt; Raskin further noted that “rendering support to terrorists is already a felony”,&lt;ref&gt;Raskin was quoted in Gazley (2024). In fact, &quot;[[w:Providing material support for terrorism|Providing material support for terrorism]]&quot; is a felony under the USA Patriot Act of 2001 punishable by fines and imprisonment of up to 15 years or 20 years if human(s) convicted ''know(s)'' they were aiding an organization so classified by the US State Department and life in prison if the &quot;death of a person&quot; has resulted, where &quot;person&quot; in this context is a &quot;legal entity capable of holding a legal or beneficial interest in property&quot;. In ''[[w:Holder v. the Humanitarian Law Project|Holder v. the Humanitarian Law Project]]'' (2010), the US Supreme Court ruled that teaching nonviolence to someone designated as a &quot;terrorist&quot; was &quot;providing material support for terrorism&quot;. [[w:David D. Cole|David D. Cole]], attorney for the [[w:Humanitarian Law Project|Humanitarian Law Project]], said that under that ruling, even asking the State Department to explain why some individual or group was designated as a &quot;terrorist&quot; was similarly &quot;providing material support&quot;, a major felony with penalties as just described.&lt;/ref&gt; and this bill could end all rights to due process.&lt;ref name=Gazley/&gt; 

== Michael Novick == 

Novick has described himself as antiracist, antisexist, anti-imperialist, and anti-authoritarian. Between 2022 and November 2024, he was the interim general manager of [[w:KPFK|KPFK]],&lt;ref&gt;Novick (2022) noted that he began as interim general manager of KKFK in 2022. In this interview, he said he was no longer in that position.&lt;/ref&gt; the second [[w:Pacifica Foundation|station in the Pacifica Radio Network]].&lt;ref&gt;The Pacifica Radio Network includes stations owned by the Pacifica Foundation plus over 200 that are &quot;affiliates&quot;.&lt;/ref&gt; 

Novick can be reached at antiracistaction_la@yahoo.com or changelinks2@gmail.com. The latter is for the Change Links community calendar.&lt;ref name=Change-Links&gt;&lt;!-- Change-Links--&gt;{{cite Q|Q131544553}}&lt;/ref&gt; &quot;antiracist.org&quot; is the website for ''Turning the Tide'',&lt;ref&gt;&lt;!-- Turning the Tide--&gt;{{cite Q|Q131544806}}&lt;/ref&gt; which Novick has been doing since 1988. 

== HR 9495 == 

HR 9495 says that &quot;the term ‘terrorist supporting organization’ means any organization which is designated by the Secretary [of Treasury] as having provided, during the 3-year period ending on the date of such designation, material support or resources&quot; to a designated terrorist organization. Before an organization can be so designated, the Secretary is required to mail a written notice of such impending designation and giving them 90 days to &quot;demonstrated to the satisfaction of the Secretary that such organization did not provide the material support or resources&quot;.&lt;ref name=HR9495/&gt; 

== Selected comments == 

Novik noted that 9495 is not likely to pass the Senate this year,

{{blockquote|
but they are going to bring it back immediately when the new Congress is seated, which is even prior to the inauguration of the new president. ... It's also related to a separate initiative of [[w:Project 2025|Project 2025]] that Trump, of course, said he never read ... but he's been appointing all sorts of people involved in that Project 2025 to his administration. And he has already said he'll be appointing the person who wrote the section of 2025 on media, who is a current member of the [[w:Federal Communications Commission|FCC]], ... [[w:Brendan Carr|Brendan Carr]]. And in that document, they talk about actually not just defunding the [[w:Corporation for Public Broadcasting|Corporation for Public Broadcasting]] and public media efforts like [[w:NPR|NPR]]. ... But they actually want to remove the non-commercial educational licensing entirely. And they mentioned Pacifica by name in that report 2025. 

So we're expecting a lot of attacks of this nature to come down the pike. Because ... nonprofits and non-commercial media have been an important avenue for exposing some of the ills of the society and whistleblowing ... . They want to really contain and control the philanthropic sector and the public media sector to carry out some of their other goals ... that have been spelled out pretty clearly in the campaign of mass deportations, ... privatization ... . They want to try to force everything into the commercial enterprises, ... the billionaire owned media.&quot;
}} 

Regarding Trump suing [[w:American Broadcasting Company|ABC]] and ''[[w:The Des Moines Register|The Des Moines Register]]'',&lt;ref&gt;Gold (2024).&lt;/ref&gt; Novick said, &quot;I think it's part and parcel of this whole attack on on freedom of speech, freedom of the press, the whole thing about fake news. ... [T]his effort internationally and nationally to really control the free flow of information because they understand that an informed public is less likely to sit still for its own rights being violated. And certainly the other end of the freedom of speech is freedom of discourse and freedom of listening. If you can't hear any contrary views to those being expressed by the great leader, that's a violation of your rights, not just the rights of the speakers. And so I think ... that it is an attack on human rights and on people's ability to understand what's going on in the world and do something about it.&quot; 

Graves asked Novick about Trump saying that Liz Cheney, a Republican who represented Wyoming in the US House, should be prosecuted and jailed for her role in a Trump impeachment proceeding during Trump's first term.&lt;ref&gt;Mascaro (2024).&lt;/ref&gt; Novick replied, 

{{blockquote|
I think it's a much deeper problem. It it started before him. ... The Biden administration ... prosecuted [[w:Julian Assange|Julian Assange]] and actually won a conviction. They got him to plead guilty to a violation of the Espionage act for releasing data that was not espionage at all. It was whistleblowing about a war crime by the United States killing of reporters in Iraq. 

And similarly the Biden Administration is the one that pursued the case of the [[w:Uhuru Movement|Uhuru 3]] ... from the [[w:African People's Socialist Party|African People's Socialist party]] ... accusing them of being foreign agents for opposing the war in Iraq and ... the genocide in Palestine. So I think that this is a bipartisan issue. In fact, there were votes on both sides of the aisle for 9495.

One of the first things that Richard Nixon did [as president of the US] was introduce the [[w: Tax Reform Act of 1969|Tax Reform Act of 1969]], as they were trying to dismantle the great society and some of those programs that were about empowering communities, particularly poor people, people of color. The Tax Reform Act of 1969 specifically ... said that any ... organization that wanted nonprofit status could not support voter registration drives or ... activities that ... affected legislation. ... This is a very similar effort, I think,&quot; though 9495 has a much more authoritarian stamp. ... 9495 is targeted directly at organizations that are engaged with international solidarity, particularly with the Palestinian cause. But ... the terrorism term has been used extensively as the so-called Communist threat faded ... . 

I think the head&lt;ref&gt;[[w:Mufid Abdulqader|Mufid Abdulqader]] was released 2024-12-12 after 16 years in federal prison. He was described as a &quot;top fundraiser&quot; and &quot;leader&quot; of the [[w:Holy Land Foundation for Relief and Development|Holy Land Foundation]]&lt;/ref&gt; of the [[w:Holy Land Foundation for Relief and Development|Holy Land Foundation ]] was just recently released from prison. ... This was a humanitarian project, ... based in, obviously, the Muslim community ... . [I]t was humanitarian aid, but it was criminalized. And I think that's what they're trying to do here is to really prevent people from any kind of person to person diplomacy outside the bounds of what the State Department is carrying out which is really militarized. The State Department, I think, follows the same dictates as the Department of Defense, so-called, and the CIA. They're basically involved in, you know, trying to identify forces within different societies that will follow the dictates of US Policy. And anybody that does not want to do that is identified as a potential targeted terrorist or someone supporting terrorism. ... 

I've been associated for many years with the Los Angeles Chapter of the [[w:Anti-Racist Action|Anti-Racist Action Network]] ... . The idea was, be part of the solution. 

But ... terror is, you know, very widespread in this world, and has mainly been used actually by the right and by State actors including the United States. You know when [[w:George W. Bush|Bush]] [[w:2003 invasion of Iraq|went into Iraq]], ... the second bush and the second [[w:Iraq War|Iraq War]], they talked about &quot;[[w:Shock and awe|shock and awe]]&quot;. Well, it's just a polite name for terror. Right? You're bombing people into submission. You're trying to intimidate them through violence. ... it can be classified as terror as well as genocide. They're terrorizing the entire population.  

Historically, the [[w:Ku Klux Klan|Ku Klux Klan]], and a lot of other organizations have been terrorist organizations. But that's not what they're talking about. They're talking about resistance to white supremacy, resistance to colonialism. ... If there's some action against the German occupation, or in this case the Israeli occupation, they're going to punish people ... in the area where it happened without regard to who is responsible. ... The term is used is to justify that kind of actual terrorism by labelling any resistances as terrorism. ...

The case of the [[w:Humanitarian Law Project|Humanitarian Law Project]] ... went all the way to the Supreme Court ... [which] ruled that even providing nonviolence training was a form of material support. 

Lydia Brazon&lt;ref&gt;Pacifica in Exile (2015).&lt;/ref&gt; ... was with the Humanitarian Law Project for a long time. ... She was at one point the executive director of Pacifica. ...

Pacifica's mission is to identify the causes of conflict and try to resolve them without violence. ... It was created by a group of pacifists who actually resisted even World War 2. 

[[w:Lewis Hill (Pacifica Radio)|Lew Hill]] and a group of others ... formed the Pacifica Foundation and launched this project of listener sponsored non-commercial radio. But that's seen as a threat, trying to to solve things, because the State wants to reserve that power of the use of violence. And if you oppose violence by the state, then you're somehow a subversive. 

When 9495 passed, [[w:Mike Johnson|Mike Johnson]], who is the [[w:Speaker of the United States House of Representatives|Speaker of the House]], sent a tweet to a number of organizations, saying, &quot;We're thinking about you.&quot; That included, for example, a [[w:Jewish Voice for Peace|Jewish Voice for Peace]]; ... because they believe in supporting Palestinian rights, they're targeted. We have a program on our station [[w:KPFK|KPFK]], which is Middle Eastern focus for many years, and the current co-host is the head of the LA chapter of a Jewish Voice for Peace, trying to bring about peace in the Middle East. But that's seen as a threat. I also work on a newspaper called ''Change-Links''.&lt;ref name=Change-Links/&gt; It's a community calendar for [[w:Los Angeles|Los Angeles]]. We publish every month with a list of activities that people might be interested in, cultural, political, and otherwise. ... It's not a nonprofit itself. But we have a fiscal sponsor which is the Alliance for Global Justice based in Tucson, Arizona.&lt;ref&gt;&lt;!--Alliance for Global Justice--&gt;{{cite Q|Q129502246}}&lt;/ref&gt; They serve this purpose for a number of smaller projects around the country. Media and other community service organizations that are not full nonprofits themselves have a fiscal sponsor. The Alliance for Global Justice is also in Mike Johnson's Tweet. He tweeted out to 5 or 6 or maybe 8 organizations. This is something that's very clearly directed at not just the activities but the information. They want everything to be like the right wing echo chamber of right wing talk media. Anything that's outside those bounds becomes a fair target. 
}}

Graves noted that in August he had interviewed Heidi Beirich,&lt;ref name=Beirich&gt;&lt;!-- Heidi Beirich--&gt;{{cite Q|Q128844587}}&lt;/ref&gt; co-founder and Chief Strategy Officer of the [[Global Project Against Hate &amp; Extremism (GPAHE)]].&lt;ref name=GPAHE&gt;&lt;!-- GPAHE--&gt;{{cite Q|Q125952435}}&lt;/ref&gt; She noted that recent [[w:National Defense Authorization Act|National Defense Authorization Act]]s have included provisions that explicitly prohibited the Secretary of Defense from attempting to root violent extremists out of the Us. Military.&lt;ref&gt;Donnelly (2022).&lt;/ref&gt;

Novick replied, 

{{blockquote|
It's not surprising. There is a big struggle in the military. Trump has come in saying he wants to get rid of &quot;[[w:woke|Woke]]&quot; generals.&lt;ref&gt;Axe (2024).&lt;/ref&gt; And there is a group that focuses on the question of religious freedom in the military, to be free, free from religion if you want. And there's a number of quite fundamentalist Christian people in high positions of authority in the military that are trying to enforce Christian nationalism. You see a lot of these right wing groups specifically targeting members of the military. We saw that both law enforcement and the military were overrepresented in the people involved in [[w:January 6 United States Capitol attack|January 6 storming of the Capitol]]. 

It's a longstanding phenomenon. ... I was just reading a book called ''Morningside'' about the [[w:Greensboro massacre|1979 massacre of anti-clan activists in Greensboro, North Carolina]]. The people involved in that were included people in the so-called [[w:White Patriot Party|White Patriot Party]], which was based at a marine base in North Carolina, and law enforcement, ..., the Nazis and the Klan and the United Racist front.&lt;ref&gt;Shetterly (2024).&lt;/ref&gt;  
}}

Novick continued, 

{{blockquote|
The militia movement got its start from a couple of sources. One of them was a guy named [[w:John Singlaub|John Singlaub]], who was a general, removed, similar to what happened with [[w:Douglas MacArthur|MacArthur]] in [[w:Korean War|Korea]]. ... He formed something called the [[w:World League for Freedom and Democracy|World Anti-Communist League]] and then proceeded to use right wing Christian forces in the Philippines and Guatemala as a model for organizing similar forces in the United States. They collected money in the United States for these right wing militias in Guatemala and in the Philippines that were involved in terroristic activities of a supposedly anti-communist nature. And once they got that going, they started using it to build up militia groups in the United States on the same model. And you saw some of the repercussions of that with, you know, the [[w:Oklahoma City bombing|Federal building in Oklahoma City]], and other actions that came out of that. 

So I think that people need to take the threat of terrorism seriously, but that we need to understand where it's coming from. It's not coming from nonprofit humanitarian aid for poor people around the world or poor people in this country. It is coming from very well established and well rooted right wing forces in this country. 
}}

== The threat == 

Internet company executives have knowingly increased political polarization and violence including the [[w:Rohingya genocide|Rohingya genocide]] in [[w:Myanmar|Myanmar]], because doing otherwise might have reduced their profits. Documentation of this is summarized in other interviews regarding &quot;Media &amp; Democracy&quot;, available on Wikiversity under [[:Category:Media reform to improve democracy]].

==Discussion == 

:''[Interested readers are invite to comment here, subject to the Wikimedia rules of [[w:Wikipedia:Neutral point of view|writing from a neutral point of view]] [[w:Wikipedia:Citing sources|citing credible sources]]&lt;ref name=NPOV/&gt; and treating others with respect.&lt;ref name=AGF/&gt;]''

== Notes ==
{{reflist}}

== Bibliography ==

* &lt;!--David Axe (2024-12-05) &quot;Trump is planning to rip the guts out of the US armed forces&quot;, The Telegraph--&gt;{{cite Q|Q131545681}}
* &lt;!--John M. Donnelly (2022-12-14) Final NDAA removes most House provisions on hate groups, Roll Call--&gt;{{cite Q|Q130545466}}
* &lt;!--Beth Gazley (2024-11-22) &quot;US House passes measure that could punish nonprofits Treasury Department decides are ‘terrorist’&quot;, The Conversation--&gt;{{cite Q|Q131543053}}
* &lt;!--Hadas Gold (2024-12-16) &quot;Emboldened by ABC settlement, Trump threatens more lawsuits against the press&quot;, CNN--&gt;{{cite Q|Q131545105}}
* &lt;!-- Sophie Hurwitz (2024-11-21) &quot;The House Passes Bill Allowing Trump Admin to Declare Nonprofits Terrorist Supporters&quot;--&gt;{{cite Q|Q131540369}} 
* &lt;!-- Lisa Mascaro (2024-12-16) &quot; After investigating Jan. 6, House GOP sides with Trump and goes after Liz Cheney--&gt;{{cite Q|Q131545154}}
* &lt;!--Michael Novick (2022-11-15) &quot;General Manager Report&quot;, KPFK--&gt;{{cite Q|Q131543205}} 
* &lt;!--Pacifica in Exile (2015-09-14) &quot;Lydia Brazon, Executive Director&quot;, Pacifica in Exile Newsletter --&gt;{{cite Q|Q131545325|author=Pacifica in Exile}}
* &lt;!--Aran Shetterly (2024-10-15) Morningside: The 1979 Greensboro Massacre and the Struggle for an American City's Soul--&gt;{{cite Q|Q131545762}}
* &lt;!--US House (2024-11-21) H.R.9495 - Stop Terror-Financing and Tax Penalties on American Hostages Act--&gt;{{cite Q|Q131540249|author = US House of Representatives}}

[[Category:Politics]]
[[Category:Freedom and abundance]]
[[Category:Media reform to improve democracy]]</text>
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      <text bytes="3830" sha1="74cxj6206qi5pruosvgxrvhqhqh99ne" xml:space="preserve">==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly.
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.</text>
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      <text bytes="3891" sha1="9acwmjmqp3jhoaakv11dw2kfk8h8pwg" xml:space="preserve">==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly.
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.</text>
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      <text bytes="6792" sha1="qcf4659odutsmaeskjifjsmutmqu47l" xml:space="preserve">==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly.
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.

== 9.2 - Recognizing Symptoms ==
'''Physical Symptoms and Immediate Action:'''

Physical injuries like those from accidents or sports are often addressed immediately due to visible symptoms, such as limited movement or severe pain. However, less obvious symptoms or non-life-threatening conditions are frequently ignored or delayed in receiving medical attention.

'''Psychological Factors Influencing Delays:'''

# '''Misattributions:'''
#* People sometimes downplay serious symptoms, as humorously illustrated in ''Monty Python and the Holy Grail'' with the knight who dismisses losing limbs as “just a flesh wound.”
#* Misattribution can lead to delayed care, as individuals wrongly link symptoms to less serious causes.
# '''Confirmation Bias:'''
#* Believing symptoms aren’t serious leads to selectively seeking information that supports this belief.
#* For instance, skin discoloration may be dismissed as harmless, reinforcing a false sense of health.
#* This bias can result in underestimating the need for medical care and overestimating personal resilience.
# '''Attributions of Symptoms:'''
#* Cultural and personal beliefs influence how symptoms are interpreted.
#* For example, spiritual or cultural attributions, like considering epilepsy a sign of shamanism, can affect treatment choices.
# '''Self-Fulfilling Prophecies:'''
#* Misattributing symptoms, such as attributing tiredness to a cold rather than lack of sleep, can amplify anxiety and reinforce false conclusions.
# '''Physician Biases:'''
#* Physicians may also misattribute physical symptoms to psychological issues, leading to underdiagnosis and mistreatment.

'''Personality Traits and Symptom Recognition:'''

* High anxiety and neuroticism often result in heightened sensitivity to symptoms and frequent health complaints.
* Conversely, optimism and high self-esteem may delay care as individuals believe in their body’s ability to heal.
* Those with health anxiety (hypochondriasis) may excessively seek medical attention for minor changes.

'''Cultural and Social Influences:'''

* Norms around health and medical decision-making vary by culture, affecting symptom reporting and treatment-seeking behaviors.
* Gender differences: Women often report more symptoms due to higher private body consciousness.

'''Individual Differences in Health Involvement:'''

* Patients vary in their desire for information and involvement in care, which influences satisfaction and outcomes. Matching physician communication style with patient preferences can improve care experiences.

'''Key Illness-Specific Factors:'''

* Illness type influences symptom reporting and treatment delays. For example, lung cancer symptoms may be ignored due to stigma or lack of knowledge.

Understanding these psychological, cultural, and individual factors can help address delays in seeking medical treatment and improve health outcomes.</text>
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      <text bytes="6929" sha1="by1vsualvvixii650qgvv2nwcycoqoc" xml:space="preserve">==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly.
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.

== 9.2 - Recognizing Symptoms ==
'''Physical Symptoms and Immediate Action:'''

Physical injuries like those from accidents or sports are often addressed immediately due to visible symptoms, such as limited movement or severe pain. However, less obvious symptoms or non-life-threatening conditions are frequently ignored or delayed in receiving medical attention.

'''Psychological Factors Influencing Delays:'''

* '''Misattributions:'''
** People sometimes downplay serious symptoms, as humorously illustrated in ''Monty Python and the Holy Grail'' with the knight who dismisses losing limbs as “just a flesh wound.”
** Misattribution can lead to delayed care, as individuals wrongly link symptoms to less serious causes.
* '''Confirmation Bias:'''
** Believing symptoms aren’t serious leads to selectively seeking information that supports this belief.
** For instance, skin discoloration may be dismissed as harmless, reinforcing a false sense of health.
** This bias can result in underestimating the need for medical care and overestimating personal resilience.
* '''Attributions of Symptoms:'''
** Cultural and personal beliefs influence how symptoms are interpreted.
** For example, spiritual or cultural attributions, like considering epilepsy a sign of shamanism, can affect treatment choices.
* '''Self-Fulfilling Prophecies:'''
** Misattributing symptoms, such as attributing tiredness to a cold rather than lack of sleep, can amplify anxiety and reinforce false conclusions.
* '''Physician Biases:'''
** Physicians may also misattribute physical symptoms to psychological issues, leading to underdiagnosis and mistreatment.
*'''Illusory Correlation:'''
**People believe they are right about an association between variables more often than they actually have. 

'''Personality Traits and Symptom Recognition:'''

* High anxiety and neuroticism often result in heightened sensitivity to symptoms and frequent health complaints.
* Conversely, optimism and high self-esteem may delay care as individuals believe in their body’s ability to heal.
* Those with health anxiety (hypochondriasis) may excessively seek medical attention for minor changes.

'''Cultural and Social Influences:'''

* Norms around health and medical decision-making vary by culture, affecting symptom reporting and treatment-seeking behaviors.
* Gender differences: Women often report more symptoms due to higher private body consciousness.

