Wikiversity enwikiversity https://en.wikiversity.org/wiki/Wikiversity:Main_Page MediaWiki 1.44.0-wmf.5 first-letter Media Special Talk User User talk Wikiversity Wikiversity talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk School School talk Portal Portal talk Topic Topic talk Collection Collection talk Draft Draft talk TimedText TimedText talk Module Module talk 12 1654 2690212 2669079 2024-12-04T04:21:46Z 38.158.204.171 /* Arrow icon */ DawnawHsihsi(dawnawhsihsi) 2690212 wikitext text/x-wiki [[w:Hyperlink|Hyperlinks]] allow users to move between pages. For some basic information about using hyperlinks, see [[Help:Editing#Links, URLs]]. There are three general types of hyperlinks recognized by [[MediaWiki]], each with associated [[w:Cascading Style Sheets|CSS formatting]] to distinguish them. This page (below) is like a user manual page about links. If you are new to making links, you might prefer to explore [[Making links]], a short tutorial about how to make links on [[Wikiversity]] pages. == Wikilinks == A '''wikilink''' or '''internal link''' links a page to another page within the same project. To link to a page, you need to put the name of the page within double square brackets <nowiki>[[like this]]</nowiki>. So, for example, if you add <nowiki>[[Technology in the classroom]]</nowiki> to a page in edit mode, it will create a link to [[Technology in the classroom]]. You can also name this link anything by adding a "|" (not the letter l, but the vertical line character) and other descriptive text after this character - eg. adding <nowiki>[[Technology in the classroom|a page about teaching with technology]]</nowiki> will display as: [[Technology in the classroom|a page about teaching with technology]]. '''Further detail:''' *<nowiki>[[a]]</nowiki> gives [[a]]. *<nowiki>[[a|b]]</nowiki> gives [[a|b]] (link to a, labelled b). *<nowiki>[[a]]b</nowiki> gives [[a]]b, just like <nowiki>[[a|ab]]</nowiki> does: [[a|ab]]. *<nowiki>[[a|b]]c</nowiki> gives [[a|b]]c, just like <nowiki>[[a|bc]]</nowiki> does: [[a|bc]]. *<nowiki>a[[b]]</nowiki> gives a[[b]]. *<nowiki>[[a]]<</nowiki>nowiki>b</nowiki> gives [[a]]<nowiki>b</nowiki>. *<nowiki>[[a]]''b''</nowiki> gives [[a]]''b''. *<nowiki>''[[a]]''b</nowiki> gives ''[[a]]''b. *<nowiki>[[a|b]]c<</nowiki>nowiki>d</nowiki> gives [[a|b]]c<nowiki>d</nowiki>. *<nowiki>[[a]][[b]]</nowiki> gives [[a]][[b]] (two links, but looking equal to the single link [[ab]]), even if the links are underlined ([[a]] [[b]] and [[a b]] look the same only if links are not underlined). Links with parameters (the link name) are said to be "piped" because of the pipe symbol used ( | ). MediaWiki automatically checks if the target of a wikilink exists ("existence detection"). If the page doesn't exist, the link leads to the editing screen, and it is assigned the class "new". Such wikilinks are nicknamed "red links" because they are colored red in the default stylesheet on a default installation of MediaWiki. Red links are useful in determining the current status of the page (created or not created), create incoming links to a future page, facilitates and incites page creation. Note that the image, category, and interlanguage syntax are the same as the wikilink syntax. Attempting to link normally will place the image on the page, add the page to the category and create an interlanguage link at the edge of the page. This can be prevented by prefixing a colon, which escapes the specific syntax. For example, <code><nowiki>[[:Category:Help]]</nowiki></code>, <code><nowiki>[[:fr:Help:Link]]</nowiki></code>, and <code><nowiki>[[:Image:Mediawiki.png]]</nowiki></code>. The existence of an internal link from a page to an existing or non-existing page is recorded in the [[pagelinks table]]. ===Stub feature=== A wikilink to an existing page will be in class 'stub' if the page is in the main namespace, it is not a redirect, '''''and''''' the number of bytes of the wikitext is less than the "threshold for stub display" set in the [[Help:Preferences|user's preferences]]. This allows users to immediately identify links to very short pages that probably need to be expanded. Alternately, a user may set a very high threshold to achieve any of the following: * Identify links to very large pages. However, the criterion is the size of the wikitext; possible inclusion of templates and images can make the rendered page large, even if the amount of wikitext is small. * Determine at a glance whether a link leads to the main namespace or not. However, this does not take into account ''redirects'' to the main namespace (even if the redirect itself is in the main namespace). * Identify links to redirects, for clean-up work such as bypassing redirects. However, section linking to a "stub" does not work. Although this is normally a minor issue, this may cause problems with users who set a very high threshold. == Interwiki links == An '''[[Help:Interwiki linking|interwiki link]]''' links a page to a page on another website. Unlike the name suggests, the target site need not be a wiki, but it has to be on the [[m:Interwiki map|interwiki map]] specified for the source wiki. These links have the associated CSS class "extiw". These are in the same form as wikilinks above, but take a prefix which specifies the target site. For example, on Wikimedia projects and many other wikis <code><nowiki>[[wikipedia:Main Page]]</nowiki></code> links to Wikipedia's main page. The prefix can be hidden using the same piped syntax as wikilinks. === Interwiki links to the same project === Although interwiki links can be used to point to a wiki from itself, this is not generally recommended. MediaWiki does not detect whether or not the target page of an interwiki list exists, so there is no special formatting and the link is always to the view page. Further, MediaWiki does not check if the page is linking to itself. A [[Help:Self link|self wikilink]] is bolded (like [[{{NAMESPACE}}:{{PAGENAME}}]]), whereas a self interwiki link is normal ([[m:{{NAMESPACE}}:{{PAGENAME}}]]). Pros: * A copy of the wikitext on a sister project may still point to the same page. Sometimes two prefixes are needed for that purpose, e.g. [[w:de:a]]. == External links == {{for|the policy proposal on which links are appropriate|Wikiversity:External links}} External links use absolute URLs that link directly to any webpage. External links are in the form <code><nowiki>[http://www.example.org link name]</nowiki></code> (resulting in [http://www.example.org link name]), with the link name separated from the URL by a space. Links without link names will be numbered: <code><nowiki>[http://www.example.org]</nowiki></code> becomes [http://www.example.org]. Links with no square brackets will be displayed in their entirety: http://www.example.org. See [[m:Help:URL|URLs in external links]] for more detailed information. [[Special:Linksearch]] finds all pages linking to a given site. === External links to the same project === External links are often used to use special URL parameters in links. This allows links directly to the edit history of a page, to a page in edit view, a diff of two versions, et cetera. They can also be used to create a [[Help:Navigational image|navigational image]]. However, the use of external links to link to a normal page on the same project is not recommended. These links benefit from none of the features of a wikilink, and may break the web of links when the content is exported to another domain. ===Arrow icon=== Monobook skin produces an arrow icon after every external link. This can be suppressed with class="plainlinks": *<nowiki><</nowiki>span class="plainlinks">http<nowiki>://a</</nowiki>span> gives <span class="plainlinks">http://a</span> *http<nowiki>://a</nowiki> gives http://a DawnawHsihsi(dawnawhsihsi)wikimedia ယခုနေရာကစာရေးရမရတော့မသိပါဘူးခင်ဗျာ။ ကျနော့ဆရာတွေက အိမ်လိုက်ပို့ကြတယ်။သိပ်ချစ်စရာကောင်းသော ရိုသေလေးစားရသူတွေပါ။ ကျနော်ကလတ်တလောပြန်ရန်အစီအစဥ်မရှိသေးပါ။ လောကကြီးထဲလေ့လာစရာတွေကို နိုင်သလောက် wikimedia ၏နောက်ပါအဖြစ်လိုက်ခွင့်ရရင် ကျနော်ကံကောင်ပါပြီ၊ ခတ်တာက ကျနော်လိုက်နာရမည့်စနစ်ကိုနားမလည်ခြင်းပါ။ ယခင်ကဆို fbနှင့်goole အကောင့်များစွာဖြစ်သွားတာ အဲ့တာကြောင့်ပါခင်ဗျာ။ တတ်လေးချခွင့်ရလို့ တက်ပြလိုသည်ကိုတင်ပြခဲ့ခြင်းပါ။ ကျနော့အနေဖြင့်တော့ ထိန်းသိမ်းနိုင်ဖိုးကြိုးပန်းရင်း ပျက်ယွင်းမှု့များနှင့်အတူ ပြုတ်ကျကျခဲ့တာပါပဲ။ မိသားစုများ ကျန်းမာကြပါစေ@DawnawHsihsi(dawnawhsihsi) == Section linking == === Headings === Links in the form <code><nowiki>[[#heading_name]]</nowiki></code> will link to the corresponding section header on the same page. === Anchors === {{shortcut|WV:ANCHOR}} Links in the form <code><nowiki>[[#anchor_name]]</nowiki></code> will link to any anchor named "anchor_name" on the page. This may be either a heading named "anchor_name", or an arbitrary position. <code><nowiki>[[#top]]</nowiki></code> is a reserved name that links to the [[#top|top of a page]]. It is possible to create an arbitrary anchor name using the HTML code <code><nowiki><div id="anchor_name"></div></nowiki></code>. Anchor links can also be appended to any type of link; for more information, see [[w:Help:Section#Section_linking]]. === Problems with page name conversion === Note that if the page name is automatically converted (for example, from "/wiki/main Page" to "/wiki/Main Page"), the section link will still work but will disappear from the address bar. As a consequence, this will make it more difficult to bookmark the section itself. This is not applicable for wikilinks, because the conversions have already taken place on Preview or Save of the referring page. For example, consider [[w:Wikipedia:how_to_edit_a_page#Links_and_URLs|http://en.wikipedia.org/wiki/Wikipedia:how_to_edit_a_page#Links_and_URLs]]. In this case, the anchor part of the address will disappear because the "how" will be converted to "How". === Redirects with section links === A [[Help:Redirect|redirect]] to a page section does not go to the section. However, one can add the section anyway as a clarification, and it will work if the redirect is manually clicked from the redirect page. However, links with a section to a redirect will lead to the section on the redirect's page. ==Subpage feature== MediaWiki has a subpage feature, although activation depends on project and namespace. If activated, the following applies (if not, "A/b" is just a page with that name). A [[w:tree structure|tree structure]] of pages is established by using forward slashes in pagenames: A/b is a child of A, hence A is a parent of A/b; also A/b/c is a child of A/b; A/a, A/b, and A/c are siblings. At the top of the subpage body links to all ancestor pages are shown automatically, without any corresponding wikitext. The links show up even if the child page does not exist, but the sequence of ancestors stops before any non-existing ancestor page (e.g., if the grandparent page does not exist, the parent page is not shown either). Like most letters of a page name, the first letter after the slash is case-sensitive; "/subpage" and "/Subpage" are different pages. [[Help:What links here|What links here]] and [[Help:Related changes|Related changes]] ignore these automatic links. === Relative links === Relative links still work if all pages of a tree are renamed according a name change of the root, including making it a child of a new root. Inside a subpage hierarchy the following relative links can be used: * <nowiki>[[../]]</nowiki> links to the parent of the current subpage, e.g., on A/b it links to A, on A/b/c it links to A/b. * <nowiki>[[../s]]</nowiki> links to a sibling of the current subpage, e.g., on A/b, it links to A/s. *<nowiki>[[/s]]</nowiki> links to a subpage, e.g. on A it is the same as <nowiki>[[A/s]]</nowiki>. See also [[w:Wikipedia:Subpages]], and the example pages [[m:Link/a/b]] and [[m:Help:Link/a/b]]. For the latter the subpage feature does not work because of the namespace. === User space === Subpages of a user page (<code><nowiki>[[User:Username/Subpage]]</nowiki></code>) are considered to be in that user's "user space". Rules are often relaxed in a user's own subpages, whereas they are typically tightened for a user editing another user's subpages. ===Unintended subpage structure=== Any slash in a pagename causes a subpage structure, e.g. [[Subpage demo Season 2006/2007]] is a subpage of "Subpage demo Season 2006". As long as the latter does not exist, this has no effect on the former, However, a page with a slash in its name cannot be the root page of a subpage structure. For example, [[Subpage demo Season 2006/2007 /soccer]] does not show its parent, because its unintended grandparent does not exist. A dummy grandparent page can fix this. === Subpage activation === Wikipedia has this feature activated in all talk namespaces and the user and project namespace. The Meta-Wiki also has it in the main namespace. The default is set in [[mw:Help:Configuration settings|DefaultSettings.php]][http://cvs.sourceforge.net/viewcvs.py/wikipedia/phpwiki/newcodebase/DefaultSettings.php?rev=1.21&view=markup]. As of revision 1.21, the following namespaces have it activated by default: Special, Main talk, User and User_talk, Meta_talk, and Image_talk. Settings per project are changed in [[LocalSettings.php]][http://cvs.sourceforge.net/viewcvs.py/wikipedia/phpwiki/newcodebase/LocalSettings.php?rev=1.25&view=markup]. == Miscellaneous == === Linking to a page with images === It is possible to use images as links to other pages. For more information, see [[Help:Navigational images|use an image as a link to a page]]. === "Hover box" on links === On some browsers, holding the cursor over link will show a hover box containing the text of the link's HTML title attribute. MediaWiki sets this to the target page name (without the possible section indication) if it's a wikilink, the page name with prefix if it's an interwiki link, and the URL if it's an external link. This can be switched off in the [[Help:Preferences|user preferences]]. The browser may also show similar info, but with the possible section indication, in the address bar. For these effects a piped link is useful even if it not followed; for example, for displaying the meaning of an acronym (e.g. [[neutral point of view|NPOV]]) or any other remark. It is possible to produce a hover box without a link, see {{tim|H:title}}. === Disallowed characters === In internal and interwiki link style, a plus sign in a page name is not allowed, the HTML and hence the rendered page just shows the wikitext, e.g. [[a+b]]. In external link style a plus sign in the URL is retained. It is often equivalent with a space. See also below. In accordance with the rules explained in [[Help:Page name]], conversions are automatically made to [[Help:Special characters|non-literal characters]] in wiki and interwiki links. For example, "<code><nowiki>[[Help:Page%20name]]</nowiki></code>" becomes "[[Help:Page name]]". However, the opposite is true for external links; literal characters are converted into non-literal characters. For example, most browsers will convert ".../wiki/!" to ".../wiki/%21". A code like %70 in a redirect disables it, although the link works from the redirect page. For a redirect that works, the redirect page shows the canonical form of the target, unlike its preview page, which renders the link in the usual way. === Special pipe syntax === Using an empty pipe syntax on wiki and interwiki links will hide interwiki prefixes and parentheses. For example, <nowiki>[[w:Mercury (planet)|]]</nowiki> becomes [[w:Mercury (planet)|Mercury]]. This pipe syntax should only be used where the unqualified reference is not ambiguous, such as in an article about the solar system. See [[Help:Piped link]]. === Additional effects of links === *[[Help:Related changes|Related changes]] *[[Help:What links here|Backlink]]s *[[Help:Preferences#Date_format|Date format]] * Using a space after the pipe syntax (<nowiki>[[Main page| ]]</nowiki>) produces (perhaps depending on the browser) a space only, not a link ("[[Main page| ]]"), but it is treated as a link for the "what links here" feature. ===Links from a page=== With [[query]] the links from page ''pagename'', sorted by namespace, and for each namespace alphabetically, are given by <nowiki>{{SERVER}}{{SCRIPTPATH}}</nowiki>/query.php?what=links&titles=''pagename'' , e.g. {{SERVER}}{{SCRIPTPATH}}/query.php?what=links&titles={{FULLPAGENAME}} . ==See also== *[[Help:Calculation]] *[[Help:Interwiki linking]] *[[Help:Piped link]] *[[Help:Self link]] *[[Help:Template#Restrictions]] (and the next section) *[[Help:URL]] *[[Help:What links here]] *[[m:Parser testing/replaceInternalLinks]] *[[m:Parser testing/replaceExternalLinks]] *[[m:Links table]] *[[m:Brokenlinks table]] *[[w:Hyperlink|Hyperlink]] *[[w:Template:linkless|Linkless]] *[[Making links]] *[[w:Red Link|Red Link]] *[[w:Wikipedia:Canonicalization|Wikipedia:Canonicalization]] [[Category:Help]] [[es:Ayuda:Enlace]] ci30qjoeaplqzmxg7t98m7ag1it5e12 102 1664 2690213 2607670 2024-12-04T04:23:02Z 2600:1012:B138:9A50:9806:D10A:21C7:B9D6 2690213 wikitext text/x-wiki __NOTOC__ __NOEDITSECTION__ {{{{#titleparts:Portal:Humanities|1}}/start tab}} {{box-transclude|Introduction|The Humanities Portal}} <div style="float:left; width:66%; min-width:300px;"> {{Portal:Humanities/box-header|Featured Resource|Portal:Humanities/Featured Resource}} {{#invoke:Portals|lede|{{#invoke:Portals|randomlink|Portal:Humanities/Featured Resource}}}} {{clear}} {{Portal:Humanities/box-footer|}} {{Portal:Humanities/box-header|Featured Picture|Portal:Humanities/Featured Picture}} [[{{#invoke:Portals|randomlink|Portal:Humanities/Featured Picture}}]] {{Portal:Humanities/box-footer|}} </div> <div style="float:right; width:33%; min-width:150px;"> {{box-transclude|Categories}} {{box-transclude|Related Categories}} {{box-transclude|Related Portals}} </div> {{clear}} {{Portal:Humanities/box-header|Major Wikiversity Portals|Portal:Humanities}} {{Portals}} {{Portal:Humanities/box-footer|}} {{Portal:Humanities/box-header|Wikimedia|Portal:Humanities}} {{Wikimedia for portals|page={{titleparts|1}}}} {{Portal:Humanities/box-footer|}} {{Reflist}} {{end tab}} [[Category:Humanities| Portal:Humanities]] [[Category:Humanities portals|Humanities]] [[Category:Subject portals|Humanities]] [[hu:Wikiegyetem]] oaoldctquuh2eqae1jwssfjzlku1tng 2690214 2690213 2024-12-04T04:23:43Z 2600:1012:B138:9A50:9806:D10A:21C7:B9D6 2690214 wikitext text/x-wiki __NOTOC__ __NOEDITSECTION__ {{{{#titleparts:Portal:Humanities|1}}/start tab}} {{box-transclude|Introduction|The Humanities Portal}} <div style="float:left; width:66%; min-width:300px;"> {{Portal:Humanities/box-header|Featured Resource|Portal:Humanities/Featured Resource}} {{#invoke:Portals|lede|{{#invoke:Portals|randomlink|Portal:Humanities/Featured Resource}}}} {{clear}} {{Portal:Humanities/box-footer|}} {{Portal:Humanities/box-header|Featured Picture|Portal:Humanities/Featured Picture}} [[{{#invoke:Portals|randomlink|Portal:Humanities/Featured Picture}}]] {{Portal:Humanities/box-footer|}} </div> <div style="float:right; width:33%; min-width:150px;"> {{box-transclude|Categories}} {{box-transclude|Related Categories}} {{box-transclude|Related Portals}} </div> {{clear}} {{Portal:Humanities/box-header|Major Wikiversity Portals|Portal:Humanities}} {{Portals}} {{Portal:Humanities/box-footer|}} {{Portal:Humanities/box-header|Wikimedia|Portal:Humanities}} {{Wikimedia for portals|page={{titleparts|1}}}} {{Portal:Humanities/box-footer|}} {{Reflist}} {{end tab}} [[hu:Wikiegyetem]] [[Category:Humanities| Portal:Humanities]] [[Category:Humanities portals|Humanities]] [[Category:Subject portals|Humanities]] optnmx1kp7o23ohcyh8xzw9r4yq807s 2690215 2690214 2024-12-04T04:23:58Z 2600:1012:B138:9A50:9806:D10A:21C7:B9D6 2690215 wikitext text/x-wiki __NOTOC__ __NOEDITSECTION__ {{{{#titleparts:Portal:Humanities|1}}/start tab}} {{box-transclude|Introduction|The Humanities Portal}} <div style="float:left; width:66%; min-width:300px;"> {{Portal:Humanities/box-header|Featured Resource|Portal:Humanities/Featured Resource}} {{#invoke:Portals|lede|{{#invoke:Portals|randomlink|Portal:Humanities/Featured Resource}}}} {{clear}} {{Portal:Humanities/box-footer|}} {{Portal:Humanities/box-header|Featured Picture|Portal:Humanities/Featured Picture}} [[{{#invoke:Portals|randomlink|Portal:Humanities/Featured Picture}}]] {{Portal:Humanities/box-footer|}} </div> <div style="float:right; width:33%; min-width:150px;"> {{box-transclude|Categories}} {{box-transclude|Related Categories}} {{box-transclude|Related Portals}} </div> {{clear}} {{Portal:Humanities/box-header|Major Wikiversity Portals|Portal:Humanities}} {{Portals}} {{Portal:Humanities/box-footer|}} {{Portal:Humanities/box-header|Wikimedia|Portal:Humanities}} {{Wikimedia for portals|page={{titleparts|1}}}} {{Portal:Humanities/box-footer|}} {{Reflist}} {{end tab}} [[Category:Humanities| Portal:Humanities]] [[Category:Humanities portals|Humanities]] [[Category:Subject portals|Humanities]] haj9f961c44j0jafyidmgtmckubxgi9 4 1786 2690158 2690022 2024-12-03T19:48:24Z Tres Libras 2993673 /* Vandalism */ Reply 2690158 wikitext text/x-wiki {{Shortcut|WV:NOTICE|WV:AN}} {{/Header}} == [[Special:Contribs/84.126.165.13]] == Vandalism. – [[User:Tryvix1509|Tryvix1509]] ([[User talk:Tryvix1509|discuss]] • [[Special:Contributions/Tryvix1509|contribs]]) 14:42, 11 January 2023 (UTC) :CC {{ping|Antandrus}} since you were deleted a vandalism page. – [[User:Tryvix1509|Tryvix1509]] ([[User talk:Tryvix1509|discuss]] • [[Special:Contributions/Tryvix1509|contribs]]) 15:23, 11 January 2023 (UTC) :I'm not able to block, only protect and delete - I can protect it from re-creation though. [[User:Antandrus|Antandrus]] ([[User talk:Antandrus|discuss]] • [[Special:Contributions/Antandrus|contribs]]) 15:25, 11 January 2023 (UTC) ::Blocked and hidden. Thank you, &mdash;Hasley&nbsp;[[user talk:Hasley|<span style="color: #0645AD; vertical-align: super; font-size: smaller;">talk</span>]] 16:10, 11 January 2023 (UTC) :::See also [[Special:Contributions/Goggdoggdetroyer]]. This is a long-term abuser who will edit from several IPs. —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:54, 12 January 2023 (UTC) ::::[[Special:Contributions/201.146.32.131]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:55, 12 January 2023 (UTC) :::::Please make sure to revdel all of these as well. —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:56, 12 January 2023 (UTC) ::::::[[Special:Contributions/189.129.121.186]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 02:17, 12 January 2023 (UTC) :::::::[[Special:Contributions/189.223.219.134]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 03:20, 12 January 2023 (UTC) ::::::::{{done}}. &mdash;Hasley&nbsp;[[user talk:Hasley|<span style="color: #0645AD; vertical-align: super; font-size: smaller;">talk</span>]] 15:16, 12 January 2023 (UTC) == [[Special:Contribs/41.214.18.231]] == Long-term abuse. [[User:Tryvix1509|Tryvix1509]] ([[User talk:Tryvix1509|discuss]] • [[Special:Contributions/Tryvix1509|contribs]]) 08:05, 24 January 2023 (UTC) :{{done}} by GV. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:33, 24 January 2023 (UTC) == [[Special:Contribs/ApprenticeFan]] == Long-term abuse. – [[Special:Contributions/2405:4802:1AB:E140:91F9:4320:8977:E239|2405:4802:1AB:E140:91F9:4320:8977:E239]] ([[User talk:2405:4802:1AB:E140:91F9:4320:8977:E239|discuss]]) 14:59, 28 January 2023 (UTC) :Globally locked. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 15:17, 28 January 2023 (UTC) == [[Special:Contribs/41.202.78.57]] == Long-term abuse: Globally+WMF banned: [[:w:en:WP:LTA/GRP]]. – [[Special:Contributions/2405:4802:36C:3B0:1C90:9B74:603F:E6F|2405:4802:36C:3B0:1C90:9B74:603F:E6F]] ([[User talk:2405:4802:36C:3B0:1C90:9B74:603F:E6F|discuss]]) 13:02, 30 January 2023 (UTC) :I will take no action on this because I am confused: One IP user is requesting that action be taken against another IP user. Who is [[User:2405:4802:36C:3B0:1C90:9B74:603F:E6F]]?--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 00:43, 31 January 2023 (UTC) == [[Special:Contributions/2A02:1210:5493:6F00:8D60:CF27:AC3E:C328]] == Block and revdel, please. —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 22:29, 13 February 2023 (UTC) :{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:59, 13 February 2023 (UTC) == [[Special:Contributions/KEMONO PANTSU X]] == Vandalism, please block. [[User:Blua lago|Blua lago]] ([[User talk:Blua lago|discuss]] • [[Special:Contributions/Blua lago|contribs]]) 08:29, 29 March 2023 (UTC) : {{done}} The user has been locked. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 09:15, 29 March 2023 (UTC) ==[[Special:Contributions/2600:1003:B03E:C660:0:19:5833:C401]]== Revdel, please. --[[User:Jan.Kamenicek|Jan Kameníček]] ([[User talk:Jan.Kamenicek|discuss]] • [[Special:Contributions/Jan.Kamenicek|contribs]]) 19:12, 23 April 2023 (UTC) :@[[User:Jan.Kamenicek|Jan.Kamenicek]]: {{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 16:13, 24 April 2023 (UTC) == GRP socks == * {{user|170.83.119.121}} * {{user|181.115.60.123}} Long-term abuse: [[w:WP:LTA/GRP]]. [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 02:13, 4 May 2023 (UTC) :{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 03:26, 4 May 2023 (UTC) ::Revdel request: [[Special:Contributions/154.246.203.175]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 20:44, 7 May 2023 (UTC) == [[special:contribs/189.223.144.31|189.223.144.31]] == * {{user|189.223.144.31}} * Report reason: Open proxy (used by [[w:WP:LTA/GRP|GRP]]), left an abusive edit summary on my talk page. [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 01:50, 14 May 2023 (UTC) :{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 02:09, 14 May 2023 (UTC) == [[special:contribs/2601:206:8580:35D0:714E:77DC:EAE3:DFE3|2601:206:8580:35D0:714E:77DC:EAE3:DFE3]] == * {{user|2601:206:8580:35D0:714E:77DC:EAE3:DFE3}} * Report reason: Edit warring on [[Types of Dinosaur]] (see [[special:diff/2521104|1]], [[special:diff/2521102|2]], [[special:diff/2521100|3]], [[special:diff/2521098|4]]) [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 23:10, 16 May 2023 (UTC) :Now blocked, thanks! -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:56, 17 May 2023 (UTC) == [[special:contribs/I Join john|I Join john]] == * {{user|I Join john}} * Report reason: spam [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 02:58, 10 June 2023 (UTC) :Late notice, but for recording purposes: blocked by Dave Braunschweig on June 17. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:52, 3 October 2023 (UTC) == New special page to fight spam == {{int:please-translate}} <div lang="en" dir="ltr" class="mw-content-ltr"> Hello, We are replacing most of the functionalities of [[MediaWiki:Spam-blacklist]] with a new special page called [[Special:BlockedExternalDomains]]. In this special page, admins can simply add a domain and notes on the block (usually reasoning and/or link to a discussion) and the added domain would automatically be blocked to be linked in Wikis anymore (including its subdomains). Content of this list is stored in [[MediaWiki:BlockedExternalDomains.json]]. You can see [[:w:fa:Special:BlockedExternalDomains]] as an example. Check [[phab:T337431|the phabricator ticket]] for more information. This would make fighting spam easier and safer without needing to know regex or accidentally breaking wikis while also addressing the need to have some notes next to each domain on why it’s blocked. It would also make the list of blocked domains searchable and would make editing Wikis in general faster by optimizing matching links added against the blocked list in every edit (see [[phab:T337431#8936498]] for some measurements). If you want to migrate your entries in [[MediaWiki:Spam-blacklist]], there is a python script in [[phab:P49299]] that would produce contents of [[MediaWiki:Spam-blacklist]] and [[MediaWiki:BlockedExternalDomains.json]] for you automatically migrating off simple regex cases. Note that this new feature doesn’t support regex (for complex cases) nor URL paths matching. Also it doesn’t support bypass by spam whitelist. For those, please either keep using [[MediaWiki:Spam-blacklist]] or switch to an abuse filter if possible. And adding a link to the list might take up to five minutes to be fully in effect (due to server-side caching, this is already the case with the old system) and admins and bots automatically bypass the blocked list. Let me know if you have any questions or encounter any issues. Happy editing. [[User:Ladsgroup|Amir]] ([[User talk:Ladsgroup|talk]]) 09:41, 19 June 2023 (UTC) </div> <!-- Message sent by User:Ladsgroup@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Ladsgroup/target_ANs&oldid=25167735 --> ==Vandal: [[User:Ceoalphonso]]== They were spamming on Wikipedia, later claimed that their account was hacked. They were blocked for having a compromised account. They have started editing Wikiversity. High risk of future vandalism. They should be blocked for having a compromised account, in spite of the fact that this is dubious, because of AGF. [[User:Janhrach|Janhrach]] ([[User talk:Janhrach|discuss]] • [[Special:Contributions/Janhrach|contribs]]) 07:45, 30 September 2023 (UTC) :This user hasn't edited since February. Unless their editing picks back up and becomes problematic, there's no action necessary at this time. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 12:47, 30 September 2023 (UTC) ::{{ping|Atcovi}} They have not been active here since February, but they have made several edits across other wikis in the meantime. Their edits include highly visible vandalism, such as spamming in TemplateData. I would highly recommend a block. [[User:Janhrach|Janhrach]] ([[User talk:Janhrach|discuss]] • [[Special:Contributions/Janhrach|contribs]]) 14:52, 30 September 2023 (UTC) :::Since I still personally disagree, I'll leave this another custodian to take whatever action they deem reasonable. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 17:06, 30 September 2023 (UTC) == [[Special:Contributions/2600:1003:B05E:6EC6:0:33:95BF:E701]] == * {{user|2600:1003:B05E:6EC6:0:33:95BF:E701}} Cross-wiki vandalism. --[[User:SHB2000|SHB2000]] ([[User talk:SHB2000|discuss]] • [[Special:Contributions/SHB2000|contribs]]) 01:21, 2 June 2024 (UTC) :{{done}} —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:22, 2 June 2024 (UTC) ::Thank you, Koavf! --[[User:SHB2000|SHB2000]] ([[User talk:SHB2000|discuss]] • [[Special:Contributions/SHB2000|contribs]]) 01:26, 2 June 2024 (UTC) == Maintenance vs administration == Bumping a [[User_talk:Tule-hog#Wikiversity:Administration|redirect for discussion]] concerning custodianship. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:50, 6 October 2024 (UTC) == Vandalism == Please block [[Special:Contributions/76.121.217.240]]. --[[User:Tres Libras|Tres Libras]] ([[User talk:Tres Libras|discuss]] • [[Special:Contributions/Tres Libras|contribs]]) 03:09, 24 November 2024 (UTC) :Not a local sysop here but {{done}}. --[[User:SHB2000|SHB2000]] ([[User talk:SHB2000|discuss]] • [[Special:Contributions/SHB2000|contribs]]) 03:18, 24 November 2024 (UTC) :: {{comment}} Page deleted. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 03:21, 24 November 2024 (UTC) :::Hi it's me again. Please block [[Special:Contributions/216.186.51.108]] &mdash; @[[User:MathXplore|MathXplore]] @[[User:SHB2000|SHB2000]]. [[User:Tres Libras|Tres Libras]] ([[User talk:Tres Libras|discuss]] • [[Special:Contributions/Tres Libras|contribs]]) 19:54, 2 December 2024 (UTC) ::::{{done}} —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 19:58, 2 December 2024 (UTC) :::::Hello. Again and again. Please block [[Special:Contributions/152.22.75.23]]. [[User:Tres Libras|Tres Libras]] ([[User talk:Tres Libras|discuss]] • [[Special:Contributions/Tres Libras|contribs]]) 19:48, 3 December 2024 (UTC) ssyxm6ifi7gjxwq260xdjkc5y327xxz 2690159 2690158 2024-12-03T19:52:52Z Tres Libras 2993673 /* Vandalism */ Reply 2690159 wikitext text/x-wiki {{Shortcut|WV:NOTICE|WV:AN}} {{/Header}} == [[Special:Contribs/84.126.165.13]] == Vandalism. – [[User:Tryvix1509|Tryvix1509]] ([[User talk:Tryvix1509|discuss]] • [[Special:Contributions/Tryvix1509|contribs]]) 14:42, 11 January 2023 (UTC) :CC {{ping|Antandrus}} since you were deleted a vandalism page. – [[User:Tryvix1509|Tryvix1509]] ([[User talk:Tryvix1509|discuss]] • [[Special:Contributions/Tryvix1509|contribs]]) 15:23, 11 January 2023 (UTC) :I'm not able to block, only protect and delete - I can protect it from re-creation though. [[User:Antandrus|Antandrus]] ([[User talk:Antandrus|discuss]] • [[Special:Contributions/Antandrus|contribs]]) 15:25, 11 January 2023 (UTC) ::Blocked and hidden. Thank you, &mdash;Hasley&nbsp;[[user talk:Hasley|<span style="color: #0645AD; vertical-align: super; font-size: smaller;">talk</span>]] 16:10, 11 January 2023 (UTC) :::See also [[Special:Contributions/Goggdoggdetroyer]]. This is a long-term abuser who will edit from several IPs. —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:54, 12 January 2023 (UTC) ::::[[Special:Contributions/201.146.32.131]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:55, 12 January 2023 (UTC) :::::Please make sure to revdel all of these as well. —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:56, 12 January 2023 (UTC) ::::::[[Special:Contributions/189.129.121.186]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 02:17, 12 January 2023 (UTC) :::::::[[Special:Contributions/189.223.219.134]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 03:20, 12 January 2023 (UTC) ::::::::{{done}}. &mdash;Hasley&nbsp;[[user talk:Hasley|<span style="color: #0645AD; vertical-align: super; font-size: smaller;">talk</span>]] 15:16, 12 January 2023 (UTC) == [[Special:Contribs/41.214.18.231]] == Long-term abuse. [[User:Tryvix1509|Tryvix1509]] ([[User talk:Tryvix1509|discuss]] • [[Special:Contributions/Tryvix1509|contribs]]) 08:05, 24 January 2023 (UTC) :{{done}} by GV. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:33, 24 January 2023 (UTC) == [[Special:Contribs/ApprenticeFan]] == Long-term abuse. – [[Special:Contributions/2405:4802:1AB:E140:91F9:4320:8977:E239|2405:4802:1AB:E140:91F9:4320:8977:E239]] ([[User talk:2405:4802:1AB:E140:91F9:4320:8977:E239|discuss]]) 14:59, 28 January 2023 (UTC) :Globally locked. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 15:17, 28 January 2023 (UTC) == [[Special:Contribs/41.202.78.57]] == Long-term abuse: Globally+WMF banned: [[:w:en:WP:LTA/GRP]]. – [[Special:Contributions/2405:4802:36C:3B0:1C90:9B74:603F:E6F|2405:4802:36C:3B0:1C90:9B74:603F:E6F]] ([[User talk:2405:4802:36C:3B0:1C90:9B74:603F:E6F|discuss]]) 13:02, 30 January 2023 (UTC) :I will take no action on this because I am confused: One IP user is requesting that action be taken against another IP user. Who is [[User:2405:4802:36C:3B0:1C90:9B74:603F:E6F]]?--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 00:43, 31 January 2023 (UTC) == [[Special:Contributions/2A02:1210:5493:6F00:8D60:CF27:AC3E:C328]] == Block and revdel, please. —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 22:29, 13 February 2023 (UTC) :{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:59, 13 February 2023 (UTC) == [[Special:Contributions/KEMONO PANTSU X]] == Vandalism, please block. [[User:Blua lago|Blua lago]] ([[User talk:Blua lago|discuss]] • [[Special:Contributions/Blua lago|contribs]]) 08:29, 29 March 2023 (UTC) : {{done}} The user has been locked. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 09:15, 29 March 2023 (UTC) ==[[Special:Contributions/2600:1003:B03E:C660:0:19:5833:C401]]== Revdel, please. --[[User:Jan.Kamenicek|Jan Kameníček]] ([[User talk:Jan.Kamenicek|discuss]] • [[Special:Contributions/Jan.Kamenicek|contribs]]) 19:12, 23 April 2023 (UTC) :@[[User:Jan.Kamenicek|Jan.Kamenicek]]: {{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 16:13, 24 April 2023 (UTC) == GRP socks == * {{user|170.83.119.121}} * {{user|181.115.60.123}} Long-term abuse: [[w:WP:LTA/GRP]]. [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 02:13, 4 May 2023 (UTC) :{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 03:26, 4 May 2023 (UTC) ::Revdel request: [[Special:Contributions/154.246.203.175]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 20:44, 7 May 2023 (UTC) == [[special:contribs/189.223.144.31|189.223.144.31]] == * {{user|189.223.144.31}} * Report reason: Open proxy (used by [[w:WP:LTA/GRP|GRP]]), left an abusive edit summary on my talk page. [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 01:50, 14 May 2023 (UTC) :{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 02:09, 14 May 2023 (UTC) == [[special:contribs/2601:206:8580:35D0:714E:77DC:EAE3:DFE3|2601:206:8580:35D0:714E:77DC:EAE3:DFE3]] == * {{user|2601:206:8580:35D0:714E:77DC:EAE3:DFE3}} * Report reason: Edit warring on [[Types of Dinosaur]] (see [[special:diff/2521104|1]], [[special:diff/2521102|2]], [[special:diff/2521100|3]], [[special:diff/2521098|4]]) [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 23:10, 16 May 2023 (UTC) :Now blocked, thanks! -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:56, 17 May 2023 (UTC) == [[special:contribs/I Join john|I Join john]] == * {{user|I Join john}} * Report reason: spam [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 02:58, 10 June 2023 (UTC) :Late notice, but for recording purposes: blocked by Dave Braunschweig on June 17. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:52, 3 October 2023 (UTC) == New special page to fight spam == {{int:please-translate}} <div lang="en" dir="ltr" class="mw-content-ltr"> Hello, We are replacing most of the functionalities of [[MediaWiki:Spam-blacklist]] with a new special page called [[Special:BlockedExternalDomains]]. In this special page, admins can simply add a domain and notes on the block (usually reasoning and/or link to a discussion) and the added domain would automatically be blocked to be linked in Wikis anymore (including its subdomains). Content of this list is stored in [[MediaWiki:BlockedExternalDomains.json]]. You can see [[:w:fa:Special:BlockedExternalDomains]] as an example. Check [[phab:T337431|the phabricator ticket]] for more information. This would make fighting spam easier and safer without needing to know regex or accidentally breaking wikis while also addressing the need to have some notes next to each domain on why it’s blocked. It would also make the list of blocked domains searchable and would make editing Wikis in general faster by optimizing matching links added against the blocked list in every edit (see [[phab:T337431#8936498]] for some measurements). If you want to migrate your entries in [[MediaWiki:Spam-blacklist]], there is a python script in [[phab:P49299]] that would produce contents of [[MediaWiki:Spam-blacklist]] and [[MediaWiki:BlockedExternalDomains.json]] for you automatically migrating off simple regex cases. Note that this new feature doesn’t support regex (for complex cases) nor URL paths matching. Also it doesn’t support bypass by spam whitelist. For those, please either keep using [[MediaWiki:Spam-blacklist]] or switch to an abuse filter if possible. And adding a link to the list might take up to five minutes to be fully in effect (due to server-side caching, this is already the case with the old system) and admins and bots automatically bypass the blocked list. Let me know if you have any questions or encounter any issues. Happy editing. [[User:Ladsgroup|Amir]] ([[User talk:Ladsgroup|talk]]) 09:41, 19 June 2023 (UTC) </div> <!-- Message sent by User:Ladsgroup@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Ladsgroup/target_ANs&oldid=25167735 --> ==Vandal: [[User:Ceoalphonso]]== They were spamming on Wikipedia, later claimed that their account was hacked. They were blocked for having a compromised account. They have started editing Wikiversity. High risk of future vandalism. They should be blocked for having a compromised account, in spite of the fact that this is dubious, because of AGF. [[User:Janhrach|Janhrach]] ([[User talk:Janhrach|discuss]] • [[Special:Contributions/Janhrach|contribs]]) 07:45, 30 September 2023 (UTC) :This user hasn't edited since February. Unless their editing picks back up and becomes problematic, there's no action necessary at this time. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 12:47, 30 September 2023 (UTC) ::{{ping|Atcovi}} They have not been active here since February, but they have made several edits across other wikis in the meantime. Their edits include highly visible vandalism, such as spamming in TemplateData. I would highly recommend a block. [[User:Janhrach|Janhrach]] ([[User talk:Janhrach|discuss]] • [[Special:Contributions/Janhrach|contribs]]) 14:52, 30 September 2023 (UTC) :::Since I still personally disagree, I'll leave this another custodian to take whatever action they deem reasonable. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 17:06, 30 September 2023 (UTC) == [[Special:Contributions/2600:1003:B05E:6EC6:0:33:95BF:E701]] == * {{user|2600:1003:B05E:6EC6:0:33:95BF:E701}} Cross-wiki vandalism. --[[User:SHB2000|SHB2000]] ([[User talk:SHB2000|discuss]] • [[Special:Contributions/SHB2000|contribs]]) 01:21, 2 June 2024 (UTC) :{{done}} —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:22, 2 June 2024 (UTC) ::Thank you, Koavf! --[[User:SHB2000|SHB2000]] ([[User talk:SHB2000|discuss]] • [[Special:Contributions/SHB2000|contribs]]) 01:26, 2 June 2024 (UTC) == Maintenance vs administration == Bumping a [[User_talk:Tule-hog#Wikiversity:Administration|redirect for discussion]] concerning custodianship. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:50, 6 October 2024 (UTC) == Vandalism == Please block [[Special:Contributions/76.121.217.240]]. --[[User:Tres Libras|Tres Libras]] ([[User talk:Tres Libras|discuss]] • [[Special:Contributions/Tres Libras|contribs]]) 03:09, 24 November 2024 (UTC) :Not a local sysop here but {{done}}. --[[User:SHB2000|SHB2000]] ([[User talk:SHB2000|discuss]] • [[Special:Contributions/SHB2000|contribs]]) 03:18, 24 November 2024 (UTC) :: {{comment}} Page deleted. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 03:21, 24 November 2024 (UTC) :::Hi it's me again. Please block [[Special:Contributions/216.186.51.108]] &mdash; @[[User:MathXplore|MathXplore]] @[[User:SHB2000|SHB2000]]. [[User:Tres Libras|Tres Libras]] ([[User talk:Tres Libras|discuss]] • [[Special:Contributions/Tres Libras|contribs]]) 19:54, 2 December 2024 (UTC) ::::{{done}} —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 19:58, 2 December 2024 (UTC) :::::Hello. Again and again. Please block [[Special:Contributions/152.22.75.23]]. [[User:Tres Libras|Tres Libras]] ([[User talk:Tres Libras|discuss]] • [[Special:Contributions/Tres Libras|contribs]]) 19:48, 3 December 2024 (UTC) ::::::Alreyady done by Aramil. I think Wikiversity should take action against proxies. I suspect that these IPs are proxies and belong to the same person. [[User:Tres Libras|Tres Libras]] ([[User talk:Tres Libras|discuss]] • [[Special:Contributions/Tres Libras|contribs]]) 19:52, 3 December 2024 (UTC) cvea795s5066h6oywemg371o6a9zvus 2690160 2690159 2024-12-03T19:53:04Z Tres Libras 2993673 /* Vandalism */ 2690160 wikitext text/x-wiki {{Shortcut|WV:NOTICE|WV:AN}} {{/Header}} == [[Special:Contribs/84.126.165.13]] == Vandalism. – [[User:Tryvix1509|Tryvix1509]] ([[User talk:Tryvix1509|discuss]] • [[Special:Contributions/Tryvix1509|contribs]]) 14:42, 11 January 2023 (UTC) :CC {{ping|Antandrus}} since you were deleted a vandalism page. – [[User:Tryvix1509|Tryvix1509]] ([[User talk:Tryvix1509|discuss]] • [[Special:Contributions/Tryvix1509|contribs]]) 15:23, 11 January 2023 (UTC) :I'm not able to block, only protect and delete - I can protect it from re-creation though. [[User:Antandrus|Antandrus]] ([[User talk:Antandrus|discuss]] • [[Special:Contributions/Antandrus|contribs]]) 15:25, 11 January 2023 (UTC) ::Blocked and hidden. Thank you, &mdash;Hasley&nbsp;[[user talk:Hasley|<span style="color: #0645AD; vertical-align: super; font-size: smaller;">talk</span>]] 16:10, 11 January 2023 (UTC) :::See also [[Special:Contributions/Goggdoggdetroyer]]. This is a long-term abuser who will edit from several IPs. —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:54, 12 January 2023 (UTC) ::::[[Special:Contributions/201.146.32.131]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:55, 12 January 2023 (UTC) :::::Please make sure to revdel all of these as well. —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:56, 12 January 2023 (UTC) ::::::[[Special:Contributions/189.129.121.186]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 02:17, 12 January 2023 (UTC) :::::::[[Special:Contributions/189.223.219.134]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 03:20, 12 January 2023 (UTC) ::::::::{{done}}. &mdash;Hasley&nbsp;[[user talk:Hasley|<span style="color: #0645AD; vertical-align: super; font-size: smaller;">talk</span>]] 15:16, 12 January 2023 (UTC) == [[Special:Contribs/41.214.18.231]] == Long-term abuse. [[User:Tryvix1509|Tryvix1509]] ([[User talk:Tryvix1509|discuss]] • [[Special:Contributions/Tryvix1509|contribs]]) 08:05, 24 January 2023 (UTC) :{{done}} by GV. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:33, 24 January 2023 (UTC) == [[Special:Contribs/ApprenticeFan]] == Long-term abuse. – [[Special:Contributions/2405:4802:1AB:E140:91F9:4320:8977:E239|2405:4802:1AB:E140:91F9:4320:8977:E239]] ([[User talk:2405:4802:1AB:E140:91F9:4320:8977:E239|discuss]]) 14:59, 28 January 2023 (UTC) :Globally locked. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 15:17, 28 January 2023 (UTC) == [[Special:Contribs/41.202.78.57]] == Long-term abuse: Globally+WMF banned: [[:w:en:WP:LTA/GRP]]. – [[Special:Contributions/2405:4802:36C:3B0:1C90:9B74:603F:E6F|2405:4802:36C:3B0:1C90:9B74:603F:E6F]] ([[User talk:2405:4802:36C:3B0:1C90:9B74:603F:E6F|discuss]]) 13:02, 30 January 2023 (UTC) :I will take no action on this because I am confused: One IP user is requesting that action be taken against another IP user. Who is [[User:2405:4802:36C:3B0:1C90:9B74:603F:E6F]]?--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 00:43, 31 January 2023 (UTC) == [[Special:Contributions/2A02:1210:5493:6F00:8D60:CF27:AC3E:C328]] == Block and revdel, please. —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 22:29, 13 February 2023 (UTC) :{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:59, 13 February 2023 (UTC) == [[Special:Contributions/KEMONO PANTSU X]] == Vandalism, please block. [[User:Blua lago|Blua lago]] ([[User talk:Blua lago|discuss]] • [[Special:Contributions/Blua lago|contribs]]) 08:29, 29 March 2023 (UTC) : {{done}} The user has been locked. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 09:15, 29 March 2023 (UTC) ==[[Special:Contributions/2600:1003:B03E:C660:0:19:5833:C401]]== Revdel, please. --[[User:Jan.Kamenicek|Jan Kameníček]] ([[User talk:Jan.Kamenicek|discuss]] • [[Special:Contributions/Jan.Kamenicek|contribs]]) 19:12, 23 April 2023 (UTC) :@[[User:Jan.Kamenicek|Jan.Kamenicek]]: {{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 16:13, 24 April 2023 (UTC) == GRP socks == * {{user|170.83.119.121}} * {{user|181.115.60.123}} Long-term abuse: [[w:WP:LTA/GRP]]. [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 02:13, 4 May 2023 (UTC) :{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 03:26, 4 May 2023 (UTC) ::Revdel request: [[Special:Contributions/154.246.203.175]] —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 20:44, 7 May 2023 (UTC) == [[special:contribs/189.223.144.31|189.223.144.31]] == * {{user|189.223.144.31}} * Report reason: Open proxy (used by [[w:WP:LTA/GRP|GRP]]), left an abusive edit summary on my talk page. [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 01:50, 14 May 2023 (UTC) :{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 02:09, 14 May 2023 (UTC) == [[special:contribs/2601:206:8580:35D0:714E:77DC:EAE3:DFE3|2601:206:8580:35D0:714E:77DC:EAE3:DFE3]] == * {{user|2601:206:8580:35D0:714E:77DC:EAE3:DFE3}} * Report reason: Edit warring on [[Types of Dinosaur]] (see [[special:diff/2521104|1]], [[special:diff/2521102|2]], [[special:diff/2521100|3]], [[special:diff/2521098|4]]) [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 23:10, 16 May 2023 (UTC) :Now blocked, thanks! -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:56, 17 May 2023 (UTC) == [[special:contribs/I Join john|I Join john]] == * {{user|I Join john}} * Report reason: spam [[User:Leonidlednev|Leonidlednev]] ([[User talk:Leonidlednev|discuss]] • [[Special:Contributions/Leonidlednev|contribs]]) 02:58, 10 June 2023 (UTC) :Late notice, but for recording purposes: blocked by Dave Braunschweig on June 17. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:52, 3 October 2023 (UTC) == New special page to fight spam == {{int:please-translate}} <div lang="en" dir="ltr" class="mw-content-ltr"> Hello, We are replacing most of the functionalities of [[MediaWiki:Spam-blacklist]] with a new special page called [[Special:BlockedExternalDomains]]. In this special page, admins can simply add a domain and notes on the block (usually reasoning and/or link to a discussion) and the added domain would automatically be blocked to be linked in Wikis anymore (including its subdomains). Content of this list is stored in [[MediaWiki:BlockedExternalDomains.json]]. You can see [[:w:fa:Special:BlockedExternalDomains]] as an example. Check [[phab:T337431|the phabricator ticket]] for more information. This would make fighting spam easier and safer without needing to know regex or accidentally breaking wikis while also addressing the need to have some notes next to each domain on why it’s blocked. It would also make the list of blocked domains searchable and would make editing Wikis in general faster by optimizing matching links added against the blocked list in every edit (see [[phab:T337431#8936498]] for some measurements). If you want to migrate your entries in [[MediaWiki:Spam-blacklist]], there is a python script in [[phab:P49299]] that would produce contents of [[MediaWiki:Spam-blacklist]] and [[MediaWiki:BlockedExternalDomains.json]] for you automatically migrating off simple regex cases. Note that this new feature doesn’t support regex (for complex cases) nor URL paths matching. Also it doesn’t support bypass by spam whitelist. For those, please either keep using [[MediaWiki:Spam-blacklist]] or switch to an abuse filter if possible. And adding a link to the list might take up to five minutes to be fully in effect (due to server-side caching, this is already the case with the old system) and admins and bots automatically bypass the blocked list. Let me know if you have any questions or encounter any issues. Happy editing. [[User:Ladsgroup|Amir]] ([[User talk:Ladsgroup|talk]]) 09:41, 19 June 2023 (UTC) </div> <!-- Message sent by User:Ladsgroup@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Ladsgroup/target_ANs&oldid=25167735 --> ==Vandal: [[User:Ceoalphonso]]== They were spamming on Wikipedia, later claimed that their account was hacked. They were blocked for having a compromised account. They have started editing Wikiversity. High risk of future vandalism. They should be blocked for having a compromised account, in spite of the fact that this is dubious, because of AGF. [[User:Janhrach|Janhrach]] ([[User talk:Janhrach|discuss]] • [[Special:Contributions/Janhrach|contribs]]) 07:45, 30 September 2023 (UTC) :This user hasn't edited since February. Unless their editing picks back up and becomes problematic, there's no action necessary at this time. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 12:47, 30 September 2023 (UTC) ::{{ping|Atcovi}} They have not been active here since February, but they have made several edits across other wikis in the meantime. Their edits include highly visible vandalism, such as spamming in TemplateData. I would highly recommend a block. [[User:Janhrach|Janhrach]] ([[User talk:Janhrach|discuss]] • [[Special:Contributions/Janhrach|contribs]]) 14:52, 30 September 2023 (UTC) :::Since I still personally disagree, I'll leave this another custodian to take whatever action they deem reasonable. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 17:06, 30 September 2023 (UTC) == [[Special:Contributions/2600:1003:B05E:6EC6:0:33:95BF:E701]] == * {{user|2600:1003:B05E:6EC6:0:33:95BF:E701}} Cross-wiki vandalism. --[[User:SHB2000|SHB2000]] ([[User talk:SHB2000|discuss]] • [[Special:Contributions/SHB2000|contribs]]) 01:21, 2 June 2024 (UTC) :{{done}} —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 01:22, 2 June 2024 (UTC) ::Thank you, Koavf! --[[User:SHB2000|SHB2000]] ([[User talk:SHB2000|discuss]] • [[Special:Contributions/SHB2000|contribs]]) 01:26, 2 June 2024 (UTC) == Maintenance vs administration == Bumping a [[User_talk:Tule-hog#Wikiversity:Administration|redirect for discussion]] concerning custodianship. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:50, 6 October 2024 (UTC) == Vandalism == Please block [[Special:Contributions/76.121.217.240]]. --[[User:Tres Libras|Tres Libras]] ([[User talk:Tres Libras|discuss]] • [[Special:Contributions/Tres Libras|contribs]]) 03:09, 24 November 2024 (UTC) :Not a local sysop here but {{done}}. --[[User:SHB2000|SHB2000]] ([[User talk:SHB2000|discuss]] • [[Special:Contributions/SHB2000|contribs]]) 03:18, 24 November 2024 (UTC) :: {{comment}} Page deleted. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 03:21, 24 November 2024 (UTC) :::Hi it's me again. Please block [[Special:Contributions/216.186.51.108]] &mdash; @[[User:MathXplore|MathXplore]] @[[User:SHB2000|SHB2000]]. [[User:Tres Libras|Tres Libras]] ([[User talk:Tres Libras|discuss]] • [[Special:Contributions/Tres Libras|contribs]]) 19:54, 2 December 2024 (UTC) ::::{{done}} —[[User:Koavf|Justin (<span style="color:grey">ko'''a'''vf</span>)]]<span style="color:red">❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯</span> 19:58, 2 December 2024 (UTC) :::::Hello. Again and again. Please block [[Special:Contributions/152.22.75.23]]. [[User:Tres Libras|Tres Libras]] ([[User talk:Tres Libras|discuss]] • [[Special:Contributions/Tres Libras|contribs]]) 19:48, 3 December 2024 (UTC) ::::::Already done by Aramil. I think Wikiversity should take action against proxies. I suspect that these IPs are proxies and belong to the same person. [[User:Tres Libras|Tres Libras]] ([[User talk:Tres Libras|discuss]] • [[Special:Contributions/Tres Libras|contribs]]) 19:52, 3 December 2024 (UTC) dfgy432u4nfnwnk9md499g9wu785hgb 0 3276 2690182 2690039 2024-12-04T01:11:27Z Magnetic Chutney 2989916 corrected mistake 2690182 wikitext text/x-wiki <small>Part of the [[School:Strategic_Studies|Strategic Studies]] curriculum</small> '''Political Science''', in rudimentary terms, is the study of power. It is considered a social science and is interdisciplinary by nature. Its interconnectedness to many other fields and must be viewed, compared and contrasted though each relative field in order to fully understand the [[subject matter]]. Political Science relates to the way humans will organize themselves into a working society that is in the interest of the [[public good]]. By doing this, the society will advance and benefit as a whole through a process known as [[collective action]], and will be able to live fairly and justly. Political Science observes many aspects of how societies accomplish this goal through four major fields of study. In addition, these fields are usually studies along with other relative fields such as: [[w:Anthropology]], [[w:Economics]], [[w:Geography]], [[w:Religion]], [[w:Philosophy]], [[w:Psychology]], and [[w:Sociology]]. == Political Theory == The field of [[Political theory|Political Theory]] is one of the four major fields in the study of Political Science. It will explore and analyze the philosophy by which a society has chosen to organize its government, construct its laws, and achieve its desired goals (Political, Economic, or Social). Political Theorists do '''not''' compare and contrast which theories are '''better''' than others. Political Theorists simply compare and contrast different political theories, and see how well they meet the needs of the people and the goals for which this theory was created so that it may accomplish. == Government & Politics == The field of Government & Politics is one of the four major fields in the study of Political Science. It explores the product(s) of political theories on people and nations. When studying Government & Politics, it is important to carefully consider all aspects of how a society is meant to function under the laws and institutions they have created. Many government types are explored, but only briefly. Depending on the country a student is in, this field is dominated by an in-depth analysis of that country's government and political structure. == Comparative Politics == The field of [[Comparative Politics]] is one of the four major fields in the study of Political Science. Unlike the field of Government & Politics, in comparative politics, students are usually given two or more types of governments and asked to conduct an in-depth analysis on how each form of government is either beneficial for the people, or a burden on the people, as well as see how well each government type does in yielding the desired goals for society. == International Politics == The field of International Politics is one of the four major fields in the study of Political Science. This field is considered quite new when compared to all other fields in Political Science. However, International Politics dates back to Ancient Greece and the relationship the individual city-states had between themselves. This field looks at how societies form governments that must work and cooperate to coexist with other governments of other societies in an increasingly international community. Such topics include: International [[School:Law|Law]], [[International Relations]], International Organization, Global Political Economy, and Foreign Policy. == See also == * [[School:Political science]] * [[Indian Government]] * [[Introduction to political science]] [[Category:Political science| ]] [[Category:Introductions]] [[Category:Strategic Studies|{{PAGENAME}}]] efp4r7wmvvpam7mx4gh5mlwgbuvhcr6 0 34753 2690161 2690058 2024-12-03T20:22:04Z Ekbreckenridge 2994477 2690161 wikitext text/x-wiki {{Robelbox|theme=1|title=Mechatronics I}} <div style="{{Robelbox/pad}}"> <big>An introductory course in Mechatronics</big> </div> {{Robelbox/close}} {{Robelbox|theme=3|title=Syllabus}} <div style="{{Robelbox/pad}}"> [[Electricity]] [[DC Generator]] [[DC Motor]] [[Testing of DC Machines]] [[Transformer]] [[Synchronous Motors]] [[Induction Motor|Induction/asynchronous motor]] [[Alternators]] </div> {{Robelbox/close}} This course assumes you have at least a beginners introduction to the [[Electricity]] course, especially the [[Electricity/Introduction]] section. Mechatronics is the combination of a few different disciples of engineering. An understanding of electrical circuits, mechanical systems, pneumatic and hydraulics, and the software associated with them to adequately build, troubleshoot, and repair industrial systems. == Electrical Symbols and Terms == ==== Units: ==== {| class="wikitable" |+ !Unit Name !Symbol !Quantity !Definition !Measurement |- |Ampere |A |Electrical Current (I) |Electrical current is the flow rate of electric charge in electric field, usually in electrical circuit. |1V = 1J / 1C |- |Volts |V |Voltage (V, E) |Electrical voltage is defined as electric potential difference between two points of an electric field. |1A = 1C / 1s |- |Ohm |Ω |Resistance (R) |Resistance is an electrical quantity that measures how the device or material reduces the electric current flow through it. |1Ω = 1V / 1A |- |Watt |W |Electrical Power (P) |Electric power is the rate of energy consumption in an electrical circuit. |1W = 1J / 1s 1W = 1V ⋅ 1A |- |Decibel-milliwatt |dBm |Electric Power (P) |Decibel-milliwatt or dBm is a unit of electric power, measured with logarithmic scale referenced to 1mW. |10dBm = 10 ⋅ log₁₀(10mW / 1mW) |- |Decibel-Watt |dBW |Electric Power (P) |Decibel-watt or dBW is a unit of electric power, measured with logarithmic scale referenced to 1W. |10dBW = 10 ⋅ log₁₀(10W / 1W) |- |Volt-Ampere-Reactive |var |Reactive Power (Q) | | |- |Volt-Ampere |VA |Apparent Power (S) |VA is a unit of apparent power |1VA = 1V * 1A |- |Farad |F |Capacitance (C) |Farad is the unit of capacitance. It represents the amount of electric charge in coulombs that is stored per 1 volt. |1F = 1C / 1V |- |Henry |H |Inductance (L) |Henry is the unit of inductance. |1H = 1Wb / 1A |- |siemens / mho |S |Conductance (G) Admittance (Y) |siemens is the unit of conductance, which is the opposite of resistance. |1S = 1 / 1Ω |- |Coulomb |C |Electrical Charge (Q) |Coulomb is the unit of electric charge. |1C = 6.238792×10¹⁸ electron charges |- |Ampere-hour |Ah |Electrical Charge (Q) |One ampere-hour is the electric charge that flow in electrical circuit, when a current of 1 ampere is applied for 1 hour. |1Ah = 1A ⋅ 1hour One ampere-hour is equal to 3600 coulombs. 1Ah = 3600C |- |Joule |J |Energy (E) |Joule is the unit of energy. |1J = 1 kg ⋅ m² / s² |- |Kilowatt-hour |kWh |Energy (E) |Kilowatt-hour is a unit of energy. |1kWh = 1kW ⋅ 1h = 1000W ⋅ 1h |- |Electron-volt |eV |Energy (E) | | |- |Ohm-meter |Ω*m |Resistivity (''ρ'') | | |- |siemens per meter |S/m |Conductivity (''σ'') | | |- |Volts per meter | |Electric field (E) | | |- |Newtons per coulomb | |Electric field (E) | | |- |Volt-meter | |Electric flux (Φ_e) | | |- |Tesla | |Magnetic field (B) |Tesla is the unit of magnetic field. |1T = 1Wb / 1m² |- |Gauss | |Magnetic field (B) |Weber is the unit of magnetic flux. |1Wb = 1V ⋅ 1s |- |Weber | |Magnetic flux (Φ_m) | | |- |Hertz | |Frequency (f) | | |- |Seconds | |Time (t) | | |- |Meter / metre | |Length (l) | | |- |Square-meter | |Area (A) | | |- |Decibel | | | | |- |Parts per million | | | | |} Definitions for the table came from Rapid Tables<ref>{{Cite web|url=https://www.rapidtables.com/electric/Electric_units.html|title=Electrical units of measurment (V,A,Ω,W,...)|website=www.rapidtables.com|access-date=2024-12-03}}</ref>. == DC Generator == An Electrical Generator converts mechanical energy (or power) into electrical energy (or power).And motor converts electrical energy to mechanical energy. '''Principle''' It is based on the principle of production of dynamically (or motionally) induced e.m.f (Electromotive Force). Whenever a conductor cuts magnetic flux, dynamically induced e.m.f. is produced in it according to [[Wikipedia:Faraday's law of induction|Faraday's Laws of Electromagnetic Induction]]. This e.m.f. causes a current to flow if the conductor circuit is closed. Hence, the basic essential parts of an electric generator are : *A magnetic field, *A conductor or conductors which can so move as to cut the flux. === Simple Loop Generator === ===='Construction==== A single turn rectangular copper coil ''''ABCD'''' rotates about it's own axis in a magnetic field. In practice, this field can be due to permanent magnets or electromagnets. The two ends of the coil are connected to slip rings ''''a'''' and ''''b'''' which are insulated from each other and from the central shaft. Two collecting brushed made up of carbon or copper press against these slip rings in order to collect the current induced in the coil. This current is conveyed to the external resistance ''''R'''' The rotating coil is referred to as the 'Armature' and the magnets are called 'Field Magnets' ====Working==== [[File:AC DC gen smoothed.svg|thumb|right|Current produced by an AC slip-ring generator, DC split-ring generator, and smoothed DC split-ring generator]] If the coil rotates in clockwise direction, the flux lined with it changes as it assumes successive positions in the field.Hence, an e.m.f is induced in it and this e.m.f is proportional to the rate of change of flux linkages, i.e ''e=NdΦ/dt'' [[File:Britannica Dynamo 7.jpg|thumb|left|Split ring dynamo showing unidirectional, non-continuous current.]] When the plane of the coil is at right angles to the lines of flux, i.e. position '1' in the figure, the flux,''Φ'', is maximum but the rate of change of flux,''dΦ/dt'' is minimum. This is because the segments ''''AB'''' and ''''CD'''' don't cut the flux but move along parallel to it. Thus, no e.m.f. is induced in the coil. This position is assumed as the starting position and hence, the angle of rotation is measured from here. As the coil rotates further, ''dΦ/dt'' increases till it reaches a maximum value at position 3 where the angle of rotation,θ, reaches a value of 90 degrees. Since the coil plane is now horizontal, the flux linked is minimum, but the rate of change of flux is maximum. In a similar manner,as the angle varies from 90 degrees to 180 degrees, the flux increases and rate of change of flux decreases till position 5. According to [[Wikipedia:Fleming's right hand rule|Fleming's Right Hand Rule]], the current is found to be flowing from '''A''' to '''B''' and '''C''' to '''D'''. The same process is repeated as the coil continues to rotate through angles 180 degrees to 360 degrees and positions 5 to 8, back to 1. However, by Fleming's Right Hand Rule, the current is found to be flowing from '''D''' to '''C''' and then '''B''' to '''A''' Thus, the direction of current is reversed every half cycle and this is called '''ALTERNATING CURRENT'''. This is illustrated in the figure above. A.C current, unlike D.C current does not maintain a constant direction, or even a constant magnitude in one direction. For making the flow of current unidirectional, slip rings are replaced by split rings. These are made up of conducting cylinders, cut into two halves or segments, insulated from each other by a thin mica sheet or other insulating material. Slit rings result in unidirectional current, but not this current is not continous like pure DC current. === Practical Generator === [[File:Dynamo (PSF).png|thumb|right|A cutaway drawing of a dynamo, showing the commutator]] The basic principle of a generator was explained in the above section. In practice, a generator has the following parts : 1.'''Frame or Yoke''' The yoke serves two purposes. The first one is to provide an outer covering, i.e. it should provide mechanical suppot for the motor. The second use is to provide a path for the magnetic field. Since the field is stationary( caused by DC) there are is no need to laminate the yoke. It is made from cast iron in cheap machines or sometimes using fabricated steel to obtain high values of permeability. 2.'''Pole''' The poles house the field coils around them. They also need not be laminated as they carry stationary field. Poles are usually made from cast iron for small machines and fabricated steel for high power machines. The pole shoes present at the end of poles act as support for the field coils and spread out the magnetic flux generated. The pole shoes thereby, reduce the reluctance of the air gap. This reduces the requirement of field currrent. 3.'''Field Coils''' The objective of the field coils is to provide the necessary mmf resulting in flux. Now, mmf is the product of number of turns and current. To reduce the current drawn, more number of turns are normally wound on the pole. The windings are usually made with copper. By reducing the currrent, the diameter of wire is reduced, leading to critical copper saving in the field coils. 4.'''Armature core''' It is the rotating part of the machine, and is cylindrical in shape. The purpose of the armature is to rotate the conductors in a uniform magnetic field. The armature is slotted and these slots house the armature conductors. The armature conductors are made of copper and are insulated. The field produced from these conductors is not stationary. Therfore, the armature is made from silicon steel stampings to reduce the hysteresis and eddy current losses. There are small key holes present throughout the armature to aid in proper cooling. The armature conductors are placed in the slots in different patterns to control the performance of the machine. 5.'''Armature windings or conductors''' The armature windings as previously specified are made of copper and are insulated from each other. There are placed in the slots present in the armature. The armature windings have diffferent arrangements leading to a different performance of the machine. Some popular armature winding arrangements are Wave, Lap, Drum, etc. 6.'''Commutator''' The commutator is one of the most important parts of the DC machine. It is like a rotating switch placed between the armature and the external circuit. It is arranged in such a way that it will reverse the connections to the external circuit at the instant of each reversal of current in the armature coil. The commutator essentially converts alternating current generated in the armature conductors to a unidirectional current. Coomutator is made using high conductivity copper segments seperated by thin layers of mica. 7.'''Brushes and Bearings''' The function of the brushes is to collect current from the commutator segments and supply it to the external load circuit. The brushes are rectangular in shape and rest on the commutator. Brushes are made from a variety of materials like carbon, graphite and copper. Copper brushes are costlier and are used only in machines with very high current ratings. Carbon is the preferred material for making brushes for the smaller rating machines. == DC Motor == The theory behind DC Motors are near identical to DC Generators. The main difference between DC Generators and DC Motors is as follows; DC Motors convert electrical energy into mechanical motion, whereas DC Generators convert mechanical motion into electrical energy. That is how electric cars have regenerative breaking. The battery provides electrical current to the motor units, the motors spin the wheels, and the car moves. When the car starts to brake, through the use of some software and some electrical properties, the motors slows the rotation of the wheel by converting the rotation back into electrical energy for the batteries. == Testing of DC Machines == == Transformer == == Induction Motor == == Alternators == == Synchronous Motors == A synchronous electric motor is an AC motor in which, at steady state,[1] the rotation of the shaft is synchronized with the frequency of the supply current; the rotation period is exactly equal to an integral number of AC cycles. Synchronous motors contain electromagnets on the stator of the motor that create a magnetic field which rotates in time with the oscillations of the line current. The rotor turns in step with this field, at the same rate. The motor does not rely on "slip" under usual operating conditions, and as a result produces torque at synchronous speed. Synchronous motors can be contrasted with induction motors, which must slip in order to produce the rotor magnetic field and to provide torque. The speed of the synchronous motor is determined by the number of magnetic poles and the line frequency. Synchronous motors are available in sub-fractional self-excited sizes[2] to high-horsepower industrial sizes.[1] In the fractional horsepower range, most synchronous motors are used where precise constant speed is required. In high-horsepower industrial sizes, the synchronous motor provides two important functions. First, it is a highly efficient means of converting AC energy to work. Second, it can operate at leading or unity power factor and thereby provide power-factor correction. ==Active Participants== [http://en.wikiversity.org/wiki/User:Laxmi.nair17 Laxmi Nair] - B.Tech,EEE,Amrita Vishwa Vidyapeetham Amit Kumar - B.Tech,EEE, Amrita Vishwa Vidyapeetham ==See also== [[Mechatronics II]] [http://en.wikiversity.org/wiki/School:Electrical_engineering School of Engineering] {{yawn}} {{engineering}} {{tertiary}} [[Category:Electrical engineering]] [[Category:Technology courses]] 6uyt830ta2ku6hzccqatdadvlztpqsx 0 54669 2690192 2543002 2024-12-04T03:00:23Z 199.19.145.45 /* The text with sources highlighted */ 2690192 wikitext text/x-wiki [[File:Modern document hypothesis.svg|thumb|240px|Diagram of one version of the Documentary Hypothesis. {|style="background:none" |<nowiki>*</nowiki>||includes most of Leviticus |- valign="top" |^†||includes most of Deuteronomy |- valign="top" |^‡||"''Deuteronomic history''": Joshua, Judges, 1 & 2 Samuel, 1 & 2 Kings |}]] The [[w:documentary hypothesis|documentary hypothesis]] hypothesizes four primary sources (traditionally known as J, E, P, and D) for the [[w:torah|Torah]]. These translations are based on the [[MetaWikipedia:wikisource:Bible (King James)|King James version]] of the Bible. This learning resource employs the latest iteration of the Documentary Hypothesis, known as the New Documentary Hypothesis. The New Documentary Hypothesis considers the four main sources to have been independent at the moment of redaction into the Torah, with a number of insertions into the redacted document by later scribes. The resource provides two ways to view the sources. The first method highlights the various sources as one reads through the Torah. The second method extracts each source's content from the Torah, and compiles it into a single, flowing document. == The text with sources highlighted == * [[Bible/King James/Documentary Hypothesis/Genesis|Genesis]] * [[Bible/King James/Documentary Hypothesis/Exodus|Exodus]] * [[Bible/King James/Documentary Hypothesis/Leviticus|Leviticus]] * [[Bible/King James/Documentary Hypothesis/Numbers|Numbers]] * [[Bible/King James/Documentary Hypothesis/Deuteronomy|Deuteronomy]] * Joshua == The Sources == *[[Bible/King James/Documentary Hypothesis/Jahwist source|Jahwist source]] ("J") **The [[Bible/King James/Documentary Hypothesis/Jahwist source/Song of Lamech|Song of Lamech]] **The [[Bible/King James/Documentary Hypothesis/Jahwist source/Blessing of Jacob|Blessing of Jacob]] **The [[Bible/King James/Documentary Hypothesis/Jahwist source/Song of the Sea|Song of the Sea]] *[[Bible/King James/Documentary Hypothesis/Elohist source|Elohist source]] ("E") **The [[Bible/King James/Documentary Hypothesis/Elohist source/Covenant Code|Covenant Code]] * [[Bible/King James/Documentary Hypothesis/Priestly source|Priestly source]] ("P") **The [[Bible/King James/Documentary Hypothesis/Priestly source/Narrative|narrative elements of P]] **The legal elements in "P" ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Levitical Laws|Levitical laws]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Holiness code|Holiness code]] ("H") ****The [[Bible/King James/Documentary Hypothesis/Priestly source/Holiness Code/Sexual Prohibitions|list of sexual prohibitions]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Kosher|list of clean and unclean animals]] **Ritual elements in "P" ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Levitical ritual|guides to ritual]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Levitical object descriptions|description of the tabernacle, incense, and vestments]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Levitical duties|list of duties of the Levite families]] **Tallies in "P" ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Altar dedication list|list of altar dedication offerings]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Midinite spoils list|list of spoils from the midianites]] **Genealogies in "P" ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Genealogy of the Children of Abraham|Genealogy of the children of Abraham]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Genealogy of Nations|genealogy of nations]] **Specifications of the components of Israel in "P" ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Census|Israelite census]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Borders of Canaan|description of the limits of Canaan]] * [[Bible/King James/Documentary Hypothesis/Deuteronomist source|Deuteronomist source]] ("D") ** [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version|First Deuteronomists Versio]]n ("Dtr1") *** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Narrative|Narrative elements in "Dtr1"]] *** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Deuteronomic Laws|Deuteronomic Laws]] *** Words for rituals in "Dtr1" **** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Prayer of the Tithe|Prayer of the Tithe]] **** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Prayer of Firstfruits|Prayer of Firstfruits]] **** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Mount Ebal Curse List|List of Mount Ebal curses]] **** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Curse blessing pairs|Pairs of Curses and Blessings]] *** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Kosher|List of clean and unclean food]] ** Additions for the Second Deuteronomist Version ("Dtr2") *** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/Secondary Deuteronomist Additions/Song of Moses|Song of Moses]] *** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/Secondary Deuteronomist Additions/Blessing of Moses|Blessing of Moses]] *** [[Bible/King James/Documentary Hypothesis/Deuteronomist source/Secondary Deuteronomist Additions/Threats and Promises|Threats and Promises]] * Redaction Sources ("R") ** [[Bible/King James/Documentary Hypothesis/Redaction Sources/Book of generations|Book of generations]] ** [[Bible/King James/Documentary Hypothesis/Redaction Sources/Stations List|The stations list]] ** [[Bible/King James/Documentary Hypothesis/Redaction Sources/Additional Rituals|Additional Rituals]] ** [[Bible/King James/Documentary Hypothesis/Redaction Sources/Explanatory Additions|Explanatory Additions]] ** [[Bible/King James/Documentary Hypothesis/Redaction Sources/Conflict resolution|Resolution of conflicts between sources]] * [[Sources by Chapter and Verse]] [[Category:Documentary hypothesis]] [[Category:Judaism]] akzpzsjzxazinwsfhzm3b65838wh30i 2690193 2690192 2024-12-04T03:03:38Z Lucasrbrown23 2994536 added Joshua link 2690193 wikitext text/x-wiki [[File:Modern document hypothesis.svg|thumb|240px|Diagram of one version of the Documentary Hypothesis. {|style="background:none" |<nowiki>*</nowiki>||includes most of Leviticus |- valign="top" |^†||includes most of Deuteronomy |- valign="top" |^‡||"''Deuteronomic history''": Joshua, Judges, 1 & 2 Samuel, 1 & 2 Kings |}]] The [[w:documentary hypothesis|documentary hypothesis]] hypothesizes four primary sources (traditionally known as J, E, P, and D) for the [[w:torah|Torah]]. These translations are based on the [[MetaWikipedia:wikisource:Bible (King James)|King James version]] of the Bible. This learning resource employs the latest iteration of the Documentary Hypothesis, known as the New Documentary Hypothesis. The New Documentary Hypothesis considers the four main sources to have been independent at the moment of redaction into the Torah, with a number of insertions into the redacted document by later scribes. The resource provides two ways to view the sources. The first method highlights the various sources as one reads through the Torah. The second method extracts each source's content from the Torah, and compiles it into a single, flowing document. == The text with sources highlighted == * [[Bible/King James/Documentary Hypothesis/Genesis|Genesis]] * [[Bible/King James/Documentary Hypothesis/Exodus|Exodus]] * [[Bible/King James/Documentary Hypothesis/Leviticus|Leviticus]] * [[Bible/King James/Documentary Hypothesis/Numbers|Numbers]] * [[Bible/King James/Documentary Hypothesis/Deuteronomy|Deuteronomy]] * [[Bible/King James/Documentary Hypothesis/Joshua|Joshua]] == The Sources == *[[Bible/King James/Documentary Hypothesis/Jahwist source|Jahwist source]] ("J") **The [[Bible/King James/Documentary Hypothesis/Jahwist source/Song of Lamech|Song of Lamech]] **The [[Bible/King James/Documentary Hypothesis/Jahwist source/Blessing of Jacob|Blessing of Jacob]] **The [[Bible/King James/Documentary Hypothesis/Jahwist source/Song of the Sea|Song of the Sea]] *[[Bible/King James/Documentary Hypothesis/Elohist source|Elohist source]] ("E") **The [[Bible/King James/Documentary Hypothesis/Elohist source/Covenant Code|Covenant Code]] * [[Bible/King James/Documentary Hypothesis/Priestly source|Priestly source]] ("P") **The [[Bible/King James/Documentary Hypothesis/Priestly source/Narrative|narrative elements of P]] **The legal elements in "P" ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Levitical Laws|Levitical laws]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Holiness code|Holiness code]] ("H") ****The [[Bible/King James/Documentary Hypothesis/Priestly source/Holiness Code/Sexual Prohibitions|list of sexual prohibitions]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Kosher|list of clean and unclean animals]] **Ritual elements in "P" ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Levitical ritual|guides to ritual]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Levitical object descriptions|description of the tabernacle, incense, and vestments]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Levitical duties|list of duties of the Levite families]] **Tallies in "P" ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Altar dedication list|list of altar dedication offerings]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Midinite spoils list|list of spoils from the midianites]] **Genealogies in "P" ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Genealogy of the Children of Abraham|Genealogy of the children of Abraham]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Genealogy of Nations|genealogy of nations]] **Specifications of the components of Israel in "P" ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Census|Israelite census]] ***The [[Bible/King James/Documentary Hypothesis/Priestly source/Borders of Canaan|description of the limits of Canaan]] * [[Bible/King James/Documentary Hypothesis/Deuteronomist source|Deuteronomist source]] ("D") ** [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version|First Deuteronomists Versio]]n ("Dtr1") *** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Narrative|Narrative elements in "Dtr1"]] *** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Deuteronomic Laws|Deuteronomic Laws]] *** Words for rituals in "Dtr1" **** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Prayer of the Tithe|Prayer of the Tithe]] **** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Prayer of Firstfruits|Prayer of Firstfruits]] **** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Mount Ebal Curse List|List of Mount Ebal curses]] **** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Curse blessing pairs|Pairs of Curses and Blessings]] *** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/First Deuteronomist Version/Kosher|List of clean and unclean food]] ** Additions for the Second Deuteronomist Version ("Dtr2") *** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/Secondary Deuteronomist Additions/Song of Moses|Song of Moses]] *** The [[Bible/King James/Documentary Hypothesis/Deuteronomist source/Secondary Deuteronomist Additions/Blessing of Moses|Blessing of Moses]] *** [[Bible/King James/Documentary Hypothesis/Deuteronomist source/Secondary Deuteronomist Additions/Threats and Promises|Threats and Promises]] * Redaction Sources ("R") ** [[Bible/King James/Documentary Hypothesis/Redaction Sources/Book of generations|Book of generations]] ** [[Bible/King James/Documentary Hypothesis/Redaction Sources/Stations List|The stations list]] ** [[Bible/King James/Documentary Hypothesis/Redaction Sources/Additional Rituals|Additional Rituals]] ** [[Bible/King James/Documentary Hypothesis/Redaction Sources/Explanatory Additions|Explanatory Additions]] ** [[Bible/King James/Documentary Hypothesis/Redaction Sources/Conflict resolution|Resolution of conflicts between sources]] * [[Sources by Chapter and Verse]] [[Category:Documentary hypothesis]] [[Category:Judaism]] 729qnm37ou2ctjg815ij46m817p0yw4 0 71910 2690162 2243356 2024-12-03T20:24:21Z Ekbreckenridge 2994477 Added a table for Symbols and Abbreviations 2690162 wikitext text/x-wiki [[Image:Wikiversity-logo-Snorky.svg|right|thumb|80px|[[school:Engineering|Engineering]]]] {{engineering}} {{secondary}} {{tertiary}} Let us begin with a few fundamental ideas about electricity to anchor all of your future lessons... __TOC__ ==Fundamental Background== First of all, you might ask yourself, 'what exactly is electricity?' At the level of atomic physics, electricity is one of the fundamental forces of nature, arising from an "electric charge" possessed by subatomic particles (notably protons and electrons). ==Electricity in Practice== The preceding description in terms of fundamental particles and forces is perhaps too theoretical for practical use. What is electricity in practice? ===Electric charge=== The tiny imbalance of positive and negative charges discussed above is caused by electrons moving (in enormous numbers at the atomic scale but very tiny numbers percentage-wise) away from the atomic nuclei to which they belong. The unit of quantity of electric charge is the ''coulomb'', abbreviated "C", and named after Charles-Augustin Coulomb. It is 6.241&nbsp;x&nbsp;10¹⁸ elementary charges. Or equivalently, the elementary charge (charge on a single electron or proton) is 1.602&nbsp;x&nbsp;10^-19 coulombs. ===Electric current=== Flow of charge&mdash;what we call current&mdash;could be thought of as flow of positive charge in one direction, or of negative charge in the other direction. ''By convention, current flow is always considered to be the flow of positive charge, even though that is contrary to the actual flow of (negative) electrons.'' Hence the current is considered to flow ''out'' of the positive terminal of a battery, through whatever is being powered, and ''back into'' the negative terminal, even though electron flow through the wires is in the opposite direction. The unit of current flow is the ''ampere'', abbreviated "A", which is a flow rate of one coulomb per second. It is named after André-Marie Ampère. In the hydraulic analogy, it is analogous to the amount of flow through a pipe, or over a dam, etc., which might be measured in liters per second with the hydraulic analogy. ===Kirchoff's Laws=== There are two famous "laws" of electrical engineering, known as [[Kirchhoff's Voltage Law]] and [[Kirchhoff's Current Law]]. They are really just straightforward applications of what has been discussed above. '''Kirchhoff's Voltage Law''' (sometimes abbreviated KVL) The sum of the voltage drops around any closed path in a circuit is zero This is just conservation of energy&mdash;a quantity of electric charge could pick up energy for free by going around a closed loop with a nonzero total voltage drop. Remember that "voltage drop" between two points can be either positive or negative. '''Kirchhoff's Current Law '''(sometimes abbreviated KCL) The sum of the currents flowing into a point in a circuit is zero This is just conservation of charge. Remember that current flow "into" a point is negative if the current is flowing out. now ===[[Ohm's Law]]=== There is a similar principle for electricity: Ohm's law, discovered by Georg Simon Ohm in the 1820's Ohm's law states that The current through a resistive medium is proportional to the applied voltage :<math>V = IR\,</math>&nbsp;&nbsp;&nbsp;Voltage equals current times resistance. :Also stated, of course, as: :<math>I = \frac{V}{R}</math> :<math>R = \frac{V}{I}</math> Here are a few approximate conductivities, in siemens per meter: *Superconductors: infinity (because of complicated quantum-mechanical phenomena) *Silver: 6 * 10⁷ *Silicon: 2 * 10^-3 (but, in semiconductor materials, it is "doped" with impurities, giving it a much higher conductivity) *Glass: about 10^-12 *Air: about 10^-14 *Paraffin: about 10^-17 *Teflon: about 10^-23 ===[[Watt's Law]]=== Watt's law, discovered by Watt in the 1820's, states that the power through a resistive medium is proportional to the applied voltage :<math>P = IV = </math>&nbsp;&nbsp;&nbsp;Power equals current times voltage. :Also stated, of course, as: :<math>I = \frac{P}{V}</math> :<math>V = \frac{P}{I}</math> ==="I-squared-R" and Joule's law=== One sometimes encounters phrases like "I-squared-R losses" in a wire. This is a combination of the power formula and Ohm's law. :<math>P = VI = (IR) I = I^2 R\,</math> Notice that the amount of power lost in a wire is proportional to the ''square'' of the current. The phenomenon of heat being evolved when electricity passes through a conductor is sometimes called ''Joule's law''. It's really just a consequence of conservation of energy and the equivalence of heat to other forms of energy. ==Symbols and Abbreviations== The symbols used for quantities in electrical engineering can be confusing, since the symbol for a quantity may be different from the symbol for the units in which it is measured. We list the common symbols here, even though we have not yet defined all of the concepts involved. ===[[Electrical charge]] === :is typically denoted <math>Q</math>, measured in coulombs, abbreviated <math>C</math>. ===[[Current]] === :is typically denoted <math>I</math>, measured in amperes, abbreviated <math>A</math>. An ampere is, among other things, a coulomb per second. :Example: <math>V = IR\,</math>&nbsp;&nbsp;&nbsp;Ohm's law; voltage equals current times resistance. :Example: "<math>I = 28mA\,</math>"&nbsp;&nbsp;&nbsp;"The current is 28 milliamperes." === [[Voltage]] === :is typically denoted <math>V</math> (or sometimes <math>E</math>), and measured in volts, abbreviated <math>V</math>. The use of "<math>E</math>" stands for "emf" (electro-motive force.) A volt is, among other things, a joule per coulomb. :Example: "<math>V = 28mV\,</math>"&nbsp;&nbsp;&nbsp;"The voltage is 28 millivolts." ===[[Resistance]] === :is typically denoted <math>R</math>, measured in ohms, abbreviated with the capital Greek omega: <math>\Omega</math>. An ohm is, among other things, a volt per ampere. :Example: "<math>R = 2.7K\Omega\,</math>"&nbsp;&nbsp;&nbsp;"The resistance is 2.7 kilohms." ===[[Conductance]] === :It is sometimes useful to speak of the reciprocal of resistance. This is called conductance, and is typically denoted <math>G</math>, traditionally measured in "mhos" ("mho" is "ohm" spelled backwards), abbreviated with an upside-down omega: <math>\mho</math>. A less flippant term than "mho" has been adopted: the siemens, abbreviated <math>S</math>. A mho/siemens is, among other things, an ampere per volt. :Example: <math>I = VG\,</math>&nbsp;&nbsp;&nbsp;Ohm's law rewritten in terms of conductance. :Example: "<math>G = 65m\mho\,</math>"&nbsp;&nbsp;&nbsp;"The conductance is 65 millimhos." :Example: "<math>G = 65mS\,</math>"&nbsp;&nbsp;&nbsp;"The conductance is 65 millisiemens." ===[[Capacitance]]=== :is typically denoted <math>C</math>, measured in farads, abbreviated <math>f</math>. A farad is, among other things, a second per ohm, or a coulomb per volt. :Example: <math>t = RC\,</math>&nbsp;&nbsp;&nbsp;The time constant is the resistance times the capacitance. :Example: "<math>C = 75pf\,</math>"&nbsp;&nbsp;&nbsp;"The capacitance is 75 picofarads." ===[[Inductance]]=== :is typically denoted <math>L</math>, measured in henries, abbreviated <math>h</math>. A henry is, among other things, an ohm-second. :Example: <math>f = \frac{1}{2\ \pi\ \sqrt{L\ C}}</math>&nbsp;&nbsp;&nbsp;is the formula for the frequency of a resonant circuit. :Example: "<math>L = 120nh\,</math>"&nbsp;&nbsp;&nbsp;"The inductance is 120 nanohenries." ===[[Power]]=== :is typically denoted <math>P</math>, measured in watts, abbreviated <math>W</math>. A watt is, among other things, a joule per second, or a volt-ampere. :Example: <math>P = VI\,</math>&nbsp;&nbsp;&nbsp;The power is the voltage times the current. :Example: "<math>P = 75W\,</math>"&nbsp;&nbsp;&nbsp;"The power is 75 watts." ===[[The frequency]]=== :of an oscillation or signal is typically denoted <math>f</math>, measured in hertz, abbreviated <math>Hz</math>. A hertz is really just a reciprocal second. In fact, the unit of frequency used to be just "cycles per second" or simply "cycles". :Example: "<math>f = 102.5 Mc\,</math>"&nbsp;&nbsp;&nbsp;"102.5 megacycles on the FM dial" (old way.) :Example: "<math>f = 102.5 MHz\,</math>"&nbsp;&nbsp;&nbsp;"102.5 megahertz on the FM dial" (new way.) It happens that, in a lot of the mathematical formulas the unit of ''radians per second'' is superior. A frequency in radians per second is <math>2\ \pi</math> times the frequency in hertz. When measured this way, the symbol <math>f</math> is replaced with the lower-case Greek omega: <math>\omega</math>. Many occurrences of <math>2\ \pi</math> disappear from various formulas when radians are used. :Example: <math>\omega = \frac{1}{\sqrt{L\ C}}</math>&nbsp;&nbsp;&nbsp;is the formula for the frequency of a resonant circuit, in radians per second. :Example: <math>X_C = \frac{1}{2\ \pi\ f\ C}</math>&nbsp;&nbsp;&nbsp;is the formula for capacitive reactance, calibrated in hertz. :Example: <math>X_C = \frac{1}{\omega\ C}</math>&nbsp;&nbsp;&nbsp;is the formula for capacitive reactance, calibrated in radians per second. :Example: "<math>\omega = 644.0265mrad/s\,</math>"&nbsp;&nbsp;&nbsp;"644.0265 megaradians per second on the FM dial" (not known to have ever been announced.) ==== Units: ==== {| class="wikitable" |+ !Unit Name !Symbol !Quantity !Definition !Measurement |- |Ampere |A |Electrical Current (I) |Electrical current is the flow rate of electric charge in electric field, usually in electrical circuit. |1V = 1J / 1C |- |Volts |V |Voltage (V, E) |Electrical voltage is defined as electric potential difference between two points of an electric field. |1A = 1C / 1s |- |Ohm |Ω |Resistance (R) |Resistance is an electrical quantity that measures how the device or material reduces the electric current flow through it. |1Ω = 1V / 1A |- |Watt |W |Electrical Power (P) |Electric power is the rate of energy consumption in an electrical circuit. |1W = 1J / 1s 1W = 1V ⋅ 1A |- |Decibel-milliwatt |dBm |Electric Power (P) |Decibel-milliwatt or dBm is a unit of electric power, measured with logarithmic scale referenced to 1mW. |10dBm = 10 ⋅ log₁₀(10mW / 1mW) |- |Decibel-Watt |dBW |Electric Power (P) |Decibel-watt or dBW is a unit of electric power, measured with logarithmic scale referenced to 1W. |10dBW = 10 ⋅ log₁₀(10W / 1W) |- |Volt-Ampere-Reactive |var |Reactive Power (Q) | | |- |Volt-Ampere |VA |Apparent Power (S) |VA is a unit of apparent power |1VA = 1V * 1A |- |Farad |F |Capacitance (C) |Farad is the unit of capacitance. It represents the amount of electric charge in coulombs that is stored per 1 volt. |1F = 1C / 1V |- |Henry |H |Inductance (L) |Henry is the unit of inductance. |1H = 1Wb / 1A |- |siemens / mho |S |Conductance (G) Admittance (Y) |siemens is the unit of conductance, which is the opposite of resistance. |1S = 1 / 1Ω |- |Coulomb |C |Electrical Charge (Q) |Coulomb is the unit of electric charge. |1C = 6.238792×10¹⁸ electron charges |- |Ampere-hour |Ah |Electrical Charge (Q) |One ampere-hour is the electric charge that flow in electrical circuit, when a current of 1 ampere is applied for 1 hour. |1Ah = 1A ⋅ 1hour One ampere-hour is equal to 3600 coulombs. 1Ah = 3600C |- |Joule |J |Energy (E) |Joule is the unit of energy. |1J = 1 kg ⋅ m² / s² |- |Kilowatt-hour |kWh |Energy (E) |Kilowatt-hour is a unit of energy. |1kWh = 1kW ⋅ 1h = 1000W ⋅ 1h |- |Electron-volt |eV |Energy (E) | | |- |Ohm-meter |Ω*m |Resistivity (''ρ'') | | |- |siemens per meter |S/m |Conductivity (''σ'') | | |- |Volts per meter | |Electric field (E) | | |- |Newtons per coulomb | |Electric field (E) | | |- |Volt-meter | |Electric flux (Φ_e) | | |- |Tesla | |Magnetic field (B) |Tesla is the unit of magnetic field. |1T = 1Wb / 1m² |- |Gauss | |Magnetic field (B) |Weber is the unit of magnetic flux. |1Wb = 1V ⋅ 1s |- |Weber | |Magnetic flux (Φ_m) | | |- |Hertz | |Frequency (f) | | |- |Seconds | |Time (t) | | |- |Meter / metre | |Length (l) | | |- |Square-meter | |Area (A) | | |- |Decibel | | | | |- |Parts per million | | | | |} Definitions for the table came from Rapid Tables<ref>{{Cite web|url=https://www.rapidtables.com/electric/Electric_units.html|title=Electrical units of measurment (V,A,Ω,W,...)|website=www.rapidtables.com|access-date=2024-12-03}}</ref> ==Static Electricity == Electricity manifests itself in two seemingly different ways. ''They are different manifestations of the same thing.'' "Static" electricity was known to the ancients. It involves very high voltages and very low currents&mdash;the currents are so low that one doesn't always realize how high the voltage is. In order for such high voltages to persist somewhere, the insulation must be extremely good, that is, the resistances must be extremely high. Fortunately for the history of science, materials like glass, amber, and some types of rubber and other materials, have the necessary high resistance. (The word "electricity" comes from the Greek word for amber.) The voltages involved with static electricity are high enough to make the leaves of an electroscope move, but the currents are so low that we would normally not notice any effect of the current. =="Current" Electricity== "Current" electricity involves lower voltages and currents large enough to power light bulbs, motors, and such. Rubbing a glass rod with a piece of silk can't come anywhere near to providing the required level of sustained current. To get the required sustained levels of current requires either ongoing chemical reactions (as in a battery) or electromechanical devices (as in a generator.) The ability to do this was discovered in the 18^th and 19^th centuries by Luigi Galvani, Alessandro Volta and Michael Faraday. The study of electronics and electrical engineering involve "current" electricity almost exclusively. ==Series and Parallel Connections== The terms "series" and "parallel" are actually used quite loosely by electrical engineers, to describe aspects of circuit topology. * Series connection * Parallel connection : [[Image:Seriesparallel.jpg|right|thumb|500 px|Schematic diagram showing series and parallel connections.]] * 2 port network ==How Are the Units Defined?== As one can tell from the connections among the electrical units and the physical units such as newtons, joules, and watts, a lot of care went into the design of the system of units. But how is the coulomb defined? Why is it equal to 6.241&nbsp;x&nbsp;10¹⁸ elementary charges? The coulomb and volt are defined in terms of the ampere, so that a volt times an ampere equals a watt, that is, a newton-meter per second. And a coulomb is an ampere-second. The ampere was determined experimentally, as follows: it is the amount of current flowing in each of two infinitely long and infinitely thin parallel wires separated by a distance of one meter that causes an attractive magnetic force of <math>2 \times 10^{-7}</math> newtons per meter along the length of the wires. Why the factor of <math>2 \times 10^{-7}</math>? This was chosen to make the volt a reasonable quantity relative to the voltage coming out of batteries. This definition of the units in terms of the magnetic force has the effect of defining the fundamental constant of the magnetic force, labeled <math>\mu\,</math>, to be <math>4 \pi \times 10^{-7}\,</math>. The fundamental constant of the electric force, labeled <math>\epsilon\,</math>, is related to this, according to the formula :<math>c = \frac{1}{\sqrt{\epsilon \mu}}\,</math> where <math>c\,</math>, the speed of light, was traditionally determined experimentally. <ref>The constant <math>c\,</math>, the speed of light, is now defined to be 299,792,458 meters per second. A second is officially defined in terms of a cesium clock and the meter is derived from that.