'''Individual Differences in Health Involvement:'''

* Patients vary in their desire for information and involvement in care, which influences satisfaction and outcomes. Matching physician communication style with patient preferences can improve care experiences.

'''Key Illness-Specific Factors:'''

* Illness type influences symptom reporting and treatment delays. For example, lung cancer symptoms may be ignored due to stigma or lack of knowledge.

Understanding these psychological, cultural, and individual factors can help address delays in seeking medical treatment and improve health outcomes.</text>
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      <text bytes="7042" sha1="m9usn85g2lnrxhm13o4zok136avgbkq" xml:space="preserve">==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly.
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.

== 9.2 - Recognizing Symptoms ==
'''Physical Symptoms and Immediate Action:'''

Physical injuries like those from accidents or sports are often addressed immediately due to visible symptoms, such as limited movement or severe pain. However, less obvious symptoms or non-life-threatening conditions are frequently ignored or delayed in receiving medical attention.

'''Psychological Factors Influencing Delays:'''

* '''Misattributions:'''
** People sometimes downplay serious symptoms, as humorously illustrated in ''Monty Python and the Holy Grail'' with the knight who dismisses losing limbs as “just a flesh wound.”
** Misattribution can lead to delayed care, as individuals wrongly link symptoms to less serious causes.
* '''Confirmation Bias:'''
** Believing symptoms aren’t serious leads to selectively seeking information that supports this belief.
** For instance, skin discoloration may be dismissed as harmless, reinforcing a false sense of health.
** This bias can result in underestimating the need for medical care and overestimating personal resilience.
* '''Attributions of Symptoms:'''
** Cultural and personal beliefs influence how symptoms are interpreted.
** For example, spiritual or cultural attributions, like considering epilepsy a sign of shamanism, can affect treatment choices.
* '''Self-Fulfilling Prophecies:'''
** Misattributing symptoms, such as attributing tiredness to a cold rather than lack of sleep, can amplify anxiety and reinforce false conclusions.
* '''Physician Biases:'''
** Physicians may also misattribute physical symptoms to psychological issues, leading to underdiagnosis and mistreatment.
*'''Illusory Correlation:'''
**People believe they are right about an association between variables more often than they actually have. 

'''Personality Traits and Symptom Recognition:'''

* High anxiety and neuroticism often result in heightened sensitivity to symptoms and frequent health complaints.
* Conversely, optimism and high self-esteem may delay care as individuals believe in their body’s ability to heal.
* Those with health anxiety (hypochondriasis) may excessively seek medical attention for minor changes.

'''Cultural and Social Influences:'''

* Norms around health and medical decision-making vary by culture, affecting symptom reporting and treatment-seeking behaviors.
* Gender differences: Women often report more symptoms due to higher private body consciousness.

'''Individual Differences in Health Involvement:'''

* Patients vary in their desire for information and involvement in care, which influences satisfaction and outcomes. Matching physician communication style with patient preferences can improve care experiences.

'''Key Illness-Specific Factors:'''

* Illness type influences symptom reporting and treatment delays. For example, lung cancer symptoms may be ignored due to stigma or lack of knowledge.
'''Informational Involvement''':

* When people want to know more concerning their illnesses and treatment plans

Understanding these psychological, cultural, and individual factors can help address delays in seeking medical treatment and improve health outcomes.</text>
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      <text bytes="10171" sha1="dyk1mtxa9vnc94kf4ei9sn0dd7zpbx2" xml:space="preserve">==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly.
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.

== 9.2 - Recognizing Symptoms ==
'''Physical Symptoms and Immediate Action:'''

Physical injuries like those from accidents or sports are often addressed immediately due to visible symptoms, such as limited movement or severe pain. However, less obvious symptoms or non-life-threatening conditions are frequently ignored or delayed in receiving medical attention.

'''Psychological Factors Influencing Delays:'''

* '''Misattributions:'''
** People sometimes downplay serious symptoms, as humorously illustrated in ''Monty Python and the Holy Grail'' with the knight who dismisses losing limbs as “just a flesh wound.”
** Misattribution can lead to delayed care, as individuals wrongly link symptoms to less serious causes.
* '''Confirmation Bias:'''
** Believing symptoms aren’t serious leads to selectively seeking information that supports this belief.
** For instance, skin discoloration may be dismissed as harmless, reinforcing a false sense of health.
** This bias can result in underestimating the need for medical care and overestimating personal resilience.
* '''Attributions of Symptoms:'''
** Cultural and personal beliefs influence how symptoms are interpreted.
** For example, spiritual or cultural attributions, like considering epilepsy a sign of shamanism, can affect treatment choices.
* '''Self-Fulfilling Prophecies:'''
** Misattributing symptoms, such as attributing tiredness to a cold rather than lack of sleep, can amplify anxiety and reinforce false conclusions.
* '''Physician Biases:'''
** Physicians may also misattribute physical symptoms to psychological issues, leading to underdiagnosis and mistreatment.
*'''Illusory Correlation:'''
**People believe they are right about an association between variables more often than they actually have. 

'''Personality Traits and Symptom Recognition:'''

* High anxiety and neuroticism often result in heightened sensitivity to symptoms and frequent health complaints.
* Conversely, optimism and high self-esteem may delay care as individuals believe in their body’s ability to heal.
* Those with health anxiety (hypochondriasis) may excessively seek medical attention for minor changes.

'''Cultural and Social Influences:'''

* Norms around health and medical decision-making vary by culture, affecting symptom reporting and treatment-seeking behaviors.
* Gender differences: Women often report more symptoms due to higher private body consciousness.

'''Individual Differences in Health Involvement:'''

* Patients vary in their desire for information and involvement in care, which influences satisfaction and outcomes. Matching physician communication style with patient preferences can improve care experiences.

'''Key Illness-Specific Factors:'''

* Illness type influences symptom reporting and treatment delays. For example, lung cancer symptoms may be ignored due to stigma or lack of knowledge.
'''Informational Involvement''':

* When people want to know more concerning their illnesses and treatment plans

Understanding these psychological, cultural, and individual factors can help address delays in seeking medical treatment and improve health outcomes.

== 9.3 - Seeking and Adhering to Treatment ==

* '''Illness Representations''': Personal beliefs and understandings of a health problem.
* '''Exploratory Model (Kleinman, 1980)''': A framework describing three overlapping health-care systems:
*# '''Popular Sector''': Culturally based family and personal health beliefs.
*# '''Folk Sector''': Cultural traditions and specialized non-professional healers.
*# '''Professional Sector''': Western medical professionals and systems.

----

* '''Treatment Decisions''':
** People primarily consult the popular sector (family or personal beliefs).
** Cross-cultural illness interviews involve questions about the cause, onset, impact, treatment preferences, and fears.
* '''Cultural Influences on Treatment''':
** '''Collectivist Cultures''': Families or communities play a central role in caregiving (e.g., Middle Eastern, Native American).
** '''Stigma''': Disabilities or illnesses may be hidden to protect family reputation (e.g., tuberculosis in Haitian culture).
** '''Spiritual Healers''': Common first choice in cultures with strong spiritual beliefs (e.g., curandero, root-worker).

----

==== Barriers to Seeking Treatment ====

* '''Misinterpretation of Symptoms''': People may underestimate or misattribute symptoms (e.g., indigestion vs. heart attack).
* '''Social Concerns''': Fear of false alarms, inconvenience, or troubling others.
* '''Financial Barriers''': Lack of health insurance or cost concerns.

----

==== Delays in Treatment ====

# '''Appraisal Delay''': Time to recognize symptoms.
# '''Illness Delay''': Time between recognizing symptoms and deciding to seek care.
# '''Use Delay''': Time between deciding to seek care and obtaining it.

----

==== Triggers for Seeking Treatment (Zola, 1964) ====

# Severity and visibility of symptoms.
# Pain level or interference with daily life.
# Interpersonal crises affecting relationships.
# Social interference (e.g., work or vacation disruption).
# Social sanctions (e.g., employer pressures).

----

==== Cultural and Demographic Patterns ====

* '''Gender and Age''': Women and elderly seek treatment more often than men and younger individuals.
* '''Ethnicity''':
** Non-European Americans often rely on lay-referral systems (family/friends).
** Close-knit communities may promote or hinder seeking care.
* '''Socioeconomic Status (SES)''':
** SES affects treatment decisions and access.
** Low-income groups may delay treatment due to costs or mistrust of the system.

----

==== Cultural Examples ====

* '''Middle Eastern Cultures''': Hidden disabilities to avoid societal stigma.
* '''Haitian American Culture''': Tuberculosis patients isolated outside the home.
* '''Orthodox Jewish Communities''': Weak eyes may go untreated to enhance family marriage prospects.

----

==== Conclusions ====

* Health-seeking behaviors are shaped by cultural norms, financial barriers, social triggers, and personal beliefs.
* Psychological and cultural barriers can delay treatment, increasing severity at the time of care.
* Socioeconomic and demographic factors significantly impact health care access and choices.</text>
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      <text bytes="12734" sha1="8mtwvg6ospd9rb2a72674gsd8kbwmb7" xml:space="preserve">==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly.
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.

== 9.2 - Recognizing Symptoms ==
'''Physical Symptoms and Immediate Action:'''

Physical injuries like those from accidents or sports are often addressed immediately due to visible symptoms, such as limited movement or severe pain. However, less obvious symptoms or non-life-threatening conditions are frequently ignored or delayed in receiving medical attention.

'''Psychological Factors Influencing Delays:'''

* '''Misattributions:'''
** People sometimes downplay serious symptoms, as humorously illustrated in ''Monty Python and the Holy Grail'' with the knight who dismisses losing limbs as “just a flesh wound.”
** Misattribution can lead to delayed care, as individuals wrongly link symptoms to less serious causes.
* '''Confirmation Bias:'''
** Believing symptoms aren’t serious leads to selectively seeking information that supports this belief.
** For instance, skin discoloration may be dismissed as harmless, reinforcing a false sense of health.
** This bias can result in underestimating the need for medical care and overestimating personal resilience.
* '''Attributions of Symptoms:'''
** Cultural and personal beliefs influence how symptoms are interpreted.
** For example, spiritual or cultural attributions, like considering epilepsy a sign of shamanism, can affect treatment choices.
* '''Self-Fulfilling Prophecies:'''
** Misattributing symptoms, such as attributing tiredness to a cold rather than lack of sleep, can amplify anxiety and reinforce false conclusions.
* '''Physician Biases:'''
** Physicians may also misattribute physical symptoms to psychological issues, leading to underdiagnosis and mistreatment.
*'''Illusory Correlation:'''
**People believe they are right about an association between variables more often than they actually have. 

'''Personality Traits and Symptom Recognition:'''

* High anxiety and neuroticism often result in heightened sensitivity to symptoms and frequent health complaints.
* Conversely, optimism and high self-esteem may delay care as individuals believe in their body’s ability to heal.
* Those with health anxiety (hypochondriasis) may excessively seek medical attention for minor changes.

'''Cultural and Social Influences:'''

* Norms around health and medical decision-making vary by culture, affecting symptom reporting and treatment-seeking behaviors.
* Gender differences: Women often report more symptoms due to higher private body consciousness.

'''Individual Differences in Health Involvement:'''

* Patients vary in their desire for information and involvement in care, which influences satisfaction and outcomes. Matching physician communication style with patient preferences can improve care experiences.

'''Key Illness-Specific Factors:'''

* Illness type influences symptom reporting and treatment delays. For example, lung cancer symptoms may be ignored due to stigma or lack of knowledge.
'''Informational Involvement''':

* When people want to know more concerning their illnesses and treatment plans

Understanding these psychological, cultural, and individual factors can help address delays in seeking medical treatment and improve health outcomes.

== 9.3 - Seeking and Adhering to Treatment ==

* '''Illness Representations''': Personal beliefs and understandings of a health problem.
* '''Exploratory Model (Kleinman, 1980)''': A framework describing three overlapping health-care systems:
*# '''Popular Sector''': Culturally based family and personal health beliefs.
*# '''Folk Sector''': Cultural traditions and specialized non-professional healers.
*# '''Professional Sector''': Western medical professionals and systems.

----

* '''Treatment Decisions''':
** People primarily consult the popular sector (family or personal beliefs).
** Cross-cultural illness interviews involve questions about the cause, onset, impact, treatment preferences, and fears.
* '''Cultural Influences on Treatment''':
** '''Collectivist Cultures''': Families or communities play a central role in caregiving (e.g., Middle Eastern, Native American).
** '''Stigma''': Disabilities or illnesses may be hidden to protect family reputation (e.g., tuberculosis in Haitian culture).
** '''Spiritual Healers''': Common first choice in cultures with strong spiritual beliefs (e.g., curandero, root-worker).

----

==== Barriers to Seeking Treatment ====

* '''Misinterpretation of Symptoms''': People may underestimate or misattribute symptoms (e.g., indigestion vs. heart attack).
* '''Social Concerns''': Fear of false alarms, inconvenience, or troubling others.
* '''Financial Barriers''': Lack of health insurance or cost concerns.

----

==== Delays in Treatment ====

# '''Appraisal Delay''': Time to recognize symptoms.
# '''Illness Delay''': Time between recognizing symptoms and deciding to seek care.
# '''Use Delay''': Time between deciding to seek care and obtaining it.

----

==== Triggers for Seeking Treatment (Zola, 1964) ====

# Severity and visibility of symptoms.
# Pain level or interference with daily life.
# Interpersonal crises affecting relationships.
# Social interference (e.g., work or vacation disruption).
# Social sanctions (e.g., employer pressures).

----

==== Cultural and Demographic Patterns ====

* '''Gender and Age''': Women and elderly seek treatment more often than men and younger individuals.
* '''Ethnicity''':
** Non-European Americans often rely on lay-referral systems (family/friends).
** Close-knit communities may promote or hinder seeking care.
* '''Socioeconomic Status (SES)''':
** SES affects treatment decisions and access.
** Low-income groups may delay treatment due to costs or mistrust of the system.

----

==== Cultural Examples ====

* '''Middle Eastern Cultures''': Hidden disabilities to avoid societal stigma.
* '''Haitian American Culture''': Tuberculosis patients isolated outside the home.
* '''Orthodox Jewish Communities''': Weak eyes may go untreated to enhance family marriage prospects.

----

=== Hospital Setting ===

* '''Types of Hospitals''': For-profit and nonprofit hospitals often compete for patients in cities, benefiting patients with discounts/special services.
* '''Challenges''':
** Health care is viewed as a business, leading to patient dissatisfaction.
** Millions remain uninsured despite the Affordable Care Act.
** Hospital visits often involve lengthy waiting periods, form-filling, and procedural delays.
* '''Physician Interaction''':
** Physicians spend limited time with patients due to quotas and insurance demands.
** Poor patient–physician communication is a significant dissatisfaction factor.

=== Stress and Environment ===

* '''Stress Factors''': Long waits, noise, and intimidating equipment.
* '''Improvements''':
** Better lighting, reduced noise, and nature scenes in waiting areas lower stress.
** Avoiding uncontrollable daytime TV in waiting rooms helps reduce anxiety.

=== Staff Relations ===

* '''Diversity''': Hospitals employ culturally diverse staff (e.g., Indian, Chinese, Middle Eastern doctors; Mexican, Filipino nurses).
* '''Cultural Influences''':
** Male doctors from some cultures may show sexism.
** Asian/Latinx nurses may avoid conflict or questioning authority.
* '''Religious Conflicts''': Staff may refuse procedures like blood transfusions or abortions due to religious beliefs.
* '''Gender Dynamics''':
** Female doctors may face intimidation from male counterparts.
** Male nurses from patriarchal cultures may struggle with hierarchical roles.

=== Adherence to Treatment ===

* '''Definition''': Adherence = following prescribed treatments (e.g., timing, dosage, lifestyle changes).
* '''Impact''':
** Poor adherence costs $100–$300 billion annually and worsens health outcomes.
** Specific risks: kidney transplant failures, AIDS-related fatalities.
* '''Rates''':
** ~33% nonadherence for acute illnesses, ~55% for chronic illnesses.
** Influenced by treatment complexity and personal preferences.

=== Cultural &amp; Practical Barriers ===

* '''Cultural Factors''':
** Dietary restrictions (e.g., Ramadan fasting, kosher laws) may conflict with treatment plans.
** Different cultural beliefs about rest periods and medical authority affect adherence.
* '''Creative Nonadherence''': Patients modify treatments (e.g., skipping doses or overusing asthma sprays).

=== Innovations to Improve Adherence ===

* '''Technology''': Digital tools like pill monitors and automated programs improve compliance.
* '''Parental Involvement''': Supervised adherence in children yields better outcomes.

==== Conclusions ====

* Health-seeking behaviors are shaped by cultural norms, financial barriers, social triggers, and personal beliefs.
* Psychological and cultural barriers can delay treatment, increasing severity at the time of care.
* Socioeconomic and demographic factors significantly impact health care access and choices.</text>
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      <text bytes="12803" sha1="oep8rileiqeji29okj66m7nx98dhkxj" xml:space="preserve">==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly.
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.

== 9.2 - Recognizing Symptoms ==
'''Physical Symptoms and Immediate Action:'''

Physical injuries like those from accidents or sports are often addressed immediately due to visible symptoms, such as limited movement or severe pain. However, less obvious symptoms or non-life-threatening conditions are frequently ignored or delayed in receiving medical attention.

'''Psychological Factors Influencing Delays:'''

* '''Misattributions:'''
** People sometimes downplay serious symptoms, as humorously illustrated in ''Monty Python and the Holy Grail'' with the knight who dismisses losing limbs as “just a flesh wound.”
** Misattribution can lead to delayed care, as individuals wrongly link symptoms to less serious causes.
* '''Confirmation Bias:'''
** Believing symptoms aren’t serious leads to selectively seeking information that supports this belief.
** For instance, skin discoloration may be dismissed as harmless, reinforcing a false sense of health.
** This bias can result in underestimating the need for medical care and overestimating personal resilience.
* '''Attributions of Symptoms:'''
** Cultural and personal beliefs influence how symptoms are interpreted.
** For example, spiritual or cultural attributions, like considering epilepsy a sign of shamanism, can affect treatment choices.
* '''Self-Fulfilling Prophecies:'''
** Misattributing symptoms, such as attributing tiredness to a cold rather than lack of sleep, can amplify anxiety and reinforce false conclusions.
* '''Physician Biases:'''
** Physicians may also misattribute physical symptoms to psychological issues, leading to underdiagnosis and mistreatment.
*'''Illusory Correlation:'''
**People believe they are right about an association between variables more often than they actually have. 

'''Personality Traits and Symptom Recognition:'''

* High anxiety and neuroticism often result in heightened sensitivity to symptoms and frequent health complaints.
* Conversely, optimism and high self-esteem may delay care as individuals believe in their body’s ability to heal.
* Those with health anxiety (hypochondriasis) may excessively seek medical attention for minor changes.

'''Cultural and Social Influences:'''

* Norms around health and medical decision-making vary by culture, affecting symptom reporting and treatment-seeking behaviors.
* Gender differences: Women often report more symptoms due to higher private body consciousness.

'''Individual Differences in Health Involvement:'''

* Patients vary in their desire for information and involvement in care, which influences satisfaction and outcomes. Matching physician communication style with patient preferences can improve care experiences.

'''Key Illness-Specific Factors:'''

* Illness type influences symptom reporting and treatment delays. For example, lung cancer symptoms may be ignored due to stigma or lack of knowledge.
'''Informational Involvement''':

* When people want to know more concerning their illnesses and treatment plans

Understanding these psychological, cultural, and individual factors can help address delays in seeking medical treatment and improve health outcomes.

== 9.3 - Seeking and Adhering to Treatment ==

* '''Illness Representations''': Personal beliefs and understandings of a health problem.
* '''Exploratory Model (Kleinman, 1980)''': A framework describing three overlapping health-care systems:
*# '''Popular Sector''': Culturally based family and personal health beliefs.
*# '''Folk Sector''': Cultural traditions and specialized non-professional healers.
*# '''Professional Sector''': Western medical professionals and systems.

----

* '''Treatment Decisions''':
** People primarily consult the popular sector (family or personal beliefs).
** Cross-cultural illness interviews involve questions about the cause, onset, impact, treatment preferences, and fears.
* '''Cultural Influences on Treatment''':
** '''Collectivist Cultures''': Families or communities play a central role in caregiving (e.g., Middle Eastern, Native American).
** '''Stigma''': Disabilities or illnesses may be hidden to protect family reputation (e.g., tuberculosis in Haitian culture).
** '''Spiritual Healers''': Common first choice in cultures with strong spiritual beliefs (e.g., curandero, root-worker).

----

==== Barriers to Seeking Treatment ====

* '''Misinterpretation of Symptoms''': People may underestimate or misattribute symptoms (e.g., indigestion vs. heart attack).
* '''Social Concerns''': Fear of false alarms, inconvenience, or troubling others.
* '''Financial Barriers''': Lack of health insurance or cost concerns.

----

==== Delays in Treatment ====

# '''Appraisal Delay''': Time to recognize symptoms.
# '''Illness Delay''': Time between recognizing symptoms and deciding to seek care.
# '''Use Delay''': Time between deciding to seek care and obtaining it.

----

==== Triggers for Seeking Treatment (Zola, 1964) ====

# Severity and visibility of symptoms.
# Pain level or interference with daily life.
# Interpersonal crises affecting relationships.
# Social interference (e.g., work or vacation disruption).
# Social sanctions (e.g., employer pressures).

----

==== Cultural and Demographic Patterns ====

* '''Gender and Age''': Women and elderly seek treatment more often than men and younger individuals.
* '''Ethnicity''':
** Non-European Americans often rely on lay-referral systems (family/friends).
** Close-knit communities may promote or hinder seeking care.
* '''Socioeconomic Status (SES)''':
** SES affects treatment decisions and access, and is the largest cultural factor that predicts treatment seeking. 
** Low-income groups may delay treatment due to costs or mistrust of the system.