</ref> ==The Next Lecture== For the next lecture, see [[Introduction to Electricity II]]. ==Footnotes and References== <references/> ==See Also== * [[Ohm's law]] * [[Kirchhoff's Voltage Law]] * [[Kirchhoff's Current Law]] * [[Maxwell's Equations]] * [[w:Semiconductor]] [[Category:Electrical engineering]] [[Category:Electronic engineering]] [[Category:Electricity]] kayli5wefajlvssst40huikw4juo7dh 2690221 2690162 2024-12-04T04:50:38Z Ekbreckenridge 2994477 /* Units: */ 2690221 wikitext text/x-wiki [[Image:Wikiversity-logo-Snorky.svg|right|thumb|80px|[[school:Engineering|Engineering]]]] {{engineering}} {{secondary}} {{tertiary}} Let us begin with a few fundamental ideas about electricity to anchor all of your future lessons... __TOC__ ==Fundamental Background== First of all, you might ask yourself, 'what exactly is electricity?' At the level of atomic physics, electricity is one of the fundamental forces of nature, arising from an "electric charge" possessed by subatomic particles (notably protons and electrons). ==Electricity in Practice== The preceding description in terms of fundamental particles and forces is perhaps too theoretical for practical use. What is electricity in practice? ===Electric charge=== The tiny imbalance of positive and negative charges discussed above is caused by electrons moving (in enormous numbers at the atomic scale but very tiny numbers percentage-wise) away from the atomic nuclei to which they belong. The unit of quantity of electric charge is the ''coulomb'', abbreviated "C", and named after Charles-Augustin Coulomb. It is 6.241&nbsp;x&nbsp;10¹⁸ elementary charges. Or equivalently, the elementary charge (charge on a single electron or proton) is 1.602&nbsp;x&nbsp;10^-19 coulombs. ===Electric current=== Flow of charge&mdash;what we call current&mdash;could be thought of as flow of positive charge in one direction, or of negative charge in the other direction. ''By convention, current flow is always considered to be the flow of positive charge, even though that is contrary to the actual flow of (negative) electrons.'' Hence the current is considered to flow ''out'' of the positive terminal of a battery, through whatever is being powered, and ''back into'' the negative terminal, even though electron flow through the wires is in the opposite direction. The unit of current flow is the ''ampere'', abbreviated "A", which is a flow rate of one coulomb per second. It is named after André-Marie Ampère. In the hydraulic analogy, it is analogous to the amount of flow through a pipe, or over a dam, etc., which might be measured in liters per second with the hydraulic analogy. ===Kirchoff's Laws=== There are two famous "laws" of electrical engineering, known as [[Kirchhoff's Voltage Law]] and [[Kirchhoff's Current Law]]. They are really just straightforward applications of what has been discussed above. '''Kirchhoff's Voltage Law''' (sometimes abbreviated KVL) The sum of the voltage drops around any closed path in a circuit is zero This is just conservation of energy&mdash;a quantity of electric charge could pick up energy for free by going around a closed loop with a nonzero total voltage drop. Remember that "voltage drop" between two points can be either positive or negative. '''Kirchhoff's Current Law '''(sometimes abbreviated KCL) The sum of the currents flowing into a point in a circuit is zero This is just conservation of charge. Remember that current flow "into" a point is negative if the current is flowing out. now ===[[Ohm's Law]]=== There is a similar principle for electricity: Ohm's law, discovered by Georg Simon Ohm in the 1820's Ohm's law states that The current through a resistive medium is proportional to the applied voltage :<math>V = IR\,</math>&nbsp;&nbsp;&nbsp;Voltage equals current times resistance. :Also stated, of course, as: :<math>I = \frac{V}{R}</math> :<math>R = \frac{V}{I}</math> Here are a few approximate conductivities, in siemens per meter: *Superconductors: infinity (because of complicated quantum-mechanical phenomena) *Silver: 6 * 10⁷ *Silicon: 2 * 10^-3 (but, in semiconductor materials, it is "doped" with impurities, giving it a much higher conductivity) *Glass: about 10^-12 *Air: about 10^-14 *Paraffin: about 10^-17 *Teflon: about 10^-23 ===[[Watt's Law]]=== Watt's law, discovered by Watt in the 1820's, states that the power through a resistive medium is proportional to the applied voltage :<math>P = IV = </math>&nbsp;&nbsp;&nbsp;Power equals current times voltage. :Also stated, of course, as: :<math>I = \frac{P}{V}</math> :<math>V = \frac{P}{I}</math> ==="I-squared-R" and Joule's law=== One sometimes encounters phrases like "I-squared-R losses" in a wire. This is a combination of the power formula and Ohm's law. :<math>P = VI = (IR) I = I^2 R\,</math> Notice that the amount of power lost in a wire is proportional to the ''square'' of the current. The phenomenon of heat being evolved when electricity passes through a conductor is sometimes called ''Joule's law''. It's really just a consequence of conservation of energy and the equivalence of heat to other forms of energy. ==Symbols and Abbreviations== The symbols used for quantities in electrical engineering can be confusing, since the symbol for a quantity may be different from the symbol for the units in which it is measured. We list the common symbols here, even though we have not yet defined all of the concepts involved. ===[[Electrical charge]] === :is typically denoted <math>Q</math>, measured in coulombs, abbreviated <math>C</math>. ===[[Current]] === :is typically denoted <math>I</math>, measured in amperes, abbreviated <math>A</math>. An ampere is, among other things, a coulomb per second. :Example: <math>V = IR\,</math>&nbsp;&nbsp;&nbsp;Ohm's law; voltage equals current times resistance. :Example: "<math>I = 28mA\,</math>"&nbsp;&nbsp;&nbsp;"The current is 28 milliamperes." === [[Voltage]] === :is typically denoted <math>V</math> (or sometimes <math>E</math>), and measured in volts, abbreviated <math>V</math>. The use of "<math>E</math>" stands for "emf" (electro-motive force.) A volt is, among other things, a joule per coulomb. :Example: "<math>V = 28mV\,</math>"&nbsp;&nbsp;&nbsp;"The voltage is 28 millivolts." ===[[Resistance]] === :is typically denoted <math>R</math>, measured in ohms, abbreviated with the capital Greek omega: <math>\Omega</math>. An ohm is, among other things, a volt per ampere. :Example: "<math>R = 2.7K\Omega\,</math>"&nbsp;&nbsp;&nbsp;"The resistance is 2.7 kilohms." ===[[Conductance]] === :It is sometimes useful to speak of the reciprocal of resistance. This is called conductance, and is typically denoted <math>G</math>, traditionally measured in "mhos" ("mho" is "ohm" spelled backwards), abbreviated with an upside-down omega: <math>\mho</math>. A less flippant term than "mho" has been adopted: the siemens, abbreviated <math>S</math>. A mho/siemens is, among other things, an ampere per volt. :Example: <math>I = VG\,</math>&nbsp;&nbsp;&nbsp;Ohm's law rewritten in terms of conductance. :Example: "<math>G = 65m\mho\,</math>"&nbsp;&nbsp;&nbsp;"The conductance is 65 millimhos." :Example: "<math>G = 65mS\,</math>"&nbsp;&nbsp;&nbsp;"The conductance is 65 millisiemens." ===[[Capacitance]]=== :is typically denoted <math>C</math>, measured in farads, abbreviated <math>f</math>. A farad is, among other things, a second per ohm, or a coulomb per volt. :Example: <math>t = RC\,</math>&nbsp;&nbsp;&nbsp;The time constant is the resistance times the capacitance. :Example: "<math>C = 75pf\,</math>"&nbsp;&nbsp;&nbsp;"The capacitance is 75 picofarads." ===[[Inductance]]=== :is typically denoted <math>L</math>, measured in henries, abbreviated <math>h</math>. A henry is, among other things, an ohm-second. :Example: <math>f = \frac{1}{2\ \pi\ \sqrt{L\ C}}</math>&nbsp;&nbsp;&nbsp;is the formula for the frequency of a resonant circuit. :Example: "<math>L = 120nh\,</math>"&nbsp;&nbsp;&nbsp;"The inductance is 120 nanohenries." ===[[Power]]=== :is typically denoted <math>P</math>, measured in watts, abbreviated <math>W</math>. A watt is, among other things, a joule per second, or a volt-ampere. :Example: <math>P = VI\,</math>&nbsp;&nbsp;&nbsp;The power is the voltage times the current. :Example: "<math>P = 75W\,</math>"&nbsp;&nbsp;&nbsp;"The power is 75 watts." ===[[The frequency]]=== :of an oscillation or signal is typically denoted <math>f</math>, measured in hertz, abbreviated <math>Hz</math>. A hertz is really just a reciprocal second. In fact, the unit of frequency used to be just "cycles per second" or simply "cycles". :Example: "<math>f = 102.5 Mc\,</math>"&nbsp;&nbsp;&nbsp;"102.5 megacycles on the FM dial" (old way.) :Example: "<math>f = 102.5 MHz\,</math>"&nbsp;&nbsp;&nbsp;"102.5 megahertz on the FM dial" (new way.) It happens that, in a lot of the mathematical formulas the unit of ''radians per second'' is superior. A frequency in radians per second is <math>2\ \pi</math> times the frequency in hertz. When measured this way, the symbol <math>f</math> is replaced with the lower-case Greek omega: <math>\omega</math>. Many occurrences of <math>2\ \pi</math> disappear from various formulas when radians are used. :Example: <math>\omega = \frac{1}{\sqrt{L\ C}}</math>&nbsp;&nbsp;&nbsp;is the formula for the frequency of a resonant circuit, in radians per second. :Example: <math>X_C = \frac{1}{2\ \pi\ f\ C}</math>&nbsp;&nbsp;&nbsp;is the formula for capacitive reactance, calibrated in hertz. :Example: <math>X_C = \frac{1}{\omega\ C}</math>&nbsp;&nbsp;&nbsp;is the formula for capacitive reactance, calibrated in radians per second. :Example: "<math>\omega = 644.0265mrad/s\,</math>"&nbsp;&nbsp;&nbsp;"644.0265 megaradians per second on the FM dial" (not known to have ever been announced.) === Units: === {| class="wikitable" |+ !Unit Name !Symbol !Quantity !Definition !Measurement |- |Ampere |A |Electrical Current (I) |Electrical current is the flow rate of electric charge in electric field, usually in electrical circuit. |1V = 1J / 1C |- |Volts |V |Voltage (V, E) |Electrical voltage is defined as electric potential difference between two points of an electric field. |1A = 1C / 1s |- |Ohm |Ω |Resistance (R) |Resistance is an electrical quantity that measures how the device or material reduces the electric current flow through it. |1Ω = 1V / 1A |- |Watt |W |Electrical Power (P) |Electric power is the rate of energy consumption in an electrical circuit. |1W = 1J / 1s 1W = 1V ⋅ 1A |- |Decibel-milliwatt |dBm |Electric Power (P) |Decibel-milliwatt or dBm is a unit of electric power, measured with logarithmic scale referenced to 1mW. |10dBm = 10 ⋅ log₁₀(10mW / 1mW) |- |Decibel-Watt |dBW |Electric Power (P) |Decibel-watt or dBW is a unit of electric power, measured with logarithmic scale referenced to 1W. |10dBW = 10 ⋅ log₁₀(10W / 1W) |- |Volt-Ampere-Reactive |var |Reactive Power (Q) | | |- |Volt-Ampere |VA |Apparent Power (S) |VA is a unit of apparent power |1VA = 1V * 1A |- |Farad |F |Capacitance (C) |Farad is the unit of capacitance. It represents the amount of electric charge in coulombs that is stored per 1 volt. |1F = 1C / 1V |- |Henry |H |Inductance (L) |Henry is the unit of inductance. |1H = 1Wb / 1A |- |siemens / mho |S |Conductance (G) Admittance (Y) |siemens is the unit of conductance, which is the opposite of resistance. |1S = 1 / 1Ω |- |Coulomb |C |Electrical Charge (Q) |Coulomb is the unit of electric charge. |1C = 6.238792×10¹⁸ electron charges |- |Ampere-hour |Ah |Electrical Charge (Q) |One ampere-hour is the electric charge that flow in electrical circuit, when a current of 1 ampere is applied for 1 hour. |1Ah = 1A ⋅ 1hour One ampere-hour is equal to 3600 coulombs. 1Ah = 3600C |- |Joule |J |Energy (E) |Joule is the unit of energy. |1J = 1 kg ⋅ m² / s² |- |Kilowatt-hour |kWh |Energy (E) |Kilowatt-hour is a unit of energy. |1kWh = 1kW ⋅ 1h = 1000W ⋅ 1h |- |Electron-volt |eV |Energy (E) | | |- |Ohm-meter |Ω*m |Resistivity (''ρ'') | | |- |siemens per meter |S/m |Conductivity (''σ'') | | |- |Volts per meter | |Electric field (E) | | |- |Newtons per coulomb | |Electric field (E) | | |- |Volt-meter | |Electric flux (Φ_e) | | |- |Tesla | |Magnetic field (B) |Tesla is the unit of magnetic field. |1T = 1Wb / 1m² |- |Gauss | |Magnetic field (B) |Weber is the unit of magnetic flux. |1Wb = 1V ⋅ 1s |- |Weber | |Magnetic flux (Φ_m) | | |- |Hertz | |Frequency (f) | | |- |Seconds | |Time (t) | | |- |Meter / metre | |Length (l) | | |- |Square-meter | |Area (A) | | |- |Decibel | | | | |- |Parts per million | | | | |} Definitions for the table came from Rapid Tables<ref>{{Cite web|url=https://www.rapidtables.com/electric/Electric_units.html|title=Electrical units of measurment (V,A,Ω,W,...)|website=www.rapidtables.com|access-date=2024-12-03}}</ref> ==Static Electricity == Electricity manifests itself in two seemingly different ways. ''They are different manifestations of the same thing.'' "Static" electricity was known to the ancients. It involves very high voltages and very low currents&mdash;the currents are so low that one doesn't always realize how high the voltage is. In order for such high voltages to persist somewhere, the insulation must be extremely good, that is, the resistances must be extremely high. Fortunately for the history of science, materials like glass, amber, and some types of rubber and other materials, have the necessary high resistance. (The word "electricity" comes from the Greek word for amber.) The voltages involved with static electricity are high enough to make the leaves of an electroscope move, but the currents are so low that we would normally not notice any effect of the current. =="Current" Electricity== "Current" electricity involves lower voltages and currents large enough to power light bulbs, motors, and such. Rubbing a glass rod with a piece of silk can't come anywhere near to providing the required level of sustained current. To get the required sustained levels of current requires either ongoing chemical reactions (as in a battery) or electromechanical devices (as in a generator.) The ability to do this was discovered in the 18^th and 19^th centuries by Luigi Galvani, Alessandro Volta and Michael Faraday. The study of electronics and electrical engineering involve "current" electricity almost exclusively. ==Series and Parallel Connections== The terms "series" and "parallel" are actually used quite loosely by electrical engineers, to describe aspects of circuit topology. * Series connection * Parallel connection : [[Image:Seriesparallel.jpg|right|thumb|500 px|Schematic diagram showing series and parallel connections.]] * 2 port network ==How Are the Units Defined?== As one can tell from the connections among the electrical units and the physical units such as newtons, joules, and watts, a lot of care went into the design of the system of units. But how is the coulomb defined? Why is it equal to 6.241&nbsp;x&nbsp;10¹⁸ elementary charges? The coulomb and volt are defined in terms of the ampere, so that a volt times an ampere equals a watt, that is, a newton-meter per second. And a coulomb is an ampere-second. The ampere was determined experimentally, as follows: it is the amount of current flowing in each of two infinitely long and infinitely thin parallel wires separated by a distance of one meter that causes an attractive magnetic force of <math>2 \times 10^{-7}</math> newtons per meter along the length of the wires. Why the factor of <math>2 \times 10^{-7}</math>? This was chosen to make the volt a reasonable quantity relative to the voltage coming out of batteries. This definition of the units in terms of the magnetic force has the effect of defining the fundamental constant of the magnetic force, labeled <math>\mu\,</math>, to be <math>4 \pi \times 10^{-7}\,</math>. The fundamental constant of the electric force, labeled <math>\epsilon\,</math>, is related to this, according to the formula :<math>c = \frac{1}{\sqrt{\epsilon \mu}}\,</math> where <math>c\,</math>, the speed of light, was traditionally determined experimentally. <ref>The constant <math>c\,</math>, the speed of light, is now defined to be 299,792,458 meters per second. A second is officially defined in terms of a cesium clock and the meter is derived from that.</ref> ==The Next Lecture== For the next lecture, see [[Introduction to Electricity II]]. ==Footnotes and References== <references/> ==See Also== * [[Ohm's law]] * [[Kirchhoff's Voltage Law]] * [[Kirchhoff's Current Law]] * [[Maxwell's Equations]] * [[w:Semiconductor]] [[Category:Electrical engineering]] [[Category:Electronic engineering]] [[Category:Electricity]] bftcdkgniavfe2r2h9ad4ri48zhepco 0 88088 2690224 2237654 2024-12-04T06:07:37Z CommonsDelinker 9184 Removing [[:c:File:Flag_of_Western_Abenaki.svg|Flag_of_Western_Abenaki.svg]], it has been deleted from Commons by [[:c:User:Krd|Krd]] because: No license since 23 November 2024. 2690224 wikitext text/x-wiki The Abenaki people, also known as the Abnaki, Wabanaki or the Alnôbak, are one of the indigenous tribes of northeastern North America, some of the original occupants of New England, southern Quebec and the southern Canadian Maritimes. The name ''Abenaki'' is derived from the word Wabanaki, the eastern Algonquian word for "Dawn Land", which is their name for their homeland. The Abenakis were one of the original five members of the [[w:Wabanaki Confederacy|Wabanaki Confederacy]]. == Readings == * [[Wikipedia: Abenaki]] * [[Wikipedia: Wabanaki]] == Handouts == * [[/Primary school handout/]] [[Category:Ethnology]] 16gkj73ilkrf3pxnyngq6vepsvhj5gs 0 150742 2690163 2570941 2024-12-03T20:34:18Z CommonsDelinker 9184 Removing [[:c:File:Wikibully.jpg|Wikibully.jpg]], it has been deleted from Commons by [[:c:User:Ymblanter|Ymblanter]] because: per [[:c:Commons:Deletion requests/File:Wikibully.jpg|]]. 2690163 wikitext text/x-wiki {| cellpadding="10" cellspacing="5" style="width: 100%; background-color: Lightpurple; margin-left: auto; margin-right: auto" | style="width: 50%; background-color:Pink; border: 1px solid Gray; vertical-align: top; -moz-border-radius-topleft: 10px; -moz-border-radius-bottomleft: 10px; -moz-border-radius-topright: 10px; -moz-border-radius-bottomright: 10px;" <!--rowspan="2"--> | {{center top}}<gallery> </gallery>{{center bottom}} {{center top}}<p style ="line-height:70px; font-family: Fantasy; font-size: xx-large;">'''Bullying and Emotion''':</p><p style ="line-height:50px; font-family: Cursive; font-size: xx-large;">What role does emotion play in bullying?<br> What are the emotional affects of bullying?<br></p>{{center bottom}}{{center top}} <gallery> </gallery>{{center bottom}} |} {{MECR|http://screencast-o-matic.com/watch/cIX6h0V8rs}} {{RoundBoxTop|theme=14}} {{MEB}} {{100%done}} __TOC__ __TOC__ {{RoundBoxBottom}} {{RoundBoxTop|theme=7}} === The Reality of Bullying === Many people believe that they are educated about bullying, that they understand the consequences of bullying and may even be aware of the systems in place to prevent bullying. However, the reality of the issue of bullying is more confronting, darker and real than one might originally expect. In 2007, a 17 year old student who was frequently taunted by his peers, stabbed six classmates with a razor that was used for sharpening pencils. Two students were killed and four were seriously injured (Huang, 2013). Today, bullying is estimated to impact over one third of students, with the greatest frequency happening in secondary school (Cooper, 2013). <br> The purpose of this chapter is to examine the impact of emotion on both the bully and the victim and to explain how emotions felt during periods of bullying can have lasting consequences. So whether you are a student wanting more information on bullying, an adult experiencing bullying in the workplace, a concerned parent wanting to be aware of the impact bullying may have on your child, or perhaps even a bully yourself, hopefully you will find the information contained in this chapter useful. {{RoundBoxBottom}} {{RoundBoxTop|theme=4}} === What is Bullying? === Bullying involves repeated aggressive acts directed at a target who is at a disadvantage in the exchanges and who does not instigate the attacks (Terranova, 2008). The disadvantages in these exchanges are usually caused from an imbalance of power. An imbalance of power between the victim and the bully can be caused due to a variety of reasons. According to Jose, (2012) this imbalance of power may stem from the victims smaller size or strength in comparison to the bully, the victims affiliation with a minority or unpopular group, the victims fear of the bully, or the beliefs held by the victim which may make them unwilling to stand up for him or herself.<br> Bullying is a universal phenomenon. Other cultures may not share a single word which captures the Westernised concept of bullying, however bullying is present in nearly all cultures. In China, for example, the word qifu is defined as arrogant and unreasonable treatment of others, involving hitting, slapping, punching, threatening, extorting, isolating, and insulting in order to upset others. Qifu includes both direct and indirect forms of aggression, and can by instigated by an individual or a group of individuals whose purpose is to gain goods, prestige or power. (Huang, 2013) {{RoundBoxBottom}} {{RoundBoxTop|theme=5}} === Shocking Statistics === A common misconception is that bullying is declining in our world today, however these statistics unfortunately prove otherwise: * Approximately one in four Year 4 to Year 9 Australian students (27%) report being frequently bullied (every few weeks or more) (Department of Education, Training and Employment, 2013). * 84% of students who were bullied online were also bullied offline (Department of Education, Training and Employment, 2013). * 90% of lesbian, gay and bisexual youths have been verbally or physically harassed (Levasseur, 2013). * Peers are present as onlookers in 87% of bullying interactions and play a central role in the bullying process (Department of Education, Training and Employment, 2013). * Hurtful teasing is the most prevalent of all bullying behaviours experienced by students, followed by having hurtful lies told about them (Department of Education, Training and Employment, 2013). * Youths who report any involvement in bullying are more likely to report seriously considering or attempting suicide (Levasseur, 2013). * 60% of bullies in middle school will incur at least one criminal conviction by the age of 24 and a staggering 40% will incur three or more (Garby, 2013). {{RoundBoxBottom}} {{RoundBoxTop|theme=9}} === Types of Bullying === There are several different types of bullying. These include (Hunter, 2004; Cooper, 2013; Jose, 2012; Garby, 2013):<br> * Verbal Bullying: name calling, teasing. * Relational Bullying aka Indirect Bullying: exclusion, spreading rumours. * Direct Bullying aka Behavioural: violence, property damage or theft * Cyber Bullying: utilising electronic means such as a computer or a phone<br> From the list of bullying identified above cyber bullying has been found to be least emotionally affecting (Jose, 2012). This may be due to the perceived distance of the bully. The transactional theory of stress and coping, detailed later in the chapter, would suggest that when it comes to this form of bullying, victims may appraise the incident as less personally threatening (Ortega, 2012). <br> Both verbal and relational bullying involves actions that can be taken without leaving a paper trail or physical scar (Cooper, 2013) and they tend to be the least reported incidents as many people feel they do not have sufficient proof. Studies have shown that participating in one type of bullying does not equal future engagement in other types of bullying (Terranova, 2008), however victims of one type of bullying, have an increased risk of being victims of other types of bullying (Jose, 2012).<br> [[File:Bullies.jpg|thumb|left|270px]] Bullying can occur in a variety of different environments, including school and the workplace. Workplace bullying takes place when one or more persons systematically and over time feel that they have been subjected to negative treatment on the part of one or more persons at work, and where the persons exposed to the treatment have difficulty in defending themselves against these actions (Vie, 2012). More information about workplace bullying can be found here: [[https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2011/Toxic_workplace]]<br> There are several behaviours which do not constitute bullying. These behaviours include, mutual arguments where there is no power imbalance, not liking someone, a single act of social rejection, one-off acts of spite, isolated incidents of violence (Department of Education, Training and Employment, 2013). However, these types of conflicts still need to be resolved. {{RoundBoxBottom}} {{RoundBoxTop|theme=7}} === Gender and Age Differences === There are several research findings associated with bullying and gender. Males are generally known to be the more aggressive gender, and considering that bullying is an aggressive act, it is not surprising that males are often more strongly linked to bullying than females. (Huang, 2013; Levasseur, 2013; Garner, 2010) Research suggests that males tend to be victimised through physical aggression and that girls were more likely to experience relational aggression (Garner, 2010). When it comes to seeking help, girls are more willing than boys and it appears that the younger victims of school bullying are more inclined to ask for help than the older students (Hunter, 2004; Levasseur, 2013).<br> The table below by Hunter (2004), illustrates the role of both gender and age differences from numerous studies examining the use of social support among victims of school bullying.<br> ''''''Table 1'''.''' Studies examining the use of social support among victims of school bullying (Hunter, 2004).<br> {| class="wikitable" |- ! Study !! Sample !! Age Range !! Findings |- | Borg (1998) || 6,282 Maltese pupils || 9-14 || Younger pupils more likely than older to seek help from friends, teachers and parents; girls more likely to seek help from best friend or parents, boys more likely to seek help from a friend or teacher |- | Eslea (2001) || 198 English pupils || 11-15 || 16% of pupils reported telling if called names, 22% if rumours spread about them, 25% if physically hurt and 49% if belongings were stolen |- | Glover (2000) || 4,700 English pupils || 11-16 || Younger pupils more likely than older to seek help; female pupils more likely to seek help than male; telling a friend is most common, followed by mother and then form tutor |- | Hunter and Boyle (2004) || 459 Scottish pupils || 9-14 || Younger pupils more likely than older to seek help; female pupils more likely to seek help than male |- | Pateraki and Houndoumadi (2001) || 1,312 Greek pupils || 9-14 || Victims equally likely to ask adults and friends for help; people who are both bullies and victims seem less willing to seek help than victims |- | Sharp (1995) || 703 English pupils || 13-16 || Younger pupils more likely than older to seek help; female pupils more likely to seek help than male |- | Smith || 413 English pupils || 13-16 || Female pupils more likely to seek help than male; students most often spoke to parents, followed by friends, teachers, then siblings; students reporting being bullied over 2 year period less likely to have used social support tan pupils resolving bullying over that same period |} {{RoundBoxBottom}} {{RoundBoxTop|theme=4}} === Emotions and Bullying === {| cellpadding="10" cellspacing="5" style="float: right; width: 70%; background-color:LemonChiffon; margin-left: auto; margin-right: auto" | style="width: 30%; background-color:LemonChiffon; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px; height: 10px;" | {{center top}} {{big2|'''''"Could a scar be like the rings of a tree, reopened with each emotional season?"'''''}} Magenta Periwrinkle, Cutting Class {{center bottom}} |} Emotions are specific reactions to particular events, existing of several components, including experiential feeling, cognitions and physiological reactions (Vie, 2012). Emotions can vary in intensity and type and they direct our attention to events, stimuli or thoughts as well as organise perceptual and thought processes, activating and motivating most aspects of behaviour. Positive emotions include: enthusiasm, alert social activity and satisfaction. Negative emotions include: being upset or unpleasantly aroused and are linked to stress poor coping and health complaints. <br> Many emotions may follow the experience of being bullied. These emotions include anxiety, fear, anger, distress, irritability, helplessness, despair, guilt and shame (Vie, 2012). Both the bully and the victim can develop psychological and social maladjustment problems (Jose, 2012). ==== The Bully ==== Emotions play a role in the way a bully acts both before, during and after a bullying incident. Studies have shown that children who identified as a bully exhibit a variety of externalising behaviours, such as aggression and impulsivity (Huang, 2013). Bullies generally have high self-concept, accompanied with poorer academic performances, inadequate coping skills, trouble with emotional regulation and higher levels of psychoticism including recklessness, interpersonal hostility and antisocial behaviour (Cooper, 2013; Huang, 2013). Bullies often struggle maintaining interpersonal relationships, experience peer rejection and affiliate with anti-social peer groups (Cooper, 2013).<br> A person who bullies another may exhibit any number of the following behaviours. They may repeatedly tease, imitate, exclude, ignore or make fun of the same target. They also show no compassions for someone who is experiencing bullying and feel the need to dominate or control others (Department of Education, Training and Employment, 2013). Bullies are usually skilled manipulators who use their psychological skills to control the minds of others and cause them distress (Menesini, 2003).<br> A factor which may put people at risk of developing bullying patterns is low levels of fear reactivity. Fear reactivity involves unpleasant effect, reactivity or avoidance in the presence of new, strange or threatening stimuli (Terranova, 2008). Low fear reactivity is a particularly important risk fact for bullying behaviours as it disrupts the moral development of conscience and empathy. A bully with low fear reactivity are not distressed enough by the potential negative consequences, such as punishment, harm or retaliation, or the inappropriateness of aggression to motivate the avoidance of its use (Terranova, 2008). ===== The Homophily Hypothesis ===== {| cellpadding="10" cellspacing="5" style="float: right; width: 70%; background-color:LemonChiffon; margin-left: auto; margin-right: auto" | style="width: 30%; background-color:LemonChiffon; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px; height: 10px;" | {{center top}} {{big2|'''''"Birds of a feather... Flock together!"'''''}} {{center bottom}} |} Homophily is the tendency of individual people to associate and bond with other people who are similar. Individuals who are in homophilic relationships generally share common characteristics, such as values, education and beliefs, which make communication and relationships form more easily (Huang, 2013). Adolescence is a period where friendships and peer support are essential for development (Cooper, 2013). Generally peer groups are usually formed based on shared similarities. Therefore, according to the homophily hypothesis, students who associate with friends and peers who bully others are more likely to engaged in bullying themselves (Huang, 2013). As this bullying trend progresses into adulthood, bullies are more likely to continue their behaviour in the workplace, become involved in gang membership, misuse substances and have a higher chance of becoming involved in criminal activity (Jose, 2012).<br> The homophily hypothesis links quite nicely to the Social Identity Theory. This theory assumes that part of an individual’s identity comes from membership of social groups and that people are motivated to find positive differences between their own group and others (Jones, 2012). Social identity mechanisms are important because they affect emotional reactions to bullying. In 2012, Jones conducted a study which investigated a link between group-based emotions (those that take groups rather than individuals as the subject and object of the emotion), action tendencies and group membership in the context of bullying. The results showed that pride was associated with a tendency to affiliate with a bullying group, whereas regret was linked with a disposition to apologise to the target, and anger with the likelihood of telling an adult about the incident (Jones, 2012). ===== Emotional Display Rule Knowledge ===== Emotional display rule knowledge is concerned with the understanding of the guidelines that govern the expression and management of emotions in social situations and their associated motives (Garner, 2010). This knowledge develops during primary school, as this is usually when children start to understand they can or should conceal their internal feelings by using one of a variety of different strategies, including masking their true emotion, maintaining a neutral facial expression or varying the intensity of their emotional expression (Garner, 2010). Having strong emotional display rule knowledge is a vital part of development. Being emotionally competent requires for people to understand that at times it is necessary to be concerned about other people’s feelings and to try to prevent people from experiencing hurt or harm. Children with low display rule knowledge to tend generate aggressive solutions to conflict, which is how bullies tend to deal with conflict. Children who bully have difficulty accurately perceiving the emotional signals of others, attribute anger to the actions and statements of others when it is not present and show indifference to other children’s displays of negative emotion (Garner, 2010). ===== Moral Emotions ===== A bullies behaviour is significantly related to their moral understanding of the consequences of their antisocial behaviour, it often appears that bullies may not understand that victimising others for personal gains in morally wrong (Menesini, 2003). The emotions of guilt, shame, indifference and pride are often referred to as moral emotions. Moral emotions serve as an emotional barometer giving people feedback on their social and moral acceptability, they are founded on social relationship in which people not only interact but also evaluate and judge themselves and others (Ttofi, 2008). These emotions are highly correlated to moral behaviour and play a large role in regulating the individuals sense of responsibility towards other people (Menesini, 2003). During a bullying incident the bully may experience guilt or shame for the harm done to the victim or feel proud of his or her success.<br> '''Guilt:''' involves a sense of tension, remorse and regret over a bad action. Guilt is often elicited in an event in which an individual violates the rule that a person should not hurt or disadvantage others. Children who demonstrate higher levels of guilt are more likely to try to repair a negative action. Guilt is usually a less painful feeling than shame as its primary concern is with a particular behaviour (Menesini, 2003).<br> '''Shame:''' Is a highly painful emotion that is normally accompanied by a sense of worthlessness and powerlessness. Shame often induces a desire to flee from the shame-inducing situation. Unlike guilt, shame is not exclusively related to the moral value event, but also to the personal sense of having adopted an ‘unwanted identity’ (Menesini, 2003).<br> '''Indifference:''' If a bully is indifferent to the response of a detrimental behaviour, which is shown through the lack of negative emotions such as guilt or shame, it can reveal the absence of empathy toward the victim (Menesini, 2003). <br> '''Pride:''' is generally considered a positive self-evaluative emotion that occurs in situations where a person is satisfied with their own performance. However, in the case of a bully, the feeling of pride focuses just on personal gains of the bully without considering the consequences for the victim (Menesini, 2003). <br> A study on the impact of moral emotions on bullying found that bullies differed from victims and the control group (neither bullies or victims) in moral reasoning processes. Bullies showed a higher level of indifference and pride, and a lower level of moral responsibility through guilt and shame, when asked to put themselves in the role of bully in a hypothetical scenario (Ttofi, 2008). ==== The Victim ==== [[File:Bully Free Zone.jpg|thumb|right|270px]] Victims of bullying experience a wide range of emotions whilst they are being victimised. However, exploring the emotional experiences which are associated with bullying can be problematic as often high emotions are difficult to verbalise and may not be accessed from consciousness (Tehrani, 2009). The consequences of being bullied during adolescences may extend into adulthood (Cooper, 2013) and persistence of episodes over time is related to an increased emotional impact on mental health (Ortega, 2012). Victims often display high levels of emotions in response to provocation by a bully, however victims who respond to bullying with nonchalance or expressions of neutrality may reduce their chances of being victimised again (Garner, 2010). Victims of bullying often display internalising behaviours, including lower self-esteem, depression and feeling socially isolated. Victims also display a higher level of neuroticism (Huang, 2013). Bullying is damaging and can lead to a range of psychological disorders including physical conditions and post-traumatic stress (Tehrani, 2009). Irrespective of age or gender bullying victims tend to be more afraid, upset, angry, guilty, hostile, nervous, frustrated, ashamed, stressed and scared then non-victims (Vie, 2012). Victims of school bullying may experience a range of academic problems which are exhibited by truancy, absenteeism and eventually school dropout (Jose, 2012). Adjustment problems may also occur and these include feelings of rejection, negative self-concept, withdrawal, loneliness, depression, helplessness and a sense that he or she deserves to be bullied (Cooper, 2013). Bullies are equally likely to display positive and negative emotions towards their victims. However often victims lack the ability to interpret the ‘true’ meaning behind these displays and this may signal to the bully that these children can be easily intimidated (Garner, 2010). This may suggest that in some cases, a victim may have a lack of emotion-related knowledge, and may approach peer interactions in ways which provoke negative behaviour, in turn creating a cycle of victimisation and poor emotional understanding (Garner, 2010).<br> Victims of workplace bullying generally report low levels of job satisfaction and well-being, along with feelings of social isolation, social maladjustment, low self-esteem, sleeping difficulties, concentration problems, chronic fatigue and depression (Vie, 2012).<br> In 2012, Ortega conducted a study which investigated the emotional impact of cyber victimisation. The results demonstrated the 93% of cyber victims were negatively affected by the bullying incident, with participants reporting feelings of sadness, hopelessness, depression and anxiety. Emotional responses of the victims of chat room bullying were as follows; 41% felt angry, 30% were upset, 20% felt frustrated, 15% vulnerable, 15% felt depressed and lastly 8% reported they felt frightened (Ortega, 2012). === Reducing the Impact - How to Cope === [[File:StompLOGO 2012 flat Vector.jpg|thumb]] Coping has been defined as ‘the way people manage life conditions that are stressful’ (Hunter, 2004). A vital element of reducing the emotional impact of bullying on the victims is to tell someone in order for them to help to resolve the situation (Hunter, 2004). Students who are victimised may wish to tell their teachers, parents or guardians. Victims of workplace bullying are encouraged to seek support from their superiors. <br> Process theories of coping explain the large role that a persons perception of any given situation play in determining coping behaviour (Menesini, 2003). Such perceptions, known as appraisals, include the anticipation of loss or harm, the degree of perceived control over the stressor and the emphasising of potential gains. These appraisals have been shown to be important factors in coping strategy choice in a range of different situations (Menesini, 2003). Being able to correctly appraise the emotions of others may help children to avoid certain forms of peer-related aggression (Garner, 2010). Emotions also play a part in the coping process. In Lazarus’ appraisal model, appraisals influence coping strategies, which in turn influence one’s emotional reaction to events (Menesini, 2003). The more negative emotion people experience when they are being bullied the more they are likely to seek out help in order to deal with those emotions. <br> A central step in the counselling process is to help victims become aware of their emotional and cognitive reactions associated with bullying. According to Lazarus, being aware of the emotions associated with stressful encounters, such as bullying, creates an opportunity for a reappraisal of the situation, which in turn may help the person to gain control and be more able to cope with the situation (Vie, 2012). <br> To reduce aggression and violence, workplaces and school communities should focus on developing safe social and physical environments, provide health, counselling and social services and train staff to promote safety (Levasseur, 2013). Researchers have suggested that schools and workplaces should encourage cooperative norms, rather than competitive ones (Jones, 2012). {{RoundBoxBottom}} {{RoundBoxTop|theme=3}} === Test Yourself === <quiz display=simple> {Calling another person fat is an example of which type of bullying: |type="[]"} - A – Direct Bullying + B - Verbal Bullying - C - Relational Bullying {If you are a cyber bully, you are more likely to also participate in verbal bullying: |type="[]"} - A - True + B - False {Which of the following responses to bullying may reduce the chances of being victimised again: |type="[]"} - A - Sadness - B - Anger + C - Neutrality </quiz> {{RoundBoxBottom}} {{RoundBoxTop|theme=5}} === For Further Information === The following links may be useful for further information: * For information about toxic workplaces [[https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2011/Toxic_workplace]] * For information about dealing with conflict [[https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2011/Dealing_with_conflict]] * For information about building resilience [[https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2011/Psychological_resilience]] * Bullying resources http://bullyingnoway.gov.au/ * For help dealing with bullying http://au.reachout.com/Tough-Times/Bullying-Abuse-and-Violence/Bullying {| cellpadding="10" cellspacing="5" style="float: right; width: 70%; background-color:LemonChiffon; margin-left: auto; margin-right: auto" | style="width: 30%; background-color:LemonChiffon; border: 1px solid #777777; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px; height: 10px;" | {{center top}} {{big2|'''''A final thought "Be kind to everyone, including yourself."'''''}} {{center bottom}} |} {{RoundBoxBottom}} {{RoundBoxTop|theme=1}} === References === {{Hanging indent|1= Cooper, L. (2013). Parent Retrospective Recollections of Bullying and Current Views, Concerns, and Strategies to Cope with Children's Bullying. Journal Of Child & Family Studies, 22(4), 526-540. Department of Education, Training and Employment. (2013). Bullying! No Way! Retrieved October 20, 2013 from http://bullyingnoway.gov.au/ Garby, L. (2013). DIRECT BULLYING: CRIMINAL ACT OR MIMICKING WHAT HAS BEEN LEARNED?. Education, 133(4), 448-450. Garner, P. (2010). Emotional display rules and emotion self-regulation: Associations with bullying and victimization in community-based after school programs. Journal Of Community & Applied Social Psychology, 20(6), 480-496. Huang, H. (2013). Understanding Factors Associated with Bullying and Peer Victimization in Chinese Schools Within Ecological Contexts. Journal Of Child & Family Studies, 22(7), 881-892. Hunter, S. (2004). Help seeking amongst child and adolescent victims of peer-aggression and bullying: The influence of school-stage, gender, victimisation, appraisal, and emotion. British Journal Of Educational Psychology, 74(3), 375-390. Jones, S. (2012). The influence of norms and social identities on children's responses to bullying. British Journal Of Educational Psychology, 82(2), 241-256. Jose, P. (2012). The Joint Development of Traditional Bullying and Victimization With Cyber Bullying and Victimization in Adolescence. Journal Of Research On Adolescence (Wiley-Blackwell), 22(2), 301-309. Levasseur, M. A. (2013). Intersecting Identities and the Association Between Bullying and Suicide Attempt Among New York City Youths: Results From the 2009 New York City Youth Risk Behavior Survey. American Journal Of Public Health, 103(6), 1082-1089. Menesini, E. (2003). Moral emotions and bullying: A cross-national comparison of differences between bullies, victims and outsiders. Aggressive Behavior, 29(6), 515-530. Ortega, R. (2012). The Emotional Impact of Bullying and Cyberbullying on Victims: A European Cross-National Study. Aggressive Behavior, 38(5), 342-356. Tehrani, N. (2009). Lost in translation - using bilingual differences to increase emotional mastery following bullying. Counselling & Psychotherapy Research, 9(1), 11-17. Terranova, A. (2008). Fear reactivity and effortful control in overt and relational bullying: a six-month longitudinal study. Aggressive Behavior, 34(1), 104-115. Ttofi, M. P. (2008). Reintegrative Shaming Theory, moral emotions and bullying. Aggressive Behavior, 34(4), 352-368. Vie, T. (2012). How does it feel? Workplace bullying, emotions and musculoskeletal complaints. Scandinavian Journal Of Psychology, 53(2), 165-173. }} {{RoundBoxBottom}} 22uj9dozggmrjnqomd7jwwq9lnhfzob 0 202967 2690195 2626007 2024-12-04T03:14:32Z 174.17.179.128 2690195 wikitext text/x-wiki [[File:Annotating Text.jpg|thumbnail|right|Annotated Text]] Marking and/or highlighting a text is like having a conversation with a book - it allows you to ask questions, comment on meaning, and mark events and passages you wanted to revisit. Annotating is a permanent record of your intellectual conversations with the text. As you work with your text, think about all the ways that you can connect with what you are [[reading]]. What follows are some suggestions that will help with annotating. == Beginning to Annotate == * Use a pen, pencil, post-it notes, or a highlighter (use it sparingly) * Summarize important ideas in your own words. * Add examples from real life, other books, TV, movies, and so forth. * Define words that are new to you * Mark passages that you find confusing with question marks * Write questions that you might have for later discussion in class. * Comment on the actions or development of characters. * Comment on things that intrigue, impress, surprise, disturb, etc. * Note how the author uses language. A list of possible literary devices is attached. * Feel free to draw picture when a visual connection is appropriate. * Explain the historical context or traditions/social customs used in the passage. * If possible, summarize paragraphs, especially those you do not understand. === Suggested methods for marking a text === * If you are a person who does not like to write in a book, you may want to invest in a supply of post it notes. * If you feel really creative, or are just super organized, you can even color code your annotations by using different color post-its, highlighters, or pens * Brackets: If several lines seem important, just draw a line down the margin and underline/highlight only the key phrases. * Asterisks: Place and asterisk next to an important passage; use two if it is really important * Marginal Notes: Use the space in the margins to make comments, define words, ask questions, etc. * Underline/highlight; Caution! Do not underline or highlight too much! You want to concentrate on the important elements, not entire pages (use brackets for that). * Use circles, boxes, triangles, squiggly lines, stars, etc. * Make sure you don't plagiarize. ==Literary Term Definitions== [[File:Idioms Screenshot.PNG|frameless|right]] :''See also: [[Literary Terms]]'' *''Alliteration'' - the practice of beginning several consecutive or neighboring words with the same sound: e.g., "The twisting trout twinkled below" *''Allusion'' - A reference to a mythological, literary, or historical person, place, or thing: e.g., "He met his Waterloo" *''Flashback'' - A scene that interrupts the action of a work to show a previous event. *''Foreshadowing'' - The use of hints or clues in a narrative to suggest future action. *''Hyperbole'' - A deliberate, extravagant, and often outrageous exaggeration; it may be used for either serious or comic effect: e.g., "The shot heard 'round the world" *''Idiom'' - An accepted phrase or expression having a meaning different from the literal: e.g., to drive someone up the wall. *''Imagery'' - The words or phrases a writer uses that appeal to the senses. *''Metaphor'' - A comparison of two unlike things not using like or as:: e.g. "Time is money" *''Mood'' - The atmosphere or predominant emotion in a literary work. <br> *''Oxymoron'' - A form of paradox that combines a pair of opposite terms into a signal unusual expression: ''Long shorts'', ''Jumbo Shrimp'', ''Sad Smiles'' *''Paradox'' - occurs when the elements of a statement contradict each other. Although the statement may appear illogical, impossible, or absurd, it turns out to have a coherent meaning that reveals a hidden truth: e.g., "Much madness is divinest sense." *''Personification'' - A kind of metaphor that gives inanimate objects or abstract ideas human characteristics: e.g., "The wind cried in the dark." *''Rhetoric'' - The art of using words to persuade in writing or speaking. *''Simile'' - A comparison of two different things or ideas using words such as "like" or "as": e.g., "The warrior fought like a lion." <br> *''Suspense'' - A quality that makes the reader or audience uncertain or tense about the outcome of events. *''Symbol'' - any object, person, place, or action that has both a meaning in itself and that stands for something larger than itself, such as quality, attitude, belief, or value: e.g., a tortoise represents slow but steady progress. *''Theme'' - The Central message of a literary work. It is expressed as a sentence or general statement about life or human nature. A literary work can have more than one theme, and most themes are not directly stated but are implied: e.g., pride often precedes a fall.] *''Tone'' - The Writer's or speaker's attitude toward a subject, character, or audience; It is conveyed through the author's choice of words (diction) and details. Tone can be serious, humorous, sarcastic, indignant, etc. *''Understatement'' (meiosis, litotes) - The opposite of hyperbole. It is a kind of irony that deliberately represents something as being much less than it really is; e.g., "I could probably manage to survive on a salary of two million dollars per year." === Irony === There are three types of irony ;Verbal Irony When a speaker or narrator says one thing while meaning the opposite; sarcasm is a form or verbal irony: e.g., "It is easy to stop smoking. I've done it many times" ;Situation Irony When a situation turns out differently from what one would normally expect; often the twist is oddly appropriate: e.g., a deep sea diver drowning in a bathtub is ironic ;Dramatic Irony When a character or speaker says or does something that has different meaning from what he or she thinks it means, though the audience and other characters understand the full implications : e.g., Anne Frank looks forward to growing up, but sadly, we (as readers) know that will never be. [[Category:Literature for teens]] [[Category:Reading]] 8zu8fth2apf9f946qg78d2yp6rtvp9a 2690197 2690195 2024-12-04T03:17:47Z 174.17.179.128 2690197 wikitext text/x-wiki [[File:Annotating Text.jpg|thumbnail|right|Annotated Text Example]] Marking and/or highlighting a text is like having a conversation with a book - it allows you to ask questions, comment on meaning, and mark events and passages you wanted to revisit. Annotating is a permanent record of your intellectual conversations with the text. As you work with your text, think about all the ways that you can connect with what you are [[reading]]. What follows are some suggestions that will help with annotating. == Beginning to Annotate == * Use a pen, pencil, post-it notes, or a highlighter (use it sparingly) * Summarize important ideas in your own words. * Add examples from real life, other books, TV, movies, and so forth. * Define words that are new to you * Mark passages that you find confusing with question marks * Write questions that you might have for later discussion in class. * Comment on the actions or development of characters. * Comment on things that intrigue, impress, surprise, disturb, etc. * Note how the author uses language. A list of possible literary devices is attached. * Feel free to draw picture when a visual connection is appropriate. * Explain the historical context or traditions/social customs used in the passage. * If possible, summarize paragraphs, especially those you do not understand. === Suggested methods for marking a text === * If you are a person who does not like to write in a book, you may want to invest in a supply of post it notes. * If you feel really creative, or are just super organized, you can even color code your annotations by using different color post-its, highlighters, or pens * Brackets: If several lines seem important, just draw a line down the margin and underline/highlight only the key phrases. * Asterisks: Place and asterisk next to an important passage; use two if it is really important * Marginal Notes: Use the space in the margins to make comments, define words, ask questions, etc. * Underline/highlight; Caution! Do not underline or highlight too much! You want to concentrate on the important elements, not entire pages (use brackets for that). * Use circles, boxes, triangles, squiggly lines, stars, etc. * Make sure you don't plagiarize. ==Literary Term Definitions== [[File:Idioms Screenshot.PNG|frameless|right]] :''See also: [[Literary Terms]]'' *''Alliteration'' - the practice of beginning several consecutive or neighboring words with the same sound: e.g., "The twisting trout twinkled below" *''Allusion'' - A reference to a mythological, literary, or historical person, place, or thing: e.g., "He met his Waterloo" *''Flashback'' - A scene that interrupts the action of a work to show a previous event. *''Foreshadowing'' - The use of hints or clues in a narrative to suggest future action. *''Hyperbole'' - A deliberate, extravagant, and often outrageous exaggeration; it may be used for either serious or comic effect: e.g., "The shot heard 'round the world" *''Idiom'' - An accepted phrase or expression having a meaning different from the literal: e.g., to drive someone up the wall. *''Imagery'' - The words or phrases a writer uses that appeal to the senses. *''Metaphor'' - A comparison of two unlike things not using like or as:: e.g. "Time is money" *''Mood'' - The atmosphere or predominant emotion in a literary work. <br> *''Oxymoron'' - A form of paradox that combines a pair of opposite terms into a signal unusual expression: ''Long shorts'', ''Jumbo Shrimp'', ''Sad Smiles'' *''Paradox'' - occurs when the elements of a statement contradict each other. Although the statement may appear illogical, impossible, or absurd, it turns out to have a coherent meaning that reveals a hidden truth: e.g., "Much madness is divinest sense." *''Personification'' - A kind of metaphor that gives inanimate objects or abstract ideas human characteristics: e.g., "The wind cried in the dark." *''Rhetoric'' - The art of using words to persuade in writing or speaking. *''Simile'' - A comparison of two different things or ideas using words such as "like" or "as": e.g., "The warrior fought like a lion." <br> *''Suspense'' - A quality that makes the reader or audience uncertain or tense about the outcome of events. *''Symbol'' - any object, person, place, or action that has both a meaning in itself and that stands for something larger than itself, such as quality, attitude, belief, or value: e.g., a tortoise represents slow but steady progress. *''Theme'' - The Central message of a literary work. It is expressed as a sentence or general statement about life or human nature. A literary work can have more than one theme, and most themes are not directly stated but are implied: e.g., pride often precedes a fall.] *''Tone'' - The Writer's or speaker's attitude toward a subject, character, or audience; It is conveyed through the author's choice of words (diction) and details. Tone can be serious, humorous, sarcastic, indignant, etc. *''Understatement'' (meiosis, litotes) - The opposite of hyperbole. It is a kind of irony that deliberately represents something as being much less than it really is; e.g., "I could probably manage to survive on a salary of two million dollars per year." === Irony === There are three types of irony ;Verbal Irony When a speaker or narrator says one thing while meaning the opposite; sarcasm is a form or verbal irony: e.g., "It is easy to stop smoking. I've done it many times" ;Situation Irony When a situation turns out differently from what one would normally expect; often the twist is oddly appropriate: e.g., a deep sea diver drowning in a bathtub is ironic ;Dramatic Irony When a character or speaker says or does something that has different meaning from what he or she thinks it means, though the audience and other characters understand the full implications : e.g., Anne Frank looks forward to growing up, but sadly, we (as readers) know that will never be. [[Category:Literature for teens]] [[Category:Reading]] owugd9txxqpys1ewlqiezblj8cy3n70 0 203694 2690231 1597159 2024-12-04T07:26:25Z Dunncorrect 2994540 Reworded and removed the reference to the Thomas Parker gate. Thomas Parker invented and patented a modified bear trap gate. The Tainter gate had nothing to do with the Parker gate except that they were both invented in Menomonie. 2690231 wikitext text/x-wiki [[File:Tainter gate lower back view.jpeg|thumb|291x291px|Lower-side view of the Tainter gate in Menomonie, WI]]The '''Tainter gate''' is a type [[w:Floodgate|floodgate]] used for dams. The design was invented by Jeremiah Burnham [[Menomonie, Wisconsin History/schroeja|Tainter.]] The idea came to Tainter when he set out to create an efficient water control device to be used for the logging industry . His brother, Andrew Tainter was part owner of the [http://digital.library.wisc.edu/1711.dl/wiarchives.uw-whs-stou000b Knapp Stout and Company, Company]. Floodgates were used to control water levels in order to move lumber downstream on the [[wikipedia:Red_Cedar_River_(Wisconsin)|Red Cedar River]] to [[wikipedia:Dunnville,_Wisconsin|Dunnville]], the [[w:Chippewa_River_(Wisconsin)|Chippewa River]] and on to the [[wikipedia:Mississippi_River|Mississippi River]]. The Tainter gate design has been very successful and is still used today throughout the world. There are currently 321 Tainter gates being used in the upper basin of the [[w:Mississippi_River|Mississippi River]]. == Tainter Gate == [[File:Close-up side view of Tainter gate.jpeg|left|thumb|Side view of Tainter gate in Menomonie, WI. Notice the distinct design of the Tainter gate arms on the inside of each section.]] ==== History ==== Jeremiah B. Tainter simply redesigned a basic but clumsy floodgate that was originally developed in the east. His floodgate was designed to use an arm like gate that can be lifted to control the water level using chains. Today we use gearboxes or electric motors to power the gate. Tainter’s idea of the floodgate had become such popular design for dams that it is used very often today as water control dams for the Upper Mississippi River, the Columbia River Basin, including the Bonneville and Grand Coulee dams. The floodgate is also being used around the world such as Switzerland, Italy and many other countries. === Uses of the Tainter gate === Tainter's had designed the floodgate to open while releasing a rush of water that would carry [[Menomonie, Wisconsin History/Spontaneous Turtle|lumber]] down to Dunnville and the larger part of the Chippewa River. Today the Tainter gate now applies to what dams are made for: flood suppression, irrigation, human consumption, industrial use, aquaculture, and navigability. == Jeremiah Burnham Tainter == === Background === Jeremiah B. Tainter was never seen as one of the popular siblings. He often hid in his older, and more successful brother, [[Menomonie, Wisconsin History/Andrew Tainter/SarahBeth19|Andrew Tainter]]. However, he had many ideas when designing water control devices. At the age of 26, Tainter came to Menomonie and worked in the Knapp, Stout mills. While working as a millwright, he wanted a way to release enough water to help workers move lumber from his company’s territory to Dunnville and the Chippewa River. By doing some surveying around the town, he eventually came to the conclusion of creating a gate to open up and let a rush of water strong enough to carry the logs down stream, “...he cleverly designed it so that the rush of water helped both to open and to close the gates with a minimum of manpower”.<ref> Lynch, L., & Russell, J. (Eds.). (n.d.). ''Where the wild rice grows''. Menomonie, WI: Menomonie Sesquicentennial Committee. </ref> Jeremiah B. Tainter was known for many things because of his popularity, however, the Tainter gate will always honor his name today by still being a popular design for a floodgate. == External Links == [[w:Tainter_gate|Tainter Gate]] [[w:Jeremiah_Burnham_Tainter|Jeremiah Burnham Tainter]] [http://www.dunnhistory.org/history/exgate.html Tainter Gate History] == References == {{CourseCat}} g6bx6no9azi7a8m7z9qv5c4a22gc181 0 203942 2690225 2690052 2024-12-04T06:19:19Z Young1lim 21186 /* Lambda Calculus */ 2690225 wikitext text/x-wiki ==Introduction== * Overview I ([[Media:HSKL.Overview.1.A.20160806.pdf |pdf]]) * Overview II ([[Media:HSKL.Overview.2.A.20160926.pdf |pdf]]) * Overview III ([[Media:HSKL.Overview.3.A.20161011.pdf |pdf]]) * Overview IV ([[Media:HSKL.Overview.4.A.20161104.pdf |pdf]]) * Overview V ([[Media:HSKL.Overview.5.A.20161108.pdf |pdf]]) </br> ==Applications== * Sudoku Background ([[Media:Sudoku.Background.0.A.20161108.pdf |pdf]]) * Bird's Implementation :- Specification ([[Media:Sudoku.1Bird.1.A.Spec.20170425.pdf |pdf]]) :- Rules ([[Media:Sudoku.1Bird.2.A.Rule.20170201.pdf |pdf]]) :- Pruning ([[Media:Sudoku.1Bird.3.A.Pruning.20170211.pdf |pdf]]) :- Expanding ([[Media:Sudoku.1Bird.4.A.Expand.20170506.pdf |pdf]]) </br> ==Using GHCi== * Getting started ([[Media:GHCi.Start.1.A.20170605.pdf |pdf]]) </br> ==Using Libraries== * Library ([[Media:Library.1.A.20170605.pdf |pdf]]) </br> </br> ==Types== * Constructors ([[Media:Background.1.A.Constructor.20180904.pdf |pdf]]) * TypeClasses ([[Media:Background.1.B.TypeClass.20180904.pdf |pdf]]) * Types ([[Media:MP3.1A.Mut.Type.20200721.pdf |pdf]]) * Primitive Types ([[Media:MP3.1B.Mut.PrimType.20200611.pdf |pdf]]) * Polymorphic Types ([[Media:MP3.1C.Mut.Polymorphic.20201212.pdf |pdf]]) ==Functions== * Functions ([[Media:Background.1.C.Function.20180712.pdf |pdf]]) * Operators ([[Media:Background.1.E.Operator.20180707.pdf |pdf]]) * Continuation Passing Style ([[Media:MP3.1D.Mut.Continuation.20220110.pdf |pdf]]) ==Expressions== * Expressions I ([[Media:Background.1.D.Expression.20180707.pdf |pdf]]) * Expressions II ([[Media:MP3.1E.Mut.Expression.20220628.pdf |pdf]]) * Non-terminating Expressions ([[Media:MP3.1F.Mut.Non-terminating.20220616.pdf |pdf]]) </br> </br> ==Lambda Calculus== * Lambda Calculus - informal description ([[Media:LCal.1A.informal.20220831.pdf |pdf]]) * Lambda Calculus - Formal definition ([[Media:LCal.2A.formal.20221015.pdf |pdf]]) * Expression Reduction ([[Media:LCal.3A.reduction.20220920.pdf |pdf]]) * Normal Forms ([[Media:LCal.4A.Normal.20220903.pdf |pdf]]) * Encoding Datatypes :- Church Numerals ([[Media:LCal.5A.Numeral.20230627.pdf |pdf]]) :- Church Booleans ([[Media:LCal.6A.Boolean.20230815.pdf |pdf]]) :- Functions ([[Media:LCal.7A.Function.20231230.pdf |pdf]]) :- Combinators ([[Media:LCal.8A.Combinator.20241202.pdf |pdf]]) :- Recursions ([[Media:LCal.9A.Recursion.20241204.pdf |pdf]]) </br> </br> ==Function Oriented Typeclasses== === Functors === * Functor Overview ([[Media:Functor.1.A.Overview.20180802.pdf |pdf]]) * Function Functor ([[Media:Functor.2.A.Function.20180804.pdf |pdf]]) * Functor Lifting ([[Media:Functor.2.B.Lifting.20180721.pdf |pdf]]) === Applicatives === * Applicatives Overview ([[Media:Applicative.3.A.Overview.20180606.pdf |pdf]]) * Applicatives Methods ([[Media:Applicative.3.B.Method.20180519.pdf |pdf]]) * Function Applicative ([[Media:Applicative.3.A.Function.20180804.pdf |pdf]]) * Applicatives Sequencing ([[Media:Applicative.3.C.Sequencing.20180606.pdf |pdf]]) === Monads I : Background === * Side Effects ([[Media:Monad.P1.1A.SideEffect.20190316.pdf |pdf]]) * Monad Overview ([[Media:Monad.P1.2A.Overview.20190308.pdf |pdf]]) * Monadic Operations ([[Media:Monad.P1.3A.Operations.20190308.pdf |pdf]]) * Maybe Monad ([[Media:Monad.P1.4A.Maybe.201900606.pdf |pdf]]) * IO Actions ([[Media:Monad.P1.5A.IOAction.20190606.pdf |pdf]]) * Several Monad Types ([[Media:Monad.P1.6A.Types.20191016.pdf |pdf]]) === Monads II : State Transformer Monads === * State Transformer : - State Transformer Basics ([[Media:MP2.1A.STrans.Basic.20191002.pdf |pdf]]) : - State Transformer Generic Monad ([[Media:MP2.1B.STrans.Generic.20191002.pdf |pdf]]) : - State Transformer Monads ([[Media:MP2.1C.STrans.Monad.20191022.pdf |pdf]]) * State Monad : - State Monad Basics ([[Media:MP2.2A.State.Basic.20190706.pdf |pdf]]) : - State Monad Methods ([[Media:MP2.2B.State.Method.20190706.pdf |pdf]]) : - State Monad Examples ([[Media:MP2.2C.State.Example.20190706.pdf |pdf]]) === Monads III : Mutable State Monads === * Mutability Background : - Inhabitedness ([[Media:MP3.1F.Mut.Inhabited.20220319.pdf |pdf]]) : - Existential Types ([[Media:MP3.1E.Mut.Existential.20220128.pdf |pdf]]) : - forall Keyword ([[Media:MP3.1E.Mut.forall.20210316.pdf |pdf]]) : - Mutability and Strictness ([[Media:MP3.1C.Mut.Strictness.20200613.pdf |pdf]]) : - Strict and Lazy Packages ([[Media:MP3.1D.Mut.Package.20200620.pdf |pdf]]) * Mutable Objects : - Mutable Variables ([[Media:MP3.1B.Mut.Variable.20200224.pdf |pdf]]) : - Mutable Data Structures ([[Media:MP3.1D.Mut.DataStruct.20191226.pdf |pdf]]) * IO Monad : - IO Monad Basics ([[Media:MP3.2A.IO.Basic.20191019.pdf |pdf]]) : - IO Monad Methods ([[Media:MP3.2B.IO.Method.20191022.pdf |pdf]]) : - IORef Mutable Variable ([[Media:MP3.2C.IO.IORef.20191019.pdf |pdf]]) * ST Monad : - ST Monad Basics ([[Media:MP3.3A.ST.Basic.20191031.pdf |pdf]]) : - ST Monad Methods ([[Media:MP3.3B.ST.Method.20191023.pdf |pdf]]) : - STRef Mutable Variable ([[Media:MP3.3C.ST.STRef.20191023.pdf |pdf]]) === Monads IV : Reader and Writer Monads === * Function Monad ([[Media:Monad.10.A.Function.20180806.pdf |pdf]]) * Monad Transformer ([[Media:Monad.3.I.Transformer.20180727.pdf |pdf]]) * MonadState Class :: - State & StateT Monads ([[Media:Monad.9.A.MonadState.Monad.20180920.pdf |pdf]]) :: - MonadReader Class ([[Media:Monad.9.B.MonadState.Class.20180920.pdf |pdf]]) * MonadReader Class :: - Reader & ReaderT Monads ([[Media:Monad.11.A.Reader.20180821.pdf |pdf]]) :: - MonadReader Class ([[Media:Monad.12.A.MonadReader.20180821.pdf |pdf]]) * Control Monad ([[Media:Monad.9.A.Control.20180908.pdf |pdf]]) === Monoid === * Monoids ([[Media:Monoid.4.A.20180508.pdf |pdf]]) === Arrow === * Arrows ([[Media:Arrow.1.A.20190504.pdf |pdf]]) </br> ==Polymorphism== * Polymorphism Overview ([[Media:Poly.1.A.20180220.pdf |pdf]]) </br> ==Concurrent Haskell == </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] ==External links== * [http://learnyouahaskell.com/introduction Learn you Haskell] * [http://book.realworldhaskell.org/read/ Real World Haskell] * [http://www.scs.stanford.edu/14sp-cs240h/slides/ Standford Class Material] [[Category:Haskell|programming in plain view]] htvnb7qdgktvlekp28w2jgi89n2k8n2 0 215039 2690164 2193740 2024-12-03T20:34:27Z CommonsDelinker 9184 Removing [[:c:File:Wikibully.jpg|Wikibully.jpg]], it has been deleted from Commons by [[:c:User:Ymblanter|Ymblanter]] because: per [[:c:Commons:Deletion requests/File:Wikibully.jpg|]]. 2690164 wikitext text/x-wiki {{title|Bullying and social needs:<br>What is the role of social needs for bullies and victims?}} {{MECR3|https://prezi.com/voxskacyddox/bullying-and-social-needs/}} __TOC__ == Overview == {{Warning|'''Warning:''' ''If you are experiencing bullying please talk to a family member, friend or professional. Contact numbers can be found in the external links at the end of this chapter.''}} {{RoundBoxTop}}A young girl in her first term of Year 7 walked toward her mother, who was waiting in the car, at the end of the school day. As she got closer her mother could tell something was not right. When she got into the car, she was clearly upset. Her mother asked her what was wrong, and she started crying. The young girl proceeded to recall an incident that happened at the lockers earlier that day. She told her mother how, when she was at her locker that she was confronted by five girls. The girls had surrounded her, as she knelt down to get her books, so that she could not move away from them. They proceeded to taunt her, with one girl – the ringleader - yelling abusively at her. She recalled that as she attempted to stand up, the ringleader proceeded to push her back down. The ringleader was smaller in statute, and was not known for her sporting or academic abilities, but nevertheless, at this time she was intimidating. With no clear sight of how to escape the taunts, the young girl started crying. She expressed to her mother - “Mum, I couldn’t help it, I just started crying”. There were other girls around, but they chose to ignore the incident, possibly from fear of being targeted. Alternatively, it may have been that they simply accepted this as "normal" school behaviour. {{RoundBoxBottom}} <blockquote>'''''This type of incident, and many other ones similar are all too common, with other such [http://www.adelaidenow.com.au/news/south-australia/victims-of-bullying/story-e6frea83-1111117332518 case studies] very similar{{rewrite}}. What motivates an individual, or group of individuals, to behave in such a way? Why are some people targets and others not? Why do those that are bullied react the way they do? And, why do some people stand by and watch it happen?'''''</blockquote> Bullying is a social issue as it is based on social interactions and inter-personal relationships (Department of Education and Training, 2015). The origins of bullying can be traced back to 1538, where it was used to describe someone who was "cruel to others who are weaker" (Volk, Dane & Marini, 2014, p. 328). Exposure to bullying has shown to have a correlation with psychological illnesses such as depression, anxiety, eating disorders and suicide intentions (Department of Education and Training, 2015). Within the school social system, bullying gets significant attention, possibly as it at this developmental stage that younger children start to "interpret, reproduce and become part of the social order around them" (Department of Education and Training, 2015, p. 15). Yet bullying is also prominent in the workplace and as Trepanier, Fernet and Austin (2015) highlight their{{grammar}} is an increasing occurrence of bullying in the workplace that it is having "damaging effects on both employees and the organisation" (p. 105). Needs Theory, as proposed by McClelland (1967), focuses on three dominant needs that motivate individuals. These three needs provide a framework in which to consider the behaviours evident in bullying. This analysis will help support an informed understanding of the drivers and therefore the role of social needs of bullies and the victims of bullying. == What is bullying? == {{expanda}} === Definition of bullying === [[File:Dont Bullying.jpg|thumb|''Figure 1:'' Diagram identifying the unacceptable nature of bullying]] [[w:Bullying|Bullying]] is “an act of intentional aggression involving the selection of specific targets by bullies for specific reasons” (Wong, Cheng & Chen, 2013, p. 278). The term aggression should not be confined solely to physical aggression. According to Farrington (1993, as cited in Ireland & Ireland, 2003), more common definitions include that for {{awkward}} behaviours should include those that are physical, psychological or verbal. Interestingly, bullying is defined differently across age groups, such that adults provide a more comprehensive definition than children (Naylor, Cowie, Cossin, de Betterncourt & Lemme, 2006), possibly as a reflection of social experience. In an attempt to provide more rigour and consistency to the definition of bullying, a literature review conducted by Goldsmid and Howie (2014) identified five criteria that were most common across all age groups, these include:  * '''Repetition''' – the behaviour must be repeated; * '''Intentional''' – as opposed to an unintentional or accidental act; * '''Power inequity''' – one party is in a position of power relative to the other that is either physical, psychological, hierarchical or economical; * '''Victim distress''' – ranging from what might be identified as annoying behaviour to behaviour that is more acute and harmful; and * '''Provocation''' – influence or coercion from another person which could include the victim. One of the most commonly cited definitions for bullying in the empirical research is that provided by Olweus, 1993 (as cited in Volk, Dane & Marini, 2014, p. 328)''':''' <blockquote>"It is a negative action when someone intentionally inflicts injury or discomfort upon another, basically what is implied in the definition of aggressive behaviour. Negative actions can be carried out by physical contact, by words, or in other ways, such as making faces or mean gestures, and intentional exclusion from a group..... In my definition, the phenomenon of bullying is thus characterized by the following criteria: it is aggressive behaviour or intentional 'harm doing,' which is carried out repeatedly and over time in an interpersonal relationship characterized by an imbalance of power."</blockquote> === Prevalence of bullying === Bullying is not confined to an age group or culture. It occurs in school, outside of school, and in the workplace, within Australia, and abroad. ==== School ==== <blockquote>'''''"Slightly more than 1 in 3 students between the ages of 13 and 15 worldwide experience bullying on a regular basis."''''' ''-'' United Nations Children's Fund </blockquote>Within the school environment Cross et al. (2009) identified that approximately 29 percent of children in Years Four to Nine, were subject to bullying on a regular basis and 9 percent report that they bully others. The highest was for students in Year Five, at approximately 32 percent (Cross et al., 2009). Approximately 70 percent of teachers identify that a student reported a bullying incident to them in a school term (Cross et al., 2009). {{RoundBoxTop|theme=4}} Cross et al., (2009) identifies: * hurtful teasing and lies are reported as the most prevalent bullying behaviour * cyber bullying is increasing and occurs more by secondary students * covert forms of bullying are reported to be used more than overt bullying as children get older * girls are more likely to engage in covert bullying, while boys are more likely to engage in overt bullying {{RoundBoxBottom|theme=4}} {{RoundBoxTop|theme=5}} In addition, Cross et al., (2009) report that when students were asked their opinion on why people bullied, responses included that the bully: * did not like the other person; * was doing it for fun; * was trying to feel tough; and * wanted to be popular and in control. {{RoundBoxBottom|theme=5}} ==== Workplace ==== <blockquote>'''''"All work health and safety laws in Australia recognise workplace bullying as a work heath and safety issue with the responsibility to prevent workplace bullying covered by the primary duty of care held by employers." -''''' Safe Work Australia </blockquote> According to Safe Work Australia (2012), when provided with a precise definition of bullying, the reported occurrence of bullying in the workplace is between one to four percent{{when}}. However, when individuals are provided with an open question such as, 'have your ever been bullied in the workplace?', this increases to 10-25 percent (Safe Work Australia, 2012). The increase in workplace bullying is reflecting in workplace mental health claims. Safe Work Australia (2015) identify that while mental health claims reduced between 2001-02 and 2011-12, bullying claims actually increased. In 2011-12 bullying claims comprised 21.5 percent of all mental health claims (Safe Work Australia, 2015). The majority of reported incidents of bullying include verbal assault. More precisely, being yelled at or sworn at in the workplace - over 33 percent - followed largely by being humiliated in front of co-workers - over 22 percent (Safe Work Australia, 2012). These figures are similar to the school environment, with interpersonal bullying behaviours most common and often more damaging to psychological health of victims. === The impact of bullying === Several studies have highlighted the long-term negative health impacts of bullying on children and adults (Department of Education and Training, 2015; Safe Work Australia, 2014; Commonwealth of Australia, 2012; Sharkey, et al, 2015; Cross, Shaw, Hearn, Epstein, Monks, Lester & Thomas, 2009). ==== School ==== In young children and adolescents, bullying has been linked to health issues, both physical and psychological, behavioural issues and poor academic achievement (Turner, Finkelhor, Shattuck, Hamby & Mitchell, 2014).  Children subject to bullying, and those that are engaged in bullying others, are reported to be more likely to suffer from depression, anxiety, eating disorders, and socially withdrawal (United Nations Children’s Fund, 2014).   ==== Workplace ==== In the workplace, bullying and harassment has been linked to increases in the incidence of anxiety, burnout, and reduced self-esteem, job satisfaction and commitment to the organisation (Bowling & Beehr, 2006). The Commonwealth of Australia, House of Representatives report, [http://www.aph.gov.au/Parliamentary_Business/Committees/House_of_Representatives_committees?url=ee/bullying/report.htm ''Workplace bullying: we just want it to'' ''stop''], (2012), estimates that bullying costs “the Australian economy between $6 billion and $36 billion annually” (p. 10).      '''Which group of people is most likely to be bullied?''' Studies suggest that most people who are bullied are termed passive victims (Wolke, 2015). It is those people who are sensitive, quiet, withdrawn, shy , anxious and insecure about themselves are the ones who are usually targeted when it comes to bullying (Wolke, 2015). == What motivates bullying behaviour? - McClelland's theory of needs == [[File:David McClelland.jpg|thumb|''Figure 2'': David C. McClelland{{expand}}]] [[w:David_McClelland|David McClelland]] proposed that “motives drive, orient and select behaviour” (McClelland, 1987, p. 226). McClelland (1967) considered the link between motivation and behaviour and proposed that individuals are motivated by the "desires for social approval, power, or knowledge " (p. 39) and the strength of this is different for individuals. To test this, he sought to arouse motives in participants and then test their "spontaneous thoughts" (McClelland, 1967, p. 39). This was undertaken by asking participants to write a story to describe what was occurring in a picture (known also as the [[w:Thematic_Apperception_Test|Thematic Apperception Test).]] McClelland proposed three key motives were driving behaviour. These were the need for, [[w:Need_for_achievement|achievement]], [[w:Need_for_affiliation|affiliation]] and [[w:Need_for_power|power.]] It is the basis of these that McClelland's work is often referred to as the [[w:Need_theory|Three Needs Theory]]. Therefore, when seeking to better understand the role of social needs for bullies, and victims of bullying, McClelland's Needs Theory provides a valuable framework. It is from here a more informed understanding that interventions and prevention can be better targeted. === Achievement needs === <blockquote>'''''"Bullying consists of the least competent most aggressive employee projecting their incompetence on to the least aggressive most competent employee and winning."''''' ― Tim Field</blockquote> Characteristics common in individuals high in [[w:Need_for_achievement|achievement motivation]] include striving to accomplish or master something of significant difficultly, and doing so to a high standard (McClelland, 1987). Additional behavioural characteristics include, manipulating to achieve a high level of mastery and rivalry, so as to surpass others (McClelland, 1987). Individuals that are high in the need for achievement are found to be just as focused on the possibility of failure, as they are on success (McClelland, 1987). Indeed, it is this fear of failure that can produce significant stress and anxiety (McClelland, 1987). Individuals high in achievement motivation are less likely to consider others as they pursue their goals, and they are less able to identify how others perceive their behaviour (McClelland, 1987). [[File:Jack London Studying.jpg|thumb|''Figure 3:'' A picture similar to what might be produced in a Thematic Apperception Test use to elicit stories from participants to identifying their need for achievement]] Considering these characteristics, individuals with a high motive for achievement may be easily threatened by another person, especially where that person’s performance puts their achievement at risk. Additionally, they could be easily threatened in an environment that has a high level of competition. Children high in achievement motivation have been found to be more likely to cheat, in an attempt to reach a goal, where there is a level of competition (McClelland, 1987). Similarly, bullies use aggression as a way to compete for, or maintain, social status with their peers (Pellegrini, Bartini & Brooks, 1999).     Bowling and Beehr's (2006) meta-analysis identified that workplace bullying is common in environments where there is conflict over what needs to be achieved, ambiguity, workplace constraints and competition. Environments that reduced the opportunity for autonomy also had a higher rate of bullying (Bowling & Beehr, 2006). In these workplace environments, individuals with high achievement needs are constrained. As such, it is more likely that levels of frustration would be present and therefore a greater inclination to engage in bullying behaviours. It would be expected that high need achievement individuals would also engage in bullying behaviours to impede their rivals performance, making their chances of achievement greater (Tuckey et al., 2009). In examining the incident of bullying and its relationship with workplace factors, Tuckey et al. (2009) identified that in jobs where individuals had little control over their work, where the work was challenging, and where resource support was low, there were higher incidents of bullying. Individuals with a high need for achievement when in an environment that restricts or places their need for achievement at risk, could become easily threatened and react negatively. Specifically, as identified from Tuckey et al. (2009), these work environments raise “employee arousal and lowering of the threshold for anger, aggression, and conflict” (p. 228). The result is the demonstration of behaviours such as anger and frustration projected at the immediate work group, or at others (Tuckey et al., 2009).  === Affiliation needs === <blockquote>'''''"You should be nicer to him,' a schoolmate had once said to me of some awfully ill-favored boy. 'He has no friends.' This, I realized with a pang of pity that I can still remember, was only true as long as everybody agreed to it."''''' ― Christopher Hitchens, Hitch-22: A Memoir</blockquote> The need for [[w:Need_for_affiliation|affiliation]] is associated with characteristics that include seeking to be near other individuals, those that are similar to the person, or seeking to be near others that ‘like’ the person (McClelland, 1987). McClelland (1987) also identifies behaviours such as attempting to win the affection of another/others, or seeking to please. Pellegrini, Bartini, and Brooks (1999) expand this by defining affiliation need as seeking to gain the approval of others. Pellgerini, Bartini and Brooks (1999) examined the extent to which the need for affiliation, more specifically the motivation to be near others that are similar, applied to both bullies and victims. They identified dominant friendship groups in so far that bullies associated more with other bullies, and victims associated more with other victims (Pellegrini, Bartini & Brooks, 1999). Effectively, bullies “had reciprocal friendships mostly among other bullies” (Pellegrini, Bartini & Brooks, 1999, p. 222). This finding helps explain why it is not unusual that there is more than one person doing the bullying. It also reinforces that the social need for bullies to seek company of other bullies, and victims to seek the company of other victims. Individuals high in the need for affiliation also “dislike a person whose views differ from their own” (Byrne, 1961b, as cited in McClelland, 1987, p. 356). Interestingly, Pellegrini, Bartini and Brooks (1999) identified that the attitudes of both bullies and their victims, towards bullying, were similar. The findings of Nickerson and Mele-Taylor (2014) reinforce this, as they identified that students who had friends that were bullies, had attitudes that supported the bullying behaviour, and were also more likely to be involved in bullying themselves. In general, it appears that the motivation for affiliation with others, drives individuals to seek consistency with others in their views and behaviours. [[File:A student group part of 'FREE HUGS', Chile.jpg|thumb|''Figure 4'': Individuals with a high need for affiliation seek to be close to others.]] Individuals with a high need for affiliation seek to please and will perform better when their is an affiliation incentive (McClelland, 1987). Evidence identifies that when using self-report measures for bullying, over half of the students reporting identify as a defender of bullying victims (Nickerson and Mele-Taylor, 2014). Interestingly, this figure is below national reports, where less than half of the witnesses to bullying intervened (Department of Education and Training, 2015). The motivation of individuals in self-reports appears to be that they seek to see themselves agreeing with social expectations and not letting others down (Nickerson and Mele-Taylor, 2014), particularly where social conventions are anti-bullying. Those high in the need for affiliation also seek social environments that have positive interpersonal relationships (McClelland, 1987). While seeking conformity is not recognised as a dominant behaviour, individuals high in affiliation do seek to avoid conflict (McClelland, 1987). This characteristic would help explain the behaviours of bystanders, or observers, to bullying incidents and their tendency not to intervene. For victims of bullying there is evidence to suggest that having friends who are bullies also provides some social protection against being bullied, effectively avoiding conflict (Pellegrini, Bartini & Brooks, 1999). This is reinforced by Farmer, Hall, Leung, Estell and Brooks (2011), where students that identified as a victim of bullying had low social status with their peers. Victims of bullying high in the need for affiliation may be motivated to seek a broad and varied set of friendships so as to act as a protection from negative interpersonal relationships and conflict.   Finally, those high in the need for affiliation may use this as a protection against bullying. Pellegrini, Bartini and Brooks (1999) identified that in general, where individuals were popular and had a variety of friends, and were liked by others, there was correlation with lower report of being bullied. Similarly, Visconti, Sechler and Kochenderfer-Ladd (2013) identified that were social status was similar between a bully and their victim, the victim is more likely to defend themselves. === Power needs === <blockquote>'''''"Those in powerless positions aren't about to complain about bullying bosses, abusive supervisors and corrupt co-workers. There is no safe way to do so and no process that promises redress."''''' ― Margaret Heffernan</blockquote> Individuals with a high need for [[w:Need_for_power|power]] tend to display characteristics that include the need to control, influence and direct the behaviour of others. This is mostly achieved through behaviour that includes commanding, persuasion and suggestion (McClelland, 1987). They are more likely to surround themselves with others that they can easily direct and control, and those that generally are not as well-known as they are seeking to ingratiate themselves with the dominant individual with positive and reinforcing comments (McClelland, 1987). Ultimately, individuals with a high need for power seek to stand-out in a group and like to have people around them, “who respect them and are loyal supporters” (McClelland, 1987, p. 286).   Bullies with a high need for power target individuals that are vulnerable due to their lower social status, or atypical characteristics (Wong, Cheng & Chen, 2013).  According to Wong et al. (2013), vulnerable students, those that may be considered introverted, shy or have an obvious physical or mental disability, become easy targets for bullies due to their obvious power imbalance. This makes it easier for bullies with a high need for power to achieve elevated social standing in their peer group (Wong et al., 2013). Bullying is considered to be largely associated with, “establishing social status or procuring benefits” (Wong et al., 2013). This high need for power that is often evident in bullying, is also largely independent of demographics (Turner, Finkelhor, Shattuck, Hamby & Mitchell, 2014). Generally speaking, individuals with a high need for power that engage in bullying are not easily identifiable due to their age group, culture and socio-economic status. Surprisingly, victims of bullying don’t readily identify with a power imbalance in their situation. Others around them, such as teachers and bystanders, this power imbalance is more obvious (Department of Education and Training, 2015). Where individuals that identify as a victim of bullying do associate with a power imbalance, it is largely where the form of bullying involves physical, verbal, relational or sexual incidents (Turner et al., 2014). However, Turner et al. (2014) did identify that even where a power imbalance is not recognised by a victim of bullying, there was still a negative impact on that individual such as missing school and feeling fearful. It is clear that the lack of a recognised power imbalance by a victim of bullying "does not shield victims from negative effects” (Turner, et al., 2014, p. 375). The high need for power that is evident as a driver for bullying continues into the workplace. Tuckey, Dollard, Hosking and Winefield (2009) considered the incident of bullying within the policing occupation. Tuckey et al. (2009) identified that where bullying had occurred, it was largely by those higher ranking officers. The workplace context is also provide individuals with a high need for power to seek to control and direct others. Katrinli, Atabay, Gunay and Cangarli, (2010) identified that the need for power was the single most significant personal characteristic associated with an individual’s bullying behaviour in the workplace.   Interestingly, Peets, Juvonen, Poyhonen and Salmivalli (2015) have identified that students high in power, primarily through popularity, can actually increase their social standing by positively intervening in bullying situations. However, this is primarily in environments that actively discourage bullying, and where bullying is seen as socially unacceptable. This finding demonstrates the impact that a positive environment, or organisational culture, can have to reduce incidents of bullying by individuals with a high power need. Interestingly, however, where a popular student seeks to increase their social status through bullying, other popular students are less likely to intervene for fear of losing their popularity status (Peet et al., 2015).   Lastly, power imbalance is not evident in all reports of bullying. This would imply that whilst the presence of a power imbalance may indeed increase the negative effects on victims of bullying, not all bullies are motivated by a need to assert power over another, however, it is more likely to be present when bullying is occurring. === Three needs summary characteristics === Table 1 ''Summary of the typical characteristics of the three needs.'' (McClelland, 1987). {| class="wikitable" |'''Need''' |'''Characteristic of the need''' |- |Need for Achievement - (N-Ach) | * Setting difficult goals and seek challenges - will work hard in all attempts to reach those goals * Work hard until completely satisfied and is very focused on the end result * Need feedback, not for seeking praise but more so for bettering oneself - may get frustrated if feedback is not provided |- |Need for Affiliation - (N-Affil) | * Most enjoyable for them to be around people and want to approval of those around them * Very attached to friends and friendship groups * Prefers being with a group of people and likes to make those around them feel included and as though they are a part of something * Will go out of their way to be with friends and with others |- |Need for Power - (N-Pow) | * Enjoy organising and directing others, which can manipulate others or the situation to satisfy this need * Argue point of view against the point of view of others, which can be helpful but may also be destructive * Influence others as opposed to being influenced by others * Can dominate social situation but can also feel frustrated when they feel they don't have control of a situation |} == Quick quiz == Test your knowledge of bullying and motivation needs theory: <quiz display="simple"> {Does physical bullying need to be present for a behaviour to be defined as bullying? |type="()"} + No. - Yes. {Bullying has no financial impacts, organisations shouldn't worry about workplace bullying? |type="()"} -True. +False. {Individuals motivated by the need for power: |type="()"} - Need to be around similar others. + Need to be in control. - Set high goals for themselves. {Individuals with a high need for achievement generally bully others because they need to control others? |type="()"} - True. + False. {Choose a common characteristic of individuals with a high affiliation need from the list below: |type="()"} + avoid conflict. - dominate others. - are very shy. </quiz> == Conclusions == Bullying is a significant social issue that is costly in terms of its impact on psychological health and well-being, including illnesses such as depression, anxiety, eating disorders and suicide intentions. Bullying is also shown to have negative financial implications for the economy. It occurs regardless of age, culture, gender or ability. McClelland's needs theory with its focus on achievement, affiliation and power needs, provides a framework for understanding the social needs of bullies and victims of bullying. It is with a more informed understanding of the motivations for such behaviours, that interventions and support can be better targeted ultimately reducing the incidents and impacts of bullying. == See also == *[[Motivation_and_emotion/Book/2016/Bystander_intervention_motivation|Bystander intervention motivation]] (Book chapter, 2016) *[[Motivation and emotion/Book/2015/Bullying and pack behavior motivation in adolescents|Bullying and pack behaviour motivation]] (Book chapter, 2015) *[[Motivation and emotion/Book/2014/Cyber-bullying motivation|Cyber-bullying motivation]] (Book chapter, 2014) * [[Motivation and emotion/Book/2014/Workplace bullying motivation|Workplace bullying motivation]] (Book chapter, 2014) * [[Motivation and emotion/Book/2013/Affiliation motivation|Affiliation motivation]] (Book chapter, 2013) == References == {{Hanging indent| Bowling, N. A., & Beehr, T. A. (2006). Workplace harassment from the victim's perspective: A theoretical model and meta-analysis. 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Empathetic responsiveness, group norms, and prosocial affiliations in bullying roles. ''School Psychology Quarterly, 29,'' (1), 99-109.}} {{Hanging indent| Peet, K., Puyhonen, V., Juvonen, J. & Salmivalli, C. (2015). Classroom norms of bullying alter the degree to which children defend in response to their affective empathy and power. ''Developmental Psychology, 51, ''(7), 913-920.}} {{Hanging indent| Pellegrini, A. D., Bartini, M. & Brooks, F. (1999). School bullies, victims, and aggressive victims: Factors relating to group affiliation and victimization in early adolescence. ''Journal of Educational Psychology, 91,'' (2), 216-224.}} {{Hanging indent| Safe Work Australia.(2012). ''The Australian Workplace Barometer: Report on Psychosocial Safety Climate and Worker Health in Australia.'' Safe Work Australia, Canberra. Retrieved from: http://www.safeworkaustralia.gov.au/sites/swa/about/Publications/Documents/748/The-Australian-Workplace-Barometer-report.pdf}} {{Hanging indent|Safe Work Australia.(2015). ''Psychosocial Health and Safety and Bullying in Australian Workplaces: Indicators from accepted workers compensation claims. Annual Statement, 2nd Edition'' Safe Work Australia, Canberra. Retrieved from: http://www.safeworkaustralia.gov.au/sites/SWA/about/Publications/Documents/857/Psychosocial-bullying-statement.pdf}} {{Hanging indent| Sharkey, J. D., Ruderman, M. A., Mayworm, A. M., Green, J. G., Furlong, M. J., Rivera, N. & Purisch, L. (2014). Psychosocial functioning of bullied youth who adopt versus deny the bully-victim label. ''School Psychology Quarterly, 30, ''(1), 91-104.}} {{Hanging indent| Tuckey, M. R, Dollard, M. F., Hoskings, P. J., & Winefield, A. H. (2009). Workplace bullying: The role of psychosocial work environment factors. ''International Journal of Stress Management, 16,'' (3), 215-232. }} {{Hanging indent| Turner, H. A., Finkelhor, D., Shattuck, A., Hamby, S., & Mitchell, K. (2014). Beyond bullying: Aggravating elements of peer victimization episodes. ''School Psychology Quarterly, 30,'' (3), 366-384. }} {{Hanging indent| United Nations Children's Fund. (2014) ''Hidden in Plain Sight: A statistical analysis of violence against children.'' Unicef, New York.}} {{Hanging indent| Visconti, K. J., Sechler, C. M. & Kochenderfer-Ladd, B. (2013). Coping with peer victimization: The role of children's attributions. ''School Psychology Quarterly, 28,'' (2), 122-140.}} {{Hanging indent| Volk, A. A., Dane, A. V., & Marini, Z. A. (2014). What is bullying? A theoretical redefinition. ''Developmental Review, 34,'' 327-343. Doi:10.1016/j.dr.2014.09.001 }} {{Hanging indent| Wang, W., Vaillancourt, T., Brittain, H. L., McDougall, P., Krygsman, A., Smith, D., Cunningham, C. E., Haltigan, J. D., & Hymel, S. (2014). 'School climate, peer victimization, and academic achievement: Results from a multi-informant study. ''School Psychology Quarterly, 29,'' (3), 360-377.}} {{Hanging indent| Wong, C. T., Cheng, Y.Y., & Chen, L.M. (2013). Multiple perspectives on the targets and causes of school bullying. ''Educational Psychology in Practice, 29,'' (3), 278-292 }} {{Hanging indent| Yamada, S. M., Cappadocia, C., & Pepler, D. (2013). Workplace bullying in Canadian graduate psychology programs: Student perspectives of student-supervisor relationships. ''Training and Educational Professional Psychology, 8,'' (1), 58-67 }} == External links == * [https://www.lifeline.org.au/ LifeLine Contact Details] * [https://bullyingnoway.gov.au/need-help-now To Seek Help from Bullying] * [https://www.ted.com/playlists/191/stand_up_to_bullying TedTalk Stand Up To Bullying] * [http://www.mightyfighter.com/why-do-people-bully/ Fact Sheet Nine Reasons for Bullying ] * [https://bullyingnoway.gov.au/ Bullying. No Way! ] * [http://www.safeworkaustralia.gov.au/sites/SWA Safe Work Australia ] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Bullying]] dwrfcdj717279sh372vsgr6sbcd4scc 0 230360 2690217 2615792 2024-12-04T04:24:54Z 2600:1012:B138:9A50:9806:D10A:21C7:B9D6 2690217 wikitext text/x-wiki [[File:Global Open Educational Resources Logo.svg|thumb|right|Open Educational Resources Logo]] [[hu:Wikiegyetem]] '''Open educational resources''' ('''OER''') are freely accessible, openly licensed text, media, and other digital assets that are useful for teaching, learning, and assessing as well as for research purposes<ref>[[Wikipedia:Open educational resources]]</ref>. Communities use and alter OER according to their requirements and constraints. A scientific analysis of these alteration, forking or extension of OER provide insights in the drivers and needs of communities. == Contents == The following resources can be found in these {{Subpages/Simple}}: * [[/Introduction/]] - Introduction to OER * [[/Lesson/]] - Lesson on OER * [[/Sources/]] - Sources of OER (table of resources w/ counts of data available from each) * [[/Student Authoring/]] - Resources supporting student-authored content * [[/Adoptions/]] - Schools and courses using OER * [[Classifying educational resources]] * [[/Open Courses/]] - Open course lists * [[/Open Textbooks/]] - Open textbook lists * [[/Training/]] - For teachers * [[/Localization/|Geographic Information Systems and tailored educational resources for a specific region]] * [[/Tailored WikiBooks/]] * [[Green Open Access]] * [[Wikiversity:Edit-a-thon]] to create OER == Learning Activities == * '''([[w:en:UNESCO]])''' Explore the recommendation of UNESCO on Open Educational Resources and derive an application to your institutional setting: ** as a '''teacher''' for designing classroom activities, ** as a '''learner/student''' to perform the learning tasks in the classroom (e.g. supporting material as OER for performing a learning task) * '''(Digital Public Good)''' Explore and compare the concept of ** digital public good, ** [[w:common good|common goods]] and ** OER : and identify similarities and differences between these concepts. How can digital public goods can trigger as building blocks for an [[Open Innovation Ecosystem]]. What are the benefits, challenges and constraints? == See Also == * [[Intellectual Honesty]] * [[Open academia]] * [[Open Badges]] as digital certificates and record of achievements for OER courses and learning activities * [[Open Community Approach]] and OER as one main constituent * [[PanDocElectron]] for using Wikiversity Resource as Slide Presentations with the option to annotate slides in a browser with a stylus * [[Reproducible Science]] * [[Wikipedia: Open educational resources|Open educational resources]] (Wikipedia) * [[Open Innovation Ecosystem]] == External Learning Resources for OER == * [https://courses.lumenlearning.com/pathways Lumen Learning: Adopting Open Educational Resources in the Classroom] * [http://pressbooks.oer.hawaii.edu/oertraining2018 Hawaii.edu: OER Training] == References == {{reflist}} [[Category:Capacity Building]] [[Category:Learning]] [[Category:Resources]] <noinclude> [[de:Open Educational Resources]] </noinclude> <noinclude> [[fr:Aide:Ressources_éducatives_libres]] </noinclude> <noinclude> [[zh:開放教育資源]] </noinclude> mpewi1xjfcu2jaeyfg0m5fqm0wgytr8 0 232469 2690227 2690055 2024-12-04T07:20:03Z Young1lim 21186 /* ARM Assembly Programming (II) */ 2690227 wikitext text/x-wiki == '''Background''' == '''Combinational and Sequential Circuits''' * [[Media:DD2.B.4..Adder.20131007.pdf |Adder]] * [[Media:DD3.A.1.LatchFF.20160308.pdf |Latches and Flipflops]] '''FSM''' * [[Media:DD3.A.3.FSM.20131030.pdf |FSM]] * [[Media:CArch.2.A.Bubble.20131021.pdf |FSM Example]] '''Tiny CPU Example''' * [[Media:CDsgn6.TinyCPU.2.A.ISA.20160511.pdf |Instruction Set]] * [[Media:CDsgn6.TinyCPU.2.B.DPath.20160502.pdf |Data Path]] * [[Media:CDsgn6.TinyCPU.2.C.CPath.20160427.pdf |Control Path]] * [[Media:CDsgn6.TinyCPU.2.D.Implement.20160513.pdf |FPGA Implementation]] </br> == '''Microprocessor Architecture''' == * ARM Architecture : - Programmer's Model ([[Media:ARM.1Arch.1A.Model.20180321.pdf |pdf]]) : - Pipelined Architecture ([[Media:ARM.1Arch.2A.Pipeline.20180419.pdf |pdf]]) * ARM Organization * ARM Cortex-M Processor Architecture * ARM Processor Cores </br> == '''Instruction Set Architecture''' == * ARM Instruction Set : - Overview ([[Media:ARM.2ISA.1A.Overview.20190611.pdf |pdf]]) : - Addressing Modes ([[Media:ARM.2ISA.2A.AddrMode.20191108.pdf |pdf]]) : - Multiple Transfer ([[Media:ARM.2ISA.3A.MTransfer.20190903.pdf |pdf]]) : - Assembler Format :: - Data Processing ([[Media:ARM.2ISA.4A.Proc.Format.20200204.pdf |pdf]]) :: - Data Transfer ([[Media:ARM.2ISA.4B.Trans.Format.20200205.pdf |pdf]]) :: - Coprocessor ([[Media:ARM.2ISA.4C.CoProc.Format.20191214.pdf |pdf]]) :: - Summary ([[Media:ARM.2ISA.4D.Summary.Format.20200205.pdf |pdf]]) : - Binary Encoding ([[Media:ARM.2ISA.5A.Encoding.201901105.pdf |pdf]]) * Thumb Instruction Set </br> == '''Assembly Programming''' == === ARM Assembly Programming (I) === * 1. Overview ([[Media:ARM.2ASM.1A.Overview.20200101.pdf |pdf]]) * 2. Example Programs ([[Media:ARM.2ASM.2A.Program.20200108.pdf |pdf]]) * 3. Addressing Modes ([[Media:ARM.2ASM.3A.Address.20200127.pdf |pdf]]) * 4. Data Transfer ([[Media:ARM.2ASM.4A.DTransfer.20230726.pdf |pdf]]) * 5. Data Processing ([[Media:ARM.2ASM.5A.DProcess.20200208.pdf |pdf]]) * 6. Control ([[Media:ARM.2ASM.6A.Control.20200215.pdf |pdf]]) * 7. Arrays ([[Media:ARM.2ASM.7A.Array.20200311.pdf |pdf]]) * 8. Data Structures ([[Media:ARM.2ASM.8A.DataStruct.20200718.pdf |pdf]]) * 9. Finite State Machines ([[Media:ARM.2ASM.9A.FSM.20200417.pdf |pdf]]) * 10. Functions ([[Media:ARM.2ASM.10A.Function.20210115.pdf |pdf]]) * 11. Parameter Passing ([[Media:ARM.2ASM.11A.Parameter.20210106.pdf |pdf]]) * 12. Stack Frames ([[Media:ARM.2ASM.12A.StackFrame.20210611.pdf |pdf]]) :: :: === ARM Assembly Programming (II) === :: * 1. Branch and Return Methods ([[Media:ARM.2ASM.Branch.20241204.pdf |pdf]]) * 2. PC Relative Addressing ([[Media:ARM.2ASM.PCRelative.20241123.pdf |pdf]]) * 3. Thumb instruction Set ([[Media:ARM.2ASM.Thumb.20241123.pdf |pdf]]) * 4. Exceptions ([[Media:ARM.2ASM.Exception.20220722.pdf |pdf]]) * 5. Exception Programming ([[Media:ARM.2ASM.ExceptionProg.20220311.pdf |pdf]]) * 6. Exception Handlers ([[Media:ARM.2ASM.ExceptionHandler.20220131.pdf |pdf]]) * 7. Interrupt Programming ([[Media:ARM.2ASM.InterruptProg.20211030.pdf |pdf]]) * 8. Interrupt Handlers ([[Media:ARM.2ASM.InterruptHandler.20211030.pdf |pdf]]) * 9. Vectored Interrupt Programming ([[Media:ARM.2ASM.VectorInt.20230610.pdf |pdf]]) * 10. Tail Chaining ([[Media:ARM.2ASM.TailChain.20230816.pdf |pdf]]) </br> * ARM Assembly Exercises ([[Media:ESys.3.A.ARM-ASM-Exercise.20160608.pdf |A.pdf]], [[Media:ESys.3.B.Assembly.20160716.pdf |B.pdf]]) :: === ARM Assembly Programming (III) === * 1. Fixed point arithmetic (integer division) * 2. Floating point arithmetic * 3. Matrix multiply === ARM Linking === * arm link ([[Media:arm_link.20211208.pdf |pdf]]) </br> === ARM Microcontroller Programming === * 1. Input / Output * 2. Serial / Parallel Port Interfacing * 3. Analog I/O Interfacing * 4. Communication </br> == '''Memory Architecture''' == </br> === '''Memory Hierarchy''' === </br> === '''System and Peripheral Buses''' === </br> === '''Architectural Support''' === * High Level Languages * System Development * Operating Systems </br> == '''Peripheral Architecture''' == </br> === '''Vectored Interrupt Controller ''' === </br> === '''Timers ''' === * Timer / Counter ([[Media:ARM.4ASM.Timer.20220801.pdf |pdf]]) * Real Time Clock * Watchdog Timer </br> === '''Serial Bus''' === * '''UART''' : Universal Asynchronous Receiver/Transmitter ([[Media:ARM.4ASM.UART.20220924.pdf |pdf]]) * '''I2C''' : Inter-Integrated Circuit * '''SPI''' : Serial Peripheral Interface * '''USB''' : Universal Serial Bus Device Controller </br> === '''I/Os ''' === * General Purpose Input/Output ports (GPIO) * Pulse Width Modulator * Analog-to-Digital Converter (ADC) * Digital-to-Analog Converter (DAC) </br> <!-- == '''Interrupts and Exceptions ''' == --> </br> == '''Synchrnoization'''== </br> === H/W and S/W Synchronization === * busy wait synchronization * handshake interface </br> === Interrupt Synchronization === * interrupt synchronization * reentrant programming * buffered IO * periodic interrupt * periodic polling </br> ==''' Interfacing '''== </br> === Time Interfacing === * input capture * output compare </br> === Serial Interfacing === * Programming UART * Programming SPI * Programming I2C * Programming USB </br> === Analog Interfacing === * OP Amp * Filters * ADC * DAC </br> == '''Old materials''' == === '''Instruction Set Architecture''' === * ARM Instruction Set :: - Overview ([[Media:ARM.2ISA.1A.Overview.20180528.pdf |pdf]]) :: - Binary Encoding ([[Media:ARM.2ISA.2A.Encoding.20180528.pdf |pdf]]) :: - Assembler Format ([[Media:ARM.2ISA.3A.Format.20180528.pdf |pdf]]) * Thumb Instruction Set * ARM Assembly Language ([[Media:ESys3.1A.Assembly.20160608.pdf |pdf]]) * ARM Machine Language ([[Media:ESys3.2A.Machine.20160615.pdf |pdf]]) </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] d6msmwldahk7hdowmon2cllse0i7bxk 0 255265 2690114 2606635 2024-12-03T15:05:36Z 2603:8080:2E00:2347:AD92:DD13:9690:7E53 no 2690114 wikitext text/x-wiki This decision matrix can be used to choose among several new car alternatives being considered for purchase. {| class="wikitable" |- ! !! Mazda 6 !!Nissan Altima !!Nissan Maxima |- |Safety<br>High = 5 || 5 <br>Cell contribution<br>is 5x5=25 || 5 || 5 |- |Reliability<br> High = 5 || 5|| 3|| 5 |- |Low Cost<br>Medium = 4 ||4|| 4|| 2 |- |Space<br>Medium = 4 ||4|| 4|| 5 |- |Service<br>Medium =4 ||5|| 4 ||4 |- |Performance<br>Low = 2|| 5|| 4|| 5 |- |Aesthetics<br>Low = 2 ||5|| 3|| 5 |- |'''Total:'''|| 122 ||97 ||114 |} Begin by creating an [[Thinking_Tools#Affinity_Diagram|affinity diagram]] on the topic “What is important to consider when choosing a new car”. Using the resulting affinity diagram as a starting point, create a [[Thinking_Tools#Tree_Diagram|tree diagram]] with the topic “What decision criteria will be used to choose a new car”. Each row label represents a decision criterion identified from the tree diagram. The importance of each criterion is determined, quantified and recorded. Here high importance is assigned a weight of 5. Each column represents an alternative being evaluated, in this case three different car models. The rating of each alternative for each criterion is decided, quantified, and recorded in the corresponding cell. For example, the Mazda 6 is high in safety, so it is rated 5. The contribution of that rating is calculated as the score (5) multiplied by the criterion weight (5) for a total of 25 for that cell. The total score of each alternative is computed by summing the contribution of each cell in the column representing that alternative. Here the Mazda 6 gets the highest score of 122. {{CourseCat}} mw7n7b29dp7qz4bjmyw8f1lr394bxzs 0 261066 2690177 2459405 2024-12-04T00:17:11Z Therapulse 2994530 /* Information for Trainees */ Added information about a free clinical hour tracking resource for trainees, highlighting its cost advantage compared to paid services. Included a link for more details. 2690177 wikitext text/x-wiki <noinclude>{{Helping Give Away Psychological Science Banner}}</noinclude> {{TOC right}}{{psychology}}{{contrib-creator|Arvm}}{{contrib-major|Emmagch}}{{bymetoo|Eanderson8}} This page is intended for clinicians who provide psychological services. '''If you are a patient''' or someone looking for information about receiving telepsychology services, you can find more information on [[Helping Give Away Psychological Science/Telepsychology Guide for Patients|<u>Telepsychology Guide for Patients</u>]]. The [[w:Coronavirus disease 2019|coronavirus]] pandemic is causing a lot of clinics and clinicians to use [[w:Telehealth|telehealth]]. This page provides information and practical considerations for the clinician, as well as tips and suggestions for how to make telepsychology most successful. {{Font color||beige| We have a suggestion box '''<u>[https://docs.google.com/document/d/1E3v204LjV1d1hS1nUXHdG6JhDRbd07YsQWSxIJdTfFY/edit?usp here]</u>'''where you can drop links, add ideas, and leave comments. You also can make edits directly on this page or on the [[Talk:Helping Give Away Psychological Science/Telepsychology| '''<u>discuss page</u>''']] if you are comfortable with editing.}} '''Share this page by clicking the following social media and interactive platforms: <small>{{Share email|icon=true|subject=Journal article: {{SUBPAGENAME}}|contents={{{email|http://en.wikiversity.org/wiki/{{FULLPAGENAMEE}}}}}}} | {{Share facebook|icon=true}} | {{Share twitter|icon=true|via={{WikiJXyz}}|related=WikiJMed,WikiJSci,WikiJHum,Wikipedia,OpenAccess}} | {{Share linkedin|icon=true}}</small>| {{Share mendeley|icon=true}} |{{#ifeq:{{{icon|true}}}|true|[[File:Researchgate logo.svg|13px|alt=|link=http://www.addthis.com/bookmark.php?v=300&s=researchgate&url=https://en.wikiversity.org/wiki/WikiJournal_of_Medicine/{{PAGENAMEE}}&title={{SUBPAGENAMEE}}]]&nbsp;}}<span class="plainlinks">[http://www.addthis.com/bookmark.php?v=300&s=researchgate&url=https://en.wikiversity.org/wiki/{{PAGENAMEE}}&title={{SUBPAGENAMEE}} ResearchGate]</span>''' = '''Guidelines for conducting mental health services with technology''' = Watch this Youtube video, "[https://youtu.be/Wn6Vewl42X8 Introduction to Telehealth with Dr. Bosch]", by [https://www.ptsd.va.gov/about/divisions/dissemination/bosch_j.asp Jeane Bosch, PhD, MPH] for an introduction to telemental health research, getting started, preparing for the first session, conduction telemental health sessions, and common issues and troubleshooting in the case of technological issue.<ref>{{Citation|title=Introduction to Telehealth with Dr. Bosch|url=https://www.youtube.com/watch?v=Wn6Vewl42X8|accessdate=2022-08-13|language=en}}</ref> == Getting started == Telepsychology is defined as the provision of psychological services using telecommunication technologies, which include telephones/smartphones, video conferencing, email, texting, and self-help materials (blogs, social media, etc.). The services can be delivered synchronously, with multiple parties interacting in real-time or asynchronously, with parties responding to one another at their convenience.<ref>{{Cite news|url=https://www.apa.org/practice/guidelines/telepsychology|title=Guidelines for the practice of telepsychology|publisher=APA|website=www.apa.org|access-date=2020-04-09|language=en}}</ref> Telepsychology offers convenience and can be helpful for coaching patients/clients between appointments. There are also circumstances during which it is not possible to see patients in person, and telepsychology is necessary to provide continuity of care. This is an overview, including resources to help practitioners provide telepsychology safely, effectively, and in alignment with professional standards. In order to build competence in telepsychology, consider taking an [https://apa.content.online/catalog/product.xhtml?eid=15132 online course] to familiarize yourself with telepsychology and read [https://www.apa.org/practice/guidelines/telepsychology American Psychological Association], [https://www.psychiatry.org/psychiatrists/practice/telepsychiatry/toolkit American Psychiatric Association], and [https://www.appic.org/Portals/0/downloads/APA%20Telepsychology%20Guidelines.pdf APPIC] guidelines on the topic. To find recommendations and tips on conducting Telepsychology, read [https://psycnet.apa.org/fulltext/2020-39749-002.html Recommendations for Policy and Practice of Telepsychology]. Additional resources can be found on [https://www.apaservices.org/practice/clinic APA’s website]. Specific information on conducting teletherapy during COVID-19 can be found at [https://psycnet.apa.org/record/2020-39749-001 Intro to Telepsychology in the Age of COVID-19] and [https://psycnet.apa.org/record/2020-39749-017 Telepsychology in the Age of COVID-19], [https://psycnet.apa.org/record/2020-39749-003 Telepsychology during a pandemic], [https://psycnet.apa.org/record/2020-39749-007 Psychotherapists' attitudes toward online therapy during COVID-19] and [https://psycnet.apa.org/record/2020-39749-008 Psychotherapists' experiences with telepsychotherapy]. Additionally, [https://telehealth.hhs.gov/ Health and Human Services has a site dedicated to Telehealth], which provides up-to-date information about government-related policies, including reimbursement. == Consent for telepsychology == It is important to introduce the idea of telepsychology and to give your patient/client an opportunity to ask questions about it and to make a choice about whether [https://www.hgaps.org/assessment-center.html telepsychology] is right for them. * If your original consent for treatment did not include telepsychology (including communication by text message or email), it is important to talk with your patient/client about what telepsychology entails and to collect and document their consent for these services. * Some patients/clients may choose to consent to only some services (e.g., email and phone therapy, but not video). * You should create a new consent form or update your existing form and go over it with your patient/client over the phone. You can then email them a copy to sign and return to you. If it is not possible for them to print/sign the document, you can consider an online signing service, such as [https://www.docusign.com/ DocuSign] or [http://dochub.com DocHub]. Examples of consent for telepsychology can be found [https://parma.trustinsurance.com/Resource-Center/Document-Library here] and [https://drive.google.com/open?id=1nVzmYxR2wY4NnnokGvCy0hOwAaLvZRVX here]. * When explaining telepsychology, ask whether the patient/client has ever seen a doctor on a phone or computer. If the patient has not used telehealth, it may be helpful to explain how it works by relating telehealth to technology (i.e., [https://support.apple.com/en-us/HT204380 Facetime], [https://www.skype.com/en/ Skype], or [https://zoom.us/ Zoom]) with which they are likely to have some familiarity. * Let patients/clients know why telepsychology is being used and whether there are alternatives available. * Discuss security and address any concerns about who else can hear or see them. Additional information regarding technical specifications should be available if requested. Some patients appreciate being reassured that the session is not “on the internet” in the sense that it can neither be openly viewed nor will it be made available online. * It is important to inform patients if a session is being recorded. If you want to record a session you must obtain explicit consent from the patient/client. ==Consent for resuming in person sessions== It also may be helpful to document informed consent when you and the client decide to resume in person sessions. The American Psychological Association has provided an example consent form [https://www.apaservices.org/practice/clinic/covid-19-informed-consent here]. == Technology == === Email === Email is a convenient, but not necessarily secure, method of communication. Some organizations provide encrypted email for their employees, which enables the safe transmission of protected health information. Even when the message is encrypted, there are some risks to using email and other things of which to be aware. It is wise to have a conversation with your patient/client about how the two of you will use email. Some use email only for scheduling and other logistical matters, whereas others will engage in coaching and other services by email. Many professionals include an agreement about email as part of their consent form. If this was not done initially, you might want to have a conversation with your patient/client and then send an email indicating your agreement. They can respond affirming the agreement, and this exchange becomes part of their record. Email is not secure. Even when encrypted, it can be forwarded or compromised in other ways. It can be helpful to include a [https://docs.google.com/document/d/1GNeCpQPiaXK8S4M9yPJoEaWZwLcdyh7nbMNELPpOw6E/edit?usp=sharing message after the signature] to remind patients of this. === Phone === Most practitioners are comfortable communicating with patients/clients through the phone to set appointments and occasionally check-in. Conducting therapy over the phone can be more complicated. A few things to keep in mind: * Make a plan with your patient/client ahead of time, so that they are prepared for the call and are situated in a quiet, private place. * Set expectations, so that your patient/client knows how long the call will last and whether it will be a “typical” therapy session over the phone or something else (e.g., a short check-in). * If you are using a cell phone, make sure you have adequate reception to limit call disruptions. * Consider using a hands-free headset, so that you can take notes. * Find a quiet, private place to conduct the call, so you are not distracted and there is no background noise. * Prepare materials you might need ahead of time. For example, make sure you have your notepad and a pen. If you use worksheets or other materials, make sure your patient/client has a copy ahead of time, so you can review it together. ==== Mental Health Applications (Apps) ==== * [https://onemindpsyberguide.org/apps/ Mental Health App Guide: One Mind PsyberGuide] * [https://www.abct.org/for-professionals/recommended-apps/ ABCT's Recommended Apps] === Video Conferencing === Videoconferencing is a nice alternative to phone for communicating with patients/clients and particularly for conducting therapy or assessment. It also presents some extra challenges for people who are not familiar with the technology. Although recent circumstances have led to the [https://www.hhs.gov/hipaa/for-professionals/special-topics/emergency-preparedness/notification-enforcement-discretion-telehealth/index.html relaxation of HIPAA] for the provision of teletherapy, typically, order to assure the Health Insurance Portability and Accountability Act ([[wikipedia:Health_Insurance_Portability_and_Accountability_Act|HIPAA]])-compliance of a software tool, it is important to have a [https://www.hhs.gov/hipaa/for-professionals/covered-entities/sample-business-associate-agreement-provisions/index.html Business Associate Agreement] (BAA) with the service provider. A business associate is someone who performs functions or provides services on behalf of a covered entity which requires them to have access to protected health information. The BAA establishes the permissible uses and disclosures of protected health information and ensures that the business associate will uphold these rules and take appropriate measures to safeguard protected health information from any non-permitted uses or disclosures. Not all video conferencing software is HIPAA-compliant. It is important to be aware of this, and to consider the functionality you need (e.g., do you conduct groups that require multiple participants) when [https://www.apaservices.org/practice/business/technology/tech-column/telehealth-solutions choosing a platform to use]. There are several options (e.g., [https://products.office.com/en-us/skype-for-business/download-app Skype for Business / Microsoft Teams], [https://info.updox.com/telehealth-video-chat-platform?utm_source=adwords&utm_campaign=Updox+-+Brand&utm_medium=ppc&utm_term=updox&hsa_grp=83660725651&hsa_mt=b&hsa_ver=3&hsa_cam=6498267086&hsa_ad=382008651744&hsa_net=adwords&hsa_kw=updox&hsa_tgt=kwd-311739789025&hsa_src=g&hsa_acc=8689332529&gclid=Cj0KCQjwj7v0BRDOARIsAGh37iq8iAfpJp8QeJVA-pj5CV7RO5AQLwAcofQkLxSLU_WYFBSHVU4N-b4aAsOoEALw_wcB Updox], [https://vsee.com/ VSee], [https://zoom.us/healthcare Zoom for Healthcare], [https://doxy.me/ Doxy.me], [https://www.zeboc.com/ ZEBOC], [https://gsuite.google.com/products/meet/ Google G Suite Hangouts, Meet], [https://www.webex.com/video-conferencing Cisco Webex Meetings/Webex Teams], [https://aws.amazon.com/chime/?chime-blog-posts.sort-by=item.additionalFields.createdDate&chime-blog-posts.sort-order=desc Amazon Chime], [https://www.gotomeeting.com/lp/sem?cid=g2m_noam_ggs_cpc_71700000060694846_58700005493369263_p50143970146&gclsrc=aw.ds&&gclid=CjwKCAjwmrn5BRB2EiwAZgL9oj4Zy3HtfDzKsdlFGXaZ1T7WfdufQwMocxIuu5Q9MPrAx_AL703ZURoC7BEQAvD_BwE GoToMeeting], [https://www.sprucehealth.com/ Spruce Healthcare Messenger]). '''Better Connection Tips:''' To reduce technical issues with video conferencing services, clear your browser history (under the History menu for most internet browsers), close all unnecessary windows and applications before and during sessions, and use incompatible web browser; encourage your patient to do the same. If you are experiencing delays, try using cloud web-based services (e.g. Zoom), instead of peer-to-peer services (e.g. doxy.me, ZEBOC), as they tend to have fewer bandwidth-related issues.<ref>{{Cite web|url=https://help.doxy.me/en/articles/95861-five-tips-for-a-great-experience|title=Five tips for a great experience|website=help.doxy.me|language=en|access-date=2020-05-07}}</ref> '''Commonly used video conferencing software:''' '''[https://doxy.me/ Doxy.me]''' * Both free and premium versions are available and easy-to-use on all devices. * All versions are fully functional, HIPAA-compliant, and include a Business Associate Agreement at no cost. * The premium versions give providers the freedom to customize features including the waiting room, logo, text and videos. * Other benefits to the premium versions include real-time support, file transfer, payment processing and text and email notifications. * Doxy.me operates using any web-browser; there is no installment or download necessary for provider or patient * It may not be best for those with average to weak internet connections, but for those with higher speed connections, it will provide high-quality audio and video. * Check out these tips for a better experience while videoconferencing with [https://help.doxy.me/en/articles/95861-five-tips-for-a-great-experience Doxy.me]. ==== '''[https://www.thera-link.com/ thera-LINK]''' ==== * A HIPAA-compliant option that provides a Business Associate Agreement * It can be used on all devices. * There are three packages: Basic plan, at $30, per month, offers five sessions a month for one provider and a scheduler. The Plus plan and Ultimate plan, at $45 and $60 per month offer unlimited monthly sessions, secure file sharing, advanced payment and scheduling options, and office manager accounts; the Ultimate plan also includes client notes, secure messaging and a branded portal. * theraLINK requires both providers and patients to have their own login. * theraLINK is relatively easy to navigate and offers the ability to customize aesthetic features such as imagery and music options for the waiting room. * theraLINK can only be used on WiFi and may be harder to master than other options. ==== [https://www.zeboc.com/ '''ZEBOC'''] ==== * ZEBOC is fully equipped to support a telepsychology session. * It’s free business model is aimed at empowering solo practitioners. * It provides all the premium features including Stripe-powered payments, Conversational transcription and more for free. * It’s [https://www.hhs.gov/hipaa/index.html HIPAA]-compliant and provides [https://www.hhs.gov/hipaa/for-professionals/covered-entities/sample-business-associate-agreement-provisions/index.html Business Associate Agreement] for free. * Allows providers focus on patient care while ZEBOC takes patient notes with automatic text-to-speech conversion in real-time. * No download or installation required. Works intuitively in most popular browsers. * Instant appointments allow providers to send an invitation to their patients in just two clicks. * Appointment booking website widget can be configured in providers’ practice website. ==== '''[https://zoom.us/ Zoom]''' ==== * Zoom is not tailored specifically for mental health, but it is popular for business and education, so many people are familiar with it. * Its healthcare version is HIPAA-compliant and includes a Business Associate Agreement. Plan costs start at $200 per month. * Zoom is customizable and works on all devices, though it may not be suited for low bandwidths. * Due to the cost, Zoom may be best for those who have midsize to large practices which require the tool to have multiple functions (i.e. training, recording, seminars, etc.). * Zoom’s popularity has also made it a target for mischief. "[[wikipedia:Zoombombing|Zoombombing]]" is when an uninvited participant uses Zoom’s screen-sharing feature to disrupt meetings. ** It is important to take steps to [https://blog.zoom.us/wordpress/2020/03/20/keep-uninvited-guests-out-of-your-zoom-event/ ensure that your video call is secure] and accessible only by you and your client, this includes keeping the link private and setting a password. View additional guidelines [https://it.miami.edu/about-umit/resources/zoombombing/index.html here]. == Get ready for your telepsychology session == *Some clinicians make the mistake of not preparing for a telepsychology session because it may feel more informal than an in-person session. However, it can be more challenging to keep a client engaged in telepsychology, and it is especially important to set an agenda and to have your goals for the session planned ahead. * As noted above, you may want to use worksheets or other materials in your session. These can be emailed to the patient/client ahead of time. You may also want to use the “[https://support.zoom.us/hc/en-us/articles/201362153-Sharing-your-screen share your screen]” feature that most video conferencing services provide. Other features might include a “[https://www.youtube.com/watch?v=jQ4-wrwHAxk whiteboard]” or [https://www.tomsguide.com/news/how-to-chat-in-zoom chat functions] that can help you to share materials with your patient/client. * If you want to use some of the special features, be sure to test them beforehand, so you know how everything works. ==== '''Prepare your space and practice''' ==== * Make an effort to minimize potential distractions in your environment. This means things that will be visible in the background to your patient/client and things that may distract you during the session. * Turn off all email and messaging notifications on your computer and cell phone and encourage your patient/client to do the same. * Pick a spot that is quiet and private. Try to use the same space week-to-week to facilitate familiarity and an office-like experience. Many video conferencing programs have a "[https://support.zoom.us/hc/en-us/articles/210707503-Virtual-Background Virtual Background]" option where you can use an image to cover the actual scene behind you. *Remember that lighting is critical; back lighting will darken your face. Position your device so you have adequate front lighting or add front lights. * Make sure you are comfortable and have everything you need (water, notes, etc.) before you start. * Ensure your video is sufficiently “zoomed in” for the patient to see your facial expressions * Try to maintain a constant gaze into the camera, rather than frequently looking away at your computer or notes. It can be tough to maintain a constant gaze while on a video call, but there are ways you can simulate eye contact with your patients with just a few tricks. # Try to focus on a point behind the camera lens; this will focus your eyes and make it clearer where you are looking. Much of perceived eye contact through video calling is related to the rotation of your eyes. The further back you sit, the less your eyes need to rotate, so sit further from the screen and zoom in closer to your face if you need to. # Center the video of your patient/client under your webcam, so when you look at their eyes, you are looking directly into the camera. * If possible, use picture-in-picture feature (e.g., where you can see both yourself and the patient) to see how you are being viewed by the patient, or if there is something distracting in the background (e.g., your cat!) * Ask a friend or colleague to do a practice session with you before you attempt a video session with a patient/client - there will be early snafus, and it is good to figure them out before you are in a real session. * Wear office-appropriate clothing. * If possible, give yourself a break between sessions to stretch or take a brief walk. [[File:Preparing for Your Telepsychology Session Infographic.pdf|thumb|left|How to be prepared for your telepsychology appointment.]] ==== '''Prepare your patient/client''' ==== * As with phone calls, encourage your patient/client to find a quiet and private space for the session. * Using a laptop or desktop computer is likely to be more comfortable, but a smartphone can also be used. * Set the client’s expectations for the session and send any materials (e.g., worksheets, mood rating scales) ahead of time * Make your expectations clear. Let your patient/client know that they should arrive on time, complete their homework, have the room set-up to minimize distractions, and dress appropriately. * Make a contingency plan, in case the technology doesn’t work. * Consider showing patients/clients your workplace/office. Using the camera’s zoom and pan features or manually moving your device, you can give patients a virtual tour to assure them that no one else is present and to provide context. * Immediately discuss any technical difficulties as they arise. For instance, if there is a slight lag in audio that makes it seem as if you and the patient are talking over each other, you can suggest adding a small pause after each statement ==='''Guidelines for conducting individual teletherapy'''=== Below are some resources for how to adapt psychotherapy while practicing physical distancing and via telecommunication instead of in-person sessions and practice: * [https://oxcadatresources.com Cognitive therapy] * [https://mfr.osf.io/render?url=https://osf.io/ucg96/?direct%26mode=render%26action=download%26mode=render Social anxiety exposures while physical distancing]<ref>{{Cite journal|last=French|first=Noah J.|last2=Teachman|first2=Bethany|date=2020-04-16|title=Social Anxiety Exposures While Physical Distancing|url=https://osf.io/b2e5n/|language=en|doi=10.17605/OSF.IO/B2E5N}}</ref> *[https://iocdf.org/covid19/information-for-therapists/ Treatment for OCD] * [https://psycnet.apa.org/record/2020-39749-005 Telepsychology for General Anxiety Disorder] * [https://psycnet.apa.org/record/2020-39749-012 Telepsychotherapy with youth at high risk for psychosis] *[https://mfr.osf.io/render?url=https://osf.io/undgp/?direct%26mode=render%26action=download%26mode=render Behavioral Activation Techniques while Physical Distancing]<ref>{{Cite journal|last=Fleischmann, Madeline|last2=Namaky, Nauder|last3=Teachman, Bethany|date=2020|title=Behavioral Activation Techniques while Physical Distancing|url=https://osf.io/rh7nt/|doi=10.17605/OSF.IO/RH7NT}}</ref> === Guidelines for conducting group teletherapy === Group therapy can be conducted effectively remotely using phone or video conferencing, but special care is often necessary to ensure that all group members participate and are able to benefit. It can be helpful to review group rules and consider whether additional guidelines are necessary when moving an in-person group to a virtual format. Privacy can be a particular concern if some group members are in close proximity to others while attending the group. It is also important to set expectations for whether everyone will be required to keep their camera on and other guidelines to ensure all group members are comfortable. Below are some additional tips for conducting group therapy online: * [https://www.apaservices.org/practice/legal/technology/group-therapy-telehealth-covid-19 APA Guidelines for conducting group therapy online] * [https://www.agpa.org/home/practice-resources/connecting-online American Group Psychotherapy Association guidelines] * [https://ctacny.org/sites/default/files/Telemental%20Health%20Tip%20Sheet-Virtual%20Therapy%20Groups_4.16.20.pdf Tip sheet for virtual group therapy] == Appropriate clients == Meeting virtually may not be appropriate for all patients/clients. Some may not be comfortable with the technology or may have privacy concerns. Other patients/clients may be high risk, which can lead to safety and liability issues when communicating with them through email, phone, or video. It is important to consider these issues and to discuss other options with your patient/client. ===='''Patients/Clients who are not comfortable with technology'''==== [[File:Is Telepsychology Right for Your Clients? Infographic.pdf|thumb|Signs that telepsychology is a good fit for your clients.]] Many patients/clients may be unfamiliar with videoconferencing and hesitant to use this technology for mental health services. Plan to spend some time answering questions and helping them to get set-up prior to your appointment. * Ask if there is a software they already use to communicate with family or other providers and try to use the same one, if possible. * YouTube is a good source for [https://www.youtube.com/watch?v=3IRdViKT87k#action=share tutorials on setting up a video conference]. * Your patient/client may also have friends/family who can help them get set-up, encourage them to seek help. * ==== '''Patients/Clients who have privacy concerns''' ==== * Some patients/clients may not have access to a private space in their home. Help them brainstorm other options. For example, can they sit in their car? Or go to a quiet place in a local park? * Others may be concerned about the possibility that communication (whether email, phone, video) will be breached in some way. You can help with these concerns by making sure to use HIPAA-compliant services and encrypted email. However, if the patient/client is not comfortable with telepsychology, it is important to have alternative options for them. This may mean referring them to another provider who is offering in-person services. ==== '''Patients/clients at high risk''' ==== Patients at high risk for suicide present special concerns for telepsychology<ref>{{Cite journal|last=Timm|first=Maria|date=2011|title=Crisis counselling online : building rapport with suicidal youth|url=https://doi.library.ubc.ca/10.14288/1.0054473|language=en|doi=10.14288/1.0054473}}</ref>. Taking the steps below will help ensure that you are able to adequately manage risk. * Update emergency contact information before providing any telepsychology services. * Make sure you know the patient/client location (address, apartment number) at the start of the session in case you need to contact emergency services. * Make a plan for how you will stay on the phone with the client while arranging emergency rescue if needed. It may be helpful to recruit a colleague who can support you during this process (i.e., call 911 on your behalf). Do not hang-up on the patient/client if there is an imminent risk. * The circumstances that make telepsychology necessary (e.g., illness, injury) may also increase suicide risk, it is important to continue to assess suicidal thoughts and behaviors on a regular basis. * Risk may also increase if the patient/client has access to lethal means while house-bound. Reviewing and updating existing safety plans to account for current circumstances is wise. * As part of safety planning, work with the patient/client to identify the closest emergency facility and how they could get there if necessary. * Consider making a plan for more frequent check-ins until risk abates. * Provide crisis hotline numbers like the [https://suicidepreventionlifeline.org/ National Suicide Prevention Lifeline]: 1-800-273-8255 and they can Text HOME to 741741 to connect with a Crisis Counselor to help at [https://www.crisistextline.org/text-us/ Crisis Text Line]. * Provide disaster distress helplines like [https://www.samhsa.gov/ SAMHSA]'s free 24/7 counseling via 1-800-985-5990, they can text: "TalkWithUs" to 66746, or visit [https://www.samhsa.gov/find-help/disaster-distress-helpline DisasterDistress.samhsa.gov] to help them maintain and improve their mental health during distress. * More information for working with high risk patients is available: #[https://drive.google.com/open?id=1XNUPOA1fjNhMLtlg5Kv-ExnyC3-y1X8h Telehealth tips for suicidal clients] #[http://www.sprc.org/events-trainings/treating-suicidal-patients-during-covid-19-best-practices-telehealth Telehealth treatment for suicidal patients] #[http://zerosuicide.edc.org/covid-19 Zero Suicide Guidelines] #[https://mfr.osf.io/render?url=https%3A%2F%2Fosf.io%2Fwbgn5%2Fdownload Guidelines for telepsychology with youth at risk for suicide or self injury] # [https://psycnet.apa.org/record/2020-39749-006 The COVID-19 pandemic and treating suicidal risk] * It is also important to consider the risk of '''domestic violence''' and '''child abuse''' during this time. [https://www.samhsa.gov/sites/default/files/social-distancing-domestic-violence.pdf SAMHSA has guidelines for helping those at risk] and [https://drive.google.com/open?id=1JI4LRLgVB2UlOjBGEldiPfqgj6W43HzJ this list of resources] is also helpful. ==== Patients/clients with ASD or intellectual disabilities ==== In some cases, patients with ASD or other intellectual disabilities may particularly benefit from telepsychology, as it enables them to remain in an environment where they are comfortable. However, it can also present some challenges. If the patient is a child, many/all of the considerations listed below may be relevant. Additional considerations for working with people with ASD or ID include: Do they have a caregiver who will be able to assist them with technical difficulties if need be? Are they able to participate productively, with or without the assistance of a caregiver, during a remote session? If they need help staying in frame and engaged, is there someone with them to fill that role? Do you have the necessary resources to maintain evidence-based services while working remotely (e.g., online-friendly assessment and therapeutic tools)? These resources provide additional helpful information for working with these populations: *[https://casproviders.org/wp-content/uploads/2020/03/PracticeParametersTelehealthABA_033020F2.pdf Considerations and tips for providing Applied Behavior Analysis via telehealth] *[https://pro.psychcentral.com/child-therapist/2020/03/tele-aba-activities-for-kids-7-telehealth-activities-aba-providers-can-use-with-children-with-asd/ Tele-ABA activities for youth with ASD] *[https://drive.google.com/open?id=1W6zRlkurMlDfoA0nZei7lsZzAUNhgxtn COVID-19 resources for people with I/DD or ASD] *[https://myemail.constantcontact.com/COVID-19-Resources-for-Parents-of-Children-with-Intellectual-or-Other-Developmental-Disabilities.html?soid=1114625386453&aid=7uHDuQO0UDE COVID 19 Resources for Parents of Children With Intellectual or Other Developmental Disabilities] == Working with children == Telepsychology with youth can be effective but requires some special considerations.<ref>{{Cite journal|last=Gloff|first=Nicole E.|last2=LeNoue|first2=Sean R.|last3=Novins|first3=Douglas K.|last4=Myers|first4=Kathleen|date=2015-11-02|title=Telemental health for children and adolescents|url=http://www.tandfonline.com/doi/full/10.3109/09540261.2015.1086322|journal=International Review of Psychiatry|language=en|volume=27|issue=6|pages=513–524|doi=10.3109/09540261.2015.1086322|issn=0954-0261}}</ref><ref>{{Cite journal|last=Myers|first=Kathleen|last2=Nelson|first2=Eve-Lynn|last3=Rabinowitz|first3=Terry|last4=Hilty|first4=Donald|last5=Baker|first5=Deborah|last6=Barnwell|first6=Sara Smucker|last7=Boyce|first7=Geoffrey|last8=Bufka|first8=Lynn F.|last9=Cain|first9=Sharon|date=2017-10|title=American Telemedicine Association Practice Guidelines for Telemental Health with Children and Adolescents|url=https://www.liebertpub.com/doi/10.1089/tmj.2017.0177|journal=Telemedicine and e-Health|language=en|volume=23|issue=10|pages=779–804|doi=10.1089/tmj.2017.0177|issn=1530-5627}}</ref><ref>{{Cite journal|last=Nelson|first=Eve-Lynn|last2=Patton|first2=Susana|date=2016-04|title=Using Videoconferencing to Deliver Individual Therapy and Pediatric Psychology Interventions with Children and Adolescents|url=http://www.liebertpub.com/doi/10.1089/cap.2015.0021|journal=Journal of Child and Adolescent Psychopharmacology|language=en|volume=26|issue=3|pages=212–220|doi=10.1089/cap.2015.0021|issn=1044-5463|pmc=PMC5220559|pmid=26745607}}</ref><ref>{{Cite journal|last=Myers|first=Kathleen M.|last2=Valentine|first2=Jeanette M.|last3=Melzer|first3=Sanford M.|date=2008-03|title=Child and Adolescent Telepsychiatry: Utilization And Satisfaction|url=https://www.liebertpub.com/doi/10.1089/tmj.2007.0035|journal=Telemedicine and e-Health|language=en|volume=14|issue=2|pages=131–137|doi=10.1089/tmj.2007.0035|issn=1530-5627}}</ref> Adolescents are likely to be comfortable with phone or video, but it may be a challenge to get them to focus on you and limit distractions. Younger children may also be distracted by their environment or may struggle to stay engaged. It may be necessary to modify your typical approach to work effectively with youth. Check out [https://youtu.be/ML4pEa_KVm8 this video] that covers the basics of telepsychology with youth. If you conduct groups with youth [https://www.youtube.com/watch?v=L1W7nuc9B84&feature=youtu.be this video] may also be helpful. ==== '''Setting the scene''' ==== * Encourage caregivers to minimize distractions in the room where the young patient/client will be completing the session by: **Removing toys, books, extra screens/electronic devices/games, pets, and food **Providing a clear desk/table space **Notifying everyone in the home that the child will need privacy and quietness especially if the child is undergoing testing<ref name=":0">{{Cite web|url=https://www.apaservices.org/practice/legal/technology/telehealth-testing-children-covid-19|title=Telehealth testing with children: Important factors to consider|last=|first=|date=|website=|language=en|archive-url=|archive-date=|access-date=2020-04-26}}</ref> * Young patients may prefer a “less formal” room set-up, so you might want to avoid having a table between the patient and the video-recording device (or you and the video-recording device). *Ask the guardian to make sure that the youth wakes up at least an hour before the session, has eaten, used the restroom at least 15 minutes beforehand, and taken their prescribed medications.<ref name=":0" /> * Consider the best seating arrangement.<ref>{{Cite web|url=https://www.psychiatry.org/psychiatrists/practice/telepsychiatry/toolkit/child-adolescent/participant-arrangement|title=Participant Arrangement|website=www.psychiatry.org|access-date=2020-04-08}}</ref> Young children can sit next to a caregiver, between the caregivers, on a caregiver’s lap, or in front of the caregiver in either their own chair or on the floor. * You may want to ask the caregiver to put a blanket on the floor to indicate the "therapy boundary" that the child needs to stay within during the session. This helps ensure that you can see them at all times and that they aren't too active during the session. * A hyperactive child or a child on the autism spectrum may have difficulty remaining in the camera frame. Consider keeping the caregivers in frame and call the child back to the camera when they need to answer a question. * If an anxious or defiant youth refuses to sit within the camera frame, try to use typical behavior management strategies first. Then, prior to the next session, ask the caregiver to turn off the self-monitor image and seat the youth farther away from the camera so as to remain in the frame. Another strategy is to allow the youth to have more privacy for part or all of the session. * If possible, larger rooms tend to work best with younger patients, so they can move around. In addition, if a child's motor skills, play, exploration, and movements are being assessed, the room should be large enough for this activity to fit within the camera frame. * Adolescents may prefer to be seen without a caregiver present or within earshot. Help them brainstorm how to create privacy, even in tight quarters. * Establish that you are seeing the patient/client in real-time. Young children may enjoy seeing you mimic their gestures, or comment on what they are wearing. * Socialize youth to the videoconferencing system, and highlight that it might take time to acclimate to the technology and ‘‘not talk over each other.’’ * Give patients an opportunity to ask questions before starting the session. * Ask children or caregivers to prepare some toys, drawing materials or other supplies that you may want to work with during the session at least 24-hours ahead of time and send them a reminder. Try to recreate your office as much as possible.<ref>{{Cite web|url=https://www.psychiatry.org/psychiatrists/practice/telepsychiatry/toolkit|title=Telepsychiatry Toolkit Home|website=www.psychiatry.org|access-date=2020-04-08}}</ref> * ==== '''Maintaining engagement''' ==== * It is especially important to leave adequate time to build rapport and adjust to the new circumstances when working with youth.<ref>{{Cite journal|last=Goldstein|first=Felissa|last2=Glueck|first2=Dehra|date=2016-04|title=Developing Rapport and Therapeutic Alliance During Telemental Health Sessions with Children and Adolescents|url=http://www.liebertpub.com/doi/10.1089/cap.2015.0022|journal=Journal of Child and Adolescent Psychopharmacology|language=en|volume=26|issue=3|pages=204–211|doi=10.1089/cap.2015.0022|issn=1044-5463}}</ref> * If you are using or creating worksheets or other visual activities, consider allowing the patient to choose the colors/fonts/pictures in order to provide them with some control. * Use exaggerated expressions and gestures if needed to engage the youth (virtual high fives, thumbs up, etc.). * Children may enjoy drawing pictures that they can then share through the camera while telling a story. These drawings may help you assess children’s attention, fine motor skills and creativity. Children may also use play figures (e.g., dolls, action figures) to demonstrate their ability for symbolic play and reveal their thought content. * For younger children, ask them to share their favorite things about home — toys, books, blankets, etc. as long as it is related to clinical activities and is not disruptive. * For older youth, ask if they have any art, journaling, music, or anything else to share with you. Consider engaging adolescents by exploring an online site, such as YouTube or Facebook through screen sharing * Children and teens may appreciate getting to know clinicians as well. Consider using a brief question-and-answer game to share some facts about you and gather information about your patient. For example, you and your patient can take turns answering: “What is your favorite TV show?”, “What is your favorite color?”, “What is your favorite food?”, “How many siblings do you have?” * Mirror the language patterns of the youth and handle any threats to rapport with genuineness (including using informal language). * Arts-based therapeutic methods may help engage younger patients. You can have the patient show you their work on the camera or use screen share options to create art together (based on your platform’s capabilities). * Consider sharing handouts and working through them in session if your platform has the functionality (e.g., Zoom screen share with editable documents or PowerPoints). * Try utilizing different functions to increase engagement (e.g., [https://www.youtube.com/watch?v=jQ4-wrwHAxk Zoom has a “whiteboard” feature where a patient and clinician can draw together or play tic-tac-toe]). Check with technology services at your site for specific training/tips on functionality for your platform. * Especially with younger patients, recognize that staying engaged via telehealth is challenging. Adjust your expectations of how long sessions should last if you are having a hard time keeping your patient engaged. * Consider incorporating games or other activities as appropriate. There are online games available that can be helpful for maintaining interest such as [https://en.boardgamearena.com/ Board Game Arena] or [http://playingcards.io/ PlayingCards.io] * Research shows that youth’s satisfaction with telehealth will likely increase with repeated use; encourage young clients to stick with it for a few sessions to see if they become comfortable.<ref>Boydell KM, Volpe T, Pignatiello A. A qualitative study of young people's perspectives on receiving psychiatric services via televideo. Journal of the Canadian Academy of Child and Adolescent Psychiatry = Journal de L'academie Canadienne de Psychiatrie de L'enfant et de L'adolescent. 2010 Feb;19(1):5-11.</ref> * It is important to continue conversations related to technical difficulties, unique challenges, or benefits that come from using telehealth throughout the treatment course. Keep an open dialogue about how things are going. ====Additional resources==== # [https://clsprogram.ucsf.edu/s/resources Comprehensive guide for supporting children and families] #[https://www.apaservices.org/practice/legal/technology/telehealth-testing-children-covid-19 Telehealth testing with children: Important factors to consider] # [https://drive.google.com/open?id=1u4nuufhVuItYyRv5GYgJrpjiD27kWtP0 Yale Child Study Family Resources and Suggestions for Coping with Coronavirus] # [https://www.guidancett.com/blog/interventions-for-online-therapy-with-children-and-youth-2020 Interventions and activities for children and youth teletherapy] # [http://teacher.scholastic.com/education/coronavirusworkbook/index.html First Aid for Feelings: A Workbook to Help Kids Cope During the Coronavirus Pandemic] # [https://drive.google.com/file/d/1qxrSvL3s2QDH8rzBHrNq3tcmaiUOUSio/view Webinar on family mental health during the pandemic] # [http://piploproductions.com/trinka-and-sam-virus/ Book for young children about coronavius] # [https://www.choc.org/programs-services/integrative-health/guided-imagery/ Guided Imagery audio clips for kids] # [http://www.7-dippity.com/docs/Helping-Children-Cope-with-COVID-19-(7-Dippity-Web-Version).pdf Helping Children and Families Cope with the COVID-19 Pandemic] # [https://mfr.osf.io/render?url=https%3A%2F%2Fosf.io%2Fwbgn5%2Fdownload Considerations for telepsychology with youth at risk for suicide or self injury] # [https://psycnet.apa.org/record/2020-39749-013 Telepsychology with children and families] == Conducting assessment == Conducting assessment through telepsychology may seem challenging, but it is possible to continue to incorporate assessment in your practice. In some cases, it may be necessary to split an appointment to conduct some assessments via telepsychology and save others for when an in-person meeting is possible. APA has issued multiple statements on [https://www.apaservices.org/practice/clinic/covid-19-neuropsychological-psychological-testing psychological and neuropsychological testing], [https://www.apaservices.org/practice/reimbursement/health-codes/testing/psychological-telehealth important considerations when conducting teleassessment], and [https://www.apaservices.org/practice/reimbursement/health-codes/testing/tele-assessment-covid-19], including information about [https://www.apaservices.org/practice/clinic/covid-19-neuropsychological-psychological-testing reimbursement and billing]. There are also [https://www.apaservices.org/practice/legal/technology/telehealth-testing-children-covid-19 guidelines] for conducting assessment with youth. ==== '''Self-report''' ==== Many practitioners administer self-report rating scales to assess patients over time. These are relatively easy to continue: * Self-reports can be emailed to patient/clients to be completed and sent back * Self-reports can be administered through HIPAA-compliant [https://effectivechildtherapy.org/assessment-center/ survey tools] * Self-reports can be read to the patient and they can respond orally * ==== '''Interview-based''' ==== * Diagnostic interviews and clinical rating scales are often feasible to administer via telepsychology * Behavior ratings may be more difficult to ascertain, though, so it is important to consider the information you need to collect and plan accordingly. If a certain interview relies on behavior observations, consider whether there is an alternative that may be more appropriate * ==== '''Cognitive/Achievement and Neuropsychology''' ==== * Tests of cognition are likely to be the most difficult to administer via telepsychology. * Given the importance of administering these tests under circumstances similar to those under which the norms were established, it is important to look into data supporting the administration of specific tests with telepsychology. * Some tests have online versions. Although there would likely be additional costs associated with this approach, it is likely to be easier and more valid than adapting tests intended to be administered in person * The [https://iopc.online/ Inter Organizational Practice Committee (IOPC)]​ work-group has released [https://drive.google.com/file/d/1BRYeEtjh03vpbIx7h9bPV3aFYt-UrqG5/view?usp=sharing guidelines] for teleneuropsychology (Tele-NP) that may be helpful.<ref>{{Cite web|url=https://iopc.online/teleneuropsychology|title=Tele-neuropsychology|website=Inter Organizational Practice Committee|language=en-US|access-date=2020-06-11}}</ref> *IOPC has also released provisional recommendations and guidance regarding teleneuropsychology during the pandemic [https://iopc.online/teleneuropsychology-guidelines Practice Guidelines and Recommendations for Tele-NP] == Legal considerations == As noted above, it is important that your patient/client understand the potential risks of telepsychology (e.g., confidentiality, safety) and that they consent to the provision of services using telepsychology. In addition to patient consent, it is incumbent upon the provider to follow the rules related to HIPAA and other legal and professional guidelines. Although some of these [https://www.hhs.gov/hipaa/for-professionals/special-topics/emergency-preparedness/notification-enforcement-discretion-telehealth/index.html rules have been relaxed] due to the COVID-19 crisis, it is best to confirm the current rules ''in your area'' before engaging in telepsychology. Rules about telepsychology are typically governed by [https://www.apaservices.org/practice/legal/technology/state-telehealth-guidance states], so you should be familiar with the rules in the state where you are licensed and practice as well as the state(s) where your patient/client may be at the time of the service. == Reimbursement and fee collection == [[File:Physicians and Other Clinicians CMS Flexibilities to Fight COVID-19.pdf|thumb|Physicians and Other Clinicians CMS Flexibilities to Fight COVID-19]] Services delivered via phone or video are billed under a [https://www.cms.gov/Medicare/Medicare-General-Information/Telehealth/Telehealth-Codes separate code] and, under typical circumstances, may be reimbursed at a different rate than in-person services. Medicare has modified its rules and will cover a [[c:File:Physicians_and_Other_Clinicians_CMS_Flexibilities_to_Fight_COVID-19.pdf|wider range of telepsychology services]], including testing and [[wikipedia:Group_psychotherapy|group therapy]], during the COVID-19 crisis. Most private health insurance providers are also reimbursing for telelpsychology, but in order to ensure payment, practitioners should check with individual payers prior to providing services and submitting bills. If there are financial implications for patients/clients related to using telepsychology, these must be discussed and agreed upon. Practitioners in private practice may be used to collecting fees by cash or check. Alternative methods for payment may be preferable for telepsychology. Patients/clients can mail a check, but the practitioner should consider where the check is sent and whether they are comfortable receiving payment at their home address. Electronic payment methods avoid this complication, but not all patients/clients will be comfortable transferring funds. Providing some education about the pros/cons of electronic payment and coaching on how to implement it will be helpful. A few options include: * [https://www.zellepay.com/ Zelle] is a payment method that moves funds between bank accounts. It works across different banks and is integrated into many banking apps. * [https://www.paypal.com/us/home PayPal] is a more flexible option that can link with both credit cards and bank accounts. It also includes accounts for both businesses and individuals, which may be appealing for some who plan to collect fees electronically on an ongoing basis. * [https://venmo.com/ Venmo] is a popular payment tool that allows users to send funds from their bank account or from their Venmo account (if they have been paid by others through Venmo). An important consideration with Venmo is that payments are not necessarily private. You can set your preferences to be private, but if this is not done, others on the app can see payment exchanges. If your practice is significantly affected by the COVID-19 crisis, you may be able to get a business [https://www.apaservices.org/practice/clinic/covid-19-small-business-loan-assistance loan]. == Information for Trainees == Trainees should follow the guidelines set by their institution and rely on their supervisors to provide instruction and support. Additionally, the [https://www.cctcpsychology.org/ Council of Chairs of Training Councils (CCTC)] published [https://drive.google.com/open?id=1yK93OI6KTHfAk32X6FWpKlNg74q--hqE guidelines] related to training during the COVID-19 crisis. A [https://www.youtube.com/watch?v=Wn6Vewl42X8 video] summarizing telepsychology guidelines for trainees is also available. [https://www.apa.org/topics/covid-19/student-stress Self care] is also important to pay attention to during this challenging time when may aspects of training may be in upheaval. To further aid trainees, free [https://www.therapulse.ai/resources/theratrack/ clinical hour tracking software] is available, which contrasts with other services that typically charge monthly fees. This resource can be a significant support in managing and organizing clinical hours at no cost to students and professionals seeking licensure. == Supervision == Supervision can be especially valuable when initiating a new approach to mental health services - including telepsychology. Trainees should be sure to maintain a consistent meeting schedule with their clinical supervisor, and even licensed practitioners may want to seek supervision from someone experienced in telepsychology until they feel comfortable with it. Although some aspects of supervision can be conducted without modification (e.g., session planning, self-report about a previous session), other aspects [http://blog.time2track.com/supervision-telehealth/ require some change], similar to modifications that are necessary for providing services. [https://leader.pubs.asha.org/do/10.1044/telesupervision-the-supervision-revolution/full/ Telesupervision] is remote clinical supervision by mentor health professionals over their graduate students, trainees, fellows, or assistants through innovative means like video-conferencing, teleconferencing, and emailing. Fortunately, [https://doi.apa.org/fulltext/2020-39749-016.html evidence suggests] that telesupervision can be just as effective as supervision received in person Seek guidance from your program to ensure supervision continues to meet [https://www.apaservices.org/practice/news/psychology-training-covid19 APA] or other professional requirements. The APA posted [https://psycnet.apa.org/record/2020-39749-014 considerations] for training clinics conducting telesupervision during COVID-19. The Association for Behavioral & Cognitive Therapies has released videos on strategies for [http://www.abct.org/Resources/index.cfm?m=mResources&fa=Telehealth_Erika_Shearer effective telesupervision] and on the experience of being a [http://www.abct.org/Resources/index.cfm?m=mResources&fa=Telehealth_Carly_McCord trainee conducting telepsychology]. ==== '''Observation''' ==== * Many programs are set-up to video or audio record assessment and therapy sessions so that supervisors can watch/listen to them later and provide feedback. Some video conferencing programs allow for the recording of sessions, which is helpful, but before using this option, make sure that: # The video service is HIPAA-compliant and that the recording is stored in a HIPAA-compliant fashion # The video is shared with the supervisor in a HIPAA-compliant way (e.g., secured file sharing program) * Sessions can also be audio recorded, particularly if done through speakerphone, but the way the audio file is shared with the supervisor must be HIPAA-compliant ==== '''Progress Notes''' ==== * Many organizations use an electronic medical record (EMR) to store notes. If you have access to this from outside the office, no change in your typical approach may be necessary. * Other organizations have paper records or an EMR that is not accessible outside the institution. In these cases, it is still important to document what occurred in your sessions and to make plans for transferring this information to the record when possible. Be sure you have a HIPAA-compliant way of storing these notes until you have access again to the EMR, this could be an encrypted digital folder or in a paper file. ==== '''Evidence-Informed Practical Tips for Telesupervision''' <ref name=":1">{{Cite journal|last=Martin|first=Priya|last2=Kumar|first2=Saravana|last3=Lizarondo|first3=Lucylynn|date=2017-06|title=Effective use of technology in clinical supervision|url=https://linkinghub.elsevier.com/retrieve/pii/S2214782917300131|journal=Internet Interventions|language=en|volume=8|pages=35–39|doi=10.1016/j.invent.2017.03.001|pmc=PMC6096199|pmid=30135826}}</ref> ==== These tips are adapted from a [https://www.sciencedirect.com/science/article/pii/S2214782917300131 published literature review in 2017] on effective and efficient use of technology in clinical supervision.<ref name=":1" /> # The first step in a successful telesupervision partnership is to set explicit goals and expectations in an agreement or contract. This should be done within the first couple of sessions face to face (or via video conference) and revisited regularly. # There is no one size fits all with the type and way of telesupervision. Consider trying different types of telecommunication to find out what is going to be most feasible/effective for the people involved. # As with in-person supervision, guidance should be based within an established framework. This will help provide structure to supervision sessions and connect back to therapy sessions. # The supervisory relationship is critical for success. Fostering a positive relationship will help make telesupervision feel more like face-to-face supervision. # Make a plan to manage technical problems. This should be included in the telesupervision agreement that was made in the beginning, so that there is a set protocol when tech issues arise. This will help to save time and avoid miscommunication. # Pay attention to communication, especially when there is a lack of physical cues available. This means taking turns talking, allowing silence for reflection, limiting distractions, muting sound when appropriate, and avoiding multi-tasking while in a supervision session. # To make up for the lack of proximity, supervisors should make sure to be available to the supervisee between sessions. The expectations for availability should be discussed and written out during the formation of the telesupervision partnership. # Protect online security, safety, and confidentiality. # Factor in additional time to accommodate technical problems and make sure to set an agenda, so that the time is used efficiently. # Discuss how telesupervision is going on a regular basis. This means evaluating set goals, the quality of the relationship, the success of the current telecommunication mediums, the helpfulness of supervisor feedback, the satisfaction level of learning from the supervisee, etc. Update the supervision contract as necessary to ensure both parties remain pleased. ==Telepsychology Services== If you are not comfortable or able to provide telepsychology services, consider referring patients/clients to an alternative provider to ensure they are able to get the help they need when you may not be available. * [https://www.optum.com/covid-19/covid-19-emotional-support.html Optum online] * [https://joyable.com/start-joyable Joyable] * [https://www.talkspace.com/ Talkspace] * [https://psycnet.apa.org/record/2020-39749-009 Popular mental health apps] * For those with OCD or related disorders like Hoarding, Skin excoriation, and Trichotillomania [https://www.treatmyocd.com/ NOCD] ==Research on the effectiveness of telepsychology== {{reading list}} Research comparing clinic-based psychotherapy to video-based services have largely found that therapy delivered via telecommunication has similar outcomes. Similarly, although the administration of assessment can be more complicated, in may cases valid results can be achieved. Below is a list of references comparing in-person and telepsychology services. ===Psychotherapy=== [https://www.div12.org/ APA Division 12 (Society of Clinical Psychology)] compiled a list of publications on [https://www.div12.org/telepsychology-resources/ teletherapy.] The publications are grouped by disorder (e. g. Depression) or directed focus of the therapy (e.g. Couples and Family Therapy). This systematic review also provides a [https://psycnet.apa.org/fulltext/2020-39749-004.html helpful summary]. The [https://www.apa.org/pubs/journals/int Journal of Psychotherapy Integration] also published a [https://psycnet.apa.org/PsycARTICLES/journal/int/30/2 Special Issue on Telepsychotherapy in the Age of COVID-19]. All articles are open access. '''Anxiety''' Arnberg, F. K., Linton, S. J., Hultcrantz, M., Heintz, E., & Jonsson, U. (2014). Internet-delivered psychological treatments for mood and anxiety disorders: A systematic review of their efficacy, safety, and cost-effectiveness. ''[https://journals.plos.org/plosone/ PloS ONE]''<ref>{{Cite journal|last=Arnberg|first=Filip K.|last2=Linton|first2=Steven J.|last3=Hultcrantz|first3=Monica|last4=Heintz|first4=Emelie|last5=Jonsson|first5=Ulf|date=2014-05-20|title=Internet-Delivered Psychological Treatments for Mood and Anxiety Disorders: A Systematic Review of Their Efficacy, Safety, and Cost-Effectiveness|url=https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0098118|journal=PLOS ONE|language=en|volume=9|issue=5|pages=e98118|doi=10.1371/journal.pone.0098118|issn=1932-6203|pmc=PMC4028301|pmid=24844847}}</ref> Brenes, G. A., Ingram, C. W., & Danhauer, S. C. (2012). Telephone-delivered psychotherapy for late-life anxiety. ''[https://www.apa.org/pubs/journals/ser/ Psychological Services]'', ''9''(2), 219.<ref>{{Cite journal|last=Brenes|first=Gretchen A.|last2=Ingram|first2=Cobi W.|last3=Danhauer|first3=Suzanne C.|date=2012-05|title=Telephone-delivered psychotherapy for late-life anxiety.|url=https://doi.org/10.1037/a0025950|journal=Psychological Services|language=en|volume=9|issue=2|pages=219–220|doi=10.1037/a0025950|issn=1939-148X|pmc=PMC3512560|pmid=22662740}}</ref> Carpenter, A. L., Pincus, D. B., Furr, J. M., & Comer, J. S. (2018). Working from home: An initial pilot examination of videoconferencing-based cognitive behavioral therapy for anxious youth delivered to the home setting. ''[https://www.journals.elsevier.com/behavior-therapy Behavior Therapy]'', ''49''(6), 917-930.<ref>{{Cite journal|last=Carpenter|first=Aubrey L.|last2=Pincus|first2=Donna B.|last3=Furr|first3=Jami M.|last4=Comer|first4=Jonathan S.|date=2018-11|title=Working From Home: An Initial Pilot Examination of Videoconferencing-Based Cognitive Behavioral Therapy for Anxious Youth Delivered to the Home Setting|url=https://linkinghub.elsevier.com/retrieve/pii/S0005789418300315|journal=Behavior Therapy|language=en|volume=49|issue=6|pages=917–930|doi=10.1016/j.beth.2018.01.007|pmc=PMC6190606|pmid=30316490}}</ref> Durland, L., Interian, A., Pretzer-Aboff, I., Dobkin, R. D. (2014). Effect of telehealth-to-home interventions on quality of life for individuals with depressive and anxiety disorders. ''[https://www.dovepress.com/smart-homecare-technology-and-telehealth-journal Smart Homecare Technology and Telehealth]'', ''2'', 101-119.<ref>{{Cite web|url=https://www.dovepress.com/effect-of-telehealth-to-home-interventions-on-quality-of-life-for-indi-peer-reviewed-article-SHTT|title=Effect of telehealth-to-home interventions on quality of life for individuals with depressive and anxiety disorders|last=Durland|first=Logan|last2=Interian|first2=Alejandro|date=2014-11-07|website=Smart Homecare Technology and TeleHealth|language=English|doi=10.2147/shtt.s45044|access-date=2020-04-13|last3=Pretzer-Aboff|first3=Ingrid|last4=Dobkin|first4=Roseanne D.}}</ref> Khatri, N., Marziali, E., Tchernikov, I., & Shepherd, N. (2014). Comparing telehealth-based and clinic-based group cognitive behavioral therapy for adults with depression and anxiety: A pilot study. ''[https://www.dovepress.com/clinical-interventions-in-aging-journal Clinical Interventions in Aging]'', ''9'', 765.<ref>{{Cite journal|last=Khatri|first=Nasreen|last2=Marziali|first2=Elsa|last3=Tchernikov|first3=Illia|last4=Shepherd|first4=Nancy|date=2014-05-07|title=Comparing telehealth-based and clinic-based group cognitive behavioral therapy for adults with depression and anxiety: a pilot study|url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4019624/|journal=Clinical Interventions in Aging|volume=9|pages=765–770|doi=10.2147/CIA.S57832|issn=1176-9092|pmc=4019624|pmid=24855345}}</ref> McCall, T., Bolton, C. I., McCall, R., & Khairat, S. (2019). The Use of Culturally-Tailored Telehealth Interventions in Managing Anxiety and Depression in African American Adults: A Systematic Review. ''[https://www.iospress.nl/html/shti.php Studies in Health Technology and Informatics]'', ''264'', 1728-1729.<ref>{{Cite web|url=http://dx.doi.org/10.2196/preprints.15801|title=The Acceptability of Text Messaging to Help African American Women Manage Anxiety and Depression: Cross-Sectional Survey Study (Preprint)|last=McCall|first=Terika|last2=Schwartz|first2=Todd A|date=2019-08-08|website=dx.doi.org|access-date=2020-04-13|last3=Khairat|first3=Saif}}</ref> Rees, C. S., & Maclaine, E. (2015). A systematic review of videoconference‐delivered psychological treatment for anxiety disorders. ''[https://aps.onlinelibrary.wiley.com/journal/17429544 Australian Psychologist]'', ''50''(4), 259-264.<ref>{{Cite journal|last=Rees|first=Clare S.|last2=Maclaine|first2=Ellen|date=2015|title=A Systematic Review of Videoconference-Delivered Psychological Treatment for Anxiety Disorders|url=https://aps.onlinelibrary.wiley.com/doi/abs/10.1111/ap.12122|journal=Australian Psychologist|language=en|volume=50|issue=4|pages=259–264|doi=10.1111/ap.12122|issn=1742-9544}}</ref> Varker, T., Brand, R. M., Ward, J., Terhaag, S., & Phelps, A. (2018). Efficacy of synchronous telepsychology interventions for people with anxiety, depression, posttraumatic stress disorder, and adjustment disorder: A rapid evidence assessment. ''[https://www.apa.org/pubs/journals/ser/ Psychological Services.]''<ref>{{Cite journal|last=Varker|first=Tracey|last2=Brand|first2=Rachel M.|last3=Ward|first3=Janine|last4=Terhaag|first4=Sonia|last5=Phelps|first5=Andrea|date=2019-11|title=Efficacy of synchronous telepsychology interventions for people with anxiety, depression, posttraumatic stress disorder, and adjustment disorder: A rapid evidence assessment.|url=https://doi.org/10.1037/ser0000239|journal=Psychological Services|language=en|volume=16|issue=4|pages=621–635|doi=10.1037/ser0000239|issn=1939-148X}}</ref> Whiteside, S. P. (2016). Mobile device-based applications for childhood anxiety disorders. ''[https://home.liebertpub.com/publications/journal-of-child-and-adolescent-psychopharmacology/29 Journal of Child and Adolescent Psychopharmacology]'', ''26''(3), 246-251.<ref>{{Cite journal|last=Whiteside|first=Stephen P. H.|date=2015-08-05|title=Mobile Device-Based Applications for Childhood Anxiety Disorders|url=https://www.liebertpub.com/doi/10.1089/cap.2015.0010|journal=Journal of Child and Adolescent Psychopharmacology|volume=26|issue=3|pages=246–251|doi=10.1089/cap.2015.0010|issn=1044-5463}}</ref> Wootton, B. M., Steinman, S. A., Czerniawski, A., Norris, K., Baptie, C., Diefenbach, G. J., & Tolin, D. F. (2018). An evaluation of the effectiveness of a transdiagnostic bibliotherapy program for anxiety and related disorders: Results from two studies using a benchmarking approach. ''[https://www.springer.com/journal/10608 Cognitive Therapy and Research]'', ''42'', 565-580.<ref>{{Cite journal|last=Wootton|first=Bethany M.|last2=Steinman|first2=Shari A.|last3=Czerniawski|first3=Alana|last4=Norris|first4=Kimberly|last5=Baptie|first5=Colin|last6=Diefenbach|first6=Gretchen|last7=Tolin|first7=David F.|date=2018-10|title=An Evaluation of the Effectiveness of a Transdiagnostic Bibliotherapy Program for Anxiety and Related Disorders: Results From Two Studies Using a Benchmarking Approach|url=http://link.springer.com/10.1007/s10608-018-9921-x|journal=Cognitive Therapy and Research|language=en|volume=42|issue=5|pages=565–580|doi=10.1007/s10608-018-9921-x|issn=0147-5916}}</ref> Yuen, E. K., Herbert, J. D., Forman, E. M., Goetter, E. M., Juarascio, A. S., Rabin, S., … & Bouchard, S. (2013). Acceptance based behavior therapy for social anxiety disorder through videoconferencing. ''[https://www.journals.elsevier.com/journal-of-anxiety-disorders Journal of Anxiety Disorders]'', ''27''(4), 389-397.<ref>{{Cite journal|last=Yuen|first=Erica K.|last2=Herbert|first2=James D.|last3=Forman|first3=Evan M.|last4=Goetter|first4=Elizabeth M.|last5=Juarascio|first5=Adrienne S.|last6=Rabin|first6=Stephanie|last7=Goodwin|first7=Christina|last8=Bouchard|first8=Stéphane|date=2013-05-01|title=Acceptance based behavior therapy for social anxiety disorder through videoconferencing|url=http://www.sciencedirect.com/science/article/pii/S0887618513000388|journal=Journal of Anxiety Disorders|language=en|volume=27|issue=4|pages=389–397|doi=10.1016/j.janxdis.2013.03.002|issn=0887-6185}}</ref> '''Autism Spectrum''' Ferguson, J., Craig, E. A., & Dounavi, K. (2019). Telehealth as a model for providing behaviour analytic interventions to individuals with autism spectrum disorder: A systematic review. ''[https://www.springer.com/journal/10803 Journal of Autism and Developmental Disorders]'', ''49''(2), 582-616.<ref>{{Cite journal|last=Ferguson|first=Jenny|last2=Craig|first2=Emma A.|last3=Dounavi|first3=Katerina|date=2019-02-01|title=Telehealth as a Model for Providing Behaviour Analytic Interventions to Individuals with Autism Spectrum Disorder: A Systematic Review|url=https://doi.org/10.1007/s10803-018-3724-5|journal=Journal of Autism and Developmental Disorders|language=en|volume=49|issue=2|pages=582–616|doi=10.1007/s10803-018-3724-5|issn=1573-3432|pmc=PMC6373531|pmid=30155578}}</ref> Hepburn, S. L., Blakeley-Smith, A., Wolff, B., & Reaven, J. A. (2016). Telehealth delivery of cognitive-behavioral intervention to youth with autism spectrum disorder and anxiety: A pilot study. 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''[https://www.tandfonline.com/toc/ntcn20/current The Clinical Neuropsychologist]'', ''27''(5), 808–817. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3692573/<ref>{{Cite journal|last=Parikh|first=Mili|last2=Grosch|first2=Maria C.|last3=Graham|first3=Lara L.|last4=Hynan|first4=Linda S.|last5=Weiner|first5=Myron|last6=Shore|first6=James H.|last7=Cullum|first7=C. Munro|date=2013-7|title=Consumer Acceptability of Brief Videoconference-based Neuropsychological Assessment in Older Individuals with and without Cognitive Impairment|url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3692573/|journal=The Clinical neuropsychologist|volume=27|issue=5|pages=808–817|doi=10.1080/13854046.2013.791723|issn=1385-4046|pmc=3692573|pmid=23607729}}</ref> Tun, P. A., & Lachman, M. E. (2006). Telephone assessment of cognitive function in adulthood: The Brief Test of Adult Cognition by Telephone. ''Age and Ageing'', ''35''(6), 629-632. https://academic.oup.com/ageing/article/35/6/629/14743<ref>{{Cite journal|last=Tun|first=Patricia A.|last2=Lachman|first2=Margie E.|date=2006-11-01|title=Telephone assessment of cognitive function in adulthood: the Brief Test of Adult Cognition by Telephone|url=https://academic.oup.com/ageing/article/35/6/629/14743|journal=Age and Ageing|language=en|volume=35|issue=6|pages=629–632|doi=10.1093/ageing/afl095|issn=0002-0729}}</ref> Unverzagt, F. W., Monahan, P. O., Moser, L. R., Zhao, Q., Carpenter, J. S., Sledge, G. W., & Champion, V. L. (2007). The Indiana University telephone-based assessment of neuropsychological status: A new method for large scale neuropsychological assessment. ''Journal of the International Neuropsychological Society'', ''13''(5), 799-806. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2747375/<ref>{{Cite journal|last=UNVERZAGT|first=FREDERICK W.|last2=MONAHAN|first2=PATRICK O.|last3=MOSER|first3=LYNDSI R.|last4=ZHAO|first4=QIANQIAN|last5=CARPENTER|first5=JANET S.|last6=SLEDGE|first6=GEORGE W.|last7=CHAMPION|first7=VICTORIA L.|date=2007-9|title=The Indiana University Telephone-Based Assessment of Neuropsychological Status: A new method for large scale neuropsychological assessment|url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2747375/|journal=Journal of the International Neuropsychological Society : JINS|volume=13|issue=5|pages=799–806|doi=10.1017/S1355617707071020|issn=1355-6177|pmc=2747375|pmid=17697411}}</ref> Vestal, L., Smith-Olinde, L., Hicks, G., Hutton, T., & Hart, J. (2006). Efficacy of language assessment in Alzheimer's disease: Comparing in-person examination and telemedicine. ''[https://www.dovepress.com/clinical-interventions-in-aging-journal Clinical Interventions in Aging]'', ''1''(4), 467-471. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2699639/<ref>{{Cite journal|last=Vestal|first=Lindsey|last2=Smith-Olinde|first2=Laura|last3=Hicks|first3=Gretchen|last4=Hutton|first4=Terri|last5=Hart|first5=John|date=2006-12|title=Efficacy of language assessment in Alzheimer’s disease: comparing in-person examination and telemedicine|url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2699639/|journal=Clinical Interventions in Aging|volume=1|issue=4|pages=467–471|issn=1176-9092|pmc=2699639|pmid=18046923}}</ref> Wadsworth, H. E., Galusha-Glasscock, J. M., Womack, K. B., Quiceno, M., Weiner, M. F., Hynan, L. S., Shore,&nbsp;J., Cullum,&nbsp;C. M. (2016). Remote neuropsychological assessment in rural American Indians with and without cognitive impairment. ''[https://academic.oup.com/acn Archives of Clinical Neuropsychology],''&nbsp;''31''(5) 420–425.https://academic.oup.com/acn/article/31/5/420/2726825<ref>{{Cite journal|last=Wadsworth|first=Hannah E.|last2=Galusha-Glasscock|first2=Jeanine M.|last3=Womack|first3=Kyle B.|last4=Quiceno|first4=Mary|last5=Weiner|first5=Myron F.|last6=Hynan|first6=Linda S.|last7=Shore|first7=Jay|last8=Cullum|first8=C. Munro|date=2016-08-01|title=Remote Neuropsychological Assessment in Rural American Indians with and without Cognitive Impairment|url=https://academic.oup.com/acn/article/31/5/420/2726825|journal=Archives of Clinical Neuropsychology|language=en|volume=31|issue=5|pages=420–425|doi=10.1093/arclin/acw030|issn=0887-6177}}</ref> == References == h4fvqq53gfg6p9p9jodgry0gkyxgxyp 14 273009 2690235 2688094 2024-12-04T09:04:51Z DavidMCEddy 218607 /* Table of episodes */ add "Media literacy for the Arab World per Ahmed Al-Rawi" to the table 2690235 wikitext text/x-wiki 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]] "started ... with five hundred volunteers<ref>Ressa (2022, pp. 147-8).</ref> (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.<ref>Ressa (2022, pp. 152-3).</ref> 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.<ref>Ressa (2022, p. 158ff) and Wikipedia, "[[w:Leila de Lima|Leila de Lima]]", accessed 2024-07-22.</ref> 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.<ref>Ressa (2022, pp. 152-3) and Wikipedia, "[[w:Maria Ressa|Maria Ressa]]", accessed 2024-07-22.</ref> 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.<ref>Ressa (2022, pp. 152-3).</ref> [[w:H. R. McMaster|H. R. McMaster]], former President Trump's second National Security advisor, said that "The internet and social media thus provided [Russia] with a low-cost, easy way to divide and weaken America from within."<ref>McMaster (2020, pp. 47-48).</ref> 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 "Category:Media reform to improve democracy" include videos of interviews with experts and activists working this issue along with 29:00 mm:ss audio files submitted to a ''Media & Democracy'' series syndicated on the [[w:List of Pacifica Radio stations and affiliates|Pacifica radio network]]<ref><!--Media & Democracy on Audioport-->{{cite Q|Q127839818}}</ref> plus text and space for a moderated discussion. The 2024-09-11 episode of Sprouts:Radio from the Grassroots<ref><!--Sprouts: Radio From the Grassroots-->{{cite Q|Q98781702}}</ref> [[Media & 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="wikitable sortable" |+ Episodes of "Media & Democracy" 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 |- | 2024-12-02 || 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 & 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 == * <!-- H. R. McMaster (2020) Battlegrounds: The Fight to Defend the Free World-->{{cite Q|Q104774898}} * <!--Maria Ressa (2022) How to Stand Up To a Dictator-->{{cite Q|Q117559286}} [[Category:Interdisciplinary studies]] [[Category:Political science]] [[Category:Economics]] [[Category:Freedom and abundance]] [[Category:Videoconferences on media and democracy]] 19abr3hccmk88pw3rs4nfevfhvslouo 0 282423 2690185 2474046 2024-12-04T02:12:12Z CommonsDelinker 9184 Removing [[:c:File:ComponentSelection.png|ComponentSelection.png]], it has been deleted from Commons by [[:c:User:Krd|Krd]] because: No license since 21 November 2024. 2690185 wikitext text/x-wiki == Getting Started: == # Make an [https://osf.io/ OSF] account #* Get the group leader to add you as a contributor to these two projects: Helping Give Away Psychological Science & Assessment Center # Make a [https://www.zotero.org/ Zotero] Account #* Get the team leader to share the HGAPS Group Library with you on Zotero #* Download Zotero desktop app and browser extension # Click [https://osf.io/6wgcz/ here] to see a template OSF component. == Step 1: Getting to Right Project == Navigate to [https://osf.io/kvwmn/ OtoPS (Open Teaching of Psychological Science) /Measure component] within OSF == Step 2: Creating a Component for the Assessment == [[File:Creating a New Component.png|thumb|385x385px|Once you've confirmed that the assessment you're working with does not have a previously created component, click the "Add Component" button shown in the image above to create a new one. ]] === Step 2a: Add and Name the Component === * Search the assessment center project to see if there is already a component created for the assessment in question * If not, then create a component for the assessment. ** Click “Add Component” on the right side of the screen under the Components section ** Name the component ‘Full Measure Name (Measure Acronym)’. For example: Child Mania Rating Scale (CMRS) *** If you want all contributors to have access to this component, select "Add contributors from [Component]" **Click "Create" === Step 2b: Rename the files before uploading them on OSF === The Child Mania Rating Scale will be used as an explicative example. * Measure: ACRONYM_Version_Language_ShortForm <blockquote>ACRONYM: Use abbreviation of the first letters (in capital form) of each word of the measure name. Version: Caregiver; Clinician; Parent; Relative (other than parent); Self-report; Teacher. Language: If there are different versions of the measure in the same language (e.g., Mexican vs Cuban Spanish) specify the type after the word Language and the symbol “-” (see the example below). ShortForm: add the term “ShortForm”only in case of a shortened version of the measure. If the measure is full length, omit specifying this. Examples: CMRS_Teacher_English CMRS_Teacher_English_ShortForm CMRS_Caregiver_English CMRS_Teacher_Spanish CMRS_Teacher_Spanish-Mexican</blockquote> * Anchor article: ACRONYM_Version_AnchorArticle <blockquote>Examples: CMRS_Caregiver_AnchorArticle CMRS_Caregiver&Teacher_AnchorArticle</blockquote> * Validation article in a different language:  ACRONYM_Version_Validation_Language <blockquote>Examples: CMRS_Caregiver_Validation_Spanish CMRS_Teacher_Validation_Spanish-Mexican CMRS_Teacher_Validation_Spanish-Cuban </blockquote> * For other types of articles, specify the specific topic in the third spot of the file name:  ACRONYM_Version_?????_Language <blockquote>Examples: CMRS_Caregiver_PsychometricProprieties_Spanish CMRS_Teacher_DevelopingShortForm_English </blockquote> === Step 2c: Add Tags === Once the component has been created, on the bottom right-hand side of the page you will see a box labeled ‘Tags’. Here, create tags specific to the measure. These include: * The informant (e.g., ‘Self Report’, ‘Teacher Report’). * The acronym for the measure (e.g., ‘BDI’). * If the measure is in the Assessment Center, add the tag ‘AC’. * A tag for each of the versions present (e.g., ‘Short Form’, ‘Work’, ‘Updated’). * A tag for each language present (e.g., ‘English’, ‘Spanish’, ‘Korean’). == Step 3: Adding Information to the Component Wiki == Add information about the measure to the wiki of the newly created component according to the questions outlined in the template (also listed below). === Step 3a: Description of the Measure: === * Is it in the HGAPS Assessment Center? ** If so which battery or batteries? ** Is there a stand-alone version? ** Is it in the process of being added to Qualtrics? ** Which versions are in the Assessment Center? If it is a stand-alone measure or in an assessment battery then provide the link to the assessment center measure. * Is it free? ** Is it free to use or open access? ** Do we have permission to use it? * Who is it for? ** What Age/developmental stage? ** What Demographic? (in-patient, out-patient) ** Is it for the client, associate of the client or clinician, etc.? * What is it for? ** What is it assessing/measuring? *** Does it measure opinions, feelings, thoughts, behaviors, family history, health, habits? ** Is it a screener, symptom tracker, scale, survey, clinical, collect background information, progress measure meant to be given periodically to check progression in therapy? ** What type of diagnosis? ** What are the constructs and/or subcategories it is measuring? ** Is this a measure meant to be given at the initial interview? * How long ** Does it take 20 minutes on average to complete? ** How many questions in total? ** How many questions per section or construct/category? * Measurement concerning time ** Is it for behavior/feelings/thoughts over the past week, month, three months, year, lifetime? ** Is it asking for how they are feeling at that exact moment so their current state? ** Is it asking how that person is in general like their character traits, usual demeanor/temperament? * How many versions? ** How many versions of the measure are there? ** Is there an original, a revised (revised by who), is there a short version or extended version that added additional questions/sub construct added? ** Is there a self-report, parent-report, clinician-report, teacher-report, etc.? ** What languages does it come in? * When? ** When was it first made and published? ** When was it updated? * Summary of Scoring ** How is it scored? ** Are there subscores and which questions do they draw from? ** What is the max total score? ** What do the scores tell you or mean? == Step 4: Creating Components Within the Measure Component == Within the measure component that was just created, create the five sub-components with the detailed wiki outlined below along with adding the appropriate files/subcomponents if they are required for one of the five subcomponents below: === Step 4a: Anchor Article(s) === * Add the article that describes the making of the original measure, later versions including validation of different language versions. * Add the pdfs if any that we are required to cite as a condition of permission of use. * Specify which article is for what in the wiki like so... * <u>Anchor Article for Original:</u> citation or name of PDF. * <u>Article(s) required to Cite:</u> citations and name of PDFs. === Step 4b: Supplemental/Supporting Articles: === This component should not host '''Anchor Articles''' or '''Permissions of Use Articles''' but articles that fall under the following types: * Articles about validity, reliability, psychometrics, the measure being. * Use/validation process with certain demographics using the measure like ages/developmental stage, in-patient, out-patient, race, SES, countries, bi-lingual, etc. or in translations of different languages. * Articles comparing the measure and its performance and diagnostic capabilities/prediction abilities to other measures or other versions of that measure (comparing the performance of the revised version to the original version). === Step 4c: Permissions of Use/Conditions === * Is it free? * Is it only allowed to be used if the author permits you? ** Is there an online request process? What is the email of the person to contact to ask for permission from? ** Is it only allowed to be used for research and if so does that exclude commercial research? ** Include a copy of emails, printed screen of stated permission of use as a pdf in this component. Alternatively, provide a link of where it states the conditions of use for the measure inside this Wiki and then add a document or excerpt that describes the conditions of use or permission in this component. * What are the conditions laid out by the author for using this measure? * Do we need to cite them inside the qualities? If so, is there a specified way they want us to cite/give credit to the owner/author of the measure. ** For instance, is there a watermark or caption we need to put somewhere like: "Copyrighted by the APA, Author Name, Year." * Did they provide you with the citation they want you to include? * Do we just need to cite it if we write a paper about or using the measure? * Are the conditions of use to share the data with the owner/author or to send published papers of the study that it was used in or send a link of the Qualtrics to them for approval or just for them to have? === Step 4d: Original Version of Measure === * By original I mean the first version of the measure, not the revised, not extended, not the short version but the measure that is referenced in the anchor article. * Specify if this is the version used in the Assessment Center here in the description. * This component should have the following: ** PDF or Word Document of Scoring: how it is scored, sub scoring, which questions it uses, the value for each answer choice, and what each score means. ** A manual of the measure if it exists and open access. Sometimes the author will send it to you. ** PDF AND Word Document version of the measure which includes the instructions, questions, and answers. ** If a text/notepad (.txt) version of the measure exists or has been made by someone to upload into Qualtrics so it builds the questions for them then it should also be inside this component. ** '''All parts of the English version of the measure should go directly into this component. If the measure comes in another language and you have all its materials:''' *** Make a component for other languages if you have it inside this component and just label it as Spanish Version, Arabic Version, Albanian Version, etc. *** Inside those versions just put the PDF and Word Document of the actual measure in that language and any other testing materials in that language. Also, put a different report version if it exists and you have it in that language. For example, self-report original Spanish version pdf, teacher-report, etc. ** If there are long-form and short-form options for the measure, create another component inside of the language component (if there are multiple languages) for those forms. *** For example, under the ‘original version’, there could be an ‘English version’ and ‘Spanish version’, and under those subcomponents, you would create the components ‘long-form’ and ‘short-form’. === Step 4e: Revised Version of the Measure === * This component could be called, for example, CMRS_Teacher_English_ShortForm ==== What to put in this Component’s Wiki: ==== * Everything that you put in the Original Measure Component Wiki you should put here but specifically for the Revised Version. * Specifically, state key differences from the original: what was omitted or added, changes in scoring, subscores, or constructs that were taken out or new ones added changes in names of constructs, etc. * If this version is in the Assessment Center then say that here and specify where/which batteries. You can even add the links that go directly to it! * If there is a different author for this version of the measure then state that here and provide the citation for that measure and the anchor article for the making of this version of the measure. * This component should have the same type of files as the Original Version component! == Step 5: Upload all Files == * Download all of the files assembled, then upload them to OSF in their respective components. * Go to the measure component, and then go to the specific component to which you want to upload the file. ** Example: Supplemental/Supporting Articles. * To upload go to the relevant component within the measures and select "OSF Storage (United States)" on the left hand side and then you will see the upload button. * Manuals and scoring documents should be uploaded into the same components as the original version of the measure (and if applicable, the English version). [[File:UploadingFiles.png|thumb|250x250px|Once you've opened the desired component, select "OSF Storage" on the left side of the screen as shown in blue and circled with red in the image above. Once you've done that, the Upload button, circled in red, will show up and you can select it to upload your files. ]] == Step 6: Zotero == === Step 6a: Zotero Setup === * If you do not already have Zotero, [https://www.zotero.org/download/ download Zotero]. ** If you use Google Chrome, it would also be very useful to get the [https://chrome.google.com/webstore/detail/zotero-connector/ekhagklcjbdpajgpjgmbionohlpdbjgc?hl=en Zotero Chrome extension]. ** This will make citing pages a lot easier as well as setting up a desktop version. Zotero browser extensions are useful as they automatically sense content you access online and allow you to save information to Zotero easily. <ref>{{Cite web|url=https://www.zotero.org/download/|title=Zotero {{!}} Downloads|website=www.zotero.org|access-date=2023-02-09}}</ref> ** If you use a browser other than Google Chrome, such as Firefox or Safari, there is also an option to download [https://www.zotero.org/download/ Zotero browser-specific extension]. Upon accessing the download page, Zotero should sense your default browser and give you the option to download the extension specific to your computer. === Step 6b: Where and What === * On Zotero, go to the Assessment Center Folder under the HGAPS library. ** Navigate to the measure’s respective subgroup (e.g. sleep, affective disorders, substance abuse, eating disorders). * Once there, create a subfolder for the specific measure. ** Name the folder ‘Name of Measure (Measure abbreviation)”. ** For example, “Beck Depression Inventory (BDI)”. Then, in the newly created folder, create two subfolders: Anchor Publication and Supplemental/Supporting Articles. === Step 6c: Add Zotero to OSF === * In OSF, navigate to the measure component. * Once there, click on the ‘Add-ons’ tab near the top right-hand side of the page. * In the ‘Select Add-ons’ box, scroll down until you find the Zotero add-on and enable it. ** Zotero should show up in a separate box at the bottom of the page. * On the right of the Zotero add-on, click ‘connect account’. ** The add-on should then connect to your Zotero account. * Finally, select the HGAPS library and respective Zotero folder within the Add-on. * The Zotero citations should now show up as a separate box near the bottom of that measure’s main component. [[File:ZoteroInterface.png|thumb|288x288px|If you do not have the Zotero browser extension, enter the DOI or article information in the box in the upper left hand corner as shown above. ]] === Step 6d: Cite the anchor publication(s) and supporting articles in Zotero === * First, open the article on your browser. * If you have the chrome extension, click the Zotero icon in the top right-hand corner of the browser and Zotero should automatically cite the page. ** The extension will let you select which folder you want the article in. ** Check Zotero to make sure it ended up in the right folder, if not, you can change its location by dragging the citation to the correct folder. * If you don’t have the chrome extension, you can also create citations manually. ** Navigate to the correct folder in Zotero, then click the green plus on the upper left-hand side of the page. ** Select the type of media, then record the correct information in the citation. ** Alternatively, you can simply enter the DOI if your source has one (see picture below). *** Zotero should then cite the source automatically, however, you should look over the citation and correct/add information when necessary. j02q1e1e4vwhwcymw2xihh8r3hd7j19 2690186 2690185 2024-12-04T02:12:39Z CommonsDelinker 9184 Removing [[:c:File:Creating_a_New_Component.png|Creating_a_New_Component.png]], it has been deleted from Commons by [[:c:User:Krd|Krd]] because: No license since 21 November 2024. 2690186 wikitext text/x-wiki == Getting Started: == # Make an [https://osf.io/ OSF] account #* Get the group leader to add you as a contributor to these two projects: Helping Give Away Psychological Science & Assessment Center # Make a [https://www.zotero.org/ Zotero] Account #* Get the team leader to share the HGAPS Group Library with you on Zotero #* Download Zotero desktop app and browser extension # Click [https://osf.io/6wgcz/ here] to see a template OSF component. == Step 1: Getting to Right Project == Navigate to [https://osf.io/kvwmn/ OtoPS (Open Teaching of Psychological Science) /Measure component] within OSF == Step 2: Creating a Component for the Assessment == === Step 2a: Add and Name the Component === * Search the assessment center project to see if there is already a component created for the assessment in question * If not, then create a component for the assessment. ** Click “Add Component” on the right side of the screen under the Components section ** Name the component ‘Full Measure Name (Measure Acronym)’. For example: Child Mania Rating Scale (CMRS) *** If you want all contributors to have access to this component, select "Add contributors from [Component]" **Click "Create" === Step 2b: Rename the files before uploading them on OSF === The Child Mania Rating Scale will be used as an explicative example. * Measure: ACRONYM_Version_Language_ShortForm <blockquote>ACRONYM: Use abbreviation of the first letters (in capital form) of each word of the measure name. Version: Caregiver; Clinician; Parent; Relative (other than parent); Self-report; Teacher. Language: If there are different versions of the measure in the same language (e.g., Mexican vs Cuban Spanish) specify the type after the word Language and the symbol “-” (see the example below). ShortForm: add the term “ShortForm”only in case of a shortened version of the measure. If the measure is full length, omit specifying this. Examples: CMRS_Teacher_English CMRS_Teacher_English_ShortForm CMRS_Caregiver_English CMRS_Teacher_Spanish CMRS_Teacher_Spanish-Mexican</blockquote> * Anchor article: ACRONYM_Version_AnchorArticle <blockquote>Examples: CMRS_Caregiver_AnchorArticle CMRS_Caregiver&Teacher_AnchorArticle</blockquote> * Validation article in a different language:  ACRONYM_Version_Validation_Language <blockquote>Examples: CMRS_Caregiver_Validation_Spanish CMRS_Teacher_Validation_Spanish-Mexican CMRS_Teacher_Validation_Spanish-Cuban </blockquote> * For other types of articles, specify the specific topic in the third spot of the file name:  ACRONYM_Version_?????_Language <blockquote>Examples: CMRS_Caregiver_PsychometricProprieties_Spanish CMRS_Teacher_DevelopingShortForm_English </blockquote> === Step 2c: Add Tags === Once the component has been created, on the bottom right-hand side of the page you will see a box labeled ‘Tags’. Here, create tags specific to the measure. These include: * The informant (e.g., ‘Self Report’, ‘Teacher Report’). * The acronym for the measure (e.g., ‘BDI’). * If the measure is in the Assessment Center, add the tag ‘AC’. * A tag for each of the versions present (e.g., ‘Short Form’, ‘Work’, ‘Updated’). * A tag for each language present (e.g., ‘English’, ‘Spanish’, ‘Korean’). == Step 3: Adding Information to the Component Wiki == Add information about the measure to the wiki of the newly created component according to the questions outlined in the template (also listed below). === Step 3a: Description of the Measure: === * Is it in the HGAPS Assessment Center? ** If so which battery or batteries? ** Is there a stand-alone version? ** Is it in the process of being added to Qualtrics? ** Which versions are in the Assessment Center? If it is a stand-alone measure or in an assessment battery then provide the link to the assessment center measure. * Is it free? ** Is it free to use or open access? ** Do we have permission to use it? * Who is it for? ** What Age/developmental stage? ** What Demographic? (in-patient, out-patient) ** Is it for the client, associate of the client or clinician, etc.? * What is it for? ** What is it assessing/measuring? *** Does it measure opinions, feelings, thoughts, behaviors, family history, health, habits? ** Is it a screener, symptom tracker, scale, survey, clinical, collect background information, progress measure meant to be given periodically to check progression in therapy? ** What type of diagnosis? ** What are the constructs and/or subcategories it is measuring? ** Is this a measure meant to be given at the initial interview? * How long ** Does it take 20 minutes on average to complete? ** How many questions in total? ** How many questions per section or construct/category? * Measurement concerning time ** Is it for behavior/feelings/thoughts over the past week, month, three months, year, lifetime? ** Is it asking for how they are feeling at that exact moment so their current state? ** Is it asking how that person is in general like their character traits, usual demeanor/temperament? * How many versions? ** How many versions of the measure are there? ** Is there an original, a revised (revised by who), is there a short version or extended version that added additional questions/sub construct added? ** Is there a self-report, parent-report, clinician-report, teacher-report, etc.? ** What languages does it come in? * When? ** When was it first made and published? ** When was it updated? * Summary of Scoring ** How is it scored? ** Are there subscores and which questions do they draw from? ** What is the max total score? ** What do the scores tell you or mean? == Step 4: Creating Components Within the Measure Component == Within the measure component that was just created, create the five sub-components with the detailed wiki outlined below along with adding the appropriate files/subcomponents if they are required for one of the five subcomponents below: === Step 4a: Anchor Article(s) === * Add the article that describes the making of the original measure, later versions including validation of different language versions. * Add the pdfs if any that we are required to cite as a condition of permission of use. * Specify which article is for what in the wiki like so... * <u>Anchor Article for Original:</u> citation or name of PDF. * <u>Article(s) required to Cite:</u> citations and name of PDFs. === Step 4b: Supplemental/Supporting Articles: === This component should not host '''Anchor Articles''' or '''Permissions of Use Articles''' but articles that fall under the following types: * Articles about validity, reliability, psychometrics, the measure being. * Use/validation process with certain demographics using the measure like ages/developmental stage, in-patient, out-patient, race, SES, countries, bi-lingual, etc. or in translations of different languages. * Articles comparing the measure and its performance and diagnostic capabilities/prediction abilities to other measures or other versions of that measure (comparing the performance of the revised version to the original version). === Step 4c: Permissions of Use/Conditions === * Is it free? * Is it only allowed to be used if the author permits you? ** Is there an online request process? What is the email of the person to contact to ask for permission from? ** Is it only allowed to be used for research and if so does that exclude commercial research? ** Include a copy of emails, printed screen of stated permission of use as a pdf in this component. Alternatively, provide a link of where it states the conditions of use for the measure inside this Wiki and then add a document or excerpt that describes the conditions of use or permission in this component. * What are the conditions laid out by the author for using this measure? * Do we need to cite them inside the qualities? If so, is there a specified way they want us to cite/give credit to the owner/author of the measure. ** For instance, is there a watermark or caption we need to put somewhere like: "Copyrighted by the APA, Author Name, Year." * Did they provide you with the citation they want you to include? * Do we just need to cite it if we write a paper about or using the measure? * Are the conditions of use to share the data with the owner/author or to send published papers of the study that it was used in or send a link of the Qualtrics to them for approval or just for them to have? === Step 4d: Original Version of Measure === * By original I mean the first version of the measure, not the revised, not extended, not the short version but the measure that is referenced in the anchor article. * Specify if this is the version used in the Assessment Center here in the description. * This component should have the following: ** PDF or Word Document of Scoring: how it is scored, sub scoring, which questions it uses, the value for each answer choice, and what each score means. ** A manual of the measure if it exists and open access. Sometimes the author will send it to you. ** PDF AND Word Document version of the measure which includes the instructions, questions, and answers. ** If a text/notepad (.txt) version of the measure exists or has been made by someone to upload into Qualtrics so it builds the questions for them then it should also be inside this component. ** '''All parts of the English version of the measure should go directly into this component. If the measure comes in another language and you have all its materials:''' *** Make a component for other languages if you have it inside this component and just label it as Spanish Version, Arabic Version, Albanian Version, etc. *** Inside those versions just put the PDF and Word Document of the actual measure in that language and any other testing materials in that language. Also, put a different report version if it exists and you have it in that language. For example, self-report original Spanish version pdf, teacher-report, etc. ** If there are long-form and short-form options for the measure, create another component inside of the language component (if there are multiple languages) for those forms. *** For example, under the ‘original version’, there could be an ‘English version’ and ‘Spanish version’, and under those subcomponents, you would create the components ‘long-form’ and ‘short-form’. === Step 4e: Revised Version of the Measure === * This component could be called, for example, CMRS_Teacher_English_ShortForm ==== What to put in this Component’s Wiki: ==== * Everything that you put in the Original Measure Component Wiki you should put here but specifically for the Revised Version. * Specifically, state key differences from the original: what was omitted or added, changes in scoring, subscores, or constructs that were taken out or new ones added changes in names of constructs, etc. * If this version is in the Assessment Center then say that here and specify where/which batteries. You can even add the links that go directly to it! * If there is a different author for this version of the measure then state that here and provide the citation for that measure and the anchor article for the making of this version of the measure. * This component should have the same type of files as the Original Version component! == Step 5: Upload all Files == * Download all of the files assembled, then upload them to OSF in their respective components. * Go to the measure component, and then go to the specific component to which you want to upload the file. ** Example: Supplemental/Supporting Articles. * To upload go to the relevant component within the measures and select "OSF Storage (United States)" on the left hand side and then you will see the upload button. * Manuals and scoring documents should be uploaded into the same components as the original version of the measure (and if applicable, the English version). [[File:UploadingFiles.png|thumb|250x250px|Once you've opened the desired component, select "OSF Storage" on the left side of the screen as shown in blue and circled with red in the image above. Once you've done that, the Upload button, circled in red, will show up and you can select it to upload your files. ]] == Step 6: Zotero == === Step 6a: Zotero Setup === * If you do not already have Zotero, [https://www.zotero.org/download/ download Zotero]. ** If you use Google Chrome, it would also be very useful to get the [https://chrome.google.com/webstore/detail/zotero-connector/ekhagklcjbdpajgpjgmbionohlpdbjgc?hl=en Zotero Chrome extension]. ** This will make citing pages a lot easier as well as setting up a desktop version. Zotero browser extensions are useful as they automatically sense content you access online and allow you to save information to Zotero easily. <ref>{{Cite web|url=https://www.zotero.org/download/|title=Zotero {{!