----

==== Cultural Examples ====

* '''Middle Eastern Cultures''': Hidden disabilities to avoid societal stigma.
* '''Haitian American Culture''': Tuberculosis patients isolated outside the home.
* '''Orthodox Jewish Communities''': Weak eyes may go untreated to enhance family marriage prospects.

----

=== Hospital Setting ===

* '''Types of Hospitals''': For-profit and nonprofit hospitals often compete for patients in cities, benefiting patients with discounts/special services.
* '''Challenges''':
** Health care is viewed as a business, leading to patient dissatisfaction.
** Millions remain uninsured despite the Affordable Care Act.
** Hospital visits often involve lengthy waiting periods, form-filling, and procedural delays.
* '''Physician Interaction''':
** Physicians spend limited time with patients due to quotas and insurance demands.
** Poor patient–physician communication is a significant dissatisfaction factor.

=== Stress and Environment ===

* '''Stress Factors''': Long waits, noise, and intimidating equipment.
* '''Improvements''':
** Better lighting, reduced noise, and nature scenes in waiting areas lower stress.
** Avoiding uncontrollable daytime TV in waiting rooms helps reduce anxiety.

=== Staff Relations ===

* '''Diversity''': Hospitals employ culturally diverse staff (e.g., Indian, Chinese, Middle Eastern doctors; Mexican, Filipino nurses).
* '''Cultural Influences''':
** Male doctors from some cultures may show sexism.
** Asian/Latinx nurses may avoid conflict or questioning authority.
* '''Religious Conflicts''': Staff may refuse procedures like blood transfusions or abortions due to religious beliefs.
* '''Gender Dynamics''':
** Female doctors may face intimidation from male counterparts.
** Male nurses from patriarchal cultures may struggle with hierarchical roles.

=== Adherence to Treatment ===

* '''Definition''': Adherence = following prescribed treatments (e.g., timing, dosage, lifestyle changes).
* '''Impact''':
** Poor adherence costs $100–$300 billion annually and worsens health outcomes.
** Specific risks: kidney transplant failures, AIDS-related fatalities.
* '''Rates''':
** ~33% nonadherence for acute illnesses, ~55% for chronic illnesses.
** Influenced by treatment complexity and personal preferences.

=== Cultural &amp; Practical Barriers ===

* '''Cultural Factors''':
** Dietary restrictions (e.g., Ramadan fasting, kosher laws) may conflict with treatment plans.
** Different cultural beliefs about rest periods and medical authority affect adherence.
* '''Creative Nonadherence''': Patients modify treatments (e.g., skipping doses or overusing asthma sprays).

=== Innovations to Improve Adherence ===

* '''Technology''': Digital tools like pill monitors and automated programs improve compliance.
* '''Parental Involvement''': Supervised adherence in children yields better outcomes.

==== Conclusions ====

* Health-seeking behaviors are shaped by cultural norms, financial barriers, social triggers, and personal beliefs.
* Psychological and cultural barriers can delay treatment, increasing severity at the time of care.
* Socioeconomic and demographic factors significantly impact health care access and choices.</text>
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==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly.
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.

== 9.2 - Recognizing Symptoms ==
'''Physical Symptoms and Immediate Action:'''

Physical injuries like those from accidents or sports are often addressed immediately due to visible symptoms, such as limited movement or severe pain. However, less obvious symptoms or non-life-threatening conditions are frequently ignored or delayed in receiving medical attention.

'''Psychological Factors Influencing Delays:'''

* '''Misattributions:'''
** People sometimes downplay serious symptoms, as humorously illustrated in ''Monty Python and the Holy Grail'' with the knight who dismisses losing limbs as “just a flesh wound.”
** Misattribution can lead to delayed care, as individuals wrongly link symptoms to less serious causes.
* '''Confirmation Bias:'''
** Believing symptoms aren’t serious leads to selectively seeking information that supports this belief.
** For instance, skin discoloration may be dismissed as harmless, reinforcing a false sense of health.
** This bias can result in underestimating the need for medical care and overestimating personal resilience.
* '''Attributions of Symptoms:'''
** Cultural and personal beliefs influence how symptoms are interpreted.
** For example, spiritual or cultural attributions, like considering epilepsy a sign of shamanism, can affect treatment choices.
* '''Self-Fulfilling Prophecies:'''
** Misattributing symptoms, such as attributing tiredness to a cold rather than lack of sleep, can amplify anxiety and reinforce false conclusions.
* '''Physician Biases:'''
** Physicians may also misattribute physical symptoms to psychological issues, leading to underdiagnosis and mistreatment.
*'''Illusory Correlation:'''
**People believe they are right about an association between variables more often than they actually have. 

'''Personality Traits and Symptom Recognition:'''

* High anxiety and neuroticism often result in heightened sensitivity to symptoms and frequent health complaints.
* Conversely, optimism and high self-esteem may delay care as individuals believe in their body’s ability to heal.
* Those with health anxiety (hypochondriasis) may excessively seek medical attention for minor changes.

'''Cultural and Social Influences:'''

* Norms around health and medical decision-making vary by culture, affecting symptom reporting and treatment-seeking behaviors.
* Gender differences: Women often report more symptoms due to higher private body consciousness.

'''Individual Differences in Health Involvement:'''

* Patients vary in their desire for information and involvement in care, which influences satisfaction and outcomes. Matching physician communication style with patient preferences can improve care experiences.

'''Key Illness-Specific Factors:'''

* Illness type influences symptom reporting and treatment delays. For example, lung cancer symptoms may be ignored due to stigma or lack of knowledge.
'''Informational Involvement''':

* When people want to know more concerning their illnesses and treatment plans

Understanding these psychological, cultural, and individual factors can help address delays in seeking medical treatment and improve health outcomes.

== 9.3 - Seeking and Adhering to Treatment ==

* '''Illness Representations''': Personal beliefs and understandings of a health problem.
* '''Exploratory Model (Kleinman, 1980)''': A framework describing three overlapping health-care systems:
*# '''Popular Sector''': Culturally based family and personal health beliefs.
*# '''Folk Sector''': Cultural traditions and specialized non-professional healers.
*# '''Professional Sector''': Western medical professionals and systems.

----

* '''Treatment Decisions''':
** People primarily consult the popular sector (family or personal beliefs).
** Cross-cultural illness interviews involve questions about the cause, onset, impact, treatment preferences, and fears.
* '''Cultural Influences on Treatment''':
** '''Collectivist Cultures''': Families or communities play a central role in caregiving (e.g., Middle Eastern, Native American).
** '''Stigma''': Disabilities or illnesses may be hidden to protect family reputation (e.g., tuberculosis in Haitian culture).
** '''Spiritual Healers''': Common first choice in cultures with strong spiritual beliefs (e.g., curandero, root-worker).

----

==== Barriers to Seeking Treatment ====

* '''Misinterpretation of Symptoms''': People may underestimate or misattribute symptoms (e.g., indigestion vs. heart attack).
* '''Social Concerns''': Fear of false alarms, inconvenience, or troubling others.
* '''Financial Barriers''': Lack of health insurance or cost concerns.

----

==== Delays in Treatment ====

# '''Appraisal Delay''': Time to recognize symptoms.
# '''Illness Delay''': Time between recognizing symptoms and deciding to seek care.
# '''Use Delay''': Time between deciding to seek care and obtaining it.

----

==== Triggers for Seeking Treatment (Zola, 1964) ====

# Severity and visibility of symptoms.
# Pain level or interference with daily life.
# Interpersonal crises affecting relationships.
# Social interference (e.g., work or vacation disruption).
# Social sanctions (e.g., employer pressures).

----

==== Cultural and Demographic Patterns ====

* '''Gender and Age''': Women and elderly seek treatment more often than men and younger individuals.
* '''Ethnicity''':
** Non-European Americans often rely on lay-referral systems (family/friends).
** Close-knit communities may promote or hinder seeking care.
* '''Socioeconomic Status (SES)''':
** SES affects treatment decisions and access, and is the largest cultural factor that predicts treatment seeking. 
** Low-income groups may delay treatment due to costs or mistrust of the system.

----

==== Cultural Examples ====

* '''Middle Eastern Cultures''': Hidden disabilities to avoid societal stigma.
* '''Haitian American Culture''': Tuberculosis patients isolated outside the home.
* '''Orthodox Jewish Communities''': Weak eyes may go untreated to enhance family marriage prospects.

----

=== Hospital Setting ===

* '''Types of Hospitals''': For-profit and nonprofit hospitals often compete for patients in cities, benefiting patients with discounts/special services.
* '''Challenges''':
** Health care is viewed as a business, leading to patient dissatisfaction.
** Millions remain uninsured despite the Affordable Care Act.
** Hospital visits often involve lengthy waiting periods, form-filling, and procedural delays.
* '''Physician Interaction''':
** Physicians spend limited time with patients due to quotas and insurance demands.
** Poor patient–physician communication is a significant dissatisfaction factor.

=== Stress and Environment ===

* '''Stress Factors''': Long waits, noise, and intimidating equipment.
* '''Improvements''':
** Better lighting, reduced noise, and nature scenes in waiting areas lower stress.
** Avoiding uncontrollable daytime TV in waiting rooms helps reduce anxiety.

=== Staff Relations ===

* '''Diversity''': Hospitals employ culturally diverse staff (e.g., Indian, Chinese, Middle Eastern doctors; Mexican, Filipino nurses).
* '''Cultural Influences''':
** Male doctors from some cultures may show sexism.
** Asian/Latinx nurses may avoid conflict or questioning authority.
* '''Religious Conflicts''': Staff may refuse procedures like blood transfusions or abortions due to religious beliefs.
* '''Gender Dynamics''':
** Female doctors may face intimidation from male counterparts.
** Male nurses from patriarchal cultures may struggle with hierarchical roles.

=== Adherence to Treatment ===

* '''Definition''': Adherence = following prescribed treatments (e.g., timing, dosage, lifestyle changes).
* '''Impact''':
** Poor adherence costs $100–$300 billion annually and worsens health outcomes.
** Specific risks: kidney transplant failures, AIDS-related fatalities.
* '''Rates''':
** ~33% nonadherence for acute illnesses, ~55% for chronic illnesses.
** Influenced by treatment complexity and personal preferences.

=== Cultural &amp; Practical Barriers ===

* '''Cultural Factors''':
** Dietary restrictions (e.g., Ramadan fasting, kosher laws) may conflict with treatment plans.
** Different cultural beliefs about rest periods and medical authority affect adherence.
* '''Creative Nonadherence''': Patients modify treatments (e.g., skipping doses or overusing asthma sprays).

=== Innovations to Improve Adherence ===

* '''Technology''': Digital tools like pill monitors and automated programs improve compliance.
* '''Parental Involvement''': Supervised adherence in children yields better outcomes.

==== Conclusions ====

* Health-seeking behaviors are shaped by cultural norms, financial barriers, social triggers, and personal beliefs.
* Psychological and cultural barriers can delay treatment, increasing severity at the time of care.
* Socioeconomic and demographic factors significantly impact health care access and choices.</text>
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==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly.
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.

== 9.2 - Recognizing Symptoms ==
'''Physical Symptoms and Immediate Action:'''

Physical injuries like those from accidents or sports are often addressed immediately due to visible symptoms, such as limited movement or severe pain. However, less obvious symptoms or non-life-threatening conditions are frequently ignored or delayed in receiving medical attention.

'''Psychological Factors Influencing Delays:'''

* '''Misattributions:'''
** People sometimes downplay serious symptoms, as humorously illustrated in ''Monty Python and the Holy Grail'' with the knight who dismisses losing limbs as “just a flesh wound.”
** Misattribution can lead to delayed care, as individuals wrongly link symptoms to less serious causes.
* '''Confirmation Bias:'''
** Believing symptoms aren’t serious leads to selectively seeking information that supports this belief.
** For instance, skin discoloration may be dismissed as harmless, reinforcing a false sense of health.
** This bias can result in underestimating the need for medical care and overestimating personal resilience.
* '''Attributions of Symptoms:'''
** Cultural and personal beliefs influence how symptoms are interpreted.
** For example, spiritual or cultural attributions, like considering epilepsy a sign of shamanism, can affect treatment choices.
* '''Self-Fulfilling Prophecies:'''
** Misattributing symptoms, such as attributing tiredness to a cold rather than lack of sleep, can amplify anxiety and reinforce false conclusions.
* '''Physician Biases:'''
** Physicians may also misattribute physical symptoms to psychological issues, leading to underdiagnosis and mistreatment.
*'''Illusory Correlation:'''
**People believe they are right about an association between variables more often than they actually have. 

'''Personality Traits and Symptom Recognition:'''

* High anxiety and neuroticism often result in heightened sensitivity to symptoms and frequent health complaints.
* Conversely, optimism and high self-esteem may delay care as individuals believe in their body’s ability to heal.
* Those with health anxiety (hypochondriasis) may excessively seek medical attention for minor changes.

'''Cultural and Social Influences:'''

* Norms around health and medical decision-making vary by culture, affecting symptom reporting and treatment-seeking behaviors.
* Gender differences: Women often report more symptoms due to higher private body consciousness.

'''Individual Differences in Health Involvement:'''

* Patients vary in their desire for information and involvement in care, which influences satisfaction and outcomes. Matching physician communication style with patient preferences can improve care experiences.

'''Key Illness-Specific Factors:'''

* Illness type influences symptom reporting and treatment delays. For example, lung cancer symptoms may be ignored due to stigma or lack of knowledge.
'''Informational Involvement''':

* When people want to know more concerning their illnesses and treatment plans

Understanding these psychological, cultural, and individual factors can help address delays in seeking medical treatment and improve health outcomes.

== 9.3 - Seeking and Adhering to Treatment ==

* '''Illness Representations''': Personal beliefs and understandings of a health problem.
* '''Exploratory Model (Kleinman, 1980)''': A framework describing three overlapping health-care systems:
*# '''Popular Sector''': Culturally based family and personal health beliefs.
*# '''Folk Sector''': Cultural traditions and specialized non-professional healers.
*# '''Professional Sector''': Western medical professionals and systems.

----

* '''Treatment Decisions''':
** People primarily consult the popular sector (family or personal beliefs).
** Cross-cultural illness interviews involve questions about the cause, onset, impact, treatment preferences, and fears.
* '''Cultural Influences on Treatment''':
** '''Collectivist Cultures''': Families or communities play a central role in caregiving (e.g., Middle Eastern, Native American).
** '''Stigma''': Disabilities or illnesses may be hidden to protect family reputation (e.g., tuberculosis in Haitian culture).
** '''Spiritual Healers''': Common first choice in cultures with strong spiritual beliefs (e.g., curandero, root-worker).

----

==== Barriers to Seeking Treatment ====

* '''Misinterpretation of Symptoms''': People may underestimate or misattribute symptoms (e.g., indigestion vs. heart attack).
* '''Social Concerns''': Fear of false alarms, inconvenience, or troubling others.
* '''Financial Barriers''': Lack of health insurance or cost concerns.

----

==== Delays in Treatment ====

# '''Appraisal Delay''': Time to recognize symptoms.
# '''Illness Delay''': Time between recognizing symptoms and deciding to seek care.
# '''Use Delay''': Time between deciding to seek care and obtaining it.

----

==== Triggers for Seeking Treatment (Zola, 1964) ====

# Severity and visibility of symptoms.
# Pain level or interference with daily life.
# Interpersonal crises affecting relationships.
# Social interference (e.g., work or vacation disruption).
# Social sanctions (e.g., employer pressures).

----

==== Cultural and Demographic Patterns ====

* '''Gender and Age''': Women and elderly seek treatment more often than men and younger individuals.
* '''Ethnicity''':
** Non-European Americans often rely on lay-referral systems (family/friends).
** Close-knit communities may promote or hinder seeking care.
* '''Socioeconomic Status (SES)''':
** SES affects treatment decisions and access, and is the largest cultural factor that predicts treatment seeking. 
** Low-income groups may delay treatment due to costs or mistrust of the system.

----

==== Cultural Examples ====

* '''Middle Eastern Cultures''': Hidden disabilities to avoid societal stigma.
* '''Haitian American Culture''': Tuberculosis patients isolated outside the home.
* '''Orthodox Jewish Communities''': Weak eyes may go untreated to enhance family marriage prospects.

----

=== Hospital Setting ===

* '''Types of Hospitals''': For-profit and nonprofit hospitals often compete for patients in cities, benefiting patients with discounts/special services.
* '''Challenges''':
** Health care is viewed as a business, leading to patient dissatisfaction.
** Millions remain uninsured despite the Affordable Care Act.
** Hospital visits often involve lengthy waiting periods, form-filling, and procedural delays.
* '''Physician Interaction''':
** Physicians spend limited time with patients due to quotas and insurance demands.
** Poor patient–physician communication is a significant dissatisfaction factor.

=== Stress and Environment ===

* '''Stress Factors''': Long waits, noise, and intimidating equipment.
* '''Improvements''':
** Better lighting, reduced noise, and nature scenes in waiting areas lower stress.
** Avoiding uncontrollable daytime TV in waiting rooms helps reduce anxiety.

=== Staff Relations ===

* '''Diversity''': Hospitals employ culturally diverse staff (e.g., Indian, Chinese, Middle Eastern doctors; Mexican, Filipino nurses).
* '''Cultural Influences''':
** Male doctors from some cultures may show sexism.
** Asian/Latinx nurses may avoid conflict or questioning authority.
* '''Religious Conflicts''': Staff may refuse procedures like blood transfusions or abortions due to religious beliefs.
* '''Gender Dynamics''':
** Female doctors may face intimidation from male counterparts.
** Male nurses from patriarchal cultures may struggle with hierarchical roles.

=== Adherence to Treatment ===

* '''Definition''': Adherence = following prescribed treatments (e.g., timing, dosage, lifestyle changes).
* '''Impact''':
** Poor adherence costs $100–$300 billion annually and worsens health outcomes.
** Specific risks: kidney transplant failures, AIDS-related fatalities.
* '''Rates''':
** ~33% nonadherence for acute illnesses, ~55% for chronic illnesses.
** Influenced by treatment complexity and personal preferences.

=== Cultural &amp; Practical Barriers ===

* '''Cultural Factors''':
** Dietary restrictions (e.g., Ramadan fasting, kosher laws) may conflict with treatment plans.
** Different cultural beliefs about rest periods and medical authority affect adherence.
* '''Creative Nonadherence''': Patients modify treatments (e.g., skipping doses or overusing asthma sprays).

=== Innovations to Improve Adherence ===

* '''Technology''': Digital tools like pill monitors and automated programs improve compliance.
* '''Parental Involvement''': Supervised adherence in children yields better outcomes.

==== Conclusions ====

* Health-seeking behaviors are shaped by cultural norms, financial barriers, social triggers, and personal beliefs.
* Psychological and cultural barriers can delay treatment, increasing severity at the time of care.
* Socioeconomic and demographic factors significantly impact health care access and choices.

== 9.4 - Patient-Practitioner Interactions ==</text>
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==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly.
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.

== 9.2 - Recognizing Symptoms ==
'''Physical Symptoms and Immediate Action:'''

Physical injuries like those from accidents or sports are often addressed immediately due to visible symptoms, such as limited movement or severe pain. However, less obvious symptoms or non-life-threatening conditions are frequently ignored or delayed in receiving medical attention.

'''Psychological Factors Influencing Delays:'''

* '''Misattributions:'''
** People sometimes downplay serious symptoms, as humorously illustrated in ''Monty Python and the Holy Grail'' with the knight who dismisses losing limbs as “just a flesh wound.”
** Misattribution can lead to delayed care, as individuals wrongly link symptoms to less serious causes.
* '''Confirmation Bias:'''
** Believing symptoms aren’t serious leads to selectively seeking information that supports this belief.
** For instance, skin discoloration may be dismissed as harmless, reinforcing a false sense of health.
** This bias can result in underestimating the need for medical care and overestimating personal resilience.
* '''Attributions of Symptoms:'''
** Cultural and personal beliefs influence how symptoms are interpreted.
** For example, spiritual or cultural attributions, like considering epilepsy a sign of shamanism, can affect treatment choices.
* '''Self-Fulfilling Prophecies:'''
** Misattributing symptoms, such as attributing tiredness to a cold rather than lack of sleep, can amplify anxiety and reinforce false conclusions.
* '''Physician Biases:'''
** Physicians may also misattribute physical symptoms to psychological issues, leading to underdiagnosis and mistreatment.
*'''Illusory Correlation:'''
**People believe they are right about an association between variables more often than they actually have. 

'''Personality Traits and Symptom Recognition:'''

* High anxiety and neuroticism often result in heightened sensitivity to symptoms and frequent health complaints.
* Conversely, optimism and high self-esteem may delay care as individuals believe in their body’s ability to heal.
* Those with health anxiety (hypochondriasis) may excessively seek medical attention for minor changes.

'''Cultural and Social Influences:'''

* Norms around health and medical decision-making vary by culture, affecting symptom reporting and treatment-seeking behaviors.
* Gender differences: Women often report more symptoms due to higher private body consciousness.

'''Individual Differences in Health Involvement:'''

* Patients vary in their desire for information and involvement in care, which influences satisfaction and outcomes. Matching physician communication style with patient preferences can improve care experiences.

'''Key Illness-Specific Factors:'''

* Illness type influences symptom reporting and treatment delays. For example, lung cancer symptoms may be ignored due to stigma or lack of knowledge.
'''Informational Involvement''':

* When people want to know more concerning their illnesses and treatment plans

Understanding these psychological, cultural, and individual factors can help address delays in seeking medical treatment and improve health outcomes.