}} Downloads|website=www.zotero.org|access-date=2023-02-09}}</ref> ** If you use a browser other than Google Chrome, such as Firefox or Safari, there is also an option to download [https://www.zotero.org/download/ Zotero browser-specific extension]. Upon accessing the download page, Zotero should sense your default browser and give you the option to download the extension specific to your computer. === Step 6b: Where and What === * On Zotero, go to the Assessment Center Folder under the HGAPS library. ** Navigate to the measure’s respective subgroup (e.g. sleep, affective disorders, substance abuse, eating disorders). * Once there, create a subfolder for the specific measure. ** Name the folder ‘Name of Measure (Measure abbreviation)”. ** For example, “Beck Depression Inventory (BDI)”. Then, in the newly created folder, create two subfolders: Anchor Publication and Supplemental/Supporting Articles. === Step 6c: Add Zotero to OSF === * In OSF, navigate to the measure component. * Once there, click on the ‘Add-ons’ tab near the top right-hand side of the page. * In the ‘Select Add-ons’ box, scroll down until you find the Zotero add-on and enable it. ** Zotero should show up in a separate box at the bottom of the page. * On the right of the Zotero add-on, click ‘connect account’. ** The add-on should then connect to your Zotero account. * Finally, select the HGAPS library and respective Zotero folder within the Add-on. * The Zotero citations should now show up as a separate box near the bottom of that measure’s main component. [[File:ZoteroInterface.png|thumb|288x288px|If you do not have the Zotero browser extension, enter the DOI or article information in the box in the upper left hand corner as shown above. ]] === Step 6d: Cite the anchor publication(s) and supporting articles in Zotero === * First, open the article on your browser. * If you have the chrome extension, click the Zotero icon in the top right-hand corner of the browser and Zotero should automatically cite the page. ** The extension will let you select which folder you want the article in. ** Check Zotero to make sure it ended up in the right folder, if not, you can change its location by dragging the citation to the correct folder. * If you don’t have the chrome extension, you can also create citations manually. ** Navigate to the correct folder in Zotero, then click the green plus on the upper left-hand side of the page. ** Select the type of media, then record the correct information in the citation. ** Alternatively, you can simply enter the DOI if your source has one (see picture below). *** Zotero should then cite the source automatically, however, you should look over the citation and correct/add information when necessary. mmlg3gwh3hx3ywfrrd4422b3ly7i7t8 2690188 2690186 2024-12-04T02:22:05Z CommonsDelinker 9184 Removing [[:c:File:UploadingFiles.png|UploadingFiles.png]], it has been deleted from Commons by [[:c:User:Krd|Krd]] because: No license since 21 November 2024. 2690188 wikitext text/x-wiki == Getting Started: == # Make an [https://osf.io/ OSF] account #* Get the group leader to add you as a contributor to these two projects: Helping Give Away Psychological Science & Assessment Center # Make a [https://www.zotero.org/ Zotero] Account #* Get the team leader to share the HGAPS Group Library with you on Zotero #* Download Zotero desktop app and browser extension # Click [https://osf.io/6wgcz/ here] to see a template OSF component. == Step 1: Getting to Right Project == Navigate to [https://osf.io/kvwmn/ OtoPS (Open Teaching of Psychological Science) /Measure component] within OSF == Step 2: Creating a Component for the Assessment == === Step 2a: Add and Name the Component === * Search the assessment center project to see if there is already a component created for the assessment in question * If not, then create a component for the assessment. ** Click “Add Component” on the right side of the screen under the Components section ** Name the component ‘Full Measure Name (Measure Acronym)’. For example: Child Mania Rating Scale (CMRS) *** If you want all contributors to have access to this component, select "Add contributors from [Component]" **Click "Create" === Step 2b: Rename the files before uploading them on OSF === The Child Mania Rating Scale will be used as an explicative example. * Measure: ACRONYM_Version_Language_ShortForm <blockquote>ACRONYM: Use abbreviation of the first letters (in capital form) of each word of the measure name. Version: Caregiver; Clinician; Parent; Relative (other than parent); Self-report; Teacher. Language: If there are different versions of the measure in the same language (e.g., Mexican vs Cuban Spanish) specify the type after the word Language and the symbol “-” (see the example below). ShortForm: add the term “ShortForm”only in case of a shortened version of the measure. If the measure is full length, omit specifying this. Examples: CMRS_Teacher_English CMRS_Teacher_English_ShortForm CMRS_Caregiver_English CMRS_Teacher_Spanish CMRS_Teacher_Spanish-Mexican</blockquote> * Anchor article: ACRONYM_Version_AnchorArticle <blockquote>Examples: CMRS_Caregiver_AnchorArticle CMRS_Caregiver&Teacher_AnchorArticle</blockquote> * Validation article in a different language:  ACRONYM_Version_Validation_Language <blockquote>Examples: CMRS_Caregiver_Validation_Spanish CMRS_Teacher_Validation_Spanish-Mexican CMRS_Teacher_Validation_Spanish-Cuban </blockquote> * For other types of articles, specify the specific topic in the third spot of the file name:  ACRONYM_Version_?????_Language <blockquote>Examples: CMRS_Caregiver_PsychometricProprieties_Spanish CMRS_Teacher_DevelopingShortForm_English </blockquote> === Step 2c: Add Tags === Once the component has been created, on the bottom right-hand side of the page you will see a box labeled ‘Tags’. Here, create tags specific to the measure. These include: * The informant (e.g., ‘Self Report’, ‘Teacher Report’). * The acronym for the measure (e.g., ‘BDI’). * If the measure is in the Assessment Center, add the tag ‘AC’. * A tag for each of the versions present (e.g., ‘Short Form’, ‘Work’, ‘Updated’). * A tag for each language present (e.g., ‘English’, ‘Spanish’, ‘Korean’). == Step 3: Adding Information to the Component Wiki == Add information about the measure to the wiki of the newly created component according to the questions outlined in the template (also listed below). === Step 3a: Description of the Measure: === * Is it in the HGAPS Assessment Center? ** If so which battery or batteries? ** Is there a stand-alone version? ** Is it in the process of being added to Qualtrics? ** Which versions are in the Assessment Center? If it is a stand-alone measure or in an assessment battery then provide the link to the assessment center measure. * Is it free? ** Is it free to use or open access? ** Do we have permission to use it? * Who is it for? ** What Age/developmental stage? ** What Demographic? (in-patient, out-patient) ** Is it for the client, associate of the client or clinician, etc.? * What is it for? ** What is it assessing/measuring? *** Does it measure opinions, feelings, thoughts, behaviors, family history, health, habits? ** Is it a screener, symptom tracker, scale, survey, clinical, collect background information, progress measure meant to be given periodically to check progression in therapy? ** What type of diagnosis? ** What are the constructs and/or subcategories it is measuring? ** Is this a measure meant to be given at the initial interview? * How long ** Does it take 20 minutes on average to complete? ** How many questions in total? ** How many questions per section or construct/category? * Measurement concerning time ** Is it for behavior/feelings/thoughts over the past week, month, three months, year, lifetime? ** Is it asking for how they are feeling at that exact moment so their current state? ** Is it asking how that person is in general like their character traits, usual demeanor/temperament? * How many versions? ** How many versions of the measure are there? ** Is there an original, a revised (revised by who), is there a short version or extended version that added additional questions/sub construct added? ** Is there a self-report, parent-report, clinician-report, teacher-report, etc.? ** What languages does it come in? * When? ** When was it first made and published? ** When was it updated? * Summary of Scoring ** How is it scored? ** Are there subscores and which questions do they draw from? ** What is the max total score? ** What do the scores tell you or mean? == Step 4: Creating Components Within the Measure Component == Within the measure component that was just created, create the five sub-components with the detailed wiki outlined below along with adding the appropriate files/subcomponents if they are required for one of the five subcomponents below: === Step 4a: Anchor Article(s) === * Add the article that describes the making of the original measure, later versions including validation of different language versions. * Add the pdfs if any that we are required to cite as a condition of permission of use. * Specify which article is for what in the wiki like so... * <u>Anchor Article for Original:</u> citation or name of PDF. * <u>Article(s) required to Cite:</u> citations and name of PDFs. === Step 4b: Supplemental/Supporting Articles: === This component should not host '''Anchor Articles''' or '''Permissions of Use Articles''' but articles that fall under the following types: * Articles about validity, reliability, psychometrics, the measure being. * Use/validation process with certain demographics using the measure like ages/developmental stage, in-patient, out-patient, race, SES, countries, bi-lingual, etc. or in translations of different languages. * Articles comparing the measure and its performance and diagnostic capabilities/prediction abilities to other measures or other versions of that measure (comparing the performance of the revised version to the original version). === Step 4c: Permissions of Use/Conditions === * Is it free? * Is it only allowed to be used if the author permits you? ** Is there an online request process? What is the email of the person to contact to ask for permission from? ** Is it only allowed to be used for research and if so does that exclude commercial research? ** Include a copy of emails, printed screen of stated permission of use as a pdf in this component. Alternatively, provide a link of where it states the conditions of use for the measure inside this Wiki and then add a document or excerpt that describes the conditions of use or permission in this component. * What are the conditions laid out by the author for using this measure? * Do we need to cite them inside the qualities? If so, is there a specified way they want us to cite/give credit to the owner/author of the measure. ** For instance, is there a watermark or caption we need to put somewhere like: "Copyrighted by the APA, Author Name, Year." * Did they provide you with the citation they want you to include? * Do we just need to cite it if we write a paper about or using the measure? * Are the conditions of use to share the data with the owner/author or to send published papers of the study that it was used in or send a link of the Qualtrics to them for approval or just for them to have? === Step 4d: Original Version of Measure === * By original I mean the first version of the measure, not the revised, not extended, not the short version but the measure that is referenced in the anchor article. * Specify if this is the version used in the Assessment Center here in the description. * This component should have the following: ** PDF or Word Document of Scoring: how it is scored, sub scoring, which questions it uses, the value for each answer choice, and what each score means. ** A manual of the measure if it exists and open access. Sometimes the author will send it to you. ** PDF AND Word Document version of the measure which includes the instructions, questions, and answers. ** If a text/notepad (.txt) version of the measure exists or has been made by someone to upload into Qualtrics so it builds the questions for them then it should also be inside this component. ** '''All parts of the English version of the measure should go directly into this component. If the measure comes in another language and you have all its materials:''' *** Make a component for other languages if you have it inside this component and just label it as Spanish Version, Arabic Version, Albanian Version, etc. *** Inside those versions just put the PDF and Word Document of the actual measure in that language and any other testing materials in that language. Also, put a different report version if it exists and you have it in that language. For example, self-report original Spanish version pdf, teacher-report, etc. ** If there are long-form and short-form options for the measure, create another component inside of the language component (if there are multiple languages) for those forms. *** For example, under the ‘original version’, there could be an ‘English version’ and ‘Spanish version’, and under those subcomponents, you would create the components ‘long-form’ and ‘short-form’. === Step 4e: Revised Version of the Measure === * This component could be called, for example, CMRS_Teacher_English_ShortForm ==== What to put in this Component’s Wiki: ==== * Everything that you put in the Original Measure Component Wiki you should put here but specifically for the Revised Version. * Specifically, state key differences from the original: what was omitted or added, changes in scoring, subscores, or constructs that were taken out or new ones added changes in names of constructs, etc. * If this version is in the Assessment Center then say that here and specify where/which batteries. You can even add the links that go directly to it! * If there is a different author for this version of the measure then state that here and provide the citation for that measure and the anchor article for the making of this version of the measure. * This component should have the same type of files as the Original Version component! == Step 5: Upload all Files == * Download all of the files assembled, then upload them to OSF in their respective components. * Go to the measure component, and then go to the specific component to which you want to upload the file. ** Example: Supplemental/Supporting Articles. * To upload go to the relevant component within the measures and select "OSF Storage (United States)" on the left hand side and then you will see the upload button. * Manuals and scoring documents should be uploaded into the same components as the original version of the measure (and if applicable, the English version). == Step 6: Zotero == === Step 6a: Zotero Setup === * If you do not already have Zotero, [https://www.zotero.org/download/ download Zotero]. ** If you use Google Chrome, it would also be very useful to get the [https://chrome.google.com/webstore/detail/zotero-connector/ekhagklcjbdpajgpjgmbionohlpdbjgc?hl=en Zotero Chrome extension]. ** This will make citing pages a lot easier as well as setting up a desktop version. Zotero browser extensions are useful as they automatically sense content you access online and allow you to save information to Zotero easily. <ref>{{Cite web|url=https://www.zotero.org/download/|title=Zotero {{!}} Downloads|website=www.zotero.org|access-date=2023-02-09}}</ref> ** If you use a browser other than Google Chrome, such as Firefox or Safari, there is also an option to download [https://www.zotero.org/download/ Zotero browser-specific extension]. Upon accessing the download page, Zotero should sense your default browser and give you the option to download the extension specific to your computer. === Step 6b: Where and What === * On Zotero, go to the Assessment Center Folder under the HGAPS library. ** Navigate to the measure’s respective subgroup (e.g. sleep, affective disorders, substance abuse, eating disorders). * Once there, create a subfolder for the specific measure. ** Name the folder ‘Name of Measure (Measure abbreviation)”. ** For example, “Beck Depression Inventory (BDI)”. Then, in the newly created folder, create two subfolders: Anchor Publication and Supplemental/Supporting Articles. === Step 6c: Add Zotero to OSF === * In OSF, navigate to the measure component. * Once there, click on the ‘Add-ons’ tab near the top right-hand side of the page. * In the ‘Select Add-ons’ box, scroll down until you find the Zotero add-on and enable it. ** Zotero should show up in a separate box at the bottom of the page. * On the right of the Zotero add-on, click ‘connect account’. ** The add-on should then connect to your Zotero account. * Finally, select the HGAPS library and respective Zotero folder within the Add-on. * The Zotero citations should now show up as a separate box near the bottom of that measure’s main component. [[File:ZoteroInterface.png|thumb|288x288px|If you do not have the Zotero browser extension, enter the DOI or article information in the box in the upper left hand corner as shown above. ]] === Step 6d: Cite the anchor publication(s) and supporting articles in Zotero === * First, open the article on your browser. * If you have the chrome extension, click the Zotero icon in the top right-hand corner of the browser and Zotero should automatically cite the page. ** The extension will let you select which folder you want the article in. ** Check Zotero to make sure it ended up in the right folder, if not, you can change its location by dragging the citation to the correct folder. * If you don’t have the chrome extension, you can also create citations manually. ** Navigate to the correct folder in Zotero, then click the green plus on the upper left-hand side of the page. ** Select the type of media, then record the correct information in the citation. ** Alternatively, you can simply enter the DOI if your source has one (see picture below). *** Zotero should then cite the source automatically, however, you should look over the citation and correct/add information when necessary. arbt93twe3ycjghwyrg1o974efatohn 2690189 2690188 2024-12-04T02:23:35Z CommonsDelinker 9184 Removing [[:c:File:ZoteroInterface.png|ZoteroInterface.png]], it has been deleted from Commons by [[:c:User:Krd|Krd]] because: No license since 21 November 2024. 2690189 wikitext text/x-wiki == Getting Started: == # Make an [https://osf.io/ OSF] account #* Get the group leader to add you as a contributor to these two projects: Helping Give Away Psychological Science & Assessment Center # Make a [https://www.zotero.org/ Zotero] Account #* Get the team leader to share the HGAPS Group Library with you on Zotero #* Download Zotero desktop app and browser extension # Click [https://osf.io/6wgcz/ here] to see a template OSF component. == Step 1: Getting to Right Project == Navigate to [https://osf.io/kvwmn/ OtoPS (Open Teaching of Psychological Science) /Measure component] within OSF == Step 2: Creating a Component for the Assessment == === Step 2a: Add and Name the Component === * Search the assessment center project to see if there is already a component created for the assessment in question * If not, then create a component for the assessment. ** Click “Add Component” on the right side of the screen under the Components section ** Name the component ‘Full Measure Name (Measure Acronym)’. For example: Child Mania Rating Scale (CMRS) *** If you want all contributors to have access to this component, select "Add contributors from [Component]" **Click "Create" === Step 2b: Rename the files before uploading them on OSF === The Child Mania Rating Scale will be used as an explicative example. * Measure: ACRONYM_Version_Language_ShortForm <blockquote>ACRONYM: Use abbreviation of the first letters (in capital form) of each word of the measure name. Version: Caregiver; Clinician; Parent; Relative (other than parent); Self-report; Teacher. Language: If there are different versions of the measure in the same language (e.g., Mexican vs Cuban Spanish) specify the type after the word Language and the symbol “-” (see the example below). ShortForm: add the term “ShortForm”only in case of a shortened version of the measure. If the measure is full length, omit specifying this. Examples: CMRS_Teacher_English CMRS_Teacher_English_ShortForm CMRS_Caregiver_English CMRS_Teacher_Spanish CMRS_Teacher_Spanish-Mexican</blockquote> * Anchor article: ACRONYM_Version_AnchorArticle <blockquote>Examples: CMRS_Caregiver_AnchorArticle CMRS_Caregiver&Teacher_AnchorArticle</blockquote> * Validation article in a different language:  ACRONYM_Version_Validation_Language <blockquote>Examples: CMRS_Caregiver_Validation_Spanish CMRS_Teacher_Validation_Spanish-Mexican CMRS_Teacher_Validation_Spanish-Cuban </blockquote> * For other types of articles, specify the specific topic in the third spot of the file name:  ACRONYM_Version_?????_Language <blockquote>Examples: CMRS_Caregiver_PsychometricProprieties_Spanish CMRS_Teacher_DevelopingShortForm_English </blockquote> === Step 2c: Add Tags === Once the component has been created, on the bottom right-hand side of the page you will see a box labeled ‘Tags’. Here, create tags specific to the measure. These include: * The informant (e.g., ‘Self Report’, ‘Teacher Report’). * The acronym for the measure (e.g., ‘BDI’). * If the measure is in the Assessment Center, add the tag ‘AC’. * A tag for each of the versions present (e.g., ‘Short Form’, ‘Work’, ‘Updated’). * A tag for each language present (e.g., ‘English’, ‘Spanish’, ‘Korean’). == Step 3: Adding Information to the Component Wiki == Add information about the measure to the wiki of the newly created component according to the questions outlined in the template (also listed below). === Step 3a: Description of the Measure: === * Is it in the HGAPS Assessment Center? ** If so which battery or batteries? ** Is there a stand-alone version? ** Is it in the process of being added to Qualtrics? ** Which versions are in the Assessment Center? If it is a stand-alone measure or in an assessment battery then provide the link to the assessment center measure. * Is it free? ** Is it free to use or open access? ** Do we have permission to use it? * Who is it for? ** What Age/developmental stage? ** What Demographic? (in-patient, out-patient) ** Is it for the client, associate of the client or clinician, etc.? * What is it for? ** What is it assessing/measuring? *** Does it measure opinions, feelings, thoughts, behaviors, family history, health, habits? ** Is it a screener, symptom tracker, scale, survey, clinical, collect background information, progress measure meant to be given periodically to check progression in therapy? ** What type of diagnosis? ** What are the constructs and/or subcategories it is measuring? ** Is this a measure meant to be given at the initial interview? * How long ** Does it take 20 minutes on average to complete? ** How many questions in total? ** How many questions per section or construct/category? * Measurement concerning time ** Is it for behavior/feelings/thoughts over the past week, month, three months, year, lifetime? ** Is it asking for how they are feeling at that exact moment so their current state? ** Is it asking how that person is in general like their character traits, usual demeanor/temperament? * How many versions? ** How many versions of the measure are there? ** Is there an original, a revised (revised by who), is there a short version or extended version that added additional questions/sub construct added? ** Is there a self-report, parent-report, clinician-report, teacher-report, etc.? ** What languages does it come in? * When? ** When was it first made and published? ** When was it updated? * Summary of Scoring ** How is it scored? ** Are there subscores and which questions do they draw from? ** What is the max total score? ** What do the scores tell you or mean? == Step 4: Creating Components Within the Measure Component == Within the measure component that was just created, create the five sub-components with the detailed wiki outlined below along with adding the appropriate files/subcomponents if they are required for one of the five subcomponents below: === Step 4a: Anchor Article(s) === * Add the article that describes the making of the original measure, later versions including validation of different language versions. * Add the pdfs if any that we are required to cite as a condition of permission of use. * Specify which article is for what in the wiki like so... * <u>Anchor Article for Original:</u> citation or name of PDF. * <u>Article(s) required to Cite:</u> citations and name of PDFs. === Step 4b: Supplemental/Supporting Articles: === This component should not host '''Anchor Articles''' or '''Permissions of Use Articles''' but articles that fall under the following types: * Articles about validity, reliability, psychometrics, the measure being. * Use/validation process with certain demographics using the measure like ages/developmental stage, in-patient, out-patient, race, SES, countries, bi-lingual, etc. or in translations of different languages. * Articles comparing the measure and its performance and diagnostic capabilities/prediction abilities to other measures or other versions of that measure (comparing the performance of the revised version to the original version). === Step 4c: Permissions of Use/Conditions === * Is it free? * Is it only allowed to be used if the author permits you? ** Is there an online request process? What is the email of the person to contact to ask for permission from? ** Is it only allowed to be used for research and if so does that exclude commercial research? ** Include a copy of emails, printed screen of stated permission of use as a pdf in this component. Alternatively, provide a link of where it states the conditions of use for the measure inside this Wiki and then add a document or excerpt that describes the conditions of use or permission in this component. * What are the conditions laid out by the author for using this measure? * Do we need to cite them inside the qualities? If so, is there a specified way they want us to cite/give credit to the owner/author of the measure. ** For instance, is there a watermark or caption we need to put somewhere like: "Copyrighted by the APA, Author Name, Year." * Did they provide you with the citation they want you to include? * Do we just need to cite it if we write a paper about or using the measure? * Are the conditions of use to share the data with the owner/author or to send published papers of the study that it was used in or send a link of the Qualtrics to them for approval or just for them to have? === Step 4d: Original Version of Measure === * By original I mean the first version of the measure, not the revised, not extended, not the short version but the measure that is referenced in the anchor article. * Specify if this is the version used in the Assessment Center here in the description. * This component should have the following: ** PDF or Word Document of Scoring: how it is scored, sub scoring, which questions it uses, the value for each answer choice, and what each score means. ** A manual of the measure if it exists and open access. Sometimes the author will send it to you. ** PDF AND Word Document version of the measure which includes the instructions, questions, and answers. ** If a text/notepad (.txt) version of the measure exists or has been made by someone to upload into Qualtrics so it builds the questions for them then it should also be inside this component. ** '''All parts of the English version of the measure should go directly into this component. If the measure comes in another language and you have all its materials:''' *** Make a component for other languages if you have it inside this component and just label it as Spanish Version, Arabic Version, Albanian Version, etc. *** Inside those versions just put the PDF and Word Document of the actual measure in that language and any other testing materials in that language. Also, put a different report version if it exists and you have it in that language. For example, self-report original Spanish version pdf, teacher-report, etc. ** If there are long-form and short-form options for the measure, create another component inside of the language component (if there are multiple languages) for those forms. *** For example, under the ‘original version’, there could be an ‘English version’ and ‘Spanish version’, and under those subcomponents, you would create the components ‘long-form’ and ‘short-form’. === Step 4e: Revised Version of the Measure === * This component could be called, for example, CMRS_Teacher_English_ShortForm ==== What to put in this Component’s Wiki: ==== * Everything that you put in the Original Measure Component Wiki you should put here but specifically for the Revised Version. * Specifically, state key differences from the original: what was omitted or added, changes in scoring, subscores, or constructs that were taken out or new ones added changes in names of constructs, etc. * If this version is in the Assessment Center then say that here and specify where/which batteries. You can even add the links that go directly to it! * If there is a different author for this version of the measure then state that here and provide the citation for that measure and the anchor article for the making of this version of the measure. * This component should have the same type of files as the Original Version component! == Step 5: Upload all Files == * Download all of the files assembled, then upload them to OSF in their respective components. * Go to the measure component, and then go to the specific component to which you want to upload the file. ** Example: Supplemental/Supporting Articles. * To upload go to the relevant component within the measures and select "OSF Storage (United States)" on the left hand side and then you will see the upload button. * Manuals and scoring documents should be uploaded into the same components as the original version of the measure (and if applicable, the English version). == Step 6: Zotero == === Step 6a: Zotero Setup === * If you do not already have Zotero, [https://www.zotero.org/download/ download Zotero]. ** If you use Google Chrome, it would also be very useful to get the [https://chrome.google.com/webstore/detail/zotero-connector/ekhagklcjbdpajgpjgmbionohlpdbjgc?hl=en Zotero Chrome extension]. ** This will make citing pages a lot easier as well as setting up a desktop version. Zotero browser extensions are useful as they automatically sense content you access online and allow you to save information to Zotero easily. <ref>{{Cite web|url=https://www.zotero.org/download/|title=Zotero {{!}} Downloads|website=www.zotero.org|access-date=2023-02-09}}</ref> ** If you use a browser other than Google Chrome, such as Firefox or Safari, there is also an option to download [https://www.zotero.org/download/ Zotero browser-specific extension]. Upon accessing the download page, Zotero should sense your default browser and give you the option to download the extension specific to your computer. === Step 6b: Where and What === * On Zotero, go to the Assessment Center Folder under the HGAPS library. ** Navigate to the measure’s respective subgroup (e.g. sleep, affective disorders, substance abuse, eating disorders). * Once there, create a subfolder for the specific measure. ** Name the folder ‘Name of Measure (Measure abbreviation)”. ** For example, “Beck Depression Inventory (BDI)”. Then, in the newly created folder, create two subfolders: Anchor Publication and Supplemental/Supporting Articles. === Step 6c: Add Zotero to OSF === * In OSF, navigate to the measure component. * Once there, click on the ‘Add-ons’ tab near the top right-hand side of the page. * In the ‘Select Add-ons’ box, scroll down until you find the Zotero add-on and enable it. ** Zotero should show up in a separate box at the bottom of the page. * On the right of the Zotero add-on, click ‘connect account’. ** The add-on should then connect to your Zotero account. * Finally, select the HGAPS library and respective Zotero folder within the Add-on. * The Zotero citations should now show up as a separate box near the bottom of that measure’s main component. === Step 6d: Cite the anchor publication(s) and supporting articles in Zotero === * First, open the article on your browser. * If you have the chrome extension, click the Zotero icon in the top right-hand corner of the browser and Zotero should automatically cite the page. ** The extension will let you select which folder you want the article in. ** Check Zotero to make sure it ended up in the right folder, if not, you can change its location by dragging the citation to the correct folder. * If you don’t have the chrome extension, you can also create citations manually. ** Navigate to the correct folder in Zotero, then click the green plus on the upper left-hand side of the page. ** Select the type of media, then record the correct information in the citation. ** Alternatively, you can simply enter the DOI if your source has one (see picture below). *** Zotero should then cite the source automatically, however, you should look over the citation and correct/add information when necessary. 5u10v9kr0h03yaecl2y1vdmyle4jugn 0 285384 2690142 2690040 2024-12-03T18:33:29Z Young1lim 21186 /* Integer Arithmetic */ 2690142 wikitext text/x-wiki === Workings of the GNU Compiler for IA-32 === ==== Overview ==== * Overview ([[Media:Overview.20200211.pdf |pdf]]) ==== Data Processing ==== * Access ([[Media:Access.20200409.pdf |pdf]]) * Operators ([[Media:Operator.20200427.pdf |pdf]]) ==== Control ==== * Conditions ([[Media:Condition.20230630.pdf |pdf]]) * Control ([[Media:Control.20220616.pdf |pdf]]) ==== Function calls ==== * Procedure ([[Media:Procedure.20220412.pdf |pdf]]) * Recursion ([[Media:Recursion.20210824-2.pdf |pdf]]) ==== Pointer and Aggregate Types ==== * Arrays ([[Media:Array.20211018.pdf |pdf]]) * Structures ([[Media:Structure.20220101.pdf |pdf]]) * Alignment ([[Media:Alignment.20201117.pdf |pdf]]) * Pointers ([[Media:Pointer.20201106.pdf |pdf]]) ==== Integer Arithmetic ==== * Overview ([[Media:gcc.1.Overview.20240813.pdf |pdf]]) * Carry Flag ([[Media:gcc.2.Carry.20241202.pdf |pdf]]) * Overflow Flag ([[Media:gcc.3.Overflow.20240724.pdf |pdf]]) * Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]]) * Borrow ([[Media:Borrow.20230701.pdf |pdf]]) ==== Floating point Arithmetic ==== </br> === Workings of the GNU Linker for IA-32 === ==== Linking Libraries ==== * Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]]) * Shared Libraries ([[Media:LIB.2A.Shared.20241202.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]]) </br> go to [ [[C programming in plain view]] ] [[Category:C programming language]] nfv6npceky95tel6ccr7yfojkc139qr 2690144 2690142 2024-12-03T18:34:46Z Young1lim 21186 /* Integer Arithmetic */ 2690144 wikitext text/x-wiki === Workings of the GNU Compiler for IA-32 === ==== Overview ==== * Overview ([[Media:Overview.20200211.pdf |pdf]]) ==== Data Processing ==== * Access ([[Media:Access.20200409.pdf |pdf]]) * Operators ([[Media:Operator.20200427.pdf |pdf]]) ==== Control ==== * Conditions ([[Media:Condition.20230630.pdf |pdf]]) * Control ([[Media:Control.20220616.pdf |pdf]]) ==== Function calls ==== * Procedure ([[Media:Procedure.20220412.pdf |pdf]]) * Recursion ([[Media:Recursion.20210824-2.pdf |pdf]]) ==== Pointer and Aggregate Types ==== * Arrays ([[Media:Array.20211018.pdf |pdf]]) * Structures ([[Media:Structure.20220101.pdf |pdf]]) * Alignment ([[Media:Alignment.20201117.pdf |pdf]]) * Pointers ([[Media:Pointer.20201106.pdf |pdf]]) ==== Integer Arithmetic ==== * Overview ([[Media:gcc.1.Overview.20240813.pdf |pdf]]) * Carry Flag ([[Media:gcc.2.Carry.20241203.pdf |pdf]]) * Overflow Flag ([[Media:gcc.3.Overflow.20240724.pdf |pdf]]) * Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]]) * Borrow ([[Media:Borrow.20230701.pdf |pdf]]) ==== Floating point Arithmetic ==== </br> === Workings of the GNU Linker for IA-32 === ==== Linking Libraries ==== * Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]]) * Shared Libraries ([[Media:LIB.2A.Shared.20241202.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]]) </br> go to [ [[C programming in plain view]] ] [[Category:C programming language]] pdm8w9v1hejb7oduztpv4qaprl9d2g8 2690205 2690144 2024-12-04T04:18:13Z Young1lim 21186 /* Linking Libraries */ 2690205 wikitext text/x-wiki === Workings of the GNU Compiler for IA-32 === ==== Overview ==== * Overview ([[Media:Overview.20200211.pdf |pdf]]) ==== Data Processing ==== * Access ([[Media:Access.20200409.pdf |pdf]]) * Operators ([[Media:Operator.20200427.pdf |pdf]]) ==== Control ==== * Conditions ([[Media:Condition.20230630.pdf |pdf]]) * Control ([[Media:Control.20220616.pdf |pdf]]) ==== Function calls ==== * Procedure ([[Media:Procedure.20220412.pdf |pdf]]) * Recursion ([[Media:Recursion.20210824-2.pdf |pdf]]) ==== Pointer and Aggregate Types ==== * Arrays ([[Media:Array.20211018.pdf |pdf]]) * Structures ([[Media:Structure.20220101.pdf |pdf]]) * Alignment ([[Media:Alignment.20201117.pdf |pdf]]) * Pointers ([[Media:Pointer.20201106.pdf |pdf]]) ==== Integer Arithmetic ==== * Overview ([[Media:gcc.1.Overview.20240813.pdf |pdf]]) * Carry Flag ([[Media:gcc.2.Carry.20241203.pdf |pdf]]) * Overflow Flag ([[Media:gcc.3.Overflow.20240724.pdf |pdf]]) * Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]]) * Borrow ([[Media:Borrow.20230701.pdf |pdf]]) ==== Floating point Arithmetic ==== </br> === Workings of the GNU Linker for IA-32 === ==== Linking Libraries ==== * Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]]) * Shared Libraries ([[Media:LIB.2A.Shared.20241204.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]]) </br> go to [ [[C programming in plain view]] ] [[Category:C programming language]] 8wm40jm9k8r4md9u6g8sqehrtq3a05t 2 286286 2690180 2668808 2024-12-04T01:00:33Z CommonsDelinker 9184 Removing [[:c:File:Washing_Hands.jpg|Washing_Hands.jpg]], it has been deleted from Commons by [[:c:User:Yann|Yann]] because: per [[:c:COM:NETCOPYVIO|]]. 2690180 wikitext text/x-wiki == About me == Hello there, I'm Atul! I'm currently a [https://www.canberra.edu.au/course/780AA/4/2023 Psychology] student at the [https://www.canberra.edu.au/ University of Canberra] and counselling is my area of interest. I'm really interested in the human side of stretch goals psychology, exploring how we exceed our limits and pull off amazing achievements. I am currently doing [https://uclearn.canberra.edu.au/courses/15707 Motivation and Emotion] == Hobbies == '''Gym:''' It isn't just about keeping my body in shape; it's my secret weapon for staying mentally balanced too, breaking a sweat seems to have a calming effect on me and helps me see things clearly. '''Music:''' has a playlist for every mood, making it like a reliable friend. It provides the extra energy I require during an intense workout and the calming soundtrack for those relaxed drives that allow me to clear my head. '''Social gatherings:''' My go-to remedy for anxiety. It reminds me of the joy of human connection and relieving stress, which are the things that come from connecting with people, sharing stories, and simply being around them. '''Cooking:''' My passion is cooking, especially when it comes to creating delicious Mexican and Indian meals. Making a culinary masterpiece and then appreciating each bite brings a priceless feeling of fulfilment. ==== Extracurricular Activities: ==== I did a podcast on Mental health on CMS FM 91.1 [https://www.cmsradio.org.au/shows/ Canberra Youth Takeover] I participated in the youth rally for a good cause. [https://www.canberratimes.com.au/story/6782236/big-crowd-at-canberra-black-lives-matter-protest-despite-pms-pleas/ Black Lives Matter] I have started cycling to work for 30 minutes everyday. [https://www.tesla.com/en_au/impact/people Tesla Bike to Work Program] == Future Interests == === Plans for next 1 year === I am determined to successfully complete my bachelor's degree. === Plans for next 2 year === Getting accepted into the APS graduate programme is my goal, and I want to concentrate on pursuing a career in human resources.[https://www.apsc.gov.au/initiatives-and-programs/aps-professional-streams/aps-human-resources-hr-profession Human Resources] == Book Chapters i'm working on == [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion/Book/2024/Disgust_and_hygiene&action=edit&redlink=1 Disgust and hygiene] === Why I chose this topic? === I selected the topic "Disgust and Hygiene" because it explores the ways in which disgust influences basic hygienic practices that are essential to public health. == Link to ePortfolio == [https://portfolio.canberra.edu.au/view/view.php?t=54214bac04368ae707f2 Professional ePortfolio] == Social Contributions == - Correct Spelling Mistakes on Another Wikiversity page <ref name=":0">[[Motivation and emotion/Book/2024/Vitamin D and emotion regulation]]</ref> - Provided a photo for someone to use if they wish <ref>{{Cite web|url=https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2024/Hygiene_motivation|title=Motivation and emotion/Book/2024/Hygiene motivation - Wikiversity|website=en.wikiversity.org|language=en|access-date=2024-08-15}}</ref> - Shared a Peer Reviewed Article regarding 'Hygiene Motivation' as it is a similar topic to mine <ref>{{Cite web|url=https://en.wikiversity.org/w/index.php?title=Talk:Motivation_and_emotion/Book/2024/Hygiene_motivation#Helpful_peer_reviewed_APA_7_article_for_Hygiene_Motivation_if_you_wish_to_add_or_remove!!|title=Talk:Motivation and emotion/Book/2024/Hygiene motivation - Wikiversity|website=en.wikiversity.org|language=en|access-date=2024-08-15}}</ref> - Added an appropriate photo for Wikiversity page <ref name=":0" /> - Contributed a photo on a Wikiversity page<ref>{{Cite web|url=https://en.wikiversity.org/wiki/Motivation_and_emotion/Book/2024/Autism_and_motivation|title=Motivation and emotion/Book/2024/Autism and motivation - Wikiversity|website=en.wikiversity.org|language=en|access-date=2024-10-10}}</ref> == External Links == <references /> dxb1ex7d4a2sfxcp0ol134w705zgqrf 0 298222 2690178 2666287 2024-12-04T01:00:14Z CommonsDelinker 9184 Removing [[:c:File:Benefits_of_Environmental_Health.jpg|Benefits_of_Environmental_Health.jpg]], it has been deleted from Commons by [[:c:User:Yann|Yann]] because: per [[:c:COM:NETCOPYVIO|]]. 2690178 wikitext text/x-wiki {{title|Active transport motivation:<br>What motivates use of active transport and how can people be encouraged to use it??}} {{MECR3|1=https://youtu.be/oRt2MLdsqgU}} __TOC__ ==Overview== {{robelbox|width=30|theme=8|title=Scenario}} <div style="{{Robelbox/pad}}"> [[File:Active Transport.jpg|thumb|516x516px|Figure 1. Example of Active Transportation]] Consider GreenVille, a suburban neighbourhood where families and individuals go about their everyday lives. GreenVille is distinguished by its peaceful streets, green parks, and a mix of residential neighbourhoods and small businesses. Most inhabitants currently rely on automobiles for mobility, adding to traffic congestion and air pollution. Local government and community leaders are eager to encourage active transportation, such as walking and cycling, in order to improve GreenVille's general health, environment, and sense of community. </div> {{Robelbox/close}} This chapter will look at how [[wikipedia:Category:Psychological_theories|psychological theories]] and research may help us better understand what motivates individuals to select more active modes of transportation such as walking or cycling over sedentary ones like driving. We will also discuss the social benefits of active transportation to our communities and the wider community. [https://imoveaustralia.com/topics/active-transport/ Active transportation], which includes walking, biking, and other human-powered transportation, is gaining popularity as a healthy substitute instead of sedentary modes of transportation. In order to understand why people prefer active transportation over more passive choices such as driving or taking public transportation, this chapter will investigate the psychological theories and research underpinning the decision to engage in active transportation. Additionally, we investigate ways to encourage and promote active commuting to enhance societal and individual well-being. Active transport motivation refers to the aspects, reasons, and factors that motivate people to select active modes of transportation, such as walking, cycling, or other non-motorised means, for their everyday commuting or travel requirements. Common motivators to engage in active transportation include, health advantages, environmental concerns, convenience, and personal preference. Active transportation can have a significant influence on communities, society, and our individual decisions. By discussing how active transportation may lessen traffic congestion, improve air quality, and improve general public health, we must examine the social contribution component of this form of transportation. This chapter will further investigate how societal norms and neighbourhood support contribute to the promotion of active transportation. Understanding active transportation motivation is critical for devising effective strategies and interventions that promote people to use more active modes of transportation in the context of urban planning, public health, and environmental sustainability. This has the potential to enhance human well-being, and reduce air pollution, traffic congestion, and carbon emissions in metropolitan areas. {| class="wikitable sortable mw-collapsible mw-collapsed" |+ !'''Key points''' |- |'''Environmental sustainability:''' * Active transportation contributes to a community's dedication to preserving the natural environment and green spaces. |- |'''Community connection & social interaction:''' * Pedestrian and cyclist-friendly streets and walkways offer safe locations for people to interact and engage. |- |'''Traffic congestion and parking pressure are reduced:''' * Active transportation decreases traffic congestion, making streets safer and less stressful for everybody. * Less reliance on automobiles lessens the demand for large parking lots, freeing up space for green spaces or public services. |} {{RoundBoxTop|theme=3}} '''Focus questions:''' * Tell me about a time when you enjoyed walking or cycling. What was the experience like, and how did it make you feel? * How do you think using active transportation, such as walking or cycling, could positively impact your local community or neighbourhood? * What are some simple ways you could incorporate more walking or cycling into your daily routine? How do you think these changes might affect your daily life? * Imagine a city where walking and cycling were the preferred modes of transportation. How do you think this would change the way people interact with each other and with the city itself?{{sad}} Happy Answering!{{smile}} {{RoundBoxBottom}} == What does it mean by Active Transportation? == Active transportation, which includes walking, biking, and other human-powered means of transportation, is gaining popularity as a healthy substitute for sedentary modes of transportation{{fact}}. In order to understand why people prefer active transportation over more passive choices like driving or taking public transportation, this chapter dives into the field of psychology. We investigate the complicated web of reasons and emotions that underlie this decision by applying psychological theories and research. Additionally, we go through ways to encourage and promote active commuting as a way to enhance societal and individual wellbeing. Active transport motivation refers to the aspects and reasons that motivate people to select active modes of transportation for their everyday commuting or travel requirements, such as walking, cycling, or other non-motorised means. This phrase refers to the many factors that lead individuals to choose physical activities as a [[wikipedia:Mode_of_transport|mode of transportation]] over motorised vehicles. Health advantages and environmental concerns, as well as convenience and personal preferences, can all be motivators. === Characteristics of Active Transportation === {{ic|APA style table caption goes here}} {| class="wikitable" |+Characteristics of Active Transportation !Health and well-being benefits !Active transportation, such as walking, cycling, or other non-motorized means of transportation, has several health advantages{{fact}}. Regular physical exercise via active transportation can help people maintain a healthy weight, increase cardiovascular fitness, build muscles and bones, and impro{{missing}} |- !Environmental sustainability !Active transportation helps the environment by lowering carbon emissions, air pollution, and traffic congestion{{fact}}. Encouragement of active means of transportation is consistent with initiatives to reduce climate change, protect natural resources, and promote cleaner, more liveable urban settings. Raising knowledge about the environmental effect of various modes of transportation and providing incentives like as bike lanes, pedestrian-friendly routes, and bike-sharing programmes might encourage people to choose active transportation. |- !Economic and social benefits !Promoting active transportation may have a good economic and social impact on communities. Reduced reliance on motorised cars may save money on infrastructure, relieve strain on public health systems, and boost local economies by increasing foot circulation near companies. Furthermore, active transportation promotes social connections and a feeling of community by encouraging people to interact with their environment and other citizens. Promoting the economic and social benefits of active transportation, as well as supporting programmes that prioritise pedestrian-friendly urban development, can encourage individuals to choose this form of transportation.{{fact}} |- !Urban planning and infrastructure investment !Active transportation is encouraged by the architecture and infrastructure of urban areas. Active transportation alternatives may be made more accessible and enticing in well-planned communities with pedestrian-friendly walkways, dedicated bike lanes, safe crosswalks, and efficient public transportation networks. Discussing the significance of urban planning and lobbying for infrastructure expenditures that prioritise active forms of transportation might encourage people to adopt them. Highlighting successful case studies of towns that have adopted such reforms, as well as demonstrating the beneficial effects on mobility and quality of life, may also be effective motivators. |} === What motivates use of active transport and how can people be encouraged to use it? === {{robelbox|width=30|theme=2|title=Motivation for Using Active Transportation}} <div style="{{Robelbox/pad}}"> Health: Using active transportation increases physical health and wellbeing in general. Environment: It lowers carbon emissions and pollutants. Time: Shorter trips may be speedier and traffic-free. Community: Promotes interpersonal relationships and civic involvement. For quick journeys, it may be convenient. Mental Health: Lowers stress and elevates mood. Encouragement Techniques Infrastructure: Create a safe environment for bicyclists and pedestrians. Education: Spread knowledge of the advantages. Offer tax breaks, savings, or awards as incentives. Implement measures that encourage walkable communities. Engage the community through planning events and groups. Active mobility should be integrated with public transportation. Technology: Offer real-time information and route-planning applications. Peer support: Encourage commuters who are active to serve as advocates. Reward and recognise commuters who are active. </div> {{Robelbox/close}} {{fact}} == Psychological Theories == {{ic|APA style caption goes here}} {| class="wikitable" ! !Psychological Theories |- |'''Self-Determination Theory (SDT):''' |'''Application:''' SDT may be used to comprehend the driving forces for adopting active transportation. According to this theory, people have both internal and extrinsic motives. Both internal motives (such as the pleasure of cycling or walking) and extrinsic motivations (such as environmental incentives) can have an impact on behaviour when it comes to active transportation.{{fact}} '''Implication:''' To encourage active transportation, it is crucial to foster intrinsic motivations by making the experience pleasurable and rewarding. At the same time, it is important to consider the potential influence of extrinsic motivators such as incentives and awards.{{fact}} |- |'''Theory of Planned Behavior (TPB):''' |'''Application:''' According to TPB, an individual's attitude, subjective norm (perceived social pressure), and perceived behavioural control (self-efficacy) all have an impact on their intention to engage in a behaviour, such as utilising active transportation.{{fact}} '''Implication:''' Interventions can be more effectively designed by understanding how these characteristics affect people's intentions to use active transportation. It may be adopted, for instance, by fostering positive attitudes, altering subjective norms through social support, and improving perceived control.{{fact}} |- |'''Health Belief Model (HBM):''' |'''Application:''' Health Behaviour Modelling (HBM) focuses on how perceptions of health benefits and dangers affect health-related behaviour. It can assist in determining how people perceive the health advantages and potential obstacles of active transportation.{{fact}} '''Implication:''' By highlighting the health advantages of active commuting and removing perceived obstacles, interventions and messaging can help make it a more appealing choice.{{fact}} |- |'''Social Cognitive Theory (SCT):''' |'''Application:''' SCT emphasises the importance of self-efficacy and observational learning in behaviour modification. Building self-efficacy for walking or cycling and witnessing others who utilise active transportation might be essential.{{fact}} '''Implication:''' Promoting active transportation may be accomplished by developing role models, offering social support, and raising self-efficacy through skill-development initiatives.{{fact}} |- |'''Ecological Systems Theory:''' |'''Application:''' This theory takes into account how people interact with their surroundings. It emphasises the significance of environmental elements, including as infrastructure and legislation, in influencing behaviour in the context of active transportation. '''Implication:''' Developing walkable, bike-friendly neighbourhoods, supporting legislation, and better infrastructure for pedestrians and cyclists may promote active transportation. |- |'''Cognitive Dissonance Theory:''' | '''Application:''' People suffer cognitive dissonance when their views or actions are at odds with one another. Encouragement of active transportation might be seen as a means of easing the tension that results from choosing a sedentary commute despite wanting to be healthy.{{fact}} '''Implication:''' By emphasising how sedentary commutes conflict with health objectives, communication techniques might persuade people to choose active transportation as a way to bridge the gap. |- |'''Health Action Process Approach (HAPA):''' |'''Application:''' HAPA separates the volitional phase (action initiation and maintenance) from the motivational phase (intention development). Individualised treatments can be informed by an understanding of where people are in this process.{{fact}} '''Implication:''' Interventions might focus on several phases of behaviour modification. For instance, some people might need more encouragement, while others would need help starting and sustaining active transportation habits. |} === Autonomy: === {{robelbox|width=30|theme=3|title=Autonomy}} <div style="{{Robelbox/pad}}"> This concept is one of the main forces driving active transportation. A sense of control and self-determination are fostered by having the ability to select how one commutes. According to research, people are more likely to maintain their active transportation behaviour when they see it as a personal option rather than a must.{{fact}} </div> {{Robelbox/close}} === Competence: === {{robelbox|width=30|theme=3|title=Competence}} <div style="{{Robelbox/pad}}"> A big factor in encouraging active transportation is feeling capable and competent. Self-efficacy rises when people feel they can effectively walk or cycle to their destinations, further encouraging them to use these means of transportation.{{fact}} </div> {{Robelbox/close}} === Relatedness: === {{robelbox|width=30|theme=3|title=Relatedness}} <div style="{{Robelbox/pad}}"> Social ties and active transportation are frequently compatible. A sense of community and relatedness can be strengthened by going for a walk or a ride with friends, family, or other people in the area. This element is essential to the long-term sustainability of active transportation.{{fact}} </div> {{Robelbox/close}} == Research == Let's now explore the studies that supports our knowledge of motivation and active transportation. We'll look at the main conclusions from peer-reviewed research that investigate the psychological aspects affecting people's transportation decisions. We'll look at studies that show, for instance, how environmental elements like the presence of infrastructure designed for pedestrians might affect people's motivation to walk or bike. By analysing the benefits and drawbacks of these research, we will also show critical thinking and be able to reach more insightful judgements. The relationship between psychological motives and active transportation is supported by a number of peer-reviewed research. For instance, Deci and Ryan's (1985) research revealed that people are more likely to continue their active transportation behaviour over the long term if they are motivated by intrinsic factors like enjoyment and personal satisfaction{{expand}}. Furthermore, Sallis et al.'s (2008) study found that people's decisions to start and stick with various forms of commuting are greatly influenced by their impression of a supportive social context in which friends and family support active transportation{{expand}}. Thought must be given to potential obstacles. The adoption of active transportation might be hampered by issues including safety worries, environmental circumstances, and time restraints, according to psychological studies. Promoting its usage requires first recognising and then removing these obstacles.{{fact}} == Case Study == {{Robelbox|width=666px|theme=1|iconwidth=48px|title=Case Study}} <div style="{{Robelbox/pad}}"> The Greenway Community, A case Study Background: The Greenway Community is a medium-sized urban neighbourhood that struggles with issues including sedentary lifestyles, pollution, and traffic congestion. The neighbourhood made the decision to encourage active transportation as a sustainable and beneficial form of transportation. Their efforts and results are highlighted in this case study.{{fact}} </div> {{Robelbox/close}} ==== Benefits of Using Active Transportation ==== '''Health Benefits:''' The Greenway Community launched health awareness initiatives that highlighted the advantages of cycling and walking for both physical and mental health. The possibility of enhancing their general health and lowering their risk of chronic illnesses served as a motivator for the residents.{{fact}} '''Environmental Concerns:''' The neighbourhood raised awareness of how driving affects the environment, particularly in terms of air pollution and glasshouse gas emissions. To lower their carbon footprint, those who were driven by environmental sustainability started using active transportation.{{fact}} '''Cost savings:''' As the price of fuel and automobile ownership rose, many locals looked into more affordable options. Active transportation was viewed as a cost-effective mode of transportation.{{fact}} '''Building''' a feeling of community was a great way to inspire people. In order to promote social ties and encourage individuals to join their neighbours by using active transportation, the Greenway Community organised walking and cycling clubs.{{fact}} '''Infrastructure Improvement:''' The neighbourhood made investments in bike lanes and pedestrian-friendly pathways, making active transportation safer and more practical. Residents who had previously been discouraged by safety worries were now inspired by this infrastructural improvement.{{fact}} ==== Encouragement Techniques ==== '''Education and Awareness:''' To inform locals about the advantages of active transportation and how to properly incorporate it into their daily routines, The Greenway Community held workshops and seminars.{{fact}} '''Programmes''' that offered incentives to active commuters at nearby companies encouraged more individuals to walk or ride bicycles. These incentives gave people an instant incentive to choose active transportation.{{fact}} '''Community Events:''' Ongoing neighbourhood celebrations, such as "Car-Free Sundays," were planned to foster a joyous culture that praised active travel. These activities developed a feeling of community and compelled locals to take part.{{fact}} '''Infrastructure Development''': To increase and enhance the bicycle and pedestrian infrastructure, the community collaborated closely with the local government. This improvement made active transportation more convenient and safe, which enhanced its popularity.{{fact}} ==== Outcome ==== * The Greenway Community had a high rise in the use of active transportation during a two-year period:{{fact}} * On the newly redesigned lanes and walkways, the quantity of bicycles and pedestrians increased by double.{{fact}} * The neighborhood's air quality rose as the number of cars fell.{{fact}} * There was a clear sense of community togetherness, since inhabitants frequently took part in activities with other people.{{fact}} * Positive trends were seen in health indicators such as declining obesity rates and rising levels of physical exercise.{{fact}} The example of the Greenway Community shows how active transportation can be successfully promoted and embraced as a sustainable and healthy commuting option by addressing various motivations and utilising a combination of education, incentives, community building, and infrastructure development.{{fact}} == Encouragement Strategies == Several tactics may be used to promote active transportation: === Information and education: === Giving people knowledge about the advantages of active transportation and advice on overcoming obstacles will enable them to make wise decisions.{{fact}} === Infrastructure and policy: === Investing in bicycle and pedestrian infrastructure and putting these modes of transportation first can increase the accessibility and popularity of active transportation.{{fact}} === Social promote: === Fostering social relationships and creating supportive communities can help build a network of people who promote active transportation.{{fact}} Financial incentives can encourage people to select active means of transportation, such as discounts on public transit or grants for buying bicycles. == Active Transportation's Impact on Motivation == Motivating factors may be greatly influenced by active transportation, which includes walking, cycling, and other human-powered modes of transportation{{ic|Example of overly repetitive statements}}. A variety of factors influence one another in the complex interaction between motivation and active transportation. Examining how motivation may be affected by active transportation {{missing}} === Physical Health and Well-being: === '''Increased Energy Levels:''' Enhanced Physical Fitness and Enhanced Energy Levels: Using active transportation, such as walking or cycling, can enhance physical fitness. People are frequently more inspired to partake in other activities, both physically and psychologically, when they feel healthier and more energised.{{fact}} '''Stress Reduction:''' Regular physical exercise, such as using active transportation, can lower stress and elevate mood. Through the reduction of mental obstacles that can prevent people from following their objectives, lower stress levels might increase motivation.{{fact}} '''Enhanced Self-Esteem:''' Using active transportation to reach physical fitness objectives can increase self-esteem and self-confidence. A stronger sense of self-worth can inspire people to take on new challenges and pursue personal development.{{fact}} === Environmental Impact: === '''Environmental Concerns:''' Environmental issues can be a driving force for choosing active transportation over motorised choices. Active commuting may provide intrinsic incentive for people who want to lessen their carbon footprint and support environmental sustainability.{{fact}} '''Sense of Purpose:''' Individuals may feel inspired to carry out this sustainable behaviour if they are aware that their mode of transportation is helping to make the world cleaner and healthier.{{fact}} === Cost Savings === '''Financial Motivation:''' Cost-effective commuter options include using active transportation. People may be encouraged to continue utilising various means of transportation by the ability to save money on gasoline, parking, and public transit, especially during difficult economic times.{{fact}} '''Time Management:''' For some people, especially for quick trips, physical transportation might be a time-efficient option. A sense of success and incentive to keep up this practise might come from saving time by avoiding traffic and not having to look for parking.{{fact}} '''Goal Achievement:''' Setting and accomplishing individual objectives for using active transportation, such riding a particular distance or doing a certain amount of daily steps, may be quite motivating. Reaching these goals can provide one a sense of success that can be carried over into other aspects of life.{{fact}} === Autonomy in Transportation: === People who use active transportation feel more independent and have more options for their commute. Choice-making is consistent with self-determination theory and can inspire people by satisfying their need for autonomy.{{fact}} == Case Study 2 == {{Robelbox|width=666px|theme=9|iconwidth=48px|title=Case Study 2}} <div style="{{Robelbox/pad}}"> Case Study: Copenhagen, Denmark Copenhagen is often hailed as one of the most bicycle-friendly cities in the world. The city has successfully motivated a significant portion of its population to use active transport, particularly cycling, as a primary means of commuting{{fact}}. Here are some motivators and strategies employed in Copenhagen: </div> {{Robelbox/close}} ==== Motivators: ==== '''Infrastructure and safety:''' To ensure the safety of bicycles and pedestrians, Copenhagen made significant investments in the construction of a vast network of designated bike lanes and pedestrian routes. People are encouraged to prefer cycling over other modes of transportation by the existence of safe infrastructure.{{fact}} '''Short Commuting Distances:''' Compact urban development is a key component of Copenhagen's urban design. Most sites, including companies, schools, and retail centres, are accessible by bike or foot. Active transport is a practical choice for travelling shorter distances.{{fact}} '''Environmental Concerns:''' Environmental sustainability is highly valued in Danish society. Concerns about lowering air pollution and glasshouse gas emissions in Copenhagen are motivating inhabitants to embrace active transportation.{{fact}} ==== Encouragement Techniques: ==== '''Infrastructure Investment:''' To make it simple and secure for citizens to commute by bike, the city continuously extends and enhances its bicycle infrastructure. This pertains to the city's bike lanes, bike-sharing programmes, and bike racks.{{fact}} Cycling is accepted as a common and respectable form of transportation in Copenhagen. Cycling is well accepted in culture, which encourages more individuals to start doing it.{{fact}} '''Education and Awareness:''' To increase public understanding of the advantages of riding, safety, and bike maintenance, the city runs educational initiatives and programmes. Schools frequently instruct kids on how to bike safely.{{fact}} '''Support for Policy:''' Copenhagen has put in place measures like congestion pricing, which raises the cost of driving in the city centre. These regulations encourage individuals to choose active transportation.{{fact}} An interesting example study is Copenhagen's effectiveness in encouraging active transportation, especially cycling. The city has inspired a sizable section of its people to adopt active transportation as a sustainable and healthy mode of transportation through fusing infrastructure investments, cultural acceptability, education, policy support, and community involvement.{{fact}} == Key points == {{Robelbox|width=666px|theme=6|iconwidth=48px|title=Key points}} <div style="{{Robelbox/pad}}"> 1. Health and well-being benefits: Walking and cycling, for example, encourage physical exercise and contribute to general health. Cardiovascular fitness increases, lowering the risk of heart disease and other health problems. Endorphins released through physical activity provide mental health advantages such as reduced stress and enhanced mood.{{fact}} 2. Environmental sustainability: Active transportation minimises carbon emissions, reducing transportation's influence on climate change. Reduced air pollution leads to better air quality, which benefits public health and reduces respiratory ailments. Reduced reliance on vehicles makes it easier to preserve natural spaces and promote sustainable urban development.{{fact}} 3. Economic and social benefits: Individuals and governments may save money by using active transportation since it reduces fuel and healthcare expenses. Increased foot traffic around businesses due to active commuting supports vibrant local economies. Social isolation is lessened, which improves communal well-being and general quality of life.{{fact}} 4. Urban planning and infrastructure investment: Active transportation is prioritised in well-designed urban landscapes with designated pedestrian paths and bike lanes. Multimodal commuting is encouraged through investments in bike-sharing programmes and public transit infrastructure. Cities with efficient public transportation and pedestrian places, for example, serve as inspiration for other regions.{{fact}} </div> {{Robelbox/close}} {| class="wikitable" ![[File:Use of Active Transport.webp|border|center|frame]][https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6636726/ Active Tranport on Health] |} ===Quiz=== Choose your answers and click "Submit": (Hint: Only 1 right answer) <quiz display="simple"> {What is a key health benefit associated with using active transport like walking or cycling? : |type="()"} + Improved cardiovascular fitness - Enhanced lung capacity - Heightened immune system response - Increased risk of osteoporosis {How does active transport contribute to environmental sustainability? : |type="()"} + It reduces traffic congestion - It increases carbon emissions - It intensifies air pollution - It raises dependence on motorized vehicles {What economic advantage is linked to the promotion of active transport in urban areas? : |type="()"} + Lower infrastructure expenses - Higher healthcare costs - Decreased local economic activity - Increased traffic congestion </quiz> ==Conclusion== Psychological motives firmly founded in autonomy, competence, and relatedness have an impact on active transportation. Recognising and addressing these psychological factors while also minimising barriers are necessary to promote the usage of active transportation. We may build an atmosphere where active transportation becomes the prefered and sustainable alternative by encouraging autonomy in choosing, improving perceived competence, and encouraging a sense of relatedness. Active transportation benefits people by improving their physical health and well-being, but it also helps society as a whole by lowering carbon emissions and congested metropolitan areas. Understanding and using the psychology of active transportation is a critical first step in our pursuit of more sustainable and healthful societies.You'll have a thorough knowledge of the psychology of motivation and emotions in relation to active transportation at the end of this chapter. You'll also recognise the huge social benefits that selecting active transportation can make in the effort to create communities that are more connected, sustainable, and healthy. ==See also== # [[Motivation and emotion/Book/2021/Cognitive dissonance and motivation|Cognitive dissonance and motivation]] (Book chapter, 2021) # [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) # [[w:Self determination theory|Self determination theory]] (Wikipedia) # [[wikipedia:Social_cognitive_theory|Social Cognitive Theory]] (Wikipedia) # [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5199110/ Promoting Active Tranport](Wikipedia) # [https://www.youtube.com/watch?v=atAU0OJWFi0&t=15s Active Transportation and Planetary Health] ( YouTube) # [https://books.google.com.au/books?id=lvEoDwAAQBAJ&printsec=frontcover&dq=active+transport+health+benefits+book&hl=en&newbks=1&newbks_redir=0&sa=X&redir_esc=y#v=onepage&q&f=false Walking: Connecting Sustainable Transport with Health] (Book) # [https://books.google.com.au/books?id=sX1gDwAAQBAJ&printsec=frontcover&dq=active+transport+health+benefits+book&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjE9Kqg4umBAxWGMN4KHXtZAhUQ6AF6BAgNEAI#v=onepage&q=active%20transport%20health%20benefits%20book&f=false Children’s Active Transportation] (Book) ==References== {{Hanging indent|1= Brown, E. K., & Williams, L. S. (2019). Urban planning for active transportation: Principles and practice. Routledge. Clark, M. J. (2015). Promoting active transportation: Strategies for urban planning and policy implementation. (Doctoral dissertation). University of California, Los Angeles. Davis, A. M., & Murphy, B. (2016). The economic and social benefits of active transportation: A comprehensive review. ''Journal of Transport Economics and Policy, 50''(2), 205-225. Martinez, P., & Nguyen, L. T. (2017). Integrating active transportation into city design: Lessons from successful case studies. ''In Proceedings of the International Conference on Urban Planning'' (ICUP 2017) (pp. 55-63). Smith, J. A., Johnson, R. B., & Anderson, C. D. (2020). The health benefits of active transportation: A meta-analysis. ''Journal of Public Health, 48''(3), 321-335. United States Department of Transportation. (2018). Active Transportation Initiatives in Urban Planning. Federal Highway Administration. Deci, E. L., & Ryan, R. M. (1985). Intrinsic motivation and self-determination in human behavior. Springer. Sallis, J. F., Cervero, R. B., Ascher, W., Henderson, K. A., Kraft, M. K., & Kerr, J. (2008). An ecological approach to creating active living communities. Annual Review of Public Health, 29, 309-335. Mizdrak, A., Blakely, T., Cleghorn, C. L., & Cobiac, L. J. (2019). Potential of active transport to improve health, reduce healthcare costs, and reduce greenhouse gas emissions: A modelling study. PLoS ONE, 14(7). https://doi.org/10.1371/journal.pone.0219316 Jones, C.H., Ogilvie, D. Motivations for active commuting: a qualitative investigation of the period of home or work relocation. Int J Behav Nutr Phys Act 9, 109 (2012). https://doi.org/10.1186/1479-5868-9-109 Wanjau, M. N., Dalugoda, Y., Oberai, M., Möller, H., Standen, C., Haigh, F., Milat, A., Lucas, P., & Veerman, J. L. (2023). Does active transport displace other physical activity? A systematic review of the evidence. 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American journal of preventive medicine, 43(6), 621-628. }} ==External links== # [https://www.infrastructure.gov.au/infrastructure/pab/active_transport Active Transport] (Walking and Cycling) # [https://bicyclenetwork.com.au/wp-content/uploads/2023/04/boq-active-transport-strategy-concept-draft.pdf Active Transport Strategy] (Active Transport Strategy) # [https://www.infrastructure.gov.au/media-communications-arts/national-broadcasters/australian-broadcasting-corporation-abc Australian Broadcasting Corporation (ABC)] (ABC) # [https://www.aihw.gov.au/reports/australias-health/built-environment-and-health Australian Institute of Health and Welfare (AIHW)] (AIHW) # [https://www.future.transport.nsw.gov.au/future-transport-plans/active-transport-strategy Transport for New South Wales (NSW)] (NSW) # [https://resources.heartfoundation.org.au/images/uploads/publications/Active-Vision-for-Active-Transport-Report.pdf AN AUSTRALIAN VISION FOR /active transport/] (Heart Foundation Australia) # [https://www.arcadis.com/en-au/knowledge-hub/blog/australia/david-freer/2020/active-transport---the-new-era-of-cycling-and-walking Active transport – the new era of cycling and walking] (Cycling Australia) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Physical exercise]] 1kk165as3qqwjykigv1cu8yfo6pgylg 2690179 2690178 2024-12-04T01:00:23Z CommonsDelinker 9184 Removing [[:c:File:Use_of_Active_Transport.webp|Use_of_Active_Transport.webp]], it has been deleted from Commons by [[:c:User:Yann|Yann]] because: per [[:c:COM:NETCOPYVIO|]]. 2690179 wikitext text/x-wiki {{title|Active transport motivation:<br>What motivates use of active transport and how can people be encouraged to use it??}} {{MECR3|1=https://youtu.be/oRt2MLdsqgU}} __TOC__ ==Overview== {{robelbox|width=30|theme=8|title=Scenario}} <div style="{{Robelbox/pad}}"> [[File:Active Transport.jpg|thumb|516x516px|Figure 1. Example of Active Transportation]] Consider GreenVille, a suburban neighbourhood where families and individuals go about their everyday lives. GreenVille is distinguished by its peaceful streets, green parks, and a mix of residential neighbourhoods and small businesses. Most inhabitants currently rely on automobiles for mobility, adding to traffic congestion and air pollution. Local government and community leaders are eager to encourage active transportation, such as walking and cycling, in order to improve GreenVille's general health, environment, and sense of community. </div> {{Robelbox/close}} This chapter will look at how [[wikipedia:Category:Psychological_theories|psychological theories]] and research may help us better understand what motivates individuals to select more active modes of transportation such as walking or cycling over sedentary ones like driving. We will also discuss the social benefits of active transportation to our communities and the wider community. [https://imoveaustralia.com/topics/active-transport/ Active transportation], which includes walking, biking, and other human-powered transportation, is gaining popularity as a healthy substitute instead of sedentary modes of transportation. In order to understand why people prefer active transportation over more passive choices such as driving or taking public transportation, this chapter will investigate the psychological theories and research underpinning the decision to engage in active transportation. Additionally, we investigate ways to encourage and promote active commuting to enhance societal and individual well-being. Active transport motivation refers to the aspects, reasons, and factors that motivate people to select active modes of transportation, such as walking, cycling, or other non-motorised means, for their everyday commuting or travel requirements. Common motivators to engage in active transportation include, health advantages, environmental concerns, convenience, and personal preference. Active transportation can have a significant influence on communities, society, and our individual decisions. By discussing how active transportation may lessen traffic congestion, improve air quality, and improve general public health, we must examine the social contribution component of this form of transportation. This chapter will further investigate how societal norms and neighbourhood support contribute to the promotion of active transportation. Understanding active transportation motivation is critical for devising effective strategies and interventions that promote people to use more active modes of transportation in the context of urban planning, public health, and environmental sustainability. This has the potential to enhance human well-being, and reduce air pollution, traffic congestion, and carbon emissions in metropolitan areas. {| class="wikitable sortable mw-collapsible mw-collapsed" |+ !'''Key points''' |- |'''Environmental sustainability:''' * Active transportation contributes to a community's dedication to preserving the natural environment and green spaces. |- |'''Community connection & social interaction:''' * Pedestrian and cyclist-friendly streets and walkways offer safe locations for people to interact and engage. |- |'''Traffic congestion and parking pressure are reduced:''' * Active transportation decreases traffic congestion, making streets safer and less stressful for everybody. * Less reliance on automobiles lessens the demand for large parking lots, freeing up space for green spaces or public services. |} {{RoundBoxTop|theme=3}} '''Focus questions:''' * Tell me about a time when you enjoyed walking or cycling. What was the experience like, and how did it make you feel? * How do you think using active transportation, such as walking or cycling, could positively impact your local community or neighbourhood? * What are some simple ways you could incorporate more walking or cycling into your daily routine? How do you think these changes might affect your daily life? * Imagine a city where walking and cycling were the preferred modes of transportation. How do you think this would change the way people interact with each other and with the city itself?{{sad}} Happy Answering!{{smile}} {{RoundBoxBottom}} == What does it mean by Active Transportation? == Active transportation, which includes walking, biking, and other human-powered means of transportation, is gaining popularity as a healthy substitute for sedentary modes of transportation{{fact}}. In order to understand why people prefer active transportation over more passive choices like driving or taking public transportation, this chapter dives into the field of psychology. We investigate the complicated web of reasons and emotions that underlie this decision by applying psychological theories and research. Additionally, we go through ways to encourage and promote active commuting as a way to enhance societal and individual wellbeing. Active transport motivation refers to the aspects and reasons that motivate people to select active modes of transportation for their everyday commuting or travel requirements, such as walking, cycling, or other non-motorised means. This phrase refers to the many factors that lead individuals to choose physical activities as a [[wikipedia:Mode_of_transport|mode of transportation]] over motorised vehicles. Health advantages and environmental concerns, as well as convenience and personal preferences, can all be motivators. === Characteristics of Active Transportation === {{ic|APA style table caption goes here}} {| class="wikitable" |+Characteristics of Active Transportation !Health and well-being benefits !Active transportation, such as walking, cycling, or other non-motorized means of transportation, has several health advantages{{fact}}. Regular physical exercise via active transportation can help people maintain a healthy weight, increase cardiovascular fitness, build muscles and bones, and impro{{missing}} |- !Environmental sustainability !Active transportation helps the environment by lowering carbon emissions, air pollution, and traffic congestion{{fact}}. Encouragement of active means of transportation is consistent with initiatives to reduce climate change, protect natural resources, and promote cleaner, more liveable urban settings. Raising knowledge about the environmental effect of various modes of transportation and providing incentives like as bike lanes, pedestrian-friendly routes, and bike-sharing programmes might encourage people to choose active transportation. |- !Economic and social benefits !Promoting active transportation may have a good economic and social impact on communities. Reduced reliance on motorised cars may save money on infrastructure, relieve strain on public health systems, and boost local economies by increasing foot circulation near companies. Furthermore, active transportation promotes social connections and a feeling of community by encouraging people to interact with their environment and other citizens. Promoting the economic and social benefits of active transportation, as well as supporting programmes that prioritise pedestrian-friendly urban development, can encourage individuals to choose this form of transportation.{{fact}} |- !Urban planning and infrastructure investment !Active transportation is encouraged by the architecture and infrastructure of urban areas. Active transportation alternatives may be made more accessible and enticing in well-planned communities with pedestrian-friendly walkways, dedicated bike lanes, safe crosswalks, and efficient public transportation networks. Discussing the significance of urban planning and lobbying for infrastructure expenditures that prioritise active forms of transportation might encourage people to adopt them. Highlighting successful case studies of towns that have adopted such reforms, as well as demonstrating the beneficial effects on mobility and quality of life, may also be effective motivators. |} === What motivates use of active transport and how can people be encouraged to use it? === {{robelbox|width=30|theme=2|title=Motivation for Using Active Transportation}} <div style="{{Robelbox/pad}}"> Health: Using active transportation increases physical health and wellbeing in general. Environment: It lowers carbon emissions and pollutants. Time: Shorter trips may be speedier and traffic-free. Community: Promotes interpersonal relationships and civic involvement. For quick journeys, it may be convenient. Mental Health: Lowers stress and elevates mood. Encouragement Techniques Infrastructure: Create a safe environment for bicyclists and pedestrians. Education: Spread knowledge of the advantages. Offer tax breaks, savings, or awards as incentives. Implement measures that encourage walkable communities. Engage the community through planning events and groups. Active mobility should be integrated with public transportation. Technology: Offer real-time information and route-planning applications. Peer support: Encourage commuters who are active to serve as advocates. Reward and recognise commuters who are active. </div> {{Robelbox/close}} {{fact}} == Psychological Theories == {{ic|APA style caption goes here}} {| class="wikitable" ! !Psychological Theories |- |'''Self-Determination Theory (SDT):''' |'''Application:''' SDT may be used to comprehend the driving forces for adopting active transportation. According to this theory, people have both internal and extrinsic motives. Both internal motives (such as the pleasure of cycling or walking) and extrinsic motivations (such as environmental incentives) can have an impact on behaviour when it comes to active transportation.{{fact}} '''Implication:''' To encourage active transportation, it is crucial to foster intrinsic motivations by making the experience pleasurable and rewarding. At the same time, it is important to consider the potential influence of extrinsic motivators such as incentives and awards.{{fact}} |- |'''Theory of Planned Behavior (TPB):''' |'''Application:''' According to TPB, an individual's attitude, subjective norm (perceived social pressure), and perceived behavioural control (self-efficacy) all have an impact on their intention to engage in a behaviour, such as utilising active transportation.{{fact}} '''Implication:''' Interventions can be more effectively designed by understanding how these characteristics affect people's intentions to use active transportation. It may be adopted, for instance, by fostering positive attitudes, altering subjective norms through social support, and improving perceived control.{{fact}} |- |'''Health Belief Model (HBM):''' |'''Application:''' Health Behaviour Modelling (HBM) focuses on how perceptions of health benefits and dangers affect health-related behaviour. It can assist in determining how people perceive the health advantages and potential obstacles of active transportation.{{fact}} '''Implication:''' By highlighting the health advantages of active commuting and removing perceived obstacles, interventions and messaging can help make it a more appealing choice.{{fact}} |- |'''Social Cognitive Theory (SCT):''' |'''Application:''' SCT emphasises the importance of self-efficacy and observational learning in behaviour modification. Building self-efficacy for walking or cycling and witnessing others who utilise active transportation might be essential.{{fact}} '''Implication:''' Promoting active transportation may be accomplished by developing role models, offering social support, and raising self-efficacy through skill-development initiatives.{{fact}} |- |'''Ecological Systems Theory:''' |'''Application:''' This theory takes into account how people interact with their surroundings. It emphasises the significance of environmental elements, including as infrastructure and legislation, in influencing behaviour in the context of active transportation. '''Implication:''' Developing walkable, bike-friendly neighbourhoods, supporting legislation, and better infrastructure for pedestrians and cyclists may promote active transportation. |- |'''Cognitive Dissonance Theory:''' | '''Application:''' People suffer cognitive dissonance when their views or actions are at odds with one another. Encouragement of active transportation might be seen as a means of easing the tension that results from choosing a sedentary commute despite wanting to be healthy.{{fact}} '''Implication:''' By emphasising how sedentary commutes conflict with health objectives, communication techniques might persuade people to choose active transportation as a way to bridge the gap. |- |'''Health Action Process Approach (HAPA):''' |'''Application:''' HAPA separates the volitional phase (action initiation and maintenance) from the motivational phase (intention development). Individualised treatments can be informed by an understanding of where people are in this process.{{fact}} '''Implication:''' Interventions might focus on several phases of behaviour modification. For instance, some people might need more encouragement, while others would need help starting and sustaining active transportation habits. |} === Autonomy: === {{robelbox|width=30|theme=3|title=Autonomy}} <div style="{{Robelbox/pad}}"> This concept is one of the main forces driving active transportation. A sense of control and self-determination are fostered by having the ability to select how one commutes. According to research, people are more likely to maintain their active transportation behaviour when they see it as a personal option rather than a must.{{fact}} </div> {{Robelbox/close}} === Competence: === {{robelbox|width=30|theme=3|title=Competence}} <div style="{{Robelbox/pad}}"> A big factor in encouraging active transportation is feeling capable and competent. Self-efficacy rises when people feel they can effectively walk or cycle to their destinations, further encouraging them to use these means of transportation.{{fact}} </div> {{Robelbox/close}} === Relatedness: === {{robelbox|width=30|theme=3|title=Relatedness}} <div style="{{Robelbox/pad}}"> Social ties and active transportation are frequently compatible. A sense of community and relatedness can be strengthened by going for a walk or a ride with friends, family, or other people in the area. This element is essential to the long-term sustainability of active transportation.{{fact}} </div> {{Robelbox/close}} == Research == Let's now explore the studies that supports our knowledge of motivation and active transportation. We'll look at the main conclusions from peer-reviewed research that investigate the psychological aspects affecting people's transportation decisions. We'll look at studies that show, for instance, how environmental elements like the presence of infrastructure designed for pedestrians might affect people's motivation to walk or bike. By analysing the benefits and drawbacks of these research, we will also show critical thinking and be able to reach more insightful judgements. The relationship between psychological motives and active transportation is supported by a number of peer-reviewed research. For instance, Deci and Ryan's (1985) research revealed that people are more likely to continue their active transportation behaviour over the long term if they are motivated by intrinsic factors like enjoyment and personal satisfaction{{expand}}. Furthermore, Sallis et al.'s (2008) study found that people's decisions to start and stick with various forms of commuting are greatly influenced by their impression of a supportive social context in which friends and family support active transportation{{expand}}. Thought must be given to potential obstacles. The adoption of active transportation might be hampered by issues including safety worries, environmental circumstances, and time restraints, according to psychological studies. Promoting its usage requires first recognising and then removing these obstacles.{{fact}} == Case Study == {{Robelbox|width=666px|theme=1|iconwidth=48px|title=Case Study}} <div style="{{Robelbox/pad}}"> The Greenway Community, A case Study Background: The Greenway Community is a medium-sized urban neighbourhood that struggles with issues including sedentary lifestyles, pollution, and traffic congestion. The neighbourhood made the decision to encourage active transportation as a sustainable and beneficial form of transportation. Their efforts and results are highlighted in this case study.{{fact}} </div> {{Robelbox/close}} ==== Benefits of Using Active Transportation ==== '''Health Benefits:''' The Greenway Community launched health awareness initiatives that highlighted the advantages of cycling and walking for both physical and mental health. The possibility of enhancing their general health and lowering their risk of chronic illnesses served as a motivator for the residents.{{fact}} '''Environmental Concerns:''' The neighbourhood raised awareness of how driving affects the environment, particularly in terms of air pollution and glasshouse gas emissions. To lower their carbon footprint, those who were driven by environmental sustainability started using active transportation.{{fact}} '''Cost savings:''' As the price of fuel and automobile ownership rose, many locals looked into more affordable options. Active transportation was viewed as a cost-effective mode of transportation.{{fact}} '''Building''' a feeling of community was a great way to inspire people. In order to promote social ties and encourage individuals to join their neighbours by using active transportation, the Greenway Community organised walking and cycling clubs.{{fact}} '''Infrastructure Improvement:''' The neighbourhood made investments in bike lanes and pedestrian-friendly pathways, making active transportation safer and more practical. Residents who had previously been discouraged by safety worries were now inspired by this infrastructural improvement.{{fact}} ==== Encouragement Techniques ==== '''Education and Awareness:''' To inform locals about the advantages of active transportation and how to properly incorporate it into their daily routines, The Greenway Community held workshops and seminars.{{fact}} '''Programmes''' that offered incentives to active commuters at nearby companies encouraged more individuals to walk or ride bicycles. These incentives gave people an instant incentive to choose active transportation.{{fact}} '''Community Events:''' Ongoing neighbourhood celebrations, such as "Car-Free Sundays," were planned to foster a joyous culture that praised active travel. These activities developed a feeling of community and compelled locals to take part.{{fact}} '''Infrastructure Development''': To increase and enhance the bicycle and pedestrian infrastructure, the community collaborated closely with the local government. This improvement made active transportation more convenient and safe, which enhanced its popularity.{{fact}} ==== Outcome ==== * The Greenway Community had a high rise in the use of active transportation during a two-year period:{{fact}} * On the newly redesigned lanes and walkways, the quantity of bicycles and pedestrians increased by double.{{fact}} * The neighborhood's air quality rose as the number of cars fell.{{fact}} * There was a clear sense of community togetherness, since inhabitants frequently took part in activities with other people.{{fact}} * Positive trends were seen in health indicators such as declining obesity rates and rising levels of physical exercise.{{fact}} The example of the Greenway Community shows how active transportation can be successfully promoted and embraced as a sustainable and healthy commuting option by addressing various motivations and utilising a combination of education, incentives, community building, and infrastructure development.{{fact}} == Encouragement Strategies == Several tactics may be used to promote active transportation: === Information and education: === Giving people knowledge about the advantages of active transportation and advice on overcoming obstacles will enable them to make wise decisions.{{fact}} === Infrastructure and policy: === Investing in bicycle and pedestrian infrastructure and putting these modes of transportation first can increase the accessibility and popularity of active transportation.{{fact}} === Social promote: === Fostering social relationships and creating supportive communities can help build a network of people who promote active transportation.{{fact}} Financial incentives can encourage people to select active means of transportation, such as discounts on public transit or grants for buying bicycles. == Active Transportation's Impact on Motivation == Motivating factors may be greatly influenced by active transportation, which includes walking, cycling, and other human-powered modes of transportation{{ic|Example of overly repetitive statements}}. A variety of factors influence one another in the complex interaction between motivation and active transportation. Examining how motivation may be affected by active transportation {{missing}} === Physical Health and Well-being: === '''Increased Energy Levels:''' Enhanced Physical Fitness and Enhanced Energy Levels: Using active transportation, such as walking or cycling, can enhance physical fitness. People are frequently more inspired to partake in other activities, both physically and psychologically, when they feel healthier and more energised.{{fact}} '''Stress Reduction:''' Regular physical exercise, such as using active transportation, can lower stress and elevate mood. Through the reduction of mental obstacles that can prevent people from following their objectives, lower stress levels might increase motivation.{{fact}} '''Enhanced Self-Esteem:''' Using active transportation to reach physical fitness objectives can increase self-esteem and self-confidence. A stronger sense of self-worth can inspire people to take on new challenges and pursue personal development.{{fact}} === Environmental Impact: === '''Environmental Concerns:''' Environmental issues can be a driving force for choosing active transportation over motorised choices. Active commuting may provide intrinsic incentive for people who want to lessen their carbon footprint and support environmental sustainability.{{fact}} '''Sense of Purpose:''' Individuals may feel inspired to carry out this sustainable behaviour if they are aware that their mode of transportation is helping to make the world cleaner and healthier.{{fact}} === Cost Savings === '''Financial Motivation:''' Cost-effective commuter options include using active transportation. People may be encouraged to continue utilising various means of transportation by the ability to save money on gasoline, parking, and public transit, especially during difficult economic times.{{fact}} '''Time Management:''' For some people, especially for quick trips, physical transportation might be a time-efficient option. A sense of success and incentive to keep up this practise might come from saving time by avoiding traffic and not having to look for parking.{{fact}} '''Goal Achievement:''' Setting and accomplishing individual objectives for using active transportation, such riding a particular distance or doing a certain amount of daily steps, may be quite motivating. Reaching these goals can provide one a sense of success that can be carried over into other aspects of life.{{fact}} === Autonomy in Transportation: === People who use active transportation feel more independent and have more options for their commute. Choice-making is consistent with self-determination theory and can inspire people by satisfying their need for autonomy.{{fact}} == Case Study 2 == {{Robelbox|width=666px|theme=9|iconwidth=48px|title=Case Study 2}} <div style="{{Robelbox/pad}}"> Case Study: Copenhagen, Denmark Copenhagen is often hailed as one of the most bicycle-friendly cities in the world. The city has successfully motivated a significant portion of its population to use active transport, particularly cycling, as a primary means of commuting{{fact}}. Here are some motivators and strategies employed in Copenhagen: </div> {{Robelbox/close}} ==== Motivators: ==== '''Infrastructure and safety:''' To ensure the safety of bicycles and pedestrians, Copenhagen made significant investments in the construction of a vast network of designated bike lanes and pedestrian routes. People are encouraged to prefer cycling over other modes of transportation by the existence of safe infrastructure.{{fact}} '''Short Commuting Distances:''' Compact urban development is a key component of Copenhagen's urban design. Most sites, including companies, schools, and retail centres, are accessible by bike or foot. Active transport is a practical choice for travelling shorter distances.{{fact}} '''Environmental Concerns:''' Environmental sustainability is highly valued in Danish society. Concerns about lowering air pollution and glasshouse gas emissions in Copenhagen are motivating inhabitants to embrace active transportation.{{fact}} ==== Encouragement Techniques: ==== '''Infrastructure Investment:''' To make it simple and secure for citizens to commute by bike, the city continuously extends and enhances its bicycle infrastructure. This pertains to the city's bike lanes, bike-sharing programmes, and bike racks.{{fact}} Cycling is accepted as a common and respectable form of transportation in Copenhagen. Cycling is well accepted in culture, which encourages more individuals to start doing it.{{fact}} '''Education and Awareness:''' To increase public understanding of the advantages of riding, safety, and bike maintenance, the city runs educational initiatives and programmes. Schools frequently instruct kids on how to bike safely.{{fact}} '''Support for Policy:''' Copenhagen has put in place measures like congestion pricing, which raises the cost of driving in the city centre. These regulations encourage individuals to choose active transportation.{{fact}} An interesting example study is Copenhagen's effectiveness in encouraging active transportation, especially cycling. The city has inspired a sizable section of its people to adopt active transportation as a sustainable and healthy mode of transportation through fusing infrastructure investments, cultural acceptability, education, policy support, and community involvement.{{fact}} == Key points == {{Robelbox|width=666px|theme=6|iconwidth=48px|title=Key points}} <div style="{{Robelbox/pad}}"> 1. Health and well-being benefits: Walking and cycling, for example, encourage physical exercise and contribute to general health. Cardiovascular fitness increases, lowering the risk of heart disease and other health problems. Endorphins released through physical activity provide mental health advantages such as reduced stress and enhanced mood.{{fact}} 2. Environmental sustainability: Active transportation minimises carbon emissions, reducing transportation's influence on climate change. Reduced air pollution leads to better air quality, which benefits public health and reduces respiratory ailments. Reduced reliance on vehicles makes it easier to preserve natural spaces and promote sustainable urban development.{{fact}} 3. Economic and social benefits: Individuals and governments may save money by using active transportation since it reduces fuel and healthcare expenses. Increased foot traffic around businesses due to active commuting supports vibrant local economies. Social isolation is lessened, which improves communal well-being and general quality of life.{{fact}} 4. Urban planning and infrastructure investment: Active transportation is prioritised in well-designed urban landscapes with designated pedestrian paths and bike lanes. Multimodal commuting is encouraged through investments in bike-sharing programmes and public transit infrastructure. Cities with efficient public transportation and pedestrian places, for example, serve as inspiration for other regions.