== 9.3 - Seeking and Adhering to Treatment ==

* '''Illness Representations''': Personal beliefs and understandings of a health problem.
* '''Exploratory Model (Kleinman, 1980)''': A framework describing three overlapping health-care systems:
*# '''Popular Sector''': Culturally based family and personal health beliefs.
*# '''Folk Sector''': Cultural traditions and specialized non-professional healers.
*# '''Professional Sector''': Western medical professionals and systems.

----

* '''Treatment Decisions''':
** People primarily consult the popular sector (family or personal beliefs).
** Cross-cultural illness interviews involve questions about the cause, onset, impact, treatment preferences, and fears.
* '''Cultural Influences on Treatment''':
** '''Collectivist Cultures''': Families or communities play a central role in caregiving (e.g., Middle Eastern, Native American).
** '''Stigma''': Disabilities or illnesses may be hidden to protect family reputation (e.g., tuberculosis in Haitian culture).
** '''Spiritual Healers''': Common first choice in cultures with strong spiritual beliefs (e.g., curandero, root-worker).

----

==== Barriers to Seeking Treatment ====

* '''Misinterpretation of Symptoms''': People may underestimate or misattribute symptoms (e.g., indigestion vs. heart attack).
* '''Social Concerns''': Fear of false alarms, inconvenience, or troubling others.
* '''Financial Barriers''': Lack of health insurance or cost concerns.

----

==== Delays in Treatment ====

# '''Appraisal Delay''': Time to recognize symptoms.
# '''Illness Delay''': Time between recognizing symptoms and deciding to seek care.
# '''Use Delay''': Time between deciding to seek care and obtaining it.

----

==== Triggers for Seeking Treatment (Zola, 1964) ====

# Severity and visibility of symptoms.
# Pain level or interference with daily life.
# Interpersonal crises affecting relationships.
# Social interference (e.g., work or vacation disruption).
# Social sanctions (e.g., employer pressures).

----

==== Cultural and Demographic Patterns ====

* '''Gender and Age''': Women and elderly seek treatment more often than men and younger individuals.
* '''Ethnicity''':
** Non-European Americans often rely on lay-referral systems (family/friends).
** Close-knit communities may promote or hinder seeking care.
* '''Socioeconomic Status (SES)''':
** SES affects treatment decisions and access, and is the largest cultural factor that predicts treatment seeking. 
** Low-income groups may delay treatment due to costs or mistrust of the system.

----

==== Cultural Examples ====

* '''Middle Eastern Cultures''': Hidden disabilities to avoid societal stigma.
* '''Haitian American Culture''': Tuberculosis patients isolated outside the home.
* '''Orthodox Jewish Communities''': Weak eyes may go untreated to enhance family marriage prospects.

----

=== Hospital Setting ===

* '''Types of Hospitals''': For-profit and nonprofit hospitals often compete for patients in cities, benefiting patients with discounts/special services.
* '''Challenges''':
** Health care is viewed as a business, leading to patient dissatisfaction.
** Millions remain uninsured despite the Affordable Care Act.
** Hospital visits often involve lengthy waiting periods, form-filling, and procedural delays.
* '''Physician Interaction''':
** Physicians spend limited time with patients due to quotas and insurance demands.
** Poor patient–physician communication is a significant dissatisfaction factor.

=== Stress and Environment ===

* '''Stress Factors''': Long waits, noise, and intimidating equipment.
* '''Improvements''':
** Better lighting, reduced noise, and nature scenes in waiting areas lower stress.
** Avoiding uncontrollable daytime TV in waiting rooms helps reduce anxiety.

=== Staff Relations ===

* '''Diversity''': Hospitals employ culturally diverse staff (e.g., Indian, Chinese, Middle Eastern doctors; Mexican, Filipino nurses).
* '''Cultural Influences''':
** Male doctors from some cultures may show sexism.
** Asian/Latinx nurses may avoid conflict or questioning authority.
* '''Religious Conflicts''': Staff may refuse procedures like blood transfusions or abortions due to religious beliefs.
* '''Gender Dynamics''':
** Female doctors may face intimidation from male counterparts.
** Male nurses from patriarchal cultures may struggle with hierarchical roles.

=== Adherence to Treatment ===

* '''Definition''': Adherence = following prescribed treatments (e.g., timing, dosage, lifestyle changes).
* '''Impact''':
** Poor adherence costs $100–$300 billion annually and worsens health outcomes.
** Specific risks: kidney transplant failures, AIDS-related fatalities.
* '''Rates''':
** ~33% nonadherence for acute illnesses, ~55% for chronic illnesses.
** Influenced by treatment complexity and personal preferences.

=== Cultural &amp; Practical Barriers ===

* '''Cultural Factors''':
** Dietary restrictions (e.g., Ramadan fasting, kosher laws) may conflict with treatment plans.
** Different cultural beliefs about rest periods and medical authority affect adherence.
* '''Creative Nonadherence''': Patients modify treatments (e.g., skipping doses or overusing asthma sprays).

=== Innovations to Improve Adherence ===

* '''Technology''': Digital tools like pill monitors and automated programs improve compliance.
* '''Parental Involvement''': Supervised adherence in children yields better outcomes.

==== Conclusions ====

* Health-seeking behaviors are shaped by cultural norms, financial barriers, social triggers, and personal beliefs.
* Psychological and cultural barriers can delay treatment, increasing severity at the time of care.
* Socioeconomic and demographic factors significantly impact health care access and choices.

== 9.4 - Patient-Practitioner Interactions ==

=== Patient’s Journey and Interaction with Health Care ===

* '''Initial Steps''':
** Patients must navigate insurance, hospital paperwork, and registration.
** Quality of interaction with doctors impacts recovery and adherence.

=== Patient–Practitioner Interaction Models (Szasz &amp; Hollender, 1956): ===

# '''Active-Passive Model''':
#* Doctor makes decisions; patient has little/no input.
# '''Guidance-Cooperation Model''':
#* Doctor leads; patient answers questions but doesn’t decide on treatment.
# '''Mutual Cooperation Model''' (Optimal):
#* Collaborative planning between doctor and patient.

=== Communication Types and Barriers ===

* '''Communication Styles''':
** Biomedical: Focus on jargon; closed-ended questions.
** Consumerist: Patient-driven discussion.
* '''Cultural Factors''':
** '''Individualism vs. Collectivism''':
*** Collectivists prioritize harmony, may withhold some info.
*** Individualists prefer directness, potentially causing frustration in mismatched interactions.
** '''Language Challenges''':
*** Jargon, technical terms, and word meanings vary (e.g., “positive” results).
*** Misunderstandings arise from differences in English dialects and other languages.
* '''Doctor’s Role in Communication Issues''':
** Interruptions (avg. after 18 seconds per Beckman &amp; Frankel, 1984).
** Overuse of jargon or “dumbing down” messages.
** Insufficient explanation of uncertain outcomes.
* '''Patient’s Role in Communication Issues''':
** Anxiety leads to incomplete symptom reporting.
** SES and language differences affect understanding.

=== Key Influences on Patient–Practitioner Communication ===

* '''Cultural Dimensions''':
** Varying use of small talk across cultures.
** Interpretation of symptoms and social norms differ.
* '''Uncertainty and Decision Making''':
** Increasing trend for shared decisions.
** Patients often struggle with probabilities and risk communication.

=== Gender Bias and Stereotypes ===

* '''Gender Bias''':
** Stereotyping based on gender leads to differential treatment.
* '''Cultural Sensitivity''':
** Symptoms can have private connotations across cultures, affecting reporting.

=== Importance of Intercultural Skills ===

* '''Training for Practitioners''':
** Incorporate intercultural and patient-centered communication skills.
** Emphasize empathy and adaptability to improve care quality.

# '''Stereotypes''': Widely held, oversimplified beliefs that people have certain characteristics due to group membership.
#* Examples:
#** Asians: Good at math.
#** Women: Bad at math.
#** Middle Eastern/Indian Americans: Vocal about pain.
#** Asian Americans: Quiet and stoic.
#** Mexican Americans: Large families.
# '''Cultural Competency''': The combination of culturally appropriate attitudes, knowledge, and skills to deliver effective healthcare to diverse groups.
#* '''Cultural Awareness''': Appreciation of external signs of diversity (e.g., arts, dress, food).
#* '''Cultural Sensitivity''': Avoiding offensive actions/statements based on cultural differences.
# '''Perceived Discrimination''': Patient perception of biased or unequal treatment based on cultural or gender differences.
# '''Gender Bias in Healthcare''': Unequal treatment based on gender, leading to disparities in diagnosis, procedures, and outcomes.
#* Examples:
#** Women less likely to receive ICU care or heart-related devices.
#** Men more likely to be recommended knee surgery.

----

=== Key Information ===

==== Stereotyping in Healthcare ====

* Stereotypes influence communication and decisions in patient care.
* Harmful effects:
** Generalizations can lead to poor care or malpractice.
** Stereotypes based on race, gender, or age often dictate treatment decisions.

==== Examples of Healthcare Disparities ====

* '''Racial Bias''':
** Black, Latinx/e, and low-SES patients receive less information and care (IOM, 2002).
* '''Gender Bias''':
** Heart disease devices used more in men than women despite similar symptoms (Curtis et al., 2007).
** Older women face shorter ICU stays and higher mortality risks (Fowler et al., 2007).
* '''Ethnic Stereotypes''':
** Language-based discrimination impacts help-seeking behavior (Spencer &amp; Chen, 2004).

==== Cultural Competency ====

* Essential for effective communication and care.
* Poor cultural competency leads to:
** Miscommunication.
** Lower patient trust and satisfaction.
** Discrimination.
* '''Measurement Tools''':
** Healthcare Provider Cultural Competency scale (Lucas et al., 2008).

==== Impact of Discrimination ====

* Language barriers result in patients seeking informal care instead of formal treatment.
* Women more likely than men to seek emotional support through informal means.

----

=== Actionable Steps ===

* Develop cultural competency through awareness, sensitivity, and skills.
* Avoid relying on stereotypes; assess individual patient needs.
* Educate healthcare providers on the impact of bias and disparities.
* Use standardized tools to evaluate cultural competency and improve patient satisfaction.</text>
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==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly. Involve the ways that individuals monitor internal states. 
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.

== 9.2 - Recognizing Symptoms ==
'''Physical Symptoms and Immediate Action:'''

Physical injuries like those from accidents or sports are often addressed immediately due to visible symptoms, such as limited movement or severe pain. However, less obvious symptoms or non-life-threatening conditions are frequently ignored or delayed in receiving medical attention.

'''Psychological Factors Influencing Delays:'''

* '''Misattributions:'''
** People sometimes downplay serious symptoms, as humorously illustrated in ''Monty Python and the Holy Grail'' with the knight who dismisses losing limbs as “just a flesh wound.”
** Misattribution can lead to delayed care, as individuals wrongly link symptoms to less serious causes.
* '''Confirmation Bias:'''
** Believing symptoms aren’t serious leads to selectively seeking information that supports this belief.
** For instance, skin discoloration may be dismissed as harmless, reinforcing a false sense of health.
** This bias can result in underestimating the need for medical care and overestimating personal resilience.
* '''Attributions of Symptoms:'''
** Cultural and personal beliefs influence how symptoms are interpreted.
** For example, spiritual or cultural attributions, like considering epilepsy a sign of shamanism, can affect treatment choices.
* '''Self-Fulfilling Prophecies:'''
** Misattributing symptoms, such as attributing tiredness to a cold rather than lack of sleep, can amplify anxiety and reinforce false conclusions.
* '''Physician Biases:'''
** Physicians may also misattribute physical symptoms to psychological issues, leading to underdiagnosis and mistreatment.
*'''Illusory Correlation:'''
**People believe they are right about an association between variables more often than they actually have. 

'''Personality Traits and Symptom Recognition:'''

* High anxiety and neuroticism often result in heightened sensitivity to symptoms and frequent health complaints.
* Conversely, optimism and high self-esteem may delay care as individuals believe in their body’s ability to heal.
* Those with health anxiety (hypochondriasis) may excessively seek medical attention for minor changes.

'''Cultural and Social Influences:'''

* Norms around health and medical decision-making vary by culture, affecting symptom reporting and treatment-seeking behaviors.
* Gender differences: Women often report more symptoms due to higher private body consciousness.

'''Individual Differences in Health Involvement:'''

* Patients vary in their desire for information and involvement in care, which influences satisfaction and outcomes. Matching physician communication style with patient preferences can improve care experiences.

'''Key Illness-Specific Factors:'''

* Illness type influences symptom reporting and treatment delays. For example, lung cancer symptoms may be ignored due to stigma or lack of knowledge.
'''Informational Involvement''':

* When people want to know more concerning their illnesses and treatment plans

Understanding these psychological, cultural, and individual factors can help address delays in seeking medical treatment and improve health outcomes.

== 9.3 - Seeking and Adhering to Treatment ==

* '''Illness Representations''': Personal beliefs and understandings of a health problem.
* '''Exploratory Model (Kleinman, 1980)''': A framework describing three overlapping health-care systems:
*# '''Popular Sector''': Culturally based family and personal health beliefs.
*# '''Folk Sector''': Cultural traditions and specialized non-professional healers.
*# '''Professional Sector''': Western medical professionals and systems.

----

* '''Treatment Decisions''':
** People primarily consult the popular sector (family or personal beliefs).
** Cross-cultural illness interviews involve questions about the cause, onset, impact, treatment preferences, and fears.
* '''Cultural Influences on Treatment''':
** '''Collectivist Cultures''': Families or communities play a central role in caregiving (e.g., Middle Eastern, Native American).
** '''Stigma''': Disabilities or illnesses may be hidden to protect family reputation (e.g., tuberculosis in Haitian culture).
** '''Spiritual Healers''': Common first choice in cultures with strong spiritual beliefs (e.g., curandero, root-worker).

----

==== Barriers to Seeking Treatment ====

* '''Misinterpretation of Symptoms''': People may underestimate or misattribute symptoms (e.g., indigestion vs. heart attack).
* '''Social Concerns''': Fear of false alarms, inconvenience, or troubling others.
* '''Financial Barriers''': Lack of health insurance or cost concerns.

----

==== Delays in Treatment ====

# '''Appraisal Delay''': Time to recognize symptoms.
# '''Illness Delay''': Time between recognizing symptoms and deciding to seek care.
# '''Use Delay''': Time between deciding to seek care and obtaining it.

----

==== Triggers for Seeking Treatment (Zola, 1964) ====

# Severity and visibility of symptoms.
# Pain level or interference with daily life.
# Interpersonal crises affecting relationships.
# Social interference (e.g., work or vacation disruption).
# Social sanctions (e.g., employer pressures).

----

==== Cultural and Demographic Patterns ====

* '''Gender and Age''': Women and elderly seek treatment more often than men and younger individuals.
* '''Ethnicity''':
** Non-European Americans often rely on lay-referral systems (family/friends).
** Close-knit communities may promote or hinder seeking care.
* '''Socioeconomic Status (SES)''':
** SES affects treatment decisions and access, and is the largest cultural factor that predicts treatment seeking. 
** Low-income groups may delay treatment due to costs or mistrust of the system.

----

==== Cultural Examples ====

* '''Middle Eastern Cultures''': Hidden disabilities to avoid societal stigma.
* '''Haitian American Culture''': Tuberculosis patients isolated outside the home.
* '''Orthodox Jewish Communities''': Weak eyes may go untreated to enhance family marriage prospects.

----

=== Hospital Setting ===

* '''Types of Hospitals''': For-profit and nonprofit hospitals often compete for patients in cities, benefiting patients with discounts/special services.
* '''Challenges''':
** Health care is viewed as a business, leading to patient dissatisfaction.
** Millions remain uninsured despite the Affordable Care Act.
** Hospital visits often involve lengthy waiting periods, form-filling, and procedural delays.
* '''Physician Interaction''':
** Physicians spend limited time with patients due to quotas and insurance demands.
** Poor patient–physician communication is a significant dissatisfaction factor.

=== Stress and Environment ===

* '''Stress Factors''': Long waits, noise, and intimidating equipment.
* '''Improvements''':
** Better lighting, reduced noise, and nature scenes in waiting areas lower stress.
** Avoiding uncontrollable daytime TV in waiting rooms helps reduce anxiety.

=== Staff Relations ===

* '''Diversity''': Hospitals employ culturally diverse staff (e.g., Indian, Chinese, Middle Eastern doctors; Mexican, Filipino nurses).
* '''Cultural Influences''':
** Male doctors from some cultures may show sexism.
** Asian/Latinx nurses may avoid conflict or questioning authority.
* '''Religious Conflicts''': Staff may refuse procedures like blood transfusions or abortions due to religious beliefs.
* '''Gender Dynamics''':
** Female doctors may face intimidation from male counterparts.
** Male nurses from patriarchal cultures may struggle with hierarchical roles.

=== Adherence to Treatment ===

* '''Definition''': Adherence = following prescribed treatments (e.g., timing, dosage, lifestyle changes).
* '''Impact''':
** Poor adherence costs $100–$300 billion annually and worsens health outcomes.
** Specific risks: kidney transplant failures, AIDS-related fatalities.
* '''Rates''':
** ~33% nonadherence for acute illnesses, ~55% for chronic illnesses.
** Influenced by treatment complexity and personal preferences.

=== Cultural &amp; Practical Barriers ===

* '''Cultural Factors''':
** Dietary restrictions (e.g., Ramadan fasting, kosher laws) may conflict with treatment plans.
** Different cultural beliefs about rest periods and medical authority affect adherence.
* '''Creative Nonadherence''': Patients modify treatments (e.g., skipping doses or overusing asthma sprays).

=== Innovations to Improve Adherence ===

* '''Technology''': Digital tools like pill monitors and automated programs improve compliance.
* '''Parental Involvement''': Supervised adherence in children yields better outcomes.

==== Conclusions ====

* Health-seeking behaviors are shaped by cultural norms, financial barriers, social triggers, and personal beliefs.
* Psychological and cultural barriers can delay treatment, increasing severity at the time of care.
* Socioeconomic and demographic factors significantly impact health care access and choices.

== 9.4 - Patient-Practitioner Interactions ==

=== Patient’s Journey and Interaction with Health Care ===

* '''Initial Steps''':
** Patients must navigate insurance, hospital paperwork, and registration.
** Quality of interaction with doctors impacts recovery and adherence.

=== Patient–Practitioner Interaction Models (Szasz &amp; Hollender, 1956): ===

# '''Active-Passive Model''':
#* Doctor makes decisions; patient has little/no input.
# '''Guidance-Cooperation Model''':
#* Doctor leads; patient answers questions but doesn’t decide on treatment.
# '''Mutual Cooperation Model''' (Optimal):
#* Collaborative planning between doctor and patient.

=== Communication Types and Barriers ===

* '''Communication Styles''':
** Biomedical: Focus on jargon; closed-ended questions.
** Consumerist: Patient-driven discussion.
* '''Cultural Factors''':
** '''Individualism vs. Collectivism''':
*** Collectivists prioritize harmony, may withhold some info.
*** Individualists prefer directness, potentially causing frustration in mismatched interactions.
** '''Language Challenges''':
*** Jargon, technical terms, and word meanings vary (e.g., “positive” results).
*** Misunderstandings arise from differences in English dialects and other languages.
* '''Doctor’s Role in Communication Issues''':
** Interruptions (avg. after 18 seconds per Beckman &amp; Frankel, 1984).
** Overuse of jargon or “dumbing down” messages.
** Insufficient explanation of uncertain outcomes.
* '''Patient’s Role in Communication Issues''':
** Anxiety leads to incomplete symptom reporting.
** SES and language differences affect understanding.

=== Key Influences on Patient–Practitioner Communication ===

* '''Cultural Dimensions''':
** Varying use of small talk across cultures.
** Interpretation of symptoms and social norms differ.
* '''Uncertainty and Decision Making''':
** Increasing trend for shared decisions.
** Patients often struggle with probabilities and risk communication.

=== Gender Bias and Stereotypes ===

* '''Gender Bias''':
** Stereotyping based on gender leads to differential treatment.
* '''Cultural Sensitivity''':
** Symptoms can have private connotations across cultures, affecting reporting.

=== Importance of Intercultural Skills ===

* '''Training for Practitioners''':
** Incorporate intercultural and patient-centered communication skills.
** Emphasize empathy and adaptability to improve care quality.

# '''Stereotypes''': Widely held, oversimplified beliefs that people have certain characteristics due to group membership.
#* Examples:
#** Asians: Good at math.
#** Women: Bad at math.
#** Middle Eastern/Indian Americans: Vocal about pain.
#** Asian Americans: Quiet and stoic.
#** Mexican Americans: Large families.
# '''Cultural Competency''': The combination of culturally appropriate attitudes, knowledge, and skills to deliver effective healthcare to diverse groups.
#* '''Cultural Awareness''': Appreciation of external signs of diversity (e.g., arts, dress, food).
#* '''Cultural Sensitivity''': Avoiding offensive actions/statements based on cultural differences.
# '''Perceived Discrimination''': Patient perception of biased or unequal treatment based on cultural or gender differences.
# '''Gender Bias in Healthcare''': Unequal treatment based on gender, leading to disparities in diagnosis, procedures, and outcomes.
#* Examples:
#** Women less likely to receive ICU care or heart-related devices.
#** Men more likely to be recommended knee surgery.

----

=== Key Information ===

==== Stereotyping in Healthcare ====

* Stereotypes influence communication and decisions in patient care.
* Harmful effects:
** Generalizations can lead to poor care or malpractice.
** Stereotypes based on race, gender, or age often dictate treatment decisions.