{{fact}} </div> {{Robelbox/close}} {| class="wikitable" ! [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6636726/ Active Tranport on Health] |} ===Quiz=== Choose your answers and click "Submit": (Hint: Only 1 right answer) <quiz display="simple"> {What is a key health benefit associated with using active transport like walking or cycling? : |type="()"} + Improved cardiovascular fitness - Enhanced lung capacity - Heightened immune system response - Increased risk of osteoporosis {How does active transport contribute to environmental sustainability? : |type="()"} + It reduces traffic congestion - It increases carbon emissions - It intensifies air pollution - It raises dependence on motorized vehicles {What economic advantage is linked to the promotion of active transport in urban areas? : |type="()"} + Lower infrastructure expenses - Higher healthcare costs - Decreased local economic activity - Increased traffic congestion </quiz> ==Conclusion== Psychological motives firmly founded in autonomy, competence, and relatedness have an impact on active transportation. Recognising and addressing these psychological factors while also minimising barriers are necessary to promote the usage of active transportation. We may build an atmosphere where active transportation becomes the prefered and sustainable alternative by encouraging autonomy in choosing, improving perceived competence, and encouraging a sense of relatedness. Active transportation benefits people by improving their physical health and well-being, but it also helps society as a whole by lowering carbon emissions and congested metropolitan areas. Understanding and using the psychology of active transportation is a critical first step in our pursuit of more sustainable and healthful societies.You'll have a thorough knowledge of the psychology of motivation and emotions in relation to active transportation at the end of this chapter. You'll also recognise the huge social benefits that selecting active transportation can make in the effort to create communities that are more connected, sustainable, and healthy. ==See also== # [[Motivation and emotion/Book/2021/Cognitive dissonance and motivation|Cognitive dissonance and motivation]] (Book chapter, 2021) # [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) # [[w:Self determination theory|Self determination theory]] (Wikipedia) # [[wikipedia:Social_cognitive_theory|Social Cognitive Theory]] (Wikipedia) # [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5199110/ Promoting Active Tranport](Wikipedia) # [https://www.youtube.com/watch?v=atAU0OJWFi0&t=15s Active Transportation and Planetary Health] ( YouTube) # [https://books.google.com.au/books?id=lvEoDwAAQBAJ&printsec=frontcover&dq=active+transport+health+benefits+book&hl=en&newbks=1&newbks_redir=0&sa=X&redir_esc=y#v=onepage&q&f=false Walking: Connecting Sustainable Transport with Health] (Book) # [https://books.google.com.au/books?id=sX1gDwAAQBAJ&printsec=frontcover&dq=active+transport+health+benefits+book&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjE9Kqg4umBAxWGMN4KHXtZAhUQ6AF6BAgNEAI#v=onepage&q=active%20transport%20health%20benefits%20book&f=false Children’s Active Transportation] (Book) ==References== {{Hanging indent|1= Brown, E. K., & Williams, L. S. (2019). Urban planning for active transportation: Principles and practice. Routledge. Clark, M. J. (2015). Promoting active transportation: Strategies for urban planning and policy implementation. (Doctoral dissertation). University of California, Los Angeles. Davis, A. M., & Murphy, B. (2016). The economic and social benefits of active transportation: A comprehensive review. ''Journal of Transport Economics and Policy, 50''(2), 205-225. Martinez, P., & Nguyen, L. T. (2017). Integrating active transportation into city design: Lessons from successful case studies. ''In Proceedings of the International Conference on Urban Planning'' (ICUP 2017) (pp. 55-63). Smith, J. A., Johnson, R. B., & Anderson, C. D. (2020). The health benefits of active transportation: A meta-analysis. ''Journal of Public Health, 48''(3), 321-335. United States Department of Transportation. (2018). Active Transportation Initiatives in Urban Planning. Federal Highway Administration. Deci, E. L., & Ryan, R. M. (1985). Intrinsic motivation and self-determination in human behavior. Springer. Sallis, J. F., Cervero, R. B., Ascher, W., Henderson, K. A., Kraft, M. K., & Kerr, J. (2008). An ecological approach to creating active living communities. Annual Review of Public Health, 29, 309-335. Mizdrak, A., Blakely, T., Cleghorn, C. L., & Cobiac, L. J. (2019). Potential of active transport to improve health, reduce healthcare costs, and reduce greenhouse gas emissions: A modelling study. PLoS ONE, 14(7). https://doi.org/10.1371/journal.pone.0219316 Jones, C.H., Ogilvie, D. Motivations for active commuting: a qualitative investigation of the period of home or work relocation. Int J Behav Nutr Phys Act 9, 109 (2012). https://doi.org/10.1186/1479-5868-9-109 Wanjau, M. N., Dalugoda, Y., Oberai, M., Möller, H., Standen, C., Haigh, F., Milat, A., Lucas, P., & Veerman, J. L. (2023). Does active transport displace other physical activity? A systematic review of the evidence. Journal of Transport & Health, 31, 101631. https://doi.org/10.1016/j.jth.2023.101631 Chen, I., & Lui, F. (2022). Physiology, Active Transport. In StatPearls. StatPearls Publishing. Beck, B., Thorpe, A., Timperio, A., Giles-Corti, B., William, C., De Leeuw, E., Christian, H., Corben, K., Stevenson, M., Backhouse, M., Ivers, R., Hayek, R., Raven, R., Bolton, S., Ameratunga, S., Shilton, T., & Zapata-Diomedi, B. (2022). Active transport research priorities for Australia. Journal of Transport & Health, 24, 101288. https://doi.org/10.1016/j.jth.2021.101288 Renninger, D., Kelso, A., Reimers, A. K., Marzi, I., Beck, F., Engels, E. S., Standage, M., & Demetriou, Y. (2022). Motivation and active travel in adolescent girls and boys in Germany – Findings from the ARRIVE study. Transportation Research Part F: Traffic Psychology and Behaviour, 90, 425-437. https://doi.org/10.1016/j.trf.2022.09.015 Batool, T., Ross, V., Brijs, K., Neven, A., Smeets, C. J., Scherrenberg, M., Dendale, P., Vanrompay, Y., Janssens, D., & Wets, G. (2022). It’s how you say it – The extended Theory of Planned Behaviour explains active transport use in cardiac patients depending on the type of self-report in a hypothesis-generating study. Transportation Research Part F: Traffic Psychology and Behaviour, 90, 120-135. https://doi.org/10.1016/j.trf.2022.08.005 Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. The American psychologist, 55(1), 68–78. https://doi.org/10.1037//0003-066x.55.1.68 Bosnjak, M., Ajzen, I., & Schmidt, P. (2020). The Theory of Planned Behavior: Selected Recent Advances and Applications. Europe's Journal of Psychology, 16(3), 352-356. https://doi.org/10.5964/ejop.v16i3.3107 Jones, C. L., Jensen, J. D., Scherr, C. L., Brown, N. R., Christy, K., & Weaver, J. (2015). The Health Belief Model as an Explanatory Framework in Communication Research: Exploring Parallel, Serial, and Moderated Mediation. Health Communication, 30(6), 566. https://doi.org/10.1080/10410236.2013.873363 OpenAI. (2023). ChatGPT (September 25 Version) [Large language model]. https://chat.openai.com OpenAI. (2023). ChatGPT (September 25 Version) [Large language model]. https://chat.openai.com Wen, L. M., Rissel, C., & Fu, H. (2013). The Effect of Active Transport, Transport Systems, and Urban Design on Population Health. Journal of Environmental and Public Health, 2013. https://doi.org/10.1155/2013/457159 Martin, A., Goryakin, Y., & Suhrcke, M. (2014). Does active commuting improve psychological wellbeing? Longitudinal evidence from eighteen waves of the British Household Panel Survey. Preventive Medicine, 69, 296-303. https://doi.org/10.1016/j.ypmed.2014.08.023 Huang, M., Lv, H., Lv, A., Yang, F., Tang, Y., Li, Y., Hua, Y., Liu, H., & Ni, C. (2023). Applying self‐determination theory towards motivational factors of physical activity in people undergoing haemodialyses: A qualitative interview study. Health Expectations : An International Journal of Public Participation in Health Care and Health Policy, 26(3), 1368-1379. https://doi.org/10.1111/hex.13757 Götschi, T., Brand, C., Gerike, R., & Consortium, P. (2017). Towards a Comprehensive Conceptual Framework of Active Travel Behavior: A Review and Synthesis of Published Frameworks. Current Environmental Health Reports, 4(3), 286-295. https://doi.org/10.1007/s40572-017-0149-9 Mueller, N., Rojas-Rueda, D., Cole-Hunter, T., De Nazelle, A., Dons, E., Gerike, R., ... & Nieuwenhuijsen, M. (2015). Health impact assessment of active transportation: a systematic review. Preventive medicine, 76, 103-114. Sallis, J. F., Frank, L. D., Saelens, B. E., & Kraft, M. K. (2004). Active transportation and physical activity: opportunities for collaboration on transportation and public health research. Transportation research part A: policy and Practice, 38(4), 249-268. Giles-Corti, B., Foster, S., Shilton, T., & Falconer, R. (2010). The co-benefits for health of investing in active transportation. New South Wales public health bulletin, 21(6), 122-127. Furie, G. L., & Desai, M. M. (2012). Active transportation and cardiovascular disease risk factors in US adults. American journal of preventive medicine, 43(6), 621-628. }} ==External links== # [https://www.infrastructure.gov.au/infrastructure/pab/active_transport Active Transport] (Walking and Cycling) # [https://bicyclenetwork.com.au/wp-content/uploads/2023/04/boq-active-transport-strategy-concept-draft.pdf Active Transport Strategy] (Active Transport Strategy) # [https://www.infrastructure.gov.au/media-communications-arts/national-broadcasters/australian-broadcasting-corporation-abc Australian Broadcasting Corporation (ABC)] (ABC) # [https://www.aihw.gov.au/reports/australias-health/built-environment-and-health Australian Institute of Health and Welfare (AIHW)] (AIHW) # [https://www.future.transport.nsw.gov.au/future-transport-plans/active-transport-strategy Transport for New South Wales (NSW)] (NSW) # [https://resources.heartfoundation.org.au/images/uploads/publications/Active-Vision-for-Active-Transport-Report.pdf AN AUSTRALIAN VISION FOR /active transport/] (Heart Foundation Australia) # [https://www.arcadis.com/en-au/knowledge-hub/blog/australia/david-freer/2020/active-transport---the-new-era-of-cycling-and-walking Active transport – the new era of cycling and walking] (Cycling Australia) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Physical exercise]] 1r700nmy05ndzak6pkexm38ddiqzdoj 0 301480 2690100 2690099 2024-12-03T12:06:18Z Private lecturer (celestial) 2975755 /* Legal standards */ Ignorantia legis non excusat / Lex naturalis 2690100 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. pcrh7hxve711m8k9mhk42i4c8wiucoc 2690101 2690100 2024-12-03T12:10:16Z Private lecturer (celestial) 2975755 /* Lex naturalis */ Holiness of mankind 2690101 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. e6dbf7pq7xn4q8hsqkbbtwyqj6fwglh 2690102 2690101 2024-12-03T12:21:35Z Private lecturer (celestial) 2975755 /* Lex naturalis */ Son of God 2690102 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a child on a university would naturally occur by a doctoral advisor (German Doktorvater means “doctor father”). === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. h16ho2x6n5cqniy45s69ysqzcfxl5hd 2690103 2690102 2024-12-03T12:23:30Z Private lecturer (celestial) 2975755 /* Son of God */ 2690103 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a young adult on a university would, for instance, naturally occur by a doctoral advisor (German Doktorvater means “doctor father”). === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. 430s8gvzgv9eyh31tf1bg1dqryae6xq 2690104 2690103 2024-12-03T12:32:55Z Private lecturer (celestial) 2975755 A proposal for better education 2690104 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a young adult on a university would, for instance, naturally occur by a doctoral advisor (German Doktorvater means “doctor father”). === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. == Education == === A proposal for better education === Useful appears to be the goal to make pupils envision their own path to heaven, for instance as a repeating home work, refining that goal every year during middle school and high school and freely developing and researching their own perspective on the topic. Developing one’s own perspective with independent and creative thought is good on the one hand, but on the other hand it is actually not reliable enough and thus one would complement that with cultural education that defines cultural limitations and certification, for instance through ethics mentors (like, metaphorically, the apostles) or equivalent education. Freedom of thought appears necessary and desirable, but a certain limitation of the resulting culture also appears to be indispensable, just as the logical and responsible Will of God must be limited by [[#Failure_to_reach_consensus|ethically and morally possible consensus decisions in heaven]]. A potential problem of an increased believe in an afterlife can, however, also increase the risk of teenager suicide, so one would logically restrict this pedagogy to teenagers where no such risk is allowed to occur. Unfortunately this would mean that in general this pedagogy cannot be recommended to arbitrary families. oqvjcmg69ea1oj5ywg175e7c3mmrzw2 2690105 2690104 2024-12-03T12:34:50Z Private lecturer (celestial) 2975755 /* A proposal for better education */ [[#The_Twelve_Apostles|the apostles]] 2690105 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a young adult on a university would, for instance, naturally occur by a doctoral advisor (German Doktorvater means “doctor father”). === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. == Education == === A proposal for better education === Useful appears to be the goal to make pupils envision their own path to heaven, for instance as a repeating home work, refining that goal every year during middle school and high school and freely developing and researching their own perspective on the topic. Developing one’s own perspective with independent and creative thought is good on the one hand, but on the other hand it is actually not reliable enough and thus one would complement that with cultural education that defines cultural limitations and certification, for instance through ethics mentors (like, metaphorically, [[#The_Twelve_Apostles|the apostles]]) or equivalent education. Freedom of thought appears necessary and desirable, but a certain limitation of the resulting culture also appears to be indispensable, just as the logical and responsible Will of God must be limited by [[#Failure_to_reach_consensus|ethically and morally possible consensus decisions in heaven]]. A potential problem of an increased believe in an afterlife can, however, also increase the risk of teenager suicide, so one would logically restrict this pedagogy to teenagers where no such risk is allowed to occur. Unfortunately this would mean that in general this pedagogy cannot be recommended to arbitrary families. 38o6s61tsvlhjml6jdye6tvfcl5lsfw 2690106 2690105 2024-12-03T12:45:55Z Private lecturer (celestial) 2975755 /* Son of God */ omniscient celestial doctoral advisor 2690106 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a young adult on a university would, for instance, naturally occur by a doctoral advisor (German Doktorvater means “doctor father”) and could, of course, be easily envisioned to occur through a omniscient celestial doctoral advisor. === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. == Education == === A proposal for better education === Useful appears to be the goal to make pupils envision their own path to heaven, for instance as a repeating home work, refining that goal every year during middle school and high school and freely developing and researching their own perspective on the topic. Developing one’s own perspective with independent and creative thought is good on the one hand, but on the other hand it is actually not reliable enough and thus one would complement that with cultural education that defines cultural limitations and certification, for instance through ethics mentors (like, metaphorically, [[#The_Twelve_Apostles|the apostles]]) or equivalent education. Freedom of thought appears necessary and desirable, but a certain limitation of the resulting culture also appears to be indispensable, just as the logical and responsible Will of God must be limited by [[#Failure_to_reach_consensus|ethically and morally possible consensus decisions in heaven]]. A potential problem of an increased believe in an afterlife can, however, also increase the risk of teenager suicide, so one would logically restrict this pedagogy to teenagers where no such risk is allowed to occur. Unfortunately this would mean that in general this pedagogy cannot be recommended to arbitrary families. 9yrf818aic4cc1iov1luvp5ycvuc4g2 2690107 2690106 2024-12-03T12:47:12Z Private lecturer (celestial) 2975755 /* Son of God */ 2690107 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a young adult on a university would, for instance, naturally occur by a doctoral advisor (German Doktorvater means “doctor father”) and could, of course, be easily envisioned to occur through an omniscient celestial doctoral advisor. === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. == Education == === A proposal for better education === Useful appears to be the goal to make pupils envision their own path to heaven, for instance as a repeating home work, refining that goal every year during middle school and high school and freely developing and researching their own perspective on the topic. Developing one’s own perspective with independent and creative thought is good on the one hand, but on the other hand it is actually not reliable enough and thus one would complement that with cultural education that defines cultural limitations and certification, for instance through ethics mentors (like, metaphorically, [[#The_Twelve_Apostles|the apostles]]) or equivalent education. Freedom of thought appears necessary and desirable, but a certain limitation of the resulting culture also appears to be indispensable, just as the logical and responsible Will of God must be limited by [[#Failure_to_reach_consensus|ethically and morally possible consensus decisions in heaven]]. A potential problem of an increased believe in an afterlife can, however, also increase the risk of teenager suicide, so one would logically restrict this pedagogy to teenagers where no such risk is allowed to occur. Unfortunately this would mean that in general this pedagogy cannot be recommended to arbitrary families. 1tegpkg33s47cxp91w9sxgda3jfvrvw 2690110 2690107 2024-12-03T13:09:20Z Private lecturer (celestial) 2975755 [[File:Funny theory about the ancient kingdom of Edom.png|right|float]] 2690110 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == [[File:Funny theory about the ancient kingdom of Edom.png|right|float]] === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a young adult on a university would, for instance, naturally occur by a doctoral advisor (German Doktorvater means “doctor father”) and could, of course, be easily envisioned to occur through an omniscient celestial doctoral advisor. === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. == Education == === A proposal for better education === Useful appears to be the goal to make pupils envision their own path to heaven, for instance as a repeating home work, refining that goal every year during middle school and high school and freely developing and researching their own perspective on the topic. Developing one’s own perspective with independent and creative thought is good on the one hand, but on the other hand it is actually not reliable enough and thus one would complement that with cultural education that defines cultural limitations and certification, for instance through ethics mentors (like, metaphorically, [[#The_Twelve_Apostles|the apostles]]) or equivalent education. Freedom of thought appears necessary and desirable, but a certain limitation of the resulting culture also appears to be indispensable, just as the logical and responsible Will of God must be limited by [[#Failure_to_reach_consensus|ethically and morally possible consensus decisions in heaven]]. A potential problem of an increased believe in an afterlife can, however, also increase the risk of teenager suicide, so one would logically restrict this pedagogy to teenagers where no such risk is allowed to occur. Unfortunately this would mean that in general this pedagogy cannot be recommended to arbitrary families. 8uvvk87s7ucm4n61v52kh2ti246x565 2690113 2690110 2024-12-03T14:56:25Z Private lecturer (celestial) 2975755 Priesthood of all believers 2690113 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == [[File:Funny theory about the ancient kingdom of Edom.png|right|float]] === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. ==== Priesthood of all believers ==== The priesthood of all believers is the concept, that all believers do have a natural obligation (like a natural right, only obligation instead of right) to conduct ethical education and that can easily be deduced to apply, for instance in order to reach consensus or to create ethical [[#Social_network|social networks]] and to be an [[#The_Sodom_and_Gomorrah_equation|ethics mentor]] in order to make people [[#Is_it_true_that_there_will_be_a_judgment_of_one's_sins?|suitable candidates for heaven]]. Thus the obligation exists automatically (is a natural obligation). == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a young adult on a university would, for instance, naturally occur by a doctoral advisor (German Doktorvater means “doctor father”) and could, of course, be easily envisioned to occur through an omniscient celestial doctoral advisor. === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. == Education == === A proposal for better education === Useful appears to be the goal to make pupils envision their own path to heaven, for instance as a repeating home work, refining that goal every year during middle school and high school and freely developing and researching their own perspective on the topic. Developing one’s own perspective with independent and creative thought is good on the one hand, but on the other hand it is actually not reliable enough and thus one would complement that with cultural education that defines cultural limitations and certification, for instance through ethics mentors (like, metaphorically, [[#The_Twelve_Apostles|the apostles]]) or equivalent education. Freedom of thought appears necessary and desirable, but a certain limitation of the resulting culture also appears to be indispensable, just as the logical and responsible Will of God must be limited by [[#Failure_to_reach_consensus|ethically and morally possible consensus decisions in heaven]]. A potential problem of an increased believe in an afterlife can, however, also increase the risk of teenager suicide, so one would logically restrict this pedagogy to teenagers where no such risk is allowed to occur. Unfortunately this would mean that in general this pedagogy cannot be recommended to arbitrary families. oz94fgmkbrx0qdtvp1m36ijq6af6bni 2690115 2690113 2024-12-03T15:21:21Z Private lecturer (celestial) 2975755 /* Priesthood of all believers */ [[#Lex_naturalis|natural right]] 2690115 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == [[File:Funny theory about the ancient kingdom of Edom.png|right|float]] === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. ==== Priesthood of all believers ==== The priesthood of all believers is the concept, that all believers do have a natural obligation (like a [[#Lex_naturalis|natural right]], only obligation instead of right) to conduct ethical education and that can easily be deduced to apply, for instance in order to reach consensus or to create ethical [[#Social_network|social networks]] and to be an [[#The_Sodom_and_Gomorrah_equation|ethics mentor]] in order to make people [[#Is_it_true_that_there_will_be_a_judgment_of_one's_sins?|suitable candidates for heaven]]. Thus the obligation exists automatically (is a natural obligation). == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a young adult on a university would, for instance, naturally occur by a doctoral advisor (German Doktorvater means “doctor father”) and could, of course, be easily envisioned to occur through an omniscient celestial doctoral advisor. === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. == Education == === A proposal for better education === Useful appears to be the goal to make pupils envision their own path to heaven, for instance as a repeating home work, refining that goal every year during middle school and high school and freely developing and researching their own perspective on the topic. Developing one’s own perspective with independent and creative thought is good on the one hand, but on the other hand it is actually not reliable enough and thus one would complement that with cultural education that defines cultural limitations and certification, for instance through ethics mentors (like, metaphorically, [[#The_Twelve_Apostles|the apostles]]) or equivalent education. Freedom of thought appears necessary and desirable, but a certain limitation of the resulting culture also appears to be indispensable, just as the logical and responsible Will of God must be limited by [[#Failure_to_reach_consensus|ethically and morally possible consensus decisions in heaven]]. A potential problem of an increased believe in an afterlife can, however, also increase the risk of teenager suicide, so one would logically restrict this pedagogy to teenagers where no such risk is allowed to occur. Unfortunately this would mean that in general this pedagogy cannot be recommended to arbitrary families. es8h9w099hrkdx7rb2dr7v56k87vzh8 2690116 2690115 2024-12-03T15:24:55Z Private lecturer (celestial) 2975755 /* Priesthood of all believers */ Quod erat demonstrandum 2690116 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == [[File:Funny theory about the ancient kingdom of Edom.png|right|float]] === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. ==== Priesthood of all believers ==== The priesthood of all believers is the concept, that all believers do have a natural obligation (like a [[#Lex_naturalis|natural right]], only obligation instead of right) to conduct ethical education and that can easily be deduced to apply, for instance in order to reach consensus or to create ethical [[#Social_network|social networks]] and to be an [[#The_Sodom_and_Gomorrah_equation|ethics mentor]] in order to make people [[#Is_it_true_that_there_will_be_a_judgment_of_one's_sins?|suitable candidates for heaven]]. Thus the obligation exists automatically (is a natural obligation). Quod erat demonstrandum. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a young adult on a university would, for instance, naturally occur by a doctoral advisor (German Doktorvater means “doctor father”) and could, of course, be easily envisioned to occur through an omniscient celestial doctoral advisor. === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[w:natural rights|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. == Education == === A proposal for better education === Useful appears to be the goal to make pupils envision their own path to heaven, for instance as a repeating home work, refining that goal every year during middle school and high school and freely developing and researching their own perspective on the topic. Developing one’s own perspective with independent and creative thought is good on the one hand, but on the other hand it is actually not reliable enough and thus one would complement that with cultural education that defines cultural limitations and certification, for instance through ethics mentors (like, metaphorically, [[#The_Twelve_Apostles|the apostles]]) or equivalent education. Freedom of thought appears necessary and desirable, but a certain limitation of the resulting culture also appears to be indispensable, just as the logical and responsible Will of God must be limited by [[#Failure_to_reach_consensus|ethically and morally possible consensus decisions in heaven]]. A potential problem of an increased believe in an afterlife can, however, also increase the risk of teenager suicide, so one would logically restrict this pedagogy to teenagers where no such risk is allowed to occur. Unfortunately this would mean that in general this pedagogy cannot be recommended to arbitrary families. jtmjemxefkh7nngki0qgm1obthlis5p 2690146 2690116 2024-12-03T18:57:18Z Private lecturer (celestial) 2975755 /* The Peaceable Kingdom */ [[#Lex_naturalis|natural right]] 2690146 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == [[File:Funny theory about the ancient kingdom of Edom.png|right|float]] === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. ==== Priesthood of all believers ==== The priesthood of all believers is the concept, that all believers do have a natural obligation (like a [[#Lex_naturalis|natural right]], only obligation instead of right) to conduct ethical education and that can easily be deduced to apply, for instance in order to reach consensus or to create ethical [[#Social_network|social networks]] and to be an [[#The_Sodom_and_Gomorrah_equation|ethics mentor]] in order to make people [[#Is_it_true_that_there_will_be_a_judgment_of_one's_sins?|suitable candidates for heaven]]. Thus the obligation exists automatically (is a natural obligation). Quod erat demonstrandum. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a young adult on a university would, for instance, naturally occur by a doctoral advisor (German Doktorvater means “doctor father”) and could, of course, be easily envisioned to occur through an omniscient celestial doctoral advisor. === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[#Lex_naturalis|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. == Education == === A proposal for better education === Useful appears to be the goal to make pupils envision their own path to heaven, for instance as a repeating home work, refining that goal every year during middle school and high school and freely developing and researching their own perspective on the topic. Developing one’s own perspective with independent and creative thought is good on the one hand, but on the other hand it is actually not reliable enough and thus one would complement that with cultural education that defines cultural limitations and certification, for instance through ethics mentors (like, metaphorically, [[#The_Twelve_Apostles|the apostles]]) or equivalent education. Freedom of thought appears necessary and desirable, but a certain limitation of the resulting culture also appears to be indispensable, just as the logical and responsible Will of God must be limited by [[#Failure_to_reach_consensus|ethically and morally possible consensus decisions in heaven]]. A potential problem of an increased believe in an afterlife can, however, also increase the risk of teenager suicide, so one would logically restrict this pedagogy to teenagers where no such risk is allowed to occur. Unfortunately this would mean that in general this pedagogy cannot be recommended to arbitrary families. thqkszp4lvbvr27lsurhwgsyyqqw1fi 2690232 2690146 2024-12-04T07:32:26Z Private lecturer (celestial) 2975755 /* The Twelve Apostles */ 2690232 wikitext text/x-wiki [[File:Judicium_Divinum_in_BMPN_2.0.png|thumb|right|577px|Principal workflow]] == Metaphorical language == [[File:Funny theory about the ancient kingdom of Edom.png|right|float]] === Evolution vs. creationism === Evolution represents the predator while creationism represents civilization. Obviously evolution favors the predator as the often most intelligent being and therefore the predator is a winner. Thus the metaphorical dispute about evolution vs. creationism should much rather be the topic of whether and how the civilization can dominate the predator sufficiently. Angels are referred to as "created beings", which implies a state of pure civilization (apart from the fact that angels are created beings, while the evolution that created the homo sapiens was both, evolution and creation at the same time, but this is just fact, not metaphor). === Sodom and Gomorrah === The tale of [[w:Sodom and Gomorrah|Sodom and Gomorrah]] tells the story of a city that was apparently bombed, or something very like that. The archfather Abraham negotiates with God that the city should be spared if 10 righteous (starting from 50 righteous) can be found within the city. The metaphor here is that ten percent is a sorry yield rate and that discarding ninety percent of the population as predators is as if asking God to bomb whole cities. Abraham negotiating down from fifty percent to ten percent is, of course, the wrong direction and would make him look bad, but as the archfather of the Jews he lived in an early era that could not have benefitted from good education, because there were no Jews yet. The perspective of the tale is, of course, the biblical message, that [[w:Judaism|Judaism]] (or rather [[w:Yahwism|Yahwism]]) addressed this issue (which it, in fact, does). ==== Social network ==== Easily deduced is the problem of social networks. Lot's wife "looked back to the city" (which was prohibited) and turned into a pillar of salt. Logically there is a social network surrounding any citizen (e.g. Lot) and his wife would be a person who, especially in ancient times, can easily be imagined to be the one to go to the market place and gossip, leading to a social network of people she may be unwilling to give up. If some people go to heaven while others do not this network must be disassembled somewhere. It may seem an unlikely disassembly to take away somebody's wife, but society consists mostly of interrelated families. Logically there is no other point where disassembly can occur, if can merely shift to other families. Thus the message here is that good ethical education is important and the family should hold together and form a sufficiently strong social network and then that disassembly logically cannot happen in one's own family. But why was Lot's wife turned into a pillar of salt? It may not have been her own failure, but strong social ties to predators and thus one is responsible for one's social network. People who are important should have received sufficient ethical education to make disassembly sufficiently unlikely and all other people should be sufficiently irrelevant to make Lot's wife not "look back". This aspect of the tale therefore explains that some people may be admitted (Lot as a nephew of Abraham is admitted), but people close to them may have failed so badly that they have to be excluded (the majority of the city's inhabitants). In the tale the link from one side to the other is necessarily very short and somebody has to lose. Of course one can only speculate about why Lot didn't like his wife enough or why she was better acquainted with other people, but the true meaning is that society consists of families. Lot's family is thus metaphorically an arbitrary family, but in the unlikely situation of being surrounded by the city's inhabitants, who are all doomed. If the network has to break it has to break within a family, consequently it has to break in this family. This being understood, all families should aim not to be in this situation and the perfect society would result. ==== The Sodom and Gomorrah equation ==== The Sodom and Gomorrah equation can be interpretatively gained from the tale. The equation basically says that Jews (the [[w:in-group|in-group]] of the Bible, which can, of course, be extended to include any ethically responsible culture, for instance Christianity, as one of the dominant examples for such an extended in-group) do have ethical mentors, who form a chain of mentors (described by the Archfather() relation), that links them to an angel. The angel here being a metaphor for a human being with an excellent prognosis for going to heaven and becoming "like an angel". Abraham is, of course, in the biblical context not officially referred to as an angel, but he speaks with God, which is meant to convey a similar status ("speaking with God ''like'' an angel"). : &forall; j &in; JEWS &exist; a &in; ANGELS: Archfather (j) = a The necessity for ethical mentoring (or equivalent education) is what the equation describes and the quality of that education may not be arbitrary, but must, so to speak, be certified by an angel, or may otherwise be insufficient. The inhabitants of the city, of course, logically had no chance to have Abraham as the archfather, because when he still was alive he was not able to at the same time be the archfather of Yahwism. What should be easy to deduce is, of course, that the mentoring function archfather() requires too much time, because it requires many generations to become the archfather of a population. Thus a sensible relation would be called archmentor() or archteacher() and create a chain of mentors within the living population. ==== Angels cannot guarantee what they do not control ==== At the same time the tale warns that angels cannot guarantee what they do not control. Abraham, one should assume, would have included Lot's wife personally as a personal acquaintance, but he was not present in the city at the time of destruction. Thus the mentoring chain logically cannot be fully certified by a single person and can still break, if people fail to understand and apply moral culture and ethical standards in their lives, as the people of Sodom and Gomorrah supposedly did. ==== Can a live after death be guaranteed? ==== More usually there is no guarantee that any particular person will enjoy a life after death. The guarantee is more systematically anchored in society itself and thus in the social networks that constitute society, but may be limited by people's moral culture and ethical standards. Consequently there is also no guarantee for a society that it must include persons who will go to heaven. In the tale of Sodom and Gomorrah Lot just leaves the city. Logically he could have done so at any time and then the society of Sodom and Gomorrah would no longer have contained the tiny group of righteous people from his family, thus turning the society of Sodom and Gomorrah into a doomed society without anybody ascending to heaven. Consequently one should strive to be a morally and ethically acceptable person until oneself is satisfied with the result and that should in theory be sufficient motivation to accomplish the goal. Life after death is meant to be a self-fulfilling prophecy and thus the aim to join heaven is meant to be the salvation, but without legalizing arbitrary misconduct, of course, and with increasing ability to act and intelligence comes also increasing responsibility to do so. === Image of God === The [[w:Image of God|Image of God]] is a metaphor with multiple meanings. One meaning is that the [[w:Kingship_and_kingdom_of_God|Kingdom of Heaven]] is not actually a monarchy. Angels do have [[w:free will|free will]], of course; everything else should be unimaginable. The monarchy of heaven is thus rather a democracy, but a democracy with the unimaginable perfection to act in consensus, according to the will of God, thus every voter is a constituent of the group that confirmed or defined the will of the sovereign of heaven. By human standards this could easily be discarded as impossible to achieve, but in heaven this is the goal, because one is civilized and all voters thus strive for the perfect consensus as a cultural dimension. (One is a very cultural dimension up there in heaven.) In theory angels would take the time to educate each other sufficiently until perfection becomes possible, but that is, given the assembled education, wisdom and intelligence, of course, usually not required. ==== Failure to reach consensus ==== The question if God can move an [[w:Irresistible_force_paradox|immovable object]] is just an invalid question, because immovable objects do not exist. More disconcerting is the issue of problems that do not have perfect solutions. (Another tale tells that Zeus, Lord of the Sky, has been known to have turned such a paradox into [[w:Teumessian_fox|static constellations in heaven]].) Of course heaven can fail to reach consensus, because the perfect choice may not exist. It is easy to construct choices where there is no ideal decision. Given a failure to reach consensus heaven can, as one possible option, agree to disagree and postpone the result until a desirable or required consensus can be reached. Sometimes heaven may act conservatively because of the goal to reach consensus and reluctance to change a previous perfect decision. One could see the Peaceable Kingdom as an example for such a situation: It is the perfect decision to demand of humanity to fulfill human rights as a convergence criterion. Acting conservatively heaven would hesitate to come to a new evaluation of the situation, since the previous perfect consensus decision still seemed quite reasonable. Thus slow progress in the human rights situation may be seen as irrelevant, even though observers might be inclined to see the positive change as an indicator for the final success to tame the predator. ==== Priesthood of all believers ==== The priesthood of all believers is the concept, that all believers do have a natural obligation (like a [[#Lex_naturalis|natural right]], only obligation instead of right) to conduct ethical education and that can easily be deduced to apply, for instance in order to reach consensus or to create ethical [[#Social_network|social networks]] and to be an [[#The_Sodom_and_Gomorrah_equation|ethics mentor]] in order to make people [[#Is_it_true_that_there_will_be_a_judgment_of_one's_sins?|suitable candidates for heaven]]. Thus the obligation exists automatically (is a natural obligation). Quod erat demonstrandum. == Judgment == === Legal standards === A relevant legal standard in heaven is the non-exploitation of the regulatory framework, meaning an intention to explicitly use the regulatory framework as a source of behavior near the lowest common denominator can be punishable. Jeff Bezos, for instance, explicitly once referred to the lowest common denominator as his guiding principle and would thus be punishable under this legislation. The Twelve Apostles do have the slightly humorous, but still serious, additional connotation that ten letters of personal ethics would be required for ethical certification and thus eleven letters would be seen as exploitation of the regulatory framework, making twelve the minimum number of ethics mentors required for certification. ==== Nulla poena sine lege ==== As a consequence nulla poena sine lege (no penalty without law) would also not be applied as strictly in heaven, meaning the regulatory framework is allowed to differ from the expectation, especially for juridical persons (who should have been striving for higher goals than the lowest common denominator to barely be within legal requirements) and especially as an option for the court to either apply or not apply older or newer legislation to a case. On the other hand the very ancient legislation of heaven, of course, does not change very much anyway and the judges are, of course, omniscient, meaning they will not misapply this opportunity, but find the perfect judgement. ==== The Twelve Apostles ==== The Twelve Apostles represent the social network of Jesus as a duality, the state of the social network being a variable depending on the (existence or non-existence of) culture. From inside Christianity the culture would certainly be Christian, but otherwise it would be undefined. ''(omitted text; currently still unsuitable for public debate)'' Thus the importance of the social network is emphasized and Jesus as another “angel” would “certify” the social network of the Twelve Apostles, but the Twelve Apostles would also mutually “certify” the ethical standards (teachings) of Jesus, thus create a mutually certified ethical social network. In the absence of any certification there is, of course, no strict requirement on Earth. Ten would be the sensible requirement, that is easily invented and understood. Non-exploitation of the regulatory framework is easily applied to this new regulation, even if not strictly specified to apply, so this would more be an interpretation by superiors, but not strictly required. Alternatively one could also observe that a minimum fulfillment would show that apparently the topic had not been interesting enough. Consequently, because – wanting to be prepared – one should logically want to fulfill this requirement for most of one’s lifetime and one would have at least ten to twelve ethics mentors from adolescence, but later in life would permanently seek to gain new ethics mentors and new certifications, especially when rising in rank oneself, because mentors from adolescence can easily be perceived as very insufficient later in life and especially by superiors. Pensioners could again see a need to improve this network, because their perspective would more focus on a future in heaven and thus provide new motivation. 120 cardinals form a papal conclave, which would, of course, be over-fulfillment, but understandably serve the '''very''' purpose. The Twelve Apostles, being both young adults or adults, would also be two groups at once, thus the “earlier 12” or the “later 12”. Jesus apparently also would have had Twelve Apostles at about the age of thirty, which would be an age where ascension in society could motivate exactly the behavior to form new relationships with the second group of mentors. One wouldn’t expect a man at that age to die at all, but – wanting to be prepared – one would maintain the perspective and resulting motivation and thus continue to build a social network of ethics mentors. The apostles are later mentioned as visitors in Rome, Athens and other cities and as old men, which would make this a reference to the third group of ethics mentors, one would gather as a pensioner. Also the network apparently would in that era count as “worldwide”, so pensioners are presented as having the opportunity to extend their network to, at least, other cities, but in effect contributing to worldwide networking. ==== Ignorantia legis non excusat ==== Also the Heaven’s Gate does, logically, not strictly apply ignorantia legis non excusat (ignorance of the law is no excuse), because, quite clearly, ignorance should have a (very limited) power to excuse at the Heaven’s Gate. ==== Lex naturalis ==== Lex naturalis (natural law) is seen as to dominate over subordinate legislation and the resulting problem of financial assets is (while not being relevant anyway) lessened by founding the financial systems in contractual law, meaning use of any financial system first requires a founding contract and there is no national financial system to compete with that. The advantage is that, as in the Jewish culture, all contracts are subject to the cultural (e.g. rabbinical, beth din) courts required by the cultural social contract and are therefore necessarily in agreement with the intended culture. Jesus supposedly responded to a question about taxation with the well-known quote “Render therefore unto Caesar what is Caesar's; and to God what is God's.” (Matthew 22:21). A son of God would ''(omitted text; currently still unsuitable for public debate)'' and consequently in theory utilize multiple financial systems, but be himself, as a citizen of utopia (a “holy man”, mankind is holy – all basic rights fulfilled), be above the need for finance. ===== Son of God ===== Holiness of mankind would be another reference to human rights as the [[#The_Peaceable_Kingdom|convergence criteria]]: The holy man is the Son of God, has a “holy” certification and can then ascend to heaven. The Son of God metaphor would also carry the meaning that the social network on Earth would somehow have to undergo a kind of tunnel effect to suddenly contain members of the social network in heaven. The magic of that tunnel effect would be adoption. And adoption could be adoption of a child or adoption of a culture and ethical standards, both of which have a potentially beneficial effect. Adoption of a young adult on a university would, for instance, naturally occur by a doctoral advisor (German Doktorvater means “doctor father”) and could, of course, be easily envisioned to occur through an omniscient celestial doctoral advisor. === Is it true that there will be a judgment of one's sins? === That is definitely true and because angels watch everything humans do the judgment starts immediately with the sin, usually not much later. Mankind does, however, not have a reliable book of law that would detail the actual laws of heaven. All works that try to describe heavenly law were written by humans and contain cultural bias, human opinion and moral standards considered adequate at the time of writing. They may, of course, also contain an unknown amount of fact and/or metaphorical language originating in heaven. The educated reader may be able to distinguish the different types of content. As tourists people often travel to foreign countries without first learning all their laws. It is thus not really unusual not to be aware of the legislation of a state. As a rule of thumb any legislation can be approximated with the [[w:categorical imperative|categorical imperative]], especially heavenly law favors the categorical imperative and resulting moral culture and ethical standards. === The Peaceable Kingdom === The [[w:Peaceable Kingdom (theology)|Peaceable Kingdom]] is a future society that is supposed to precede the [[#Image of God|Kingdom of Heaven]]. What this actually means is that the predator (the homo sapiens is a predator) must be tamed and that people do have [[#Lex_naturalis|natural rights]], which must be guaranteed. The Peaceable Kingdom is thus neither more nor less than a future state of society in which natural rights are sufficiently guaranteed. This is a necessary, but not a sufficient convergence criterion for the Kingdom of Heaven. The Kingdom of Heaven will require even higher standards and human rights that do not even exist as human rights today. The land [[w:Canaan|Canaan]] is associated with the Biblical [[w:Promised Land|Promised Land]], which can be reinterpreted as a promised territory in which migrants find refuge and this then would metaphorically and applying the [[w:categorical imperative|categorical imperative]] include heaven as a refuge for humanity for a live after death. According to the categorical imperative, of course, one should strive to provide refuge to migrants, especially during climate change, who may otherwise not survive in their state of origin, and thus in part satisfy the convergence criterion Peaceable Kingdom. === Duality of personal future and the future of mankind === The duality of one's personal future and the future or mankind is meant to convey that one should aim for a future of mankind that is desirable. Climate change, for instance, makes it perfectly clear that an imaginable future of humanity is a catastrophic disaster. One should, of course, choose not to be the cause of a catastrophic disaster or the all-knowing judge in heaven would have to regard that as a very serious misconduct. As a rule of thumb it makes sense to aim for a future of humanity in heaven that can actually occur, or one will not be able to enjoy it. This should be seen to include the Peaceable Kingdom as a convergence criterion: If you choose to stay divergent, applying the categorical imperative, there would as a result be no future in which you could ascend to heaven. That is, of course, not actually true. Others may create the future without your help, but the judge in heaven may object to your presence in heaven, depending on your personal misconduct, thus making the duality come true. === Is education important for the judgment or just good conduct? === Education is a very positive cultural trait, but not strictly necessary. What is urgently required is ethical education that is sufficient so that the individual has a positive prognosis to become a good citizen of heaven. Strict adherance to a sufficient religion would thus constitute a good standard to receive such a positive prognosis, but heaven aims to make perfect decisions, so that should better be a credible judgment. For instance acceptance of God in heaven as the undisputed sovereign and strict pacifism are very positive cultural traits, even lacking higher education, that could otherwise be seen as a qualifying criterion. Heaven is, however, also very selective about which higher education that would be and consequently one is definitely well advised to consider the constitution of heaven as God-given and pacifism as a self-evident necessity. Of course the inhabitants of heaven enjoy natural rights and among them are the rights to freedom of thought and freedom of speech, but the constitution of heaven should be seen as immutable and thus the free will to endorse the constitution that guarantees these rights is also a very positive cultural trait, thus heaven would be, so to speak, a monarchy (as opposed to anarchy). === What if I feel insecure about my qualification? === People can join heaven as a result of their social network requesting their presence, but only if that is permitted by the judge of heaven and subordinate authorities. There may also be unexpected problems to this approach that are not well-suited for public debate, so the recommended practice is to form an adequate social network in advance, preferably with the explicit purpose of getting one into heaven. Since the society in heaven has a tendency to become more educated over time the likelihood of a good teacher from your personal social network becoming available as mentor rises constantly. What is beneficial is a good social network, that engages in mentoring, and acceptance for people you know as mentors, that may be willing to help, on your side. Any Christian priest could be seen to fulfill that requirement for his parish, which is because that is the God-given intended function. That is, of course, again no license for sever misconduct, because the judge in heaven can object permanently. The devil is such a theoretical terrorist, who can not be allowed to enter heaven, or would have to be expelled by force. The ability to enter heaven without permission is, however, a rather theoretical thing. Angels would be able to try, but they don't do that. In an existential sense the devil is not just a theory and does exist, but he may also be encountered in actions by persons who fail to employ sufficient ethical standards and as a result act as if instructed by such an agent of evil. Heaven refers to the latter as 'collectively intelligent stupidity' or just stupidity, because one should be able to deduce that it may cause incalculable problems for one's personal future in heaven, which should logically enjoy the highest priority or be among the highest priorities. == Science == === Will science allow us to gain all the magic of heaven and do without it? === No, it won't, but that is a rather complicated analysis and you are, of course, allowed to believe in science. === Is physical entry into the otherworld possible? === Entry into the [[w:otherworld|otherworld]] is not physically possible. If it were possible normal matter (water) would become exotic matter (wine), organic chemistry and especially protein folding would break down and containers would cease to contain their content. Trivially these conditions would be unhealthy for the traveler, but this is a theoretical problem, because matter does not travel to the otherworld at all. What can enter the otherworld is only the soul, which is pure energy, light and information. It can enter the otherworld because it does not physically exist and (notice the change of interpretation) the soul in its non-existence is about virtues, values and goodness. It, however, has no need to travel, because it resides already in the otherworld. === Can the soul come back to this world? === There are multiple issues that are not well-suited for public debate, especially not, given the different interpretations of different religions, but in theory this is possible and if an angel would be sitting in a barrack somewhere in Africa and waiting for his natural rights to be acknowledged you wouldn't be able to tell the difference. He might, of course, leave once his natural rights had been granted and could, for instance, simultaneously reside in the otherworld and sit in parliament as a special rapporteur on human rights. This is very definitely possible, but not very likely, rather an adequate metaphor for the possibility and the goal to fulfill human rights. === Is the soul immortal and eternal? === There are different ways to see this. What is most important is that the soul should be seen as an integral part of the human being from somewhere between conception and birth on. Whether it exists before conception or not is, again, not well-suited for public debate and a somewhat academic question: Yes and No. Only this way, from birth on, the soul can grant the most perfect immortality that can be conferred. It is certainly eternal in the sense that it does not have a limited life time. == Education == === A proposal for better education === Useful appears to be the goal to make pupils envision their own path to heaven, for instance as a repeating home work, refining that goal every year during middle school and high school and freely developing and researching their own perspective on the topic. Developing one’s own perspective with independent and creative thought is good on the one hand, but on the other hand it is actually not reliable enough and thus one would complement that with cultural education that defines cultural limitations and certification, for instance through ethics mentors (like, metaphorically, [[#The_Twelve_Apostles|the apostles]]) or equivalent education. Freedom of thought appears necessary and desirable, but a certain limitation of the resulting culture also appears to be indispensable, just as the logical and responsible Will of God must be limited by [[#Failure_to_reach_consensus|ethically and morally possible consensus decisions in heaven]]. A potential problem of an increased believe in an afterlife can, however, also increase the risk of teenager suicide, so one would logically restrict this pedagogy to teenagers where no such risk is allowed to occur. Unfortunately this would mean that in general this pedagogy cannot be recommended to arbitrary families. 3or2yzpst9nv83sk1v16n1uxfjmmhkh 0 302374 2690239 2688269 2024-12-04T10:28:42Z Gavin R Putland 2838145 Appendix: Mathematizing Huygens' principle... 2690239 wikitext text/x-wiki {{Article info | first = Gavin R. | last = Putland | orcid = 0000-0003-4757-6341 | et_al = <!-- if there are >9 authors, hyperlink to the list here --> | correspondence = [[w:Special:EmailUser/Gavin_R_Putland|Contact form]] | journal = WikiJournal of Science | keywords = vector calculus, vector identities, curvilinear coordinates, general coordinates, del operator, Huygens' principle | abstract = The gradient, the curl, the divergence, and the Laplacian are initially defined, without coordinates, as closed-surface integrals per unit volume&mdash;the definition of the Laplacian being indifferent to whether the operand is a scalar field or a vector field. Four integral theorems&mdash;including the divergence theorem&mdash;follow almost immediately, provided that the initial definitions are unambiguous. Their unambiguity, together with some examples of their usefulness, is established as follows, at a level suitable for beginners (although this abstract is for prospective instructors): * The gradient is related to an acceleration through an equation of motion; * The divergence is related to two time-derivatives of density (the partial derivative and the material derivative) through two forms of an equation of continuity; * The component of the curl in a general direction is expressed as a divergence (now known to be unambiguous); * The same is done for the general component of the gradient, yielding not only a second proof of unambiguity of the gradient, but also the relation between the gradient and the directional derivative; this together with the original definition of the Laplacian shows that the Laplacian of a ''scalar'' field is the divergence of the gradient and therefore unambiguous. The unambiguity of the Laplacian of a ''vector'' field then follows from a component argument (as for the curl) or from a linearity argument. The derivation of the relation between the gradient and the directional derivative yields a coordinate-free definition of the dot-del operator for a scalar right-hand operand. But, as the directional derivative is also defined for a non-scalar operand, the same relation offers a method of generalizing the dot-del operator, so that the definition of the Laplacian of a general field can be rewritten with that operator. The advection operator&mdash;derived without coordinates, for both scalar and vector properties&mdash;is likewise rewritten. Meanwhile comparison between the definitions of the various operators leads to coordinate-free definitions of the del-cross, del-dot, and del-squared operators. These together with the dot-del operator allow the four integral theorems to be condensed into a single generalized volume-integral theorem. If the volume of integration is reduced to a thin curved slab of uniform thickness, with an edge-face perpendicular to the broad faces, the four integral theorems are reduced to their two-dimensional forms, each of which relates an integral over a surface segment to an integral around its enclosing curve, provided that the original ''closed''-surface integral has no contribution from the broad faces of the slab. This proviso can be satisfied by construction in two of the four cases, yielding two general theorems, one of which is the Kelvin&ndash;Stokes theorem. By applying these two theorems to a segment of a closed surface, and expanding the segment to cover the entire surface, it is shown that the gradient is irrotational and the curl is solenoidal. The next part of the exposition is more conventional, but still coordinate-free. The gradient theorem is derived from the relation between the gradient and the directional derivative. An irrotational field is shown to have a scalar potential. The 1/''r''&#8202; scalar field is shown to be the field whose negative gradient is the inverse-square vector field, whose divergence is a delta function, which is therefore also the negative Laplacian of the 1/''r''&#8202; scalar field. These results enable the construction of a field with a given divergence or a given Laplacian. The wave equation is derived from small-amplitude sound waves in a non-viscous fluid, and shown to be satisfied by a spherical-wave field with a 1/''r''&#8202; amplitude, whose D'Alembertian is a delta function, enabling the construction of a wave function with a given D'Alembertian. But further progress, including the construction of a field with a given ''curl'', seems to require the introduction of coordinates. With the aid of identities already found, expressions are easily obtained for the gradient, curl, divergence, Laplacian, and advection operators in Cartesian coordinates&mdash;with indicial notation and implicit summation, for brevity. While the resulting expressions for the curl and divergence may look unfamiliar, they match the initial definitions given by J.&#8239;Willard Gibbs. The Cartesian expressions are found convenient for deriving further identities: a comprehensive collection is derived, leading to the construction of a field with a given curl in a star-shaped region and, as a by-product, a demonstration that the curl of the velocity field of a rigid body is twice the angular velocity. The curl-of-the-curl identity leads to a second definition of the Laplacian of a vector, the Helmholtz decomposition, and the prediction of electromagnetic waves. The time-honored method of deriving vector-analytic identities&mdash;treating the divergence and curl as "formal products" with the del operator, varying one field at a time, and adding the results&mdash;is found to be less than rigorous, sometimes less than clear, and hard to justify in view of the ease with which the same thing can be done with Cartesian coordinates, indicial notation, and implicit summation. The introduction of ''general'' coordinates proceeds through (non-normalized) natural and dual basis vectors, reciprocity, the Kronecker delta, covariance of the natural basis, contravariance of the dual basis, contravariant and covariant components, local bases, contravariance of coordinates, covariance of derivatives w.r.t. coordinates, the Jacobian, and handedness. Reciprocity leads to the dot-product of two vector fields and, via the permutation symbol, to the cross-products of the basis vectors, the definition of one basis in terms of the other, the cross-product of two vector fields, and reciprocity of the covariant and contravariant Jacobians. Thus the stage is set for expressing operators in general coordinates. The multivariate chain rule leads to expressions for the directional derivative (in terms of the contravariant basis), hence the gradient (del) and advection operators. The identity for the curl of the product of a scalar and a vector leads to an expression for the curl in terms of covariant components. Expressions for the curl and divergence ''operators'' are obtained from the original volume-based definitions, and are found to agree with del-cross and del-dot respectively, with del expressed in the same general coordinates. The volume-based definition of the divergence leads, by a simpler path, to an expression in terms of contravariant components, which in turn yields an expression for the Laplacian. Affine coordinates are briefly described before proceeding to orthogonal coordinates. In the latter, the Jacobian is simplified and we can choose an orthonormal basis, which is its own reciprocal, so that vectors can be specified in components w.r.t. a single basis. By expressing the old basis vectors and components in terms of the new ones, we can re-express dot-products, cross-products, and differential operators in terms of orthogonal coordinates with an orthonormal basis. In an appendix, Huygens' principle is mathematized by deriving Green's identities and thence Kirchhoff's integral theorem (''without''&#8202; assuming sinusoidal time-dependence), and then interpreting Kirchhoff's integrand as a distribution of secondary sources. ::'''&vellip;''' '''[''To be continued.'']''' }} == Introduction == [[w:Sheldon Axler|Sheldon Axler]], in his essay "Down with determinants!" ([[#axler-95|1995]]) and his ensuing book ''Linear Algebra Done Right'' (4th Ed., [[#axler-23-|2023–]]), does not entirely eliminate determinants, but introduces them as late as possible and then exploits them for what he calls their "main reasonable use in undergraduate mathematics", namely the change-of-variables formula for multiple integrals.<ref>[[#axler-95|Axler, 1995]], &sect;9. The relegation of determinants was anticipated by C.G.&#8239;Broyden ([[#broyden-75|1975]]). But Broyden's approach is less radical: he does not deal with abstract vector spaces or abstract linear transformations, and his eventual definition of the determinant, unlike Axler's, is traditional&mdash;not a product of the preceding narrative.</ref> Here I treat coordinates in vector analysis somewhat as Axler treats determinants in linear algebra: I introduce coordinates as late as possible, and then exploit them in unconventionally ''rigorous'' derivations of vector-analytic identities from (e.g.) vector-algebraic identities. But I contrast with Axler in at least two ways. First, as my subtitle suggests, I have no intention of expanding my paper into a book. Brevity is of the essence. Second, while one may well avoid determinants in ''numerical''&#8202; linear algebra,<ref>[[#axler-95|Axler, 1995]], &sect;1. But it is Broyden ([[#broyden-75|1975]]), not Axler, who discusses numerical methods at length.</ref> one can hardly avoid coordinates in ''numerical'' vector analysis! So I cannot extend the coordinate-minimizing path into computation. But I can extend it up to the threshold by expressing the operators of vector analysis in general coordinates and orthogonal coordinates, leaving it for others to specialize the coordinates and compute with them. On the way, I can satisfy readers who need the concepts of vector analysis for ''theoretical'' purposes, and who would rather read a paper than a book. Readers who stay to the end of the paper will get a more general treatment of coordinates than is offered by a typical book-length introduction to vector analysis. In the meantime, coordinates won't needlessly get in the way. === The cost of coordinates === Mathematicians define a "vector" as a member of a ''[[w:vector space|vector space]]'', which is a [[w:set (mathematics)|set]] whose members satisfy certain basic rules of algebra (called the ''vector-space axioms'') with respect to another set called a ''[[w:field (mathematics)|field]]'' (e.g., the real numbers), which has its own basic rules of algebra (the ''field axioms''), and whose members are called "scalars". Physicists are more fussy. They typically want a "vector" to be not only a member of a vector space, but also a '''first-order tensor'''&#8239;: a "tensor", meaning that it exists independently of any coordinate system with which it might be specified; and "first-order" (or "first-degree", or "first-rank"), meaning that it is specified by a ''one''-dimensional array of numbers. Similarly, a 2nd-order tensor is specified by a 2-dimensional array (a matrix), and a 3rd-order by a 3-dimensional array, and so on. Hence they want a "scalar", which is specified by a single number (a zero-dimensional array), to be a ''zero-order tensor''. In "vector analysis", we are greatly interested in applications to physical situations, and accordingly take the physicists' view on what constitutes a vector or a scalar. So, for our purposes, defining a quantity by three components in (say) a Cartesian coordinate system is not enough to make it a vector, and defining a quantity as a real function of a list of coordinates is not enough to make it a scalar, because we still need to show that the quantity has an independent existence. One way to do this is to show that its coordinate representation behaves appropriately when the coordinate system is changed. Independent existence of a ''quantity'' means that its coordinate representation changes so as to compensate for the change in the coordinate system.<ref>E.g., Feynman ([[#feynman-63|1963]], vol.&#8239;1, &sect;&#8202;11-5), having defined velocity from displacement in Cartesian coordinates, shows that velocity is a vector by showing that its coordinate representation contra-rotates (like that of displacement) if the coordinate system rotates.</ref> But independent existence of an ''operator'' means that its expression in one coordinate system (with the operand[s] and the result ''in that system'') gives the same result as the corresponding expression in another coordinate system.<ref>E.g., Feynman ([[#feynman-63|1963]], vol.&#8239;1, &sect;&#8202;11-7), having defined the magnitude and dot-product in Cartesian coordinates, proves that they are scalar functions by showing that the corresponding expressions in rotated ("primed") coordinates give the same values as the original expressions (in "unprimed" coordinates). And Tai ([[#tai-95|1995]], pp.&#8239;66–7), having found an expression for the "gradient" operator in a general coordinate system (the "unprimed" system), proves the "invariance" of the operator (its vector character in this case) by showing that the corresponding expression in any other general coordinate system (the "primed" system) has the same effect.</ref> Here we circumvent these complications by the most obvious route: by ''initially'' defining things without coordinates. If, having defined something without coordinates, we then need to represent it ''with'' coordinates, we can choose the coordinate system for convenience rather than generality. === The limitations of limits === In the branch of pure mathematics known as ''analysis'', there is a thing called a ''limit'', whereby for every positive ''&epsiv;''&#8202; there exists a positive ''&delta;'' such that if some increment is less than ''&delta;'', some error is less than ''&epsiv;''. In the branch of applied mathematics known as ''[[w:continuum mechanics|continuum mechanics]]'', there is a thing called reality, whereby if the increment is less than some positive ''&delta;'', the assumption of a continuum becomes ridiculous, so that the error cannot be made less than an ''arbitrary &epsiv;''. Yet vector "analysis" (together with higher-order tensors) is typically studied with the intention of applying it to some form of "continuum" mechanics, such as the modeling of elasticity, plasticity, fluid flow, or (widening the net) electrodynamics of ordinary matter; in short, it is studied with the intention of conveniently forgetting that, on a sufficiently small scale, matter is lumpy.{{efn|Even if we claim that "particles" of matter are wave functions and therefore continuous, this still implies that matter is lumpy in a manner not normally contemplated by continuum mechanics.}} One might therefore submit that to express the principles of vector analysis in the language of limits is to strain at a gnat and swallow a camel. Here I avoid that camel by referring to '''elements''' of length or area or volume, each of which is ''small'' enough to allow some quantity or quantities to be considered uniform within it, but, for the same reason, ''large'' enough to allow such local averaging of the said quantity or quantities as is necessary to tune out the lumpiness. We shall see bigger camels, where well-known authors define or misdefine a vector ''operator'' and then derive identities by treating it like an ordinary vector ''quantity''. These I also avoid. === Prerequisites === I assume that the reader is familiar with the algebra and geometry of vectors in 3D space, including the dot-product, the cross-product, and the scalar triple product, their geometric meanings, their expressions in Cartesian coordinates, and the identity :{{big|{{math|'''a''' &times; ('''b''' &times; '''c''')  {{=}}  '''a&#11825;&#8202;c b''' &minus; '''a&#11825;&#8202;b c''' ,}}}} which we call the "expansion" of the vector triple product.<ref>There are many proofs and interpretations of this identity. My own effort, for what it's worth, is "Trigonometric proof of vector triple product expansion", ''Mathematics Stack Exchange'', [https://math.stackexchange.com/a/4839213/307861 t.co/NM2v4DJJGo], 2024. The classic is [[#gibbs-1881-4|Gibbs, 1881]], &sect;&sect;&#8239;26–7.</ref> I further assume that the reader can generalize the concept of a derivative, so as to differentiate a vector with respect to a scalar, e.g. :<math>\mathbf{r}'(t) = \frac{d\mathbf{r}}{dt} =\, \lim_{h\to 0} \frac{\mathbf{r}(t+h) - \mathbf{r}(t)}{h} \,,</math> or so as to differentiate a function of several independent variables "partially" w.r.t. one of them while the others are held constant, e.g. :<math>\tfrac{\part}{\part y} \psi\big(x,y,z\big) =\, \lim_{h\to 0} \frac{\psi(x,y{+}h~\!,z) - \psi(x,y,z)}{h} \,.</math> But in view of the above remarks on limits, I also expect the reader to be tolerant of an argument like this: In a short time{{mvar| dt}}, let the vectors {{math|'''r'''}} and{{math| '''p'''}} change by {{math|''d'''''r'''}} and{{math| ''d'''''p'''}} respectively. Then :<math>\begin{align} \tfrac{d}{dt}\big(\mathbf{r}\!\times\!\mathbf{p}\big) &= \frac{(\mathbf{r}+d\mathbf{r})\times(\mathbf{p}+d\mathbf{p}) \,-\, \mathbf{r}\times\mathbf{p}}{dt}\\[1ex] &= \frac{\mathbf{r}\!\times\!d\mathbf{p}+d\mathbf{r}\!\times\!\mathbf{p}}{dt} ~~\quad [\mathsf{neglecting}~d\mathbf{r}\!\times\!d\mathbf{p}]\\[1ex] &=\, \mathbf{r}\times\!\tfrac{d\mathbf{p}}{dt} + \tfrac{d\mathbf{r}}{dt}\!\times\mathbf{p}\\[1ex] &=\, \mathbf{r}\times\mathbf{\dot{p}}\,+\,\mathbf{\dot{r}}\times\mathbf{p}\,, \end{align}</math> where, as always, the orders of the cross-products matter.{{efn|If {{math|'''r'''}} is the position of a particle and {{math|'''p'''}} is its momentum, the last term vanishes. If the force is toward the origin, the previous term also vanishes, and we are left with ''conservation of angular momentum'' about the origin.}} Differentiation of a ''dot''-product behaves similarly, except that the orders ''don't'' matter; and if&#8239;{{math| '''p'''&#8201;{{=}}&#8201;''m'''''v'''}}, where {{mvar|m}} is a scalar and {{math|'''v'''}} is a vector, then :<math>~~\mathbf{\dot{p}} = m\mathbf{\dot{v}} + \dot{m}\mathbf{v} \,.</math> Or an argument like this:  If<math>~z\!=\!f(x,y)</math>, then :<math>\begin{align} \frac{\part^2 z}{\part x\,\part y} &= \tfrac{\part}{\part x}\,\tfrac{\part}{\part y} f\big(x,y\big)\\ &= \frac{\part}{\part x}\,\frac{f(x,y{+}dy)-f(x,y)}{dy}\\[1ex] &= \frac{\,\frac{f(x{+}dx~\!,\,y{+}dy)\,-\,f(x{+}dx~\!,\,y)}{dy} - \frac{f(x,\,y{+}dy)\,-\,f(x,y)}{dy}\,} {dx}\\[2ex] &= \frac{\,\frac{f(x{+}dx~\!,\,y{+}dy)\,-\,f(x,\,y{+}dy)}{dx} - \frac{f(x{+}dx~\!,\,y)\,-\,f(x,y)}{dx}\,} {dy}\\[1ex] &= \frac{\part}{\part y}\,\frac{f(x{+}dx~\!,~\!y)-f(x,y)}{dx}\\[1ex] &= \tfrac{\part}{\part y}\,\tfrac{\part}{\part x} f\big(x,y\big) = \frac{\part^2 z}{\part y\,\part x} \,; \end{align}</math> that is, we can switch the order of differentiation in a "mixed" partial derivative. If{{mvar| &part;_x}} is an abbreviation for {{mvar|{{sfrac|&part;|&part;x}}&#8202;}}, etc., this rule can be written in '''operational''' terms as :{{big|{{mvar|&part;_x&part;_y {{=}} &part;_y&part;_x.}}}} More generally, if {{mvar|&part;_i}} is an abbreviation for {{mvar|{{sfrac|&part;|&part;x_i}}}}&#8202; where&#8202; {{math|''i''&#8239;&#8714;&#8202;&lcub;1,&#8202;2,&hellip;&rcub;,}}&#8202; the rule becomes :{{big|{{mvar|&part;_i&part;_j {{=}} &part;_j&part;_i.}}}} These generalizations of differentiation, however, do not go beyond differentiation w.r.t. ''real'' variables, some of which are scalars, and some of which are coordinates. Vector analysis involves quantities that may be loosely described as derivatives w.r.t. a ''vector''&mdash;usually the position vector. == Closed-surface integrals per unit volume == The term ''field'', mentioned above in the context of algebraic axioms, has an alternative meaning: if {{math|'''r'''}} is the position vector, a '''scalar field''' is a scalar-valued function of{{math| '''r''',}} and a '''vector field''' is a vector-valued function of{{math| '''r'''}}; both may also depend on time. These are the functions of which we want "derivatives" w.r.t. the vector{{math| '''r'''}}. In this section I introduce four such derivatives&mdash;the ''gradient'', the ''curl'', the ''divergence'', and the ''Laplacian''&#8202;&mdash;in a way that will seem unremarkable to those readers who aren't already familiar with them, but idiosyncratic to those who are. The gradient is commonly introduced in connection with a curve and its endpoints, the curl in connection with a surface segment and its enclosing curve, the divergence in connection with a volume and its enclosing surface, and the Laplacian as a composite of two of the above, initially applicable only to a scalar field. Here I introduce all four in connection with a volume and its enclosing surface; and I introduce the Laplacian as a concept in its own right, equally applicable to a scalar ''or vector''&#8202; field, and only later relate it to the others. My initial definitions of the gradient, the curl, and the Laplacian, although not novel, are usually thought to be more advanced than the common ones&mdash;in spite of being conceptually simpler, and in spite of being obvious variations on the same theme. === Instant integral theorems (with a caveat) === Let {{mvar|V}} be a volume (3D region) enclosed by a surface {{mvar|S}} (a mathematical surface, ''not'' generally a physical barrier). Let {{math|'''n'''&#770;}} be the unit normal vector at a general point on {{mvar|S}}, pointing ''out'' of{{mvar| V}}. Let {{mvar|n}} be the distance from {{mvar|S}} in the direction of{{math| '''n'''&#770;}} (positive outside {{mvar|V}}, negative inside), and let {{mvar|&part;_n}} be an abbreviation for{{mvar| {{sfrac|&part;|&part;n}}&#8202;}}, where the derivative&mdash;commonly called the '''normal derivative'''&mdash;is tacitly assumed to exist. In {{mvar|V}}, and on {{mvar|S}}, let {{mvar|p}} be a scalar field (e.g., pressure in a fluid, or temperature), and let {{math|'''q'''}} be a vector field (e.g., flow velocity, or heat-flow density), and let {{mvar|&psi;}} be a generic field which may be a scalar or a vector. Let a general element of the surface {{mvar|S}} have area {{mvar|dS}}, and let it be small enough to allow {{math|'''n'''&#770;}}, {{mvar|p}}, {{math|'''q'''}}, and {{mvar|&part;_n&#8202;&psi;}} to be considered uniform over the element. Then, for every element, the following four products are well defined: {{NumBlk|:|<math>\mathbf{\hat{n}} ~\!p\,dS ~,\qquad \mathbf{\hat{n}}\times\mathbf{q}\,dS ~,\qquad \mathbf{\hat{n} \cdot q}\,dS ~,\qquad \part_n \psi\;dS \,. </math>|{{EquationRef|1}}}} If {{mvar|p}} is pressure in a non-viscous fluid, the first of these products is the force exerted by the fluid in {{mvar|V}}&#8202; through the area {{mvar|dS}}. The second product does not have such an obvious physical interpretation; but if{{math| '''q'''}} is ''circulating'' clockwise about an axis directed through{{mvar| V}}, the cross-product will be exactly tangential to{{mvar| S}} and will tend to have a component in the direction of that axis. The third product is the ''flux'' of{{math| '''q'''}} through the surface element; if{{math| '''q'''}} is flow velocity, the third product is the volumetric flow rate (volume per unit time) ''out'' of{{mvar| V}}&#8202; through{{mvar| dS&#8202;}}; or if {{math|'''q'''}} is heat-flow density, the third product is the heat transfer rate (energy per unit time) ''out'' of{{mvar| V}}&#8202; through{{mvar| dS}}. The fourth product, by analogy with the third, might be called the flux of the normal derivative of{{mvar| &psi;}} through the surface element, but is equally well defined whether {{mvar|&psi;}} is a scalar or a vector&mdash;or, for that matter, a matrix, or a tensor of any order, or anything else that we can differentiate w.r.t.{{mvar| n}}. If we add up each of the four products over all the elements of the surface {{mvar|S}}, we obtain, respectively, the four '''surface integrals''' {{NumBlk|:|<math>\iint_S \!\mathbf{\hat{n}} ~\!p\,dS \,,~ \iint_S \!\mathbf{\hat{n}}\times\mathbf{q}\,dS \,,~ \iint_S \!\mathbf{\hat{n} \cdot q}\,dS \,,~ \iint_S \!\part_n \psi\;dS \,, </math>|{{EquationRef|2}}}} in which the double integral sign indicates that the range of integration is two-dimensional. The first surface integral takes a scalar field and yields a vector; the second takes a vector field and yields a vector; the third takes a vector field and yields a scalar; and the fourth takes (e.g.) a scalar field yielding a scalar, or a vector field yielding a vector. If{{mvar| p}} is pressure in a non-viscous fluid, the first integral is the force exerted by the fluid in {{mvar|V}}&#8202; on the fluid outside {{mvar|V}}. The second integral may be called the ''skew'' surface integral of{{math| '''q'''}} over {{mvar|S&#8202;}},<ref>[[#gibbs-1881-4|Gibbs, 1881]], &sect;&#8239;56.</ref> or, for the reason hinted above, the ''circulation'' of{{math| '''q'''}} over {{mvar|S}}.&#8201; The third integral, commonly called the ''flux integral'' (or simply the surface integral) of{{math| '''q'''}} over {{mvar|S}}, is the total ''flux'' of{{math| '''q'''}} out of{{mvar| V}}. And the fourth integral is the surface integral of the outward normal derivative of{{mvar| &psi;}}. Let the volume {{mvar|V}}&#8202; be divided into elements. Let a general volume element have the volume {{mvar|dV}} and be enclosed by the surface {{mvar|&delta;S}}&#8201;&mdash;not to be confused with the area {{mvar|dS}} of a surface ''element'', which may be an element of{{mvar| S}} or of{{mvar| &delta;S}}. Then consider what happens if, instead of evaluating each of the above surface integrals over {{mvar|S}}, we evaluate it over each {{mvar|&delta;S}} and add up the results for all the volume elements. In the ''interior'' of{{mvar| V}}, each surface element of area {{mvar|dS}} is on the boundary between two volume elements, for which the unit normals {{math|'''n'''&#770;}} at {{mvar|dS}}, and the respective values of{{mvar| &part;_n&#8202;&psi;}}, are equal and opposite. Hence when we add up the integrals over the surfaces {{mvar|&delta;S}}, the contributions from the elements {{mvar|dS}} cancel in pairs, except on the original surface {{mvar|S}}, so that we are left with the original integral over {{mvar|S}}. So, for the four surface integrals in ({{EquationNote|2}}), we have respectively {{NumBlk|:|<math>\begin{align} \iint_S \mathbf{\hat{n}}~\!p \,dS & \,= \sum_V\iint_{\delta S} \mathbf{\hat{n}}~\!p \,dS \,, \\ \iint_S \mathbf{\hat{n}}\times\mathbf{q} \,dS & \,= \sum_V\iint_{\delta S} \mathbf{\hat{n}}\times\mathbf{q} \,dS \,, \\ \iint_S \mathbf{\hat{n}\cdot q} \,dS & \,= \sum_V\iint_{\delta S} \mathbf{\hat{n}\cdot q} \,dS \,, \\ \iint_S \part_n \psi \;dS & \,= \sum_V\iint_{\delta S} \part_n \psi \;dS \,. \end{align}</math>|{{EquationRef|3}}}} Now comes a big "if":&#8201; ''if''&#8202; we define the '''gradient''' of{{mvar| p}} (pronounced "grad {{mvar|p}}") inside {{mvar|dV}}&#8202; as {{NumBlk|:|<math>\nabla p \,:=\, \frac{1}{dV}\iint_{\delta S} \mathbf{\hat{n}}~\!p \,dS </math>|{{EquationRef|4g}}}} and the '''curl''' of {{math|'''q'''}} inside {{mvar|dV}}&#8202; as {{NumBlk|:|<math>\operatorname{curl}\mathbf{q} \,:=\, \frac{1}{dV}\iint_{\delta S} \mathbf{\hat{n}}\times\mathbf{q} \,dS </math>|{{EquationRef|4c}}}} and the '''divergence''' of {{math|'''q'''}} inside {{mvar|dV}}&#8202; as {{NumBlk|:|<math>\operatorname{div}\mathbf{q} \,:=\, \frac{1}{dV}\iint_{\delta S} \mathbf{\hat{n}\cdot q} \,dS </math>|{{EquationRef|4d}}}} and the '''Laplacian''' of {{mvar|&psi;}} inside {{mvar|dV}}&#8202; as&#8202;{{efn|Here we use the broad triangle symbol{{math| (&#9651;)}} rather than the narrower Greek Delta{{math| (&Delta;)}}; the latter would more likely be misinterpreted as "change in&hellip;"}} {{NumBlk|:|<math>\triangle\psi \,:=\, \frac{1}{dV}\iint_{\delta S} \part_n \psi \;dS </math>|{{EquationRef|4L}}}} (where the letters after the equation number stand for ''gradient'', ''curl'', ''divergence'', and ''Laplacian'', respectively), then equations ({{EquationNote|3}}) can be rewritten :<math>\begin{align} \iint_S \mathbf{\hat{n}}~\!p \,dS & \,= \sum_V \nabla p ~dV \,, \\ \iint_S \mathbf{\hat{n}}\times\mathbf{q} \,dS & \,= \sum_V \operatorname{curl}\mathbf{q} ~dV \,, \\ \iint_S \mathbf{\hat{n}\cdot q} \,dS & \,= \sum_V \operatorname{div}\mathbf{q} ~dV \,, \\ \iint_S \part_n \psi \;dS & \,= \sum_V \triangle\psi ~dV \,. \end{align}</math> But because each term in each sum has a factor {{mvar|dV}}, we call the sum an integral; and because the range of integration is three-dimensional, we use a triple integral sign. Thus we obtain the following four theorems relating integrals over an enclosing surface {{mvar|S}}&#8202; to integrals over the enclosed volume {{mvar|V&#8202;}}: {{NumBlk|:|<math>~~~~~\!\iint_S \mathbf{\hat{n}}~\!p \,dS \,= \iiint_V \nabla p ~dV \,; </math>|{{EquationRef|5g}}}} {{NumBlk|:|<math>\iint_S \mathbf{\hat{n}}\times\mathbf{q} \,dS \,= \iiint_V \operatorname{curl}\mathbf{q} ~dV \,; </math>|{{EquationRef|5c}}}} {{NumBlk|:|<math>~~\!\iint_S \mathbf{\hat{n}\cdot q} \,dS \,= \iiint_V \operatorname{div}\mathbf{q} ~dV \,; </math>|{{EquationRef|5d}}}} {{NumBlk|:|<math>~~\iint_S \part_n \psi \;dS \,= \iiint_V \triangle\psi ~dV \,. </math>|{{EquationRef|5L}}}} Of the above four results, only the third ({{EquationNote|5d}}) seems to have a standard name; it is called the '''divergence theorem''' (or ''Gauss's theorem'' or, more properly, ''[[w:Mikhail Ostrogradsky|Ostrogradsky]]'s theorem''<ref>[[#katz-79|Katz, 1979]], pp.&#8239;146–9.</ref>), and is indeed the best known of the four&mdash;although the other three, having been derived in parallel with it, may be said to be equally fundamental. As each of the operators {{math|&nabla;,}} {{math|curl,}} and {{math|div}} calls for an integration w.r.t. area and then a division by volume, the ''dimension'' (or unit of measurement) of the result is the dimension of the operand divided by the dimension of length, as if the operation were some sort of differentiation w.r.t. position. Moreover, in each of equations ({{EquationNote|5g}}) to ({{EquationNote|5d}}), there is a triple integral on the right but only a double integral on the left, so that each of the operators {{math|&nabla;,}} {{math|curl,}} and {{math|div}} appears to compensate for a single integration. For these reasons, and for convenience, we shall describe them as '''differential operators'''. By comparison, the {{math|&#9651; }}operator in ({{EquationNote|4L}}) or ({{EquationNote|5L}}) calls for a further differentiation w.r.t.{{mvar| n&#8202;}}; we shall therefore describe {{math|&#9651;}} as a ''2nd-order'' differential operator. (An additional reason for these descriptions will emerge later.) As promised, the four definitions ({{EquationNote|4g}}) to ({{EquationNote|4L}}) are "obvious variations on the same theme" (although the fourth is somewhat less obvious than the others). But remember the "if": Theorems ({{EquationNote|5g}}) to ({{EquationNote|5L}}) depend on definitions ({{EquationNote|4g}}) to ({{EquationNote|4L}}) and are therefore only as definite as those definitions! Equations ({{EquationNote|3}}), without assuming anything about the shapes and relative sizes of the closed surfaces {{mvar|&delta;S}} (except, tacitly, that {{math|'''n'''&#770;}} is piecewise well-defined), indicate that the surface integrals are ''additive with respect to volume''. But this additivity, by itself, does not guarantee that the surface integrals are shared among neighboring volume elements ''in proportion'' to their volumes, as envisaged by "definitions" ({{EquationNote|4g}}) to ({{EquationNote|4L}}). Each of these "definitions" is unambiguous if, and only if, the ratio of the surface integral to{{mvar| dV}}&#8202; is insensitive to the shape and size of{{mvar| &delta;S}}&#8202; for a sufficiently small {{mvar|&delta;S}}. Notice that the issue here is ''not'' whether the ratios specified in equations ({{EquationNote|4g}}) to ({{EquationNote|4L}}) are true vectors or scalars, independent of the coordinates; all of the operations needed in those equations have coordinate-free definitions. Rather, the issue is whether the resulting ratios are unambiguous ''notwithstanding the ambiguity of'' {{mvar|&delta;S}}, provided only that {{mvar|&delta;S}} is sufficiently small. That is the advertised "caveat", which must now be addressed. In accordance with our "applied" mathematical purpose, our proofs of the unambiguity of the differential operators will rest on a few [[w:thought experiment|thought experiments]], each of which applies an operator to a physical field, say{{mvar| f}}, and obtains another physical field whose unambiguity is beyond dispute. The conclusion of the thought experiment is then applicable to any operand field whose ''mathematical'' properties are consistent with its interpretation as the physical field{{mvar| f&#8202;}}; the loss of generality, if any, is only what is incurred by that interpretation. === Unambiguity of the gradient === Suppose that a fluid with density {{mvar|&rho;}} (a scalar field) flows with velocity{{math| '''v'''}} (a vector field) under the influence of the internal pressure {{mvar|p}} (a scalar field). Then the integral in ({{EquationNote|4g}}) is the force exerted by the pressure of the fluid inside {{mvar|&delta;S}} on the fluid outside, so that ''minus'' the integral is the force exerted ''on'' the fluid inside{{mvar| &delta;S}}&#8202; by the pressure of the fluid outside. Dividing by {{mvar|dV}}, we find that {{math|&minus;&nabla;''p''}}, as defined by ({{EquationNote|4g}}), is the force per unit volume, due to the pressure outside the volume.<ref>In [[#feynman-63|Feynman, 1963]],&#8201; {{math|&minus;&nabla;''p'' }}as the "pressure force per unit volume" eventually appears in the 3rd-last lecture of Volume 2 (&sect;40-1).</ref> If this is the ''only'' force per unit volume acting ''on'' the volume (e.g., because the fluid is non-viscous and in a weightless environment, and the volume element is not in contact with the container), then it is equal to the acceleration times the mass per unit volume; that is, {{NumBlk|:|<math> \rho\,\frac{d\mathbf{v}}{dt} = -\nabla p \,. </math>|{{EquationRef|6g}}}} Now provided that the left side of this equation is locally continuous, it can be considered uniform inside the small {{mvar|&delta;S}}, so that the left side is unambiguous, whence&#8202; {{math|&nabla;''p'' }}''is also unambiguous''. If there are additional forces on the fluid element, e.g. due to gravity and&#10744;or viscosity, then {{math|&minus;&nabla;''p''}} is not the sole contribution to density-times-acceleration, but is still the contribution due to pressure, which is still unambiguous. By showing the unambiguity of definition ({{EquationNote|4g}}), we have confirmed theorem ({{EquationNote|5g}}). In the process we have seen that the volume-based definition of the gradient is useful for the modeling of fluids, and intuitive in that it formalizes the common notion that a pressure "gradient" gives rise to a force. === Unambiguity of the divergence === In the aforesaid fluid, in a short time{{mvar| dt}}, the volume that flows out of fixed closed surface {{mvar|&delta;S}}&#8202; through a fixed surface element of area {{mvar|dS}}&#8202; is {{math|'''v'''&#8202;''dt''&#8202;'''&#11825;&#8239;n'''&#770;&#8239;''dS''}}&#8239; (i.e., the displacement normal to the surface element, times the area).&#8201; Multiplying this by density and integrating over {{mvar|&delta;S}}, we find that the mass flowing out of{{mvar| &delta;S}}&#8202; in time{{mvar| dt}} is&#8201; <math>\textstyle\iint_{\delta S}\rho\mathbf{v}~\!dt\cdot\mathbf{\hat{n}}\,dS</math>.  Dividing this by {{mvar|dV}}, and then by {{mvar|dt}}, we get the rate of reduction of density inside {{mvar|&delta;S&#8202;}}; that is, :<math>\tfrac{1}{dV}\!\iint_{\delta S}\mathbf{\hat{n}}\cdot\rho\mathbf{v}\,dS \,= -\frac{\part\rho}{\part t} \,,</math> where the derivative w.r.t. time is evaluated at a fixed location (because {{mvar|&delta;S}} is fixed), and is therefore written as a ''partial'' derivative (because other variables on which {{mvar|&rho;}} might depend&mdash;namely the coordinates&mdash;are held constant). Provided that the right-hand side is locally continuous, it can be considered uniform inside {{mvar|&delta;S}} and is therefore unambiguous, so that the left side is likewise unambiguous. But the left side is simply{{math| div&#8239;''&rho;'''''v'''}}&#8201; as defined by ({{EquationNote|4d}}),{{efn|There is no need for parentheses around{{math| ''&rho;'''''v'''&#8202;,}} because {{math|div&#8239;''&rho;'''''v'''&#8202;}} cannot mean {{math|(div&#8239;''&rho;'')'''v'''&#8202;,}} because the divergence of a scalar field is not defined.}} which is therefore also unambiguous,<ref>A demonstration like the foregoing is outlined by Gibbs ([[#gibbs-1881-4|1881]], &sect;&#8239;55).</ref> confirming theorem ({{EquationNote|5d}}). In short, the divergence operator is that which maps {{math|''&rho;'''''v'''}} to the rate of reduction of density at a fixed point: {{NumBlk|:|<math> \operatorname{div}\rho\mathbf{v} = -\frac{\part\rho}{\part t} \,. </math>|{{EquationRef|7d}}}} This result, which expresses ''conservation of mass'', is a form of the so-called '''equation of continuity'''. The partial derivative {{mvar|{{sfrac|&part;&rho;|&part;t}}&#8202;}} in ({{EquationNote|7d}}) must be distinguished from the '''material derivative''' {{mvar|{{sfrac|d&rho;|dt}}&#8202;}}, which is evaluated at a point that moves ''with the fluid''.{{efn|The material derivative {{mvar|{{sfrac|d|dt}}}} is also called the ''substantive'' derivative, and is sometimes written {{mvar|{{sfrac|D|Dt}}}} if the result is meant to be understood as a field rather than simply a function of time ([[#kemmer-77|Kemmer, 1977]], pp.&#8239;184–5).}} [Similarly, {{math|{{sfrac|''d''&#8202;'''v'''|''dt''}}}} in ({{EquationNote|6g}}) is the ''material'' acceleration, because it is the acceleration of the mobile mass&mdash;not of a fixed point!&#8239;]&#8239; To re-derive the equation of continuity in terms of the ''material'' derivative, the volume {{math|'''v'''&#8202;''dt''&#8202;'''&#11825;&#8239;n'''&#770;&#8239;''dS''&#8202;,}} which flows out through{{mvar| dS}} in time{{mvar| dt}} (as above), is integrated over {{mvar|&delta;S}} to obtain the increase in volume of the mass ''initially'' contained in {{mvar|dV}}. Dividing this by the mass, {{mvar|&rho;&#8239;dV}}, gives the increase in ''[[w:specific volume|specific volume]]'' {{math|(1&#10744;''&rho;'')}} of that mass, and then dividing by {{mvar|dt}} gives the rate of change of specific volume; that is, :<math>\tfrac{1}{\rho~\!dV}\!\iint_{\delta S}\mathbf{\hat{n}}\cdot\mathbf{v}\,dS \,= \tfrac{d}{dt}\big(\rho^{-1}\big) = -\rho^{-2\,}\tfrac{d\rho}{dt} \,.</math> Multiplying by {{math|''&rho;''&sup2;}} and comparing the left side with ({{EquationNote|4d}}), we obtain {{NumBlk|:|<math> \rho\operatorname{div}\mathbf{v} = -\frac{d\rho}{dt} \,. </math>|{{EquationRef|7d'}}}} Whereas ({{EquationNote|7d}}) shows that {{math|div&#8239;''&rho;'''''v'''&#8202;}} is unambiguous, ({{EquationNote|7d'}}) shows that {{math|div&#8239;'''v'''&#8202;}} is unambiguous (provided that the right-hand sides are locally continuous). In accordance with the everyday meaning of "divergence", ({{EquationNote|7d'}}) also shows that {{math|div&#8239;'''v'''&#8202;}} is positive if the fluid is expanding ({{mvar|&rho; }}decreasing), negative if it is contracting ({{mvar|&rho; }}increasing), and zero if it is incompressible. In the last case, the equation of continuity reduces to {{NumBlk|:|<math> \operatorname{div}\mathbf{v} = 0 \qquad</math>[&#8202;for an incompressible fluid&#8202;].|{{EquationRef|7i}}}} For incompressible flow, any tubular surface tangential to the flow velocity, and consequently with no flow in or out of the "tube", has the same volumetric flow rate across all cross-sections of the "tube", as if the surface were the wall of a pipe full of liquid (except that the surface is not necessarily stationary). Accordingly, ''a vector field with zero divergence is described as '''solenoidal''''' (from the Greek word for "pipe"). More generally, a solenoidal vector field has the property that for any tubular surface tangential to the field, the flux integrals across any two cross-sections of the "tube" are the same&mdash;because otherwise there would be a net flux integral out of the closed surface comprising the two cross-sections and any segment of tube between them, in which case, by the divergence theorem ({{EquationNote|5d}}), the divergence would have to be non-zero somewhere inside, contrary to ({{EquationNote|7i}}). === Unambiguity of the curl (and gradient) === The unambiguity of the curl ({{EquationNote|4c}}) follows from the unambiguity of the divergence. Taking dot-products of ({{EquationNote|4c}}) with an arbitrary constant vector {{math|'''b''',}} we get :<math>\begin{align} \mathbf{b}\cdot\operatorname{curl}\mathbf{q}\, &=\, \mathbf{b}\cdot\tfrac{1}{dV}\!\iint_{\delta S} \mathbf{\hat{n}}\times\mathbf{q} \,dS \\[.5ex] &=\, \tfrac{1}{dV}\!\iint_{\delta S} \mathbf{b}\cdot\mathbf{\hat{n}}\!\times\!\mathbf{q} \,dS \\[1ex] &=\, \tfrac{1}{dV}\!\iint_{\delta S} \mathbf{\hat{n}}\cdot\mathbf{q}\!\times\!\mathbf{b} \,dS \,; \end{align}</math> that is, by ({{EquationNote|4d}}), {{NumBlk|:|<math>\operatorname{curl}\mathbf{q} \cdot \mathbf{b} = \operatorname{div}(\mathbf{q}\!\times\!\mathbf{b}) \qquad</math>[&#8202;for uniform {{math|'''b'''}}].|{{EquationRef|8c}}}} (The parentheses around&#8202; {{math|'''q'''&#8202;&times;&#8202;'''b'''}}&#8202; on the right, although helpful because of the spacing, are not strictly necessary, because the alternative binding would be {{math|(div&#8201;'''q''')}}, which is a scalar, whose cross-product with the vector {{math|'''b'''}} is not defined. And the left-hand expression does not need parentheses, because it can only mean the dot-product of a curl with the vector {{math|'''b'''}}; it cannot mean the curl of a dot-product, because the curl of a scalar field is not defined.) This result ({{EquationNote|8c}}) is an identity if the vector {{math|'''b'''}} is ''independent of location'', so that it can be taken inside or outside the surface integral; thus {{math|'''b'''}} may be a uniform vector field, and may be time-dependent. If we make {{math|'''b'''}} a ''unit'' vector, the left side of the identity is the (scalar) component of {{math|curl&#8239;'''q'''}} in the direction of{{math|&#8202; '''b''',}} and the right side is unambiguous. Thus ''the curl is unambiguous because its component in any direction is unambiguous''. This confirms theorem ({{EquationNote|5c}}). Similarly, the unambiguity of the divergence implies the unambiguity of the gradient. Starting with ({{EquationNote|4g}}), taking dot-products with an arbitrary uniform vector {{math|'''b''',}} and proceeding as above, we obtain {{NumBlk|:|<math>\nabla p \cdot \mathbf{b} = \operatorname{div} p\mathbf{b} \qquad</math>[&#8202;for uniform {{math|'''b'''}}].|{{EquationRef|8g}}}} (The left-hand side does not need parentheses, because it can only mean the dot-product of a gradient with the vector {{math|'''b'''}}; it cannot mean the gradient of the dot-product of a scalar field with a vector field, because that dot-product would not be defined.) If we make {{math|'''b'''}} a ''unit'' vector, this result ({{EquationNote|8g}}) says that the (scalar) component of{{math| &nabla;''p''}} in the direction of{{math|&#8202; '''b'''}} is given by the right-hand side, which again is unambiguous. So here we have a second explanation of the unambiguity of the gradient: like the curl, it is unambiguous because its component in any direction is unambiguous. We might well ask what happens if we take ''cross''-products with {{math|'''b'''}} on the left, instead of dot-products. If we start with ({{EquationNote|4g}}), the process is straightforward: in the end we can switch the order of the cross-product on the left, and change the sign on the right, obtaining {{NumBlk|:|<math>\nabla p \times \mathbf{b} = \operatorname{curl} p\mathbf{b} \qquad</math>[&#8202;for uniform {{math|'''b'''}}].|{{EquationRef|8p}}}} (Again no parentheses are needed.) If we start with ({{EquationNote|4c}}) instead, and take {{math|'''b'''}} inside the integral, we get a vector triple product to expand, which leads to :<math>\mathbf{b} \times \operatorname{curl}\mathbf{q} = \tfrac{1}{dV}\!\iint_{\delta S}\!\mathbf{\hat{n}}\,\mathbf{b{\cdot}q}\,dS - \tfrac{1}{dV}\!\iint_{\delta S}\!\mathbf{b{\cdot}\hat{n}\,q}\,dS \,, </math> in which the first term on the right is simply&#8202; {{math|&nabla;&#8239;'''b&#11825;q'''}}&#8201; (the gradient of the dot-product). The second term is more problematic. ''If'' we had a scalar {{mvar|p}} instead of the vector {{math|'''q''',}} we could take {{math|'''b'''}} outside the second integral, so that the second term would be (minus) {{math|'''b&#8239;&#11825;'''&#8239;&nabla;''p''}}. This suggests that the actual second term should be (minus) {{math|'''b&#8239;&#11825;'''&#8239;&nabla;'''q'''}}.&#8201; Shall we therefore adopt the second term (without the sign) as the ''definition'' of{{math|&#8202; '''b&#11825;'''&nabla;&#8239;'''q'''}} for a ''vector'' {{math|'''q'''}} (treating {{math|'''b&#11825;'''&nabla;}} as an operator), and write {{NumBlk|:|<math>\mathbf{b} \times \operatorname{curl}\mathbf{q} ~\!= \nabla\,\mathbf{b{\cdot}q} - \mathbf{b}~\!{\cdot}\nabla\,\mathbf{q} \qquad</math>[&#8202;for uniform {{math|'''b'''}}] ?|{{EquationRef|8q}}}} The proposal would be open to the objection that&#8202; {{math|'''b&#11825;'''&nabla;&#8239;'''q'''}}&#8202; had been defined only for ''uniform''{{math| '''b'''&#8202;,}} whereas&#8202; {{math|'''b&#8239;&#11825;'''&#8239;&nabla;''p''&#8202;}} (for scalar{{mvar| p}}) is defined whether {{math|'''b'''}} is uniform or not.&#8201; So, for the moment, let us put ({{EquationNote|8q}}) aside and run with ({{EquationNote|8c}}), ({{EquationNote|8g}}), and ({{EquationNote|8p}}). === Another meaning of the gradient === Let {{math|'''s&#770;'''}} be a unit vector in a given direction, and let {{mvar|s}} be a parameter measuring distance (arc length) along a path in that direction. By equation ({{EquationNote|8g}}) and definition ({{EquationNote|4d}}), we have :<math>\nabla p \cdot \mathbf{\hat{s}} = \operatorname{div} p\mathbf{\hat{s}} = \tfrac{1}{dV}\!