==== Examples of Healthcare Disparities ====

* '''Racial Bias''':
** Black, Latinx/e, and low-SES patients receive less information and care (IOM, 2002).
* '''Gender Bias''':
** Heart disease devices used more in men than women despite similar symptoms (Curtis et al., 2007).
** Older women face shorter ICU stays and higher mortality risks (Fowler et al., 2007).
* '''Ethnic Stereotypes''':
** Language-based discrimination impacts help-seeking behavior (Spencer &amp; Chen, 2004).

==== Cultural Competency ====

* Essential for effective communication and care.
* Poor cultural competency leads to:
** Miscommunication.
** Lower patient trust and satisfaction.
** Discrimination.
* '''Measurement Tools''':
** Healthcare Provider Cultural Competency scale (Lucas et al., 2008).

==== Impact of Discrimination ====

* Language barriers result in patients seeking informal care instead of formal treatment.
* Women more likely than men to seek emotional support through informal means.

----

=== Actionable Steps ===

* Develop cultural competency through awareness, sensitivity, and skills.
* Avoid relying on stereotypes; assess individual patient needs.
* Educate healthcare providers on the impact of bias and disparities.
* Use standardized tools to evaluate cultural competency and improve patient satisfaction.</text>
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==9.1 - Factors Surrounding Illness==

==== Overview of Cultural Influence on Illness Behaviors ====

* '''Definition of Illness Behaviors''': These include recognizing symptoms, seeking treatment, and adhering to prescribed treatments. Cultural factors influence these stages significantly. Involve the ways that individuals monitor internal states. 
* '''Sociodemographic Variables''': Age, gender, ethnicity, and socioeconomic status (SES) shape how individuals perceive and respond to illness.
* '''Mistrust and Disparities''': Groups like Black Americans and trans women exhibit mistrust towards the healthcare system, impacting their utilization of health services.

==== Key Cultural and Demographic Insights ====

* '''Black Americans''': Mistrust in healthcare systems contributes to racial health disparities. They may consult physicians more if it’s convenient or if illness risk feels high but rely less on social consultation.
* '''Latinx Populations''': Underutilize inpatient mental health services and exhibit better healthcare usage when treated by Spanish-speaking providers.
* '''Asian Americans''': Display high usage of complementary and alternative medicine (CAM), underutilize Western health services, and report significant reliance on dual health systems.

==== Traditional and Alternative Medicine ====

* '''CAM Use Among Minority Groups''': Asian Americans, particularly Chinese Americans, show a preference for CAM. Indian populations favor Ayurvedic medicine, emphasizing the balance of bodily humors.
* '''Dual Health Systems''': Minority groups often combine traditional and Western medicine, showing the persistence of cultural health practices.

==== Acculturation’s Dual Role ====

* '''Positive and Negative Effects''':
** Increased acculturation can lead to better access to Western healthcare but may also result in poorer health outcomes due to unhealthy lifestyle adaptations.
** Acculturation influences provider-patient dynamics, with shared language and cultural identity improving patient outcomes.

==== Illness Representation and Perception ====

* '''Concept''': Illness representations refer to the cognitive framework individuals use to interpret and react to illness.
* '''Activation''': When illness representations are triggered, behaviors align with perceived symptoms.
* '''CSM Framework''': The Commonsense Model (CSM) focuses on how individuals actively make sense of illness, influenced by personal, cultural, and environmental factors.

==== The Commonsense Model of Illness Behavior ====

* '''Core Principles''':
*# People act as problem-solvers in response to health threats.
*# Illness management is shaped by sociocultural attitudes and beliefs.
* '''Key Measures''':
** '''Illness Perception Questionnaire-Revised (IPQ-R)''': Explores symptoms, consequences, and control.
** '''Brief Illness Perception Questionnaire (Brief IPQ)''': Evaluates illness-related components in nine items.
* '''Research Insights''':
** Illness representations directly affect health outcomes.
** Coping strategies mediate between illness representations and outcomes.

==== Implications for Healthcare Systems ====

* '''Provider Ethnic Identity and Acculturation''': These factors influence care quality and cultural competence in treating diverse populations.
* '''Underutilization of Services''': Some minority groups face barriers like under-referrals by health practitioners, impacting health equity.
* '''Mistrust in Healthcare System''' due to medical errors.

==== Conclusion and Future Directions ====
The text highlights the intricate interplay between culture, demographics, and healthcare utilization. Models like the CSM provide a structured approach to understanding illness behaviors, emphasizing the need for culturally sensitive healthcare systems. Addressing mistrust, enhancing cultural competence among providers, and integrating traditional medicine can bridge gaps in health equity.

== 9.2 - Recognizing Symptoms ==
'''Physical Symptoms and Immediate Action:'''

Physical injuries like those from accidents or sports are often addressed immediately due to visible symptoms, such as limited movement or severe pain. However, less obvious symptoms or non-life-threatening conditions are frequently ignored or delayed in receiving medical attention.

'''Psychological Factors Influencing Delays:'''

* '''Misattributions:'''
** People sometimes downplay serious symptoms, as humorously illustrated in ''Monty Python and the Holy Grail'' with the knight who dismisses losing limbs as “just a flesh wound.”
** Misattribution can lead to delayed care, as individuals wrongly link symptoms to less serious causes.
* '''Confirmation Bias:'''
** Believing symptoms aren’t serious leads to selectively seeking information that supports this belief.
** For instance, skin discoloration may be dismissed as harmless, reinforcing a false sense of health.
** This bias can result in underestimating the need for medical care and overestimating personal resilience.
* '''Attributions of Symptoms:'''
** Cultural and personal beliefs influence how symptoms are interpreted.
** For example, spiritual or cultural attributions, like considering epilepsy a sign of shamanism, can affect treatment choices.
* '''Self-Fulfilling Prophecies:'''
** Misattributing symptoms, such as attributing tiredness to a cold rather than lack of sleep, can amplify anxiety and reinforce false conclusions.
* '''Physician Biases:'''
** Physicians may also misattribute physical symptoms to psychological issues, leading to underdiagnosis and mistreatment.
*'''Illusory Correlation:'''
**People believe they are right about an association between variables more often than they actually have. 

'''Personality Traits and Symptom Recognition:'''

* High anxiety and neuroticism often result in heightened sensitivity to symptoms and frequent health complaints.
* Conversely, optimism and high self-esteem may delay care as individuals believe in their body’s ability to heal.
* Those with health anxiety (hypochondriasis) may excessively seek medical attention for minor changes.

'''Cultural and Social Influences:'''

* Norms around health and medical decision-making vary by culture, affecting symptom reporting and treatment-seeking behaviors.
* Gender differences: Women often report more symptoms due to higher '''private body consciousness,''' high alert to internal body states.

'''Individual Differences in Health Involvement:'''

* Patients vary in their desire for information and involvement in care, which influences satisfaction and outcomes. Matching physician communication style with patient preferences can improve care experiences.

'''Key Illness-Specific Factors:'''

* Illness type influences symptom reporting and treatment delays. For example, lung cancer symptoms may be ignored due to stigma or lack of knowledge.
'''Informational Involvement''':

* When people want to know more concerning their illnesses and treatment plans

Understanding these psychological, cultural, and individual factors can help address delays in seeking medical treatment and improve health outcomes.

== 9.3 - Seeking and Adhering to Treatment ==

* '''Illness Representations''': Personal beliefs and understandings of a health problem.
* '''Exploratory Model (Kleinman, 1980)''': A framework describing three overlapping health-care systems:
*# '''Popular Sector''': Culturally based family and personal health beliefs.
*# '''Folk Sector''': Cultural traditions and specialized non-professional healers.
*# '''Professional Sector''': Western medical professionals and systems.

----

* '''Treatment Decisions''':
** People primarily consult the popular sector (family or personal beliefs).
** Cross-cultural illness interviews involve questions about the cause, onset, impact, treatment preferences, and fears.
* '''Cultural Influences on Treatment''':
** '''Collectivist Cultures''': Families or communities play a central role in caregiving (e.g., Middle Eastern, Native American).
** '''Stigma''': Disabilities or illnesses may be hidden to protect family reputation (e.g., tuberculosis in Haitian culture).
** '''Spiritual Healers''': Common first choice in cultures with strong spiritual beliefs (e.g., curandero, root-worker).

----

==== Barriers to Seeking Treatment ====

* '''Misinterpretation of Symptoms''': People may underestimate or misattribute symptoms (e.g., indigestion vs. heart attack).
* '''Social Concerns''': Fear of false alarms, inconvenience, or troubling others.
* '''Financial Barriers''': Lack of health insurance or cost concerns.

----

==== Delays in Treatment ====

# '''Appraisal Delay''': Time to recognize symptoms.
# '''Illness Delay''': Time between recognizing symptoms and deciding to seek care.
# '''Use Delay''': Time between deciding to seek care and obtaining it.

----

==== Triggers for Seeking Treatment (Zola, 1964) ====

# Severity and visibility of symptoms.
# Pain level or interference with daily life.
# Interpersonal crises affecting relationships.
# Social interference (e.g., work or vacation disruption).
# Social sanctions (e.g., employer pressures).

----

==== Cultural and Demographic Patterns ====

* '''Gender and Age''': Women and elderly seek treatment more often than men and younger individuals.
* '''Ethnicity''':
** Non-European Americans often rely on lay-referral systems (family/friends).
** Close-knit communities may promote or hinder seeking care.
* '''Socioeconomic Status (SES)''':
** SES affects treatment decisions and access, and is the largest cultural factor that predicts treatment seeking. 
** Low-income groups may delay treatment due to costs or mistrust of the system.

----

==== Cultural Examples ====

* '''Middle Eastern Cultures''': Hidden disabilities to avoid societal stigma.
* '''Haitian American Culture''': Tuberculosis patients isolated outside the home.
* '''Orthodox Jewish Communities''': Weak eyes may go untreated to enhance family marriage prospects.

----

=== Hospital Setting ===

* '''Types of Hospitals''': For-profit and nonprofit hospitals often compete for patients in cities, benefiting patients with discounts/special services.
* '''Challenges''':
** Health care is viewed as a business, leading to patient dissatisfaction.
** Millions remain uninsured despite the Affordable Care Act.
** Hospital visits often involve lengthy waiting periods, form-filling, and procedural delays.
* '''Physician Interaction''':
** Physicians spend limited time with patients due to quotas and insurance demands.
** Poor patient–physician communication is a significant dissatisfaction factor.

=== Stress and Environment ===

* '''Stress Factors''': Long waits, noise, and intimidating equipment.
* '''Improvements''':
** Better lighting, reduced noise, and nature scenes in waiting areas lower stress.
** Avoiding uncontrollable daytime TV in waiting rooms helps reduce anxiety.

=== Staff Relations ===

* '''Diversity''': Hospitals employ culturally diverse staff (e.g., Indian, Chinese, Middle Eastern doctors; Mexican, Filipino nurses).
* '''Cultural Influences''':
** Male doctors from some cultures may show sexism.
** Asian/Latinx nurses may avoid conflict or questioning authority.
* '''Religious Conflicts''': Staff may refuse procedures like blood transfusions or abortions due to religious beliefs.
* '''Gender Dynamics''':
** Female doctors may face intimidation from male counterparts.
** Male nurses from patriarchal cultures may struggle with hierarchical roles.

=== Adherence to Treatment ===

* '''Definition''': Adherence = following prescribed treatments (e.g., timing, dosage, lifestyle changes).
* '''Impact''':
** Poor adherence costs $100–$300 billion annually and worsens health outcomes.
** Specific risks: kidney transplant failures, AIDS-related fatalities.
* '''Rates''':
** ~33% nonadherence for acute illnesses, ~55% for chronic illnesses.
** Influenced by treatment complexity and personal preferences.

=== Cultural &amp; Practical Barriers ===

* '''Cultural Factors''':
** Dietary restrictions (e.g., Ramadan fasting, kosher laws) may conflict with treatment plans.
** Different cultural beliefs about rest periods and medical authority affect adherence.
* '''Creative Nonadherence''': Patients modify treatments (e.g., skipping doses or overusing asthma sprays).

=== Innovations to Improve Adherence ===

* '''Technology''': Digital tools like pill monitors and automated programs improve compliance.
* '''Parental Involvement''': Supervised adherence in children yields better outcomes.

==== Conclusions ====

* Health-seeking behaviors are shaped by cultural norms, financial barriers, social triggers, and personal beliefs.
* Psychological and cultural barriers can delay treatment, increasing severity at the time of care.
* Socioeconomic and demographic factors significantly impact health care access and choices.

== 9.4 - Patient-Practitioner Interactions ==

=== Patient’s Journey and Interaction with Health Care ===

* '''Initial Steps''':
** Patients must navigate insurance, hospital paperwork, and registration.
** Quality of interaction with doctors impacts recovery and adherence.

=== Patient–Practitioner Interaction Models (Szasz &amp; Hollender, 1956): ===

# '''Active-Passive Model''':
#* Doctor makes decisions; patient has little/no input.
# '''Guidance-Cooperation Model''':
#* Doctor leads; patient answers questions but doesn’t decide on treatment.
# '''Mutual Cooperation Model''' (Optimal):
#* Collaborative planning between doctor and patient.

=== Communication Types and Barriers ===

* '''Communication Styles''':
** Biomedical: Focus on jargon; closed-ended questions.
** Consumerist: Patient-driven discussion.
* '''Cultural Factors''':
** '''Individualism vs. Collectivism''':
*** Collectivists prioritize harmony, may withhold some info.
*** Individualists prefer directness, potentially causing frustration in mismatched interactions.
** '''Language Challenges''':
*** Jargon, technical terms, and word meanings vary (e.g., “positive” results).
*** Misunderstandings arise from differences in English dialects and other languages.
* '''Doctor’s Role in Communication Issues''':
** Interruptions (avg. after 18 seconds per Beckman &amp; Frankel, 1984).
** Overuse of jargon or “dumbing down” messages.
** Insufficient explanation of uncertain outcomes.
* '''Patient’s Role in Communication Issues''':
** Anxiety leads to incomplete symptom reporting.
** SES and language differences affect understanding.

=== Key Influences on Patient–Practitioner Communication ===

* '''Cultural Dimensions''':
** Varying use of small talk across cultures.
** Interpretation of symptoms and social norms differ.
* '''Uncertainty and Decision Making''':
** Increasing trend for shared decisions.
** Patients often struggle with probabilities and risk communication.

=== Gender Bias and Stereotypes ===

* '''Gender Bias''':
** Stereotyping based on gender leads to differential treatment.
* '''Cultural Sensitivity''':
** Symptoms can have private connotations across cultures, affecting reporting.

=== Importance of Intercultural Skills ===

* '''Training for Practitioners''':
** Incorporate intercultural and patient-centered communication skills.
** Emphasize empathy and adaptability to improve care quality.

# '''Stereotypes''': Widely held, oversimplified beliefs that people have certain characteristics due to group membership.
#* Examples:
#** Asians: Good at math.
#** Women: Bad at math.
#** Middle Eastern/Indian Americans: Vocal about pain.
#** Asian Americans: Quiet and stoic.
#** Mexican Americans: Large families.
# '''Cultural Competency''': The combination of culturally appropriate attitudes, knowledge, and skills to deliver effective healthcare to diverse groups.
#* '''Cultural Awareness''': Appreciation of external signs of diversity (e.g., arts, dress, food).
#* '''Cultural Sensitivity''': Avoiding offensive actions/statements based on cultural differences.
# '''Perceived Discrimination''': Patient perception of biased or unequal treatment based on cultural or gender differences.
# '''Gender Bias in Healthcare''': Unequal treatment based on gender, leading to disparities in diagnosis, procedures, and outcomes.
#* Examples:
#** Women less likely to receive ICU care or heart-related devices.
#** Men more likely to be recommended knee surgery.

----

=== Key Information ===

==== Stereotyping in Healthcare ====

* Stereotypes influence communication and decisions in patient care.
* Harmful effects:
** Generalizations can lead to poor care or malpractice.
** Stereotypes based on race, gender, or age often dictate treatment decisions.

==== Examples of Healthcare Disparities ====

* '''Racial Bias''':
** Black, Latinx/e, and low-SES patients receive less information and care (IOM, 2002).
* '''Gender Bias''':
** Heart disease devices used more in men than women despite similar symptoms (Curtis et al., 2007).
** Older women face shorter ICU stays and higher mortality risks (Fowler et al., 2007).
* '''Ethnic Stereotypes''':
** Language-based discrimination impacts help-seeking behavior (Spencer &amp; Chen, 2004).

==== Cultural Competency ====

* Essential for effective communication and care.
* Poor cultural competency leads to:
** Miscommunication.
** Lower patient trust and satisfaction.
** Discrimination.
* '''Measurement Tools''':
** Healthcare Provider Cultural Competency scale (Lucas et al., 2008).

==== Impact of Discrimination ====

* Language barriers result in patients seeking informal care instead of formal treatment.
* Women more likely than men to seek emotional support through informal means.

----

=== Actionable Steps ===

* Develop cultural competency through awareness, sensitivity, and skills.
* Avoid relying on stereotypes; assess individual patient needs.
* Educate healthcare providers on the impact of bias and disparities.
* Use standardized tools to evaluate cultural competency and improve patient satisfaction.</text>
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  <page>
    <title>Cauchy's integral formula</title>
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      <comment>New resource with &quot;==Introduction== The Cauchy integral formula, alongside the [[w:en:Cauchy's integral theorem|Cauchy's integral theorem]], is one of the central statements in [[w:en:Complex analysis|complex analysis]]. Here, we present two variants: the 'classical' formula for circular disks and a relatively general version for [[w:en:Null-homologous|null-homologous]] [[w:en:Cycle (mathematics)|cycles]]. Note that we will deduce the circular disk version from Cauchy's integral theorem, b...&quot;</comment>
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      <text bytes="8868" sha1="my03z6mlz0npzteo2csi4tot5pldmjn" xml:space="preserve">==Introduction==
The Cauchy integral formula, alongside the [[w:en:Cauchy's integral theorem|Cauchy's integral theorem]], is one of the central statements in [[w:en:Complex analysis|complex analysis]]. Here, we present two variants: the 'classical' formula for circular disks and a relatively general version for [[w:en:Null-homologous|null-homologous]] [[w:en:Cycle (mathematics)|cycles]]. Note that we will deduce the circular disk version from Cauchy's integral theorem, but for the general variant, we proceed in the opposite direction.
==For Circular Disks==
===Statement===
Let &lt;math&gt;G \subseteq \mathbb C &lt;/math&gt; be an open set, &lt;math&gt;D&lt;/math&gt; a circular disk with &lt;math&gt;\bar D \subseteq G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Then, we have
:&lt;math&gt; f(z) = \frac 1{2\pi i}\int_{\partial D} \frac{f(w)}{w-z}, dw &lt;/math&gt;
for each &lt;math&gt;z \in D&lt;/math&gt;.
===Proof 1===
By slightly enlarging the radius of the circular disk, we find an open circular disk &lt;math&gt;U&lt;/math&gt; such that &lt;math&gt;\bar D \subseteq U \subseteq G&lt;/math&gt;. Define &lt;math&gt;g \colon U \to \mathbb C&lt;/math&gt; by
:&lt;math&gt;   g(w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} &amp; w \ne z\\ f'(z) &amp; w = z \end{array} \right. &lt;/math&gt;
===Proof 2===
The function &lt;math&gt;g&lt;/math&gt; is continuous on &lt;math&gt;U&lt;/math&gt; and holomorphic on &lt;math&gt;U -{z}&lt;/math&gt;. Thus, we can apply the [[w:en:Cauchy's integral theorem|Cauchy integral theorem]] on &lt;math&gt;U&lt;/math&gt; and obtain
:&lt;math&gt; 0 = \int_{\partial D} g(w), dw = \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} &lt;/math&gt;
For &lt;math&gt;z \in D&lt;/math&gt;, define &lt;math&gt;h(z) := \int_{\partial D} \frac{dw}{w-z}&lt;/math&gt;. Then &lt;math&gt;h&lt;/math&gt; is [[w:en:Holomorphic function|holomorphic]] with
:&lt;math&gt; h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2}  &lt;/math&gt;

===Proof 3===
Since the integrand &lt;math&gt;\frac{dw}{(w-z)^2}&lt;/math&gt; has a primitive in &lt;math&gt;D&lt;/math&gt;, we find
:&lt;math&gt; h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2} = 0 &lt;/math&gt;

===Proof 4===
Because &lt;math&gt;h'(z) =0&lt;/math&gt; throughout &lt;math&gt;D&lt;/math&gt;, it follows that &lt;math&gt;h&lt;/math&gt; is constant. Thus, &lt;math&gt;h(z)&lt;/math&gt; always takes the same value as at the center &lt;math&gt;h(z_0)&lt;/math&gt; of the disk &lt;math&gt;D&lt;/math&gt;, i.e., &lt;math&gt;h(z_0) = 2\pi i&lt;/math&gt;. Hence,
:&lt;math&gt; 0 =  \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} \iff   f(z) = \frac 1{2\pi i} \int_{\partial D}\frac{f(w)}{w-z}, dw &lt;/math&gt;
This proves the statement.

==For Cycles in Arbitrary Open Sets==
===Statement===
Let &lt;math&gt;G\subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;\Gamma&lt;/math&gt; a [[w:en:Null-homologous|null-homologous]] cycle in &lt;math&gt;G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; [[w:en:Holomorphic function|holomorphic]]. Then,
:&lt;math&gt;    n(\Gamma, z)\cdot f(z) = \frac 1{2\pi i} \int_\Gamma \frac{f(w)}{w-z} , dw  &lt;/math&gt;
for each &lt;math&gt;z \in G \setminus \mathrm{spur}(\Gamma)&lt;/math&gt;, where &lt;math&gt;n(\Gamma, \cdot)&lt;/math&gt; denotes the [[w:en:Winding number|winding number]].