\iint_{\delta S}\mathbf{\hat{n}}\cdot p\mathbf{\hat{s}}\,dS\,, </math> where, by the unambiguity of the divergence, the shape of the closed surface {{mvar|&delta;S}} enclosing {{mvar|dV}}&#8202; can be chosen for convenience. So let {{mvar|&delta;S}} be a right cylinder with cross-sectional area {{mvar|&alpha;}}&#8201; and perpendicular height {{mvar|ds&#8202;,}} with the path passing perpendicularly through the end-faces at parameter-values {{mvar|s}} and {{mvar|s+ds&#8202;,}} where the outward unit normal {{math|'''n'''&#770;}} consequently takes the values {{math|&minus;'''s&#770;'''}} and {{math|'''s&#770;'''&#8202;,}} respectively. And let the cross-sectional dimensions be small compared with {{mvar|ds}}&#8202; so that the values of{{mvar| p}} at the end-faces, say {{mvar|p}} and {{mvar|p+dp}}, can be taken to be the same as where the end-faces cut the path. Then&#8202; {{mvar|dV&#8201;{{=}}&#8201;&alpha;&#8239;ds&#8202;}}, and the surface integral over{{mvar| &delta;S}} includes only the contributions from the end-faces (because {{math|'''n'''&#770;}} is perpendicular to {{math|'''s&#770;'''}} elsewhere); those contributions are respectively&#8201; <math>-\mathbf{\hat{s}}\!\cdot\!p\mathbf{\hat{s}}\,\alpha\,</math> and&#8201; <math>\mathbf{\hat{s}}\!\cdot\!(p\!+\!dp)\mathbf{\hat{s}}\,\alpha~\!,</math>  i.e.&#8239; <math>-p\alpha\,</math> and <math>(p\!+\!dp)\alpha</math>.  With these substitutions the above equation becomes :<math>\begin{align} \nabla p \cdot \mathbf{\hat{s}} &= \tfrac{1}{\alpha\,ds}\Big({-}p\alpha + (p\!+\!dp)\alpha\Big) \\[1ex] &= \frac{\,p\!+\!dp ~-~ p\,}{ds} = \frac{\part p}{\part s} ~; \end{align}</math> that is, {{NumBlk|:|<math> \nabla p \cdot \mathbf{\hat{s}} = \part_s p \,, </math>|{{EquationRef|9g}}}} where the right-hand side, commonly called the '''directional derivative''' of{{mvar| p}} in the {{math|'''s&#770;'''}} direction,<ref>[[#wilson-1901|Wilson, 1901]], pp.&#8239;147–8; [[#borisenko-tarapov-68|Borisenko &amp; Tarapov, 1968]], pp.&#8239;147–8 (again); [[#hsu-84|Hsu, 1984]], p.&#8239;92; [[#kreyszig-62-|Kreyszig, 1988]], pp.&#8239;485–6; [[#wrede-spiegel-10|Wrede &amp; Spiegel, 2010]], p.&#8239;198.</ref> is the derivative of{{mvar| p}} w.r.t. distance in that direction. Although ({{EquationNote|9g}}) has been obtained by taking that direction as fixed, the equality is evidently maintained if {{mvar|s}} measures arc length along any path ''tangential''&#8202; to{{math| '''s&#770;'''}} at the point of interest. Equation ({{EquationNote|9g}}) is an alternative definition of the gradient: it says that ''the gradient of<math>~p</math> is the vector whose scalar component in any direction is the directional derivative of<math>~p</math> in that direction''. For ''real<math>~p</math>'', this component has its maximum, namely {{math|{{abs|&nabla;''p''}}&#8202;,}} in the direction of{{math| &nabla;''p''&#8202;}}; thus ''the gradient of<math>~p</math> is the vector whose direction is that in which the derivative of<math>~p</math> w.r.t. distance is a maximum, and whose magnitude is that maximum''. This is the usual conceptual definition of the gradient.<ref>Gibbs ([[#gibbs-1881-4|1881]], &sect;&#8239;50) ''introduces'' the gradient with this definition, except that he calls {{math|&nabla;''u''}} simply the ''derivative'' of{{mvar| u}}, and {{mvar|u}} the ''primitive'' of{{math| &nabla;''u''}}. Use of the term ''gradient'' as an alternative to ''derivative'' is reported by Wilson ([[#wilson-1901|1901]], p.&#8239;138).</ref> Sometimes it is convenient to work directly from this definition. For example, in Cartesian coordinates {{math|(''x'',&#8239;''y'',&#8239;''z''),}} if a scalar field is given by {{mvar|x&#8202;,}} its gradient is obviously the unit vector in the direction of the {{mvar|x }}axis, usually called {{math|'''i'''&#8202;}}; that is, {{math|&nabla;''x''&#8201;{{=}}&#8201;'''i'''}}. Similarly, if&#8201; {{math|'''r'''&#8201;{{=}}&#8201;''r''&#8202;'''r'''&#8202;&#770;}}&#8201; is the position vector, then {{math|&nabla;''r''&#8201;{{=}}&#8239;'''r'''&#8202;&#770;}}. If&#8202; {{math|'''s&#770;'''}} is ''tangential''&#8202; to a '''level surface''' of{{mvar| p}} (a surface of constant{{mvar| p}}), then {{mvar|&part;_s&#8201;p}}&#8202; in that direction is zero, in which case ({{EquationNote|9g}}) says that {{math|&nabla;''p''}} (if not zero) is orthogonal to{{math| '''s&#770;'''}}.&#8201; So<math>\,\nabla p</math> ''is orthogonal to the surfaces of constant<math>~p\,</math>'' (as we would expect, having just shown that the direction of{{math| &nabla;''p''}} is that in which {{mvar|p}} varies most steeply). This result leads to a method of finding a vector normal to a curved surface at a given point: if the equation of the surface is&#8239; {{math|''f''&#8239;('''r''')&#8201;{{=}}&#8201;''C''&#8202;,}}&#8202; where {{math|'''r''' }}is the position vector and {{mvar|C&#8202; }}is a constant (possibly zero), a suitable vector is {{math|&nabla;''f''}}&#8202; evaluated at the given point. If {{mvar|p}} is ''uniform''&#8202;&mdash;that is, if it has no spatial variation&mdash;then its derivative w.r.t. distance in every direction is zero; that is, the component of{{math| &nabla;''p''}} in every direction is zero, so that {{math|&nabla;''p''}} must be the zero vector. In short, ''the gradient of a uniform scalar field is zero''. Conversely, if {{mvar|p}} is ''not'' uniform, there must be some location and some direction in which its derivative w.r.t. distance, if defined at all, is non-zero, so that its gradient, if defined at all, is also non-zero. Thus ''a scalar field with zero gradient in some region is uniform in that region''. === Unambiguity of the Laplacian === Armed with our new definition of the gradient ({{EquationNote|9g}}), we can revisit our definition of the Laplacian ({{EquationNote|4L}}). If{{mvar| &psi;}} is a ''scalar'' field, then, by ({{EquationNote|9g}}),  <math>\part_n \psi</math> can be replaced by <math>\nabla\psi\cdot\mathbf{\hat{n}}\,</math> in ({{EquationNote|4L}}), which then becomes {{NumBlk|:|<math>\triangle\psi \,=\, \tfrac{1}{dV}\!\iint_{\delta S} \mathbf{\hat{n}}\cdot\nabla\psi \;dS \,; </math>|{{EquationRef|9L}}}} that is, by definition ({{EquationNote|4d}}), {{NumBlk|:|<math>\triangle\psi \,=\, \operatorname{div}\nabla\psi \qquad</math>[&#8202;for scalar {{mvar|&psi;}}].|{{EquationRef|9L'}}}} So ''the Laplacian of a scalar field is the divergence of the gradient''. This is the usual ''introductory'' definition of the Laplacian&mdash;and on its face is applicable only in the case of a scalar field. The unambiguity of the Laplacian, in this case, follows from the unambiguity of the divergence and the gradient. If, on the contrary, {{mvar|&psi;}} in definition ({{EquationNote|4L}}) is a ''vector'' field, then we can again take dot-products with a uniform vector {{math|'''b''',}} obtaining :<math>(\triangle\psi)\cdot\mathbf{b} \,=\, \tfrac{1}{dV}\!\iint_{\delta S} \part_n(\psi\!\cdot\!\mathbf{b}) \,dS \,. </math> If we make {{math|'''b'''}} a ''unit'' vector, this says that ''the scalar component of the Laplacian of a vector field, in any direction, is the Laplacian of the scalar component of that vector field in that direction''. As we have just established that the latter is unambiguous, so is the former. But the unambiguity of the Laplacian can be generalized further. If :{{big|<math>~\!\psi = \textstyle\sum_i \alpha_i \varphi_i</math>}} <!-- EQUATION ENLARGED TO ENSURE SUBSCRIPTS ARE LEGIBLE. -->where each <math>\varphi_i</math> is a scalar field, and each {{mvar|&alpha;_i}} is a constant, and the counter {{mvar|i}} ranges from (say) 1 to{{mvar| k&#8202;}}, then it is clear from ({{EquationNote|4L}}) that {{NumBlk|:|<!-- ENLARGED TO ENSURE SUBSCRIPTS ARE LEGIBLE: -->{{big|<math> \triangle\big( \textstyle\sum_i \alpha_i \varphi_i \big) = \textstyle\sum_i \big( \alpha_i \triangle \varphi_i \big) \,. </math>}}|{{EquationRef|10}}}} In words, this says that ''the Laplacian of a linear combination of fields is the same linear combination of the Laplacians of the same fields''&mdash;or, more concisely, that ''the Laplacian is '''[[w:linearity|linear]]'''''. I say "it is clear" because the Laplacian as defined by ({{EquationNote|4L}}) is itself a linear combination, so that ({{EquationNote|10}}) merely asserts that we can regroup the terms of a nested linear combination; the gradient, curl, and divergence as defined by ({{EquationNote|4g}}) to ({{EquationNote|4d}}) are likewise linear. It follows from ({{EquationNote|10}}) that ''the Laplacian of a linear combination of fields is unambiguous if the Laplacians of the separate fields are unambiguous''. Now we have supposed that the fields <math>\varphi_i</math> are scalar and that the coefficients {{mvar|&alpha;_i}} are constants. But the same logic applies if the "constants" are uniform basis vectors (e.g.,{{math| '''i''',&#8202;'''j''','''k'''}}), so that the "linear combination" can represent any vector field, whence the Laplacian of any vector field is unambiguous. And the same logic applies if the "constants" are chosen as a "basis" for a space of tensors of any order, so that the Laplacian of any tensor field of that order is unambiguous, and so on. In short, ''the Laplacian of any field that we can express with a uniform basis is unambiguous''. === The dot-del, del-cross, and del-dot operators === The gradient operator {{math|&nabla;}} is also called {{mvar|'''del'''}}.{{efn|Or ''nabla'', because it allegedly looks like the ancient Phoenician harp that the Greeks called by that name.}} If it simply denotes the gradient, we tend to pronounce it "grad" in order to emphasize the result. But it can also appear in combination with other operators to give other results, and in those contexts we tend to pronounce it "del". One such combination is "dot del"&mdash;&#8202;as in "{{math|&#8202;'''b&#11825;'''&nabla;&#8202;}}", which we proposed for ({{EquationNote|8q}}), but did not quite manage to define satisfactorily for a vector operand. With our new definition of the gradient ({{EquationNote|9g}}), we can now make a second attempt. A general vector field {{math|'''q'''}} can be written {{math|{{abs|'''q'''}}&#8201;'''q'''&#770;&#8202;,}} so that :<math>\mathbf{q}\cdot\nabla\psi \,=\, |\mathbf{q}| \,\mathbf{\hat{q}}\cdot\nabla\psi \,. </math> If {{mvar|&psi;}} is a ''scalar'' field, we can apply ({{EquationNote|9g}}) to the right-hand side, obtaining :{{big|<math>\mathbf{q}\cdot\nabla\psi ~\!=~\! |\mathbf{q}| \,\part_{s_q} \psi \,, </math>}} where {{mvar|s_q}} is distance in the direction of{{math| '''q'''}}. For ''scalar'' {{mvar|&psi;}}, this result is an identity between previously defined quantities. For ''non-scalar'' {{mvar|&psi;}}, we have not yet defined the left-hand side, but the right-hand side is still well-defined and self-explanatory (provided that we can differentiate {{mvar|&psi;}} w.r.t.{{mvar| s_q}}). So we are free to adopt {{NumBlk|:|{{big|<math> \mathbf{q}\;\!{\cdot}\nabla\,\psi \,:=\, |\mathbf{q}| \,\part_{s_q} \psi\,, </math>}}|{{EquationRef|11}}}} where {{mvar|s_q}} is distance in the direction of{{math| '''q'''&#8202;,}} as the general definition of the ''operator'' {{math|'''q&#11825;'''&nabla;&#8202;,}} and to interpret it as defining both a ''unary'' operator&#8202; {{math|'''q&#11825;'''&nabla;}} which operates on a generic field, and a ''binary'' operator&#8202; {{math|'''&#11825;'''&nabla;}} which takes a (possibly uniform) vector field on the left and a generic field on the right. For any vector field {{math|'''q'''&#8202;,}} it follows from ({{EquationNote|11}}) that ''if<math>~\psi</math> is a uniform field, then<math>\,\,\mathbf{q}\;\!{\cdot}\nabla~\!\psi=0</math>''. For the special case in which {{math|'''q'''}} is a unit vector {{math|'''s&#770;'''&#8202;,}} with {{mvar|s}} measuring distance in the direction of&#8202; {{math|'''s&#770;'''&#8202;,}} definition ({{EquationNote|11}}) reduces to {{NumBlk|:|<math>\mathbf{\hat{s}}{\cdot}\nabla\,\psi = \part_s \psi \,, </math>|{{EquationRef|12}}}} which agrees with ({{EquationNote|9g}}) but now holds for a ''generic'' field {{mvar|&psi;}} [whereas ({{EquationNote|9g}}) was for a ''scalar'' field, and was derived as a ''theorem'' based on earlier definitions]. So{{math| '''s&#770;&#11825;'''&nabla;&#8202;,}} with a unit vector {{math|'''s'''&#8202;,}} is the '''directional-derivative operator''' on a generic field; and by ({{EquationNote|11}}),&#8201; {{math|'''q&#11825;'''&nabla;}} is a '''scaled directional derivative''' operator on a generic field. In particular, if&#8201; {{math|'''s&#770;'''&#8201;{{=}}&#8201;'''n'''&#770;}}&#8201; we have :<math>\part_n \psi \,=\, \mathbf{\hat{n}}\;\!{\cdot}\nabla\,\psi \,,</math> which we may substitute into the original definition of the Laplacian ({{EquationNote|4L}}) to obtain {{NumBlk|:|<math>\triangle\psi \,=\, \tfrac{1}{dV}\!\iint_{\delta S} \mathbf{\hat{n}}{\cdot}\nabla\,\psi \;dS \,, </math>|{{EquationRef|13L}}}} which is just ({{EquationNote|9L}}) again, except that it now holds for for a ''generic'' field. If our general definition of the gradient ({{EquationNote|4g}}) is also taken as the general definition of the {{math|&nabla;}} operator,<ref>''Cf''. [[#borisenko-tarapov-68|Borisenko &amp; Tarapov, 1968]], p.&#8239;157, eq.&#8239;(4.43), quoted in [[#tai-95|Tai, 1995]], p.&#8239;33, eq.&#8239;(4.19).</ref> then, comparing ({{EquationNote|4g}}) with ({{EquationNote|4c}}), ({{EquationNote|4d}}), and ({{EquationNote|13L}}), we see that :<math>\begin{align} \operatorname{curl}\mathbf{q} ~\!&= \nabla(\times\mathbf{q}) \\ \operatorname{div}\mathbf{q} ~\!&= \nabla(\cdot\,\mathbf{q}) \\ \triangle\psi ~\!&= \nabla(\cdot\nabla\,\psi) \,, \end{align}</math> where the parentheses may seem to be required on account of the closing {{mvar|dS}}&#8202; in ({{EquationNote|4g}}).<ref>The first two cases may be compared with Javid &amp; Brown, 1963, cited in [[#tai-94|Tai, 1994]], p.&#8239;15.</ref> But if we write the factor {{mvar|dS}} ''before'' the integrand, the del operator in ({{EquationNote|4g}}) becomes :<math>\nabla = \tfrac{1}{dV}\!\iint_{\delta S} dS\,\mathbf{\hat{n}} </math> &mdash;''if''&#8202; we insist that it is to be read as a operator looking for an operand, and not as a self-contained expression. Then, if we similarly bring forward the {{mvar|dS}} in ({{EquationNote|4c}}), ({{EquationNote|4d}}), and ({{EquationNote|13L}}), the respective operators become<ref>The first two cases may be compared with Neff, 1991, cited in [[#tai-94|Tai, 1994]], p.&#8239;16.</ref> {{NumBlk|:|<math>\begin{align} \operatorname{curl} &= \nabla\times \\ \operatorname{div} &= \nabla~\!\boldsymbol{\cdot} \\ \triangle &= \nabla\boldsymbol{\cdot}\nabla \end{align}</math>|{{EquationRef|14}}}} (pronounced "del cross", "del dot", and "del dot del"), of which the last is usually abbreviated as{{math| &nabla;²}}&#8201; ("del squared").<ref>But Gibbs ([[#gibbs-1881-4|1881]]) and Wilson ([[#wilson-1901|1901]]) were content to leave it as {{math|&nabla;'''&#11825;'''&nabla;}}.  And they did not call it the ''Laplacian''; they used that term with a different meaning, which has apparently fallen out of fashion.</ref> These notations are ubiquitous. Another way to obtain the {{math|&nabla;&#8202;&times;}}&#8202; and {{math|&nabla;'''&#11825;'''}}&#8202; operators (but ''not''{{math|&#8202; &nabla;²}}), again inspired by ({{EquationNote|4g}}), is to define {{NumBlk|:|<math>T(\nabla) \,:=\, \tfrac{1}{dV}\!\iint_{\delta S} T(\mathbf{\hat{n}}) \,dS \,, </math>|{{EquationRef|14s}}}} where {{mvar|T}}&#8202; is any well-defined function that takes a vector argument. Setting{{math|&#8202; ''T''&#8202;(&nabla;)}} to {{math|&nabla;''p''&#8202;,}} {{math|&nabla;&#8202;&times;&#8202;'''q'''&#8202;,}} and{{math| &nabla;'''&#11825;&#8239;q'''}}&#8239; in ({{EquationNote|14s}}), we obtain respectively {{math|&nabla;''p''&#8202;,}}&#8202; {{math|curl&#8201;'''q'''&#8202;,}} and&#8202; {{math|div&#8239;'''q'''}}&#8239; as given by ({{EquationNote|4g}}) to ({{EquationNote|4d}}). But this approach has undesirable side-effects&mdash;for example, that {{math|&nabla;''p''}}&#8202; becomes synonymous with{{math| ''p''&nabla;}}.&#8201; Accordingly, Chen-To Tai,<ref>[[#tai-fang-91|Tai &amp; Fang, 1991]], pp.&#8239;168–9.</ref> on the left of ({{EquationNote|14s}}), replaces{{math| &nabla;}} with his original symbol<math>~\nabla\!\!\!\!^{\textstyle_-}~\!\!,\,</math> which he calls the "symbolic operator" or the "{{nowrap|''S''&#8202;-operator}}" or, later, the "symbolic vector" or the "dummy vector". Tai in his later works (e.g.,&#8239;[[#tai-94|1994]],&#8239;[[#tai-95|1995]]) does not tolerate cross- or dot-products involving the del operator, but ''does'' tolerate such products involving his symbolic vector ([[#tai-95|1995]], pp.&#8239;50–52). There is a misconception that the operational equivalences in ({{EquationNote|14}}) apply ''only'' in Cartesian coordinates.<ref>Durney &amp; Johnson, in ''Introduction to Modern Electromagnetics'' (1969, p.&#8239;45, cited in [[#tai-94|Tai, 1994]], p.&#8239;12), make the absurd statement that "a{{math| &nabla;}} operator cannot be defined in the other coordinate systems&hellip;" In the context, they apparently meant to say that&#8202; {{math|div&#8202;'''A'''}} isn't&#8202; {{math|&nabla;'''&#11825;A'''}}&#8202; in other coordinate systems. Robert S. Elliott, in ''Electromagnetics'' (1966, p.&#8239;606, cited in [[#tai-94|Tai, 1994]], p.&#8239;13), says that "only in Cartesian coordinates&hellip; do the gradient and divergence operators turn out to be identical." Apparently he meant to say that only in Cartesian coordinates do the two operators differ by a dot. But what these authors apparently meant to say is still wrong, as shown with counterexamples by Kemmer (next reference).</ref> Tai does not accept them even in that case. But, because these equivalences have been derived from ''coordinate-free'' definitions of the operators, they must remain valid in any coordinate system ''provided that they are expressed correctly''&mdash;without (e.g.) inadvertently taking dependent variables inside or outside differentiations.<ref>The perception that they are restricted to Cartesian coordinates arises partly from failure to allow for the variability of the basis vectors in curvilinear coordinate systems; ''cf''. [[#kemmer-77|Kemmer, 1977]], pp.&#8239;163–5, 172–3 (Exs.&#8239;2,&#8239;3,&#8239;5), 230–33 (sol'ns). From the del operator and the derivatives of the basis vectors w.r.t. the coordinates, Kemmer finds the curl and divergence in cylindrical coordinates, notes that we can do the same "with a little greater effort" in spherical coordinates (p.&#8239;230), and finds the Laplacian of a scalar in both coordinate systems (p.&#8239;231). He further reports that the method works for the Laplacian of a vector in cylindrical and spherical coordinates and is relatively convenient for the former (p.&#8239;232), for which "differentiation of the unit vectors is very simple" (p.&#8239;165).</ref> That does ''not'' mean that they are always convenient, or easily verified, or conducive to the avoidance of error. But they sometimes make useful mnemonics; e.g., they let us rewrite identities ({{EquationNote|8c}}), ({{EquationNote|8g}}), and ({{EquationNote|8p}}) as {{NumBlk|:|<math>\left.\begin{align} \nabla\!\times\!\mathbf{q}\cdot\mathbf{b} &\,=\, \nabla\cdot\mathbf{q}\!\times\!\mathbf{b}\\[.5ex] \nabla p \cdot \mathbf{b} &\,=\, \nabla\cdot\;\! p\mathbf{b}\\[.5ex] \nabla p \times \mathbf{b} &\,=\, \nabla \times p\mathbf{b} \end{align}~\right\}\quad</math>for uniform {{math|'''b'''}}. |{{EquationRef|15}}}} These would be basic ''algebraic'' vector identities if&#8202; {{math|&nabla;}} were an ordinary vector, and one could try to derive them from the "algebraic" behavior of{{math| &nabla;}}; but they're not, because it isn't, so we didn't&#8239;!  Moreover, these simple "algebraic" rules are for a uniform {{math|'''b''',}} and do not of themselves tell us what to do if&#8202; {{math|'''b'''}} is spatially variable; for example, ({{EquationNote|8g}}) is not applicable to ({{EquationNote|7d}}). === The advection operator === Variation or transportation of a property of a medium due to motion with the medium is called '''advection''' (which, according to its Latin roots, means "carrying to"). Suppose that a medium (possibly a fluid) moves with a velocity field {{math|'''v'''}} in some inertial reference frame. Let {{mvar|&psi;}} be a field (possibly a scalar field or a vector field) expressing some property of the medium (e.g., density, or acceleration, or stress,{{efn|Stress is a second-order tensor, and the origin of the term "tensor"; but, for present purposes, it's just another possible example of a field called{{mvar| &psi;}}.}}&hellip; or even {{math|'''v''' }}itself). We have seen that the time-derivative of{{mvar| &psi;}} may be specified in two different ways: as the ''partial'' derivative {{mvar|{{sfrac|&part;&psi;|&part;t}}&#8202;,}} evaluated at a fixed point (in the chosen reference frame), or as the ''material'' derivative {{mvar|{{sfrac|d&psi;|dt}}&#8202;}}, evaluated at a point moving at velocity {{math|'''v'''}} (i.e., ''with the medium''). The difference&#8202; {{mvar|{{sfrac|d&psi;|dt}}&#8202;&minus;&#8202;{{sfrac|&part;&psi;|&part;t}}&#8202;}} is due to motion with the medium. To find another expression for this difference, let {{mvar|s}} be a parameter measuring distance along the path traveled by a particle of the medium. Then, for points along the path, the surface-plot of the small change in {{mvar|&psi;}} (or any component thereof) as a function of small changes in {{mvar|t}} and {{mvar|s&#8202;}} (plotted on perpendicular axes) can be taken as a plane through the origin, so that :{{big|<math>d\psi = \tfrac{\part\psi}{\part t}~\!dt + \tfrac{\part\psi}{\part s}~\!ds \;; </math>}} that is, the change in {{mvar|&psi;}} is the sum of the changes due to the change in {{mvar|t}} and the change in {{mvar|s&#8202;}}. Dividing by {{mvar|dt}} gives :{{big|<math>\begin{align}\tfrac{d\psi}{dt} &= \tfrac{\part\psi}{\part t}+\tfrac{\part\psi}{\part s}~\!\tfrac{ds}{dt}\\[1ex] &= \tfrac{\part\psi}{\part t}+\tfrac{\part\psi}{\part s}~\!|\mathbf{v}| \,; \end{align}</math>}} i.e., :{{big|<math>\tfrac{d\psi}{dt} = \tfrac{\part\psi}{\part t} + |\mathbf{v}|\,\part_s \psi </math>}} (and the first term on the right could have been written {{mvar|&part;_t&#8239;&psi;}}). So the second term on the right is the contribution to the material derivative due to motion with the medium; it is called the '''advective term''', and is non-zero wherever a particle of the medium moves along a path on which {{mvar|&psi;}} varies with location&mdash;even if {{mvar|&psi;}} at ''each'' location is constant over time.&#8201; So the operator&#8202; {{math|{{abs|'''v'''}}&#8201;''&part;_s''&#8202;,}} where {{mvar|s}} measures distance along the path, is the ''advection operator''&#8239;: it maps a property of a medium to the advective term in the time-derivative of that property. If{{mvar| &psi;}} is {{math|'''v''' }}itself, the above result becomes :{{big|<math>\tfrac{d\mathbf{v}}{dt} = \tfrac{\part\mathbf{v}}{\part t} + |\mathbf{v}|\,\part_s \mathbf{v} \,, </math>}} where the left-hand side (the ''material'' acceleration) is as given by Newton's second law, and the first term on the right (which we might call the "partial" acceleration) is the time-derivative of velocity in the chosen reference frame, and the second term on the right (the ''advective'' term) is the correction that must be added to the "partial" acceleration in order to obtain the material acceleration. This term is non-zero wherever velocity is non-zero and varies along a path, even if the velocity at each point on the path is constant over time (as when water speeds up while flowing at a constant volumetric rate into a nozzle). Paradoxically, while the material acceleration and the "partial" acceleration are apparently linear (first-degree) in {{math|'''v''',}} their difference (the advective term) is not. Thus the distinction between {{mvar|{{sfrac|&part;&psi;|&part;t}}}} and {{mvar|{{sfrac|d&psi;|dt}}}}&#8202; has the far-reaching implication that ''fluid dynamics is non-linear''. Applying ({{EquationNote|11}}) to the last two equations, we obtain respectively {{NumBlk|:|{{big|<math>\tfrac{d\psi}{dt} = \tfrac{\part\psi}{\part t} + \mathbf{v}{\cdot}\nabla\,\psi </math>}}|{{EquationRef|16}}}} and {{NumBlk|:|{{big|<math>\tfrac{d\mathbf{v}}{dt} = \tfrac{\part\mathbf{v}}{\part t} + \mathbf{v}{\cdot}\nabla\,\mathbf{v} \,, </math>}}|{{EquationRef|16v}}}} where, in each case, the second term on the right is the advective term. So ''the '''advection operator''' can also be written''&#8239;{{math| '''v&#11825;'''&nabla;&#8202;}}. When the generic {{mvar|&psi;&#8202;}} in ({{EquationNote|16}}) is replaced by the density {{mvar|&rho;&#8202;}}, we get a relation between {{mvar|{{sfrac|&part;&rho;|&part;t}}&#8202;}} and {{mvar|{{sfrac|d&rho;|dt}}&#8202;}}, both of which we have seen before&mdash;in equations ({{EquationNote|7d}}) and ({{EquationNote|7d'}}) above. Substituting from those equations then gives {{NumBlk|:|<math> \operatorname{div}\rho\mathbf{v} \,=\, \rho\operatorname{div}\mathbf{v} \,+\, \mathbf{v}\cdot\nabla\rho \,, </math>|{{EquationRef|17}}}} where {{math|&nabla;''&rho;''}} can be taken as a gradient since {{mvar|&rho;}} is scalar. This result is in fact an identity&mdash;a ''product rule for the divergence''&mdash;as we shall eventually confirm by another method. === Generalized volume-integral theorem === We can rewrite the fourth integral theorem ({{EquationNote|5L}}) in the "dot del" notation as {{NumBlk|:|<math>\iint_S \mathbf{\hat{n}}\;\!{\cdot}\nabla\,\psi \;dS \,= \iiint_V \triangle\psi ~dV \,. </math>|{{EquationRef|18L}}}} Then, using notations ({{EquationNote|14}}), we can condense ''all four'' integral theorems ({{EquationNote|5g}}), ({{EquationNote|5c}}), ({{EquationNote|5d}}), and ({{EquationNote|18L}}) into the single equation {{NumBlk|:|<math>\iint_S \mathbf{\hat{n}} * \psi \;dS \,= \iiint_V \nabla * \psi ~dV \,, </math>|{{EquationRef|19}}}} where the wildcard {{math|&lowast;}} (conveniently pronounced "star") is a generic binary operator which may be replaced by a null (direct juxtaposition of the operands) for theorem ({{EquationNote|5g}}), or a cross for ({{EquationNote|5c}}), or a dot for ({{EquationNote|5d}}), or&#8202; {{math|'''&#11825;'''&nabla;}} for ({{EquationNote|18L}}). This single equation is a ''generalized volume-integral theorem'', relating an integral over a volume to an integral over its enclosing surface.<ref>Kemmer ([[#kemmer-77|1977]], p.&#8239;98, eq.&#8239;4) gives an equivalent result for our first three integral theorems ({{EquationNote|5g}} to {{EquationNote|5d}}) only, and calls it the ''generalized divergence theorem'' because the divergence theorem is its most familiar special case.</ref> Theorem ({{EquationNote|19}}) is based on the following definitions, which have been found unambiguous: * the ''gradient'' of a scalar field {{mvar|p}} is the closed-surface integral of&#8202; {{math|'''n'''&#770;&#8202;''p''}} per unit volume, where {{math|'''n'''&#770;}} is the outward unit normal; * the ''curl'' of a vector field is the skew surface integral per unit volume, also called the surface circulation per unit volume; * the ''divergence'' of a vector field is the outward flux integral per unit volume; and * the ''Laplacian'' is the closed-surface integral of the outward normal derivative, per unit volume. The gradient maps a scalar field to a vector field; the curl maps a vector field to a vector field; the divergence maps a vector field to a scalar field; and the Laplacian maps a scalar field to a scalar field, or a vector field to a vector field, etc. The ''gradient'' of {{mvar|p}}, as defined above, has been shown to be also * the vector whose (scalar) component in any direction is the ''directional derivative'' of{{mvar| p}} in that direction (i.e. the derivative of{{mvar| p}} w.r.t. distance in that direction), and * the vector whose direction is that in which the directional derivative of{{mvar| p}} is a maximum, and whose magnitude is that maximum. Consistent with these alternative definitions of the gradient, we have defined the&#8202;{{math| '''&#11825;'''&nabla;}} operator so that&#8202; {{math|'''s&#770;&#11825;'''&nabla;}} (for a ''unit'' vector {{math|'''s&#770;'''}}) is the operator yielding the directional derivative in the direction of&#8202; {{math|'''s&#770;'''&#8202;,}} and we have used that notation to bring theorem ({{EquationNote|5L}}) under theorem ({{EquationNote|19}}). So far, we have said comparatively little about the curl. That imbalance will now be rectified. == Closed-circuit integrals per unit area == === Instant integral theorems (on a condition) === Theorems ({{EquationNote|5g}}) to ({{EquationNote|5L}}) are three-dimensional: each of them relates an integral over a volume {{mvar|V}}&#8202; to an integral over its enclosing surface{{mvar| S}}. We now seek analogous ''two''-dimensional theorems, each of which relates an integral over a surface segment to an integral around its enclosing curve. For maximum generality, the surface segment should be allowed to be curved into a third dimension.{{efn|In mathematical jargon, it should be a two-dimensional ''manifold'' embedded in 3D Euclidean space.}} Theorems of this kind can be obtained as special cases of theorems ({{EquationNote|5g}}) to ({{EquationNote|5L}}) by suitably choosing {{mvar|V}} and {{mvar|S&#8202;}}; this is another advantage of our "volume first" approach. Let {{mvar|&Sigma;}} be a surface segment enclosed by a curve {{mvar|C}} (a ''circuit'' or ''closed contour''), and let {{mvar|l}} be a parameter measuring arc length around {{mvar|C&#8202;}}, so that a general element of{{mvar| C}}&#8202; has length{{mvar| dl&#8202;}}; and let a general element of the surface {{mvar|&Sigma;}}&#8202; have area {{mvar|d&Sigma;}}. Let<math>~\boldsymbol{\hat{\nu}}</math> be the unit normal vector at a general point on {{mvar|&Sigma;&#8202;}}, and let {{math|'''t'''&#8202;&#770;}} be the unit ''tangent'' vector to{{mvar| C}} at a general point on {{mvar|C}}&#8202; in the direction of increasing{{mvar| l}}. In the original case of a surface enclosing a volume, we had to decide whether the unit normal pointed into or out of the volume (we chose the latter). In the present case of a circuit enclosing a surface segment, we have to decide whether {{mvar|l}} is measured clockwise or counterclockwise as seen when looking in the direction of the unit normal, and we choose clockwise. So {{mvar|l }}''is measured clockwise about<math>~\boldsymbol{\hat{\nu}},</math>'' and {{mvar|C }}is ''traversed'' clockwise about<math>~\boldsymbol{\hat{\nu}}</math>. From {{mvar|&Sigma;}}&#8202; we can construct obvious candidates for {{mvar|V}} and{{mvar| S}}. From every point on {{mvar|&Sigma;&#8202;}}, erect a perpendicular with a uniform ''small''&#8202; height {{mvar|h}} in the direction of<math>~\boldsymbol{\hat{\nu}}</math>. Then simply let {{mvar|V}} be the volume occupied by all the perpendiculars, and let {{mvar|S}} be its enclosing surface. Thus {{mvar|V}} is a (generally curved) thin slab of uniform thickness{{mvar| h}}, whose enclosing surface {{mvar|S}} consists of two close parallel (generally curved) broad faces connected by a perpendicular ''edge-face'' of uniform height{{mvar| h&#8202;}}; and we can treat<math>~\boldsymbol{\hat{\nu}}</math> as a vector ''field''&#8202; by extrapolating it perpendicularly from{{mvar| &Sigma;}}. If we can arrange for {{mvar|h}} to cancel out, the volume{{mvar| V}}&#8202; will serve as a 3D representation of the surface segment{{mvar| &Sigma;}}&#8202; while the ''edge-face'' will serve as a 2D representation of the curve{{mvar| C&#8202;}}, so that our four theorems will relate an integral around {{mvar|C}}&#8202; to an integral over {{mvar|&Sigma;}}&#8201; ''provided that there is no contribution from the broad faces to the integral over''{{mvar| S}}. For brevity, let us call this proviso the ''2D condition''. ''If''&#8202; the 2D condition is satisfied, an integral over the new {{mvar|S}}&#8202; reduces to an integral over the edge-face, on which :<math>dS = h\,dl \,,</math> so that the cancellation of{{mvar| h}} will leave an integral over {{mvar|C}}&#8202; w.r.t. length. Meanwhile, in an integral over the new{{mvar| V}}, regardless of the 2D condition, we have :<math>dV = h\,d\varSigma \,,</math> so that the cancellation of{{mvar| h}} will leave an integral over {{mvar|&Sigma;}}&#8202; w.r.t. area. So, substituting for {{mvar|dS}} and {{mvar|dV}}&#8202; in ({{EquationNote|5g}}) to ({{EquationNote|5L}}), and canceling {{mvar|h}} as planned, we obtain respectively {{NumBlk|:|<math>~~~~~\!\oint_C \mathbf{\hat{n}}~\!p \,dl \,= \iint_{\varSigma} \nabla p ~d\varSigma \,, </math>|{{EquationRef|20g}}}} {{NumBlk|:|<math>\oint_C \mathbf{\hat{n}}\times\mathbf{q} \,dl \,= \iint_{\varSigma} \operatorname{curl}\mathbf{q} ~d\varSigma \,, </math>|{{EquationRef|20c}}}} {{NumBlk|:|<math>~~\!\oint_C \mathbf{\hat{n}\cdot q} \,dl \,= \iint_{\varSigma} \operatorname{div}\mathbf{q} ~d\varSigma \,, </math>|{{EquationRef|20d}}}} {{NumBlk|:|<math>~~\oint_C \part_n \psi \;dl \,= \iint_{\varSigma} \triangle\psi ~d\varSigma \,, </math>|{{EquationRef|20L}}}} ''all subject to the 2D condition''. In each equation, the circle on the left integral sign acknowledges that the integral is around a closed loop. The unit vector {{math|'''n'''&#770;&#8202;,}} which ''was'' normal to the edge-face, is now normal to both {{math|'''t'''&#8202;&#770;}} and<math>~\boldsymbol{\hat{\nu}}</math>; that is, {{math|'''n'''&#770;}} is tangential to the surface segment {{mvar|&Sigma;}}&#8202; and projects perpendicularly outward from its bounding curve. On the left side of ({{EquationNote|20g}}), the 2D condition is satisfied if (but not only if) {{math|'''n'''&#770;''p''}} takes equal-and-opposite values at any two opposing points on opposing broad faces of{{mvar| S&#8202;,}} i.e. if {{mvar|p}} takes the ''same'' value at such points, i.e. if {{mvar|p}} has a zero directional derivative normal to{{mvar| &Sigma;&#8202;,}} i.e. if {{math|&nabla;''p''}} has no component normal to{{mvar| &Sigma;}}. Thus a sufficient "2D condition" for ({{EquationNote|20g}}) is the obvious one. Skipping forward to ({{EquationNote|20L}}), we see that the 2D condition is satisfied if<math>~\part_n \psi</math> takes equal-and-opposite values at any two opposing points on opposing broad faces of{{mvar| S&#8202;,}} i.e. if<math>~\part_{\nu}\psi</math> (where <math>\nu</math> measures distance in the direction of<math>~\boldsymbol{\hat{\nu}}</math>) takes the ''same'' value at such points, i.e. if<math>~\part^2_{\nu}\psi\!=\!0</math>. For ({{EquationNote|20c}}) and ({{EquationNote|20d}}), the 2D constraint can be satisfied by construction, with more useful results&mdash;as explained under the next two headings. To facilitate this process, we first make a minor adjustment to {{mvar|&Sigma;}} and{{mvar| C}}. Noting that any curved surface segment can be approximated to any desired accuracy by a ''polyhedral'' surface enclosed by a ''polygon'', we shall indeed consider {{mvar|&Sigma;}}&#8202; to be a polyhedral surface made up of small planar elements, {{mvar|d&Sigma;}}&#8202; being the area of a general element, and we shall indeed consider {{mvar|C}} to be a polygon with short sides, {{mvar|dl}} being the length of a general side.{{efn|If any part of our argument requires {{mvar|&Sigma;}} or {{mvar|C}} to be ''smooth'', this is not an impediment, because having approximated {{mvar|&Sigma;}} or{{mvar| C}} to any desired accuracy by a polyhedron or polygon, we can then approximate the polyhedron or polygon to any desired ''higher'' accuracy by a smooth surface or curve!}} The benefit of this trick, as we shall see, is to make the unit normal <math>\boldsymbol{\hat{\nu}}</math> uniform over each surface element, without forcing us to treat {{math|'''q'''}} (or any other field) as uniform over the same element. But, as the elements of{{mvar| C}}&#8202; can ''independently'' be made as short as we like (dividing straight sides into shorter elements if necessary!), we can still consider <math>\boldsymbol{\hat{\nu}},</math> {{math|'''q'''&#8202;,}} and {{math|'''t'''&#8202;&#770;}} to be uniform over each element of{{mvar| C}}. === Special case for the gradient === In ({{EquationNote|20c}}), the 2D condition is satisfied by<math>~\mathbf{q}\!=\!p\boldsymbol{\hat{\nu}}</math> (where {{mvar|p}} is a scalar field), because then the integrand on the left is zero on the broad faces of{{mvar| S&#8202;}}, where {{math|'''n'''}} is parallel to<math>~\boldsymbol{\hat{\nu}}</math>. Equation ({{EquationNote|20c}}) then becomes {{NumBlk|:|<math> \oint_C \mathbf{\hat{n}}{\times}\boldsymbol{\hat{\nu}}~\!p \;dl \,= \iint_{\varSigma}\operatorname{curl}p\boldsymbol{\hat{\nu}}\;d\varSigma \,. </math>|{{EquationRef|21n}}}} Now on the left,&#8201; <math>\mathbf{\hat{n}}\!\times\!\boldsymbol{\hat{\nu}}\!=\!-\mathbf{\hat{t}}~\!;\,</math> and on the right, over each surface element, the unit normal <math>\boldsymbol{\hat{\nu}}</math> is uniform so that, by ({{EquationNote|8p}}),&#8201; {{midsize|<math>\operatorname{curl}p\boldsymbol{\hat{\nu}}=~\!\!\nabla p \!\times\!\boldsymbol{\hat{\nu}}=-\boldsymbol{\hat{\nu}}\!\times\!\nabla p</math>}}.  With these substitutions, the minus signs cancel and we get {{NumBlk|:|<math> \oint_C p\mathbf{\hat{t}} \,dl \,= \iint_{\varSigma} \boldsymbol{\hat{\nu}}\times\nabla p \;d\varSigma </math>|{{EquationRef|21g}}}} or, if we write&#8201; {{math|''d'''''r'''&#8201;{{=}}&#8201;'''t'''&#8202;&#770;&#8239;''dl''}}&#8201; and&#8201; <math>\boldsymbol{d\varSigma}\!=\!\boldsymbol{\hat{\nu}}\,d\varSigma~\!,</math> {{NumBlk|:|<math> \oint_C p \,d\mathbf{r} \,= \iint_{\varSigma} \big(\boldsymbol{d\varSigma}\times\!\nabla p\big) \,. </math>|{{EquationRef|21r}}}} This result, although well attested in the literature,<ref>E.g., [[#gibbs-1881-4|Gibbs, 1884]], &sect;&#8239;165, eq.&#8239;(1); [[#wilson-1901|Wilson, 1901]], p.&#8239;255, Ex.&#8239;1; [[#kemmer-77|Kemmer, 1977]], p.&#8239;99, eq.&#8239;(6); [[#hsu-84|Hsu, 1984]], p.&#8239;146, eq.&#8239;(7.31).</ref> does not seem to have a name&mdash;unlike the next result. === Special case for the curl === In ({{EquationNote|20d}}), the 2D condition is satisfied if {{math|'''q'''}} is replaced by<math>~\boldsymbol{\hat{\nu}}{\times}\mathbf{q}~\!,\,</math> because then (again) the integrand on the left is zero on the broad faces of{{mvar| S&#8202;}}, where {{math|'''n'''}} is parallel to<math>~\boldsymbol{\hat{\nu}}</math>. Equation ({{EquationNote|20d}}) then becomes {{NumBlk|:|<math> \oint_C \mathbf{\hat{n}}\cdot\boldsymbol{\hat{\nu}}{\times}\mathbf{q} \;dl \,= \iint_{\varSigma} \operatorname{div}(\boldsymbol{\hat{\nu}}\!\times\!\mathbf{q}) \,d\varSigma \,. </math>|{{EquationRef|22n}}}} Now on the left, the integrand can be written&#8201; <math>\mathbf{\hat{n}}{\times}\boldsymbol{\hat{\nu}}\!\cdot\!\mathbf{q}\!=\!-\mathbf{\hat{t}}\!\cdot\!\mathbf{q}~\!;\,</math> and on the right,&#8201; {{midsize|<math>\operatorname{div}(\boldsymbol{\hat{\nu}}\!\times\!\mathbf{q})\!=\!-\operatorname{div}(\mathbf{q}\!\times\!\boldsymbol{\hat{\nu}})\!=\!-\operatorname{curl}\mathbf{q}\cdot\boldsymbol{\hat{\nu}}\,</math>}} by identity ({{EquationNote|8c}}), since <math>\boldsymbol{\hat{\nu}}</math> is uniform over each surface element.  With these substitutions, the minus signs cancel and we get {{NumBlk|:|<math> \oint_C \mathbf{q} \cdot \mathbf{\hat{t}} \,dl \,= \iint_{\varSigma} \operatorname{curl}\mathbf{q}\cdot\boldsymbol{\hat{\nu}} \,d\varSigma </math>|{{EquationRef|22c}}}} or, if we again write&#8201; {{math|''d'''''r'''&#8201;{{=}}&#8201;'''t'''&#8202;&#770;&#8239;''dl''}}&#8201; and&#8201; <math>\boldsymbol{d\varSigma}\!=\!\boldsymbol{\hat{\nu}}\,d\varSigma~\!,</math> {{NumBlk|:|<math> \oint_C \mathbf{q} \cdot d\mathbf{r} \,= \iint_{\varSigma} \operatorname{curl}\mathbf{q}\cdot\boldsymbol{d\varSigma} \,. </math>|{{EquationRef|22r}}}} This result&mdash;the best-known theorem relating an integral over a surface segment to an integral around its enclosing curve, and the best-known theorem involving the curl&mdash;is called ''[[w:Sir George Stokes, 1st Baronet|Stokes]]' theorem'' or, more properly, the '''[[w:Lord Kelvin|Kelvin]]&ndash;Stokes theorem''',<ref>''Cf''. [[#katz-79|Katz, 1979]], pp.&#8239;149–50.</ref> or simply the ''curl theorem''.<ref>Although Hsu ([[#hsu-84|1984]], p.&#8239;141) applies that name to our theorem ({{EquationNote|5c}}).</ref> The integral on the left of ({{EquationNote|22c}}) or ({{EquationNote|22r}}) is called the '''circulation''' of the vector field {{math|'''q'''}} around the closed curve{{mvar| C}}. So, <span id="kelvin-stokes-verbal">in words</span>, the Kelvin&ndash;Stokes theorem says that ''the circulation of a vector field around a closed curve is equal to the flux of the curl of that vector field through any surface spanning that closed curve''. Now let a general element of {{mvar|&Sigma;}} (with area {{mvar|d&Sigma;&#8202;}}) be enclosed by the curve {{mvar|&delta;C}}, traversed in the same direction as the outer curve {{mvar|C}}. Then, applying ({{EquationNote|22c}}) to the single element, we have :<math> \oint_{\delta C} \!\mathbf{q} \cdot \mathbf{\hat{t}} \,dl \,=\, \operatorname{curl}\mathbf{q}\cdot\boldsymbol{\hat{\nu}} \,d\varSigma \,; </math> that is, {{NumBlk|:|<math> \operatorname{curl}\mathbf{q}\cdot\boldsymbol{\hat{\nu}} \,=\, \frac{1}{d\varSigma}\oint_{\delta C}\!\mathbf{q}\cdot\mathbf{\hat{t}}\,dl\,, </math>|{{EquationRef|23c}}}} where the right-hand side is simply the ''circulation per unit area''. Equation ({{EquationNote|23c}}) is an alternative definition of the curl: it says that ''the curl of''{{math| '''q'''}} ''is the vector whose scalar component in any direction is the circulation of''{{math| '''q'''}} ''per unit area of a surface whose normal points in that direction''. For ''real''{{math| '''q''',}} this component has its maximum, namely {{math|{{abs|curl&#8201;'''q'''}}&#8202;,}} in the direction of{{math| curl&#8239;'''q'''&#8202;}}; thus ''the curl of''{{math| '''q'''}} ''is the vector whose direction is that which a surface must face if the circulation of''{{math| '''q'''}} ''per unit area of that surface is to be a maximum, and whose magnitude is that maximum''. This is the usual conceptual definition of the curl.<ref>E.g., [[#gibbs-1881-4|Gibbs, 1881]], &sect;&#8239;61; [[#hsu-84|Hsu, 1984]], pp.&#8239;117–18.</ref> [Notice, however, that our original volume-based definition ({{EquationNote|4c}}) is more succinct: the curl is the closed-surface circulation per unit volume, i.e. the skew surface integral per unit volume.] It should now be clear where the curl gets its name (coined by [[w:James Clerk Maxwell|Maxwell]]), and why it is also called the ''rotation'' (indeed the {{math|curl}} operator is sometimes written "{{math|rot}}", especially in Continental languages, in which "rot" does not have the same unfortunate everyday meaning as in English). It should be similarly unsurprising that ''a vector field with zero curl is described as '''irrotational''''' (which one must carefully pronounce differently from "{{nowrap|irr''i&#8202;''tational}}"!), and that the curl of the velocity of a medium is called the '''vorticity'''. [[File:Vorticity_Figure_03_a-m.gif|thumb|Animation of a non-vortex-like velocity field whose curl (like its circulation around the red loop) is non-zero due to shear.]] [[File:Vorticity_Figure_02_a-m.gif|thumb|Animation of a vortex-like velocity field whose curl is zero because the shear compensates for the rotation.]] However, a field does not need to be vortex-like in order to have a non-zero curl; for example, by identity ({{EquationNote|8p}}), in Cartesian coordinates, the velocity field {{math|''x'''''j'''}} has a curl equal to&#8201; {{math|&nabla;''x''&#8201;&times;&#8239;'''j'''&#8201;{{=}}&#8201;'''i'''&#8202;&times;&#8202;'''j'''&#8201;{{=}}&#8201;'''k'''&#8202;,}}&#8201; although it describes a ''shearing'' motion rather than a rotating motion. This is understandable because if you hold a pencil between the palms of your hands and slide one palm over the other (a shearing motion), the pencil rotates. Conversely, we can have a vortex-like field whose curl is zero everywhere except on or near the axis of the vortex. For example, the '''Maxwell&ndash;Amp&egrave;re law''' in magnetostatics says that&#8201; {{math|curl&#8201;'''H'''&#8201;{{=}}&#8201;'''J'''&#8202;,}} where {{math|'''H'''}} is the '''magnetizing field''' and {{math|'''J'''}} is the current density.{{efn|In the general case, there is an extra term {{math|{{sfrac|''&part;''&#8202;'''D'''|''&part;t''}}}} on the right; but this term is zero in the magneto''static'' case.}} So if the current is confined to a wire, {{math|curl&#8201;'''H'''&#8202;}} is zero outside the wire&mdash;although, as is well known, the field lines circle the wire. The resolution of the paradox is that {{math|'''H'''}} gets stronger as we approach the wire, making a shearing pattern, whose effect on the curl counteracts that of the rotation. === The curl-grad and div-curl operators === We have seen from ({{EquationNote|9L}}) that the Laplacian of a scalar field is the divergence of the gradient. Four more such second-order combinations make sense, namely the curl of the gradient (of a scalar field), and the divergence of the curl, the gradient of the divergence, and the curl of the curl (of a vector field). The first two&#8239;&mdash;"curl grad" and "div curl"&mdash;&#8239;can now be disposed of. Let the surface segment {{mvar|&Sigma;}} enclosed by the curve{{mvar| C}}&#8202; be a segment of the closed surface {{mvar|S}} surrounding the volume{{mvar| V}}, and let {{mvar|&Sigma;}} expand across {{mvar|S}} until it engulfs{{mvar| V},} so that {{mvar|C}} shrinks to a point on the far side of{{mvar| S}}. Then, in the nameless theorem ({{EquationNote|21g}}) and the Kelvin&ndash;Stokes theorem ({{EquationNote|22c}}), the integral on the left becomes zero while {{mvar|&Sigma;}} and <math>\boldsymbol{\hat{\nu}}</math> on the right become {{mvar|S}} and {{math|'''n'''&#770;&#8202;,}} so that the theorems respectively reduce to :<math> \iint_S \mathbf{\hat{n}}\times\nabla p \;dS \,=\, \mathbf{0} </math> and :<math> \iint_S \mathbf{\hat{n}}\cdot\operatorname{curl}\mathbf{q} \;dS \,=\, 0 \,. </math> Applying theorem ({{EquationNote|5c}}) to the first of these two equations, and the divergence theorem ({{EquationNote|5d}}) to the second, we obtain respectively :<math>\iiint_V \operatorname{curl}\nabla p \;dV ~\!=\, \mathbf{0} \,,</math> and :<math> \iiint_{V} \operatorname{div}\operatorname{curl}\mathbf{q} \;dV ~\!=\, 0 \,. </math> As the integrals vanish for ''any'' volume {{mvar|V}}&#8202; in which the integrands are defined, the integrands must be zero wherever they are defined; that is, {{NumBlk|:|<math> \operatorname{curl}\nabla p \equiv \mathbf{0} </math>|{{EquationRef|24c}}}} and {{NumBlk|:|<math> \operatorname{div}\operatorname{curl}\mathbf{q} \equiv 0 \,. </math>|{{EquationRef|24d}}}} In words, ''the curl of the gradient is zero'', and ''the divergence of the curl is zero''; or, more concisely, ''any gradient is irrotational'', and ''any curl is solenoidal''. We might well ask whether the converses are true. Is every irrotational vector field the gradient of something? And is every solenoidal vector field the curl of something? The answers are affirmative, but the proofs require more preparation. Meanwhile we may note, as a mnemonic aid, that when the left-hand sides of the last two equations are rewritten in the del-cross and del-dot notations, they become&#8201; {{math|&nabla;&#8201;&times;&#8201;&nabla;''p''}}&#8201; and&#8201; {{math|&nabla;&#8201;'''&#11825;'''&#8201;&nabla;&#8202;&times;&#8202;'''q'''&#8202;,}} respectively. The former ''looks like'' (but isn't) a cross-product of two parallel vectors, and the latter ''looks like'' (but isn't) a scalar triple product with a repeated factor, so that each expression ''looks like'' it ought to be zero (and it is). But such appearances can lead one astray, because {{math|&nabla;}} is an operator, not a self-contained vector quantity; for example,&#8201; {{math|&nabla;''p''&#8201;&times;&#8201;&nabla;''&phi;''}}&#8201; is ''not'' identically zero, because two gradients are not necessarily parallel.<ref>''Cf''. [[#feynman-63|Feynman, 1963]], vol.&#8239;2, &sect;2-8.</ref> We should also note, to tie a loose end, that identity ({{EquationNote|24d}}) was to be expected from our [[#kelvin-stokes-verbal|verbal statement]] of the Kelvin&ndash;Stokes theorem ({{EquationNote|22c}}). That statement implies that the flux of the curl through any two surfaces spanning the same closed curve is the same. So if we make a ''closed'' surface from two spanning surfaces, the flux into one spanning surface is equal to the flux out of the other, i.e. the net flux out of the closed surface is zero, i.e. the integral of the divergence over the enclosed volume is zero; and since ''any'' simple volume in which the divergence is defined can be enclosed this way, the divergence itself (of the curl) must be zero wherever it is defined. == Change per unit length == Continuing (and concluding) the trend of reducing the number of dimensions, we now seek ''one''-dimensional theorems, each of which relates an integral over a ''path'' to values at the endpoints of the path. For maximum generality, the path should be allowed to be curved into a second and a third dimension. We ''could'' do this by further specializing theorems ({{EquationNote|5g}}) to ({{EquationNote|5L}}). We could take a curve {{math|&Gamma;}} with a unit tangent vector {{math|'''s&#770;'''}}. At every point on {{math|&Gamma;}} we could mount a circular disk with a uniform ''small'' area {{mvar|&alpha;&#8202;,}} centered on{{math| &Gamma;}} and orthogonal to it. We could let {{mvar|V}} be the volume occupied by all the disks and let {{mvar|S}} be its enclosing surface; thus {{mvar|V}} would be a thin right circular cylinder, except that its axis could be curved. If we could arrange for {{mvar|&alpha;}} to cancel out, our four theorems would indeed be reduced to the desired form, ''provided'' that there were no contribution from the curved face of the "cylinder" to the integral over{{mvar| S}} (the "1D proviso"). But, as it turns out, this exercise yields only one case in which the "1D proviso" can be satisfied by a construction involving {{math|'''s&#770;'''}} and a general field, and we have already ''almost'' discovered that case by a simpler and more conventional argument&mdash;which we shall now continue. === Fundamental theorem === Equation ({{EquationNote|9g}}) is applicable where {{math|''p''('''r''')}} is a scalar field,&#8201; {{mvar|s}} is a parameter measuring arc length along a curve{{math| &Gamma;,}} and {{math|'''s&#770;'''}} is the unit tangent vector to{{math| &Gamma;}} in the direction of increasing{{mvar| s}}. Let {{mvar|s}} take the values {{math|''s''₁}} and {{math|''s''₂}} at the endpoints of{{math| &Gamma;,}} where the position vector {{math|'''r'''}} takes the values {{math|'''r'''₁}} and {{math|'''r'''₂}} respectively. Then, integrating ({{EquationNote|9g}}) w.r.t.{{mvar| s}} from {{math|''s''₁}} to {{math|''s''₂}} and applying the fundamental theorem of calculus, we get {{NumBlk|:|<math> \int_{s_1}^{s_2} \nabla p \cdot \mathbf{\hat{s}} \,ds \,=\, p(\mathbf{r}_2) - p(\mathbf{r}_1) \,. </math>|{{EquationRef|25g}}}} This is our third integral theorem involving the gradient, and the best-known of the three: it is commonly called simply the '''[[w:gradient theorem|gradient theorem]]''',<ref>Although Hsu ([[#hsu-84|1984]], p.&#8239;141) applies that name to our theorem ({{EquationNote|5g}}).</ref> or the ''fundamental theorem of the gradient'', or the ''fundamental theorem of line integrals''; it generalizes the fundamental theorem of calculus to a curved path.<ref>''Cf''. [[#gibbs-1881-4|Gibbs, 1881]], &sect;&sect;&#8239;50,&#8239;59; presumably this is one reason why Gibbs called the gradient simply the ''derivative''.</ref> If we write {{math|''d'''''r'''}}&#8202; for&#8239; {{math|'''s&#770;'''&#8239;''ds''}} (the change in the position vector), we get the theorem in the alternative form {{NumBlk|:|<math> \int_{\mathbf{r}_1}^{\mathbf{r}_2} \nabla p \cdot d\mathbf{r} \,=\, p(\mathbf{r}_2) - p(\mathbf{r}_1) \,. </math>|{{EquationRef|25r}}}} As the right-hand side of ({{EquationNote|25g}}) or ({{EquationNote|25r}}) obviously depends on the endpoints but ''not on the path in between'', so does the integral on the left. This integral is commonly called the '''work integral''' of{{math| &nabla;''p''}} over the path&mdash;because if {{math|&nabla;''p''}} is a force, the integral is the work done by the force over the path. So, in words, the gradient theorem says that ''the change in value of a scalar field from one point to another is the work integral of the gradient of that field field over any path from the one to the other''. Applying ({{EquationNote|25r}}) to a single element of the curve, we get {{NumBlk|:|<math>\nabla p \cdot d\mathbf{r} = dp \,, </math>|{{EquationRef|26g}}}} which is reminiscent of&#8201; <math>y'(x)~\!dx\,{=}\,dy\,</math> in elementary calculus.<ref>''Cf''. [[#gibbs-1881-4|Gibbs, 1881]], &sect;&sect;&#8239;50,&#8239;51; presumably this is another reason why Gibbs called the gradient the ''derivative''.</ref> Alternatively, we could have obtained ({{EquationNote|26g}}) by multiplying both sides of ({{EquationNote|9g}}) by{{mvar| ds}}, and then obtained ({{EquationNote|25r}}) by adding ({{EquationNote|26g}}) over all the elemental displacements{{math| ''d'''''r'''}} on any path from {{math|'''r'''₁}} to{{math| '''r'''₂}}. If we ''close'' the path by setting&#8201; {{math|'''r'''₂{{=}} '''r'''₁&#8202;,}} the gradient theorem reduces to {{NumBlk|:|<math>\oint \nabla p \cdot d\mathbf{r} \,=\, 0 \,, </math>|{{EquationRef|27g}}}} where the integral is around ''any'' closed loop. Applying the Kelvin&ndash;Stokes theorem then gives {{NumBlk|:|<math> \iint_{\varSigma} \operatorname{curl}\nabla p \cdot \boldsymbol{\hat{\nu}} \,d\varSigma \,=\, 0 \,, </math>|{{EquationRef|28g}}}} where {{mvar|&Sigma;}} is any surface spanning the loop and<math>~\boldsymbol{\hat{\nu}}</math> is the unit normal to{{mvar| &Sigma;}}.&#8201; As this applies to any loop spanned by any surface on which the integrand is defined,&#8201; {{math|curl&#8201;&nabla;''p''}}&#8202; must be zero wherever it is defined. This is a second proof (more conventional than the first) of theorem ({{EquationNote|24c}}). === Scalar potential: field with given gradient === '''Lemma''':  If&#8201; {{math|curl&#8239;'''q'''&#8201;{{=}}&#8201;'''0'''}}&#8201; in a simply connected region{{mvar| V}},&#8201; then&#8239; <math>\textstyle\int\!\mathbf{q}\!\cdot\!d\mathbf{r}\,</math> over any path in{{mvar| V}}&#8239; depends only on the endpoints of the path. ''Proof:''  Suppose, on the contrary, that there are two paths {{math|&Gamma;}} and {{math|&Lambda;}} in{{mvar| V}},&#8202; with a common starting point and a common finishing point, such that :<math>\textstyle\int_{\Gamma}\mathbf{q}\cdot d\mathbf{r} \,\neq \textstyle\int_{\Lambda}\mathbf{q}\cdot d\mathbf{r} \,.</math> Let&#8201; {{math|&minus;&Lambda;}} denote {{math|&Lambda;}} traversed backwards. Then for every {{math|''d'''''r'''}} on {{math|&Lambda;}}&#8201; there is an equal and opposite{{math| ''d'''''r'''}} on&#8202; {{math|&minus;&Lambda;&#8202;,}} so that we have :<math>\textstyle\int_{\Gamma}\mathbf{q}\cdot d\mathbf{r} \,\neq\, \textstyle-\!\int_{-\Lambda}\mathbf{q}\cdot d\mathbf{r} \,,</math> i.e. :<math>\textstyle\int_{\Gamma}\mathbf{q}\cdot d\mathbf{r} \,+ \textstyle\int_{-\Lambda}\mathbf{q}\cdot d\mathbf{r} \,\neq\, 0 \,,</math> where the left-hand side is now a work integral of{{math| '''q'''}} around a closed loop in{{mvar| V}}.&#8201; By the simple connectedness of{{mvar| V}},&#8202; this loop is spanned by some surface{{mvar| &Sigma;}} in{{mvar| V}}.&#8201; So we can apply the Kelvin&ndash;Stokes theorem and conclude that the flux integral of&#8202; {{math|curl&#8239;'''q'''}}&#8202; through{{mvar| &Sigma;}}&#8202; is non-zero, in which case&#8202; {{math|curl&#8239;'''q'''}}&#8202; must be non-zero somewhere on{{mvar| &Sigma;&#8202;,}} hence somewhere in{{mvar| V}}&#8201;&mdash;&#8239;contradicting the hypothesis of the lemma. &#9724; '''Corollary''':  If&#8201; {{math|curl&#8239;'''q'''&#8201;{{=}}&#8201;'''0'''}}&#8201; in a simply connected region{{mvar| V}},&#8202; there exists a scalar field {{mvar|p}} such that&#8239; {{math|'''q'''&#8201;{{=}}&#8201;&nabla;''p''}}&#8201; in{{mvar| V}}. ''Proof:''  We shall show that a suitable candidate is :<math>p(\mathbf{r}) \,= \int_{\mathbf{r}_0}^{\mathbf{r}} \!\mathbf{q}\cdot d\boldsymbol{\rho} \,, </math> where {{math|'''r'''₀}} is the position vector of any fixed point in{{mvar| V}},&#8202; and {{mvar|'''&rho;'''}} is the position vector of a general point on the path of integration, which may be any path in{{mvar| V}}. First note that {{math|''p''('''r''')}} is unambiguous because, by the preceding lemma, it is independent of the path for given {{math|'''r'''₀}} and{{math| '''r''',}} provided that the path is in{{mvar| V}}.&#8201; Now to find&#8202; {{math|&nabla;''p''('''r'''),}}&#8202; let {{mvar|&sigma;}} be the arc length along the path from {{math|'''r'''₀}} to{{mvar| '''&rho;'''&#8202;}}, so that {{mvar|&sigma;}} ranges from 0 to (say){{mvar| s}}&#8201; as {{mvar|'''&rho;'''}} ranges from {{math|'''r'''₀}} to{{math| '''r'''&#8202;}}; and let {{math|'''s&#770;'''}} be the unit vector tangential to the path at{{mvar| '''&rho;'''&#8202;}}, in the direction of increasing{{mvar| &sigma;}}.&#8201; Then&#8239; {{math|''d'''&rho;'''''&#8201;{{=}}&#8201;'''s&#770;'''&#8239;''d&sigma;''&#8202;,}} so that the above equation becomes :<math>p\big(\mathbf{r}(s)\big) \,= \int_0^s \!\mathbf{q}\cdot\mathbf{\hat{s}} \,d\sigma \,. </math> Differentiating w.r.t.{{mvar| s}} gives :<math>\part_s p = \mathbf{q}\cdot\mathbf{\hat{s}} \,,</math> where {{math|'''s&#770;'''}} is evaluated at&#8201; {{mvar|&sigma;&#8201;{{=}}&#8201;s}}&#8201; and is therefore in the direction in which the path reaches{{math| '''r'''}}.&#8201; By the generality of the path, this can be ''any'' direction. So the last equation says that {{math|'''q'''}} is the vector whose (scalar) component in any direction is the derivative of{{mvar| p}} w.r.t. arc length in that direction; that is, {{math|'''q'''&#8201;{{=}}&#8201;&nabla;''p''&#8202;,}} as required. &#9724; This is the promised converse of theorem ({{EquationNote|24c}}). ''But'', given an irrotational vector field {{math|'''q'''&#8202;,}} we usually prefer to find a scalar field whose ''negative'' gradient is{{math| '''q'''&#8202;}};&#8201; that is, we usually prefer a scalar field <math>\varphi</math> such that&#8201; <math>\mathbf{q}~\!\!=\!-\nabla\varphi</math>.&#8201; Such a field <math>\varphi</math> is called a '''scalar potential''' for{{math| '''q'''}}.&#8201; From the above expression for {{math|''p''('''r'''),}} a suitable candidate is {{NumBlk|:|<math>\varphi(\mathbf{r}) \,=\, -\!\int_{\mathbf{r}_0}^{\mathbf{r}} \!\mathbf{q}\cdot d\boldsymbol{\rho} \,. </math>|{{EquationRef|29}}}} A scalar field has zero gradient if and only if it is uniform, so that adding a uniform field, but ''only'' a uniform field, to a given scalar field leaves its gradient unchanged. Thus ''the scalar potential is determined up to an arbitrary additive uniform field''. This would be the case with or without the minus sign in front of the gradient. The reason for preferring the minus sign appears next. === Conservative fields === An irrotational vector field&mdash;or, equivalently, a field that is (plus or minus) the gradient of something&mdash;is described as '''conservative''', because if the field is a force, it does zero work around a closed loop, and consequently ''conserves energy'' around the loop (at least if the field does not change during traversal of the loop). If the only force acting on a particle is&#8201; {{math|'''F'''&#8201;{{=}}&#8201;&minus;&nabla;''U'',}}&#8201; then, by the gradient theorem, the work done on the particle over a path is the increase in {{mvar|&minus;U}},&#8201; i.e. the ''decrease'' in{{mvar| U&#8202;}}; and this work is the increase in the particle's kinetic energy{{mvar| T}}.&#8201; Hence, if we identify {{mvar|U}} with the ''potential'' energy, the total energy&#8202; {{mvar|U&#8202;+&#8202;T}}&#8201; is conserved. This interpretation of the scalar potential is possible only if the force is ''minus'' the gradient of the potential. The minus sign is also used if the conservative vector field is an '''electric field''' (force per unit charge) or a gravitational acceleration (force per unit mass); the scalar potential is potential energy per unit charge, or potential energy per unit mass, respectively. == Some special fields == === The 1/''r'' scalar potential === For the potential energy field {{NumBlk|:|<math>U = \frac{1}{\,r\,} \,</math>|{{EquationRef|30}}}} where {{mvar|r}} is the distance from the origin (and {{math|''r''&#8201;&ne;&#8201;0}}), let us find the corresponding force&#8201; {{math|'''F'''&#8201;{{=}}&#8201;&minus;&nabla;''U''}}.&#8201; The direction of&#8202; {{math|&nabla;''U''}}&#8202; is that of the steepest increase of{{mvar| U}}, which, by the spherical symmetry, can only be parallel or antiparallel to {{math|'''r'''&#8202;&#770;}} (the unit vector pointing away from the origin). So :<math>\nabla U = \big(\nabla U \cdot \mathbf{\hat{r}}\big)~\!\mathbf{\hat{r}} = \part_r U \,\mathbf{\hat{r}} = \frac{d}{dr}\Big(\!\frac{1}{\,r\,}\!\Big)~\!\mathbf{\hat{r}} = -\frac{1}{\,r^2}~\!\mathbf{\hat{r}} \,,</math> whence {{NumBlk|:|<math>\mathbf{F} = \frac{\mathbf{\hat{r}}}{\,r^2} \,. </math>|{{EquationRef|31}}}} So the negative gradient of the {{math|1/''r''}}&#8202; scalar potential ({{EquationNote|30}}) is the unit '''inverse-square radial vector field'''. Multiplying the numerator and denominator by {{mvar|r}} gives the alternative form :<math>\mathbf{F} = \frac{\mathbf{r}}{\,r^3} \,,</math> which is convenient if the center of the force is shifted from the origin to position{{math| '''r&prime;'''}}: in that case we simply replace {{math|'''r'''}} by {{math|'''r'''&#8202;&minus;&#8202;'''r&prime;''',}} and {{mvar|r}} by {{math|{{abs|'''r'''&#8202;&minus;&#8202;'''r&prime;'''}},}} so that the force becomes :<math>\mathbf{F} = \frac{\mathbf{r}\!-\!\mathbf{r}'} {|\mathbf{r}\!-\!\mathbf{r}'|^3}</math> and the corresponding scalar potential becomes :<math>U = \frac{1}{|\mathbf{r}\!-\!\mathbf{r}'|} \,.</math> === Inverse-square radial vector field === We derived the vector field ({{EquationNote|31}}) as the negative gradient of the scalar potential ({{EquationNote|30}}). Conversely, given the inverse-square radial vector field ({{EquationNote|31}}), we could derive its scalar potential from ({{EquationNote|29}}). At a general point on the path, let the position vector be&#8201; <math>\boldsymbol{\rho}~\!\!=\!\rho\boldsymbol{\hat{\rho}}\,</math> so that, by ({{EquationNote|31}}),&#8201; <math>\mathbf{F}\!=\!\boldsymbol{\hat{\rho}}/\rho^2</math>.&#8201; Then ({{EquationNote|29}}) becomes :<math>\begin{align}U(\mathbf{r}) \,&=\, -\!\int_{\mathbf{r}_0}^{\mathbf{r}} \! \mathbf{F} \cdot d\boldsymbol{\rho} \\[1ex] &=\, -\!\int_{\mathbf{r}_0}^{\mathbf{r}} \! \tfrac{1}{\,\rho^2}~\! \boldsymbol{\hat{\rho}} \!\cdot\! d\boldsymbol{\rho} \\[1ex] &=\, -\!\int_{r_0}^r \! \tfrac{1}{\,\rho^2} \,d\rho \ =\, \tfrac{1}{\,\rho\,}\bigg|^r_{r_0} \,=\, \frac{1}{\,r\,}-\frac{1}{\,r_0} \,, \end{align}</math> so that, if we choose&#8201; {{math|''r''₀&#8202;&rarr;&#8239;&infin;&#8202;,}} we recover ({{EquationNote|30}}). Because {{math|'''F''',}} given by ({{EquationNote|31}}), has a scalar potential,&#8201; {{math|curl&#8201;'''F'''}}&#8202; must be zero. This is independently obvious in that the spherical symmetry of{{math|&#8202; '''F'''}} seems to rule out any resemblance of rotation or shear&mdash;even at the origin, where {{math|'''F'''}} becomes infinite. On the last point, let us check whether&#8201; {{math|curl&#8201;'''F'''}}&#8202; has a meaningful integral over a volume containing the origin. If the volume {{mvar|V}}&#8202; is enclosed by the surface {{mvar|S}}&#8202; whose outward unit normal is {{math|'''n'''&#770;&#8202;}}, then, by theorem ({{EquationNote|5c}}), :<math>\iiint_V \operatorname{curl}\mathbf{F} ~dV \,= \iint_S \mathbf{\hat{n}}\times\mathbf{F} \,dS \,= \iint_S \mathbf{\hat{n}}\times\frac{\mathbf{\hat{r}}\,}{r^2} \,dS \,. </math> If {{mvar|V}} contains the origin, then, because&#8201; {{math|curl&#8201;'''F'''}}&#8239; is zero everywhere ''except'' at the origin, the volume {{mvar|V}}&#8202; can be replaced by any ''element'' of{{mvar| V}}&#8202; containing the origin, whatever the shape of that element may be. If we choose that element to be a spherical ball centered on the origin, then {{math|'''n'''&#770;}} is parallel to {{math|'''r'''&#8202;&#770;&#8202;,}} so that the cross-product in the integrand on the right is zero. Thus the volume integral on the left is not only meaningful, but is ''zero'', even if the volume contains the point where the integrand is infinite. In this sense, the field {{math|'''F'''}} is ''so'' irrotational that its curl may be taken as zero even where the field itself is undefined! The situation concerning the ''divergence'' of{{math|&#8202; '''F'''}} is more complicated. Again, let the volume {{mvar|V}}&#8202; be enclosed by the surface {{mvar|S}} whose outward unit normal is {{math|'''n'''&#770;}}.&#8201; By the divergence theorem ({{EquationNote|5d}}), :<math>\begin{align}\iiint_V \operatorname{div}\mathbf{F} ~dV \,= \iint_S \mathbf{\hat{n}}\cdot\mathbf{F} \,dS \,&= \iint_S \mathbf{\hat{n}}\cdot\frac{\mathbf{\hat{r}}\,}{r^2} \,dS\\[1ex] &= \iint_S \frac{\mathbf{\hat{r}}\cdot\mathbf{\hat{n}}\,dS}{\,r^2} \\[1ex] &= \iint_S d\Omega \,, \end{align}</math> where {{math|''d''&Omega;}} is the ''solid angle'' subtended at the origin by the surface element of area{{mvar| dS&#8202;}}, and is positive if the outward unit normal {{math|'''n'''&#770;}} has a positive component ''away from'' the origin ({{math|'''r'''&#8202;&#770;'''&#11825;&#8202;n'''&#770;&#8201;&gt;&#8201;0}}), and negative if {{math|'''n'''&#770;}} has a positive component ''toward'' the origin ({{math|'''r'''&#8202;&#770;'''&#11825;&#8202;n'''&#770;&#8201;&lt;&#8201;0}}). If the volume enclosed by {{mvar|S}} does ''not'' include the origin, then for every positive contribution {{math|''d''&Omega;}} there is a compensating negative contribution, so that the integral of&#8201; {{math|div&#8201;'''F'''}}&#8202; over the volume is zero. As this applies to every such volume,&#8201; {{math|div&#8201;'''F'''}}&#8202; must be zero everywhere except at the origin. If, on the contrary, the volume ''does'' include the origin, then the contributions {{math|''d''&Omega;}} add up to the total solid angle subtended by the enclosing surface, which is{{math| 4''&pi;''}}. In summary, {{NumBlk|:|<math>\mathrm{div}\Big(\frac{\mathbf{\hat{r}}}{\,r^2}\Big) =~\! 4\pi~\!\delta(\mathbf{r}) \,,</math>|{{EquationRef|32d}}}} where {{math|''&delta;''('''r'''),}} the 3D '''unit delta function''', is zero everywhere except at the origin, but has an integral of&#8202; {{math|1}} over any volume that includes the origin. For example, a unit point-mass at the origin has the density {{math|''&delta;''('''r''')}}, and a point-mass {{mvar|m}} at position {{math|'''r&prime;'''}} has the density&#8202; {{math|''m&delta;''('''r'''&#8202;&minus;&#8202;'''r&prime;''')}}. As the argument of&#8202; {{math|div}}&#8202; in ({{EquationNote|32d}}) is&#8202; {{math|&minus;&nabla;(1/''r''),}} we also have {{NumBlk|:|<math>\triangle\Big(\frac{1}{\,r\,}\Big) = -4\pi~\!\delta(\mathbf{r}) \,.</math>|{{EquationRef|32L}}}} If we shift the centers from the origin to {{math|'''r&prime;''',}} the last two results become {{NumBlk|:|<math> \mathrm{div}\bigg(\frac{ \mathbf{r}\!-\!\mathbf{r}'} {|\mathbf{r}\!-\!\mathbf{r}'|^3} \!\bigg) =~\! 4\pi~\!\delta(\mathbf{r}\!-\!\mathbf{r}') </math>|{{EquationRef|33d}}}} and {{NumBlk|:|<math> \triangle\bigg(\frac{1}{|\mathbf{r}\!-\!\mathbf{r}'|}\bigg) = -4\pi~\!\delta(\mathbf{r}\!-\!\mathbf{r}') \,. </math>|{{EquationRef|33L}}}} === Field with given divergence (and zero curl) === It follows from '''Coulomb's law''' that the electric field due to a point-charge {{mvar|Q}} at the origin, in a vacuum, is :<math>\mathbf{E} = \frac{Q}{4\pi\epsilon_0 r^2} ~\!\mathbf{\hat{r}} \,,</math> where {{math|''&epsiv;''₀}} is a physical constant (called the '''vacuum permittivity''' or simply the '''electric constant'''). In a ''vacuum'', the '''electric displacement field''', denoted by{{math| '''D'''&#8202;,}} is {{math|''&epsiv;''₀'''E'''}}.&#8201; So it is convenient to multiply the above equation by {{math|''&epsiv;''₀&#8202;,}} obtaining :<math>\mathbf{D} = \frac{Q}{4\pi} ~\!\frac{\mathbf{\hat{r}}\,}{r^2} \,.</math> This is a inverse-square radial vector field and therefore has zero curl. Now suppose that, instead of a charge {{mvar|Q}} at the origin, we have a static ''charge density'' {{math|''&rho;''('''r&prime;''')}} in a general elemental volume {{mvar|dV&prime;}}&#8202; at position{{math| '''r&prime;'''}} (the standard symbol for ''charge'' density being unfortunately the same as for ''mass'' density). Then the contribution from that element to the field{{math| '''D'''}} at position{{math| '''r'''}}&#8202; is :<math>d\mathbf{D}(\mathbf{r}) ~\!=~\! \frac{\,\rho(\mathbf{r}')\,dV'}{4\pi}\, \frac{\mathbf{r}\!-\!\mathbf{r}'}{|\mathbf{r}\!-\!\mathbf{r}'|^3} </math> provided that, for each {{math|'''r''',}} the dimensions of each volume element are small compared with {{math|{{abs|'''r'''&#8202;&minus;&#8202;'''r&prime;'''}}}}. This contribution likewise has zero curl. The total field due to static charges is then the sum of the contributions: {{NumBlk|:|<math>\mathbf{D}(\mathbf{r}) \,= \iiint \frac{\,\rho(\mathbf{r}')}{4\pi}\, \frac{\mathbf{r}\!-\!\mathbf{r}'}{|\mathbf{r}\!-\!\mathbf{r}'|^3} \,dV' </math>|{{EquationRef|34}}}} where the integral is over all space. And {{math|'''D'''('''r''')}} has zero curl because all the contributions have zero curl. Independently of the physical significance of&#8202; {{math|'''D'''('''r'''),}} we can take its divergence "term by term" (or "under the integral sign"), obtaining :<math>\begin{align}\operatorname{div}\mathbf{D}(\mathbf{r}) \,&= \iiint \frac{\,\rho(\mathbf{r}')}{4\pi}~\!\mathrm{div}\bigg( \frac{\mathbf{r}\!-\!\mathbf{r}'}{|\mathbf{r}\!-\!\mathbf{r}'|^3} \!\bigg) ~\!dV' \\[3pt] &= \iiint \frac{\,\rho(\mathbf{r}')}{4\pi}\, 4\pi~\!\delta(\mathbf{r}\!-\!\mathbf{r}') \,dV' \quad \big[\mathsf{by~eq.(33d)}\big] \\[3pt] &= \iiint \rho(\mathbf{r}')\,\delta(\mathbf{r}\!-\!\mathbf{r}')\,dV'\\[3pt] &= \iiint \rho(\mathbf{r})\,\delta(\mathbf{r}\!-\!\mathbf{r}') \,dV' ~~~ \begin{bmatrix}~\!\! \mathsf{since}~\delta(\mathbf{r}\!-\!\mathbf{r}')\!=\!0\\ \mathsf{unless}~\,\mathbf{r}'{=}~\!\mathbf{r} ~\!\!\end{bmatrix} \\ &= \,\rho(\mathbf{r})\!\iiint\delta(\mathbf{r}\!-\!\mathbf{r}')\,dV'\\[3pt] &= \,\rho(\mathbf{r})\!\iiint\delta(\mathbf{r}'{-}~\!\mathbf{r})\,dV', \end{align}</math> where the last step is permitted because the volume integral of the delta function of{{math| '''r&prime;'''}} is not changed by a "[[w:point reflection|point reflection]]" (inversion) across {{math|'''r'''}}.&#8201; As the volume of integration (all space) includes the shifted origin of the delta function, the integral is simply{{math| 1&#8202;,}} so that {{NumBlk|:|<math> \operatorname{div}\mathbf{D}=\rho \,, </math>|{{EquationRef|35}}}} where both sides are evaluated at{{math| '''r'''}}. Mathematically, this result is an identity which applies if&#8202; {{math|'''D'''}} is given by ({{EquationNote|34}}); substituting for{{math| '''D'''&#8202;,}} we can write the identity in full as {{NumBlk|:|<math>\rho(\mathbf{r}) \,\equiv\, \mathrm{div}\iiint \frac{\,\rho(\mathbf{r}')}{4\pi}\, \frac{\mathbf{r}\!-\!\mathbf{r}'}{|\mathbf{r}\!-\!\mathbf{r}'|^3} \,dV',</math>|{{EquationRef|36}}}} where the integral is over all space, or at least all of the space in which {{mvar|&rho;}} may be non-zero. Subject to the convergence of the integral, this shows that ''we can construct an irrotational vector field whose divergence is a given scalar field''{{math| ''&rho;''('''r''')}}. And of course, by theorem ({{EquationNote|24d}}), ''any curl'' can be added to that vector field without changing its divergence. In ''electrostatics'', ({{EquationNote|34}}) is a generalization of Coulomb's law; and ({{EquationNote|35}}), which follows from ({{EquationNote|34}}), is '''Gauss's law''' expressed in ''differential form''. If we integrate ({{EquationNote|35}}) over a volume enclosed by a surface{{mvar| S}} (with outward unit normal {{math|'''n'''&#770;}}) and apply the divergence theorem on the left, we get the ''integral form'' of Gauss's law: {{NumBlk|:|<math> \iint_S \mathbf{D}\cdot\mathbf{\hat{n}}\,dS \,=\, Q_{\mathrm{e}} \,, </math>|{{EquationRef|37}}}} where {{math|''Q''_e}} is the total charge ''enclosed''&#8202; by{{mvar| S}}. === Field with given Laplacian === In ({{EquationNote|36}}), we can recognize the {{math|'''r'''}}-dependent factor&#8202; {{math|{{sfrac|'''r'''&#8202;&minus;&#8202;'''r&prime;'''|{{abs|'''r'''&#8202;&minus;&#8202;'''r&prime;'''}}³}}}}&#8201; as&#8202; {{math|&minus;&nabla;{{sfrac|1|&#8202;{{abs|'''r'''&#8202;&minus;&#8202;'''r&prime;'''}}&#8202;}}}}&#8201; and take the gradient operator outside the integral, obtaining <div style="margin-top: 1em"> :<math>\rho(\mathbf{r}) \,\equiv\, \mathrm{div}\bigg(\!{-}\nabla\!\iiint \frac{\,\rho(\mathbf{r}')}{4\pi}\, \frac{1}{|\mathbf{r}\!-\!\mathbf{r}'|} \,dV' \!\bigg) \,,</math> </div> i.e. {{NumBlk|:|<math>\rho(\mathbf{r}) \,\equiv\, \triangle\bigg(\!{-}\!\iiint \frac{\,\rho(\mathbf{r}')}{4\pi}\, \frac{1}{|\mathbf{r}\!-\!\mathbf{r}'|} \,dV' \!\bigg) \,,</math>|{{EquationRef|38}}}} where again the integral is over all space, or at least all of the space in which {{mvar|&rho;}} may be non-zero. Subject to the convergence of the integral, this shows that ''we can construct a field whose Laplacian is a given field''. More precisely, it shows that we can construct a ''scalar'' field whose Laplacian is a given ''scalar''&#8202; field{{math| ''&rho;''('''r''')}}. But, due to the linearity of the Laplacian, the same applies to any given linear combination of scalar fields, including any combination whose coefficients are uniform vectors, uniform matrices, or uniform tensors of any order; that is, the same applies to any field that we can express with a uniform basis. Mathematically, ({{EquationNote|38}}) is simply an identity. To find its significance in electrostatics, we can multiply it by&#8202; {{math|&minus;1&#10744;''&epsiv;''₀&#8239;,}} obtaining {{NumBlk|:|<math>-\frac{\rho(\mathbf{r})}{\epsilon_0} \,\equiv\, \triangle\iiint \frac{\,\rho(\mathbf{r}')}{4\pi\epsilon_0}\, \frac{1}{|\mathbf{r}\!-\!\mathbf{r}'|} \,dV',</math>|{{EquationRef|39}}}} which is also an identity. But the negative gradient of the expression after the integral sign is :<math>\frac{\,\rho(\mathbf{r}')\,dV'}{4\pi\epsilon_0}\, \frac{\mathbf{r}\!-\!\mathbf{r}'}{|\mathbf{r}\!-\!\mathbf{r}'|^3}\,,</math> which is the contribution to the electric field at position{{math| '''r'''}} due to a charge&#8202; {{math|''&rho;''('''r&prime;''')&#8239;''dV&prime;''}}&#8239; at position{{math| '''r&prime;'''}} in a vacuum. So the expression after the integral sign is the corresponding contribution to the electrostatic potential, and the whole integral is the whole electrostatic potential. Denoting this by <math>\varphi~\!,\,</math> we can rewrite ({{EquationNote|39}}) as {{NumBlk|:|<math> \triangle\varphi = -\frac{\rho}{\,\epsilon_0} \,. </math>|{{EquationRef|40}}}} This is '''Poisson's equation''' in electrostatics, treating the medium as a vacuum (so that {{mvar|&rho; }}must be taken as the ''total'' charge density, including any contributions caused by the effect of the field on the medium). In a region in which&#8201; {{math|''&rho;''&#8201;{{=}}&#8201;0&#8202;,}}&#8201; Poisson's equation ({{EquationNote|40}}) reduces to {{NumBlk|:|<math> \triangle\varphi = 0 \,, </math>|{{EquationRef|41}}}} which is '''Laplace's equation''' in electrostatics. === The wave equation === It is an empirical fact that a compressible fluid, such as air, carries waves of a mechanical nature: sound waves. In establishing the unambiguity of the gradient and the divergence, we have already derived equations dealing with the inertia and continuity (mass-conservation) of non-viscous fluids. So, by introducing a relation describing the compressibility, and eliminating variables, we should be able to get ''one'' equation (the "wave equation") in ''one'' scalar or vector field (the "wave function"), with recognizably "wavelike" solutions. And we should expect this equation to be analogous to equations describing other kinds of waves. If we suppose, for simplicity, that the only force acting on an element of fluid is the pressure force, the applicable equation of motion is ({{EquationNote|6g}}). But, for reasons which will soon be apparent, let us call the pressure{{mvar| P}}, so that ({{EquationNote|6g}}) becomes :<math> \rho\,\frac{d\mathbf{v}}{dt} = -\nabla P \,. </math> Then at ''equilibrium'' we have :<math> 0 ~\!= -\nabla P_0 \,, </math> where {{math|''P''₀}} is the equilibrium pressure. Subtracting this equation from the previous one and defining :<math>p = P - P_0 \,,</math> we get :<math> \rho\,\frac{d\mathbf{v}}{dt} = -\nabla p \,, </math> which looks like ({{EquationNote|6g}}), except that {{mvar|p}} is now the '''sound pressure''' (also called "acoustic pressure", or sometimes "excess pressure"), i.e. the pressure rise above equilibrium. For the equation of continuity we can use ({{EquationNote|7d'}}), which we repeat for convenience: :<math> \rho\operatorname{div}\mathbf{v} = -\frac{d\rho}{dt} \,. </math> Eliminating {{math|'''v'''}} between the last two equations is fraught because {{math|'''v''' }}is evaluated at a moving point in the former and at a fixed point in the latter; and introducing any relation between {{mvar|p}} and {{mvar|&rho;}} is similarly fraught because {{mvar|p}} is evaluated at a fixed point and {{mvar|&rho;}} at a moving point. The obvious remedy is to apply the advection rule ({{EquationNote|16}}) to the last two equations, obtaining respectively :<math>\begin{align} \rho\Big(\tfrac{\part\mathbf{v}}{\part t} + \mathbf{v}\cdot\nabla\mathbf{v}\Big) \,&=\, -\nabla p ~; \\ \rho\operatorname{div}\mathbf{v} \,&=\, -\tfrac{\part\rho}{\part t} - \mathbf{v}\cdot\nabla\rho \,. \end{align}</math> That gets all the variables evaluated at fixed points, at the cost of making the equations more complicated and more obviously non-linear. But the equations and be simplified and linearized by '''small-amplitude approximations'''. In the parentheses in the first equation, the first term is proportional to the amplitude of the vibrations while the second term is a product of ''two'' factors proportional to the amplitude, so that, for sufficiently small amplitudes, the second term is negligible. Similarly, in the second equation, for sufficiently small amplitudes and a ''homogeneous medium'', we can neglect the second term on the right. Then, on the left side of each equation, we are left with a factor proportional to the amplitude, multiplied by{{mvar| &rho;}}. But {{mvar|&rho;}} is not proportional to the amplitude; only its deviation from the equilibrium density is so proportional. Hence, for small amplitudes,&#8201; {{mvar|&rho; }}can be replaced by the equilibrium density, which we shall call{{math| ''&rho;''₀&#8202;,}} which is independent of time and (in a homogeneous medium) independent of position. With these approximations, our equations of motion and continuity become :<math>\begin{align} \rho_0 \mathbf{\dot{v}} &= -\nabla p \,, \\[.5ex] \rho_0 \operatorname{div}\mathbf{v} &= -\dot{\rho} \,, \end{align}</math> where, for brevity, we use an overdot to denote ''partial'' differentiation w.r.t. time (i.e., at a ''fixed'' point, not a point moving with the fluid). Now we can eliminate {{math|'''v'''}}. Taking divergences in the first equation, and differentiating the second ''partially'' w.r.t. time (which can be done inside the {{math|div}} operator, which represents a linear combination), we get :<math>\begin{align} \rho_0 \operatorname{div}\mathbf{\dot{v}} &= -\triangle p \,, \\[.5ex] \rho_0 \operatorname{div}\mathbf{\dot{v}} &= -\ddot{\rho} \,, \end{align}</math> so that we can equate the right-hand sides, obtaining {{NumBlk|:|<math>\ddot{\rho} = \triangle p \,.</math>|{{EquationRef|42}}}} Maintaining the small-amplitude assumption, we can now consider compressibility. For ''small'' compressions in a ''homogeneous'' medium, we may suppose that the pressure change {{mvar|dp}} is some constant times the density change{{mvar| d&rho;}}. It is readily verified that such a constant must have the dimension of velocity squared. So we can say&#8201; {{math|''dp''&#8201;{{=}}&#8201;''c''&sup2;&#8202;''d&rho;''&#8202;,}} where {{mvar|c}} is a constant with the units of velocity.{{efn|When a gas is compressed, work is done on it, causing its temperature to rise, so that the ratio of {{mvar|dp}} to{{mvar| d&rho;}} is higher than if the compression were isothermal. In sound waves, there is typically not enough time for a significant part of the heat of compression to be conducted away; that is, the compression is near enough to '''adiabatic'''. The words "not enough time" may suggest that the adiabatic approximation is a high-frequency approximation. But in fact, in free air, it is a ''low''-frequency approximation, because as the frequency is reduced, the equalization of temperature is hindered more by the longer wavelength than it is helped by the longer period. Only in a confined space, which limits the required distance of conduction, does the adiabatic assumption require the frequency to be ''above'' some lower limit. In a musical wind instrument, that lower limit tends to be far below the audible range. Meanwhile the upper limit, due to easier heat conduction within a shorter wavelength, tends to be very far above the audible range. Thus, under typical conditions, for the purpose of calculating{{mvar| c&#8202;}}, the adiabatic assumption is reasonable. (See [[#fletcher-74|Fletcher, 1974]].)}} Dividing by {{mvar|dt}} gives&#8201; <math>\dot{p}\!=\!c^2\dot{\rho}~\!,\,</math> whence {{NumBlk|:|<math>\ddot{p} = c^2~\!\ddot{\rho} \,.</math>|{{EquationRef|43}}}} Substituting from ({{EquationNote|42}}) then gives the desired '''wave equation''': {{NumBlk|:|<math>\ddot{p} = c^2 \triangle p \,.</math>|{{EquationRef|44}}}} This is the 3D classical wave equation with the sound pressure {{mvar|p}} as the wave function. For a generic wave function {{mvar|&psi;&#8202;,}} in a homogeneous isotropic medium, we would expect the equation to be {{NumBlk|:|<math>\ddot{\psi} = c^2 \triangle\psi \,,</math>|{{EquationRef|45}}}} which may be written more compactly as {{NumBlk|:|<math>\Box\psi =~\! 0 \,,</math>|{{EquationRef|46}}}} where {{math|&#9744;,}} pronounced "wave" or "box",{{efn|Or sometimes "quabla", by analogy with "nabla".}} is called the '''D'Alembertian''' operator and is defined by {{NumBlk|:|<math> \Box\psi := \triangle\psi - \frac{1}{\,c^2}\frac{\part^2 \psi}{\part t^2} </math>|{{EquationRef|47}}}} in this paper, although other conventions exist.{{efn|In particular, some authorities change the sign, defining {{math|&#9744;}} as&#8201; {{math|{{sfrac|1|&#8239;c&sup2;}}&#8202;{{sfrac|&part;&sup2;|&part;t&sup2;}}&#8239;&minus;&#8202;&#9651;&#8239;,}}&#8239; and some write the operator (however defined) as{{math| &#9744;²}}.}} In a ''static'' situation, the second term on the right of ({{EquationNote|47}}) is zero. So one advantage of definition ({{EquationNote|47}}), over any alternative definition that changes the sign or the scale factor, is that ''in the static case, the D'Alembertian is reduced to the Laplacian'', making it especially obvious that ''in the static case, the wave equation is reduced to Laplace's equation'' [compare ({{EquationNote|46}}) and ({{EquationNote|41}})]. Also notice that the D'Alembertian, being a linear combination of two linear operators, is itself ''linear''. === Spherical waves === Having established that there are wavelike time-dependent fields described by equation ({{EquationNote|45}}), in which the constant {{mvar|c}} has the units of velocity, we can now make an informed guess at an elementary solution of the equation. Consider the candidate {{NumBlk|:|<math> \psi(\mathbf{r},t) = \tfrac{1}{\,r\,}~\!f\big(t-r/c\big) \,, </math>|{{EquationRef|48}}}} where&#8201; {{math|'''r'''&#8201;{{=}}&#8201;''r''&#8202;'''r'''&#8202;&#770;}}&#8201; is the position vector (so that {{mvar|r}} is distance from the origin),&#8201; {{mvar|f}}&#8239; is an arbitrary function (arbitrary except that it will need to be twice differentiable),&#8201; {{mvar|t }}is time, and {{mvar|c }}is a constant (and obviously {{mvar|&psi; }}is not defined at the origin even if {{mvar|f&#8202; }}is.) If, at the origin, the function {{mvar|f}}&#8239; has a certain argument at time&#8201; {{math|''t&#8201;{{=}}&#8201;&tau;''&#8202;,}}&#8201; then at any distance{{mvar| r}}&#8202; from the origin, it has the same argument at time&#8201; {{math|''t&#8201;{{=}}&#8201;&tau;&#8239;+&#8202;r''&#10744;''c''&#8202;,}}&#8201; which is&#8201; {{math|''r''&#10744;''c'' }}&#8239;''later''&#8202; than at the origin. Hence, if {{mvar|f}}&#8239; has a certain feature (e.g., a zero-crossing) at the origin, the time taken for that feature to reach any distance{{mvar| r}}&#8239; is{{math| ''r''&#10744;''c''&#8202;,}}&#8239; implying that the feature travels outward from the origin at speed{{mvar| c}}.&#8201; Another way to perceive this is to set the argument of{{mvar| f}}&#8201; equal to a constant (corresponding to some feature of the function) and differentiate w.r.t.{{mvar| t&#8202;,}} obtaining&#8201; {{math|''r''&#8202;&#775;&#8239;{{=}}&#8239;''c''}}&#8202; (the speed at which the feature recedes from the origin). Thus equation ({{EquationNote|48}}) describes ''waves''&#8202; radiating outward from the origin with speed{{mvar| c}}.&#8239;{{efn|The symbol {{mvar|c}} comes from a general-purpose Latin word for speed, but has become the usual symbol for ''wave'' speed.}} Equation ({{EquationNote|48}}) further implies that there are surfaces over which the wave function {{mvar|&psi;}}&#8239; is uniform&mdash;namely surfaces of constant{{mvar| r}},&#8201; i.e. spheres centered on the origin. These are the '''wavefronts'''. So ({{EquationNote|48}}) describes '''spherical waves'''. Because the surface area of a sphere is proportional to the square of its radius, we should expect the radiated '''intensity''' (power per unit area) to satisfy an ''inverse-square law'' (if the medium is ''lossless''&mdash;neither absorbing nor scattering the radiated power). That does ''not'' mean that the wave function itself should satisfy an inverse-square law. In a traveling wave in 3D space, there will be an "effort" variable (e.g., sound pressure) and a "flow" variable (e.g., fluid velocity), and the instantaneous intensity will be proportional to the product of the two. If the two are proportional to each other, the instantaneous intensity will be proportional to the square of one or the other. Hence if the instantaneous intensity falls off like{{math| 1/''r''&#8202;&sup2;,}} the effort and flow variables&mdash;and the wave function, if it is proportional to one or the other&mdash;will fall off like{{math| 1/''r''}}. That suggests the attenuation factor {{math|1/''r''}}&#8202; in ({{EquationNote|48}}). But there are big ''if''&#8202;s in that argument. For all we know so far, the relation between effort and flow could involve a lag, so that the ''instantaneous'' product of the two could swing negative although it averages to something positive. And for all we know so far, the lag could vary with{{mvar| r}}, allowing at least one of the two (effort or flow) to depart from the {{math|1/''r''}}&#8202; law, even if their average product still falls off like{{math| 1/''r''&#8202;&sup2;}}. The {{math|1/''r''}}&#8202; factor in ({{EquationNote|48}}) is therefore only an "informed guess". Notwithstanding these complications, we have also guessed that the form of the function {{mvar|f}}&#8202; (the '''waveform''') does not change as {{mvar|r}} increases; we have not considered whether this behavior might depend on the medium, or the waveform, or the geometry of the wavefronts. So let us carefully check whether ({{EquationNote|48}}) satisfies ({{EquationNote|45}}) or, equivalently, ({{EquationNote|46}}). As a first step, and as a useful inquiry in its own right, we find {{math|&#9651;''&psi;''}} from definition ({{EquationNote|4L}}), given that {{mvar|&psi;}} is a function of {{math|(''r'',&#8202;''t'') }}only. For the surface {{mvar|&delta;S}}&#8202; let us start with * a cone (''not'' a double cone) with its apex at the origin, subtending a ''small'' solid angle {{mvar|&omega;}} at the origin, * a sphere centered on the origin, with radius {{math|''r''}}, and * a sphere centered on the origin, with radius {{mvar|r&#8202;+&#8202;dr&#8202;}}; and let the volume element be the region inside the cone and between the spheres, so that its enclosing surface {{mvar|&delta;S}}&#8202; has three faces: a segment of the cone, a segment of the inner sphere with area{{math| ''r''&#8202;&sup2;''&#8202;&omega;''&#8202;,}} and a segment of the outer sphere with area{{math| (''r&#8202;+&#8202;dr'')²''&omega;''&#8202;}}. By the symmetry of{{mvar| &psi;&#8202;}}, the outward normal derivative {{mvar|&part;_n&#8202;&psi;}}&#8202; is equal to zero on the conical face,&#8201; {{math|+''&part;_r&#8202;&psi;''(''r&#8202;+&#8202;dr'',&#8202;''t'')}} on the outer spherical face, and&#8202; {{math|&minus;''&part;_r&#8202;&psi;''(''r'',&#8202;''t'')}} on the inner spherical face. The volume of the element is&#8201; {{math|''dV''&#8201;{{=}}&#8201;''r''&#8202;&sup2;''&#8202;&omega;&#8239;dr''}}. So, assembling the pieces of definition ({{EquationNote|4L}}), we get :<!-- SUBSCRIPTS ENLARGED FOR LEGIBILITY: --><math>\begin{align}\triangle\psi &= \frac{1}{r^2 \omega \,dr}\Big(\! (r\!+\!dr)^2 \omega ~\!\part_{\textstyle r} \psi(r\!+\!dr,t) - r^2 \omega ~\!\part_{\textstyle r} \psi(r,t) \!\Big) \\[1ex] &= \frac{1}{\,r^2}~\! \frac{(r\!+\!dr)^2 \part_{\textstyle r}\psi(r\!+\!dr,t) - r^2 \part_{\textstyle r}\psi(r,t)}{dr} \\[.5ex] &= \frac{1}{\,r^2}~\! \frac{\part}{\part r}\Big(r^2 \part_{\textstyle r}\psi(r,t)\Big) \,, \end{align}</math> i.e. {{NumBlk|:|<math> \triangle\psi(r,t) \equiv \frac{1}{\,r^2}~\!\frac{\part}{\part r} \Big(r^2 \frac{\part\psi}{\part r}\Big) \qquad \big[\mathsf{if}\,\,r\!\neq~\!\!0\big]\,. </math>|{{EquationRef|49}}}} Now we can verify our "informed guess". Differentiating ({{EquationNote|48}}) twice w.r.t.{{mvar| t}}&#8202; by the chain rule gives {{NumBlk|:|<math> \frac{\part^2\psi}{\part t^2} = \frac{1}{\,r\,}~\!f''\!\big(t-r/c\big) \,, </math>|{{EquationRef|50}}}} where each prime {{math|(&prime;)}} denotes differentiation of the function w.r.t. its own argument. Differentiating ({{EquationNote|48}}) once w.r.t.{{mvar| r}}&#8202; by the product rule and chain rule, we get {{NumBlk|:|<math> \frac{\part\psi}{\part r} \,=\, -\frac{1}{cr}~\!f'\!\big(t-r/c\big) -\frac{1}{\,r^2}~\!f\big(t-r/c\big) \,. </math>|{{EquationRef|51}}}} Proceeding as specified in ({{EquationNote|49}}), we multiply this by {{math|''r''&#8202;&sup2;}}, differentiate again w.r.t.{{mvar| r}} (giving three terms, of which two cancel), and divide by {{math|''r''&#8202;&sup2;}}, obtaining {{NumBlk|:|<math> \triangle\psi = \frac{1}{c^2 r}~\!f''\!\big(t-r/c\big) \,. </math>|{{EquationRef|52}}}} Then if we substitute ({{EquationNote|52}}) and ({{EquationNote|50}}) into ({{EquationNote|47}}), we obviously get&#8201; {{math|&#9744;''&psi;''&#8201;{{=}}&#8201;0&#8202;,}} satisfying ({{EquationNote|46}}). So we have guessed correctly. Having shown that the D'Alembertian of{{mvar| &psi;&#8202;}}, as given by ({{EquationNote|48}}), is zero everywhere except at the origin (where it is not defined), let us now find its integral over a volume{{mvar| V}} (enclosed by a surface{{mvar| S}}) that includes the origin. From ({{EquationNote|47}}), :<math>\begin{align} \iiint_V \Box\psi \,dV \,&= \iiint_V \triangle\psi \,dV - \frac{1}{\,c^2}\iiint_V \frac{\part^2 \psi}{\part t^2}\,dV\\[.5em] &= \iint_S \part_n \psi \,dS - \frac{1}{\,c^2}\iiint_V \frac{\part^2 \psi}{\part t^2}\,dV\,, \end{align}</math> where the second equality follows from theorem ({{EquationNote|5L}}). Now because the integrand on the left is zero except at the origin, ''any''{{mvar| V}} containing the origin will give the same integral. So for convenience, let {{mvar|V}} be a spherical ball of radius{{mvar| R}} centered on the origin. Then, by the spherical symmetry of{{mvar| &psi;&#8202;,}} integration over{{mvar| S}} reduces to multiplication by{{math| 4''&pi;R''&#8202;²,}} and {{mvar|&part;_n}} is equivalent to{{mvar| &part;_r&#8202;,}} and {{mvar|dV}} can be taken as{{math| 4''&pi;r''^&#8202;2''dr''}}. With these substitutions we have :<math> \iiint_V \Box\psi \,dV \,=\, 4\pi R^2 \frac{\part\psi}{\part r}\bigg|_{r=R} \! - \frac{1}{\,c^2}\!\int_0^R \!\frac{\part^2 \psi}{\part t^2}\,2\pi r\,dr </math> or, substituting from ({{EquationNote|51}}) and ({{EquationNote|50}}), :<math>\begin{align} \iiint_V \!\Box\psi \,dV ~\!\! =\,& 4\pi R^2 \!\Big(\!{-}\tfrac{1}{cR} f'\!\big(t\!-\!R/c\big) - \tfrac{1\,}{R^2} f\big(t\!-\!R/c\big)\!\Big) \\ &- \tfrac{1}{\,c^2}\!\int_0^R \!\tfrac{1}{\,r\,}~\! f''\!\big(t-r/c\big)\,2\pi r\,dr \\[1ex] =\,&-\tfrac{4\pi R}{\,c\,}~\!f'\!\big(t\!-\!R/c\big) - 4\pi f\big(t\!-\!R/c\big) \\ &- \tfrac{2\pi}{\,c^2}\!\int_0^R \!f''\!\big(t-r/c\big) \,dr \,. \end{align}</math> Again noting that any {{mvar|V}} containing the origin will give the same volume integral, we can let {{mvar|R}} approach zero, with the result that the right-hand side approaches&#8239;{{math| &minus;4''&pi;f''&#8202;(''t'')}}. This is the integral of{{math| &#9744;''&psi;''}} over any volume containing the origin, for {{mvar|&psi;}} given by ({{EquationNote|48}}). Meanwhile {{math|&#9744;''&psi;''}} is zero everywhere except that the origin. In summary, {{NumBlk|:|<math> \Box~\!\Big\{\!\tfrac{1}{\,r\,}~\!f\big(t-r/c\big)\!\Big\} \equiv -4\pi f(t)\,\delta(\mathbf{r}) \,. </math>|{{EquationRef|53}}}} Shifting the center of the spherical waves from the origin to position{{math| '''r&prime;''',}} we get {{NumBlk|:|<math> \Box~\!\Big\{\tfrac{1}{|\mathbf{r}-\mathbf{r}'|} ~\!f\big(t-\tfrac{|\mathbf{r}-\mathbf{r}'|\,}{c}\big)\Big\} \equiv -4\pi f(t)\,\delta(\mathbf{r}\!-\!\mathbf{r}') \,. </math>|{{EquationRef|54}}}} We shall refer to the field given by ({{EquationNote|48}}) as the wave function due to a '''monopole''' source with '''strength''' {{math|''f''&#8202;(''t'')}} at the origin. The D'Alembertian of this wave function is given by ({{EquationNote|53}}).<ref>Our definition of ''strength'' follows the old convention used by Baker &amp; Copson ([[#baker-copson-39|1939, p.&#8239;42]]), Born &amp; Wolf ([[#born-wolf-02|2002, p.&#8239;421]]), and Larmor ([[#larmor-1904|1904, p.&#8239;5]]). The newer convention followed by Miller ([[#miller-91|1991, p.&#8239;1371]]) would use the denominator {{math|4''&pi;r''}} instead of our {{mvar|r}} in ({{EquationNote|48}}); this would have the advantage of eliminating the factor{{math| 4''&pi;''}} from the D'Alembertian of the wave function, and the disadvantage of introducing that factor into the (denominator of the) wave function itself.</ref> Hence the field whose D'Alembertian is given by ({{EquationNote|54}}) is the wave function due to a monopole source with strength {{math|''f''&#8202;(''t'')}} at position{{math| '''r&prime;'''}}. In each case, the D'Alembertian is zero everywhere except at the source. === Field with given D'Alembertian === Now suppose that, instead of a wave source with strength {{math|''f''&#8202;(''t'')}} at the general position{{math| '''r&prime;''',}} we have at that position a wave-source ''density<math>~w(\mathbf{r}'\!,t)</math>'' in an elemental volume {{mvar|dV&prime;}}, whose contribution to the wave function {{mvar|&psi;}} at position{{math| '''r'''}}&#8202; is :<math>d\psi(\mathbf{r},t) = \tfrac{1}{|\mathbf{r}-\mathbf{r}'|}~\! w\big(\mathbf{r}',\,t-\tfrac{|\mathbf{r}-\mathbf{r}'|\,}{c}\big)\,dV' , </math> where for each {{math|'''r''',}} the dimensions of each volume element are small compared with {{math|{{abs|'''r'''&#8202;&minus;&#8202;'''r&prime;'''}}}}. Then the total wave function is the sum of the contributions: {{NumBlk|:|<math>\psi(\mathbf{r},t) = \iiint \tfrac{1}{|\mathbf{r}-\mathbf{r}'|}~\! w\big(\mathbf{r}',\,t-\tfrac{|\mathbf{r}-\mathbf{r}'|\,}{c}\big)\,dV' , </math>|{{EquationRef|55}}}} where the integral is over all space. Independently of the physical significance of{{math| ''&psi;''('''r''',&#8202;''t''),}} we can take its D'Alembertian "under the integral sign" by rule ({{EquationNote|54}}), obtaining :<math>\begin{align}\Box\psi(\mathbf{r},t) &= \iiint \Big({-}4\pi~\!w(\mathbf{r}'\!,t)\, \delta(\mathbf{r}\!-\!\mathbf{r}')\Big)\,dV' \\[.5ex] &= \iiint \Big({-}4\pi~\!w(\mathbf{r},t)\, \delta(\mathbf{r}\!-\!\mathbf{r}')\Big)\,dV' \\[.5ex] &= -4\pi~\!w(\mathbf{r},t)\! \iiint\delta(\mathbf{r}\!-\!\mathbf{r}')\,dV' \\[.5ex] &= -4\pi~\!w(\mathbf{r},t)\! \iiint\delta(\mathbf{r}'{-}~\!\mathbf{r})\,dV' ; \end{align}</math> that is, {{NumBlk|:|<math> \Box\psi(\mathbf{r},t) = -4\pi~\!w(\mathbf{r},t) \,. </math>|{{EquationRef|56}}}} Mathematically, equation ({{EquationNote|56}}) is an identity which applies if {{math|''&psi;''('''r''',&#8202;''t'')}} is given by ({{EquationNote|55}}). Substituting from ({{EquationNote|55}}) and solving for<math>~w,</math> we can write the identity in full as {{NumBlk|:|<math>w(\mathbf{r},t) \equiv \Box\bigg({-}\tfrac{1}{4\pi}\!\iiint \tfrac{1}{|\mathbf{r}-\mathbf{r}'|}~\! w\big(\mathbf{r}',\,t-\tfrac{|\mathbf{r}-\mathbf{r}'|\,}{c}\big) \,dV'\bigg) \,, </math>|{{EquationRef|57}}}} where the integral is over all space, or at least all of the space in which<math>~w</math> may be non-zero. Subject to the convergence of the integral, this shows that ''we can construct a wave function with a given D'Alembertian''. Physically, equation ({{EquationNote|56}}) gives the D'Alembertian of the wave function for a source density<math>~w</math>. It is the ''inhomogeneous wave equation'', which applies in the presence of an arbitrary source density&mdash;in contrast to the ''homogeneous wave equation'' ({{EquationNote|46}}), which applies in a region where the source density is zero. In this context the word ''homogeneous'' or ''inhomogeneous'' describes the equation, not the medium (which has been assumed homogeneous and isotropic). In a ''static'' situation, in which the D'Alembertian is reduced to the Laplacian, the inhomogeneous wave equation ({{EquationNote|56}}) is reduced to the form of Poisson's equation ({{EquationNote|40}}). As written, equation ({{EquationNote|40}}) is Poisson's equation in electro''statics''; it applies to the charge density{{math| ''&rho;''('''r''')}}, for which the scalar potential [in ({{EquationNote|39}})] is :<math>\varphi(\mathbf{r}) = \tfrac{1}{4\pi\epsilon_0} \iiint \tfrac{1}{|\mathbf{r}-\mathbf{r}'|} \rho(\mathbf{r}') \,dV'. </math> In electro''dynamics'', which takes time-dependence into account, the scalar potential due to the charge density{{math| ''&rho;''('''r''',&#8202;''t'')}} is :<math>\varphi(\mathbf{r},t) = \tfrac{1}{4\pi\epsilon_0} \iiint \tfrac{1}{|\mathbf{r}-\mathbf{r}'|} \rho\big(\mathbf{r}',\,t-\tfrac{|\mathbf{r}-\mathbf{r}'|\,}{c}\big) \,dV', </math> where the wave speed {{mvar|c}} is the speed of light; this is the same as in the static case except for the delay {{math|{{sfrac|&#8202;{{abs|'''r'''&#8202;&minus;&#8202;'''r&prime;'''}}&#8202;|''c''}}&#8202;,}} indicating that the influence of the change density at{{math| '''r&prime;'''}} travels outward from that point at the speed of light. In the dynamic case, by rule ({{EquationNote|57}}), the D'Alembertian of the scalar potential is :<math> \Box\varphi = -\frac{\rho(\mathbf{r},t)}{\,\epsilon_0} \,. </math> This result is the inhomogeneous wave equation in the scalar potential&mdash;the equation which, in the electro''static'' case, reduces to Poisson's equation ({{EquationNote|40}}). In electro''dynamics'', however, the electric field&#8202; {{math|'''E'''}} is ''not'' simply<math>\,\,{-}\nabla\varphi~\!,\,</math> but<math>~\,{-}\nabla\varphi~\!\!-\!\tfrac{\part\mathbf{A}}{\part t}~\!,\,</math> where {{math|'''A'''}} is the '''magnetic vector potential''', whose defining property is that its curl is the '''magnetic flux density''': :<math>\mathbf{B} = \operatorname{curl}\mathbf{A} \,.</math> By identity ({{EquationNote|24d}}), this property implies :<math>\operatorname{div}\mathbf{B} = 0 \,,</math> which is '''Gauss's law for magnetism'''. We have noted in passing&mdash;but not yet proven&mdash;that ({{EquationNote|24d}}) has a converse, whereby the solenoidality of{{math|&#8202; '''B'''}} implies the ''existence'' of the vector potential{{math| '''A'''}}.  Precedents suggest we might be able to prove this by finding a vector field whose curl is a delta function&mdash;perhaps through new identities relating it to a field whose divergence is a delta function&mdash;and using it to construct a vector field with a given curl. In fact we shall prove our "converse" differently, but we shall still need some new identities for the purpose. And to obtain those identities (among others), we must take the detour that we have made a virtue of ''not'' taking until now&hellip; == Cartesian coordinates == === Indicial notation; implicit summation === Considering that a scalar field is a function of three coordinates, while a vector field has three components each of which is a function of three coordinates, we can readily imagine that coordinate-based derivations of vector-analytic identities are likely to be excruciatingly repetitive&mdash;unless perhaps we choose a notation that concisely specifies the repetition. So, instead of writing the Cartesian coordinates as {{math|''x'',&#8239;''y'',&#8239;''z''&#8202;,}}&#8239; we shall usually write them as {{mvar|x_i}}&#8202; where&#8202; {{math|''i''&#8201;{{=}}&#8239;1,&#8202;2,&#8202;3&#8202;,}}&#8201; respectively;&#8202; and instead of writing the unit vectors in the directions of the respective axes as {{math| '''i''',&#8202;'''j''','''k'''&#8202;,}}&#8239; we shall usually write them as {{math|'''e'''_''i''&#8202;}}.&#8201; And for partial differentiation w.r.t.{{math| ''x_i''&#8202;,}} instead of writing {{mvar|{{sfrac|&part;|&part;x_i}}}} or even {{math|''&part;_{x_i}''&#8202;,}} we shall write {{mvar|&part;_i&#8202;}}. Now comes a stroke of genius for which we are indebted to Einstein&mdash;although he used it in a more sophisticated context!&#8201; Instead of writing the position vector as :<math>\mathbf{r} = x_1\mathbf{e}_1 + x_2\mathbf{e}_2 + x_3\mathbf{e}_3</math> or even as :{{big|<math>\mathbf{r} = \textstyle\sum_i x_i \mathbf{e}_i \,,</math>}} we shall write it simply as :{{big|<math>\mathbf{r} = x_i \mathbf{e}_i \,,</math>}} where it is ''understood''&#8202; that we ''sum over the repeated index''. More generally, we shall write the vector field {{math|'''q'''}} as :{{big|<math>\mathbf{q} = q_i \mathbf{e}_i</math>}} with implicit summation, and the vector field {{math|'''v'''}} as :{{big|<math>\mathbf{v} = v_i \mathbf{e}_i</math>}} with implicit summation, and so on. (By that nomenclature, the position vector in Cartesian coordinates should be, and often is, called {{math|'''x'''&#8202;}}; but we called it {{math|'''r'''}} because we wanted to call its magnitude {{mvar|r}}, for ''radius''.) Implicit summation not only avoids writing the {{big|{{math|&Sigma;}}}} symbol and specifying the index of summation, but also allows a summation over ''two'' repeated indices, say {{mvar|i}} and {{mvar|j&#8202;}}, to be considered as summed first over {{mvar|i}} and then over {{mvar|j}} or vice versa, removing the need for an explicit regrouping of terms. Of course, if we hide messy details behind a notation, we need to make sure that it handles those details correctly. In particular, when we perform an operation on an implicit sum, we implicitly perform it ''term-by-term'', and must therefore make sure that the operation is valid when interpreted that way. === Formulation of operators === '''Gradient''':  Putting&#8201; {{mvar|s&#8201;{{=}}&#8201;x_i}}&#8201; in ({{EquationNote|9g}}), we find that the scalar component of{{math|&#8202; &nabla;''p''}} in the direction of each {{math|'''e'''_''i''}}&#8202; is{{mvar|&#8202; &part;_i&#8201;p}}.&#8201; To obtain the vector component in that direction, we multiply by {{math|'''e'''_''i''&#8202;}}.&#8201; Assembling the components, we have (with implicit summation) {{NumBlk|:|{{big|<math> \nabla p = \mathbf{e}_i ~\!\part_i p </math>}}|{{EquationRef|58g}}}} or, in operational terms, {{NumBlk|:|{{big|<math> \nabla =~\! \mathbf{e}_i \part_i </math>}}|{{EquationRef|58o}}}} or, in traditional longhand notation, {{NumBlk|:|{{big|<math> \nabla =~\! \mathbf{i}~\!\tfrac{\part}{\part x} +~\! \mathbf{j}~\!\tfrac{\part}{\part y} +~\! \mathbf{k}~\!\tfrac{\part}{\part z} \,. </math>}}|{{EquationRef|58t}}}} It is also worth noting, from ({{EquationNote|58g}}), that the squared magnitude of{{math|&#8202; &nabla;''p'' &#8239;}}is {{NumBlk|:|{{big|<math> |\nabla p|^2 =~\! \part_i p \;\part_i p \,, </math>}}|{{EquationRef|58s}}}} where we write&#8239; {{mvar|&part;_i&#8239;p&#8201;&part;_i&#8239;p}}&#8201; rather than {{math|(''&part;_i&#8239;p'')²}}&#8239; to ensure that implicit summation applies! As reported by Tai ([[#tai-94|1994]]), there are unfortunately some textbooks in which the del operator is defined as :{{big|<math>\nabla =~\! \tfrac{\part}{\part x}~\!\mathbf{i} + \tfrac{\part}{\part y}~\!