===Proof 1===
Define a function &lt;math&gt;g\colon G^2 \to \mathbb C&lt;/math&gt; by
:&lt;math&gt;   g(z,w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} &amp; w \ne z\\ f'(z) &amp; w = z \end{array} \right. &lt;/math&gt;
defined.
===Proof 2:  continuous===
We demonstrate the continuity in both variables. Let &lt;math&gt;(w_0, z_0) \in U \times U&lt;/math&gt; with &lt;math&gt;z_0 \ne w_0&lt;/math&gt;, then &lt;math&gt;g&lt;/math&gt; is given in the vicinity of &lt;math&gt;(w_0, z_0)&lt;/math&gt;  by the above formula and is trivially continuous.Now let &lt;math&gt;z_0 = w_0&lt;/math&gt;. We choose a &lt;math&gt;\delta&lt;/math&gt;-neighborhood &lt;math&gt;U_{\delta}(z_0) \subset \subset G&lt;/math&gt; and examine &lt;math&gt;g(w,z) - g(z_0,z_0)&lt;/math&gt; auf &lt;math&gt;U_{\delta}(z_0) \times  U_{\delta}(z_0)&lt;/math&gt; &lt;br&gt;&lt;br&gt;.
a) In the case &lt;math&gt;w = z&lt;/math&gt;: &lt;br&gt;:
:&lt;math&gt;g(z,z) - g(z_0,z_0) = f'(z) - f'(z_0)&lt;/math&gt;

===Proof 3===
b) In the case &lt;math&gt;w \ne z&lt;/math&gt;:
:&lt;math&gt;g(w,z) - g(z_0,z_0) = \frac{f(w) - f(z)}{w-z} - f'(z_0) = \frac 1 {w - z} \int_{[z,w]}(f'(v) - f'(z_0)) dv&lt;/math&gt;

Now, as a consequence of Cauchy's formulas for circles! the derivative &lt;math&gt;f'&lt;/math&gt; is continuous in &lt;math&gt;z_0&lt;/math&gt;.  For a given &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; we can choose  &lt;math&gt;\delta &gt; 0&lt;/math&gt; such that
:&lt;math&gt;|f'(v) - f'(z_0)| &lt; \epsilon &lt;/math&gt;
for all &lt;math&gt;v \in U_{\delta} (z_0)&lt;/math&gt;. &lt;br&gt;
===Proof 4===
This implies, in case a:
:&lt;math&gt;|g(z,z) - g(z_0,z_0)| &lt; \epsilon;&lt;/math&gt;
and in case b:
:&lt;math&gt;|g(w,z) - g(z_0, z_0)| \leq \frac 1 {|w - z|} |w - z| \cdot  \sup\limits_{w \in [w,z]} |f'(v)-f'(z_0)| &lt; \epsilon.&lt;/math&gt;
We now define
:&lt;math&gt;h_0 (z) = \int_{\Gamma} g(w,z) dw.&lt;/math&gt;
&lt;math&gt;h_0&lt;/math&gt; function  is continuous on whole of &lt;math&gt;G&lt;/math&gt; ; we will show that it is even holomorphic. For this, we use Morera's theorem.

===Proof 5===
Let &lt;math&gt;\gamma&lt;/math&gt; be the oriented boundary of a triangle that lies entirely with in &lt;math&gt;G&lt;/math&gt; . We must show
:&lt;math&gt;\int_{\gamma} h_0(z) dz = 0&lt;/math&gt;
prove it is
:&lt;math&gt;\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\,  dw = 0.&lt;/math&gt;
because the integrations are commutable due to the continuity of the integrand on &lt;math&gt;G \times G&lt;/math&gt;  For fixed , &lt;math&gt;w&lt;/math&gt; the function  is &lt;math&gt;g(w,z)&lt;/math&gt; in the Variable &lt;math&gt;z&lt;/math&gt; continuous in  and holomorphic for &lt;math&gt;w \ne z&lt;/math&gt;, hence holomorphic everywhere.
===Proof 6===
By Goursat's theorem, it follows that
:&lt;math&gt;\int_{\gamma} g(w,z) dz = 0.&lt;/math&gt;
this of course also mean that
:&lt;math&gt;\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\,  dw = 0.&lt;/math&gt;

so far we have not yet exploited the conditions above &lt;math&gt;\Gamma&lt;/math&gt;. We will do so

:&lt;math&gt;G_0 = \{z \in \mathbb C: n (\Gamma, z) = 0\}&lt;/math&gt;.
===Proof 7===
Since on &lt;math&gt;G \cap G_0&lt;/math&gt; the function &lt;math&gt;h_0&lt;/math&gt;   has a simpler form, namely
:&lt;math&gt;h_0(z) = \int_{\Gamma}\frac {f(w)}{w- z} dw = h_1(z),&lt;/math&gt;
and since the function &lt;math&gt;h_1&lt;/math&gt;  is clearly holomorphic on the entire &lt;math&gt;G_0&lt;/math&gt;, we can extend &lt;math&gt;h_0&lt;/math&gt;  to a holomorphic function &lt;math&gt;h&lt;/math&gt;  defined on the entire by&lt;math&gt;G \cup G_0&lt;/math&gt; 
:&lt;math&gt;   h(z) = \left\{ \begin{array}{ll} h_0(z) &amp; z \in G\\ h_1(z) &amp; z \in G_0 \end{array} \right. &lt;/math&gt;

Now &lt;math&gt;\Gamma&lt;/math&gt; is null-homologous  in , and thus
:&lt;math&gt;G \cup G_0 = \mathbb C,&lt;/math&gt;
i.e. &lt;math&gt;h&lt;/math&gt;  is an entire function. 
===Proof 8===
For &lt;math&gt;h&lt;/math&gt; we have&lt;math&gt;G_0&lt;/math&gt; the notation:
:&lt;math&gt;|h(z)| = |h_1(z)| \leq \frac 1 {dist(z, \Gamma)} L(\Gamma) \max_{\Gamma}|f|\;\;\;(*);&lt;/math&gt;
where &lt;math&gt;L(\Gamma) = \sum |n_k| L(\gamma_k)&lt;/math&gt;, if &lt;math&gt;\Gamma = n_k \cdot \gamma_k&lt;/math&gt; is.

&lt;math&gt;G_0&lt;/math&gt; contains the complement of a sufficiently large circle around 0. Therefore, the above inequality holds for all &lt;math&gt;z&lt;/math&gt; in this region: it follows that  &lt;math&gt;h&lt;/math&gt; is bounded, and by Liouville's theorem, it must be constant. If we choose a sequence &lt;math&gt;z_{\nu} \in G_0&lt;/math&gt; such that &lt;math&gt;|z_{\nu}| \geq \nu&lt;/math&gt;, the inequality (*) again implies that:
:&lt;math&gt;\lim\limits_{\nu \to \infty}(z_{\nu}) = 0,&lt;/math&gt;

thus we conculude that  &lt;math&gt; h \equiv 0&lt;/math&gt;, and in particular &lt;math&gt;h_0 \equiv 0&lt;/math&gt;; this is what we wanted to prove
==Conclusions==
From the Cauchy integral formula, it follows that every holomorphic function is infinitely differentiable because the integrand in &lt;math&gt;z&lt;/math&gt; is infinitely differentiable. We obtain the following results:

===For Circular Disks===
Let &lt;math&gt;G \subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;D&lt;/math&gt; a circular disk with &lt;math&gt;\bar D \subseteq G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Then &lt;math&gt;f&lt;/math&gt; is infinitely differentiable, and for each &lt;math&gt;n\in \mathbb N&lt;/math&gt;, we have
:&lt;center&gt;&lt;math&gt; f^{(n)}(z) = \frac{n!}{2\pi i}\int_{\partial D} \frac{f(w)}{(w-z)^{n+1}}, dw &lt;/math&gt;&lt;/center&gt;
for each &lt;math&gt;z \in D&lt;/math&gt;.

===For Cycles===
Let &lt;math&gt;G\subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;\Gamma \in C(G)&lt;/math&gt; a [[w:en:Null-homologous|null-homologous]] cycle, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; [[w:en:Holomorphic function|holomorphic]]. Then
:&lt;math&gt;   n(\Gamma, z) \cdot f^{(n)}(z) = \frac {n!}{2\pi i} \int_\Gamma \frac{f(w)}{(w-z)^{n+1}} , dw &lt;/math&gt;
for each &lt;math&gt;z \in G \setminus \mathrm{spur}(\Gamma)&lt;/math&gt; and &lt;math&gt;n \in \mathbb N&lt;/math&gt;.

==Analyticity==
Moreover, every holomorphic function is analytic at every point, i.e., it can be expanded into a power series:

===Statement===
Let &lt;math&gt;G \subseteq \mathbb C&lt;/math&gt; be open, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Let &lt;math&gt;z_0 \in G&lt;/math&gt; and &lt;math&gt;r &gt; 0&lt;/math&gt; such that &lt;math&gt;\bar B_r(z_0) \subseteq G&lt;/math&gt;. Then &lt;math&gt;f&lt;/math&gt; can be represented on &lt;math&gt;B_r(z_0)&lt;/math&gt; by a convergent power series
:&lt;math&gt; f(z) = \sum_{n=0}^\infty a_n (z-z_0)^n &lt;/math&gt;
where the coefficients are given by
:&lt;math&gt; a_n = \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{(w-z_0)^{n+1}}, dw &lt;/math&gt;.</text>
      <sha1>my03z6mlz0npzteo2csi4tot5pldmjn</sha1>
    </revision>
    <revision>
      <id>2693047</id>
      <parentid>2693046</parentid>
      <timestamp>2024-12-23T21:41:05Z</timestamp>
      <contributor>
        <ip>2003:F8:2F3E:6AF0:6833:C452:10AF:847E</ip>
      </contributor>
      <comment>/* For Cycles */</comment>
      <origin>2693047</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="8869" sha1="5ro0qgr7tzmyrlc86oadkiejmirvs8e" xml:space="preserve">==Introduction==
The Cauchy integral formula, alongside the [[w:en:Cauchy's integral theorem|Cauchy's integral theorem]], is one of the central statements in [[w:en:Complex analysis|complex analysis]]. Here, we present two variants: the 'classical' formula for circular disks and a relatively general version for [[w:en:Null-homologous|null-homologous]] [[w:en:Cycle (mathematics)|cycles]]. Note that we will deduce the circular disk version from Cauchy's integral theorem, but for the general variant, we proceed in the opposite direction.
==For Circular Disks==
===Statement===
Let &lt;math&gt;G \subseteq \mathbb C &lt;/math&gt; be an open set, &lt;math&gt;D&lt;/math&gt; a circular disk with &lt;math&gt;\bar D \subseteq G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Then, we have
:&lt;math&gt; f(z) = \frac 1{2\pi i}\int_{\partial D} \frac{f(w)}{w-z}, dw &lt;/math&gt;
for each &lt;math&gt;z \in D&lt;/math&gt;.
===Proof 1===
By slightly enlarging the radius of the circular disk, we find an open circular disk &lt;math&gt;U&lt;/math&gt; such that &lt;math&gt;\bar D \subseteq U \subseteq G&lt;/math&gt;. Define &lt;math&gt;g \colon U \to \mathbb C&lt;/math&gt; by
:&lt;math&gt;   g(w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} &amp; w \ne z\\ f'(z) &amp; w = z \end{array} \right. &lt;/math&gt;
===Proof 2===
The function &lt;math&gt;g&lt;/math&gt; is continuous on &lt;math&gt;U&lt;/math&gt; and holomorphic on &lt;math&gt;U -{z}&lt;/math&gt;. Thus, we can apply the [[w:en:Cauchy's integral theorem|Cauchy integral theorem]] on &lt;math&gt;U&lt;/math&gt; and obtain
:&lt;math&gt; 0 = \int_{\partial D} g(w), dw = \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} &lt;/math&gt;
For &lt;math&gt;z \in D&lt;/math&gt;, define &lt;math&gt;h(z) := \int_{\partial D} \frac{dw}{w-z}&lt;/math&gt;. Then &lt;math&gt;h&lt;/math&gt; is [[w:en:Holomorphic function|holomorphic]] with
:&lt;math&gt; h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2}  &lt;/math&gt;

===Proof 3===
Since the integrand &lt;math&gt;\frac{dw}{(w-z)^2}&lt;/math&gt; has a primitive in &lt;math&gt;D&lt;/math&gt;, we find
:&lt;math&gt; h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2} = 0 &lt;/math&gt;

===Proof 4===
Because &lt;math&gt;h'(z) =0&lt;/math&gt; throughout &lt;math&gt;D&lt;/math&gt;, it follows that &lt;math&gt;h&lt;/math&gt; is constant. Thus, &lt;math&gt;h(z)&lt;/math&gt; always takes the same value as at the center &lt;math&gt;h(z_0)&lt;/math&gt; of the disk &lt;math&gt;D&lt;/math&gt;, i.e., &lt;math&gt;h(z_0) = 2\pi i&lt;/math&gt;. Hence,
:&lt;math&gt; 0 =  \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} \iff   f(z) = \frac 1{2\pi i} \int_{\partial D}\frac{f(w)}{w-z}, dw &lt;/math&gt;
This proves the statement.

==For Cycles in Arbitrary Open Sets==
===Statement===
Let &lt;math&gt;G\subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;\Gamma&lt;/math&gt; a [[w:en:Null-homologous|null-homologous]] cycle in &lt;math&gt;G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; [[w:en:Holomorphic function|holomorphic]]. Then,
:&lt;math&gt;    n(\Gamma, z)\cdot f(z) = \frac 1{2\pi i} \int_\Gamma \frac{f(w)}{w-z} , dw  &lt;/math&gt;
for each &lt;math&gt;z \in G \setminus \mathrm{spur}(\Gamma)&lt;/math&gt;, where &lt;math&gt;n(\Gamma, \cdot)&lt;/math&gt; denotes the [[w:en:Winding number|winding number]].

===Proof 1===
Define a function &lt;math&gt;g\colon G^2 \to \mathbb C&lt;/math&gt; by
:&lt;math&gt;   g(z,w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} &amp; w \ne z\\ f'(z) &amp; w = z \end{array} \right. &lt;/math&gt;
defined.
===Proof 2:  continuous===
We demonstrate the continuity in both variables. Let &lt;math&gt;(w_0, z_0) \in U \times U&lt;/math&gt; with &lt;math&gt;z_0 \ne w_0&lt;/math&gt;, then &lt;math&gt;g&lt;/math&gt; is given in the vicinity of &lt;math&gt;(w_0, z_0)&lt;/math&gt;  by the above formula and is trivially continuous.Now let &lt;math&gt;z_0 = w_0&lt;/math&gt;. We choose a &lt;math&gt;\delta&lt;/math&gt;-neighborhood &lt;math&gt;U_{\delta}(z_0) \subset \subset G&lt;/math&gt; and examine &lt;math&gt;g(w,z) - g(z_0,z_0)&lt;/math&gt; auf &lt;math&gt;U_{\delta}(z_0) \times  U_{\delta}(z_0)&lt;/math&gt; &lt;br&gt;&lt;br&gt;.
a) In the case &lt;math&gt;w = z&lt;/math&gt;: &lt;br&gt;:
:&lt;math&gt;g(z,z) - g(z_0,z_0) = f'(z) - f'(z_0)&lt;/math&gt;

===Proof 3===
b) In the case &lt;math&gt;w \ne z&lt;/math&gt;:
:&lt;math&gt;g(w,z) - g(z_0,z_0) = \frac{f(w) - f(z)}{w-z} - f'(z_0) = \frac 1 {w - z} \int_{[z,w]}(f'(v) - f'(z_0)) dv&lt;/math&gt;

Now, as a consequence of Cauchy's formulas for circles! the derivative &lt;math&gt;f'&lt;/math&gt; is continuous in &lt;math&gt;z_0&lt;/math&gt;.  For a given &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; we can choose  &lt;math&gt;\delta &gt; 0&lt;/math&gt; such that
:&lt;math&gt;|f'(v) - f'(z_0)| &lt; \epsilon &lt;/math&gt;
for all &lt;math&gt;v \in U_{\delta} (z_0)&lt;/math&gt;. &lt;br&gt;
===Proof 4===
This implies, in case a:
:&lt;math&gt;|g(z,z) - g(z_0,z_0)| &lt; \epsilon;&lt;/math&gt;
and in case b:
:&lt;math&gt;|g(w,z) - g(z_0, z_0)| \leq \frac 1 {|w - z|} |w - z| \cdot  \sup\limits_{w \in [w,z]} |f'(v)-f'(z_0)| &lt; \epsilon.&lt;/math&gt;
We now define
:&lt;math&gt;h_0 (z) = \int_{\Gamma} g(w,z) dw.&lt;/math&gt;
&lt;math&gt;h_0&lt;/math&gt; function  is continuous on whole of &lt;math&gt;G&lt;/math&gt; ; we will show that it is even holomorphic. For this, we use Morera's theorem.

===Proof 5===
Let &lt;math&gt;\gamma&lt;/math&gt; be the oriented boundary of a triangle that lies entirely with in &lt;math&gt;G&lt;/math&gt; . We must show
:&lt;math&gt;\int_{\gamma} h_0(z) dz = 0&lt;/math&gt;
prove it is
:&lt;math&gt;\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\,  dw = 0.&lt;/math&gt;
because the integrations are commutable due to the continuity of the integrand on &lt;math&gt;G \times G&lt;/math&gt;  For fixed , &lt;math&gt;w&lt;/math&gt; the function  is &lt;math&gt;g(w,z)&lt;/math&gt; in the Variable &lt;math&gt;z&lt;/math&gt; continuous in  and holomorphic for &lt;math&gt;w \ne z&lt;/math&gt;, hence holomorphic everywhere.
===Proof 6===
By Goursat's theorem, it follows that
:&lt;math&gt;\int_{\gamma} g(w,z) dz = 0.&lt;/math&gt;
this of course also mean that
:&lt;math&gt;\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\,  dw = 0.&lt;/math&gt;

so far we have not yet exploited the conditions above &lt;math&gt;\Gamma&lt;/math&gt;. We will do so

:&lt;math&gt;G_0 = \{z \in \mathbb C: n (\Gamma, z) = 0\}&lt;/math&gt;.
===Proof 7===
Since on &lt;math&gt;G \cap G_0&lt;/math&gt; the function &lt;math&gt;h_0&lt;/math&gt;   has a simpler form, namely
:&lt;math&gt;h_0(z) = \int_{\Gamma}\frac {f(w)}{w- z} dw = h_1(z),&lt;/math&gt;
and since the function &lt;math&gt;h_1&lt;/math&gt;  is clearly holomorphic on the entire &lt;math&gt;G_0&lt;/math&gt;, we can extend &lt;math&gt;h_0&lt;/math&gt;  to a holomorphic function &lt;math&gt;h&lt;/math&gt;  defined on the entire by&lt;math&gt;G \cup G_0&lt;/math&gt; 
:&lt;math&gt;   h(z) = \left\{ \begin{array}{ll} h_0(z) &amp; z \in G\\ h_1(z) &amp; z \in G_0 \end{array} \right. &lt;/math&gt;

Now &lt;math&gt;\Gamma&lt;/math&gt; is null-homologous  in , and thus
:&lt;math&gt;G \cup G_0 = \mathbb C,&lt;/math&gt;
i.e. &lt;math&gt;h&lt;/math&gt;  is an entire function. 
===Proof 8===
For &lt;math&gt;h&lt;/math&gt; we have&lt;math&gt;G_0&lt;/math&gt; the notation:
:&lt;math&gt;|h(z)| = |h_1(z)| \leq \frac 1 {dist(z, \Gamma)} L(\Gamma) \max_{\Gamma}|f|\;\;\;(*);&lt;/math&gt;
where &lt;math&gt;L(\Gamma) = \sum |n_k| L(\gamma_k)&lt;/math&gt;, if &lt;math&gt;\Gamma = n_k \cdot \gamma_k&lt;/math&gt; is.

&lt;math&gt;G_0&lt;/math&gt; contains the complement of a sufficiently large circle around 0. Therefore, the above inequality holds for all &lt;math&gt;z&lt;/math&gt; in this region: it follows that  &lt;math&gt;h&lt;/math&gt; is bounded, and by Liouville's theorem, it must be constant. If we choose a sequence &lt;math&gt;z_{\nu} \in G_0&lt;/math&gt; such that &lt;math&gt;|z_{\nu}| \geq \nu&lt;/math&gt;, the inequality (*) again implies that:
:&lt;math&gt;\lim\limits_{\nu \to \infty}(z_{\nu}) = 0,&lt;/math&gt;

thus we conculude that  &lt;math&gt; h \equiv 0&lt;/math&gt;, and in particular &lt;math&gt;h_0 \equiv 0&lt;/math&gt;; this is what we wanted to prove
==Conclusions==
From the Cauchy integral formula, it follows that every holomorphic function is infinitely differentiable because the integrand in &lt;math&gt;z&lt;/math&gt; is infinitely differentiable. We obtain the following results:

===For Circular Disks===
Let &lt;math&gt;G \subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;D&lt;/math&gt; a circular disk with &lt;math&gt;\bar D \subseteq G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Then &lt;math&gt;f&lt;/math&gt; is infinitely differentiable, and for each &lt;math&gt;n\in \mathbb N&lt;/math&gt;, we have
:&lt;center&gt;&lt;math&gt; f^{(n)}(z) = \frac{n!}{2\pi i}\int_{\partial D} \frac{f(w)}{(w-z)^{n+1}}, dw &lt;/math&gt;&lt;/center&gt;
for each &lt;math&gt;z \in D&lt;/math&gt;.

===For Cycles===
Let &lt;math&gt;G\subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;\Gamma \in C(G)&lt;/math&gt; a [[w:en:Null-homologous|null-homologous]] cycle, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; [[w:en:Holomorphic function|holomorphic]]. Then
:&lt;math&gt;   n(\Gamma, z) \cdot f^{(n)}(z) = \frac {n!}{2\pi i} \int_\Gamma \frac{f(w)}{(w-z)^{n+1}} , dw &lt;/math&gt;
for each &lt;math&gt;z \in G \setminus \mathrm{Trace}(\Gamma)&lt;/math&gt; and &lt;math&gt;n \in \mathbb N&lt;/math&gt;.

==Analyticity==
Moreover, every holomorphic function is analytic at every point, i.e., it can be expanded into a power series:

===Statement===
Let &lt;math&gt;G \subseteq \mathbb C&lt;/math&gt; be open, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Let &lt;math&gt;z_0 \in G&lt;/math&gt; and &lt;math&gt;r &gt; 0&lt;/math&gt; such that &lt;math&gt;\bar B_r(z_0) \subseteq G&lt;/math&gt;. Then &lt;math&gt;f&lt;/math&gt; can be represented on &lt;math&gt;B_r(z_0)&lt;/math&gt; by a convergent power series
:&lt;math&gt; f(z) = \sum_{n=0}^\infty a_n (z-z_0)^n &lt;/math&gt;
where the coefficients are given by
:&lt;math&gt; a_n = \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{(w-z_0)^{n+1}}, dw &lt;/math&gt;.</text>
      <sha1>5ro0qgr7tzmyrlc86oadkiejmirvs8e</sha1>
    </revision>
    <revision>
      <id>2693050</id>
      <parentid>2693047</parentid>
      <timestamp>2024-12-23T21:46:22Z</timestamp>
      <contributor>
        <username>Eshaa2024</username>
        <id>2993595</id>
      </contributor>
      <origin>2693050</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="10213" sha1="fg9n04fva0g4gkkkbcqtyzlgmd4ssv6" xml:space="preserve">==Introduction==
The Cauchy integral formula, alongside the [[w:en:Cauchy's integral theorem|Cauchy's integral theorem]], is one of the central statements in [[w:en:Complex analysis|complex analysis]]. Here, we present two variants: the 'classical' formula for circular disks and a relatively general version for [[w:en:Null-homologous|null-homologous]] [[w:en:Cycle (mathematics)|cycles]]. Note that we will deduce the circular disk version from Cauchy's integral theorem, but for the general variant, we proceed in the opposite direction.
==For Circular Disks==
===Statement===
Let &lt;math&gt;G \subseteq \mathbb C &lt;/math&gt; be an open set, &lt;math&gt;D&lt;/math&gt; a circular disk with &lt;math&gt;\bar D \subseteq G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Then, we have
:&lt;math&gt; f(z) = \frac 1{2\pi i}\int_{\partial D} \frac{f(w)}{w-z}, dw &lt;/math&gt;
for each &lt;math&gt;z \in D&lt;/math&gt;.
===Proof 1===
By slightly enlarging the radius of the circular disk, we find an open circular disk &lt;math&gt;U&lt;/math&gt; such that &lt;math&gt;\bar D \subseteq U \subseteq G&lt;/math&gt;. Define &lt;math&gt;g \colon U \to \mathbb C&lt;/math&gt; by
:&lt;math&gt;   g(w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} &amp; w \ne z\\ f'(z) &amp; w = z \end{array} \right. &lt;/math&gt;
===Proof 2===
The function &lt;math&gt;g&lt;/math&gt; is continuous on &lt;math&gt;U&lt;/math&gt; and holomorphic on &lt;math&gt;U -{z}&lt;/math&gt;. Thus, we can apply the [[w:en:Cauchy's integral theorem|Cauchy integral theorem]] on &lt;math&gt;U&lt;/math&gt; and obtain
:&lt;math&gt; 0 = \int_{\partial D} g(w), dw = \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} &lt;/math&gt;
For &lt;math&gt;z \in D&lt;/math&gt;, define &lt;math&gt;h(z) := \int_{\partial D} \frac{dw}{w-z}&lt;/math&gt;. Then &lt;math&gt;h&lt;/math&gt; is [[w:en:Holomorphic function|holomorphic]] with
:&lt;math&gt; h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2}  &lt;/math&gt;

===Proof 3===
Since the integrand &lt;math&gt;\frac{dw}{(w-z)^2}&lt;/math&gt; has a primitive in &lt;math&gt;D&lt;/math&gt;, we find
:&lt;math&gt; h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2} = 0 &lt;/math&gt;

===Proof 4===
Because &lt;math&gt;h'(z) =0&lt;/math&gt; throughout &lt;math&gt;D&lt;/math&gt;, it follows that &lt;math&gt;h&lt;/math&gt; is constant. Thus, &lt;math&gt;h(z)&lt;/math&gt; always takes the same value as at the center &lt;math&gt;h(z_0)&lt;/math&gt; of the disk &lt;math&gt;D&lt;/math&gt;, i.e., &lt;math&gt;h(z_0) = 2\pi i&lt;/math&gt;. Hence,
:&lt;math&gt; 0 =  \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} \iff   f(z) = \frac 1{2\pi i} \int_{\partial D}\frac{f(w)}{w-z}, dw &lt;/math&gt;
This proves the statement.

==For Cycles in Arbitrary Open Sets==
===Statement===
Let &lt;math&gt;G\subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;\Gamma&lt;/math&gt; a [[w:en:Null-homologous|null-homologous]] cycle in &lt;math&gt;G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; [[w:en:Holomorphic function|holomorphic]]. Then,
:&lt;math&gt;    n(\Gamma, z)\cdot f(z) = \frac 1{2\pi i} \int_\Gamma \frac{f(w)}{w-z} , dw  &lt;/math&gt;
for each &lt;math&gt;z \in G \setminus \mathrm{spur}(\Gamma)&lt;/math&gt;, where &lt;math&gt;n(\Gamma, \cdot)&lt;/math&gt; denotes the [[w:en:Winding number|winding number]].

===Proof 1===
Define a function &lt;math&gt;g\colon G^2 \to \mathbb C&lt;/math&gt; by
:&lt;math&gt;   g(z,w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} &amp; w \ne z\\ f'(z) &amp; w = z \end{array} \right. &lt;/math&gt;
defined.
===Proof 2:  continuous===
We demonstrate the continuity in both variables. Let &lt;math&gt;(w_0, z_0) \in U \times U&lt;/math&gt; with &lt;math&gt;z_0 \ne w_0&lt;/math&gt;, then &lt;math&gt;g&lt;/math&gt; is given in the vicinity of &lt;math&gt;(w_0, z_0)&lt;/math&gt;  by the above formula and is trivially continuous.Now let &lt;math&gt;z_0 = w_0&lt;/math&gt;. We choose a &lt;math&gt;\delta&lt;/math&gt;-neighborhood &lt;math&gt;U_{\delta}(z_0) \subset \subset G&lt;/math&gt; and examine &lt;math&gt;g(w,z) - g(z_0,z_0)&lt;/math&gt; auf &lt;math&gt;U_{\delta}(z_0) \times  U_{\delta}(z_0)&lt;/math&gt; &lt;br&gt;&lt;br&gt;.
a) In the case &lt;math&gt;w = z&lt;/math&gt;: &lt;br&gt;:
:&lt;math&gt;g(z,z) - g(z_0,z_0) = f'(z) - f'(z_0)&lt;/math&gt;

===Proof 3===
b) In the case &lt;math&gt;w \ne z&lt;/math&gt;:
:&lt;math&gt;g(w,z) - g(z_0,z_0) = \frac{f(w) - f(z)}{w-z} - f'(z_0) = \frac 1 {w - z} \int_{[z,w]}(f'(v) - f'(z_0)) dv&lt;/math&gt;

Now, as a consequence of Cauchy's formulas for circles! the derivative &lt;math&gt;f'&lt;/math&gt; is continuous in &lt;math&gt;z_0&lt;/math&gt;.  For a given &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; we can choose  &lt;math&gt;\delta &gt; 0&lt;/math&gt; such that
:&lt;math&gt;|f'(v) - f'(z_0)| &lt; \epsilon &lt;/math&gt;
for all &lt;math&gt;v \in U_{\delta} (z_0)&lt;/math&gt;. &lt;br&gt;
===Proof 4===
This implies, in case a:
:&lt;math&gt;|g(z,z) - g(z_0,z_0)| &lt; \epsilon;&lt;/math&gt;
and in case b:
:&lt;math&gt;|g(w,z) - g(z_0, z_0)| \leq \frac 1 {|w - z|} |w - z| \cdot  \sup\limits_{w \in [w,z]} |f'(v)-f'(z_0)| &lt; \epsilon.&lt;/math&gt;
We now define
:&lt;math&gt;h_0 (z) = \int_{\Gamma} g(w,z) dw.&lt;/math&gt;
&lt;math&gt;h_0&lt;/math&gt; function  is continuous on whole of &lt;math&gt;G&lt;/math&gt; ; we will show that it is even holomorphic. For this, we use Morera's theorem.

===Proof 5===
Let &lt;math&gt;\gamma&lt;/math&gt; be the oriented boundary of a triangle that lies entirely with in &lt;math&gt;G&lt;/math&gt; . We must show
:&lt;math&gt;\int_{\gamma} h_0(z) dz = 0&lt;/math&gt;
prove it is
:&lt;math&gt;\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\,  dw = 0.&lt;/math&gt;
because the integrations are commutable due to the continuity of the integrand on &lt;math&gt;G \times G&lt;/math&gt;  For fixed , &lt;math&gt;w&lt;/math&gt; the function  is &lt;math&gt;g(w,z)&lt;/math&gt; in the Variable &lt;math&gt;z&lt;/math&gt; continuous in  and holomorphic for &lt;math&gt;w \ne z&lt;/math&gt;, hence holomorphic everywhere.
===Proof 6===
By Goursat's theorem, it follows that
:&lt;math&gt;\int_{\gamma} g(w,z) dz = 0.&lt;/math&gt;
this of course also mean that
:&lt;math&gt;\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\,  dw = 0.&lt;/math&gt;

so far we have not yet exploited the conditions above &lt;math&gt;\Gamma&lt;/math&gt;. We will do so

:&lt;math&gt;G_0 = \{z \in \mathbb C: n (\Gamma, z) = 0\}&lt;/math&gt;.
===Proof 7===
Since on &lt;math&gt;G \cap G_0&lt;/math&gt; the function &lt;math&gt;h_0&lt;/math&gt;   has a simpler form, namely
:&lt;math&gt;h_0(z) = \int_{\Gamma}\frac {f(w)}{w- z} dw = h_1(z),&lt;/math&gt;
and since the function &lt;math&gt;h_1&lt;/math&gt;  is clearly holomorphic on the entire &lt;math&gt;G_0&lt;/math&gt;, we can extend &lt;math&gt;h_0&lt;/math&gt;  to a holomorphic function &lt;math&gt;h&lt;/math&gt;  defined on the entire by&lt;math&gt;G \cup G_0&lt;/math&gt; 
:&lt;math&gt;   h(z) = \left\{ \begin{array}{ll} h_0(z) &amp; z \in G\\ h_1(z) &amp; z \in G_0 \end{array} \right. &lt;/math&gt;

Now &lt;math&gt;\Gamma&lt;/math&gt; is null-homologous  in , and thus
:&lt;math&gt;G \cup G_0 = \mathbb C,&lt;/math&gt;
i.e. &lt;math&gt;h&lt;/math&gt;  is an entire function. 
===Proof 8===
For &lt;math&gt;h&lt;/math&gt; we have&lt;math&gt;G_0&lt;/math&gt; the notation:
:&lt;math&gt;|h(z)| = |h_1(z)| \leq \frac 1 {dist(z, \Gamma)} L(\Gamma) \max_{\Gamma}|f|\;\;\;(*);&lt;/math&gt;
where &lt;math&gt;L(\Gamma) = \sum |n_k| L(\gamma_k)&lt;/math&gt;, if &lt;math&gt;\Gamma = n_k \cdot \gamma_k&lt;/math&gt; is.

&lt;math&gt;G_0&lt;/math&gt; contains the complement of a sufficiently large circle around 0. Therefore, the above inequality holds for all &lt;math&gt;z&lt;/math&gt; in this region: it follows that  &lt;math&gt;h&lt;/math&gt; is bounded, and by Liouville's theorem, it must be constant. If we choose a sequence &lt;math&gt;z_{\nu} \in G_0&lt;/math&gt; such that &lt;math&gt;|z_{\nu}| \geq \nu&lt;/math&gt;, the inequality (*) again implies that:
:&lt;math&gt;\lim\limits_{\nu \to \infty}(z_{\nu}) = 0,&lt;/math&gt;

thus we conculude that  &lt;math&gt; h \equiv 0&lt;/math&gt;, and in particular &lt;math&gt;h_0 \equiv 0&lt;/math&gt;; this is what we wanted to prove
==Conclusions==
From the Cauchy integral formula, it follows that every holomorphic function is infinitely differentiable because the integrand in &lt;math&gt;z&lt;/math&gt; is infinitely differentiable. We obtain the following results:

===For Circular Disks===
Let &lt;math&gt;G \subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;D&lt;/math&gt; a circular disk with &lt;math&gt;\bar D \subseteq G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Then &lt;math&gt;f&lt;/math&gt; is infinitely differentiable, and for each &lt;math&gt;n\in \mathbb N&lt;/math&gt;, we have
:&lt;center&gt;&lt;math&gt; f^{(n)}(z) = \frac{n!}{2\pi i}\int_{\partial D} \frac{f(w)}{(w-z)^{n+1}}, dw &lt;/math&gt;&lt;/center&gt;
for each &lt;math&gt;z \in D&lt;/math&gt;.

===For Cycles===
Let &lt;math&gt;G\subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;\Gamma \in C(G)&lt;/math&gt; a [[w:en:Null-homologous|null-homologous]] cycle, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; [[w:en:Holomorphic function|holomorphic]]. Then
:&lt;math&gt;   n(\Gamma, z) \cdot f^{(n)}(z) = \frac {n!}{2\pi i} \int_\Gamma \frac{f(w)}{(w-z)^{n+1}} , dw &lt;/math&gt;
for each &lt;math&gt;z \in G \setminus \mathrm{Trace}(\Gamma)&lt;/math&gt; and &lt;math&gt;n \in \mathbb N&lt;/math&gt;.

==Analyticity==
Moreover, every holomorphic function is analytic at every point, i.e., it can be expanded into a power series:

===Statement===
Let &lt;math&gt;G \subseteq \mathbb C&lt;/math&gt; be open, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Let &lt;math&gt;z_0 \in G&lt;/math&gt; and &lt;math&gt;r &gt; 0&lt;/math&gt; such that &lt;math&gt;\bar B_r(z_0) \subseteq G&lt;/math&gt;. Then &lt;math&gt;f&lt;/math&gt; can be represented on &lt;math&gt;B_r(z_0)&lt;/math&gt; by a convergent power series
:&lt;math&gt; f(z) = \sum_{n=0}^\infty a_n (z-z_0)^n &lt;/math&gt;
where the coefficients are given by
:&lt;math&gt; a_n = \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{(w-z_0)^{n+1}}, dw &lt;/math&gt;.
===Proof 1===
For &lt;math&gt;z \in B_r(z_0)&lt;/math&gt;, &lt;math&gt;w \in \partial B_r(z_0)&lt;/math&gt; we have:
:&lt;math&gt;\begin{array}{rl}   \displaystyle \frac 1{w-z} &amp;= \displaystyle\frac 1{(w- z_0) - (z-z_0)}\\          &amp;= \displaystyle \frac 1{w-z_0} \cdot \frac 1{1  - \frac{z-z_0}{w-z_0}}\\           &amp;= \displaystyle \frac 1{w-z_0} \sum_{n=0}^\infty \frac{(z-z_0)^n}{(w-z_0)^n}.   \end{array} &lt;/math&gt;

===Proof 2===
the real  converges absolutely &lt;math&gt;|z-z_0| &lt; r = |w-z_0|&lt;/math&gt; and we obtain 
:&lt;math&gt; \begin{array}{rl}                                                                                                                                              f(z) &amp;=  \displaystyle\frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{w-z} \, dw\\                                                                                 &amp;= \displaystyle \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac 1{w-z_0} \frac{f(w)(z-z_0)^n}{(w-z_0)^n}\, dw\\                                                             &amp;= \displaystyle \frac 1{2\pi i} \sum_{n=0}^\infty \int_{\partial B_r(z_0)} \frac {f(w)}{(w-z_0)^{n+1}}\, dw \cdot (z-z_0)^n\\                                          &amp;= \displaystyle \frac 1{2\pi i}  \sum_{n=0}^\infty  \int_{\partial B_r(z_0)} \frac {f(w)}{(w-z_0)^{n+1}}\, dw \cdot (z-z_0)^n                                        \end{array} &lt;/math&gt;</text>
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      <text bytes="12610" sha1="krmkp2qb0qctkymtwi6aw2yzduf6nn5" xml:space="preserve">==Introduction==
The Cauchy integral formula, alongside the [[w:en:Cauchy's integral theorem|Cauchy's integral theorem]], is one of the central statements in [[w:en:Complex analysis|complex analysis]]. Here, we present two variants: the 'classical' formula for circular disks and a relatively general version for [[w:en:Null-homologous|null-homologous]] [[w:en:Cycle (mathematics)|cycles]]. Note that we will deduce the circular disk version from Cauchy's integral theorem, but for the general variant, we proceed in the opposite direction.
==For Circular Disks==
===Statement===
Let &lt;math&gt;G \subseteq \mathbb C &lt;/math&gt; be an open set, &lt;math&gt;D&lt;/math&gt; a circular disk with &lt;math&gt;\bar D \subseteq G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Then, we have
:&lt;math&gt; f(z) = \frac 1{2\pi i}\int_{\partial D} \frac{f(w)}{w-z}, dw &lt;/math&gt;
for each &lt;math&gt;z \in D&lt;/math&gt;.
===Proof 1===
By slightly enlarging the radius of the circular disk, we find an open circular disk &lt;math&gt;U&lt;/math&gt; such that &lt;math&gt;\bar D \subseteq U \subseteq G&lt;/math&gt;. Define &lt;math&gt;g \colon U \to \mathbb C&lt;/math&gt; by
:&lt;math&gt;   g(w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} &amp; w \ne z\\ f'(z) &amp; w = z \end{array} \right. &lt;/math&gt;
===Proof 2===
The function &lt;math&gt;g&lt;/math&gt; is continuous on &lt;math&gt;U&lt;/math&gt; and holomorphic on &lt;math&gt;U -{z}&lt;/math&gt;. Thus, we can apply the [[w:en:Cauchy's integral theorem|Cauchy integral theorem]] on &lt;math&gt;U&lt;/math&gt; and obtain
:&lt;math&gt; 0 = \int_{\partial D} g(w), dw = \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} &lt;/math&gt;
For &lt;math&gt;z \in D&lt;/math&gt;, define &lt;math&gt;h(z) := \int_{\partial D} \frac{dw}{w-z}&lt;/math&gt;. Then &lt;math&gt;h&lt;/math&gt; is [[w:en:Holomorphic function|holomorphic]] with
:&lt;math&gt; h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2}  &lt;/math&gt;

===Proof 3===
Since the integrand &lt;math&gt;\frac{dw}{(w-z)^2}&lt;/math&gt; has a primitive in &lt;math&gt;D&lt;/math&gt;, we find
:&lt;math&gt; h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2} = 0 &lt;/math&gt;

===Proof 4===
Because &lt;math&gt;h'(z) =0&lt;/math&gt; throughout &lt;math&gt;D&lt;/math&gt;, it follows that &lt;math&gt;h&lt;/math&gt; is constant. Thus, &lt;math&gt;h(z)&lt;/math&gt; always takes the same value as at the center &lt;math&gt;h(z_0)&lt;/math&gt; of the disk &lt;math&gt;D&lt;/math&gt;, i.e., &lt;math&gt;h(z_0) = 2\pi i&lt;/math&gt;. Hence,
:&lt;math&gt; 0 =  \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} \iff   f(z) = \frac 1{2\pi i} \int_{\partial D}\frac{f(w)}{w-z}, dw &lt;/math&gt;
This proves the statement.

==For Cycles in Arbitrary Open Sets==
===Statement===
Let &lt;math&gt;G\subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;\Gamma&lt;/math&gt; a [[w:en:Null-homologous|null-homologous]] cycle in &lt;math&gt;G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; [[w:en:Holomorphic function|holomorphic]]. Then,
:&lt;math&gt;    n(\Gamma, z)\cdot f(z) = \frac 1{2\pi i} \int_\Gamma \frac{f(w)}{w-z} , dw  &lt;/math&gt;
for each &lt;math&gt;z \in G \setminus \mathrm{spur}(\Gamma)&lt;/math&gt;, where &lt;math&gt;n(\Gamma, \cdot)&lt;/math&gt; denotes the [[w:en:Winding number|winding number]].