\mathbf{j} + \tfrac{\part}{\part z}~\!\mathbf{k} \quad\qquad </math>}}{{big|1=[''sic!''&#8239;]}} &mdash;which, on its face, is not an operator at all, but a self-contained expression whose value is the zero vector (because it is a sum of derivatives of constant vectors). Among the offenders is Erwin Kreyszig, who, in the 6th edition of his bestselling ''Advanced Engineering Mathematics'' ([[#kreyszig-62-|1988]], p.&#8239;486), misdefines the del operator thus and then rewrites the gradient of{{mvar|&#8202; f}}&#8239; as {{math|&nabla;&#8202;''f'',}} apparently imagining that the differentiation operators look ''through'' the constant vectors rather than ''at''&#8202; them. Six pages later, he defines the divergence in Cartesian coordinates (which we shall do shortly) and then immediately informs us that "Another common notation for the divergence of{{math| '''v'''}} is {{math|&nabla;'''&#11825;&#8202;v'''}}," where {{math|&nabla;}} is defined as before, but the resulting {{math|&nabla;'''&#11825;&#8202;v'''}} is apparently not identically zero!<ref>The latter passage, as it appears in the 5th edition (p.&#8239;397), is the one cited by Tai ([[#tai-94|1994]], p.&#8239;6).</ref> These errors persist in the 10th edition ([[#kreyszig-62-|2011]], pp.&#8239;396,&#8239;402–3). Tai finds similar howlers in mathematics texts by Wilfred Kaplan, Ladis D. Kovach, and Merle C. Potter, and in electromagnetics texts by William H. Hayt and Martin A. Plonus.<ref>Quoted by Tai ([[#tai-94|1994]]), in alphabetical order within each category. For Kovach he could have added p.&#8239;308.&#8201; Potter he misnames as Porter.</ref>&#8201; Knudsen &amp; Katz, in ''Fluid Dynamics and Heat Transfer'' (1958), avoid the misdefinition of{{math| &nabla;,}} but implicitly define the divergence of{{math| '''V'''}} as {{math|1='''V&#11825;'''&nabla;}}&#8202; (which, as we have seen, is actually an operator), and then somehow reduce it to the correct expression for{{math|&#8202; div&#8239;'''V'''}}.&#8239;<ref>Quoted by Tai ([[#tai-94|1994]], p.&#8239;23).</ref>  But I digress. '''Curl and divergence''':  Expressing the operand of the curl in components, and noting that the unit vectors are ''uniform'', we can apply ({{EquationNote|8p}}): :{{big|<math>\begin{align} \operatorname{curl}\mathbf{q} &= ~\!\mathrm{curl}(q_j ~\!\mathbf{e}_j) && \\ &= \nabla q_j \times \mathbf{e}_j && [\mathsf{\scriptstyle by~eq.(8p)}] \\ &= ~\!\mathbf{e}_i \part_i q_j \times \mathbf{e}_j && [\mathsf{\scriptstyle by~eq.(58g)}] \\ &= ~\!\mathbf{e}_i ~\!\!\times \part_i ~\!q_j \mathbf{e}_j \,. && \end{align}</math>}} If we sum over {{mvar|j}} first, this is {{NumBlk|:|{{big|<math> \operatorname{curl}\mathbf{q} =~\! \mathbf{e}_i ~\!\!\times\part_i\mathbf{q} </math>}}|{{EquationRef|59c}}}} or, in operational terms, {{NumBlk|:|{{big|<math> \operatorname{curl} =~\! \mathbf{e}_i ~\!\!\times\part_i </math>}}|{{EquationRef|59o}}}} or, in traditional longhand, :{{big|<math> \operatorname{curl} \,=\, \mathbf{i} \times ~\!\!\tfrac{\part}{\part x} +~\! \mathbf{j} \times ~\!\!\tfrac{\part}{\part y} +~\! \mathbf{k} \times ~\!\!\tfrac{\part}{\part z} \,. </math>}} For the ''divergence'' we proceed as for the curl except that, instead of ({{EquationNote|8p}}), we use ({{EquationNote|8g}}): :{{big|<math>\begin{align} \operatorname{div}\mathbf{q} &= ~\!\mathrm{div}(q_j ~\!\mathbf{e}_j) && \\ &= \nabla q_j \cdot \mathbf{e}_j && [\mathsf{\scriptstyle by~eq.(8g)}] \\ &= ~\!\mathbf{e}_i \part_i q_j \cdot \mathbf{e}_j && [\mathsf{\scriptstyle by~eq.(58g)}] \\ &= ~\!\mathbf{e}_i ~\!\!\cdot \part_i ~\!q_j \mathbf{e}_j \,; && \end{align}</math>}} that is, {{NumBlk|:|{{big|<math> \operatorname{div}\mathbf{q} =~\! \mathbf{e}_i ~\!\!\cdot \part_i\mathbf{q} </math>}}|{{EquationRef|60d}}}} or, in operational terms, {{NumBlk|:|{{big|<math> \operatorname{div} =~\! \mathbf{e}_i ~\!\!\cdot \part_i </math>}}|{{EquationRef|60o}}}} or, in traditional longhand, :{{big|<math> \operatorname{div} \,=\, \mathbf{i} \cdot \tfrac{\part}{\part x} +~\! \mathbf{j} \cdot \tfrac{\part}{\part y} +~\! \mathbf{k} \cdot \tfrac{\part}{\part z} \,. </math>}} It follows from ({{EquationNote|59c}}) and ({{EquationNote|60d}}), if it was not already obvious, that ''a uniform vector field has zero curl and zero divergence''. Although the above expressions for the divergence and curl will surprise many modern readers, they match the ''initial definitions'' of the divergence and curl given by the founder of vector analysis as we know it, [[w:Josiah Willard Gibbs|J.&#8239;Willard Gibbs]] ([[#gibbs-1881-4|1881]], &sect;&#8239;54). Gibbs even uses the {{math|&nabla;&#8202;&times;}}&#8202; and {{math|&nabla;'''&#11825;'''}}&#8202; notations on the left sides of the defining equations, and only ''after''&#8202; the equations (albeit immediately after) does he announce that&#8202; "{{math|&#8202;&nabla;'''&#11825;'''&#8202;''&omega;''}} is called the ''divergence'' of{{mvar| &omega;}}&#8239; and {{math|&nabla;&#8202;&times;''&omega;''}}&#8239; its ''curl''." (He uses Greek letters for vectors.) Our notation and Cartesian expression for the gradient ({{EquationNote|58g}}) also match Gibbs ([[#gibbs-1881-4|1881]], &sect;&#8239;52). Hence, using the Gibbs notations, we can merge definitions ({{EquationNote|58g}}), ({{EquationNote|59c}}), and ({{EquationNote|60d}}) into the general Cartesian formula {{NumBlk|:|{{big|<math> \nabla~\!\! * \psi =~\! \mathbf{e}_i ~\!\! * \part_i \psi </math>}}|{{EquationRef|60s}}}} (with implicit summation), where the {{math|&lowast;}} operator may be a null (for the gradient), a cross (for the curl), or a dot (for the divergence). Gibbs does not offer any justification for the {{math|&nabla;&#8202;&times;}}&#8202; and {{math|&nabla;'''&#11825;'''}}&#8202; notations, but nor is it difficult to find such a justification based on his definitions. As{{math| '''e'''_''i''}} is a ''uniform'' vector, we can rewrite ({{EquationNote|59c}}) ''rigorously'' as {{NumBlk|:|{{big|<math> \operatorname{curl}\mathbf{q} = \part_i(\mathbf{e}_i ~\!\!\times\mathbf{q}) </math>}}|{{EquationRef|61c}}}} and thence ''operationally'' as {{NumBlk|:|{{big|<math> \operatorname{curl}\mathbf{q} =~\! \mathbf{e}_i\part_i \times \mathbf{q} </math>}}|{{EquationRef|61o}}}} or, recalling ({{EquationNote|58o}}), :<math> \operatorname{curl}\mathbf{q} ~\!= \nabla \times \mathbf{q} \,, </math> which can be evaluated in the usual manner as :<math> \operatorname{curl}\mathbf{q} \,=\, \begin{vmatrix} \mathbf{i} & \part_x & q_x \\ \mathbf{j} & \part_y & q_y \\ \mathbf{k} & \part_z & q_z \end{vmatrix} \,, </math> where {{mvar|q_x}} is the {{mvar|x}} component of{{math| '''q'''&#8202;}}, etc. This indeed is how one evaluates the curl of a given field in Cartesian coordinates, although we shall find ({{EquationNote|59c}}) more convenient for deriving identities. Similarly, we can rewrite ({{EquationNote|60d}}) ''rigorously'' as {{NumBlk|:|{{big|<math> \operatorname{div}\mathbf{q} = \part_i(\mathbf{e}_i ~\!\!\cdot \mathbf{q}) </math>}}|{{EquationRef|62d}}}} and thence ''operationally'' as {{NumBlk|:|{{big|<math> \operatorname{div}\mathbf{q} =~\! \mathbf{e}_i\part_i \cdot \mathbf{q} </math>}}|{{EquationRef|62o}}}} or, recalling ({{EquationNote|58o}}), :<math> \operatorname{div}\mathbf{q} ~\!= \nabla \!\cdot \mathbf{q} ~. </math> For evaluating the divergence of a given field, however, we simplify ({{EquationNote|62d}}) to :{{big|<math> \operatorname{div}\mathbf{q} = \part_i q_i </math>}} or, in traditional longhand, :{{big|<math> \operatorname{div}\mathbf{q} ~\!= \frac{\part q_x}{\part x} + \frac{\part q_y}{\part y} + \frac{\part q_z}{\part z} \,, </math>}} although we shall find ({{EquationNote|60d}}) more convenient for deriving identities. But the longhand form makes it especially obvious that if{{math|&#8202; '''r'''}} is the position vector, {{NumBlk|:|<math> \operatorname{div}\mathbf{r} = 3 \,. </math>|{{EquationRef|62r}}}} Notice that we can get from ({{EquationNote|62o}}) back to ({{EquationNote|60d}}) by permuting the {{mvar|&part;_i}} with the dot, and from ({{EquationNote|61o}}) back to ({{EquationNote|59c}}) by permuting the {{mvar|&part;_i}} with the cross, as if the differentiation operator could, as it were, look through the dot or the cross&mdash;or, as Gibbs's student [[w:Edwin Bidwell Wilson|Edwin B.&#8201;Wilson]] puts it, "pass by" the dot and the cross, yielding Gibbs's original definitions.<ref>[[#wilson-1901|Wilson, 1901]], p.&#8239;150.</ref> Hence Wilson considers it helpful to regard Gibbs's {{math|&nabla;'''&#11825;'''}}&#8202; and {{math|&nabla;&#8202;&times;}}&#8202; notations as "the (formal) scalar product and the (formal) vector product of{{math|&#8202; &nabla;}} into" the operand, or "the symbolic scalar and vector products of{{math|&#8202; &nabla;}} into" the operand, and to regard {{math|&nabla;}} as a "symbolic vector"<ref>[[#wilson-1901|Wilson, 1901]], pp.&#8239;150,&#8239;152. Wilson does not announce this idea in his preface (p.&#8239;xii), although Tai ([[#tai-95|1995, p.&#8239;26]]) gets the contrary impression by omitting a comma from the relevant quote.</ref> (not to be confused with Tai's symbolic vector<math>~\nabla\!\!\!\!^{\textstyle_-}</math>). Tai ([[#tai-94|1994]], [[#tai-95|1995]]) rejects Wilson's argument together with the entire tradition of treating {{math|&nabla;&#8202;&times;}}&#8202; and {{math|&nabla;'''&#11825;'''}}&#8202; as compound operators. Of formal products, Tai says that the concept "has had a tremendously detrimental effect upon the learning of vector analysis"; he calls such a product a "meaningless assembly".<ref>[[#tai-95|Tai, 1995]], pp.&#8239;26,&#8239;38.</ref> Of the "pass by" step, he complains that "standard books on mathematical analysis do not have such a theorem."<ref>[[#tai-95|Tai, 1995]], p.&#8239;28.</ref> I submit, however, that the intermediate steps ({{EquationNote|61c}}) and ({{EquationNote|62d}}), after which we take the constant multiplier outside the operator (eqs. {{EquationNote|61o}} &amp; {{EquationNote|62o}}), support Wilson's "pass by" argument. In any event the reader may write out the sums on the right-hand sides of ({{EquationNote|59c}}) and ({{EquationNote|60d}}) and verify that they agree with the formal products {{math|&nabla;&#8202;&times;&#8202;'''q'''}}&#8202; and {{math|&nabla;'''&#11825;&#8239;q'''}}&#8202; respectively&mdash;and may notice that in the evaluation of each formal product, the cross or dot may be eliminated, leaving nothing to "pass by".<ref>The latter observation is made, or at least suggested, by Kemin et al. ([[#kemin-et-al-00|2000]], p.&#8239;605).</ref> I further submit that the great generality of our derivation of equations ({{EquationNote|14}}), above, compels us to treat the {{math|&nabla;&#8202;&times;}}&#8202; and {{math|&nabla;'''&#11825;'''}}&#8202; notations as more than mere notations. But the kicker is that Tai himself, having found the form of the del operator in ''general'' coordinates ([[#tai-95|1995]], p.&#8239;64, eq.&#8239;9.33), derives original corresponding forms of the {{math|div}} and {{math|curl}} operators (his eqs.&#8239;9.35 &amp; 9.40) which, upon reversal of the forbidden "pass by", become del-dot and del-cross! Indeed his three equations, just cited, are reminiscent of our ({{EquationNote|58o}}), ({{EquationNote|60o}}), and ({{EquationNote|59o}}) respectively. That being said, I shall find some points of agreement with Tai, and some reasons to criticize Wilson. '''Laplacian''':  If {{mvar|&psi;}} is a ''scalar'' field, then :{{big|<math>\begin{align}\triangle\psi &= \operatorname{div}\nabla\psi && [\mathsf{\scriptstyle by~eq.(9L')}] \\ &= \part_i(\mathbf{e}_i \cdot \nabla\psi) && [\mathsf{\scriptstyle by~eq.(62d)}] \\ &= \part_i(\part_i \psi) \,; && \end{align}</math>}} that is, {{NumBlk|:|{{big|<math> \triangle\psi = \part_i \part_i \psi \,, </math>}}|{{EquationRef|63L}}}} where we write&#8202; {{mvar|&part;_i&#8239;&part;_i}}&#8202; rather than {{math|''&part;_i''²}}&#8202; in order to maintain implicit summation. In traditional longhand, ({{EquationNote|63L}}) becomes :<math>\triangle\psi ~\!= \frac{\part^2 \psi}{\part x ^2} + \frac{\part^2 \psi}{\part y ^2} + \frac{\part^2 \psi}{\part z ^2} </math> or, in operational terms, :<math>\triangle ~\!= \frac{\part^2}{\part x ^2} + \frac{\part^2}{\part y ^2} + \frac{\part^2}{\part z ^2} </math> or, by comparison with ({{EquationNote|58t}}), :<math>\triangle = \nabla{\cdot}\nabla </math> &mdash;as expected. By the linearity of the Laplacian, the same applies if {{mvar|&psi;}} is any field expressible in terms of a uniform basis. For example, if {{mvar|&psi;}} is a ''vector'' field given by&#8239; {{math|''&psi;_j''&#8239;'''e'''_''j''}}&#8239; (with implicit summation), then :{{big|<math>\begin{align} \triangle\psi &= \triangle(\psi_j ~\!\mathbf{e}_j) \\ &= \mathbf{e}_j ~\!\triangle\psi_j \\ &= \mathbf{e}_j \part_i \part_i \psi_j \\ &= \part_i \part_i (\psi_j ~\!\mathbf{e}_j) = \part_i \part_i \psi \,, \end{align}</math>}} where the third line follows from ({{EquationNote|63L}}) as applied to a scalar field. Thus ({{EquationNote|63L}}) is quite general. After listing theorems ({{EquationNote|5g}}) to ({{EquationNote|5L}}) above, we gave reasons for describing {{math|&nabla;,}} {{math|curl,}} and {{math|div}} as ''differential operators'', and {{math|&#9651;}} as a ''2nd-order'' differential operator&mdash;the implication being that the others are only 1st-order. We now have the promised "additional reason" for these descriptions: when expressed in Cartesian coordinates, the {{math|&#9651;}} operator involves second derivatives, while the others involve (only) first derivatives. In the meantime we have acquired the {{math|'''q&#11825;'''&nabla;}} operator, which is also 1st-order, as we shall now confirm. '''Advection, directional derivative, etc.''':  If {{mvar|&psi;}} is a ''scalar'' field, then :{{big|<math>\begin{align} \mathbf{q}\;\!{\cdot}\nabla\,\psi &= (\mathbf{q}) \cdot (\nabla\psi) \\ &= (q_i~\!\mathbf{e}_i) \cdot (\mathbf{e}_j ~\!\part_j \psi) \\ &= \;\!\mathbf{e}_i{\cdot}\;\!\mathbf{e}_j \;q_i \part_j \psi \,. \end{align}</math>}} In this double summation, the only non-zero terms are those for which&#8202; {{mvar|j&#8239;{{=}}&#8201;i&#8202;}},&#8239; in which case&#8239; {{math|'''e'''_''i''&#8239;'''&#11825;&#8239;e'''_''j''&#8201;{{=}}&#8239;1}}.&#8201; So we have {{NumBlk|:|{{big|<math> \mathbf{q}\;\!{\cdot}\nabla\,\psi = q_i ~\!\part_i \psi </math>}}|{{EquationRef|64}}}} or, in operational terms, {{NumBlk|:|{{big|<math> \mathbf{q}\;\!{\cdot}\nabla = q_i ~\!\part_i </math>}}|{{EquationRef|64o}}}} or, in traditional longhand, :{{big|<math>\mathbf{q}\;\!{\cdot}\nabla =~\! q_x\tfrac{\part}{\part x} +~\! q_y\tfrac{\part}{\part y} +~\! q_z\tfrac{\part}{\part z} \,, </math>}} which indeed is the "formal" or "symbolic" dot-product of&#8202; {{math|'''q'''}} and{{math| &nabla;}}.&#8202; By the linearity of the directional derivative in ({{EquationNote|11}}), the same result applies if {{mvar|&psi;}} is a vector field or any field expressible in terms of a uniform basis. In particular, if{{math| '''r'''}} is the position vector, we have :{{big|<math> \mathbf{q}\;\!{\cdot}\nabla\,\mathbf{r} = q_i ~\!\part_i \mathbf{r} = q_i ~\!\mathbf{e}_i \,, </math>}} i.e., {{NumBlk|:|{{big|<math> \mathbf{q}\;\!{\cdot}\nabla\,\mathbf{r} = \mathbf{q} </math>}}|{{EquationRef|64r}}}} &mdash;which is also deducible from ({{EquationNote|11}}). For convenience in the following discussion, we shall refer to the scaled-directional-derivative operator {{math|'''q&#11825;'''&nabla;}} as an "advection" operator although, physically, it represents advection only if {{math|'''q'''}} is the material velocity. === Identities without pain === In deriving the Cartesian expressions for the gradient, curl, divergence, Laplacian, and advection operators, we used the preceding identities ({{EquationNote|9g}}), ({{EquationNote|8p}}), ({{EquationNote|8g}}), ({{EquationNote|9L'}}), and ({{EquationNote|11}}) respectively, the last being a definition generalizing ({{EquationNote|9g}}). Thus we could have derived the Cartesian expressions quite early in the exposition, although we did not find that option convenient. The other vector-analytic identities that we have previously mentioned are: * ({{EquationNote|8c}}), which showed the unambiguity of the curl; * ({{EquationNote|8q}}), which has a question mark after it; * ({{EquationNote|17}}), a product rule for the divergence, which is yet to be proven as a general identity; * ({{EquationNote|24c}}) and ({{EquationNote|24c}}), concerning "curl grad" and "div curl"; and * the identities showing that we can construct a field with a given divergence ({{EquationNote|36}}), Laplacian ({{EquationNote|38}}), or D'Alembertian ({{EquationNote|57}}). The above list exposes the following shortcomings: * we have not yet investigated "grad div" and "curl curl"; * we have only one ''product rule''&#8202;&mdash;the unverified identity ({{EquationNote|17}})&mdash;in which ''both'' factors are spatially variable fields; this needs to be verified and identities ({{EquationNote|8c}}) and ({{EquationNote|8p}}) need to be generalized; * our collection of product rules does not yet include the curl of a cross-product, or the gradient of a dot-product or of a product of scalars, or the advection of a product; and * we do not yet have any ''chain rules'' involving {{math|&nabla;,}} {{math|curl,}} or {{math|div}}. With the aid of the Cartesian forms of the various operators, we may now fill these gaps. <br /> The "'''grad div'''" and "'''curl curl'''" operators turn out to be related: :{{big|<math>\begin{align} \operatorname{curl}\operatorname{curl}\mathbf{q} \;\! &= \mathbf{e}_i \times\part_i(\operatorname{curl}\mathbf{q}) \\ &= \mathbf{e}_i \times\part_i(\mathbf{e}_j \times\part_j\mathbf{q}) \\ &= \mathbf{e}_i \times(\mathbf{e}_j \times\part_i\part_j\mathbf{q}) \,, \end{align}</math>}} whence expanding the vector triple product gives :{{big|<math>\operatorname{curl}\operatorname{curl}\mathbf{q} \;\! = \mathbf{e}_i \!\cdot~\!\!\part_i\part_j\mathbf{q} ~\mathbf{e}_j - \mathbf{e}_i {\cdot}~\!\mathbf{e}_j \,\part_i\part_j\mathbf{q} \,. </math>}} In the first term on the right, we can switch the order of partial differentiation; and in the second term&mdash;which, like the first, is a double summation&mdash;the only non-zero contributions are those for which&#8202; {{mvar|j&#8239;{{=}}&#8201;i}}&#8239; and&#8239; {{math|'''e'''_''i''&#8239;'''&#11825;&#8239;e'''_''j''&#8201;{{=}}&#8239;1}}.&#8201; So we have :{{big|<math>\begin{align} \operatorname{curl}\operatorname{curl}\mathbf{q} \;\! &= \mathbf{e}_i \!\cdot~\!\!\part_j\part_i\mathbf{q} ~\mathbf{e}_j - \part_i\part_i\mathbf{q} \\ &= \mathbf{e}_j \,\part_j(\mathbf{e}_i \!\cdot~\!\!\part_i\mathbf{q}) - \part_i\part_i\mathbf{q} \,; \end{align}</math>}} that is, {{NumBlk|:|{{big|<math> \operatorname{curl}\operatorname{curl}\mathbf{q} ~\!\equiv \nabla\operatorname{div}\mathbf{q} - \triangle\mathbf{q} \,. </math>}}|{{EquationRef|65}}}} This result may be memorized as "''curl curl is grad div minus del squared''&#8239;" and written as {{NumBlk|:|{{big|{{math|&nabla;&#8239;&times;&#8201;(&nabla;&#8239;&times;&#8201;'''q''') &equiv; &nabla; &nabla;'''&#11825;&#8239;q''' &minus; &nabla;²&#8202;'''q'''}}&#8201;,}}|{{EquationRef|66}}}} which ''looks like'' the expansion of a vector triple product; and the key step in the above derivation, based on the Gibbs definitions of the operators, ''really is''&#8202; the expansion of a vector triple product. <br /> We now turn to ''product rules'' in which neither factor is assumed uniform. The '''curl of a cross-product''' is :{{big|<math>\begin{align} &\operatorname{curl}(\mathbf{a}\!\times\!\mathbf{b}) \\ &~= \mathbf{e}_i ~\!\!\times\part_i(\mathbf{a}\times\mathbf{b}) \\ &~= \mathbf{e}_i ~\!\!\times(\part_i\mathbf{a}\times\mathbf{b} + \mathbf{a}\times\part_i\mathbf{b}) \\ &~= \mathbf{e}_i ~\!\!\times(\part_i\mathbf{a}\times\mathbf{b}) + \mathbf{e}_i ~\!\!\times(\mathbf{a}\times\part_i\mathbf{b}) \\ &~= \mathbf{e}_i{\cdot}~\!\mathbf{b} \,\part_i\mathbf{a} - \mathbf{e}_i{\cdot}~\!\part_i\mathbf{a} \;\mathbf{b} + \mathbf{e}_i{\cdot}~\!\part_i\mathbf{b} \;\mathbf{a} - \mathbf{e}_i{\cdot}~\!\mathbf{a} \,\part_i\mathbf{b} \\ &~= b_i\part_i\mathbf{a} - (\operatorname{div}\mathbf{a})~\!\mathbf{b} + (\operatorname{div}\mathbf{b})~\!\mathbf{a} - a_i\part_i\mathbf{b} \\ &~= \mathbf{b}~\!{\cdot}\nabla\,\mathbf{a} - \mathbf{b}\operatorname{div}\mathbf{a} + \mathbf{a}\operatorname{div}\mathbf{b} - \mathbf{a}~\!{\cdot}\nabla\,\mathbf{b} \,, \end{align}</math>}} i.e., {{NumBlk|:|{{big|<math> \operatorname{curl}(\mathbf{a}\!\times\!\mathbf{b}) \equiv \mathbf{a}\operatorname{div}\mathbf{b} - \mathbf{b}\operatorname{div}\mathbf{a} + \mathbf{b}~\!{\cdot}\nabla\,\mathbf{a} - \mathbf{a}~\!{\cdot}\nabla\,\mathbf{b} \,. </math>}}|{{EquationRef|67c}}}} The '''divergence of a cross-product''', as we might expect, is simpler: :{{big|<math>\begin{align}\operatorname{div}(\mathbf{a}\!\times\!\mathbf{b}) &= \mathbf{e}_i ~\!\!\cdot\part_i(\mathbf{a}\times\mathbf{b}) \\ &= \mathbf{e}_i ~\!\!\cdot(\part_i\mathbf{a}\times\mathbf{b} + \mathbf{a}\times\part_i\mathbf{b}) \\ &= \mathbf{e}_i ~\!\!\cdot\part_i\mathbf{a}\times\mathbf{b} + \mathbf{e}_i ~\!\!\cdot\mathbf{a}\times\part_i\mathbf{b} \\ &= \mathbf{e}_i ~\!\!\cdot\part_i\mathbf{a}\times\mathbf{b} - \mathbf{e}_i ~\!\!\cdot\part_i\mathbf{b}\times\mathbf{a} \\ &= \mathbf{b}\cdot\mathbf{e}_i ~\!\!\times\part_i\mathbf{a} - \mathbf{a}\cdot\mathbf{e}_i ~\!\!\times\part_i\mathbf{b} \,; \end{align}</math>}} i.e., {{NumBlk|:|{{big|<math> \operatorname{div}(\mathbf{a}\!\times\!\mathbf{b}) \equiv \mathbf{b}\cdot\operatorname{curl}\mathbf{a} - \mathbf{a}\cdot\operatorname{curl}\mathbf{b} \,. </math>}}|{{EquationRef|67d}}}} In particular, in electromagnetics,&#8201; {{math|div('''E'''&#8239;&times;&#8239;'''H''') &equiv; '''H&#8239;&#11825;'''&#8201;curl&#8201;'''E''' &minus; '''E&#8239;&#11825;'''&#8201;curl&#8201;'''H'''}}&#8239;;&#8239; this is the identity on which [[w:Poynting's theorem|Poynting's theorem]] is based. But if&#8202; {{math|'''b'''}} in ({{EquationNote|67d}}) is uniform, then ({{EquationNote|67d}}) reduces to ({{EquationNote|8c}}). The '''gradient of a dot-product''', by comparison, is surprisingly messy: :{{big|<math>\begin{align}\nabla\,\mathbf{a}{\cdot}\mathbf{b} &= \mathbf{e}_i \part_i(\mathbf{a}\!\cdot\!\mathbf{b}) \\ &= \mathbf{e}_i (\mathbf{a}\!\cdot\!\part_i\mathbf{b} + \mathbf{b}\!\cdot\!\part_i\mathbf{a}) \\ &= \mathbf{a}\!\cdot\!\part_i\mathbf{b} \;\mathbf{e}_i + \mathbf{b}\!\cdot\!\part_i\mathbf{a} \;\mathbf{e}_i \,. \end{align}</math>}} Now the first term on the right can be recognized as&#8201; {{math|'''a'''&#8202;&times;&#8239;('''e'''_''i''&#8202;&times;&#8239;''&part;_i''&#8202;'''b''')&#8201;+&#8201;'''a&#11825;&#8202;e'''_''i''&#8201;''&part;_i''&#8202;'''b'''&#8202;}};&#8201; that is,&#8201; {{math|'''a'''&#8202;&times;&#8239;('''e'''_''i''&#8202;&times;&#8239;''&part;_i''&#8202;'''b''')&#8201;+&#8201;''a_i&#8239;&part;_i''&#8202;'''b'''&#8202;}};&#8201; that is,&#8201; {{midsize|<math>\mathbf{a}\!\times\!\operatorname{curl}\mathbf{b}+\mathbf{a}~\!{\cdot}\nabla\,\mathbf{b}</math>}}.&#8201; Similarly, the second term is&#8201; {{midsize|<math>\mathbf{b}\!\times\!\operatorname{curl}\mathbf{a}+\mathbf{b}~\!{\cdot}\nabla\,\mathbf{a}</math>}}.&#8201; Thus we have {{NumBlk|:|{{big|<math> \nabla\,\mathbf{a}{\cdot}\mathbf{b} \equiv \mathbf{a}\!\times\!\operatorname{curl}\mathbf{b} + \mathbf{b}\!\times\!\operatorname{curl}\mathbf{a} + \mathbf{a}~\!{\cdot}\nabla\,\mathbf{b} + \mathbf{b}~\!{\cdot}\nabla\,\mathbf{a} \,. </math>}}|{{EquationRef|68}}}} For ''uniform''&#8202; {{math|'''b'''&#8202;,}} the first and third terms on the right vanish, and we can solve for the first term on the right, obtaining :<math>\mathbf{b}\times\operatorname{curl}\mathbf{a} ~\!= \nabla\,\mathbf{b{\cdot}a} - \mathbf{b}~\!{\cdot}\nabla\,\mathbf{a} \qquad</math>[&#8202;for uniform {{math|'''b'''}}] , so that we can now drop the question mark after ({{EquationNote|8q}}). If we write the curl operator as&#8202; {{math|&nabla;&#8202;&times;&#8239;,}}&#8239; the last equation [or ({{EquationNote|8q}})]&#8202; ''looks like'' the expansion of a vector triple product; but the identity is valid only for uniform{{math| '''b'''}}. The '''gradient of a product of scalars''', unlike that of a dot-product, is as simple as the product rule for ordinary differentiation: :{{big|<math>\begin{align}\nabla(p\varphi) &= \mathbf{e}_i \part_i(p\varphi) \\ &= \mathbf{e}_i(p~\!\part_i\varphi + \varphi~\!\part_i p) \\ &= p~\!\mathbf{e}_i\part_i\varphi + \varphi~\!\mathbf{e}_i\part_i p \,; \end{align}</math>}} that is, {{NumBlk|:|{{big|<math> \nabla(p\varphi) \equiv p\;\!\nabla\varphi + \varphi\;\!\nabla p \,. </math>}}|{{EquationRef|69}}}} The '''advection of a product''' is equally simple, ''regardless of the type of product'', except that the order of a cross-product matters. Let {{mvar|&psi;}} and {{mvar|&chi;}} be scalar or vector fields, and let {{math|''&psi;''&#8202;&lowast;''&chi;''}} denote any meaningful product of the two. Then, by ({{EquationNote|64}}), :{{big|<math>\begin{align} \mathbf{q}\;\!{\cdot}\nabla\,(\psi~\!\! * \!\chi) &= q_i \part_i (\psi~\!\! * \!\chi) \\ &= q_i (\psi * \part_i \chi + \part_i \psi * \chi) \\ &= \psi * q_i \part_i \chi + q_i \part_i \psi * \chi \,; \end{align}</math>}} that is, {{NumBlk|:|{{big|<math> \mathbf{q}\;\!{\cdot}\nabla\,(\psi~\!\! * \!\chi) \equiv \psi * (\mathbf{q}\;\!{\cdot}\nabla\chi) + (\mathbf{q}\;\!{\cdot}\nabla\psi) * \chi \,. </math>}}|{{EquationRef|70}}}} The {{math|'''q&#11825;'''&nabla;}} operator is a ''scalar'' operator in the sense that it maps the operand field to a field of the same order&mdash;a scalar field to a scalar field, a vector field to a vector field, a matrix field to a matrix field, etc.&mdash;&#8202;''as if''&#8202; it were multiplication by a scalar or differentiation w.r.t. a scalar; and indeed a differentiation w.r.t. path length appears in the coordinate-free definition ({{EquationNote|11}}) of the operator. Moreover, we did not need coordinates to obtain rule ({{EquationNote|70}}); as the reader may verify, the same rule can be obtained directly from the definition ({{EquationNote|11}}) in a similar manner. From these points of view, the simplicity of the rule is unsurprising. The '''curl of the product of a scalar and a vector''' is :{{big|<math>\begin{align}\operatorname{curl}p\mathbf{b} &= \mathbf{e}_i ~\!\!\times \part_i(p\mathbf{b}) \\ &= \mathbf{e}_i ~\!\!\times(p~\!\part_i\mathbf{b}+\part_i p\;\mathbf{b}) \\ &= p~\!\mathbf{e}_i{\times}~\!\part_i\mathbf{b} + \mathbf{e}_i\part_i p \times\mathbf{b} \\ \end{align}</math>}} that is, {{NumBlk|:|{{big|<math> \operatorname{curl}p\mathbf{b} \,\equiv\, p\operatorname{curl}\mathbf{b} ~\!+ \nabla p \times\mathbf{b} \,. </math>}}|{{EquationRef|71c}}}} For uniform {{math|'''b'''&#8202;,}} this reduces to ({{EquationNote|8p}}), which was used to derive the Cartesian form of the curl ({{EquationNote|59c}}). For the '''divergence of the product of a scalar and a vector''', we proceed likewise except that we use a dot instead of a cross. The result is {{NumBlk|:|{{big|<math> \operatorname{div}p\mathbf{b} \,\equiv\, p\operatorname{div}\mathbf{b} ~\!+ \nabla p \cdot \mathbf{b} \,, </math>}}|{{EquationRef|71d}}}} which has the same form as ({{EquationNote|17}}), delivering the promised confirmation that ({{EquationNote|17}}) is an identity. For uniform {{math|'''b'''&#8202;,}}&#8201; ({{EquationNote|71d}}) reduces to ({{EquationNote|8g}}), which was used to derive the Cartesian form of the divergence ({{EquationNote|60d}}). That exhausts the first-order product rules. For curiosity's sake, we shall also derive one second-order rule. The '''Laplacian of the product of a scalar field and a generic field''', by ({{EquationNote|63L}}), is :{{big|<math>\begin{align}\triangle(p\psi) &= \part_i \part_i (p\psi) \\ &= \part_i (p~\!\part_i \psi + \psi~\!\part_i p) \\ &= p\,\part_i \part_i \psi + \part_i \psi\,\part_i p + \psi~\!\part_i \part_i p + \part_i p\,\part_i \psi \\ &= p\,\part_i \part_i \psi + 2\part_i p\,\part_i \psi + \psi~\!\part_i \part_i p \\ &= p~\!\triangle\psi + 2\part_i p\,\part_i \psi + \psi~\!\triangle p \,. \end{align}</math>}} In the middle term, by ({{EquationNote|58g}}), {{mvar|&part;_i&#8239;p}}&#8202; is the {{mvar|i&#8202;}}th component of{{math|&#8202; &nabla;''p''}}&#8239; so that, by ({{EquationNote|64o}}),&#8201; {{mvar|&part;_i&#8239;p&#8239;&part;_i}}&#8239; is the {{math|'''q&#11825;'''&nabla;}} operator for&#8239; {{math|'''q'''&#8239;{{=}}&#8239;&nabla;''p''}}.&#8201; So we have {{NumBlk|:|{{big|<math> \triangle(p\psi) \equiv p~\!\triangle\psi + 2(\nabla p \cdot~\!\! \nabla)\psi + \psi~\!\triangle p \,. </math>}}|{{EquationRef|72}}}} The argument assumes a scalar{{mvar| p}} but is indifferent to whether {{mvar|&psi;}} is a scalar or a vector or a higher-order tensor. <br /> Finally we turn to ''chain rules''&#8202;&mdash;&#8202;especially the simple cases of the gradient, curl, divergence, advection, and Laplacian of a function of a scalar field{{mvar| u}}. As usual, let {{mvar|p}} denote a scalar field, {{math|'''q'''}} a vector field, and {{mvar|&psi;}} a generic field. '''Gradient&#8202;&#10744;&#8202;curl&#8202;&#10744;&#8202;divergence of a function of a scalar''':  By the general Cartesian formula ({{EquationNote|60s}}) and the chain rule for{{math| ''&part;_i''&#8239;,}} :{{big|<math>\begin{align}\nabla~\!\! * \big(\psi(u)\big) &= \mathbf{e}_i ~\!\! * \part_i \big(\psi(u)\big) \\ &= \mathbf{e}_i ~\!\! * \psi'~\!\!(u) ~\!\part_i u \\ &= \mathbf{e}_i \part_i u * \psi'~\!\!(u) \,; \end{align}</math>}} i.e., by ({{EquationNote|58g}}), {{NumBlk|:|{{big|<math> \nabla~\!\! * \big(\psi(u)\big) \equiv \nabla u * \psi'~\!\!(u) \,. </math>}}|{{EquationRef|73}}}} In particular, if&#8202; {{math|&lowast;}} is a null, {{NumBlk|:|<math> \nabla\big(p(u)\big) \equiv \nabla u \;p'~\!\!(u) \,; </math>|{{EquationRef|73g}}}} and if&#8202; {{math|&lowast;}} is a cross, {{NumBlk|:|<math> \mathrm{curl}\big(\mathbf{q}(u)\big) \equiv \nabla u \times \mathbf{q}'~\!\!(u) \,; </math>|{{EquationRef|73c}}}} and if&#8202; {{math|&lowast;}} is a dot, {{NumBlk|:|<math> \mathrm{div}\big(\mathbf{q}(u)\big) \equiv \nabla u \cdot \mathbf{q}'~\!\!(u) \,. </math>|{{EquationRef|73d}}}} '''Advection of a function of a scalar''': :<!-- SUBSCRIPTS ENLARGED FOR LEGIBILITY: --><math>\begin{align} \mathbf{q}\;\!{\cdot}\nabla\,\big(\psi(u)\big) &= q_{\textstyle i} \part_{\textstyle i} \big(\psi(u)\big) \\ &= q_{\textstyle i} ~\!\psi'~\!\!(u) ~\!\part_{\textstyle i} u \\ &= q_{\textstyle i} \part_{\textstyle i} u \;\psi'~\!\!(u) \,; \end{align}</math> i.e., {{NumBlk|:|{{big|<math> \mathbf{q}\;\!{\cdot}\nabla\,\big(\psi(u)\big) \equiv~\! \mathbf{q}\;\!{\cdot}\nabla u ~\psi'~\!\!(u) \,. </math>}}|{{EquationRef|73q}}}} This fits into the pattern set by ({{EquationNote|73}}) in that the gradient operator in ({{EquationNote|73g}}) is replaced by an advection operator. Of the last four results, only ({{EquationNote|73c}}) is dependent on the order of the {{math|&lowast;}} product; the others could equally well be written {{NumBlk|:|<math>\begin{align} \nabla\big(p(u)\big) &\equiv~\! p'~\!\!(u) ~\!\nabla u \\ \mathrm{div}\big(\mathbf{q}(u)\big) &\equiv~\! \mathbf{q}'~\!\!(u) \cdot~\!\! \nabla u \\ \mathbf{q}\;\!{\cdot}\nabla\,\big(\psi(u)\big) &\equiv~\! \psi'~\!\!(u)\;\mathbf{q}\;\!{\cdot}\nabla u ~. \end{align}</math>|{{EquationRef|73z}}}} The '''Laplacian of a function of a scalar''' departs from the above pattern. :{{big|<math>\begin{align}\triangle\big(\psi(u)\big) &= \part_i \part_i \big(\psi(u)\big) \\ &= \part_i\big(\psi'~\!\!(u) ~\!\part_i u\big) \\ &= \psi'~\!\!(u) ~\!\part_i\part_i u + \psi''~\!\!(u) ~\!\part_i u \,\part_i u \,, \end{align}</math>}} where the last line follows from the product rule for {{mvar|&part;_i}}&#8202; and, in the second term, the chain rule for{{mvar| &part;_i&#8202;}}.&#8201; In that second term, the implicit sum&#8202; {{mvar|&part;_i&#8202;u&#8239;&part;_i&#8202;u}}&#8239; can be recognized as&#8202; {{math|{{abs|&nabla;''u''}}²}}&#8202; by ({{EquationNote|58s}}). So we have {{NumBlk|:|{{big|<math> \triangle\big(\psi(u)\big) \equiv \psi'~\!\!(u)~\!\triangle u + \psi''~\!\!(u)~\!\big|\nabla u\big|^2. </math>}}|{{EquationRef|74}}}} '''Multivariate chain rule''':  The foregoing chain rules involve ''one'' intermediate function of ''one'' scalar variable. It will be useful to have an elementary chain rule that can handle more than one of each. Let {{math|''p''('''r''')}} be a smooth scalar field, and let {{math|'''r'''}} in turn be a smooth function of several variables, one of which, say{{mvar| t&#8202;}}, is allowed to vary while the others are held constant, so that {{math|'''r'''}} changes by {{math|''d'''''r'''}} when {{mvar|t}} changes by {{mvar|dt}}. Then dividing ({{EquationNote|26g}}) by {{mvar|dt}}&#8202; gives :<math>\part_t p = \nabla p \cdot \part_t \mathbf{r}</math> or, in indicial Cartesian coordinates with implicit summation, :{{big|<math>\part_t p = \part_i p \,\part_t x_i</math>}} or, in traditional longhand, :{{big|<math>\tfrac{\part}{\part t}~\!p(x,y,z) = \tfrac{\part p}{\part x}~\!\tfrac{\part x}{\part t} + \tfrac{\part p}{\part y}~\!\tfrac{\part y}{\part t} + \tfrac{\part p}{\part z}~\!\tfrac{\part z}{\part t} \,. </math>}} This is the desired multivariate chain rule for a scalar function of three intermediate real variables. The assumption that these variables are Cartesian coordinates is not a loss of generality, because any three real quantities can be suitably scaled and represented by perpendicular axes, so that any scalar function of them becomes a function of position, to which ({{EquationNote|26g}}) applies; and then the scaling can be reversed without changing the products in the last equation. Moreover, by the linearity of{{mvar| &part;_t&#8239;}}, the scalar field {{mvar|p}} may be replaced by any field expressible in terms of a uniform basis. For example, for a vector field{{math| '''q'''&#8202;}}, :{{big|<math>\begin{align}\part_t \mathbf{q} &= \part_t (q_j \mathbf{e}_j) \\ &= \mathbf{e}_j \part_t q_j \\ &= \mathbf{e}_j \part_i q_j \,\part_t x_i \\ &= \part_i (q_j \mathbf{e}_j) ~\!\part_t x_i = \part_i \mathbf{q} \,\part_t x_i \,, \end{align}</math>}} where the third line is obtained by applying the multivariate chain rule for a scalar field. Thus, for a generic field {{mvar|&psi;&#8202;}}, {{NumBlk|:|{{big|<math> \part_t \psi = \part_i \psi \,\part_t x_i \qquad</math>}}[&#8202;for generic {{mvar|&psi;}} and {{mvar|x_i&#8239;}}].|{{EquationRef|75}}}} '''Gradient&#8202;&#10744;&#8202;curl&#8202;&#10744;&#8202;divergence of a function of a scaled position vector''':  We end this subsection by deriving a lemma for use in the next subsection. If{{mvar| k}} is a uniform scalar multiplier and {{math|'''r'''}} is the position vector, :{{big|<math> \nabla * \psi(k\mathbf{r}) = \mathbf{e}_i * \part_i \psi(k\mathbf{r}) = k\mathbf{e}_i * \part_{(kx_{\scriptstyle i})} \psi(k\mathbf{r}) \,, </math>}} where the third expression is obtained by from the second by multiplying each denominator (change in{{mvar| x_i}}) by{{mvar| k}}&#8239; and compensating. But now we have {{NumBlk|:|{{big|<math> \nabla * \psi(k\mathbf{r}) = k\,(\nabla {*}~\! \psi)\Big|_{k\mathbf{r}} \,, </math>}}|{{EquationRef|76}}}} where the vertical bar and subscript indicate that the gradient, curl, or divergence is evaluated at{{math| ''k''&#8202;'''r'''}}. We shall be interested in the curl (for which {{math|&lowast;}} is a cross). === Field with given curl === Consider the vector field {{NumBlk|:|<math> \mathbf{v}(\mathbf{r}) = \mathbf{q}(\mathbf{r})\times\mathbf{r} \,, </math>|{{EquationRef|77}}}} where {{math|'''q'''}} is a ''solenoidal''&#8202; vector field and {{math|'''r''' }}is the position vector. By identity ({{EquationNote|67c}}), :<math>\operatorname{curl}\mathbf{v} = \mathbf{q}\operatorname{div}\mathbf{r} - \mathbf{r}\operatorname{div}\mathbf{q} + \mathbf{r}~\!{\cdot}\nabla\,\mathbf{q} - \mathbf{q}~\!{\cdot}\nabla\,\mathbf{r} </math> where, by hypothesis, {{math|div&#8239;'''q'''}}&#8202; is zero. Applying identities ({{EquationNote|62r}}) and ({{EquationNote|64r}}) then yields :<math>\begin{align} \operatorname{curl}\mathbf{v} &= 3\mathbf{q} + \mathbf{r}~\!{\cdot}\nabla\,\mathbf{q} - \mathbf{q} \\ &= 2\mathbf{q} + \mathbf{r}~\!{\cdot}\nabla\,\mathbf{q} \,. \end{align}</math> [[File:Vorticity_Figure_01_a-m.gif|thumb|Animation of a rigid-body-like velocity field, whose curl is twice the angular velocity.]] In the special case in which {{math|'''q'''}} is the ''angular velocity'' {{math|'''&omega;'''}} of a '''rigid body''' about an axis through the origin,&#8201; {{math|'''v''' }}is the velocity field ({{math|'''&omega;'''&#8239;&times;&#8239;'''r'''}}) and {{math|'''&omega;'''}} is uniform, so that the last result reduces to&#8201; {{math|curl&#8239;'''v'''&#8201;{{=}}&#8201;2'''&omega;'''&#8202;}}; that is, ''the vorticity is twice the angular velocity''. As the vorticity in this case is uniform and therefore independent of position relative to the axis, it does not change if the axis is shifted, provided that the angular velocity has the same magnitude and direction. And because a uniform velocity field has zero curl, the vorticity is also unchanged if a translational motion is superposed on the rotation. This is the most direct connection that we have seen between curl and rotation. But again I digress. Returning to the more general case in which {{math|'''q''' }}is not necessarily uniform, but merely solenoidal,<ref>The following explanation takes some hints from Christopher Ford's note on "Vector Potentials" at [https://www.maths.tcd.ie/~houghton/231/Notes/ChrisFord/vp.pdf maths.tcd.ie/~houghton/231/Notes/ChrisFord/vp.pdf], circa 2004.</ref> we have :<math>\operatorname{curl}\mathbf{v}(\mathbf{r}) = 2\mathbf{q}(\mathbf{r}) + \mathbf{r}~\!{\cdot}\nabla\,\mathbf{q}(\mathbf{r}) \,, </math> to which we can apply our lemma ({{EquationNote|76}}) with a uniform real factor {{mvar|t&#8202;}}, obtaining :<math> \operatorname{curl}\mathbf{v}(t\mathbf{r}) = 2t\mathbf{q}(t\mathbf{r}) + t\mathbf{r}~\!{\cdot}\nabla\,\mathbf{q}(t\mathbf{r}) \,. </math> On the left we can recall ({{EquationNote|77}}); and on the right we can apply ({{EquationNote|11}}), noting that the magnitude of{{math| {{abs|'''r'''}}}} is{{mvar| r&#8202;}}, which measures distance in the direction of{{math| '''r'''}}. Thus we obtain :<math> \mathrm{curl}\big(\mathbf{q}(t\mathbf{r})\times t\mathbf{r}\big) = 2t\mathbf{q}(t\mathbf{r}) + tr \part_{\textstyle r} \mathbf{q}(t\mathbf{r}) \,. </math> Now if the direction of{{math| '''r'''}} is held constant,&#8201; {{math|'''q'''(''t''&#8202;'''r''')}} is a function of{{mvar| tr&#8239;}}; and in general&#8201; {{math|''r&#8202;&part;_r&#8201;f''&#8202;(''tr'')&#8201;{{=}}&#8201;''t&#8202;&part;_t&#8201;f''&#8202;(''tr'')}}.&#8201; So we have :<math>\begin{align} \mathrm{curl}\big(\mathbf{q}(t\mathbf{r})\times t\mathbf{r}\big) &= 2t\mathbf{q}(t\mathbf{r}) + t^2 \part_t \mathbf{q}(t\mathbf{r}) \\ &= \part_t \big(t^2 \mathbf{q}(t\mathbf{r})\big) \,. \end{align}</math> Integrating w.r.t. {{mvar|t}}&#8239; from 0 to 1 gives :<math> \int_0^1\!\mathrm{curl}\big(\mathbf{q}(t\mathbf{r})\times t\mathbf{r}\big)\,dt = \big(t^2 \mathbf{q}(t\mathbf{r})\big)\Big|_0^1 =~\! \mathbf{q}(\mathbf{r}) \,; </math> that is, {{NumBlk|:|<math>\mathbf{q}(\mathbf{r}) \equiv \mathrm{curl}\int_0^1\!\mathbf{q}(t\mathbf{r})\!\times\!t\mathbf{r}\;dt\qquad </math>[&#8202;for solenoidal {{math|'''q'''&#8202;}}].|{{EquationRef|78}}}} Thus for any solenoidal vector field{{math| '''q'''}}&#8239; we can construct a '''vector potential'''&mdash;that is, a field whose curl is{{math| '''q'''&#8202;}}; such a field is given by the integral on the right. This is the long-promised proof of the "converse" of identity ({{EquationNote|24d}}). Of course the vector potential is not unique, because any conservative field&mdash;but ''only'' a conservative field&mdash;can be added to it without changing its curl. Hence the existence of ''one'' vector potential implies the existence of infinitely many. The above integral gives us ''one''. The proof of ({{EquationNote|78}}) assumes that {{math|'''q''' }}is solenoidal not only at position{{math| '''r'''&#8202;,}} but also at{{math| ''t''&#8202;'''r'''}}&#8202; where&#8239; {{math|0&#8239;&leq;&#8239;''t''&#8239;&leq;&#8202;1}}, i.e. at every point on the line-segment from the origin to{{math| '''r'''}}.&#8201; A '''star-shaped''' region is one that contains an point{{mvar| O}}&#8202; such that for every point{{mvar| P}} in the region, the line-segment {{mvar|OP}} is entirely contained in the region. We may choose any such {{mvar|O}}&#8202; as the origin in the proof of ({{EquationNote|78}}). So the proof tells us that if a vector field is solenoidal within a star-shaped region, it has a vector potential in that region. As a special case, a vector field that is solenoidal everywhere has a vector potential everywhere. === Notes on the curl of the curl === Identity ({{EquationNote|65}}), namely :<math> \operatorname{curl}\operatorname{curl}\mathbf{q} ~\!\equiv \nabla\operatorname{div}\mathbf{q} - \triangle\mathbf{q} </math> ("curl curl is grad div minus del squared"), has at least three implications worth noting here. First, it can be rearranged as {{NumBlk|:|<math>\triangle\mathbf{q} ~\!\equiv \nabla\operatorname{div}\mathbf{q} - \operatorname{curl}\operatorname{curl}\mathbf{q} </math>|{{EquationRef|79}}}} ("del squared is grad div minus curl curl"). This would serve as a coordinate-free definition of the Laplacian of a vector, if we did not already have one.<ref>''Cf''. [[#gibbs-1881-4|Gibbs, 1881]], &sect;&#8202;71, and [[#moon-spencer-65|Moon &amp; Spencer, 1965]], p.&#8239;235; quoted in [[#tai-95|Tai, 1995]], pp.&#8239;18,&#8239;43.</ref> But we do: we started with a coordinate-free definition ({{EquationNote|4L}}) for a generic field, established its unambiguity via ({{EquationNote|9L}}), and found its Cartesian form ({{EquationNote|63L}}), which we used in the derivation of ({{EquationNote|79}}). Wherever we start, we may properly assert by way of contrast that the Laplacian of a ''vector''&#8202; is given by ({{EquationNote|79}}), whereas the Laplacian of a ''scalar''&#8202; is given by the divergence of the gradient. But we should ''not'' conclude, as Moon &amp; Spencer do, that representing the scalar and vector Laplacians by the same symbol is "poor practice&hellip; since the two are basically quite different",<ref>[[#moon-spencer-65|Moon &amp; Spencer, 1965]], p.&#8239;236.</ref> because in fact the two have a common definition which is succinct, unambiguous, and coordinate-free: the Laplacian (of anything) is the closed-surface integral of the outward normal derivative, per unit volume.{{efn|Tai ([[#tai-95|1995]], pp.&#8239;43–4) also disagrees with Moon &amp; Spencer, but for a different reason: he regards the Laplacian as the divergence of the gradient even if the operand is a ''vector'' field. For better or worse, we do not consider the gradient of a vector in the present paper&mdash;although the reader can probably work out how to modify ({{EquationNote|26g}}) if&#8202; {{math|''d'''''r'''}} is written as a column vector and&#8202; {{mvar|dp}}&#8202; is ''replaced''&#8202; by a column vector (compare the later footnote on ''dyadics'').}} Second, by reason of identity ({{EquationNote|38}}) and the remarks thereunder, a given vector field{{math| '''v'''}} can be written :<math>\mathbf{v}(\mathbf{r}) \,\equiv\, \triangle\bigg(\!{-}\!\iiint \frac{\,\mathbf{v}(\mathbf{r}')}{4\pi}\, \frac{1}{|\mathbf{r}\!-\!\mathbf{r}'|} \,dV' \!\bigg) \,,</math> where the integral is over all space, or at least all of the space in which {{math|'''v'''}} may be non-zero. So, subject to the convergence of the integral, there exists a vector field{{math| '''q'''}} such that :<math>\mathbf{v} = \triangle\mathbf{q} \,;</math> that is, by ({{EquationNote|79}}), there exists{{math| '''q'''}} such that :<math>\mathbf{v} = \nabla\operatorname{div}\mathbf{q} - \operatorname{curl}\operatorname{curl}\mathbf{q} \,, </math> which implies the existence of a scalar field, say<math>\,\varphi~\!,\,</math> and a vector field, say{{math| '''&Psi;'''}}, such that :<math>\mathbf{v} = -\nabla\varphi+\operatorname{curl}\boldsymbol{\Psi} </math> (namely&#8201; {{midsize|<math>\varphi\!=\!-\!\operatorname{div}\mathbf{q}\,</math>}} and&#8201; {{math|'''&Psi;'''&#8201;{{=}}&#8201;&minus;&#8202;curl&#8239;'''q'''}}). In short, subject to the convergence of the said integral, * ''a given vector field can be resolved into [minus] a gradient plus a curl''. Such a resolution is called a '''Helmholtz decomposition''', and the proposition that it exists is the ''Helmholtz decomposition theorem''. Of course the gradient is irrotational and the curl is solenoidal so that, subject to the same convergence, * ''a given vector field can be resolved into an irrotational field plus a solenoidal field''. This is a second statement of the theorem, and follows from the first. And the first follows from the second because an irrotational field has a scalar potential by ({{EquationNote|29}}) and a solenoidal field has a vector potential by ({{EquationNote|78}}). Third, if {{math|'''q'''}} is ''solenoidal'', the term&#8201; {{math|&nabla;&#8201;div&#8239;'''q'''}}&#8239; in ({{EquationNote|65}}) or ({{EquationNote|79}}) vanishes. Hence ''for a solenoidal field, the curl of the curl is minus the Laplacian''. For example, in the ''dynamic'' case, in a ''vacuum'', the Maxwell&ndash;Amp&egrave;re law says that&#8201; {{math|curl&#8201;'''H''' {{=}} '''D'''{{big|&#775;}} {{=}} ''&epsiv;''₀&#8202;'''E&#775;'''}}.&#8201; Multiplying this by the physical constant {{math|''&mu;''₀}} (called the '''vacuum permeability''' or simply the '''magnetic constant''') gives&#8201; {{math|curl&#8201;'''B''' {{=}} ''&mu;''₀&#8202;''&epsiv;''₀&#8239;'''E&#775;'''&#8202;,}}&#8239; whence :<math>\operatorname{curl}\operatorname{curl}\mathbf{B} = \mu_0\epsilon_0\operatorname{curl}\mathbf{\dot{E}} \,. </math> But, by Gauss's law for magnetism, {{math|'''B'''}} is solenoidal so that, by ({{EquationNote|65}}), the left-hand side of the above is&#8201; {{math|&minus;&#9651;'''B'''}}.&#8201; And by '''Faraday's law''',&#8201; {{math|curl&#8201;'''E''' {{=}} &minus;'''B'''{{big|&#775;}}&#8202;,}}&#8201; so that&#8201; {{midsize|<math>\operatorname{curl}\mathbf{\dot{E}}=-\mathbf{\ddot{B}}</math>}}.&#8201; Making these substitutions, we get&#8201; {{midsize|<math>-\triangle\mathbf{B}=-\mu_0\epsilon_0\mathbf{\ddot{B}}~\!,\,</math>}} i.e. :<math>\mathbf{\ddot{B}}=\frac{1}{\mu_0\epsilon_0}~\!\triangle\mathbf{B} \,.</math> By comparison with ({{EquationNote|45}}), this is the wave equation with :<math>c=\frac{1}{\sqrt{\mu_0\epsilon_0}} \,.</math> Thus the Maxwell&ndash;Amp&egrave;re law, Gauss's law for magnetism, and Faraday's law, with the aid of ({{EquationNote|65}}), predict the existence of '''electromagnetic waves''' together with their speed. For these reasons, especially the last, one could hardly overstate the importance of identity ({{EquationNote|65}}). === Digression: Proofs from formal products === We have seen that Wilson ([[#wilson-1901|1901]], pp.&#8239;150,&#8239;152) interprets the divergence and curl as "formal" or "symbolic" scalar and vector products with the {{math|&nabla; }}operator.&#8201; {{nowrap|C.-T. Tai}}, in his [[#tai-95|1995 report]] (pp.&#8239;26–9), alleges that this interpretation began with Wilson and not with Gibbs. Here I shall submit, on the contrary, that while the terminology may not be attributable to Gibbs, the concept certainly is. Later in the same report, Tai confuses the picture by citing the first volume of [[w:Oliver Heaviside|Heaviside]]'s ''Electromagnetic Theory'' (1893), where Heaviside, although his notations for the scalar and vector products differ from those of Gibbs, nevertheless considers the {{math|&nabla;}} operator as a factor in such products. Tai continues: <blockquote>At the time of his writing he [Heaviside] was already aware of Gibbs' pamphlets on vector analysis but Wilson's book was not yet published. It seems, therefore, that Heaviside and Wilson independently introduced the misleading concept for the scalar and vector products between {{math|&nabla;}} and a vector function. Both were, perhaps, induced by Gibbs' notations for the divergence and the curl. Heaviside did not even include the word 'formal' in his description of the products.<ref>[[#tai-95|Tai, 1995]], p.&#8239;35.</ref> </blockquote> Whereas it was quite in character for Heaviside to treat an operator that way, the word "independently" would have surprised Wilson and is contradicted by Tai himself, who observes that Wilson's preface acknowledges Heaviside.<ref>[[#tai-95|Tai, 1995]], pp.&#8239;25,&#8239;29.</ref> In Wilson's own words: <blockquote>By far the greater part of the material used in the following pages has been taken from the course of lectures on Vector Analysis delivered annually at the University [Yale] by Professor Gibbs. Some use, however, has been made of the chapters on Vector Analysis in Mr. Oliver Heaviside's ''Electromagnetic Theory'' (Electrician Series, 1893) and in Professor F&ouml;ppl's lectures on ''Die Maxwell'sche Theorie der Electricit&auml;t'' (Teubner, 1894).&#8239;.... Notwithstanding the efforts which have been made during more than half a century to introduce Quaternions into physics the fact remains that they have not found wide favor.{{efn|A ''quaternion''&#8202; is a mathematical object invented by [[w:William Rowan Hamilton|William Rowan Hamilton]] in 1843, consisting of two parts which Hamilton later called the scalar part and the vector part. For most purposes the two parts were found to be more useful separately than together. By putting them together, however, Hamilton constructed a set which satisfied all the algebraic field axioms except commutativity of multiplication. This was, and is, considered a triumph.}} On the other hand there has been a growing tendency especially in the last decade toward the adoption of some form of Vector Analysis. The works of Heaviside and F&ouml;ppl referred to before may be cited in evidence. As yet however no system of Vector Analysis which makes any claim to completeness has been published. In fact Heaviside says: "I am in hopes that the chapter which I now finish may serve as a stopgap till regular vectorial treatises come to be written suitable for physicists, based upon the vectorial treatment of vectors" (''Electromagnetic Theory'', Vol.&#8239;{{serif|I}}., p.&#8239;305). Elsewhere in the same chapter Heaviside has set forth the claims of vector analysis as against Quaternions, and others have expressed similar views.<ref>[[#wilson-1901|Wilson, 1901]], pp.&#8239;ix,&#8239;xi–xii.</ref> </blockquote> Most damaging to Tai's thesis, however, is Gibbs's original pamphlet, a copy of which Heaviside received from Gibbs himself in June 1888.<ref>[[#gibbs-1881-4|Gibbs, 1881–84]], privately printed version&mdash;of which the scan linked in our bibliography is of the very copy that Gibbs sent to Heaviside, with annotations in Heaviside's hand. On the annotations see [[#rocci-20|Rocci, 2020]].</ref> Sections 62 to 65 of the pamphlet appear under the heading <blockquote style="text-align: center">{{math|&nabla;,}} {{math|&nabla;'''&#11825;'''&#8202;,}} ''and''&#8202; {{math|&nabla;&#8202;&times;}}&#8239; ''applied to Functions of Functions of Position''. </blockquote>In &sect;&#8239;62, Gibbs says that a constant scalar factor after such an operator may be placed before it (that is, taken outside the operator). {{nowrap|In &sect;&#8239;63}} he states our rule ({{EquationNote|73g}}) for the gradient of a function of a scalar field. His next section (in which I have bolded the vector field{{math| '''&omega;'''}}) is worth quoting in full: <blockquote>64.  If {{mvar|u}} or {{math|'''&omega;'''}} is a function of several scalar or vector variables, which are themselves functions of the position of a single point, the value of&#8202; {{math|&nabla;''u''}} or {{math|&nabla;'''&#11825;&#8239;&omega;'''}}&#8202; or {{math|&nabla;&#8202;&times;&#8202;'''&omega;'''}}&#8202; will be equal to the sum of the values obtained by making successively all but each one of these variables constant. </blockquote> This proposition is a ''generalized product rule'' in the sense that the "function of several scalar or vector variables" may be, but is not restricted to, any sort of product of those variables. Gibbs continues: <blockquote>65.  By the use of this principle, we easily derive the following identical equations: </blockquote> Six "equations" follow. The first says that the gradient operation is distributive over addition, and the second says the same of the divergence and curl (on one line). The last four are our identities ({{EquationNote|69}}), ({{EquationNote|71d}}), ({{EquationNote|71c}}), and ({{EquationNote|67d}}), in that order (albeit with different symbols). Gibbs then remarks (with my italics): <blockquote>The student will observe an analogy between these equations and the formul&aelig; of ''multiplication''. (In the last four equations the analogy appears most distinctly when we regard all the factors but one as constant.) Some of the more curious features of this analogy are due to the fact that the {{math|&nabla;}} contains implicitly the vectors {{math|'''i'''&#8202;,}} {{math|'''j'''&#8202;,}} and {{math|'''k'''&#8202;,}} which are to be ''multiplied''&#8202; into the following quantities. </blockquote> Indeed, if the ''first''&#8202; factor is constant, identities ({{EquationNote|69}}), ({{EquationNote|71d}}), ({{EquationNote|71c}}), and ({{EquationNote|67d}}) become :<math>\begin{align} \nabla(p\varphi) &= p\;\!\nabla\varphi \\ \nabla\cdot p\mathbf{b} &= p\,\nabla{\cdot}~\!\mathbf{b} \\ \nabla\times p\mathbf{b} &= p\,\nabla{\times}~\!\mathbf{b} \\ \nabla\cdot(\mathbf{a}\!\times\!\mathbf{b}) &= -\mathbf{a}\cdot\nabla{\times}~\!\mathbf{b} \,, \end{align}</math> whereas if the ''second''&#8202; factor is constant, they become respectively :<math>\begin{align} \nabla(p\varphi) &= \varphi\;\!\nabla p \\ \nabla\cdot p\mathbf{b} &= \nabla p \cdot \mathbf{b} \\ \nabla\times p\mathbf{b} &= \nabla p \times \mathbf{b} \\ \nabla\cdot(\mathbf{a}\!\times\!\mathbf{b}) &= \nabla{\times}~\!\mathbf{a}\cdot\mathbf{b} \,. \end{align}</math> All eight equations look like rearrangements of ''products'' involving a vector{{math| &nabla;}}.&#8201; [Concerning the last ''three'' equations, we have made that observation before; see ({{EquationNote|15}}) above.]&#8201; But only seven of the eight are explained by taking the constant outside the operator ({{nowrap|as in &sect;&#8239;62}}); the exception is the fourth, in which the minus sign is not explained by that step alone, but ''is'' explained by the change in the cyclic order of the formal triple product. And if we add the two right-hand sides corresponding to each of the four left-hand sides, we get the identities in which both factors are variable&mdash;as claimed {{nowrap|in &sect;&#8239;64}}. If &sect;&#8239;65 leaves any doubt that Gibbs approved of formal products with the symbolic vector{{math| &nabla;}} (albeit without using those terms), this is dispelled {{nowrap|by &sect;&#8202;166}}, where he writes: <blockquote>166.&#8201; To the equations in No.&#8239;65 may be added many others&hellip; </blockquote> followed by a list of seven identities terminated by "etc." Six of the seven are beyond the scope of the present paper,{{efn|They involve ''dyadics'', i.e. 2nd-order tensors written in a vector-friendly notation. The fourth of the seven is :{{math|&nabla;('''&tau;&#11825;&#8202;&omega;''') {{=}} &nabla;'''&tau;&#8239;&#11825;&#8201;&omega;''' + &nabla;'''&omega;&#8201;&#11825;&#8201;&tau;'''&#8239;,}} which is our ({{EquationNote|68}}) expressed in terms of the dyadics {{math|&nabla;'''&tau;'''}} and{{math| &nabla;'''&omega;'''&#8202;}}; the right-hand side is not to be confused with :{{math|('''&omega;&#8202;&#11825;'''&nabla;)'''&tau;''' + '''(&tau;&#11825;'''&nabla;)'''&omega;'''&#8239;,}} which would contradict our ({{EquationNote|68}}).}} while the third of the seven is our ({{EquationNote|67c}}). After the list comes the smoking gun ({{nowrap|&sect;&#8202;166, continued}}): <blockquote>The principle in all these cases is that if we have one of the operators&#8202; {{math|&nabla;,}} {{math|&nabla;'''&#11825;'''&#8202;,}} {{math|&nabla;&#8202;&times;}}&#8239; prefixed to a ''product'' of any kind, and we make any transformation of the expression which would be allowable if the {{math|&nabla;}} were a ''vector'', (viz: by changes in the order of the ''factors'', in the signs of ''multiplication'', in the parentheses written or implied, etc.,) by which changes the {{math|&nabla;}} is brought into connection with one particular factor, the expression thus transformed will represent the part of the value of the original expression which results from the variation of that factor. </blockquote> The italics are mine, but I have refrained from italicizing those instances of the word "factor" which are not applicable to{{math| &nabla;}}. In particular, at the stage when "the {{math|&nabla;}} is brought into connection with one particular factor," the "part of the value&hellip; which results from the variation of that factor" evidently means the term of the sum {{nowrap|in &sect;&#8239;64}}&#8202;&mdash;which, as we have noted, amounts to a generalized product rule. But, according to the stated "principle', we reach that stage by treating{{math| &nabla;}} as a factor. I rest my case. <br /> Wilson ([[#wilson-1901|1901]], p.&#8239;157) gives a comprehensive list of sum and product rules for the gradient, divergence, and curl, and properly states (p.&#8239;158) that the rules may be proven "most naturally" from Gibbs's definitions of the operators&mdash;our equations ({{EquationNote|58g}}), ({{EquationNote|60d}}), and ({{EquationNote|59c}}). Understandably, Wilson uses a {{math|&sum;}} sign rather than implicit summation. Less understandably, and less fortunately, he does not sum over a numerical index; e.g., he defines the curl operator as :{{big|<math>\nabla\times \,=\, \textstyle\sum\,\mathbf{i}~\!\!\times\!\frac{\part}{\part x} \qquad\quad </math>[sic]}} and explains that "The summation extends over {{math|''x'',&#8239;''y'',&#8239;''z''}}."&#8201; With these definitions he proves our identities ({{EquationNote|71c}}) and ({{EquationNote|68}}) essentially as we have done, but inevitably with greater difficulty, which may explain why he then says "The other formul&aelig; are demonstrated in a similar manner" before reverting to Gibbs's strategy of varying one factor at a time. He announces (p.&#8239;159) that the variable held constant will be written as a subscript after the product, and he combines this notation with his {{math|&sum;}} notation in a rigorous proof that varying one factor at a time is valid for our ({{EquationNote|68}}), i.e. the gradient of a dot-product. Noting that this result is analogous to :<math>d(\mathbf{u}\cdot\mathbf{v}) = \mathbf{u}\cdot d\mathbf{v} + d\mathbf{u}\cdot\mathbf{v} \,, </math> he then jumps to the conclusion that varying one factor at a time is valid for ''all''&#8202; of his product rules&mdash;notwithstanding that a small change in a vector is not related to its divergence or curl as a small change in a scalar is related to its gradient. That ''per saltum''&#8202; conclusion is his cue to go formal and symbolic. To obtain the curl of a cross-product [as in our ({{EquationNote|67c}})], he "formally" expands a vector triple product to obtain the curl when the first factor is constant, states the curl when the second factor is held constant, and adds the two partial curls ([[#wilson-1901|Wilson, 1901]], p.&#8239;161). Next he gives various arrangements of our ({{EquationNote|8q}}), except that he presents the first vector not as strictly uniform, but as merely ''held'' constant for the gradient operation. He states in passing that a proof may be effected by "expanding in terms of&#8202; {{math|'''i'''&#8202;,&#8239;'''j''',&#8239;'''k'''}}"; but instead of such a proof, he offers a "method of remembering the result" by expanding the "product"&#8239; {{math|'''u'''&#8239;&times;&#8239;(&nabla;&#8239;&times;&#8239;'''v''')}}&#8202; "formally as if&#8202; {{math|&nabla;,&#8239;'''u'''&#8202;,&#8202;'''v'''}}&#8202; were all real vectors" (pp.&#8239;161–2). Concerning the curl of the gradient, and the divergence of the curl (pp.&#8239;167,&#8239;168), he recommends expanding in terms of&#8202; {{math|'''i'''&#8202;,&#8239;'''j''',&#8239;'''k'''&#8202;,}}&#8239; but does not elaborate. Concerning the curl of the curl, however, he shows what would happen if it were "expanded formally according to the law of the triple vector product" (p.&#8239;169). In defense of the "formal product" method, we should note that the operators {{math|''&part;_x''&#8202;,}} {{math|''&part;_y''&#8202;,}} and {{math|''&part;_z''&#8202;}} are ''linear'', so that they are distributive over addition and may be permuted with multiplication by a constant, as if the operators themselves were multipliers (like components of vectors). They may be similarly permuted with other like operators&mdash;explaining why the formal-product method correctly deals with the curl of the gradient, the divergence of the curl, and the curl of the curl. But such an operator ''cannot'' be permuted with multiplication by a ''variable'', because then the product rule of differentiation applies, yielding an extra term. The formal-product system responds to this difficulty by generalizing the product rule as in &sect;&sect;&#8239;64 &amp;&#8239;166 of Gibbs ([[#gibbs-1881-4|1881–84]]). As Borisenko &amp; Tarapov put it ([[#borisenko-tarapov-68|1968]], p.&#8239;169), <blockquote>the operator {{math|&nabla;}} acts on each factor separately with the other held fixed. Thus {{math|&nabla;}} should be written after any factor regarded as a constant in a given term and before any factor regarded as variable. </blockquote> In this they differ inconsequentially from Gibbs, who requires that the operator be "brought into connection" with the factor considered variable. To illustrate, let us find the gradient of a dot-product, essentially in the manner of Borisenko &amp; Tarapov ([[#borisenko-tarapov-68|1968]], p.&#8239;180), quoted by Tai ([[#tai-95|1995]], p.&#8239;46; the next five equation numbers are Tai's). In this case the generalized product rule gives {{NumBlk|:|<math>\nabla(\mathbf{A ~\!\!\cdot B}) = \nabla(\mathbf{A}_c {\cdot}~\!\mathbf{B}) + \nabla(\mathbf{A} ~\!\!\cdot \mathbf{B}_c) \,, </math>|{{EquationRef|7.26}}}} where the subscript {{mvar|c}} marks the factor held ''constant'' during the differentiation. In Wilson's notation, this equation would be written :{{midsize|<math>\nabla(\mathbf{A ~\!\!\cdot B}) = \nabla(\mathbf{A ~\!\!\cdot B})_{\mathbf{A}} + \nabla(\mathbf{A ~\!\!\cdot B})_{\mathbf{B}} \,, </math>}} where a trailing subscript indicates which factor is held constant.&#8201; In the ''Feynman'' subscript notation, the subscript is attached to the {{math|&nabla;}} operator and indicates which factor is allowed to ''vary'', so that the same equation would be written :{{midsize|<math>\nabla(\mathbf{A ~\!\!\cdot B}) = \nabla_{\mathbf{B}}(\mathbf{A ~\!\!\cdot B}) + \nabla_{\!\mathbf{A}}(\mathbf{A ~\!\!\cdot B}) \,. </math>}} But, as we are discussing Borisenko &amp; Tarapov, we press on with ({{EquationNote|7.26}}).&#8201; By the algebraic identity {{NumBlk|:|<math>\mathbf{c}(\mathbf{a\cdot b}) \,=\, (\mathbf{a\cdot c})\mathbf{b} \,-\, \mathbf{a}\times(\mathbf{b}\times\mathbf{c}) \,, </math>|{{EquationRef|7.27}}}} i.e. :<math>\mathbf{c}(\mathbf{a\cdot b}) \,=\, (\mathbf{a\cdot c})\mathbf{b} \,+\, \mathbf{a}\times(\mathbf{c}\times\mathbf{b}) \,, </math> we can say {{NumBlk|:|<math>\nabla(\mathbf{A}_c {\cdot}~\!\mathbf{B}) \,=\, (\mathbf{A}_c {\cdot}\nabla)\mathbf{B} \,+\, \mathbf{A}_c\times(\nabla\times\mathbf{B}) \,. </math>|{{EquationRef|7.28}}}} Similarly,<ref>In the next equation as printed in Borisenko &amp; Tarapov ([[#borisenko-tarapov-68|1968]], p.&#8239;180), the first cross should be "&equals;"; Tai ([[#tai-95|1995]], p.&#8239;46) corrects it.</ref> {{NumBlk|:|<math>\nabla(\mathbf{B}_c {\cdot}~\!\mathbf{A}) \,=\, (\mathbf{B}_c {\cdot}\nabla)\mathbf{A} \,+\, \mathbf{B}_c\times(\nabla\times\mathbf{A}) \,. </math>|{{EquationRef|7.29}}}} Substituting ({{EquationNote|7.28}}) and ({{EquationNote|7.29}}) into ({{EquationNote|7.26}}), in which the order of the dot-products is immaterial, and dropping the {{mvar|c }}subscripts (because they are now outside the differentiations), we get the correct result {{NumBlk|:|{{midsize|<math>\nabla(\mathbf{A{\cdot}B}) = (\mathbf{A}{\cdot}\nabla)\mathbf{B} + (\mathbf{B}\;\!{\cdot}\nabla)\mathbf{A} + \mathbf{A}{\times}(\nabla{\times}\mathbf{B}) + \mathbf{B}{\times}(\nabla{\times}\mathbf{A}) \,, </math>}}|{{EquationRef|7.30}}}} corresponding to our ({{EquationNote|68}}). Tai ([[#tai-95|1995]], p.&#8239;47) is unimpressed, asking why we cannot apply ({{EquationNote|7.27}}) directly to the left side of ({{EquationNote|7.26}}). The answer to that is obvious: on the left side, the {{math|&nabla;}} operator is applied to a product of ''two variables'', and the variations of ''both'' must be taken into account. But there is a harder question which Tai does not ask: in ({{EquationNote|7.28}}), why can't we have {{math|&nabla;'''&#11825;A'''_c}} instead of{{math| '''A'''_c'''&#11825;'''&nabla;}}&#8239;? (Or, in terms of Feynman subscripts, why can't we have {{math|&nabla;'''_B&#8202;&#11825;&#8202;A'''}} instead of{{math| '''A&#11825;'''&nabla;_'''B'''}}?) Because that would make the term vanish? Yes, it would; but, as there is only one variable factor on the left side, why do we need two terms on the right? Because the rule says {{math|&nabla;}} should be written after the constant but before the variable? Yes, but that rule serves the purpose of varying ''each'' variable, whereas there is only one variable to vary on the left of ({{EquationNote|7.28}}). The same issue arises in ({{EquationNote|7.29}}). We cannot settle the question even by appealing to symmetry. Obviously the right side of ({{EquationNote|7.30}}), like the left, must be unchanged if we switch {{math|'''A'''}} and {{math|'''B'''}}; and indeed it is. But if the first term on the right of ({{EquationNote|7.28}}) and of ({{EquationNote|7.29}}) were to vanish, the necessary symmetry of ({{EquationNote|7.30}}) would be maintained. And unless I'm missing something, Tai's "symbolic vector" method does not circumvent the problem; Tai's "Lemma 2" ([[#tai-95|1995]], p.&#8239;53) is the Gibbs&#10744;Wilson method of "varying one factor at a time", written with Feynman subscripts attached to the symbolic vector instead of the del operator.{{efn|I don't overlook the fact that Tai's symbolic vector, unlike the del operator, is subject to commutative and anticommutative laws. Neither do I see how it helps.}} For another example of the same issue, consider the following two-liner offered by Panofsky &amp; Phillips ([[#panofsky-phillips-62|1962]], pp.&#8239;470–71) and rightly pilloried by Tai ([[#tai-95|1995]], pp.&#8239;47–8): :<math>\begin{align} & \nabla{\times}(\mathbf{A}{\times}\mathbf{B}) = (\nabla{\cdot}\;\!\mathbf{B})\mathbf{A} - (\nabla{\cdot} \mathbf{A})\mathbf{B} &&[\mathsf{sic}] \\ &= (\nabla{\cdot}\;\!\mathbf{B}_c ~\!\!)\mathbf{A} + (\nabla{\cdot}\;\!\mathbf{B}~\!\!)\mathbf{A}_c ~\!\! - (\nabla\mathbf{\cdot A}_c ~\!\!)\mathbf{B} - (\nabla\mathbf{\cdot A}~\!\!)\mathbf{B}_c \!\!\!\!\!\!\!&&[\mathsf{sic}]. \end{align}</math> If the first line were right, the authors would hardly bother to continue; but evidently it isn't, because it doesn't begin by "varying one factor at a time". The second line does not follow from the first and includes divergences of constants, which ought to vanish but somehow apparently do not. Let's try again, this time sticking to the rules: :<math>\begin{align} & \nabla\!\times\!(\mathbf{A}\!\times\!\mathbf{B}) \,=\, \nabla\!\times\!(\mathbf{A}_c \!\times\!\mathbf{B}) \,+\, \nabla\!\times\!(\mathbf{A}\!\times\!\mathbf{B}_c) \\ &~=\, (\nabla{\cdot}\;\!\mathbf{B})\mathbf{A}_c - (\mathbf{A}_c {\cdot}\nabla)\mathbf{B} \,+\, (\mathbf{B}_c {\cdot}\nabla)\mathbf{A} - (\nabla{\cdot} \mathbf{A})\mathbf{B}_c \\ &~=\, \mathbf{A}(\nabla{\cdot}\;\!\mathbf{B}) - \mathbf{B}(\nabla{\cdot} \mathbf{A}) \,+\, (\mathbf{B\;\!\cdot}\nabla)\mathbf{A} - (\mathbf{A \cdot}\nabla)\mathbf{B} \,, \end{align}</math> in agreement with our ({{EquationNote|67c}}). Here the first line comes from the generalized product rule, and the third is obtained from the second by rearranging terms and dropping the (now redundant) subscripts. The interesting line is the second, which is obtained from the first by expanding the formal vector triple products. But again, why must we have {{math|'''A'''_c'''&#11825;'''&nabla;}} and {{math|'''B'''_c'''&#11825;'''&nabla;,}} instead of {{math|&nabla;'''&#11825;A'''_c}} and {{math|&nabla;'''&#11825;B'''_c&#8202;,}} which would make the middle two terms vanish? Again symmetry does not give an answer. The right-hand side, like the left, must change sign if we switch {{math|'''A'''}} and {{math|'''B'''&#8202;}}; but the disappearance of the {{math|'''A'''_c'''&#11825;'''&nabla;}} and {{math|'''B'''_c'''&#11825;'''&nabla;}} terms would maintain the required (anti)symmetry. Funnily enough, the result would then agree with the incorrect first line given by Panofsky &amp; Phillips (above). But then how would we know that it is incorrect? The foregoing examples show that "formal product" arguments can be tenuous, even on their own terms. Before these examples, we might have been troubled by the omission of a general proof of the "generalized" product rule. After them, we might wonder whether the rule is even well defined. I submit, however, that none of this matters. I submit that the popularity of using "formal products" with the del operator, in derivations of vector-analytic identities, is a reaction to the failure of early writers to use indicial notation in the Cartesian definitions of differential operators.{{efn|Indicial notation is standard in higher-order tensor analysis, which however tends not to use unit vectors of coordinate systems, and therefore tends not to encourage the indexing of unit vectors in elementary vector analysis&mdash;whereas in the present paper, I have unapologetically indexed the unit vectors.}} The ensuing proliferation of terms in coordinate-based derivations led authors to seek shortcuts through "formal products" when more rigorous but no-less convenient shortcuts could have been taken through indicial notation, especially in combination with implicit summation. Our derivation of the gradient of a dot-product ({{EquationNote|68}}) is shorter than that of Borisenko &amp; Tarapov, and even uses the right-hand sides of their identities ({{EquationNote|7.28}}) and ({{EquationNote|7.29}}), but obtains them rigorously with no ambiguity and no {{mvar|c }}subscripts. Our derivation of the curl of a cross-product ({{EquationNote|67c}}) takes six lines with a single column of "&equals;" signs. Our subsequent formal-product derivation (not to be confused with the attempt of Panofsky &amp; Phillips) seems to take only three lines; but it is only through our earlier indicial derivation that we have any confidence in our result (not to be confused with the result of Panofsky &amp; Phillips). Our other indicial derivations of identities are mostly shorter than the two just mentioned. Having amassed so comprehensive a collection of identities so rigorously with so little effort, I submit that the use of formal products, Wilson subscripts, {{mvar|c }}subscripts, and Feynman subscripts for this purpose is a historical aberration, to be deciphered in other people's writings but avoided in one's own. That being said, it is one thing to conclude, as Tai duly does, that the del-cross and del-dot notations should not be interpreted as products in derivations and proofs, and another thing to allege, as Tai also does ([[#tai-95|1995]], p.&#8239;22), that&#8202; {{math|&nabla;'''&#11825;'''}}&#8202; and {{math|&nabla;&#8202;&times;}}&#8202; are "not compound operators" but only "assemblies", or in other words that "{{math|&#8202;&nabla; }}is not a constituent of the divergence operator nor of the curl operator." Against the latter proposition, our equations ({{EquationNote|14}}), ({{EquationNote|61o}}), and ({{EquationNote|62o}}) have been ''derived'', not merely defined, and our derivation of ({{EquationNote|14}}) is as general as we could wish. Moreover, whereas ({{EquationNote|61o}}) and ({{EquationNote|62o}}) are for Cartesian coordinates, we shall see that they have counterparts in more general coordinates. == General coordinates == From our initial definitions of the differential operators, we derived certain identities, from which we derived expressions for the operators in Cartesian coordinates, from which we derived a comprehensive collection of identities, two of which (the multivariate chain rule, and the curl of the product of a scalar and a vector) will now be useful for expressing the operators in other coordinate systems. Cartesian coordinates are traditionally called {{math|''x'',&#8239;''y'',&#8239;''z'',}}&#8201; which we renamed {{mvar|x_i}}&#8202; where&#8202; {{math|''i''&#8201;{{=}}&#8239;1,&#8202;2,&#8202;3&#8202;,}}&#8201; respectively. The best-known 3D ''non''&#8202;-Cartesian coordinate systems are the cylindrical coordinates {{math|(''&rho;'',&#8239;''&phi;'',&#8239;''z'')}} and the spherical coordinates {{math|(''r'',&#8239;''&theta;'',&#8239;''&phi;'')}}; we have already seen {{mvar|r}}&#8202; in the guise of the magnitude of the position vector{{math| '''r'''}}.&#8201; But now we want our coordinate system to be as general as possible&mdash;with the Cartesian, cylindrical, and spherical systems and many others, and even ''classes'' of systems, as special cases. === Natural and dual basis vectors === We shall call our general coordinates {{mvar|uⁱ}}&#8202; where&#8202; {{math|''i''&#8201;{{=}}&#8239;1,&#8202;2,&#8202;3&#8202;}};&#8201; yes, for reasons which will emerge, we shall write the coordinate index as a {{nowrap|''super''&#8202;script}}. But we shall write {{mvar|&part;_i}}&#8202; for{{math| ''{{sfrac|&part;|&part;uⁱ&#8202;}}''&#8202;,}}&#8202; relying on context to distinguish it from the special case{{mvar| {{sfrac|&part;|&part;x_i}}&#8202;}}.&#8201; By describing the {{mvar|uⁱ}}&#8202; as ''coordinates''&#8239; we mean two things. First, for some domain of interest, the position vector is a smooth function :<math>\mathbf{r} = \mathbf{r}(u^1,u^2,u^3) \,,</math> which possesses partial derivatives w.r.t. its arguments. Second, for every position vector in the resulting range, there is only one ordered triplet&#8239; {{math|(''uⁱ''&#8202;)&#8201;{{=}}&#8201;(''u''&sup1;,&#8239;''u''&sup2;,&#8239;''u''&sup3;),}}&#8239; so that we can think of each coordinate as :{{big|<math>u^i = u^i(\mathbf{r}) \,;</math>}} &mdash;that is, we can think of each {{mvar|uⁱ}}&#8202; as a scalar field, which possesses a gradient.{{efn|Hence we want each {{math|''uⁱ''('''r''')}} to be, as far as possible, a ''smooth'' function. This may require some tweaking of definitions. E.g., in cylindrical coordinates, the angular coordinate {{mvar|&phi;}} must be confined to some 360&deg; range in order to make it unique, and we don't want it jumping from the end of the range to the beginning within the region of interest.}} (I say "think of" because {{mvar|uⁱ}}, being obviously dependent on a coordinate system, would not normally be considered a true scalar; but sometimes we need to treat the coordinate system itself as an object under study.) These two properties of coordinates respectively suggest two simple ways of choosing basis vectors related to the coordinates: we shall define the '''natural basis''' vectors as {{NumBlk|:|{{big|<math> \mathbf{h}_i := \part_i \mathbf{r} \,, \qquad</math>}}|{{EquationRef|80a}}}} and the '''dual basis''' vectors as {{NumBlk|:|{{big|<math> \mathbf{h}^i := \nabla u^i . \qquad</math>}}|{{EquationRef|80b}}}} (We could ''normalize'' the natural basis vectors by dividing them by their magnitudes to obtain unit vectors; but, for the moment, we won't bother.) Just as we may think of each {{mvar|uⁱ}} as a scalar field and inquire after its directional derivative or its gradient or its Laplacian, so we may think of each {{math|'''h'''_''i''}} or{{math| '''h'''^''i''}} as a vector field and inquire after its directional derivative or its curl or its divergence or its Laplacian. (That the curl of{{math|&#8202; '''h'''^''i''}}&#8202; is zero&#8239; will be especially useful.) In Cartesian coordinates,&#8201; {{math|'''h'''_''i''}} and {{math|'''h'''^''i''}} are both equal to the unit vector{{math| '''e'''_''i''&#8239;}}; thus, in Cartesian coordinates, the natural basis vectors are their own duals.&#8201; In ''general'' coordinates,&#8201; {{math|'''h'''_''i''}} and {{math|'''h'''^''i''}} may differ in both direction and magnitude and are not generally unit vectors. Nevertheless, even in general coordinates, there is a simple relation between the natural and dual basis vectors. Consider the dot-product :{{big|<math> \mathbf{h}_i \cdot \mathbf{h}^j = \part_i\mathbf{r} \cdot \nabla u^j \,. </math>}} If{{math|&#8202; ''i&#8239;&ne;&#8239;j''&#8202;,}} then {{math|''&part;_i''&#8202;'''r'''&#8202;,}} being in a direction in which {{mvar|uⁱ}} varies while each other {{mvar|u&#8239;^j}} does not, is tangential to a surface of constant {{mvar|u&#8239;^j}} and therefore normal to {{math|&nabla;''u&#8239;^j'',}} so that the dot-product is zero. But by ({{EquationNote|26g}}), :{{big|<math> du^i = \nabla u^i \cdot d\mathbf{r} \,; </math>}} and if we vary {{math|'''r'''}} by varying {{mvar|uⁱ}} while holding each other {{mvar|u&#8239;^j}} constant, we can divide by {{mvar|duⁱ}} and obtain {{NumBlk|:|{{big|<math> 1 ~\!= \nabla u^i \cdot \part_i\mathbf{r} = \mathbf{h}^i \!\cdot \mathbf{h}_i \qquad</math>}}[with no summation].|{{EquationRef|81i}}}} Putting the two cases together, we have {{NumBlk|:|{{big|<math> \mathbf{h}_i \cdot \mathbf{h}^j =~\! \delta_i^j </math>}}|{{EquationRef|81}}}} where the right-hand function, known as the '''Kronecker delta''' function, is defined by {{NumBlk|:|{{big|<math>\delta_i^j = \delta_{ij} = \delta^{ij} =~</math>}}<math>\begin{cases} 0 &\mathsf{if}~\, i \neq j \\ 1 &\mathsf{if}~\, i = j \,. \end{cases}</math>|{{EquationRef|82}}}} Obviously the function is symmetric: the indices {{mvar|i }}and{{mvar| j}}&#8202; can be interchanged. If two lists of vectors are related so that the dot-product of the {{mvar|i&#8202;}}th vector in one list and the {{mvar|j&#8202;}}th in the other is{{mvar| &delta;_ij&#8202;}}, the two lists are described as '''reciprocal'''. Thus the triplets {{math|('''h'''_''i'')}} and {{math|('''h'''^''i'')}} are '''reciprocal bases''': the dual basis is the reciprocal of the natural basis and vice versa. Hence, taking the natural basis as a reference, the dual basis is sometimes called "the" reciprocal basis. In Cartesian coordinates, ({{EquationNote|81}}) becomes :{{big|<math> \mathbf{e}_i ~\!\!\cdot \mathbf{e}_j =~\! \delta_{ij} \,. </math>}} So we have a relation for general coordinates ({{EquationNote|81}}) which is just as simple as its special case for Cartesian coordinates, ''provided that we use the natural basis for one factor and the dual basis for the other''. This will be a recurring pattern. We have deduced the reciprocity relation ({{EquationNote|81}}) from prior definitions of the natural basis {{math|('''h'''_''i'')}} and the dual basis {{math|('''h'''^''i'')}}.&#8201; This result has a partial converse, in that a reciprocity relation between bases is enough to define either basis in terms of the other&mdash;as we shall see later. But first we proceed to components of vector fields. === Contravariant and covariant components === A '''coordinate grid''' is a set of intersecting curves such that on each curve, one coordinate varies while the others are constant. If we could embed such a grid in an elastic medium, and then stretch and rotate the medium, the natural basis vectors{{math| '''h'''_''i''}} given by ({{EquationNote|80a}}) would stretch and rotate ''with the medium'' and ''with the grid''. Accordingly, the ''natural'' basis is also called the '''covariant''' basis. But according to ({{EquationNote|81}}), the dot-product of a natural basis vector and a dual basis vector is '''invariant''' (independent of the coordinate system), so that the variation of one factor ''compensates''&#8202; for the variation of the other. So, as the natural basis is "covariant" with the coordinate grid, we say that the dual basis is '''contravariant'''. Notice that the {{nowrap|''co''&#8202;variant}} factor has a {{nowrap|''sub''&#8202;script}} index (easily remembered because "''co''&#8202; rhymes with ''low''&#8239;") whereas the {{nowrap|''contra''&#8202;variant}} factor has a {{nowrap|''super''&#8202;script}} index, and that one kind of variation must combine with the other in order to produce an {{nowrap|''in''&#8202;variant}} result; these will be recurring patterns. A vector field {{math|'''q'''}} may be expressed in components w.r.t. the natural (covariant) basis as {{NumBlk|:|{{big|<math> \mathbf{q} = q^i \mathbf{h}_i \qquad</math>}}|{{EquationRef|83a}}}} with summation, or in components w.r.t. the dual (contravariant) basis as {{NumBlk|:|{{big|<math> \mathbf{q} = q_i \mathbf{h}^i \qquad</math>}}|{{EquationRef|83b}}}} with summation. If{{math| '''q'''}} is to be invariant (a true vector, existing independently of the coordinate system), the components must be contravariant in the former case and covariant in the latter, and accordingly are written with superscripts and subscripts respectively. In Cartesian coordinates, the two bases are the same, so that the components w.r.t. the two bases are also the same; that's why, in the above section on Cartesian coordinates, we got away with writing component indices as subscripts. In ''general'' coordinates, however, the basis vectors have subscripts and the components have superscripts or vice versa, so that ''the index of implicit summation appears once as a superscript and once as a subscript''. Taking dot-products of ({{EquationNote|83a}}) with{{math| '''h'''&#8239;^''j''}}, applying ({{EquationNote|81}}), and noting that only one term on the right is non-zero, we obtain {{NumBlk|:|{{big|<math> q^j =~\! \mathbf{q} \cdot \mathbf{h}^j . \qquad</math>}}|{{EquationRef|83c}}}} Similarly, taking dot-products of ({{EquationNote|83b}}) with{{math| '''h'''_''j''}} yields {{NumBlk|:|{{big|<math> q_j =~\! \mathbf{q} \cdot \mathbf{h}_j \,. \qquad</math>}}|{{EquationRef|83d}}}} These results depend on the reciprocity relation ({{EquationNote|81}}) but not on the earlier definitions of the bases to which that relation applies. They say: * to find the contravariant components of a vector, take its dot-products with the contravariant basis vectors, and * to find the covariant components of a vector, take its dot-products with the covariant basis vectors; ''or'', in terms of the bases themselves: * to find the components of a vector w.r.t. either basis, take dot-products of that vector with the ''other'' basis. If a particular {{mvar|uⁱ}} has a particular name, such as{{mvar| &theta;}} or{{mvar| &phi;}}, then, if we're not using indexed summation, we may find it convenient to write that name in place of the index{{mvar| i}}&#8202; in the superscript or subscript. At the present level of generality, the basis vectors {{math|'''h'''_''i''&#8239;,}} unlike their Cartesian counterparts {{math|'''e'''_''i''&#8239;,}} are ''not''&#8202; assumed to be uniform (i.e., '''homogeneous'''). One consequence of this general non-uniformity (inhomogeneity) is that, although we can say&#8239; {{math|'''r'''&#8201;{{=}}&#8201;''x_i''&#8239;'''e'''_''i''}}&#8239; in Cartesian coordinates and&#8239; {{math|'''q'''&#8201;{{=}}&#8201;''qⁱ''&#8239;'''h'''_''i''}}&#8239; in general coordinates, we ''cannot'' say :{{big|<math>\mathbf{r} = u^i \mathbf{h}_i \qquad</math>[''sic!''&#8239;]}} in general coordinates. For example, we have seen that in spherical coordinates the position vector {{math|'''r'''}} is simply {{math|''r''&#8202;'''r'''&#8202;&#770;&#8201;{{=}}&#8201;''r''&#8202;'''h'''_''r''&#8239;}};&#8202; it is ''not''&#8201; {{math|''r''&#8202;'''h'''_''r''&#8202;+&#8202;''&theta;''&#8202;'''h'''_''&theta;''&#8202;+&#8202;''&phi;''&#8202;'''h'''_''&phi;''&#8202;,}} because {{mvar|&theta;}} and {{mvar|&phi;}} are encoded in the direction of{{math|&#8202; '''h'''_''r''&#8202;}}.&#8201; Similarly, in cylindrical coordinates the position vector {{math|'''r'''}} is {{math|''&rho;''&#8202;'''h'''_''&rho;''&#8202;+&#8239;''z''&#8202;'''h'''_''z''&#8239;}};&#8202; it is ''not''&#8201; {{math|''&rho;''&#8202;'''h'''_''&rho;''&#8202;+&#8202;''&phi;''&#8202;'''h'''_''&phi;''&#8202;+&#8239;''z''&#8202;'''h'''_''z''&#8202;,}} because {{mvar|&phi;}} is encoded in the direction of{{math|&#8202; '''h'''_''&rho;''&#8202;}}.&#8201; In both examples, encoding one coordinate in the direction of another coordinate's unit vector is circular in that the said direction depends on the position vector, which is the very thing that we want to represent. A non-uniform basis is not a ''global''&#8202; basis. It cannot give a uniform representation of a uniform vector field, because the standard of representation changes; it is like having a compass whose orientation varies from place to place and&#10744;or a measuring stick whose length varies from place to place. But it can serve as a '''local basis'''&#8202;&mdash;as in ({{EquationNote|83a}}) and ({{EquationNote|83b}}), each of which expresses a vector field at a given location in terms of a basis at that location, notwithstanding that the basis may be different at other locations. And although a local basis (as we have just seen) cannot generally represent the position vector in a non-circular manner, it ''can''&#8202; represent a ''change''&#8202; in the position vector. By the generality of the multivariate chain rule ({{EquationNote|75}}), :{{big|<math> \part_t \mathbf{r} = \part_i \mathbf{r} \,\part_t u^i . </math>}} Multiplying by {{mvar|dt&#8239;}} we get {{NumBlk|:|{{big|<math> d\mathbf{r} = \part_i \mathbf{r} \,du^i </math>}}|{{EquationRef|84}}}} or, substituting from ({{EquationNote|80a}}), {{NumBlk|:|{{big|<math> d\mathbf{r} = \mathbf{h}_i ~\!du^i . \qquad</math>}}|{{EquationRef|85}}}} Thus the small changes in the coordinates{{mvar| uⁱ}}&#8202; are the components of the true vector{{math| ''d'''''r'''}} w.r.t. the ''covariant''&#8202; basis. That means the changes in the coordinates must be ''contravariant''. Here at last is the explanation why we write general coordinates with superscript indices. And again the point is moot for Cartesian coordinates, for which the covariant basis is also contravariant. Since {{mvar|duⁱ}}&#8202; is contravariant,&#8201; {{math|''&part;_i''&#8202;'''r'''}}&#8202; in ({{EquationNote|84}}) must be covariant in order to yield the true vector{{math| ''d'''''r'''}}. This vindicates our decision to write {{mvar|&part;_i}} with a subscript. Recall, however, that {{mvar|&part;_i}}&#8202; means{{math| ''{{sfrac|&part;|&part;uⁱ&#8202;}}''&#8202;}}. Thus ''the derivative w.r.t. the contravariant quantity is covariant''&#8202;&mdash;wherefore it is said that ''a superscript in the denominator of a derivative counts as a subscript in the derivative as a whole''. In ({{EquationNote|85}}), the general term&#8239; {{math|'''h'''_''i''&#8201;''duⁱ''}} (not the sum) is the displacement of{{math|&#8202; '''r'''}} due to the small change {{mvar|duⁱ}} in the coordinate {{mvar|uⁱ}}. The three such displacements of{{math|&#8202; '''r'''}} make concurrent edges of a parallelepiped whose signed volume is :<math> dV =~\! \mathbf{h}_1~\!du^1 \cdot~\!\mathbf{h}_2~\!du^2 ~\!\!\times\mathbf{h}_3~\!du^3 \,; </math> that is, {{NumBlk|:|<math>dV = J \,du^1 du^2 du^3</math>|{{EquationRef|86}}}} where :<math>J := \mathbf{h}_1 ~\!\!\cdot \mathbf{h}_2 \!\times~\!\!\mathbf{h}_3</math> or, to use a standard abbreviation for the scalar triple product, {{NumBlk|:|<math> J := [~\!\mathbf{h}_1 \mathbf{h}_2 \mathbf{h}_3] \,. </math>|{{EquationRef|87}}}} {{mvar|J}}&#8202; is called the '''Jacobian''' of the natural (covariant) basis. We describe the basis and the associated coordinate system as '''right-handed''' if this Jacobian is ''positive'', and '''left-handed''' if this Jacobian is ''negative''. Thus the handedness depends on the standard order in which we write the vectors; e.g., the standard Cartesian basis is right-handed because we write it as{{math| ('''i''',&#8202;'''j''','''k''')}} but would be left-handed if we wrote it as{{math| ('''i''','''k''',&#8202;'''j''')}}. If the covariant basis is indeed a basis, its member vectors must not be coplanar; that is, {{mvar|J }}must not be zero. Hence, if the covariant basis is to be a local basis in some region of interest, {{mvar|J }}must not vanish anywhere in that region, and therefore must have the same sign throughout the region; that is, the handedness of the coordinate system must be the same throughout the region. === Properties of reciprocal bases === We have noted that formulae ({{EquationNote|83c}}) and ({{EquationNote|83d}}), for the components of a vector w.r.t. the covariant and contravariant bases, depend only on the reciprocity relation ({{EquationNote|81}}) between the bases. Now, retaining the designations "covariant" and "contravariant" for convenience, let us see what else we can deduce from that relation. Most obviously, the reciprocity relation leads to a simple component-based expression for the dot-product of two vector fields, say {{math|'''v'''}} and{{math| '''q'''&#8202;,}} provided that we use the contravariant components and covariant basis ({{EquationNote|83a}}) for one vector, and the covariant components and contravariant basis ({{EquationNote|83b}}) for the other: :{{big|<math>\mathbf{v} \cdot \mathbf{q} =~\! v^i ~\!\mathbf{h}_i \cdot q_j \mathbf{h}^j =~\! v^i \,\mathbf{h}_i \!\cdot\! \mathbf{h}^j \,q_j =~\! v^i ~\!\delta_i^j ~\!q_j \,, </math>}} whence selecting the non-zero terms gives {{NumBlk|:|{{big|<math>\mathbf{v} \cdot \mathbf{q} =~\! v^i q_i \,. </math>}}|{{EquationRef|88a}}}} And the two vectors, being general, can swap roles in ({{EquationNote|83a}}) and ({{EquationNote|83b}}): {{NumBlk|:|{{big|<math>\mathbf{v} \cdot \mathbf{q} =~\! v_i q^i \,. </math>}}|{{EquationRef|88b}}}} The cross-product needs a bit more preparation. First we define the '''permutation symbol''' {{mvar|&epsiv;_ijk}} or{{mvar| &epsiv;^ijk}} (also called the '''[[w:Tullio Levi-Civita|Levi-Civita]]''' symbol) as having the value&#8202; {{math|+1}} if {{math|(''i'',&#8201;''j'',&#8239;''k'')}} is a permutation of{{math| (1,&#8202;2,&#8202;3)}} in the same cyclic order,&#8201; {{math|&minus;1 }}if {{math|(''i'',&#8201;''j'',&#8239;''k'')}} is a permutation of{{math| (1,&#8202;2,&#8202;3)}} in the reverse cyclic order, and {{math|0}} if {{math|(''i'',&#8201;''j'',&#8239;''k'')}} is not a permutation, i.e. if there is at least one repeated index. To put it more formally, {{NumBlk|:|{{big|<math>\epsilon_{ijk\!} = \epsilon^{ijk\!} =</math>}} {{resize|<math>\begin{cases} +1 &\mathsf{if}\,\,(i,j,k)\in\big\{(1,2,3),~\!(2,3,1),~\!(3,1,2)\big\}\\ -1 &\mathsf{if}\,\,(i,j,k)\in\big\{(3,2,1),~\!(1,3,2),~\!(2,1,3)\big\}\\ \phantom{-}0 &\mathsf{otherwise}. \end{cases}</math>}}|{{EquationRef|89}}}} Note that because switching any two indices changes the cyclic order, ''switching any two indices changes the sign of the permutation symbol''. Now by ({{EquationNote|81}}),&#8201; {{math|'''h'''¹ }}is perpendicular to both {{math|'''h'''₂ }}and{{math| '''h'''₃}}. So we can say :<math>\mathbf{h}_2 \!\times\!\mathbf{h}_3 =~\! \alpha_1 ~\!\mathbf{h}^1</math> where {{math|''&alpha;''₁ }}is a real variable to be determined. Taking dot-products with{{math| '''h'''₁}} and applying ({{EquationNote|81}}) and ({{EquationNote|87}}), we find that&#8202; {{math|''&alpha;''₁&#8239;{{=}}&#8239;''J''&#8202;,}} so that {{NumBlk|:|<math> \mathbf{h}_2 \!\times\!\mathbf{h}_3 =~\! J \mathbf{h}^1 . </math>|{{EquationRef|90.1}}}} By the generality of the vectors we can rotate the three indices, but the sign of the left-hand side changes if we swap the two indices on the left. All six cases are covered by {{NumBlk|:|{{big|<math> \mathbf{h}_i \!\times\!\mathbf{h}_j =~\! J \epsilon_{ijk\,} \mathbf{h}^k . </math>}}|{{EquationRef|90a}}}} Here we want only one term; but we need not specify "no sum", because for given {{mvar|i&#8202; }}and{{mvar| j}}&#8201; the permutation symbol leaves only one non-zero term in the sum over{{mvar| k}}. In words, this result says that the cross-product of two covariant basis vectors, with their indices in the standard cyclic order, is the Jacobian times the contravariant basis vector with the omitted index. Similarly, or rather reciprocally, {{NumBlk|:|{{big|<math> \mathbf{h}^i \!\times\!\mathbf{h}^j =~\! J' \epsilon^{ijk\,} \mathbf{h}_k \,, </math>}}|{{EquationRef|90b}}}} where {{mvar|J&prime;}}&#8202; is the Jacobian ''of the contravariant basis''. Equations ({{EquationNote|90a}}) and ({{EquationNote|90b}}), which we have obtained from the reciprocity relation ({{EquationNote|81}}), can be solved for {{math|'''h'''^''k'' }}and{{math| '''h'''_''k''}} respectively; but now we ''do'' suppress the implicit sum, because {{mvar|k}}&#8202; is "given" instead of {{mvar|i&#8202; }}and{{mvar| j&#8239;}}: {{NumBlk|:|{{big|<math> \mathbf{h}^k = \tfrac{\,1\,}{J}~\! \mathbf{h}_i \!\times\!\mathbf{h}_j \quad </math>}} [distinct {{math|''i'',&#8201;''j'',&#8239;''k''}}  in cyclic order]; |{{EquationRef|90c}}}} {{NumBlk|:|{{big|<math> \mathbf{h}_k = \tfrac{1}{\,J'}~\! \mathbf{h}^i \!\times\!\mathbf{h}^j \quad </math>}}[distinct {{math|''i'',&#8201;''j'',&#8239;''k''}}  in cyclic order]. |{{EquationRef|90d}}}} Thus ''a reciprocity relation between bases is enough to define either basis in terms of the other''&mdash;as claimed above. If it is not convenient to suppress an implicit sum, the last two results can instead be written {{NumBlk|:|{{big|<math> \mathbf{h}^k = \tfrac{1}{2J}~\!\epsilon^{ijk\,}\mathbf{h}_i {\times}~\!\mathbf{h}_j </math>}}|{{EquationRef|90e}}}} and {{NumBlk|:|{{big|<math> \mathbf{h}_k = \tfrac{1}{2J'}~\!\epsilon_{ijk\,}\mathbf{h}^i {\times}~\!\mathbf{h}^j \,, </math>}}|{{EquationRef|90f}}}} where the factor 2 in each denominator is needed because the right-hand side has two equal non-zero terms&mdash;the sign of the permutation symbol compensating for the order of the cross-product. Now we're ready to consider the cross-product of two vector fields. In terms of the covariant basis, :{{big|<math>\begin{align}\mathbf{v} \!\times\! \mathbf{q} =~\! v^i \mathbf{h}_i ~\!\!\times q^j \mathbf{h}_j &=~\! v^i \,\mathbf{h}_i {\times}~\! \mathbf{h}_j \,q^j \\ &=~\! v^i J \epsilon_{ijk~\!} \mathbf{h}^k \;\!q^j \,; \end{align}</math>}} i.e., {{NumBlk|:|{{big|<math>\mathbf{v} \!\times\! \mathbf{q} =~\! J \epsilon_{ijk\,} v^i q^j \mathbf{h}^k . </math>}}|{{EquationRef|91a}}}} On the right, the two components and the basis vector are contravariant, but invariance is achieved by multiplying by the covariant Jacobian (which has three covariant factors). Similarly, {{NumBlk|:|{{big|<math>\mathbf{v} \!\times\! \mathbf{q} =~\! J' \epsilon^{ijk} v_i q_j \;\!\mathbf{h}_k . </math>}}|{{EquationRef|91b}}}} On the right of ({{EquationNote|91a}}) or ({{EquationNote|91b}}), the implicit triple summation has 27 terms, of which only six&mdash;corresponding to the six possible permutations of the three possible indices&mdash;can be non-zero. Thus the factor following the Jacobian can be recognized as the familiar determinant whose columns (or rows), in cyclic order, are the components of{{math| '''v'''&#8202;,}} the components of{{math| '''q'''&#8202;,}} and the three basis vectors. In Cartesian coordinates, in which the Jacobians are equal to{{math| 1}} and we don't need the co&#10744;contra distinction, both equations reduce to :{{big|<math>\mathbf{v} \!\times\! \mathbf{q} =~\! \epsilon_{ijk\,} v_i q_j \;\!\mathbf{e}_k </math>}} &mdash;a familiar result written in a possibly unfamiliar way. The Jacobian of the contravariant basis is :<math>J' =~\! \mathbf{h}^1 \cdot \mathbf{h}^2 \!\times\!\mathbf{h}^3</math> or, if we substitute from ({{EquationNote|90c}}), :<math>\begin{align}J' &= \frac{(\mathbf{h}_2 \!\times\!\mathbf{h}_3)}{J} \cdot \frac{(\mathbf{h}_3 \!\times\!\mathbf{h}_1)}{J} \times \frac{(\mathbf{h}_1 \!\times\!\mathbf{h}_2)}{J} \\[.5ex] &= \frac{(\mathbf{h}_2 \!\times\!\mathbf{h}_3) \cdot (\mathbf{h}_3 \!\times\!\mathbf{h}_1) \times (\mathbf{h}_1 \!\times\!\mathbf{h}_2)} {J^3} \,. \end{align}</math> In the numerator, the cross-product of cross-products can be read as a vector triple product in which the first factor is a cross-product. Expanding that triple product and noting that one term is a scalar triple product with a repeated factor, we get :<math> J' = \frac{(\mathbf{h}_2 \!\times\!\mathbf{h}_3) \cdot J\mathbf{h}_1}{J^3} = \frac{\,J^2}{~J^3 ~\!} = \frac{\,1\,}{J} \,, </math> so that we may write {{NumBlk|:|<math>J' =~\! J^{-1} </math>|{{EquationRef|92}}}} in ({{EquationNote|90b}}), ({{EquationNote|90d}}), ({{EquationNote|90f}}), and ({{EquationNote|91b}}). In words, ''the Jacobian of the reciprocal basis is the reciprocal of the Jacobian'' of the original basis. Therefore the two Jacobians have the same sign. Therefore ''a basis is right-handed if and only if its reciprocal is right-handed''. Thus the natural and dual bases of a coordinate system have the same handedness, and the handedness of either may be identified with the handedness of the coordinate system. === The gradient, del, and advection operators === Let {{mvar|p}}&#8202; be a scalar field, and let{{mvar| s}}&#8202; be arc length in the direction of the unit vector{{math| '''s&#770;'''}}. By the multivariate chain rule ({{EquationNote|75}}), :{{big|<math>\begin{align}\part_s p &= \part_i p \;\part_s u^i \\ &= \part_i p \;\mathbf{\hat{s}} \cdot \nabla u^i \\ &= \part_i p \;\mathbf{\hat{s}} \cdot \mathbf{h}^i \\ &=\mathbf{\hat{s}} \cdot \mathbf{h}^i \part_i p \,. \end{align}</math>}} So&#8202; {{math|'''h'''^''i''''&part;_i&#8239;p''}}&#8239; is the vector whose (invariant) scalar component in the direction of any{{math| '''s&#770;'''}} is the directional derivative of{{mvar| p}} in that direction; that is, {{NumBlk|:|{{big|<math> \nabla p = \mathbf{h}^i \part_i p \,, </math>}}|{{EquationRef|93g}}}} or, in operational terms, {{NumBlk|:|{{big|<math> \nabla =~\! \mathbf{h}^i \part_i \,. </math>}}|{{EquationRef|93o}}}} Apart from the need to pair a superscript with a subscript, these two results look as simple as their Cartesian special cases ({{EquationNote|58g}}) and ({{EquationNote|58o}}). If {{mvar|&psi;}}&#8202; is a generic field and {{math|'''q'''}} is a general vector in the direction of the same{{math| '''s'''&#8202;}} then by definition ({{EquationNote|11}}), :{{big|<math>\begin{align} \mathbf{q}\;\!{\cdot}\nabla\,\psi &= |\mathbf{q}| \,\part_s \psi \\ &= |\mathbf{q}| \,\part_i \psi \,\part_s u^i \\ &= \part_i \psi \;|\mathbf{q}| ~\!\part_s u^i \\ &= \part_i \psi \;\mathbf{q} \cdot \nabla u^i \\ &= \part_i \psi \;\mathbf{q} \cdot \mathbf{h}^i \\ &= \part_i \psi \;q^j \mathbf{h}_j \cdot \mathbf{h}^i \\ &= \part_i \psi \;q^j \epsilon_j^i \\ &= \part_i \psi \,q^i \,; \end{align}</math>}} that is, {{NumBlk|:|{{big|<math> \mathbf{q}\;\!{\cdot}\nabla\,\psi = q^i \part_i \psi \,, </math>}}|{{EquationRef|94}}}} or, in operational terms, {{NumBlk|:|{{big|<math> \mathbf{q}\;\!{\cdot}\nabla =~\! q^i \part_i \,. </math>}}|{{EquationRef|94o}}}} These results likewise look as simple as their Cartesian special cases ({{EquationNote|64}}) and ({{EquationNote|64o}}).&#8201; And by ({{EquationNote|88a}}), the {{math|'''q&#11825;'''&nabla;}} operator again turns out to be the formal dot-product of&#8202; {{math|'''q'''}} and{{math| &nabla;}}. === The curl and divergence operators === To express the curl of a vector field{{math| '''q'''&#8202;,}} we choose the contravariant basis ({{EquationNote|83b}}) and apply identity ({{EquationNote|71c}}): :{{big|<math>\begin{align}\operatorname{curl}\mathbf{q} &= \operatorname{curl} q_j \mathbf{h}^j \\ &= q_j \operatorname{curl}\mathbf{h}^j + \nabla q_j \times \mathbf{h}^j . \end{align}</math>}} On the right, the first term vanishes because {{math|'''h'''&#8239;^''j''}}&#8202; is {{math|&nabla;''u&#8239;^j''}} (and the curl of a gradient is zero). Substituting from ({{EquationNote|93o}}) in the second term, we obtain :{{big|<math>\operatorname{curl}\mathbf{q} = \mathbf{h}^i \part_i q_j \times \mathbf{h}^j = \mathbf{h}^i {\times}~\! \mathbf{h}^j ~\!\part_i q_j </math>}} or, using ({{EquationNote|90b}}), {{NumBlk|:|{{big|<math>\operatorname{curl}\mathbf{q} = J' \epsilon^{ijk\,} \mathbf{h}_k \part_i q_j </math>}}|{{EquationRef|95c}}}} or, in a more familiar form, :<math> \operatorname{curl}\mathbf{q} \,=\, J'\, \begin{vmatrix} \mathbf{h}_1 & \part_1 & q_1 \\ \mathbf{h}_2 & \part_2 & q_2 \\ \mathbf{h}_3 & \part_3 & q_3 \end{vmatrix} \,. </math> Formula ({{EquationNote|95c}}) agrees with a result obtained by Tai with his "symbolic vector" method.<ref>[[#tai-95|Tai, 1995]], p.&#8239;66, eq.&#8239;(9.41).</ref> It is also what we would get by naively using ({{EquationNote|91b}}) to evaluate {{math|&nabla;&#8202;&times;&#8202;'''q'''&#8202;;}}&#8201; it comes out so simply because each contravariant basis vector{{math| '''h'''&#8239;^''j''}}&#8202; is the actual gradient of{{mvar| u&#8239;^j}} and not (e.g.) merely a unit vector in the same direction (remember that {{mvar|q_j}} is the component w.r.t.{{math| '''h'''&#8239;^''j''&#8202;,}}&#8202; not{{math| '''h'''_''j''}}). But ({{EquationNote|95c}}) does not end in a subexpression for the operand{{math| '''q'''}}&#8202; and therefore does not directly yield an expression for the curl ''operator''. To find this operator and the divergence operator, we return to the original definitions ({{EquationNote|4g}}), ({{EquationNote|4c}}), and ({{EquationNote|4d}}), noting that they can be combined as {{NumBlk|:|<math>\nabla ~\!\!* \psi \,=\, \tfrac{1}{dV}\!\iint_{\delta S} (\mathbf{\hat{n}}~\!dS*\psi) \,, </math>|{{EquationRef|96}}}} where {{math|&lowast;}} may be a null for the gradient, a cross for the curl, or a dot for the divergence.{{efn|But not dot-del for the Laplacian, as in ({{EquationNote|19}}), because we want to use an elementary product rule inside the integral.}} Recalling that the value of this expression does not depend on the shape of{{mvar| dS&#8202;}}, let{{mvar| dS&#8202;}} be the parallelepiped defined by the six equicoordinate surfaces at {{mvar|uⁱ }}and{{mvar| uⁱ+duⁱ}}, so that {{mvar|dV}}&#8202; is given by ({{EquationNote|86}}). Then the contribution to the integral from the face at{{math| ''u''&sup1;+''du''&sup1; &#8202;}}is :<math>\Big[ \big(\mathbf{h}_2 du^2 \!\times\! \mathbf{h}_3 du^3\big) * \psi \Big]_{u^1 + du^1}</math> where the square brackets and subscripting mean "evaluated at". This can be written :<math>du^2 du^3 \Big[ (\mathbf{h}_2 {\times}~\! \mathbf{h}_3) * \psi \Big]_{u^1 + du^1}</math> or, by ({{EquationNote|90.1}}), :<math>du^2 du^3 \big[J \mathbf{h}^1 ~\!\!* \psi \big]_{u^1 + du^1} \,.</math> Similarly, the contribution from the face at{{math| ''u''&sup1;}} (where {{math|'''h'''₁}} points inward instead of outward) is :<math>-du^2 du^3 \big[J \mathbf{h}^1 ~\!\!* \psi \big]_{u^1} \,.</math> The sum of the contributions from the two opposite faces can then be written :<math>du^1 du^2 du^3 ~\!\part_1 \big(J \mathbf{h}^1 ~\!\!* \psi\big) ~,</math> so that when we add in the contributions from the other two pairs of opposite faces, the entire integral becomes :{{big|<math> du^1 du^2 du^3 ~\!\part_i \big(J \mathbf{h}^i ~\!\!* \psi\big) </math>}} (with implicit summation over{{mvar| i}}). Substituting this and ({{EquationNote|86}}) into ({{EquationNote|96}}), we get {{NumBlk|:|{{big|<math>\nabla ~\!\!* \psi = \tfrac{\,1\,}{J} ~\!\part_i \big(J \mathbf{h}^i ~\!\!* \psi\big) \,. </math>}}|{{EquationRef|97}}}} Now applying the product rule gives {{NumBlk|:|{{big|<math>\nabla ~\!\!* \psi = \mathbf{h}^i ~\!\!* \part_i \psi + \tfrac{\,1\,}{J} ~\!\part_i(J \mathbf{h}^i) * \psi \,. </math>}}|{{EquationRef|98}}}} Here the left-hand side is {{math|&nabla;&#8202;&lowast;''&psi;''}}&#8239; according to our original volume-based definition ({{EquationNote|4g}}) of the {{math|&nabla; }}operator&mdash;which is known to yield the curl or the divergence if&#8202; {{math|&lowast;}} is a cross or a dot, respectively&mdash;whereas the first term on the right is what we would get for {{math|&nabla;&#8202;&lowast;''&psi;''}}&#8239; by using our latest definition ({{EquationNote|93o}}) of the {{math|&nabla; }}operator and allowing{{mvar| &part;_i}}&#8202; to "pass by" the star in the Wilsonian manner. So, if we can show that the second term on the right is zero, we shall have established the precise sense in which the del-cross and del-dot notations are valid in general coordinates. In that second term, by ({{EquationNote|90e}}), :{{big|<math>\begin{align} \part_i(J \mathbf{h}^i) &= \part_i \big( \tfrac{\,1\,}{2}~\!\epsilon^{jki}\mathbf{h}_j {\times}~\!\mathbf{h}_k \big) \\ &= \tfrac{\,1\,}{2}~\!