===Proof 1===
Define a function &lt;math&gt;g\colon G^2 \to \mathbb C&lt;/math&gt; by
:&lt;math&gt;   g(z,w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} &amp; w \ne z\\ f'(z) &amp; w = z \end{array} \right. &lt;/math&gt;
defined.
===Proof 2:  continuous===
We demonstrate the continuity in both variables. Let &lt;math&gt;(w_0, z_0) \in U \times U&lt;/math&gt; with &lt;math&gt;z_0 \ne w_0&lt;/math&gt;, then &lt;math&gt;g&lt;/math&gt; is given in the vicinity of &lt;math&gt;(w_0, z_0)&lt;/math&gt;  by the above formula and is trivially continuous.Now let &lt;math&gt;z_0 = w_0&lt;/math&gt;. We choose a &lt;math&gt;\delta&lt;/math&gt;-neighborhood &lt;math&gt;U_{\delta}(z_0) \subset \subset G&lt;/math&gt; and examine &lt;math&gt;g(w,z) - g(z_0,z_0)&lt;/math&gt; auf &lt;math&gt;U_{\delta}(z_0) \times  U_{\delta}(z_0)&lt;/math&gt; &lt;br&gt;&lt;br&gt;.
a) In the case &lt;math&gt;w = z&lt;/math&gt;: &lt;br&gt;:
:&lt;math&gt;g(z,z) - g(z_0,z_0) = f'(z) - f'(z_0)&lt;/math&gt;

===Proof 3===
b) In the case &lt;math&gt;w \ne z&lt;/math&gt;:
:&lt;math&gt;g(w,z) - g(z_0,z_0) = \frac{f(w) - f(z)}{w-z} - f'(z_0) = \frac 1 {w - z} \int_{[z,w]}(f'(v) - f'(z_0)) dv&lt;/math&gt;

Now, as a consequence of Cauchy's formulas for circles! the derivative &lt;math&gt;f'&lt;/math&gt; is continuous in &lt;math&gt;z_0&lt;/math&gt;.  For a given &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; we can choose  &lt;math&gt;\delta &gt; 0&lt;/math&gt; such that
:&lt;math&gt;|f'(v) - f'(z_0)| &lt; \epsilon &lt;/math&gt;
for all &lt;math&gt;v \in U_{\delta} (z_0)&lt;/math&gt;. &lt;br&gt;
===Proof 4===
This implies, in case a:
:&lt;math&gt;|g(z,z) - g(z_0,z_0)| &lt; \epsilon;&lt;/math&gt;
and in case b:
:&lt;math&gt;|g(w,z) - g(z_0, z_0)| \leq \frac 1 {|w - z|} |w - z| \cdot  \sup\limits_{w \in [w,z]} |f'(v)-f'(z_0)| &lt; \epsilon.&lt;/math&gt;
We now define
:&lt;math&gt;h_0 (z) = \int_{\Gamma} g(w,z) dw.&lt;/math&gt;
&lt;math&gt;h_0&lt;/math&gt; function  is continuous on whole of &lt;math&gt;G&lt;/math&gt; ; we will show that it is even holomorphic. For this, we use Morera's theorem.

===Proof 5===
Let &lt;math&gt;\gamma&lt;/math&gt; be the oriented boundary of a triangle that lies entirely with in &lt;math&gt;G&lt;/math&gt; . We must show
:&lt;math&gt;\int_{\gamma} h_0(z) dz = 0&lt;/math&gt;
prove it is
:&lt;math&gt;\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\,  dw = 0.&lt;/math&gt;
because the integrations are commutable due to the continuity of the integrand on &lt;math&gt;G \times G&lt;/math&gt;  For fixed , &lt;math&gt;w&lt;/math&gt; the function  is &lt;math&gt;g(w,z)&lt;/math&gt; in the Variable &lt;math&gt;z&lt;/math&gt; continuous in  and holomorphic for &lt;math&gt;w \ne z&lt;/math&gt;, hence holomorphic everywhere.
===Proof 6===
By Goursat's theorem, it follows that
:&lt;math&gt;\int_{\gamma} g(w,z) dz = 0.&lt;/math&gt;
this of course also mean that
:&lt;math&gt;\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\,  dw = 0.&lt;/math&gt;

so far we have not yet exploited the conditions above &lt;math&gt;\Gamma&lt;/math&gt;. We will do so

:&lt;math&gt;G_0 = \{z \in \mathbb C: n (\Gamma, z) = 0\}&lt;/math&gt;.
===Proof 7===
Since on &lt;math&gt;G \cap G_0&lt;/math&gt; the function &lt;math&gt;h_0&lt;/math&gt;   has a simpler form, namely
:&lt;math&gt;h_0(z) = \int_{\Gamma}\frac {f(w)}{w- z} dw = h_1(z),&lt;/math&gt;
and since the function &lt;math&gt;h_1&lt;/math&gt;  is clearly holomorphic on the entire &lt;math&gt;G_0&lt;/math&gt;, we can extend &lt;math&gt;h_0&lt;/math&gt;  to a holomorphic function &lt;math&gt;h&lt;/math&gt;  defined on the entire by&lt;math&gt;G \cup G_0&lt;/math&gt; 
:&lt;math&gt;   h(z) = \left\{ \begin{array}{ll} h_0(z) &amp; z \in G\\ h_1(z) &amp; z \in G_0 \end{array} \right. &lt;/math&gt;

Now &lt;math&gt;\Gamma&lt;/math&gt; is null-homologous  in , and thus
:&lt;math&gt;G \cup G_0 = \mathbb C,&lt;/math&gt;
i.e. &lt;math&gt;h&lt;/math&gt;  is an entire function. 
===Proof 8===
For &lt;math&gt;h&lt;/math&gt; we have&lt;math&gt;G_0&lt;/math&gt; the notation:
:&lt;math&gt;|h(z)| = |h_1(z)| \leq \frac 1 {dist(z, \Gamma)} L(\Gamma) \max_{\Gamma}|f|\;\;\;(*);&lt;/math&gt;
where &lt;math&gt;L(\Gamma) = \sum |n_k| L(\gamma_k)&lt;/math&gt;, if &lt;math&gt;\Gamma = n_k \cdot \gamma_k&lt;/math&gt; is.

&lt;math&gt;G_0&lt;/math&gt; contains the complement of a sufficiently large circle around 0. Therefore, the above inequality holds for all &lt;math&gt;z&lt;/math&gt; in this region: it follows that  &lt;math&gt;h&lt;/math&gt; is bounded, and by Liouville's theorem, it must be constant. If we choose a sequence &lt;math&gt;z_{\nu} \in G_0&lt;/math&gt; such that &lt;math&gt;|z_{\nu}| \geq \nu&lt;/math&gt;, the inequality (*) again implies that:
:&lt;math&gt;\lim\limits_{\nu \to \infty}(z_{\nu}) = 0,&lt;/math&gt;

thus we conculude that  &lt;math&gt; h \equiv 0&lt;/math&gt;, and in particular &lt;math&gt;h_0 \equiv 0&lt;/math&gt;; this is what we wanted to prove
==Conclusions==
From the Cauchy integral formula, it follows that every holomorphic function is infinitely differentiable because the integrand in &lt;math&gt;z&lt;/math&gt; is infinitely differentiable. We obtain the following results:

===For Circular Disks===
Let &lt;math&gt;G \subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;D&lt;/math&gt; a circular disk with &lt;math&gt;\bar D \subseteq G&lt;/math&gt;, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Then &lt;math&gt;f&lt;/math&gt; is infinitely differentiable, and for each &lt;math&gt;n\in \mathbb N&lt;/math&gt;, we have
:&lt;center&gt;&lt;math&gt; f^{(n)}(z) = \frac{n!}{2\pi i}\int_{\partial D} \frac{f(w)}{(w-z)^{n+1}}, dw &lt;/math&gt;&lt;/center&gt;
for each &lt;math&gt;z \in D&lt;/math&gt;.

===For Cycles===
Let &lt;math&gt;G\subseteq \mathbb C&lt;/math&gt; be an open set, &lt;math&gt;\Gamma \in C(G)&lt;/math&gt; a [[w:en:Null-homologous|null-homologous]] cycle, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; [[w:en:Holomorphic function|holomorphic]]. Then
:&lt;math&gt;   n(\Gamma, z) \cdot f^{(n)}(z) = \frac {n!}{2\pi i} \int_\Gamma \frac{f(w)}{(w-z)^{n+1}} , dw &lt;/math&gt;
for each &lt;math&gt;z \in G \setminus \mathrm{Trace}(\Gamma)&lt;/math&gt; and &lt;math&gt;n \in \mathbb N&lt;/math&gt;.

==Analyticity==
Moreover, every holomorphic function is analytic at every point, i.e., it can be expanded into a power series:

===Statement===
Let &lt;math&gt;G \subseteq \mathbb C&lt;/math&gt; be open, and &lt;math&gt;f \colon G \to \mathbb C&lt;/math&gt; holomorphic. Let &lt;math&gt;z_0 \in G&lt;/math&gt; and &lt;math&gt;r &gt; 0&lt;/math&gt; such that &lt;math&gt;\bar B_r(z_0) \subseteq G&lt;/math&gt;. Then &lt;math&gt;f&lt;/math&gt; can be represented on &lt;math&gt;B_r(z_0)&lt;/math&gt; by a convergent power series
:&lt;math&gt; f(z) = \sum_{n=0}^\infty a_n (z-z_0)^n &lt;/math&gt;
where the coefficients are given by
:&lt;math&gt; a_n = \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{(w-z_0)^{n+1}}, dw &lt;/math&gt;.
===Proof 1===
For &lt;math&gt;z \in B_r(z_0)&lt;/math&gt;, &lt;math&gt;w \in \partial B_r(z_0)&lt;/math&gt; we have:
:&lt;math&gt;\begin{array}{rl}   \displaystyle \frac 1{w-z} &amp;= \displaystyle\frac 1{(w- z_0) - (z-z_0)}\\          &amp;= \displaystyle \frac 1{w-z_0} \cdot \frac 1{1  - \frac{z-z_0}{w-z_0}}\\           &amp;= \displaystyle \frac 1{w-z_0} \sum_{n=0}^\infty \frac{(z-z_0)^n}{(w-z_0)^n}.   \end{array} &lt;/math&gt;

===Proof 2===
the real  converges absolutely &lt;math&gt;|z-z_0| &lt; r = |w-z_0|&lt;/math&gt; and we obtain 
:&lt;math&gt; \begin{array}{rl}                                                                                                                                              f(z) &amp;=  \displaystyle\frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{w-z} \, dw\\                                                                                 &amp;= \displaystyle \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac 1{w-z_0} \frac{f(w)(z-z_0)^n}{(w-z_0)^n}\, dw\\                                                             &amp;= \displaystyle \frac 1{2\pi i} \sum_{n=0}^\infty \int_{\partial B_r(z_0)} \frac {f(w)}{(w-z_0)^{n+1}}\, dw \cdot (z-z_0)^n\\                                          &amp;= \displaystyle \frac 1{2\pi i}  \sum_{n=0}^\infty  \int_{\partial B_r(z_0)} \frac {f(w)}{(w-z_0)^{n+1}}\, dw \cdot (z-z_0)^n                                        \end{array} &lt;/math&gt;
== See also ==

*[[w:en:Category:Complex analysis|Category:Complex analysis]]

*[[Complex analysis/Maximum principle|Maximum principle]]

*[[Complex analysis/Cycle|Cycle]]
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  <page>
    <title>Boolf prop/3-ary/nameless 2</title>
    <ns>0</ns>
    <id>317454</id>
    <redirect title="Boolf prop/3-ary/twin mentor" />
    <revision>
      <id>2693061</id>
      <timestamp>2024-12-23T22:26:35Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>Watchduck moved page [[Boolf prop/3-ary/nameless 2]] to [[Boolf prop/3-ary/twin mentor]]</comment>
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      <text bytes="42" sha1="5qxfzqf0y5ecwce7cpbarc1o1f077zq" xml:space="preserve">#REDIRECT [[Boolf prop/3-ary/twin mentor]]</text>
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  <page>
    <title>Boolf prop/3-ary/great twin mentor</title>
    <ns>0</ns>
    <id>317455</id>
    <revision>
      <id>2693064</id>
      <timestamp>2024-12-23T22:27:50Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
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      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; &lt;/div&gt;  {| class=&quot;wikitable sortable boolf-blocks&quot; !class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt; !class=&quot;prop&quot;| great twin mentor !class=&quot;block&quot;| block |- |class=&quot;size&quot;| 16 |class=&quot;prop&quot;| 0 |class=&quot;block&quot;| &lt;span class=&quot;blo...&quot;</comment>
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      <text bytes="5006" sha1="pkhfk8tf0yb31et008l14sb7siox01k" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| great twin mentor
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 1, 40, 41, 72, 73, 96, 97, 128, 129, 168, 169, 200, 201, 224, 225]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_80879844822266053283405129358099457325829692252436074174428936667139.svg|420px]]
|-
|class=&quot;size&quot;| 16
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 3, 42, 43, 74, 75, 98, 99, 130, 131, 170, 171, 202, 203, 226, 227]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_323519379289064213133620517432397829303318769009744296697715746668556.svg|420px]]
|-
|class=&quot;size&quot;| 16
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 5, 44, 45, 76, 77, 100, 101, 132, 133, 172, 173, 204, 205, 228, 229]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1294077517156256852534482069729591317213275076038977186790862986674224.svg|420px]]
|-
|class=&quot;size&quot;| 16
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 7, 46, 47, 78, 79, 102, 103, 134, 135, 174, 175, 206, 207, 230, 231]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5176310068625027410137928278918365268853100304155908747163451946696896.svg|420px]]
|-
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[8, 9, 32, 33, 64, 65, 104, 105, 136, 137, 160, 161, 192, 193, 232, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_20705239040390522667514812134295913292233688939008497630891606326379264.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 41
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[10, 11, 34, 35, 66, 67, 106, 107, 138, 139, 162, 163, 194, 195, 234, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_82820956161562090670059248537183653168934755756033990523566425305517056.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 73
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[12, 13, 36, 37, 68, 69, 108, 109, 140, 141, 164, 165, 196, 197, 236, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_331283824646248362680236994148734612675739023024135962094265701222068224.svg|420px]]
|-
|class=&quot;size&quot;| 16
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[14, 15, 38, 39, 70, 71, 110, 111, 142, 143, 166, 167, 198, 199, 238, 239]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1325135298584993450720947976594938450702956092096543848377062804888272896.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 247
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[16, 17, 56, 57, 88, 89, 112, 113, 144, 145, 184, 185, 216, 217, 240, 241]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5300541510272028067981238557612406035305574711455650557095374793417621504.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 72
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 19, 58, 59, 90, 91, 114, 115, 146, 147, 186, 187, 218, 219, 242, 243]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_21202166041088112271924954230449624141222298845822602228381499173670486016.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 40
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 21, 60, 61, 92, 93, 116, 117, 148, 149, 188, 189, 220, 221, 244, 245]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_84808664164352449087699816921798496564889195383290408913525996694681944064.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 151
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[22, 23, 62, 63, 94, 95, 118, 119, 150, 151, 190, 191, 222, 223, 246, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_339234656657409796350799267687193986259556781533161635654103986778727776256.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 97
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[24, 25, 48, 49, 80, 81, 120, 121, 152, 153, 176, 177, 208, 209, 248, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1356938545751033293538250728033216973519827038306860900738112312205591445504.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 222
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[26, 27, 50, 51, 82, 83, 122, 123, 154, 155, 178, 179, 210, 211, 250, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5427754183004133174153002912132867894079308153227443602952449248822365782016.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 190
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|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[30, 31, 54, 55, 86, 87, 126, 127, 158, 159, 182, 183, 214, 215, 254, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_86844066928066130786448046594125886305268930451639097647239187981157852512256.svg|420px]]
|}

[[Category:Boolf prop/3-ary|great twin mentor]]</text>
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  </page>
  <page>
    <title>Boolf prop/3-ary/leveled praetor sword</title>
    <ns>0</ns>
    <id>317456</id>
    <redirect title="Boolf prop/3-ary/greater twin mentor" />
    <revision>
      <id>2693066</id>
      <timestamp>2024-12-23T22:34:14Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>Watchduck moved page [[Boolf prop/3-ary/leveled praetor sword]] to [[Boolf prop/3-ary/greater twin mentor]]</comment>
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      <text bytes="50" sha1="drtujdt5zxvwzuhur8xcfn07jzon6zc" xml:space="preserve">#REDIRECT [[Boolf prop/3-ary/greater twin mentor]]</text>
      <sha1>drtujdt5zxvwzuhur8xcfn07jzon6zc</sha1>
    </revision>
  </page>
  <page>
    <title>File:LIB.2A.Shared.20241224.pdf</title>
    <ns>6</ns>
    <id>317457</id>
    <revision>
      <id>2693081</id>
      <timestamp>2024-12-24T00:26:06Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=LIB.2A: Shared Libraries (20241224 - 20241223)
|Source={{own|Young1lim}}
|Date=2024-12-24
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
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      <text bytes="269" sha1="4ee6cr7htkh9g1v3njqggb4alq0de15" xml:space="preserve">== Summary ==
{{Information
|Description=LIB.2A: Shared Libraries (20241224 - 20241223)
|Source={{own|Young1lim}}
|Date=2024-12-24
|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}}</text>
      <sha1>4ee6cr7htkh9g1v3njqggb4alq0de15</sha1>
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  <page>
    <title>File:DIR.1A.Names.20241224.pdf</title>
    <ns>6</ns>
    <id>317458</id>
    <revision>
      <id>2693083</id>
      <timestamp>2024-12-24T03:01:55Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=DIR.1A: Shared Library Names (20241224 - 20241223)
|Source={{own|Young1lim}}
|Date=2024-12-24
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}</comment>
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      <text bytes="273" sha1="gpsb6juoi2iwt2d9cixwfz4equ1v224" xml:space="preserve">== Summary ==
{{Information
|Description=DIR.1A: Shared Library Names (20241224 - 20241223)
|Source={{own|Young1lim}}
|Date=2024-12-24
|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}}</text>
      <sha1>gpsb6juoi2iwt2d9cixwfz4equ1v224</sha1>
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  <page>
    <title>File:DIR.2A.Manage.20241224.pdf</title>
    <ns>6</ns>
    <id>317459</id>
    <revision>
      <id>2693087</id>
      <timestamp>2024-12-24T03:28:02Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=DIR.2A: Managing Shared Libraries (20241224 - 20241223)
|Source={{own|Young1lim}}
|Date=2024-12-24
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}</comment>
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      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="277" sha1="179zny3lgsjzqutalxfkerfpaxcn3rz" xml:space="preserve">== Summary ==
{{Information
|Description=DIR.2A: Managing Shared Libraries (20241224 - 20241223)
|Source={{own|Young1lim}}
|Date=2024-12-24
|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}}</text>
      <sha1>179zny3lgsjzqutalxfkerfpaxcn3rz</sha1>
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  <page>
    <title>User:Muhammad Azmi Ash Shiddiqiey</title>
    <ns>2</ns>
    <id>317460</id>
    <revision>
      <id>2693089</id>
      <timestamp>2024-12-24T03:43:29Z</timestamp>
      <contributor>
        <username>Muhammad Azmi Ash Shiddiqiey</username>
        <id>2995390</id>
      </contributor>
      <comment>Menambahkan tanggal lahir dan tempat lahir</comment>
      <origin>2693089</origin>
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      <text bytes="433" sha1="ktjx3xuh4x5i8ov0jcush76953juzii" xml:space="preserve">Halaman ini adalah untuk menampilkan profile seorang pelajar bernama Muhammad Azmi Ash Shiddiqiey yang berasal dari negara Indonesia. Dia lahir di kota bontang tanggal 10 April 2019 dengan berat sekitar 3,9 Kg dan tinggi 49 cm. Lahir di rumah sakit bernama Rumah Sakit Islam YABIS pada pukul 13.30 WITA. Muhammad Azmi Ash Shiddiqiey memiliki ayah bernama Setiawan dan ibu bernama Ani Hidayati. Dia adalah anak ke-3 dari 4 Bersaudara.</text>
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  <page>
    <title>File:VLSI.Arith.5A.CSkip.20241224.pdf</title>
    <ns>6</ns>
    <id>317461</id>
    <revision>
      <id>2693093</id>
      <timestamp>2024-12-24T04:48:44Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=VLSI.Arith: Carry Skip Adders 1A (20241224 - 20241223)
|Source={{own|Young1lim}}
|Date=2024-12-24
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
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      <text bytes="276" sha1="ndyu0ej08zd7h8z6dmmww29ya7epham" xml:space="preserve">== Summary ==
{{Information
|Description=VLSI.Arith: Carry Skip Adders 1A (20241224 - 20241223)
|Source={{own|Young1lim}}
|Date=2024-12-24
|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}}</text>
      <sha1>ndyu0ej08zd7h8z6dmmww29ya7epham</sha1>
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  <page>
    <title>User talk:98.186.206.121</title>
    <ns>3</ns>
    <id>317463</id>
    <revision>
      <id>2693100</id>
      <timestamp>2024-12-24T09:07:02Z</timestamp>
      <contributor>
        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <comment>New resource with &quot;==December 2024== {{subst:uw-vandalism1}} ~~~~&quot;</comment>
      <origin>2693100</origin>
      <model>wikitext</model>
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      <text bytes="510" sha1="3a8gksl05frbfxn42x08mwa1g25iwdk" xml:space="preserve">==December 2024==
[[File:Information.svg|25px|alt=Information icon]] Hello, I’m letting you know that one or more of your recent contributions have been reverted because they did not appear constructive. If you would like to experiment, please use the [[Wikiversity:Sandbox|sandbox]] or ask for assistance at the [[Wikiversity:Colloquium|Colloquium]]. Thank you. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 09:07, 24 December 2024 (UTC)</text>
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  <page>
    <title>File:C04.SA0.PtrOperator.1A.20241224.pdf</title>
    <ns>6</ns>
    <id>317464</id>
    <revision>
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      <timestamp>2024-12-24T10:28:38Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=C04.SA0: Address-of and de-reference operators 1A (20241224 - 20241223) 
|Source={{own|Young1lim}}
|Date=2024-12-24
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}</comment>
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      <text bytes="294" sha1="su0rbq5ecyy823edd0oagzqc5glc6bx" xml:space="preserve">== Summary ==
{{Information
|Description=C04.SA0: Address-of and de-reference operators 1A (20241224 - 20241223) 
|Source={{own|Young1lim}}
|Date=2024-12-24
|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}}</text>
      <sha1>su0rbq5ecyy823edd0oagzqc5glc6bx</sha1>
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