\epsilon^{jki} \part_i \big(\mathbf{h}_j {\times}~\!\mathbf{h}_k \big) \\[.5ex] &= \tfrac{\,1\,}{2}~\!\epsilon^{jki} \big(\part_i \mathbf{h}_j \!\times~\!\!\mathbf{h}_k + \mathbf{h}_j \!\times~\!\!\part_i \mathbf{h}_k \big) \\[.5ex] &= \tfrac{\,1\,}{2}~\!\epsilon^{jki} \big(\part_i \part_j \mathbf{r} ~\!\!\times\! \mathbf{h}_k + \mathbf{h}_j {\times}~\! \part_i \part_k \mathbf{r} \big) \,, \end{align}</math>}} where the last line follows by ({{EquationNote|80a}}). But the order of partial differentiation can be switched. So, in the sum over the permutations, for each term in{{math| ''&part;_i&#8202;&part;_j''&#8239;'''r'''}}&#8239; there is an equal term in{{math| ''&part;_j&#8202;&part;_i''&#8239;'''r'''}}&#8239; to which the permutation symbol attaches the opposite sign, so that the terms in{{math| ''&part;_i&#8202;&part;_j''&#8239;'''r'''}}&#8202; cancel. Similarly the terms in{{math| ''&part;_i&#8202;&part;_k''&#8239;'''r'''}}&#8202; cancel. Thus, as anticipated, the second term in ({{EquationNote|98}}) is zero and we have {{NumBlk|:|{{big|<math>\nabla ~\!\!* \psi = \mathbf{h}^i ~\!\!* \part_i \psi \,. </math>}}|{{EquationRef|99}}}} If&#8202; {{math|&lowast;}} is a null and {{mvar|&psi;}} is a scalar field {{math|''p''&#8202;,}} then ({{EquationNote|99}}) becomes ({{EquationNote|93g}}) and thus (fortunately!) confirms ({{EquationNote|93o}}) as the form of the del operator in general coordinates. Now let {{mvar|&psi;}} be a ''vector'' field {{math|'''q'''&#8202;}}.&#8201; If{{math|&#8202; &lowast;}} is a cross, then ({{EquationNote|99}}) becomes {{NumBlk|:|{{big|<math>\operatorname{curl}\mathbf{q} = \mathbf{h}^i ~\!\!\times \part_i \mathbf{q} </math>}}|{{EquationRef|100c}}}} or, in operational terms, {{NumBlk|:|{{big|<math>\operatorname{curl} = \mathbf{h}^i ~\!\!\times \part_i \,. </math>}}|{{EquationRef|100o}}}} If instead {{math|&lowast;}} is a dot, ({{EquationNote|99}}) becomes {{NumBlk|:|{{big|<math>\operatorname{div}\mathbf{q} = \mathbf{h}^i ~\!\!\cdot \part_i \mathbf{q} </math>}}|{{EquationRef|101d}}}} or, in operational terms, {{NumBlk|:|{{big|<math>\operatorname{div} = \mathbf{h}^i ~\!\!\cdot \part_i \,. </math>}}|{{EquationRef|101o}}}} But if we take the {{math|&nabla;}} operator as given by ({{EquationNote|93o}}) and try to construct the curl and divergence operators (in the ''same''&#8202; coordinates) as {{math|&nabla;&#8202;&times;}}&#8202; and {{math|&nabla;'''&#11825;'''}}&#8239; respectively, we get&#8202; {{math|'''h'''^''i''&#8239;''&part;_i''&#8239;&times;}}&#8239; and&#8239; {{math|'''h'''^''i''&#8239;''&part;_i''&#8239;'''&#11825;'''}}&#8201; respectively [compare ({{EquationNote|61o}}) and ({{EquationNote|62o}})]; and if we then let{{mvar| &part;_i}}&#8202; "pass by" the cross and the dot, we get ({{EquationNote|100o}}) and ({{EquationNote|101o}}), or ({{EquationNote|100c}}) and ({{EquationNote|101d}}) if we include the operand{{math| '''q'''&#8202;}}. Thus ''the del-cross and del-dot notations work in general coordinates''. Equations ({{EquationNote|100c}}) to ({{EquationNote|101o}}) are apparently due to Tai ([[#tai-95|1995]], eqs.&#8239;9.39, 9.40, 9.34, &amp; 9.35, and text on p.&#8239;66), who derives them, along with the corresponding form of the del operator (his eq.&#8239;9.33), from volume-based definitions expressed in his "symbolic vector" notation. But he does not point out that the curl and divergence operators are obtainable from that del operator, as del-cross and del-dot, via the same "pass by" step that he condemns in the Cartesian context. Speaking of which, we should note that our equations ({{EquationNote|100c}}) to ({{EquationNote|101o}}), apart from the need to pair a superscript with a subscript, are as simple as their Cartesian special cases ({{EquationNote|59c}}), ({{EquationNote|59o}}), ({{EquationNote|60d}}), and ({{EquationNote|60o}}). In ({{EquationNote|100c}}) and ({{EquationNote|101d}}), it goes without saying that&#8202; {{math|''&part;_i''&#8239;'''q'''}}&#8202; must be evaluated correctly&mdash;in particular, that if the operand is expressed in terms of non-uniform basis vectors, the non-uniformity must be taken into account. Formula ({{EquationNote|95c}}), for the curl, does not suffer from this complication, because it is already expressed in components w.r.t. the contravariant basis (whose non-uniformity has already been taken into account). To obtain a similarly convenient formula for the divergence, we use components w.r.t. the {{nowrap|''co''&#8202;variant}} basis (i.e., contravariant components): in ({{EquationNote|97}}), if{{math|&#8202; &lowast;}} is a dot and {{mvar|&psi;}} is a vector field{{math| '''q'''&#8202;,}} we have :{{big|<math>\operatorname{div}\mathbf{q} = \tfrac{\,1\,}{J} ~\!\part_i \big(J \mathbf{h}^i {\cdot}\, \mathbf{q}\big) </math>}} or, by ({{EquationNote|83c}}), {{NumBlk|:|{{big|<math>\operatorname{div}\mathbf{q} = \tfrac{\,1\,}{J} ~\!\part_i \big(J q^i \big) \,. </math>}}|{{EquationRef|102d}}}} This too agrees with Tai ([[#tai-95|1995]], p.&#8239;65, eq.&#8239;9.37). === The Laplacian === For a scalar operand, applying ({{EquationNote|101o}}) and reversing the "pass by", we find that the Laplacian operator is :{{big|<math>\operatorname{div}\nabla = \mathbf{h}^i \!\cdot \part_i \nabla = \mathbf{h}^i \part_i ~\!\!\cdot \nabla = \nabla {\cdot} \nabla = \nabla^2 . </math>}} And by the linearity of the Laplacian, the{{math| &nabla;²}} formulation remains valid if the operand is a fixed linear combination of scalars&mdash;including a vector field, because that is expressible (even if not actually expressed) w.r.t. a uniform basis. (And if it is expressed in terms of a non-uniform basis, the non-uniformity must be taken into account in differentiations.) In what follows, however, we shall find it convenient to take a different approach. If{{mvar| &psi;}}&#8202; is a scalar field, its gradient as given by ({{EquationNote|93g}}) is&#8202; {{math| '''h'''&#8239;^''j''''&part;_j&#8239;&psi;''&#8202;,}} of which the {{mvar|i&#8202;}}th contravariant component is{{math| '''h'''^''i'''''&#11825;&#8239;h'''&#8239;^''j''''&part;_j&#8239;&psi;''&#8202;,}} which takes the place of{{mvar| qⁱ}} in ({{EquationNote|102d}}), so that the divergence of the gradient of{{mvar| &psi; &#8202;}}is {{NumBlk|:|{{big|<math>\triangle\psi = \tfrac{\,1\,}{J} ~\!\part_i \big(J \mathbf{h}^i {\cdot}~\! \mathbf{h}^j \part_j \psi \big) \,. </math>}}|{{EquationRef|103L}}}} This remains well-defined if{{mvar| &psi;}}&#8202; is a generic field (although we still need to deal with any non-uniformity of the basis in which{{mvar| &psi;}}&#8202; might be expressed). === Affine coordinates === If a basis is ''uniform'' (homogeneous), so is its Jacobian. Hence, by ({{EquationNote|90c}}) and ({{EquationNote|90d}}), the dual (contravariant) basis is uniform if and only if the natural (covariant) basis is uniform. A coordinate system in which these bases are uniform is described as '''affine'''. In affine coordinates, * by ({{EquationNote|80a}}), {{math|''&part;_i''&#8239;'''r''' }}is uniform, so that the curves on which only one coordinate varies are straight parallel lines; and * by ({{EquationNote|80b}}), {{math|&nabla;''uⁱ'' }}is uniform, so that the level surfaces of each coordinate (being perpendicular to {{math|&nabla;''uⁱ''}}) are parallel planes. Obviously Cartesian coordinates are affine; but one can also construct affine coordinate systems in which the three vectors of each basis are not mutually perpendicular and&#10744;or the coordinates have different scales or different units. We have noted above that the correct application of the del-cross, del-dot, and del-squared notations must allow for non-uniformity of the basis vectors. Obviously this issue does not arise in affine coordinates, including Cartesian coordinates. Hence, while these notations are not (as is sometimes alleged) invalid in other coordinate systems, it would be fair to say that they are safer and more convenient in affine coordinates, including Cartesian coordinates. === Orthogonal coordinates === We know, e.g. from ({{EquationNote|90a}}) and ({{EquationNote|90b}}), that if two bases are reciprocal, the cross-product of the {{mvar|i&#8202;}}th and {{mvar|j&#8202;}}th members of one basis is collinear with the {{mvar|k&#8202;}}th member of the other, if {{math|''i'',&#8201;''j'',&#8239;''k''}}&#8239; are distinct. But if the first basis is ''orthogonal'' (that is, if its three member vectors are mutually orthogonal), the same cross-product is also collinear with the {{mvar|k&#8202;}}th member of the ''same'' basis, so that ''corresponding members of the two bases are collinear''. It follows that ''the natural basis of a coordinate system is orthogonal if and only if the dual basis is orthogonal''. And if the bases are orthogonal, the coordinate system itself is said to be '''orthogonal'''. Cartesian coordinates are obviously both affine and orthogonal, and we have already implied that there is a class of coordinate systems that are affine but not orthogonal. The most widely-used class of non-Cartesian systems, however, contains the systems that are orthogonal but not affine; this class, of which the cylindrical and spherical systems are the best-known members, is the class of '''curvilinear orthogonal coordinates'''. But we shall drop the word ''curvilinear''&#8202; in order to include Cartesian coordinates as a special case. In orthogonal coordinates, expressing a member of one basis in terms of its reciprocal basis is especially simple because corresponding members of the two bases are collinear, wherefore we can say :{{big|<math> \mathbf{h}^i =~\! \beta_i \mathbf{h}_i \,, </math>}} where {{mvar|&beta;_i}} is a real variable to be determined (and the single index on the left-hand side means ''no summation''). Substituting this into ({{EquationNote|81i}}) gives :{{big|<math> \beta ~\!= 1/h_i^{~2} </math>}} where {{NumBlk|:|{{big|<math> h_i = \big|\mathbf{h}_i \big| \,, </math>}}|{{EquationRef|104}}}} so that {{NumBlk|:|{{big|<math> \mathbf{h}^i =~\! \mathbf{h}_i \big/ h_i^{~2} \,. </math>}}|{{EquationRef|105}}}} And substituting that into ({{EquationNote|83c}}), and comparing the result with ({{EquationNote|83d}}), we get {{NumBlk|:|{{big|<math> q^i =~\! q_i \big/ h_i^{~2} \,. </math>}}|{{EquationRef|106}}}} Comparing ({{EquationNote|104}}) with definition ({{EquationNote|80a}}), we see that {{mvar|h_i}} is the magnitude of{{math| ''&part;_i''&#8239;'''r'''}}. Accordingly {{mvar|h_i}} is called the '''scale factor''' associated with the coordinate{{mvar| uⁱ&#8202;}}; it is the factor by which we multiply a small change in{{mvar| uⁱ}} to obtain the magnitude of the consequent change in position.{{efn|Hsu ([[#hsu-84|1984]], p.&#8239;171) implies that the scale factors are also called "metric coefficients", and Tai ([[#tai-94|1994]], [[#tai-95|1995]]) prefers the latter term. This is loose terminology because, in general, the ''metric coefficient''&#8202; is defined as :{{math|''g_ij'' {{=}} '''h'''_''i''&#8239;'''&#11825;&#8201;h'''_''j''&#8201;}}. Hence, in the special case of orthogonal coordinates, we have {{math|''g_ij''&#8201;{{=}}&#8201;0}}&#8202; for {{math|''i&#8239;&ne;&#8239;j''&#8202;,}}&#8239; and&#8202; {{math|''g_ii&#8239;{{=}}&#8201;h_i''²}}&#8202; [no sum]. Thus the scale factors are not special cases of the metric coefficients, but the ''square roots''&#8202; of special cases of the metric coefficients (''cf''. [[#tai-95|Tai, 1995]], p.&#8239;43, line 3).}} If we now define {{NumBlk|:|<math>\varsigma \,=~\! \begin{cases} +1 &\mathsf{for~a~right{\operatorname{-}}handed~system} \\[.5ex] -1 &\mathsf{for~a~left{\operatorname{-}}handed~system} ~, \end{cases}</math>|{{EquationRef|107}}}} then, due to the orthogonality,&#8201; ({{EquationNote|87}}) and ({{EquationNote|92}}) are respectively reduced to {{NumBlk|:|<math> J = \varsigma\, h_1 h_2 h_3 </math>|{{EquationRef|108}}}} and {{NumBlk|:|<math> J' = \frac{\,1\,}{J} = \frac{1}{\varsigma\, h_1 h_2 h_3} = \frac{\varsigma}{h_1 h_2 h_3} </math>|{{EquationRef|109}}}} &mdash;although, for brevity, we shall sometimes leave things in terms of{{mvar| J}}. At this point, we ''could''&#8202; substitute ({{EquationNote|105}}) and ({{EquationNote|106}}) into earlier equations and obtain a suite of formulae for the differential operators in terms of the covariant basis and {{nowrap|''co''&#8202;variant}} components! But we can avoid this confusing breach of convention by ''normalizing'' the basis vectors. An '''orthonormal''' basis is one whose members are mutually orthogonal ''unit'' vectors. The assumption of unit vectors is introduced so late because it is more useful with orthogonality than without. If one basis consisted of unit vectors that were not all orthogonal, then the reciprocal basis vectors given by ({{EquationNote|90c}}) or ({{EquationNote|90d}}) would not all be unit vectors.{{efn|Outline of proof: If the reciprocal vectors were unit vectors, then the angles between the ''original''&#8202; unit vectors would need to be equal, in order that their cross products have the same magnitude as their scalar triple product (Jacobian); and the latter condition requires the common angle to be 90&deg;.}} But if the basis{{math| ('''h'''_''i'')}} consists of orthogonal unit vectors, equation ({{EquationNote|105}}) implies that the reciprocal basis consists of the ''same'' vectors; and the converse is also true, by the symmetry of the reciprocity relations. Thus ''an orthonormal basis is its own reciprocal''. Hence, if we choose an orthonormal basis, we do not need superscripts to distinguish the reciprocal basis from the original, or to distinguish components w.r.t. the latter basis from those w.r.t. the former. An orthonormal basis is not generally covariant, because it doesn't stretch with the coordinate grid (although it does rotate with the grid). Neither is it generally contravariant, because its reciprocal (i.e. itelf) is not generally covariant. Hence, if a ''non''&#8202;-orthonormal natural or dual basis of an orthogonal coordinate system is ''normalized'' (replaced by unit vectors in the same directions), the resulting orthonormal basis is not covariant or contravariant, and components with respect thereto are not contravariant or covariant, and the new basis vectors are not given in terms of the coordinates by ({{EquationNote|80a}}) or ({{EquationNote|80b}}); the basis is therefore described as a '''non-coordinate basis'''. By default, the indices of the orthonormal basis vectors and associated components are written as subscripts, but these are not indicative of covariance. The coordinates themselves remain contravariant (e.g., if the grid dilates, the same movement in space corresponds to ''smaller'' changes in the coordinates); but, for want of covariant basis vectors to pair them with, we tend to write the coordinates with subscripts when the basis is orthonormal. Nevertheless, it is convenient to have one basis instead of two. Moreover, the components of a vector w.r.t. an orthonormal basis are '''physical components''': they have the same dimension (same units) as the represented vector, and they are the components that we would have in mind if we wanted to ''measure'' the "components" in the directions of the basis vectors. Hence an orthonormal basis is called a '''physical basis'''. Accordingly, it is indeed common practice to normalize the basis vectors of orthogonal coordinate systems. This together with the prevalence of such coordinate systems helps to account for the familiarity of subscripts as indices, and for the jarring unfamiliarity of superscript indices when general (possibly non-orthogonal) coordinates are encountered for the first time. To normalize the covariant basis, let{{math| '''h&#770;'''_''i''}} (as usual) be the unit vector in the direction of{{math|&#8202; '''h'''_''i''&#8202;.}} Then, by ({{EquationNote|104}}), {{NumBlk|:|{{big|<math> \mathbf{h}_i =~\! h_i \mathbf{\hat{h}}_i </math>}}|{{EquationRef|110}}}} (again with no summation, due to the single index on the left). Hence ({{EquationNote|105}}) becomes: {{NumBlk|:|{{big|<math> \mathbf{h}^i =~\! \mathbf{\hat{h}}_i \big/ h_i \,. </math>}}|{{EquationRef|111}}}} A vector field {{math|'''q'''}} is expressed in components w.r.t. the basis{{math| ('''h&#770;'''_''i'')}} as {{NumBlk|:|{{big|<math> \mathbf{q} = \hat{q_i} \;\!\mathbf{\hat{h}}_i \qquad</math>}}|{{EquationRef|112}}}} (with summation), where {{NumBlk|:|{{big|<math> \hat{q_i} =~\! \mathbf{q} \!\cdot\! \mathbf{\hat{h}}_i \,. \qquad</math>}}|{{EquationRef|113}}}} (Here the hat on{{math| ''q''&#770;_''i''}} is needed to distinguish the coefficient of{{math| '''h&#770;'''_''i''}} from the coefficient of{{math| '''h'''^''i'',}} and indicates that{{math| ''q''&#770;_''i''}} is the coefficient of a unit vector&mdash;''not'' that{{math| ''q''&#770;_''i''}} has unit magnitude.) Taking{{mvar| q_i}} as given by ({{EquationNote|83d}}) and applying ({{EquationNote|110}}) and ({{EquationNote|113}}), we get {{NumBlk|:|{{big|<math> q_i =~\! h_i \hat{q_i} \,, \qquad</math>}}|{{EquationRef|114}}}} whence ({{EquationNote|106}}) gives {{NumBlk|:|{{big|<math> q^i =~\! \hat{q_i} \big/ h_i \,. \qquad</math>}}|{{EquationRef|115}}}} Equation ({{EquationNote|110}}) quantifies the non-covariance of the orthonormal basis; substituting ({{EquationNote|110}}) into ({{EquationNote|85}}), we find that the components of{{math| ''d'''''r'''}} with respect to{{math| '''h&#770;'''_''i''}}&#8202; are not simply{{math| ''duⁱ'',}} but{{math| ''h_i&#8239;duⁱ''}}&#8202; [no sum]. So, as the coordinates{{mvar| uⁱ}} are still contravariant, the orthonormal basis vectors{{math| '''h&#770;'''_''i''}} are not covariant unless the scale factors{{mvar| h_i}}&#8202; are equal to{{math| 1}}&#8202;&mdash;&#8239;that is, unless the coordinates are Cartesian (except possibly for the handedness). And in Cartesian coordinates we can use subscripts throughout. This is another reason why, when using an orthonormal basis, we might as well write the coordinates as{{math| ''u_i''&#8202;}}. We can now re-express dot- and cross-products w.r.t. the orthonormal basis{{math| ('''h&#770;'''_''i'')}}. If we apply ({{EquationNote|114}}) and ({{EquationNote|115}}) in ({{EquationNote|88a}}) or ({{EquationNote|88b}}), the scale factors cancel and we are left with {{NumBlk|:|{{big|<math>\mathbf{v} \cdot \mathbf{q} =~\! \hat{v_i} \hat{q_i} \,, </math>}}|{{EquationRef|116}}}} as if the coordinates were Cartesian. And if we apply ({{EquationNote|108}}), ({{EquationNote|115}}), and ({{EquationNote|111}}) in ({{EquationNote|91a}}), the product of the scale factors cancels and we are left with :{{big|<math>\mathbf{v} \!\times\! \mathbf{q} =~\! \varsigma~\!\epsilon_{ijk\,} \hat{v_i} \hat{q_j} \;\!\mathbf{\hat{h}}_k \,, </math>}} again as if the coordinates were Cartesian, except that the handedness symbol {{mvar|&varsigma;}}&#8202; gives a change of sign for left-handed coordinates. The last result is confirmed by applying ({{EquationNote|109}}), ({{EquationNote|114}}), and ({{EquationNote|110}}) in ({{EquationNote|91b}}). It can also be written {{NumBlk|:|<math>\mathbf{v} \!\times\! \mathbf{q} \,=\, \varsigma\, \begin{vmatrix} \hat{v_1} & \hat{q_1} & \mathbf{\hat{h}}_1 \\ \hat{v_2} & \hat{q_2} & \mathbf{\hat{h}}_2 \\ \hat{v_3} & \hat{q_3} & \mathbf{\hat{h}}_3 \end{vmatrix} \,. </math>|{{EquationRef|117}}}} We can similarly re-express the first-order differential operators. Applying ({{EquationNote|111}}) in ({{EquationNote|93o}}), ({{EquationNote|101o}}), and ({{EquationNote|100o}}) gives respectively {{NumBlk|:|{{big|<math> \nabla = \tfrac{1}{\,h_{\scriptstyle i}}\;\!\mathbf{\hat{h}}_i \part_i \,, </math>}}|{{EquationRef|118}}}} {{NumBlk|:|{{big|<math> \operatorname{div} = \tfrac{1}{\,h_{\scriptstyle i}}\;\!\mathbf{\hat{h}}_i ~\!\!\cdot \part_i \,, </math>}}|{{EquationRef|119}}}} and {{NumBlk|:|{{big|<math> \operatorname{curl} = \tfrac{1}{\,h_{\scriptstyle i}}\;\!\mathbf{\hat{h}}_i ~\!\!\times \part_i \,. </math>}}|{{EquationRef|120}}}} And applying ({{EquationNote|115}}) in ({{EquationNote|94o}}) and ({{EquationNote|102d}}) gives {{NumBlk|:|{{big|<math> \mathbf{q}\;\!{\cdot}\nabla = \tfrac{1}{\,h_{\scriptstyle i}} \;\!\hat{q_i} \part_i </math>}}|{{EquationRef|121}}}} and {{NumBlk|:|{{big|<math>\operatorname{div}\mathbf{q} = \tfrac{\,1\,}{J} ~\!\part_i \Big(\tfrac{J}{\,h_{\scriptstyle i}} ~\!\hat{q_i} \Big) \,. </math>}}|{{EquationRef|122}}}} And applying ({{EquationNote|109}}), ({{EquationNote|110}}), and ({{EquationNote|114}}) in ({{EquationNote|95c}}) gives :{{big|<math>\operatorname{curl}\mathbf{q} = \tfrac{\,1\,}{J} ~\!\epsilon_{ijk\,} h_k \mathbf{\hat{h}}_k ~\!\part_i \big(h_j \hat{q_j} \big) </math>}} or, in determinant form, {{NumBlk|:|<math> \operatorname{curl}\mathbf{q} \,=\, \frac{\varsigma}{h_1 h_2 h_3}\, \begin{vmatrix} h_1 \mathbf{\hat{h}}_1 & \part_1 & h_1 \hat{q_1} \\ h_2 \mathbf{\hat{h}}_2 & \part_2 & h_2 \hat{q_2} \\ h_3 \mathbf{\hat{h}}_3 & \part_3 & h_3 \hat{q_3} \end{vmatrix} \,. </math>|{{EquationRef|123}}}} For the Laplacian, applying ({{EquationNote|111}}) twice in ({{EquationNote|103L}}) gives :{{big|<math>\triangle\psi = \tfrac{\,1\,}{J} ~\!\part_i \Big( \tfrac{J}{h_i h_j} (\mathbf{\hat{h}}_i {\cdot}~\! \mathbf{\hat{h}}_j) ~\!\part_j \psi \Big) \,, </math>}} where the parenthesized dot-product is simply{{mvar| &delta;_ij&#8202;}}.&#8201; Selecting the non-zero terms, we are left with {{NumBlk|:|{{big|<math>\triangle\psi = \tfrac{\,1\,}{J} ~\!\part_i \Big( \tfrac{J}{\,h_{\scriptstyle i}^{~2}} ~\!\part_i \psi \Big) \,. </math>}}|{{EquationRef|124}}}} Working entirely within the coordinates{{math| ''u_i''&#8202;,}} we can use equations ({{EquationNote|118}}), ({{EquationNote|121}}) to ({{EquationNote|123}}), and ({{EquationNote|124}}) for scalar{{math| ''&psi;''&#8202;,}} provided that we know the scale factors in terms of{{mvar| u_i&#8202;}}.{{efn|In ({{EquationNote|124}}), if {{mvar|&psi;}}&#8202; is a ''vector'' field, we also need the derivatives of its basis vectors w.r.t.{{mvar| u_i&#8202;}} in terms of{{mvar| u_i&#8202;}}.}}&#8201; And we can find the scale factors in terms of{{mvar| u_i}}&#8202; if we know the Cartesian coordinates{{mvar| x_i}}&#8202; in terms of{{mvar| u_i}}.&#8201; For then the position vector can be written :{{big|{{math|'''r''' {{=}} ''x_j''&#8239;'''e'''_''j'' ,}}}} whence :{{big|{{math|'''h'''_''i'' {{=}} ''&part;_{u_i}''&#8239;'''r''' {{=}} ''&part;_{u_i}&#8201;x_j''&#8201;'''e'''_''j'' ,}}}} so that the scale factors can be found from :{{big|{{math|''h_i''² {{=}} &sum;_&#8202;''j''(''&part;_{u_i}&#8201;x_j'')².}}}} In ({{EquationNote|121}}) to ({{EquationNote|123}}), the hat on{{math| ''q''&#770;_''i''}} was needed because we treated the orthonormal basis as a special case, having used a hatless{{mvar| q_i}}&#8202; in less special cases; the hat would not have been needed if we had assumed an orthonormal basis at the outset. In more elementary introductions to curvilinear orthogonal coordinates, the basis vectors are indeed chosen as unit vectors and consequently as orthonormal vectors. Hence, if the coordinates are called<math>~u,v,w\,</math> and the respective basis vectors are called<math>~\mathbf{e}_u , \mathbf{e}_v , \mathbf{e}_w</math> (understood to be unit vectors), the components of the vector{{math| '''q'''}} w.r.t. that basis are called<math>~q_u , q_v , q_w ~\!,\,</math> with no hats. In this notation, in which sums are written out longhand without numerical indices, it is convenient also to write out the Jacobian in full, in order to exploit cancellations of scale factors. If the Jacobian appears in both a numerator inside parentheses and a denominator outside, the handedness symbol{{mvar| &varsigma;}}&#8202; also cancels. Thus the equations numbered ({{EquationNote|116}}) to ({{EquationNote|124}}) can be rewritten as, respectively, {{NumBlk||<math>\begin{align} \mathbf{f} \cdot \mathbf{q} ~\!&=~\! f_u q_u + f_v q_v + f_w q_w \\[1ex] \mathbf{f} ~\!\!\times\! \mathbf{q} ~\!&=~\! \varsigma\, \begin{vmatrix} f_u & q_u & \mathbf{e}_u \\ f_v & q_v & \mathbf{e}_v \\ f_w & q_w & \mathbf{e}_w \end{vmatrix} \\[1ex] \nabla &= \tfrac{1}{~\!h_{\scriptstyle u}}\;\!\mathbf{e}_u \part_u + \tfrac{1}{~\!h_{\scriptstyle v}}\;\!\mathbf{e}_v \part_v + \tfrac{1}{~\!h_{\scriptstyle w}}\;\!\mathbf{e}_w \part_w \\[.5ex] \operatorname{div} &= \tfrac{1}{~\!h_{\scriptstyle u}} \mathbf{e}_u ~\!\!\cdot \part_u + \tfrac{1}{~\!h_{\scriptstyle v}} \mathbf{e}_v ~\!\!\cdot \part_v + \tfrac{1}{~\!h_{\scriptstyle w}} \mathbf{e}_w ~\!\!\cdot \part_w \\[.5ex] \operatorname{curl} ~\!&= \tfrac{1}{~\!h_{\scriptstyle u}} \mathbf{e}_u ~\!\!\times \part_u + \tfrac{1}{~\!h_{\scriptstyle v}} \mathbf{e}_v ~\!\!\times \part_v + \tfrac{1}{~\!h_{\scriptstyle w}} \mathbf{e}_w ~\!\!\times \part_w\\[.5ex] \mathbf{q}\;\!{\cdot}\nabla &= \tfrac{1}{~\!h_{\scriptstyle u}} \;\!q_u \part_u + \tfrac{1}{~\!h_{\scriptstyle v}} \;\!q_v \part_v + \tfrac{1}{~\!h_{\scriptstyle w}} \;\!q_w \part_w \\[.5ex] \operatorname{div}\mathbf{q} ~\!&= \tfrac{1}{h_u h_v h_w} \Big( \part_u (h_v h_w q_u) + \part_v (h_w h_u q_v) + \part_w (h_u h_v q_w) \Big) \\[.5ex] \operatorname{curl}\mathbf{q} ~\!&=~\! \frac{\varsigma}{h_u h_v h_w}\, \begin{vmatrix} h_u \mathbf{e}_u & \part_u & h_u q_u \\ h_v \mathbf{e}_v & \part_v & h_v q_v \\ h_w \mathbf{e}_w & \part_w & h_w q_w \end{vmatrix} \\[.5ex] \triangle\psi ~\!&= \tfrac{1}{h_{\scriptstyle u\;\!}h_{\scriptstyle v\;\!}h_{\scriptstyle w}\!} \bigg\{\! \tfrac{\part}{\part u\!} \Big(\!\tfrac{h_v h_w}{h_u\;\!}\tfrac{\part\psi}{\part u}\!\Big) \!+~\!\! \tfrac{\part}{\part v\!} \Big(\!\tfrac{h_w h_u}{\;\!h_v}\tfrac{\part\psi}{\part v}\!\Big) \!+~\!\! \tfrac{\part}{\part w\!} \Big(\!\tfrac{h_u h_v}{\;\!h_w}\tfrac{\part\psi}{\part w}\!\Big) \!\bigg\} . \end{align}</math>|{{EquationRef|125}}}} Only in the cross-product and the curl does the handedness factor{{mvar| &varsigma;}}&#8202; make any difference. If the system is right-handed&mdash;as is also often assumed at the outset&mdash;this factor is replaced by{{math| 1}}. For some readers, equation group ({{EquationNote|125}}) will announce a return to familiar territory. For the writer, it offers a convenient place to stop. == Appendix: Mathematizing Huygens' principle == If a wavelike disturbance originating ''outside''&#8202; a region{{math| ''V'',}} bounded by a surface{{math| ''S''&#8202;,}} enters the region, it must do so through the surface{{mvar| S}}.&#8201; Unless we believe in "action at a distance", we must conclude that ''the behavior of the wave function throughout the region is fully determined by its behavior on the bounding surface''. That reasoning, being qualitative, does not tell us precisely what aspects of the behavior at the boundary determine the behavior throughout the region, or how. In this appendix, we shall answer these questions using tools of vector analysis&mdash;some of which we shall find ready-made, and some of which require assembly. Our aim is to express the wave function in the region{{mvar| V}} as a surface integral, over the bounding surface{{math| ''S''&#8202;,}} of an integrand related to the wave function incident at a general point on that surface.<ref>The following derivation is guided by Baker &amp; Copson ([[#baker-copson-39|1939]], pp.&#8239;38–40)&#8202; but, I hope, will be found more heuristic than its model.</ref> '''[[w:Huygens' principle|Huygens' principle]]''' asserts not only that the behavior of the wave function throughout the region (containing no sources) is determined by the behavior at the boundary, but also that the behavior at the boundary is equivalent to a distribution of sources over the boundary, so that the wave function throughout the region is ''as if''&#8202; the original sources outside the region ('''primary sources''') were ''replaced''&#8202; by sources distributed over the boundary ('''secondary sources''').{{efn|Notice that the desired secondary sources are ''not''&#8202; segments of the moving wavefronts, but segments of a stationary surface influenced by the passing waves. Compare Huygens' original statement: "that ''each particle of matter''&#8202; in which a wave spreads, ought not to communicate its motion only to the next particle which is in the straight line drawn from the luminous point, but that it also imparts some of it necessarily to all the others which touch it and which oppose themselves to its movement. So it arises that around each particle there is made a wave of which ''that particle''&#8202; is the centre" ([[#huygens-1690-thompson|Huygens, 1690, tr.&#8239;Thompson]], p.&#8239;19; my emphasis). Huygens chooses secondary sources on the same primary wavefront at the same time for the purpose of constructing the "continuation" of the wavefront (the same wavefront at a later time) in the same medium (''ibid.'', pp.&#8239;19,&#8239;50–51), but ''not''&#8202; for the purpose of constructing a wavefront reflected or refracted at an interface between two media; for the latter purpose, he chooses secondary sources at various points on the reflecting or refracting surface, although the primary wavefront reaches those points at various times (''ibid.'', pp.&#8239;23–4,&#8239;35–7,&#8239;etc.).}} We shall find that by appropriately arranging the integrand for the wave function inside the region, we can indeed recognize the distribution of boundary sources that would generate the wave function. We shall also find that the distribution of secondary sources has an alternative description which is especially convenient in the case of a single monopole primary source. === Hints === If the surface integrand represents a secondary source density, it will not only be related to the primary wave function at a general point on{{mvar| S}}, but will also be delayed by the propagation time from that point to the observation point, and attenuated in accordance with the propagation distance. Hence, if{{math| ''&psi;''('''r''',&#8239;''t'')}} is the primary wave function and {{math|'''r&prime;'''}} is the position of the observation point ('''field point''') at a distance{{mvar| s}}&#8202; from position{{math| '''r''',}} then the integrand (or at least the dominant term thereof) should be proportional to {{NumBlk|:|{{big|{{math|{{sfrac|&#8239;''s''&#8239;}}[''&psi;''] ,}}}}|{{EquationRef|126}}}} where the square brackets indicate that the contents are to be ''delayed'' (or, in older literature, "retarded") by{{math| ''s''&#10744;''c''}}&#8202; relative to the default arguments{{math| ('''r''',&#8239;''t'')}}, so that {{NumBlk|:|{{big|{{math|[''&psi;''] {{=}} ''&psi;''('''r''', ''t&#8201;&minus;&#8201;s''&#10744;''c'') .}}}}|{{EquationRef|127}}}} Of course we would like our distribution of secondary sources to be valid for an arbitrarily shaped boundary{{mvar| S}}. This preference will be easier to satisfy if the distribution of secondary sources, by itself, produces a zero wave function outside{{mvar| V}}&#8202;&mdash;in other words, ''no backward secondary waves''&#8202;&mdash;because in that case, even if {{mvar|S}}&#8202; is concave outward, the wave function inside{{mvar| V}}&#8239; will not be complicated by "backward" waves generated at one point on{{mvar| ''S''}}&#8202; and entering{{mvar| V}}&#8202; through another point on{{mvar| S}}.&#8201; Accordingly, we would like our surface integral to be equal to the ''volume''&#8202; integral over{{mvar| V}}&#8239; of&#8202; {{math|''&psi;''('''r&prime;''',&#8239;''t'')&#8239;''&delta;''('''r'''&#8202;&minus;&#8202;'''r&prime;'''),}} because that volume integral will be {{math| ''&psi;''('''r&prime;''',&#8239;''t'')}}&#8202; if {{math|'''r&prime;'''}} is inside{{mvar| V}}, but zero if it is outside. In the integrand, the first factor can be replaced by{{math| [''&psi;'']}} because the delta function selects the position{{math| '''r&prime;''',}} where the propagation distance{{math| s}}&#8202; is zero. Moreover, by ({{EquationNote|33L}}), that delta function is the Laplacian of{{math|&#8202; {{sfrac|&minus;1|4''&pi;s''}}}}.&#8201; So the desired integrand, multiplied by{{math| 4''&pi;''&#8202;}}, becomes {{NumBlk|:|{{big|{{math|&minus;[''&psi;''] &#9651; {{sfrac|&#8239;''s''&#8239;}} .}}}}|{{EquationRef|128}}}} Relating the volume integral of ({{EquationNote|128}}) to the surface integral of something like ({{EquationNote|126}}) would seem to require a surface-to-volume integral identity involving two different fields. Three such identities, all named for [[w:George Green (mathematician)|George Green]], come to mind. === Green's identities === If<math>~u</math> and<math>~v</math> are scalar fields, then by identity ({{EquationNote|71d}}), :<math>\mathrm{div}(u~\!\nabla v) \equiv u~\!\triangle v + \nabla u \cdot~\!\! \nabla v \,. </math> Integrating both sides over a volume{{math| ''V''}} enclosed by a surface{{math| ''S''&#8202;,}} and applying the divergence theorem on the left, we get :<math>\iint_S u~\!\nabla v \cdot \mathbf{\hat{n}}~\!dS \equiv \iiint_V \big(u~\!\triangle v + \nabla u \cdot~\!\! \nabla v \big)\,dV \,, </math> where {{math|'''n'''&#770;}} is the unit normal to{{mvar| S}}&#8202; pointing out of{{mvar| V}}. This integral equation is called '''Green's first identity'''. Switching the roles of<math>~u</math> and<math>~v</math> yields a second integral equation, which can be subtracted from the first to obtain :<math> \iint_S \!\big(u~\!\nabla v - v~\!\nabla u \big) \cdot \mathbf{\hat{n}}~\!dS \,\equiv \iiint_V \!\big(u~\!\triangle v - v~\!\triangle u \big)\,dV \,; </math> this is '''Green's second identity'''. If {{mvar|n}} is the normal distance from{{mvar| S}} (positive outside{{math| ''V'',}} negative inside), then, by relation ({{EquationNote|9g}}) between the gradient and the directional derivative, we can rewrite Green's second identity in the alternative form {{NumBlk|:|<math> \iint_S \!\big(u~\!\part_n v - v~\!\part_n u\big)\,dS \,\equiv \iiint_V \!\big(u~\!\triangle v - v~\!\triangle u\big)\,dV \,, </math>|{{EquationRef|129}}}} which remains meaningful if one of the two operands is a ''generic'' field. And indeed, by the linearity of the various operators, the identity remains valid in that case (which is not always pointed out). If, taking the above "hints", we put&#8201; <math>u\!=\!1/s\,</math> and&#8201; <math>v\!=\![\psi]\,</math> in ({{EquationNote|129}}), we get :<math>\begin{align} \iint_S &\Big(\tfrac{\,1\,}{s}~\!\part_n [\psi] - [\psi]\,\part_n \tfrac{\,1\,}{s} \Big) \,dS \\ &= \iiint_V \tfrac{\,1\,}{s}~\!\triangle[\psi] \,dV - \iiint_V [\psi]\,\triangle~\!\tfrac{\,1\,}{s} \,dV \,, \end{align}</math> which is a particular case of what is sometimes called ''Green's third identity'' (although that label has also been attached to other things). Applying the chain rule to the second term in the surface integrand, and recalling the purpose of ({{EquationNote|128}}), we can rewrite this result as {{NumBlk|:|<math>\begin{align} \iint_S &\Big(\tfrac{\,1\,}{s}~\!\part_n [\psi] + \tfrac{1}{s^2}~\![\psi]\,\part_n s \Big) \,dS \\ &= \iiint_V \tfrac{\,1\,}{s}~\!\triangle[\psi] \,dV +\, 4\pi\!\iiint_V [\psi]~\!\delta(\mathbf{r}\!-\!\mathbf{r}') \,dV \,. \end{align}</math>|{{EquationRef|130}}}} === Kirchhoff's integral theorem === In ({{EquationNote|130}}), the first term in the surface integrand is dominant for sufficiently large{{mvar| s}}&#8202; and, as hoped, this dominant term is proportional to ({{EquationNote|126}}), because {{math|''&part;_n''&#8202;[''&psi;'']}} is proportional to{{math| [''&psi;'']}}. The second volume integral, as hoped, is{{math| ''&psi;''('''r&prime;''',&#8239;''t'')}}&#8202; if {{math|'''r&prime;'''}} is inside{{mvar| V}}, but zero if it is outside. If we can somehow convert the first volume integral to a surface integral, a trivial rearrangement will express the second volume integral as a surface integral, as hoped. And from the terms that we know so far, the surface integral looks promising. In that first term, however, the factor {{math|''&part;_n''&#8202;[''&psi;'']}} is not to be confused with{{math| [''&part;_n&#8202;&psi;'']}}; the latter holds{{mvar| s}}&#8202; constant while {{mvar|n &#8202;}}varies, whereas the former also accounts for the variation of{{mvar| s}}&#8202; with{{math| ''n''}} (and consequently{{math| '''r'''}}) at a fixed{{math| '''r&prime;'''}}. From ({{EquationNote|127}}), the contribution to{{math| ''&part;_n''&#8202;[''&psi;'']}} through the variation of{{mvar| s}}&#8202; is :<math>\frac{\part\psi(t\!-\!s/c)}{\part(t\!-\!s/c)}~\! \frac{\part(t\!-\!s/c)}{\part s}~\! \frac{\part s}{\part n} \,, </math> i.e. :{{big|<math>\big[\dot{\psi}\big]~\!\big({-}\tfrac{\,1\,}{c}\big)~\!\part_n s \,. </math>}} Putting the pieces together we get {{NumBlk|:|{{big|<math>\part_n [\psi] = [\part_n \psi] - \tfrac{\,1\,}{c}~\!\part_n s ~\!\big[\dot{\psi}\big] \,. </math>}}|{{EquationRef|131}}}} Similarly, if {{mvar|&part;_i}}&#8202; denotes{{mvar| {{sfrac|&part;|&part;x_i}}}}&#8202; in Cartesian coordinates, {{NumBlk|:|{{big|<math>\part_i [\psi] = {\color{red}[\part_i \psi] - \tfrac{\,1\,}{c}~\!\part_i s ~\!\big[\dot{\psi}\big]} \,. </math>}}|{{EquationRef|132}}}} The last result can be applied three times to the volume integrand in ({{EquationNote|130}}); its applications are shown in '''{{color|red}}''' in the following sequence, which uses Cartesian coordinates with implicit summation: :{{big|<math>\begin{align}\triangle&[\psi] = \part_i \part_i[\psi] \\ &= \part_i \Big( {\color{red}[\part_i \psi] - \tfrac{\,1\,}{c}~\!\part_i s ~\!\big[\dot{\psi}\big]} \Big) \\ &= \part_i [\part_i \psi] - \tfrac{\,1\,}{c}~\!\part_i \Big(\part_i s ~\!\big[\dot{\psi}\big]\Big) \\ &= \part_i [\part_i \psi] - \tfrac{\,1\,}{c}\Big( \part_i \part_i s ~\!\big[\dot{\psi}\big] + \part_i s \,\part_i \big[\dot{\psi}\big] \Big) \\ &= \part_i [\part_i \psi] - \tfrac{\,1\,}{c}~\!\part_i \part_i s ~\!\big[\dot{\psi}\big] - \tfrac{\,1\,}{c}~\!\part_i s \,\part_i\!\big[\dot{\psi}\big] \\[.5ex] &= \part_i[\part_i \psi] - \tfrac{\,1\,}{c}~\!\triangle s ~\!\big[\dot{\psi}\big] \\ &\qquad\qquad\,\, - \tfrac{\,1\,}{c}~\!\part_i s \,\part_i\!\big[\dot{\psi}\big] \\[.5ex] &= {\color{red}[\part_i \part_i \psi] - \tfrac{\,1\,}{c}~\!\part_i s ~\!\big[\part_i \dot{\psi}\big]} - \tfrac{\,1\,}{c}~\!\triangle s ~\!\big[\dot{\psi}\big] \\ &\qquad\qquad\,\, - \tfrac{\,1\,}{c}~\!\part_i s \Big( {\color{red}\big[\part_i \dot{\psi}\big] - \tfrac{\,1\,}{c}~\!\part_i s ~\!\big[\ddot{\psi}\big]} \Big) \\[.5ex] &= [\triangle \psi] {-}~\! \tfrac{2}{\,c\,} \part_i s \big[\part_i \dot{\psi}\big] {-}~\! \tfrac{\,1\,}{c} \triangle s \big[\dot{\psi}\big] {+}~\! \tfrac{1}{c^2} \part_i s \,\part_i s \big[\ddot{\psi}\big] ; \end{align}</math>}} i.e., {{NumBlk|:|<math>\triangle[\psi] = [\triangle \psi] - \tfrac{2}{\,c\,}~\!\part_i s ~\!\big[\part_i \dot{\psi}\big] - \tfrac{\,1\,}{c}~\!\triangle s ~\!\big[\dot{\psi}\big] + \tfrac{1}{c^2}~\!\big|\nabla s\big|^2 ~\!\big[\ddot{\psi}\big] \,. </math>|{{EquationRef|133}}}} To proceed further, we need to assign a direction to{{math| ''s''&#8202;,}} which we have defined as the propagation distance from {{math|'''r''' }}to{{math| '''r&prime;'''}}. Being a distance, {{mvar|s &#8202;}}is positive whether we measure it forwards or backwards w.r.t. the direction of propagation. But because {{math|'''r&prime;''',}} for present purposes, is fixed while {{math| '''r'''}} varies, we shall measure{{math| ''s''}} "backwards", i.e. from {{math|'''r&prime;''' }}to{{math| '''r''',}} with&#8201; {{math|'''s'''&#8201;{{=}}&#8239;''s''&#8202;'''s&#770;'''}}&#821; as the displacement vector from {{math|'''r&prime;''' }}to{{math| '''r'''}} (so that we can think of both {{mvar|r &#8202;}}and{{mvar| s}}&#8202; as coordinates of position{{math| '''r'''}}, and think of{{mvar| s}}&#8202; as a scalar field). Under that convention, {{NumBlk|:|{{big|{{math|&nabla;''s'' {{=}} '''s&#770;''' {{=}} '''s'''&#10744;''s'' {{=}} {{sfrac|'''r'''&#8202;&minus;&#8202;'''r&prime;'''|''s''}} ,}}}}|{{EquationRef|134}}}} so that&#8201; {{math|{{abs|&nabla;''s''}} {{=}}&#8201;1}}.&#8201; And because {{math|''s''&#8202;,}} like {{math|''r''&#8202;,}}&#8202; is the distance from an origin,&#8201; <math>\triangle s~\!</math> can be evaluated from ({{EquationNote|49}}): :{{big|<math> \triangle s~\! = \tfrac{1}{s^2}~\!\tfrac{d}{ds}\Big(\!s^2 \tfrac{ds}{ds}\!\Big) = \tfrac{1}{s^2}~\!\tfrac{d}{ds}\big(s^2 \big) = \tfrac{2}{\,s\,} \,. </math>}} With these substitutions, ({{EquationNote|133}}) becomes {{NumBlk|:|{{big|<math>\triangle[\psi] = [\triangle\psi] - \tfrac{2}{\,c\,}~\!\part_i s ~\!\big[\part_i \dot{\psi}\big] - \tfrac{2}{cs} \big[\dot{\psi}\big] + \tfrac{1}{c^2} \big[\ddot{\psi}\big] \,. </math>}}|{{EquationRef|135}}}} '''If<math>~\psi</math>&#8202; is a ''scalar''&#8202; field''', we can put this in a more convenient form. By identity ({{EquationNote|71d}}), :{{big|<math> \mathrm{div}\Big(\!\tfrac{\nabla s}{s}\big[\dot{\psi}\big]\!\Big) = \big[\dot{\psi}\big]\operatorname{div}\tfrac{\nabla s}{s} + \tfrac{\nabla s}{s} \cdot \nabla\big[\dot{\psi}\big] \,; </math>}} i.e., by ({{EquationNote|134}}), :{{big|<math> \mathrm{div}\Big(\!\tfrac{\nabla s}{s}\big[\dot{\psi}\big]\!\Big) = \big[\dot{\psi}\big]\operatorname{div}\tfrac{\nabla s}{s} + \frac{\mathbf{r}\!-\!\mathbf{r}'}{s^2} \cdot \nabla\big[\dot{\psi}\big] \,; </math>}} i.e., if we apply identity ({{EquationNote|73g}}) in the first term on the right, and use components in the second, :{{big|<math> \mathrm{div}\Big(\!\tfrac{\nabla s}{s}\big[\dot{\psi}\big]\!\Big) = \big[\dot{\psi}\big]\operatorname{div}\nabla\ln s + \frac{x_i\!-\!x_i'}{s^2} ~\!\part_i\!\big[\dot{\psi}\big] </math>}} (with summation over{{mvar| i}}), where{{mvar| x&prime;_i}}&#8202; is the {{mvar|i&#8202;}}th component of{{math|&#8202; '''r&prime;'''}}.&#8201; But&#8239; {{math|div&#8239;&nabla;&#8201;ln&#8239;''s''}}&#8201; is<math>\,\,\triangle\ln s~\!,\,</math> which can be evaluated from ({{EquationNote|49}}) as :{{big|<math> \triangle\ln s~\! = \tfrac{1}{s^2}~\!\tfrac{d}{ds}\Big(\!s^2 \tfrac{d}{ds}(\ln s)\Big) = \tfrac{1}{s^2}~\!\tfrac{d}{ds}\Big(\!s^2 \tfrac{\,1\,}{s}\!\Big) = \tfrac{1}{s^2} \,. </math>}} Applying this and ({{EquationNote|132}}) to the previous result gives :{{big|<math>\begin{align} \mathrm{div}&\Big(\!\tfrac{\nabla s}{s}\big[\dot{\psi}\big]\!\Big) = \tfrac{1}{s^2}\big[\dot{\psi}\big] + \frac{x_i\!-\!x_i'}{s^2} \Big(\! \big[\part_i \dot{\psi}\big] \!-\! \tfrac{\,1\,}{c}~\!\part_i s ~\!\big[\ddot{\psi}\big] \!\Big) \\ &= \tfrac{1}{s^2}\big[\dot{\psi}\big] + \frac{x_i\!-\!x_i'}{s^2}\big[\part_i \dot{\psi}\big] - \frac{x_i\!-\!x_i'}{cs^2} ~\!\part_i s ~\!\big[\ddot{\psi}\big] \,; \end{align}</math>}} i.e., since {{mvar|&part;_i&#8239;s}} is the {{mvar|i&#8202;}}th component of{{math| &nabla;''s''}}&#8239; and therefore of{{math|&#8202; '''s'''&#10744;''s''&#8202;,}} :{{big|<math> \mathrm{div}\Big(\!\tfrac{\nabla s}{s}\big[\dot{\psi}\big]\!\Big) = \tfrac{1}{s^2}\big[\dot{\psi}\big] + \tfrac{\,1\,}{s}~\!\part_i s ~\!\big[\part_i \dot{\psi}\big] - \tfrac{1}{cs} ~\!\part_i s \,\part_i s ~\!\big[\ddot{\psi}\big] \,; </math>}} i.e., since&#8201; {{math|''&part;_i&#8239;s&#8239;&part;_i&#8239;s'' {{=}} {{abs|&nabla;''s''}}² {{=}} 1&#8202;,}} :{{big|<math> \mathrm{div}\Big(\!\tfrac{\nabla s}{s}\big[\dot{\psi}\big]\!\Big) = \tfrac{1}{s^2}\big[\dot{\psi}\big] + \tfrac{\,1\,}{s}~\!\part_i s ~\!\big[\part_i \dot{\psi}\big] - \tfrac{1}{cs} ~\!\big[\ddot{\psi}\big] \,. </math>}} Multiplying this equation by {{math|2''s''&#10744;''c''}}&#8202; and adding it to equation ({{EquationNote|135}}) gives :{{big|<math>\begin{align} \triangle[\psi] + \tfrac{2s}{c}~\!\mathrm{div}\Big(\! \tfrac{\nabla s}{s}\big[\dot{\psi}\big] \!\Big) &= [\triangle\psi] - \tfrac{1}{c^2} \big[\ddot{\psi}\big] \\ &= \Big[\triangle\psi - \tfrac{1}{c^2}~\!\ddot{\psi}\Big] . \end{align}</math>}} As we are proposing to integrate over a volume containing no sources, we can invoke the (homogeneous) wave equation ({{EquationNote|45}}), so that the right-hand side is zero, leaving {{NumBlk|:|{{big|<math> \triangle[\psi] = - \tfrac{2s}{c}~\!\mathrm{div}\Big(\! \tfrac{\nabla s}{s}\big[\dot{\psi}\big] \!\Big) \,. </math>}}|{{EquationRef|136}}}} Now at last we can substitute ({{EquationNote|136}}) and ({{EquationNote|131}}) into ({{EquationNote|130}}) and get :<math>\begin{align} \iint_S &\Big(\tfrac{\,1\,}{s}~\![\part_n \psi] - \tfrac{1}{cs}~\!\part_n s ~\!\big[\dot{\psi}\big] + \tfrac{1}{s^2}~\![\psi]\,\part_n s \Big) \,dS \\ &= \iiint_V \!{-}\tfrac{2}{\,c\,}~\!\mathrm{div}\Big(\! \tfrac{\nabla s}{s}\big[\dot{\psi}\big] \!\Big) \,dV +\, 4\pi\!\iiint_V [\psi]~\!\delta(\mathbf{r}\!-\!\mathbf{r}') \,dV \,, \end{align}</math> in which we can rewrite the first volume integral as :<math>\begin{align} \iint_S \!{-}\tfrac{2}{\,c\,}~\! \tfrac{\nabla s}{s}\big[\dot{\psi}\big] \cdot \mathbf{\hat{n}}~\!dS &= \iint_S \!{-}\tfrac{2}{cs}~\! \nabla s \cdot \mathbf{\hat{n}} \,\big[\dot{\psi}\big] ~\!dS \\ &= \iint_S \!{-}\tfrac{2}{cs}~\!\part_n s ~\!\big[\dot{\psi}\big] ~\!dS \end{align}</math> and then transpose it to the left side, obtaining {{NumBlk|:|<math>\begin{align} \iint_S &\Big(\tfrac{\,1\,}{s}~\![\part_n \psi] + \tfrac{1}{cs}~\!\part_n s ~\!\big[\dot{\psi}\big] - [\psi]\,\part_n \tfrac{\,1\,}{s} \Big) \,dS \\ &= 4\pi\!\iiint_V [\psi]~\!\delta(\mathbf{r}\!-\!\mathbf{r}') \,dV \,, \end{align}</math>|{{EquationRef|137}}}} where the last term in the integrand on the left has been reverted to its original form (reversing the chain rule), and the remaining integral on the right is{{math| ''&psi;''('''r&prime;''',&#8239;''t'')}}&#8202; if position {{math|'''r&prime;'''}} is inside{{mvar| V}}, but zero if it is outside. Although we derived ({{EquationNote|137}}) by supposing, just after ({{EquationNote|135}}), that {{mvar|&psi;}}&#8202; is ''scalar'', that restriction can now be dropped on account of the linearity of the various operators in ({{EquationNote|137}}). Although we derived ({{EquationNote|137}}) by supposing that {{mvar|V &#8202;}}is a ''finite''&#8202; region, we can extend the result to an infinite region by adding another sheet to the bounding surface{{mvar| S}}&#8202; in such a way that (i) the region becomes finite, but (ii) the additional sheet makes no contribution to the surface integral. The simplest way to do this is to suppose that the additional sheet is at such a large distance that the disturbance has not reached it yet! By this expedient we can apply ({{EquationNote|137}}) not only to the region inside a closed surface, but also (e.g.) to the region outside a closed surface, or the region on one side of an infinite open surface. Although we derived ({{EquationNote|137}}) by supposing, as usual in this paper, that {{math|'''n'''&#770;}} points out of{{mvar| V}}&#8239; and that {{mvar|n &#8202;}}is measured out of{{mvar| V}}, this has the arguably counterintuitive implication that {{math|'''n'''&#770;}} is typically against the direction of propagation&mdash;''directly'' against it in the simplest case, in which {{mvar|V}}&#8202; is the exterior of a sphere with a monopole source at its center. So, in the following formal statement of our result, let us drop the symbol {{mvar|V}}&#8202; and define {{mvar|n}}&#8202; as being measured out of the region containing the sources, and consequently ''into'' the region that satisfies the homogeneous wave equation, ''changing the signs''&#8202; in ({{EquationNote|137}}). '''[[w:Gustav Kirchhoff|Kirchhoff]]'s integral theorem''':  If * the wave function {{mvar|&psi;}}&#8202; satisfies the wave equation (with speed{{mvar| c}}) in a region{{mvar| R}}&#8202; bounded by a surface{{mvar| S}}&#8202; (with all sources consequently on the other side of{{mvar| S&#8202;}}), and * {{mvar|s}}&#8202; is the distance of the general point at position{{math| '''r'''}}&#8202; from the observation point at position{{math| '''r&prime;''',&#8202;}} and * quantities in square brackets are to be delayed by{{math| ''s''&#10744;''c''&#8202;,}} and * {{mvar|n}}&#8202; is the normal coordinate measured from the general point on{{mvar| S}}&#8202; ''into''{{mvar| R}}&#8202; [contrary to the usual direction for a named region, and contrary to the convention we have used above!], then the expression {{NumBlk|:|<math>\tfrac{1}{4\pi} \!\iint_S \Big( [\psi]\,\part_n \tfrac{\,1\,}{s} - \tfrac{1}{cs}~\!\part_n s ~\!\big[\dot{\psi}\big] - \tfrac{\,1\,}{s}~\![\part_n \psi] \Big) \,dS</math>|{{EquationRef|138}}}} is equal to the wave function at{{math| '''r&prime;'''}}&#8202; if{{math| '''r&prime;'''}}&#8202; is inside{{math| ''R''&#8202;,}} but zero if it is outside.<ref>[[#born-wolf-02|Born &amp; Wolf, 2002]], pp.&#8239;420–21, eq.&#8239;(13).&#8201; ''Cf''. Baker &amp; Copson ([[#baker-copson-39|1939]], p.&#8239;37) and Miller ([[#miller-91|1991]], eq.&#8239;2), who use {{mvar|r}}&#8202; instead of{{mvar| s}}&#8202; (among other notational differences). Baker &amp; Copson, in their last equation on p.&#8239;40, give the opposite sign because on this occasion they measure the normal coordinate<math>~\nu</math> ''out'' of the region.</ref> The above derivation (guided by [[#baker-copson-39|Baker &amp; Copson, 1939]], pp.&#8239;38–40) is unusual in that it does not assume sinusoidal time-dependence at any stage&mdash;but objectionable in that (i) the quantity whose divergence we seek, after equation ({{EquationNote|135}}), is a wild guess, and (ii) there are places where a term with coefficient{{math| &pm;1}} found by one path is merged with a term with coefficient{{math| &mp;2}} found by another path, as if the argument contained hidden redundancies that ought to be eliminated. A more traditional derivation (e.g., [[#baker-copson-39|Baker &amp; Copson, 1939]], pp.&#8239;36–7; [[#born-wolf-02|Born &amp; Wolf, 2002]], pp.&#8239;420–21) would first derive the special case for sinusoidal time-dependence (due to [[w:Hermann von Helmholtz|Helmholtz]]) from Green's identities, and then generalize the time-dependence. The traditional approach has the disadvantages of depending on complex numbers and on the premise that a general function of time can be expressed as a sum of sinusoids, but the advantages of making the argument less tortuous and more readily applicable to ''dispersive''&#8202; media (in which {{mvar|c &#8202;}}is frequency-dependent). Helmholtz's integrand is a sinusoidal version of our expression ({{EquationNote|139}}) below. One can derive that expression and thence the Kirchhoff integral in a far more elementary and accessible manner, albeit with some loss of rigor, by ''assuming'' (instead of justifying) the form of the wave function due to a monopole source ([[#putland-22|Putland, 2022]]). That approach first obtains the required distribution of secondary sources and then expresses the wave function as a surface integral&mdash;instead of inferring the secondary sources ''from'' the surface integral, as we are about to do here. === Monopole and dipole secondary sources === There is a convention whereby {{math|'''q'''_{''i'',&#8202;''n''}}} denotes the derivative w.r.t.{{mvar| n}}&#8202; of the {{mvar|i&#8202;}}th component of the vector field{{math| '''q'''&#8202;,}} so that the corresponding derivative of the entire vector is written{{math| '''q'''_{,&#8202;''n''}&#8239;,}} where the strange leading comma in the subscript announces that we want a partial derivative, not a component. Accordingly, let us write the derivative w.r.t.{{mvar| n}}&#8202; of the generic field{{mvar| &psi;}}&#8202; as{{math| ''&psi;''_{,&#8202;''n''}&#8202;}}.&#8201; And let it be understood that any "comma{{math| ''n''}}" derivative is to be evaluated locally, and not as observed at{{math| '''r&prime;'''&#8202;}}; that is, it does ''not''&#8202; account for the variation of {{mvar|s}}&#8202; through{{mvar| n}}. In that notation, the integrand inside the big parentheses in ({{EquationNote|138}}) can be written out in full as :<math>\begin{align} \psi&\big(t\!-\!s/c\big)\,\part_n \tfrac{\,1\,}{s} - \tfrac{1}{cs}~\!\part_n s \,\psi'\big(t\!-\!s/c\big) - \tfrac{\,1\,}{s}~\!\psi_{,n\!}\big(t\!-\!s/c\big) \\ &= \psi\big(t\!-\!s/c\big)\,\part_n \tfrac{\,1\,}{s} + \tfrac{\,1\,}{s}~\!\psi'\big(t\!-\!s/c\big)~\! \big({-}1/c\big)~\!\part_n s - \tfrac{\,1\,}{s}~\!\psi_{,n\!}\big(t\!-\!s/c\big) \\ &= \psi\big(t\!-\!s/c\big)\,\part_n \tfrac{\,1\,}{s} + \tfrac{\,1\,}{s}~\!\part_n \psi\big(t\!-\!s/c\big) - \tfrac{\,1\,}{s}~\!\psi_{,n\!}\big(t\!-\!s/c\big) \,, \end{align}</math> i.e. {{NumBlk|:|<math> \part_n \Big(\tfrac{\,1\,}{s}~\!\psi\big(t\!-\!s/c\big)\Big) - \tfrac{\,1\,}{s}~\!\psi_{,n\!}\big(t\!-\!s/c\big) \,, </math>|{{EquationRef|139}}}} where {{mvar|&part;_n}}&#8202; ''does''&#8202; account for the variation of {{mvar|s}}&#8202; through{{mvar| n}}. If{{mvar| h}} is a ''small''&#8202; change in{{math| ''n''&#8202;,}} from&#8201; {{mvar|n&#8201;{{=}}&#8201;&minus;h}}&#8201; to&#8201; {{math|''n''&#8201;{{=}}&#8201;0&#8202;,}} the integrand can be written {{NumBlk|:|<math> h~\!\part_n \bigg(\frac{\,1\,}{s}~\!\frac{\psi\big(t\!-\!s/c\big)}{h}\bigg) - \tfrac{\,1\,}{s}~\!\psi_{,n\!}\big(t\!-\!s/c\big) \,. </math>|{{EquationRef|140}}}} The second term (including the minus sign) is recognizable as the contribution to the wave function from a monopole source with strength{{math| &minus;''&psi;''_{,&#8202;''n''}&#8202;}}.<ref>''Reminder&#8202;:''&#8201; There are rival definitions of the "strength" of a monopole source; see the text and footnote under equation ({{EquationNote|54}}) above.</ref> Similarly, in the first term, the expression in the big parentheses is the contribution from a monopole source with strength{{math| ''&psi;''&#10744;''h''&#8202;}}; and the operator {{mvar|h&#8202;&part;_n}} gives the change in that contribution due to{{mvar| n}}&#8202; increasing from {{mvar|&minus;h}}&#8202; to{{math| 0&#8202;,}}&#8201; i.e. the change in that contribution due to moving the said monopole from&#8201; {{mvar|n&#8201;{{=}}&#8201;&minus;h}}&#8201; to&#8201; {{math|''n''&#8201;{{=}}&#8201;0&#8202;,}}&#8201; i.e. the whole contribution due to the combination of a monopole with strength{{math| &minus;''&psi;''&#10744;''h''}}&#8202; at&#8201; {{mvar|n&#8201;{{=}}&#8201;&minus;h}}&#8201; and a monopole with strength{{math| ''&psi;''&#10744;''h''}}&#8202; at&#8201; {{math|''n''&#8201;{{=}}&#8201;0}}. This combination is called a '''dipole''' (or ''doublet'')<ref>The term ''doublet'', which seems to be older, is used by Baker &amp; Copson ([[#baker-copson-39|1939]]), Born &amp; Wolf ([[#born-wolf-02|2002, p.&#8239;421]]), and Larmor ([[#larmor-1904|1904]]).</ref> with strength{{mvar| &psi;}}&#8202; in the normal ({{mvar|n}}) direction. According to ({{EquationNote|138}}), the expression ({{EquationNote|140}}) is to be scaled by {{math|{{sfrac|4''&pi;''}}}}&#8202; and integrated over the surface{{mvar| S}}. Thus the secondary source distribution is a monopole distribution of strength density {{math|&minus;{{sfrac|''&psi;''_{,&#8202;''n''}|4''&pi;''}}}}&#8239; plus a normal dipole distribution of strength density{{math| {{sfrac|''&psi;''|4''&pi;''}}&#8202;,}} where "strength density" means strength per unit area. This is not to say that the specified secondary sources really exist, or even that they ''could''&#8202; exist, but only that the wave function in the region{{mvar| R}}&#8202; is ''as if''&#8202; it had been generated by the specified secondary sources (which would also give a null wave function outside the region). We should note, however, that a monopole contribution of the form ({{EquationNote|48}}) ''can''&#8202; really exist, even for a vector wave function, notwithstanding that it requires not only the magnitude but also the direction of the vector to be independent of the direction of propagation. That requirement might seem to exclude electromagnetic waves, for which the electric and magnetic fields are transverse to the direction of propagation and therefore not independent of it. But it is possible to describe such waves in terms of an electric scalar potential and a magnetic vector potential, such that the contribution to the latter from a current element has the same direction as the current element for all directions of propagation.<ref>''Cf''. [[#feynman-63|Feynman, 1963]], vol.&#8239;2, chap.&#8239;15, Table 15-1, "{{math|'''''A'''''(1,&#8239;''t''&#8202;) {{=}} &hellip;}}".</ref> === Generalized spatiotemporal-dipole (GSTD) secondary sources === The "dipole" discussed so far is a ''spatial''&#8202; dipole, in which the constituent monopoles differ only in sign and by a small spatial displacement. If we add a small time shift between the monopoles, equal to the propagation time from one to the other, we get what David A.B. Miller ([[#miller-91|1991]]) calls a ''spatiotemporal''&#8202; dipole. If we allow the time shift to be smaller than that propagation time, and allow one monopole to be attenuated by a small fraction, we get what I call a ''generalized''&#8202; spatiotemporal dipole, the usefulness of which will now be demonstrated. In the Helmholtz–Kirchhoff integrand ({{EquationNote|139}}), the second term (including the sign) represents a monopole strength density{{math| &minus;''&psi;''_{,&#8202;''n''}&#8202;,}} and the first term represents a dipole strength density{{mvar| &psi;}}&#8202; in the {{mvar|n }}direction; the dipole source per unit area of{{mvar| S}}&#8202; is a ''spatial''&#8202; dipole comprising a monopole with strength{{math| &minus;''&psi;''&#10744;''h''}}&#8202; at&#8201; {{mvar|n&#8201;{{=}}&#8201;&minus;h}}&#8202; (the ''inverted''&#8202; monopole), and a monopole with strength{{math| ''&psi;''&#10744;''h''}}&#8202; at&#8201; {{math|''n''&#8201;{{=}}&#8201;0}} (the ''uninverted''&#8202; monopole), where {{mvar|h}}&#8202; is small. Now let us see if we can eliminate the need for the separate monopole, and thus effectively reduce a tripole to a dipole, by suitably modifying the spatial dipole. ::'''&vellip;''' '''[''To be continued.'']''' == Additional information == === Acknowledgments === Professor Chen-To Tai, {{serif|FIEEE}}, died in 2004.  He first came to my attention in 2018 through his paper "On the presentation of Maxwell's theory" (''Proc.&#8239;{{serif|IEEE}}'', '''60'''(8):&#8239;936–45, 1972). In nearly every place where I mention him here, even if I do not accept his conclusion, I am entirely indebted to his works for drawing my attention to the issue raised. In particular, it was he who alerted me to Gibbs's original definitions of the divergence and curl and their suitability for expression in indicial notation ([[#tai-95|Tai, 1995]], pp.&#8239;17,&#8239;21). And although he might not have been pleased, it was through him that I first knew with certainty that the del-dot and del-cross notations work in general coordinates (''ibid.'', pp.&#8239;64–5). This article uses images from Wikimedia Commons. A derivation of "generalized" spatiotemporal-dipole secondary sources has been previously published ([[#putland-22|Putland, 2022]]), but not previously peer-reviewed. === Competing interests === None. === Ethics statement === This article does not concern research on human or animal subjects. === '''TO DO:''' === * More illustrations&hellip; == Notes == {{notelist|2}} == References == {{reflist|3}} == Bibliography == <div style="font-size: 111%"> {{refbegin|indent=yes}} *<span id="axler-95">S.J. Axler, 1995, "Down with Determinants!"&#8201; ''American Mathematical Monthly'', vol.&#8239;102, no.&#8239;2 (Feb.&#8239;1995), pp.&#8239;139–54; [https://www.jstor.org/stable/2975348 jstor.org/stable/2975348].&#8201; (Author's preprint, with different pagination: [https://www.researchgate.net/publication/265273063_Down_with_Determinants researchgate.net/publication/265273063_Down_with_Determinants].)</span> *<span id="axler-23-">S.J. Axler, 2023–, ''Linear Algebra Done Right'', 4th Ed., Springer; [https://linear.axler.net/ linear.axler.net] (open access).</span> *<span id="baker-copson-39">B.B. Baker and E.T. Copson, 1939, ''The Mathematical Theory of&#8202; Huygens' Principle'', Oxford; 3rd Ed.&#8201;(same pagination, with addenda), New York: Chelsea, 1987, [https://archive.org/details/mathematicaltheo0000bake archive.org/details/mathematicaltheo0000bake].</span> *<span id="borisenko-tarapov-68">A.I. Borisenko and I.E.&#8239;Tarapov (tr.&#8239;&amp; ed. R.A.&#8239;Silverman), 1968, ''Vector and Tensor Analysis with Applications'', Prentice-Hall; reprinted New York: Dover, 1979, [https://archive.org/details/vectortensoranal0000bori archive.org/details/vectortensoranal0000bori].<!-- Typo on p.180: First cross in equation before (4.93) should be "=". --></span> *<span id="born-wolf-02">M.&#8201;Born and E.&#8239;Wolf, 2002, ''Principles of Optics'', 7th Ed., Cambridge, 1999 (reprinted with corrections, 2002).</span> *<span id="broyden-75">C.G. Broyden, 1975, ''Basic Matrices'', London: Macmillan.</span> *<span id="feynman-63">R.P. Feynman, R.B. Leighton, &amp; M.&#8239;Sands, 1963 etc., ''The Feynman Lectures on Physics'', California Institute of Technology; [http://www.feynmanlectures.caltech.edu/ feynmanlectures.caltech.edu].</span> *<span id="fletcher-74">N.H. Fletcher, 1974, "Adiabatic assumption for wave propagation", ''American Journal of Physics'', vol.&#8239;42, no.&#8239;6 (June 1974), pp.&#8239;487–9; [https://doi.org/10.1119/1.1987757 doi.org/10.1119/1.1987757].</span> *<span id="gibbs-1881-4">J.W. Gibbs, 1881–84, "Elements of Vector Analysis", privately printed New Haven: Tuttle, Morehouse &amp; Taylor, 1881 (&sect;&sect;&#8239;1–101), 1884 (&sect;&sect;&#8239;102–189, etc.), [https://archive.org/details/elementsvectora00gibb archive.org/details/elementsvectora00gibb]; published in ''The Scientific Papers of J.&#8239;Willard Gibbs'' (ed. H.A.&#8239;Bumstead &amp; R.G.&#8239;Van Name), New York: Longmans, Green, &amp; Co., 1906, vol.&#8239;2, [https://archive.org/details/scientificpapers02gibbuoft archive.org/details/scientificpapers02gibbuoft], pp.&#8239;17–90.</span> *<span id="hsu-84">H.P. Hsu, 1984, ''Applied Vector Analysis'', Harcourt Brace Jovanovich; [https://archive.org/details/appliedvectorana00hsuh archive.org/details/appliedvectorana00hsuh].</span> *<span id="huygens-1690-thompson">C. Huygens, 1690, tr. S.P.&#8239;Thompson, ''Treatise on Light'', University of Chicago Press, 1912 / [https://gutenberg.org/files/14725/14725-h/14725-h.htm gutenberg.org/files/14725/14725-h/14725-h.htm], 2005. (See also "Errata in various editions of Huygens' ''Treatise on Light''&#8239;", ''www.grputland.com'' or ''grputland.blogspot.com'', June 2016.)</span> *<span id="katz-79">V.J. Katz, 1979, "The history of Stokes' theorem", ''Mathematics Magazine'', vol.&#8239;52, no.&#8239;3 (May 1979), pp.&#8239;146–56; [https://www.jstor.org/stable/2690275 jstor.org/stable/2690275].</span> *<span id="kemin-et-al-00">S. Kemin, X.&#8239;Zhenting, T.&#8239;Jinsheng, &amp; H.&#8239;Xuemei, 2000, "The comprehension, some problems and suggestions to symbolic vector method and some defenses for Gibbs' symbol", ''Applied Mathematics and Mechanics'' (English Ed.), vol.&#8239;21, no.&#8239;5 (May 2000), pp.&#8239;603–6; [https://doi.org/10.1007/BF02459044 doi.org/10.1007/BF02459044].</span> *<span id="kemmer-77">N. Kemmer, 1977, ''Vector Analysis: A physicist's guide to the mathematics of fields in three dimensions'', Cambridge; [https://archive.org/details/isbn_0521211581 archive.org/details/isbn_0521211581].</span> *<span id="kreyszig-62-">E. Kreyszig, 1962 etc., ''Advanced Engineering Mathematics'', New York: Wiley;&#8201; 5th Ed., 1983;&#8201; 6th Ed., 1988;&#8201; 9th Ed., 2006;&#8201; 10th Ed., 2011.</span> *<span id="larmor-1904">J. Larmor, 1904, "On the mathematical expression of the principle of&#8202; Huygens" (read 8 Jan.&#8239;1903), ''Proceedings of the London Mathematical Society'', Ser.&#8239;2, vol.&#8239;1 (1904), pp.&#8239;1–13.<!-- Listed as "Issue 1"; only issue for that volume. --></span> *<span id="miller-91">D.A.B. Miller, 1991, "Huygens's wave propagation principle corrected", ''Optics Letters'', vol.&#8239;16, no.&#8239;18 (15 Sep.&#8239;1991), pp.&#8239;1370–72; [http://ee.stanford.edu/~dabm/146.pdf stanford.edu/~dabm/146.pdf].</span> *<span id="moon-spencer-65">P.H. Moon and D.E.&#8239;Spencer, 1965, ''Vectors'', Princeton, NJ: Van Nostrand.</span> *<span id="panofsky-phillips-62">W.K.H. Panofsky and M.&#8239;Phillips, 1962, ''Classical Electricity and Magnetism'', 2nd Ed., Addison-Wesley; reprinted Mineola, NY: Dover, 2005.</span> *<span id="putland-22">G.R. Putland, 2022, "Consistent derivation of Kirchhoff's integral theorem and diffraction formula and the Maggi-Rubinowicz transformation using high-school math" (working paper), [https://doi.org/10.5281/zenodo.7205781 doi.org/10.5281/zenodo.7205781] (Creative Commons).</span> *<span id="rocci-20">A. Rocci, 2020, "Back to the roots of vector and tensor calculus: Heaviside versus Gibbs" (online 10 Nov.&#8239;2020), ''Archive for History of Exact Sciences'', vol.&#8239;75, no.&#8239;4 (July 2021), pp.&#8239;369–413. (Author's preprint, with different pagination: [https://arxiv.org/abs/2010.09679 arxiv.org/abs/2010.09679].)</span> *<span id="tai-94">C.-T. Tai, 1994, "A survey of the improper use of &nabla; in vector analysis" (Technical Report RL&#8239;909), Dept.&#8201;of Electrical Engineering &amp; Computer Science, University of Michigan; [https://deepblue.lib.umich.edu/handle/2027.42/7869 hdl.handle.net/2027.42/7869].</span> *<span id="tai-95">C.-T. Tai, 1995, "A historical study of vector analysis" (Technical Report RL&#8239;915), Dept.&#8201;of Electrical Engineering &amp; Computer Science, University of Michigan; [https://deepblue.lib.umich.edu/handle/2027.42/7868 hdl.handle.net/2027.42/7868].</span> *<span id="tai-fang-91">C.-T. Tai and N.&#8239;Fang, 1991, "A systematic treatment of vector analysis", ''{{serif|IEEE}} Transactions on Education'', vol.&#8239;34, no.&#8239;2 (May 1991), pp.&#8239;167–74; [https://doi.org/10.1109/13.81596 doi.org/10.1109/13.81596].</span> *<span id="wilson-1901">E.B.&#8201;Wilson, 1901, ''Vector Analysis: A text-book for the use of students of mathematics and physics'' ("Founded upon the lectures of J.&#8239;Willard Gibbs&hellip;"), New York: Charles Scribner's Sons; 12th printing, Yale University Press, 1958, [https://archive.org/details/vectoranalysiste0000gibb archive.org/details/vectoranalysiste0000gibb].</span> *<span id="wrede-spiegel-10">R.C.&#8201;Wrede and M.R.&#8239;Spiegel, 2010, ''Advanced Calculus'', 3rd Ed., New York: McGraw-Hill (Schaum's Outlines); [https://archive.org/details/schaumsoutlinesa0000wred archive.org/details/schaumsoutlinesa0000wred].</span> {{refend}} </div> == Further reading == M.J. Crowe, "A History of Vector Analysis" (address at the University of Louisville, Autumn term, 2002), [https://www.researchgate.net/publication/244957729_A_History_of_Vector_Analysis researchgate.net/publication/244957729_A_History_of_Vector_Analysis] (including much discussion of quaternions). P. Lynch, "Matthew O'Brien: An inventor of vector analysis", ''Bulletin of the Irish Mathematical Society'', No.&#8239;74 (Winter 2014), pp.&#8239;81–8; [https://doi.org/10.33232/BIMS.0074.81.88 doi.org/10.33232/BIMS.0074.81.88]. [[Category:Vector calculus]] [[Category:Mathematical physics]] fd9350zqaf0kxhyhghlg4qk9bl6ddnt 0 302470 2690233 2690095 2024-12-04T08:17:55Z ThaniosAkro 2805358 /* Calculaton of π */ 2690233 wikitext text/x-wiki Pi is a mathematical concept related to circles, geometry, and probably more. ----- ;Subpages {{Subpages/List}} ----- '''Notice:''' [[Pi/Real cosine function/Definition]] and [[Pi/Zero of cosine/Introduction/Section]] are two subpages to [[Pi]] that should not be deleted because they are transclusions to another learning resource. '''Please do not delete this page because it might help "protect" the subpages.''' ==Learning resources== ===Wikipedia=== * [[Wikipedia:Pi|Pi]] * [[Wikipedia:Category:Pi|Pi]] (Category) * [[Wikipedia:Irrational number|Irrational number]] * [[Wikipedia:Approximations of π|Approximations of π]] * [[Wikipedia:List of topics related to π|List of topics related to π]] * [[Wikipedia:List of formulae involving π|List of formulae involving π]] * [[Wikipedia:A History of Pi|A History of Pi]] * [[Wikipedia:Turn_(angle)#Tau_proposals|Turn_(angle)#Tau_proposals]] * [[Wikipedia:Six nines in pi|Six nines in pi]] * [[Wikipedia:Proof that π is irrational|Proof that π is irrational]] ===External=== * [https://www.exploratorium.edu/pi/history-of-pi A Brief History of Pi (π)] * [https://press.princeton.edu/ideas/pi-is-magic Pi is magic] * [https://sites.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html The History of Pi] * [https://www.math.utah.edu/~alfeld/math/pi.html pi to 10,000 digits] * [https://news.web.baylor.edu/news/story/2023/baylor-math-chair-explains-magic-mystery-p-pi Baylor Math Chair Explains Magic, Mystery of π (Pi)] * [https://curtiscenter.math.ucla.edu/are-there-any-practical-applications-of-pi-aside-from-calculating-the-area-or-circumference-of-a-circle/ Are there any practical applications of pi, aside from calculating the area or circumference of a circle?] * [https://content.byui.edu/file/b8b83119-9acc-4a7b-bc84-efacf9043998/1/Math-2-5-1.html Pi and the Circumference of a Circle] * [https://news.harvard.edu/gazette/story/2019/03/harvard-physics-lecturer-on-why-pi-endlessly-fascinates-us/ Our endless fascination with pi] ==Calculation of π== ===Radians, the natural angle=== [[File:1129radian00.png|thumb|400px|'''Diagram illustrating one radian of angular measurement.''' </br> Arc of circle (red curved line with arrows) with length equal to radius of circle subtends one radian at center. </br> In diagram above, length of radius = length of arc = 1. </br> One radian <math>= 57.29577951308232\dots^\circ.</math> ]] If you were a mathematician among the ancient Sumerians of the 3rd millennium BC and you were determined to define the angle that could be adopted as a standard to be used by all users of trigonometry, you would probably suggest the angle in an equilateral triangle. This angle is easily defined, easily constructed, easily understood and easily reproduced. It would be easy to call this angle the "natural" angle. The numeral system used by the ancient Sumerians was Sexagesimal, also known as base 60, a numeral system with sixty as its base. In practice the natural angle could be divided into 60 parts, now called degrees, and each degree could be divided into 60 parts, now called minutes, and so on. Three equilateral triangles fit neatly into a semi-circle, hence 180 degrees in a semi-circle. We know that <math>\tan 30^\circ = \frac{\sqrt{3}}{3}.</math> Therefore, <math>\arctan (\frac{\sqrt{3}}{3})</math> should be <math>0.5,</math> or one half of our concept of the natural angle. Whatever the natural angle might be, it has existed for billions of years, but it has come to light only in recent times with invention of the calculus. In mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function: <math>\arctan x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \frac{x^9}{9} + \cdots.</math> The following python code calculates <math>\arctan (\frac{\sqrt{3}}{3})</math> using Gregory's series: <math></math> <syntaxhighlight lang=python> # python code r3 = 3 ** .5 x = r3/3 arctan_x = ( x - x**3/3 + x**5/5 - x**7/7 + x**9/9 - x**11/11 + x**13/13 - x**15/15 + x**17/17 - x**19/19 + x**21/21 - x**23/23 + x**25/25 - x**27/27 + x**29/29 - x**31/31 + x**33/33 - x**35/35 + x**37/37 - x**39/39 + x**41/41 - x**43/43 + x**45/45 - x**47/47 + x**49/49 - x**51/51 + x**53/53 - x**55/55 + x**57/57 - x**59/59 + x**61/61 - x**63/63 + x**65/65 - x**67/67 + x**69/69 ) sx = 'arctan_x' ; print (sx, '=', eval(sx)) </syntaxhighlight> <syntaxhighlight> arctan_x = 0.5235987755982988 </syntaxhighlight> Our assessment of the natural angle as the angle in an equilateral triangle was a very reasonable guess. However, the natural angle is the radian, the angle subtended at center of circle by an arc on the circumference equal to the radius. Six times arctan_x <math>= 180^\circ</math> or the number of radians in a semi-circle: <syntaxhighlight lang=python> # python code sx = 'arctan_x * 6' ; print (sx, '=', eval(sx)) sx = '180/(arctan_x * 6)' ; print (sx, '=', eval(sx)) </syntaxhighlight> <syntaxhighlight> arctan_x * 6 = 3.141592653589793 180/(arctan_x * 6) = 57.29577951308232 </syntaxhighlight> <math>\pi = 3.141592653589793\dots,</math> number of radians in semi-circle. One radian <math>= 57.29577951308232\dots^\circ,</math> slightly less than <math>60^\circ.</math> Because the value <math>\frac\sqrt{3}{3}</math> is fairly large, calculation of <code>arctan_x</code> above required 34 operations to produce result accurate to 16 places of decimals. The calculation did not converge quickly. Python code below uses much smaller values of <math>x</math>, and calculation of <code>arctan_x</code> for precision of 1001 is quite fast. ===tan(A/2)=== {{RoundBoxTop|theme=2}} [[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of <math>\tan \frac{A}{2}</math>.''' </br> <math>OQ = 1;\ QP = t.</math> </br> <math>\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.</math> </br> <math>OP = OR = \sqrt{1 + t^2}</math> ]] In diagram: Point <math>P</math> has coordinates <math>(1,t).</math> Point <math>R</math> has coordinates <math>(\sqrt{1 + t^2},0).</math> Mid point of <math>PR,\ M</math> has coordinates <math>( \frac{ 1 + \sqrt{1 + t^2} }{2}, \frac{t}{2} ).</math> <math>\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 + \sqrt{1 + t^2} }{2} = \frac{t}{1 + \sqrt{1 + t^2} }</math> <math>= \frac{t}{1 + \sqrt{1 + t^2} } \cdot \frac{1 - \sqrt{1 + t^2}}{1 - \sqrt{1 + t^2} }</math> <math>= \frac{t( 1 - \sqrt{1 + t^2} )}{1-(1+t^2)}</math> <math>= \frac{t( 1 - \sqrt{1 + t^2} )}{-t^2}</math> <math>= \frac{-1 + \sqrt{1 + t^2} }{t}</math> * <math>\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 + \sqrt{1 + \tan^2 (A)} }{\tan (A)}</math> * <math>\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }</math> {{RoundBoxBottom}} ===Implementation=== {{RoundBoxTop|theme=2}} This section calculates five values of <math>\pi</math> using the following known values of <math>\tan(A):</math> {| class="wikitable" |- ! Angle <math>A</math> || <math>\tan(A)</math> |- | <math>45^\circ</math> | <math>1</math> |- | <math>36^\circ</math> | <math>\sqrt{ 5 - 2\sqrt{5} }</math> |- | <math>30^\circ</math> | <math>\frac{\sqrt{3}}{3}</math> |- | <math>27^\circ</math> | <math>\sqrt{ 11 - 4\sqrt{5} + (\sqrt{5} - 3) \sqrt{ 10 - 2\sqrt{5} } }</math> |- | <math>24^\circ</math> | <math>\frac{ (3\sqrt{5} + 7) \sqrt{5 - 2\sqrt{5}} - (\sqrt{5} + 3)\sqrt{3} }{2}</math> |} Values of <math>x</math> in table below are derived from the above values by using identity <math>\tan(\frac{A}{2}) = \frac{-1 + \sqrt{1 + \tan^2(A)}}{\tan(A)}</math>: {| class="wikitable" |- ! Angle <math>\theta</math> || <math>x = \tan(\theta)</math> |- | <math>\frac{45^\circ}{2^{33}}</math> | <code>0.00000_00000_91432_37995_4197.....089_03901_63759_3912</code> |- | <math>\frac{36^\circ}{2^{33}}</math> | <code>0.00000_00000_73145_90396_3357.....211_97500_56173_0713</code> |- | <math>\frac{30^\circ}{2^{33}}</math> | <code>0.00000_00000_60954_91996_9464.....024_32806_94580_0689</code> |- | <math>\frac{27^\circ}{2^{33}}</math> | <code>0.00000_00000_54859_42797_2518.....791_30634_03540_9738</code> |- | <math>\frac{24^\circ}{2^{32}}</math> | <code>0.00000_00000_97527_87195_1143.....736_60376_04724_6778</code> |} <syntaxhighlight lang=python> # python code desired_precision = 1001 number_of_leading_zeroes = 10 # See below. import decimal dD = decimal.Decimal # decimal object is like float with (almost) infinite precision. dgt = decimal.getcontext() Precision = dgt.prec = desired_precision + 3 # Adjust as necessary. Tolerance = dD("1e-" + str(Precision-2)) # Adjust as necessary. adjustment_to_precision = number_of_leading_zeroes * 2 + 3 def tan_halfA(tan_A) : dgt.prec += adjustment_to_precision top = -1 + (1+tan_A**2).sqrt() dgt.prec -= adjustment_to_precision tan_A_2 = top/tan_A return tan_A_2 def tan_2A (tanA) : ''' 2 * tanA tan(2A) = ----------- 1 - tanA**2 ''' if tanA in (1,-1) : return '1/0' dgt.prec += adjustment_to_precision bottom = (1 - tanA**2) output = 2*tanA/bottom dgt.prec -= adjustment_to_precision return output+0 def θ_tanθ_from_A_tanA (angleA, tanA) : ''' if input == 45,1 output is: "dD(45) / (2 ** (33))", "0.00000_00000_91432_37995_....._63759_3912" ^^^^^^^^^^^ number_of_leading_zeroes refers to these zeroes. θ,tanθ = θ_tanθ_from_A_tanA (angleA, tanA) ''' θ, tanθ = angleA, tanA for p in range (1,100) : θ /= 2 tanθ = tan_halfA(tanθ) if tanθ >= dD('1e-' + str(number_of_leading_zeroes)) : continue str1 = str(tanθ) # str1 = "n.nnnnnnnnnnnnn ..... nnnnnnnnnnnnE-11" str1a = str1[0] + str1[2:-4] list1 = [ str1a[q:q+5] for q in range (0, len(str1a), 5) ] str2 = '0.00000_00000_' + ('_'.join(list1)) dD2 = dD(str2) (dD2 == tanθ) or ({}[2]) ((θ * (2**p)) == angleA ) or ({}[3]) str3 = 'dD({}) / (2 ** ({}))'.format(angleA,p) (θ == eval(str3)) or ({}[4]) return str3, str2 ({}[5]) r3 = dD(3).sqrt() r5 = dD(5).sqrt() tan36 = (5 - 2*r5).sqrt() tan45 = dD(1) tan30 = r3/3 v1 = 3*r5+7 v2 = (5 - 2*r5).sqrt() v3 = (r5+3)*r3 tan24 = ( v1*v2 - v3 )/2 v1 = r5 - 3 ; v2 = (10 - 2*r5).sqrt() tan27 = ( 11 - 4*r5 + v1*v2 ).sqrt() values_of_A_tanA = ( (dD(45), tan45), (dD(36), tan36), (dD(30), tan30), (dD(27), tan27), (dD(24), tan24), ) values_of_θ_tanθ = [] for (A, tanA) in values_of_A_tanA : θ, tanθ = θ_tanθ_from_A_tanA (A, tanA) print() sx = 'θ' ; print (sx, '=', eval(sx)) # sx = 'tanθ' ; print (sx, '=', eval(sx)) print ('tanθ =', '{}.....{}'.format(tanθ[:30], tanθ[-20:])) values_of_θ_tanθ += [ (θ, tanθ) ] # Check for (v1,v2),(v3,v4) in zip (values_of_A_tanA, values_of_θ_tanθ) : A, tanA = v1,v2 θ = eval(v3) tanθ = dD(v4) status = 0 for p in range (1,100) : θ *= 2 tanθ = tan_2A (tanθ) if θ == A : dgt.prec = desired_precision (+tanθ == +tanA) or ({}[10]) dgt.prec = Precision status = 1 break status or ({}[11]) </syntaxhighlight> <syntaxhighlight> θ = dD(45) / (2 ** (33)) tanθ = 0.00000_00000_91432_37995_4197.....089_03901_63759_3912 θ = dD(36) / (2 ** (33)) tanθ = 0.00000_00000_73145_90396_3357.....211_97500_56173_0713 θ = dD(30) / (2 ** (33)) tanθ = 0.00000_00000_60954_91996_9464.....024_32806_94580_0689 θ = dD(27) / (2 ** (33)) tanθ = 0.00000_00000_54859_42797_2518.....791_30634_03540_9738 θ = dD(24) / (2 ** (32)) tanθ = 0.00000_00000_97527_87195_1143.....736_60376_04724_6778 </syntaxhighlight> <syntaxhighlight lang=python> # python code def calculate_π (angleθ, tanθ) : ''' angleθ may be: "dD(27) / (2 ** (33))" tanθ may be: "0.00000_00000_54859_42797_ ..... _03540_9738" π = calculate_π (angleθ, tanθ) ''' thisName = 'calculate_π (angleθ, tanθ) :' if isinstance(angleθ, dD) : pass elif isinstance(angleθ, str) : angleθ = eval(angleθ) else : ({}[21]) if isinstance(tanθ, dD) : pass elif isinstance(tanθ, str) : tanθ = dD(tanθ) else : ({}[22]) x = tanθ ; multiplier = -1 ; sum = x ; count = 0; status = 0 # x**3 x**5 x**7 x**9 # y = x - ---- + ---- - ---- + ---- # 3 5 7 9 # # Each term in the sequence is roughly the previous term multiplied by x**2. # Each value of x contains 10 leading zeroes after decimal point. # Therefore, each term in the sequence is roughly the previous term with 20 more leading zeroes. # Each pass through main loop adds about 20 digits to current value of sum # and θ is calculated to precision of 1004 digits with about 50 passes through main loop. # for p in range (3,200,2) : # This is main loop. count += 1 addendum = (multiplier * (x**p)) / p sum += addendum if abs(addendum) < Tolerance : status = 1; break multiplier = -multiplier status or ({}[23]) print(thisName, 'count =',count) π = sum * 180 / angleθ dgt.prec = desired_precision π += 0 # This forces π to adopt precision of desired_precision. dgt.prec = Precision return π # Calculate five values of π: values_of_π = [] for θ,tanθ in values_of_θ_tanθ : π = calculate_π (θ,tanθ) values_of_π += [ π ] </syntaxhighlight> Each calculation of π required about 50 passes through main loop: <syntaxhighlight> calculate_π (angleθ, tanθ) : count = 50 calculate_π (angleθ, tanθ) : count = 49 calculate_π (angleθ, tanθ) : count = 49 calculate_π (angleθ, tanθ) : count = 49 calculate_π (angleθ, tanθ) : count = 50 </syntaxhighlight> Check that all 5 values of π are equal: <syntaxhighlight lang=python> # python code set1 = set(values_of_π) sx = 'len(values_of_π)' ; print (sx, '=', eval(sx)) sx = 'len(set1)' ; print (sx, '=', eval(sx)) sx = 'set1' ; print (sx, '=', eval(sx)) π, = set1 # Note the syntax. If length of set1 is not 1, this statement fails. </syntaxhighlight> <syntaxhighlight> len(values_of_π) = 5 len(set1) = 1 set1 = {Decimal('3.141592653589793238462643383279.....12268066130019278766111959092164201989')} </syntaxhighlight> Because all five calculated values of π are equal, there is very high probability that this value of π is accurate. Print value of π as python command formatted: <syntaxhighlight lang=python> # python code newLine = ''' '''[-1:] def print_π (π) : ''' Input π is : Decimal('3.141592653589793238 ..... 66111959092164201989') This function prints: π = ( "3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510" + "58209_74944_59230_78164_06286_20899_86280_34825_34211_70679" ..... + "18577_80532_17122_68066_13001_92787_66111_95909_21642_01989" ) ''' πstr = str(π) (len(πstr) == (desired_precision + 1)) or ({}[31]) (πstr[:2] == '3.') or ({}[32]) twenty_rows = [] for p in range (2, len(πstr), 50) : str1a = πstr[p:p+50] list1a = [ str1a[q:q+5] for q in range(0, len(str1a), 5) ] str1b = '_'.join(list1a) twenty_rows += [str1b] twenty_rows[0] = '3.' + twenty_rows[0] joiner = '"{} + "'.format(newLine) str3 = '( "{}" )'.format(joiner.join(twenty_rows)) str4 = eval(str3) (dD(str4) == π) or ({}[33]) lines = str3.split(newLine) paragraphs = [ newLine.join(lines[p:p+4]) for p in range(0,len(lines),4) ] str5 = (newLine*2).join(paragraphs) str6 = eval(str5) (dD(str6) == π) or ({}[34]) print ('π =', str5) return str5 π1 = print_π (π) </syntaxhighlight> <syntaxhighlight> π = ( "3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510" + "58209_74944_59230_78164_06286_20899_86280_34825_34211_70679" + "82148_08651_32823_06647_09384_46095_50582_23172_53594_08128" + "48111_74502_84102_70193_85211_05559_64462_29489_54930_38196" + "44288_10975_66593_34461_28475_64823_37867_83165_27120_19091" + "45648_56692_34603_48610_45432_66482_13393_60726_02491_41273" + "72458_70066_06315_58817_48815_20920_96282_92540_91715_36436" + "78925_90360_01133_05305_48820_46652_13841_46951_94151_16094" + "33057_27036_57595_91953_09218_61173_81932_61179_31051_18548" + "07446_23799_62749_56735_18857_52724_89122_79381_83011_94912" + "98336_73362_44065_66430_86021_39494_63952_24737_19070_21798" + "60943_70277_05392_17176_29317_67523_84674_81846_76694_05132" + "00056_81271_45263_56082_77857_71342_75778_96091_73637_17872" + "14684_40901_22495_34301_46549_58537_10507_92279_68925_89235" + "42019_95611_21290_21960_86403_44181_59813_62977_47713_09960" + "51870_72113_49999_99837_29780_49951_05973_17328_16096_31859" + "50244_59455_34690_83026_42522_30825_33446_85035_26193_11881" + "71010_00313_78387_52886_58753_32083_81420_61717_76691_47303" + "59825_34904_28755_46873_11595_62863_88235_37875_93751_95778" + "18577_80532_17122_68066_13001_92787_66111_95909_21642_01989" ) </syntaxhighlight> {{RoundBoxTop|theme=3}} [[File:1202pi_highlighted.png|thumb|400px|'''Value of <math>\pi</math> highlighted.''']] If you highlight the above expression for <math>\pi</math> as shown in diagram, you can copy and paste it into your python source file as valid python code. {{RoundBoxBottom}} {{RoundBoxBottom}} ==Discussion questions== * What are useful applications of pi in engineering or science? * How is pi useful in computer science? ==See also== * [[Math]] * [[Geometry]] * [[Exact_Trigonometric_Values]] iymrtynwhzjiiy9vrmf8tm4e23txgr8 0 304031 2690108 2625698 2024-12-03T13:07:22Z Alandmanson 1669821 /* 72 (Head and body yellowish to brownish, not metallic, no white setae) */ 2690108 wikitext text/x-wiki Encyrtidae is a large family of parasitic wasps in the Superfamily [[w:Chalcidoidea|Chalcidoidea]]. There are more than 640 described species of [[w:Afrotropical|Afrotropical]] Encyrtidae in about 130 genera. Many encyrtid species are parasitoids of [[w:scale insect|scale insect]]s, some of which are pests that reduce the productivity of agricultural crops across the world.<br> =Key to the genera of Afrotropical Encyrtidae= This key is based on this paper: '''Prinsloo, G. L., & Annecke, D. P. (1979).''' A key to the genera of Encyrtidae from the Ethiopian region, with descriptions of three new genera (Hymenoptera: Chalcidoidea). Journal of the Entomological Society of southern Africa, 42(2), 349-382.<ref name=Prinsloo&Anneke1979>Prinsloo, G. L., & Annecke, D. P. (1979). A key to the genera of Encyrtidae from the Ethiopian region, with descriptions of three new genera (Hymenoptera: Chalcidoidea). Journal of the Entomological Society of southern Africa, 42(2), 349-382. [https://journals.co.za/doi/pdf/10.10520/AJA00128789_2641 PDF]</ref> The Universal Chalcidoidea Database<ref name=Noyes2019/>, WaspWeb<ref name=vanNoort2024>van Noort, S. 2024. WaspWeb: Hymenoptera of the Afrotropical region. https://www.waspweb.org/Chalcidoidea/Encyrtidae/Classification/index.htm (accessed 2023-2024).</ref>, and other on-line sources were used to add details. ==1 Encyrtidae == [[African Arthropods/Encyrtidae|'''Diagnostic features of Encyrtidae''']] include: mesopleuron very enlarged; mid coxae level with middle of mesopleuron in side view; cercal plates advanced; linea calva distinct; mesoscutum transverse and without distinct notauli.<ref name=Pitkin2004>Pitkin, B.R. (2004) Notes on families: Encyrtidae. Universal Chalcidoidea Database. [https://www.nhm.ac.uk/our-science/data/chalcidoids/encyrtidae.html www.nhm.ac.uk]</ref> There are illustrations of these features on another [[African Arthropods/Encyrtidae|page of the '''African Arthropods project''']].<br> 1a Tarsi with four segments ........ 2<br> 1b Tarsi with five segments ........ 3 ==2 Tarsi with four segments== *Marginal cilia of forewing very long (fig. 2 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key] and Prinsloo & Anneke, 1979<ref name=Prinsloo&Anneke1979/>); axillae indistinct (fig. 3 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb]); funicle with five or six segments - **'''''Anthemus''''' <small>HOWARD, 1896</small> ***22 species worldwide; 12 Afrotropical species. ***Photos: [http://ponent.atspace.org/fauna/ins/fam/encyrtidae/anthemus_hab.htm Ponent, Catalonia] ***Paper: Prinsloo, G. L., & Neser, O. C. (1989). A revision of the genus Anthemus Howard (Hymenoptera: Encyrtidae) in the Afrotropical region. Revue de Zoologie Africaine, 103(1), 51-72. *Marginal cilia of forewing short (cf. fig. 4 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key] and Prinsloo & Anneke, 1979<ref name=Prinsloo&Anneke1979/>), the longest cilia never much longer than the setae on the submarginal vein; axillae are distinct and meet medially; funicle with two to four segments - [[File:Mercet 1921 7 Arrenophagus parasite in Alacaspis rosae p54.jpg|thumb|''Arrhenophagus chionaspidis'' before emergence from scale host, Spain.]][[File:Mercet 1921 6 Arrhenophagus chionaspidis female antenna p53.jpg|thumb|''Arrhenophagus chionaspidis'' female antenna]] **'''''Arrhenophagus''''' <small>AURIVILLIUS, 1888</small> ***Photos: [https://www.nhm.ac.uk/our-science/data/chalcidoids/database/media.dsml?IMAGENO=chalc071&VALGENUS=Arrhenophagus&VALSPECIES=albitibiae&isVideo= Universal Chalcidoidea Database] [https://takagi.tenteki.org/%E5%A4%A9%E6%95%B5%E5%9B%B3%E9%91%912/%E3%82%AF%E3%83%AF%E3%82%B7%E3%83%AD%E3%82%AB%E3%82%A4%E3%82%AC%E3%83%A9.htm takagi.tenteki] ***Papers: [https://journals.flvc.org/mundi/article/view/129680 '''Suh S-J. 2021.''' Parasitoids (Hymenoptera: Chalcidoidea) of the white peach scale, Pseudaulacaspis pentagona (Targioni-Tozzetti) (Hemiptera: Diaspididae) on Prunus salicina Lindl. (Rosales: Rosaceae) in South Korea. Insecta Mundi 0885: 1–5.] [http://doi.org/10.5281/zenodo.3697168 '''Suh, Soo-Jung, 2018.''' Parasitoids (Hymenoptera: Chalcidoidea) reared from Pseudaulacaspis cockerelli (Cooley) (Hemiptera: Coccoidea) in the Republic of Korea, Insecta Mundi 612, pp. 1-6 : 3-4] [https://doi.org/10.4308/hjb.19.3.110 '''Muniappan, R., Watson, G. W., Evans, G. A., Rauf, A., & Von Ellenrieder, N. (2012). Cycad aulacaspis scale, a newly introduced insect pest in Indonesia. HAYATI Journal of Biosciences, 19(3), 110-114., R., Watson, G. W., Evans, G. A., Rauf, A., & Von Ellenrieder, N. (2012).''' Cycad aulacaspis scale, a newly introduced insect pest in Indonesia. HAYATI Journal of Biosciences, 19(3), 110-114.] *** 2 species worldwide; 1 Afrotropical species: ****''Arrhenophagus chionaspidis'' (worldwide) ==3 Tarsi five-segmented== *3a Forewing without stigmal, marginal or postmarginal veins, with an infuscated patch (fig. 4 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key]); on the head, the scrobes are moderately deep, in the shape of aninverted V, their confluence is separated medially by a membranous joint that extends to the front of the vertex; a similar membrane runs transversely between the eyes where the fronto-vertex adjoins the face (fig. 5 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key] and figs 1, 13, 20, 24 of Annecke & Mynhardt (1974)<ref name=AnneckeMynhardt1974>Annecke, DP & Mynhardt, M.J., 1974. On some new and described species of arrhenophagine Encyrtidae (Hymenoptera). Journal of the Entomological Society of southern Africa, 37(1), pp.35-47. [https://journals.co.za/doi/abs/10.10520/AJA00128789_2835 DOI] [https://journals.co.za/doi/pdf/10.10520/AJA00128789_2835 PDF]</ref>) - **'''''Arrhenophagoidea''''' <small>Girault, 1915</small><br> ***''Arrhenophagoidea'' and ''Arrhenophagus'' are morphologically similar, except that the tarsi are four-segmented in ''Arrhenophagus'' and five-segmented in ''Arrhenophagoidea''. Species of both genera are very small (body length about 0.5 mm). ***Four Afrotropical species: ****''Arrhenophagoidea chaetacmae'' Annecke & Prinsloo, 1974 (South Africa) ****''Arrhenophagoidea neseri'' Prinsloo, 1974 (South Africa) ****''Arrhenophagoidea rolaspidis'' Annecke & Prinsloo, 1974 (South Africa) ****''Arrhenophagoidea sierra'' Annecke & Prinsloo, 1974 (South Africa) *3b Forewing venation partly or well-developed; head without membranous features above the scrobes ........ 4 ===4 (Fore wing venation at least partly developed; head without membranous interruptions)=== *4a Posterior margin of mesosetum with two round projections, each fitting into an indentation in anterior margin of axillae (fig. 6 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key]); forewing with marginal cilia unusually long along caudal wing margin (fig. 7 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key]); egg parasitoids of Tettigometridae - **'''''Psyllechthrus''''' <small>GHESQUIERE, 1958</small> ***A single species, ''Psyllechthrus oophagus'' is known - from Congo, Democratic Republic of Congo, Kenya, Malawi, Namibia, South Africa, Zimbabwe.<ref name=Noyes2019>Noyes, J.S. 2019. Universal Chalcidoidea Database. The Natural History Museum, London. https://www.nhm.ac.uk/our-science/data/chalcidoids/database/index.dsml</ref> ***''Psyllechthrus oophagus'' has been reared from the eggs of ''Nototettigometra patruelis'', which is thought to be its only host.<ref name=Prinsloo1985>Prinsloo, G.L. 1985, Afrotropical Encyrtidae (Hymenoptera: Chalcidoidea): new records and notes. Journal of Natural History 19:281</ref> ***Photographs of ''Nototettigometra patruelis'' eggs with tiny wasps that are probably ''Psyllechthrus oophagus'': [http://www.biodiversityexplorer.info/bugs/tettigometridae/hilda_patruelis.htm] and [https://www.inaturalist.org/observations/180134054] <gallery mode=packed heights=300> Psyllechthrus oophagus 192741071 a.jpg|''Psyllechthrus oophagus'' Psyllechthrus oophagus 192741071 c.jpg|''Psyllechthrus oophagus'' on eggs of ''Nototettigometra patruelis''. </gallery> *4b Margin of mesoseutum without two round projections fitting into indentations in the anterior margin of the axillae; marginal cilia of forewing not unusually long; not parasites of Tettigometridae ........ 5 ===5 (Posterior margin of mesoscutum without two round projections fitting into the anterior margin of axillae, forewing with marginal cilia not unusually long)=== *5a Fore femur and tibia greatly swollen, the apex of the latter with two blunt spines in addition to the strigil; antenna eleven-segmented, the segments of pedicel, funicle and club similar in shape; head and body hardly encyrtiform (fig. 9 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) **'''''Sanghalia''''' <small>RISBEC, 1955</small> ***A single species from Congo, ''Sanghalia kerandeli'' *5b Fore femur and tibia at most slightly swollen, the latter without spines; antenna otherwise, usually clavate................6 ===6 (Fore femur and tibia not greatly swollen, fore tibia without spines)=== *6a Funicle with less than six segments........ 7 *6b Funicle with six or seven segments........ 16 ==7 Funicle with less than six segments== *7a Antenna (fig. 10 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) extensively flattened and expanded - both scape and flagellum leaf-like; the club is not segmented; the funicle has three to five transverse segments; Pseudococeid parasitoids -[[File:Zaplatycerus fullawayi Timberlake 1925 Plate IX Fig. 1.jpg|thumb|''Zaplatycerus fullawayi''; A. female antenna; B. Male antenna; C. Female mandible frontal view]] **'''''Zaplatycerus''''' Timberlake, 1925 ***Synonyms include: ''Tropidophryne'' Compere, 1931; ''Neoplatycerus'' Subba Rao, 1965; ''Avernes'' Noyes et Woolley, 1994; ''Assamencyrtus'' Singh, 2006.<ref name=Trjapitzin2018>Trjapitzin, V. A. (2018). A Review of the Encyrtid-Wasp Genus ''Zaplatycerus'' Timberlake, 1925 (Hymenoptera, Chalcidoidea: Encyrtidae) of the World Fauna, Parasitoids of Mealybugs (Hemiptera, Pseudococcidae). Entomological Review, 98, 787-792.</ref> ***16 species worldwide; 4 Afrotropical species<ref name=Noyes2019/> ***Description and images of ''Zaplatycerus notialis'' on [https://www.researchgate.net/publication/271666428 Researchgate] Afrotropical species *7b Antenna not extensively flattened, but the scape may be expanded ventrally........ 8 ===8 (Antenna not extensively flattened; scape may be expanded)=== *8a Funicle with four segments ........ 9 *8b Funicle with five segments ........ 10 ===9 (Funicle with four segments)=== *9a Apex of scutellum with two lamelliform (flattened) setae (cf. figs 27 & 28 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>, and ''Habrolepis'', 38b below); forewing distinctly darkened, patterned; body flattened dorsoventrally; parasitoids of armored scale insects - **'''''Caenohomalopoda''''' Tachikawa, 1979 ***11 species worldwide; 1 Afrotropical species: ****''Caenohomalopoda shikokuensis'' a parasitoid of armored scales, ''Froggattiella penicillata'', ''Odonaspis'' spp. (South Africa) ****Description and figures - [https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/9592/1/20(3-4)_p90-96.pdf Tachikawa, 1956]<ref name=Tachikawa1956>Tachikawa, T. (1956). Description of a new species of the genus Pseudhomalopoda Cirault from Japan, with a list of the known species and their hosts of the Habrolepis-like genera (Hymenoptera: Encyrtidae). Insecta matsumurana, 20(3-4), 90-96. https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/9592/1/20(3-4)_p90-96.pdf</ref> *9b Scutellum without scale-like setae; forewing transparent; body not flattened dorsoventrally; parasitoids of bees - **'''''Xylencyrtus''''' Annecke, 1968 ***Two Afrotropical species: ''Xylencyrtus mumifex'', a parasitoid of ''Allodapula melanopus'', is known from South Africa; and ''Xylencyrtus tridens'' is known from Cameroon, Kenya, South Africa, and Uganda and is a parasitoid of several xylocopine bee species (Tribe Allodapini).<ref name=Noyes2019/> ***Description and figures - [https://journals.co.za/doi/pdf/10.10520/AJA00128789_3102 Annecke, 1968]<ref name=Annecke1968>Annecke, D. P. (1968). Records and Descriptions of African Encyrtidae-4 (Hymenoptera: Chalcidoidea). Journal of the Entomological Society of southern Africa, 31(2), 249-264.</ref> ===10 (Funicle with five segments)=== *10a Antennal club not divided (a single segment) - **'''''Trechnites''''' Thomson, 1876 ***The body is blackish, with a metallic green scutellum; marginal and postmarginal veins of forewing punctiform or very short; parapsidal sulci present; ***Parasitoids of psyllids. *** 30 species worldwide; 3 Afrotropical species: ****''Trechnites angolensis'' associated with the legume ''Isoberlinia'' sp. (Angola) ****''Trechnites manaliensis'' a parasitoid of ''Euphyllura eastopi'', ''Euphyllura longiciliata'', ''Psylla hyalina'' (South Africa) ****''Trechnites morulus'' associated with ''Ceroplastes'' sp. (South Africa) *10b The antennal club has two or three segments ........ 11 ===11 (Antennal club with two or three segments)=== *11a Antennal club with two segments. (Maxillary palpi each with two segments, the labial not segmented; mandible tridentate (fig. 11 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), the upper tooth retracted; parasitic in Pseudococcidae) - [[File:Pseudectroma europaeum Fauna ibérica p192 Fig.65.jpg|thumb|Female ''Pseudectroma europaeum'', Spain]] **'''''Pseudectroma''''' Girault , 1915 ***''Timberlakia'' Mercet, 1925 is a synonym<ref name=Noyes2019/> ***16 species worldwide; 3 Afrotropical species: ''Pseudectroma cussoniae'' (Madagascar), ''Pseudectroma gilvum'' (South Africa), ''Pseudectroma signatum'' (Israel, South Africa)<ref name=Noyes2019/> ***Parasitoids - hosts include soft scales (Coccidae) and mealybugs (Pseudococcidae)<ref name=Noyes2019/> *11b Club with three segments ........ 12 ===12 (Antennal club with three segments)=== *12a Ovipositor protruding from the end of the metasoma - **'''''Acerophagus''''' Smith, 1880 ***''Pseudaphycus'' is a synonym of ''Acerophagus'' (see 13 below). ***''Acerophagus'' species are parasitoids of mealybugs (Pseudococcidae). ***iNaturalist has images of ''Acerophagus'' (CC-BY-NC).<ref name=iNatAcerophagus>https://www.inaturalist.org/taxa/250166 ''Acerophagus'' photographs on iNaturalist (CC-BY-NC)</ref> *12b Ovipositor not distinctly protruding from the end of the metasoma ........ 14 ===13 (Ovipositor protruding from the end of the metasoma - ''Acerophagus'')=== *13a Antennal club white; maxillary palpi each with four segments, the labial with three segments - **Afrotropical species of ''Acerophagus'' with a white antennal club (described as ''Pseudaphycus'') include ''A. angelicus'', ''A. dysmicocci'', ''A. ferrisianae'', ''A. maculipennis'', ''A. mundus'', ''A. notativentris '', ''A. perdignus'', ''A. prosopidis''. *13b Antennal club not white; maxillary palpi each with four segments, the labial with two segments - **Afrotropical species of ''Acerophagus'' with an antennal club that is not white (described as ''Acerophagus'') include ''A. coccois'', ''A. pallidus''. ===14 (Ovipositor not protruding or just protruding)=== *14a Mandible with two teeth; maxillary palpi each have two segments, the labial not segmented; paratergites present; Male antenna ramose, rami on funicle segments I-IV - **'''''Tetracnemoidea''''' Howard, 1898 ***''Tetracnemoidea'' species are parasitoids of mealybugs (Pseudococcidae).<ref name=Noyes2019/> ***Afrotropical species: ****''T. brevicornis'' (Girault) (Worldwide; Ghana in Afrotropics) ****''T. coffeicola'' (Kerrich) (Kenya, Uganda) ****''T. peregrina'' (Compere) (Worldwide; Ghana, South Africa in Afrotropics) ****''T. sydneyensis'' (Timberlake) (Worldwide; Ghana in Afrotropics) *14b Mandible with three or more teeth; palpi do not have two segments; no paratergites; not parasitoids of mealybugs ................15 ===15 (Mandible with three or more teeth; palpi do not have two segments; no paratergites; not parasitoids of mealybugs)=== *15a Head and body dark brown to blackish-brown, non-metallic except for frontovertex which may have a very slight metallic tinge; parasitic in aculeate Hymenoptera - **'''''Xylencyrtus''''' Annecke, 1968 ***Afrotropical species: ****''Xylencyrtus mumifex'', a parasitoid of ''Allodapula melanopus'' (South Africa); and ****''Xylencyrtus tridens'' is a parasitoid of several xylocopine bee species (Tribe Allodapini) (Cameroon, Kenya, South Africa, and Uganda).<ref name=Noyes2019/> *15b Head and body predominantly black, the scutellum brilliant metallic green in colour; parasitic in Psyllidae - **'''''Trechnites''''' Thomson, 1876 ***The body is blackish, with a metallic green scutellum; marginal and postmarginal veins of forewing punctiform or very short; parapsidal sulci present; ***Parasitoids of psyllids. ==16 Funicle with six or seven segments== *16a Hind tibia foliaceously flattened (fig. 12 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 17 *16b Hind tibia not or only slightly flattened................ 18 ===17 (Hind tibia foliaceously flattened)=== *17a Antennal club three-segmented or not segmented; parasitoids of Aphrophoridae and Cicadellidae. Male antenna may have six rami (fig. 14 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) - [[File:Neocladia iNat 170580378.jpg|thumb|''Neocladia'' sp., Australia]] **'''''Neocladia''''' Perkins, 1906 ***''Carabunia'' Waterston, 1928 is a synonym of ''Neocladia''<ref name=Noyes2019/> ***iNaturalist has images of ''Neocladia''.<ref name=iNatNeocladia>https://www.inaturalist.org/taxa/253254 ''Neocladia'' photographs on iNaturalist (including some CC-BY)</ref> ***Afrotropical species:<ref name=Noyes2019/> ****''Neocladia gigantica'' is a parasitoid of ''Ptyelus flavescens'', the Yellow Raintree Spittlebug (Uganda). ****''Neocladia senegalensis'' (Senegal, South Africa). ****''Neocladia tibialis'' is a parasitoid of ''Batrachomorphus capeneri'', a leafhopper (South Africa). ===18 (Hind tibia not or only slightly flattened)=== *18a Wings markedly reduced ................19 *18b Wings not greatly reduced ............. 25 ==19 Wings markedly reduced== *19a Scutellum with a flange or lamella (fig. 15 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), in profile this flange shows as a thin, flat, caudal projection of the apex of scutellum................20 *19b Scutellum without a flange................21 ===20 (Wings reduced, scutellum with a flange or lamella)=== *20a Mandible with two acute teeth; parasitoids of bees - [[File:Ericydnus inat 170283716 davidfdz b82, some rights reserved (CC-BY).jpg|thumb|''Ericydnus'' sp., Spain]] **'''''Ericydnus''''' Walker, 1837 *** 33 species worldwide; Afrotropical species? *** ''Ericydnus'' sp. - 2 specimens at ARC-PPRI (https://www.gbif.org/occurrence/search?dataset_key=b2ee8537-2a6c-4b4b-965a-538b47788606&taxon_key=1378896) *20b Mandible with three teeth; parasitoids of Coccidae - [[File:Paraphaenodiscus bicolor Fauna ibérica Ricardo García Mercet 1921.jpg|thumb|Female ''Paraphaenodiscus bicolor'', Spain]] **'''''Paraphaenodiscus''''' Girault, 1915 ***20 species worldwide; 10 Afrotropical species: ***Afrotropical species: ****''Paraphaenodiscus africanus'' Prinsloo (South Africa) ****''Paraphaenodiscus ceroplastodesi'' (Risbec) is a parasitoid of ''Ceroplastes'' species (Senegal) ****''Paraphaenodiscus chrysocomae'' Prinsloo (South Africa) ****''Paraphaenodiscus munroi'' Prinsloo is a parasitoid of ''Pulvinaria iceryi'' (South Africa) ****''Paraphaenodiscus niger'' Prinsloo is a parasitoid of ''Pulvinaria iceryi'' (South Africa) ****''Paraphaenodiscus paralis'' Prinsloo and Mynhardt is a parasitoid of ''Plagiochloa uniolae'' (South Africa) ****''Paraphaenodiscus pavoniae'' Risbec is a parasitoid of ''Ceroplastes'' and ''Pulvinaria'' species (Senegal, South Africa, Zimbabwe) ****''Paraphaenodiscus pedanus'' Prinsloo and Mynhardt is a parasitoid of ''Plagiochloa uniolae'' (South Africa) ****''Paraphaenodiscus risbeci'' Ghesquiere is a parasitoid of the moth ''Sesamia cretica'' (Senegal, Sudan) ****''Paraphaenodiscus rizicola'' (Risbec) has been associated with rice plants (Cameroon, Swaziland, Zimbabwe) ===21 (Wings reduced, scutellum without a flange)=== *21a Antenna nine-segmented, the club not segmented; mandible bidentate; parasitic in Pseudococcidae. Male antenna six-segmented, segments II - V each with a ramus - **'''''Tetracnemus''''' Westwood, 1837 ***iNaturalist has images of ''Tetracnemus''.<ref name=iNatTetracnemus>https://www.inaturalist.org/taxa/250503 ''Tetracnemus'' photographs on iNaturalist (some CC-BY-NC)</ref> ***37 species worldwide; 2 Afrotropical species: ****''Tetracnemus bifasciatellus'' (Mercet) (South Africa) ****''Tetracnemus gumilevi'' Pilipjuk and Trjapitzin (Ethiopia) *21b Antenna eleven-segmented, the club with three segments; mandible otherwise; not parasitic in Pseudococcidae................22 ===22 (Antenna eleven-segmented, the club with three segments)=== *22a Scutellum with a semi-erect tuft of bristles, these strong bristles rarely scattered and not forming a distinct tuft........................23 *22b Scutellar tuft of bristles absent........ 24 ===23 (Wings reduced, scutellum with a semi-erect tuft of bristles)=== *23a Mandible edentate, broadly rounded apically (fig. 16 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); gonostyli (3rd valvulae) absent - **'''''Encyrtus''''' Latreille, 1809 ***96 species worldwide; 15 Afrotropical species: ****''Encyrtus aquilus'' is a parasitoid of Coccidae ''Ceroplastes'' and ''Gascardia'' species (South Africa) ****''Encyrtus aurantii'' is a parasitoid of Hemiptera including Aleyrodidae, Coccidae, Diaspididae, Eriococcidae, Pseudococcidae (Cameroon, Gabon, Ghana, Madagascar, Malawi, Mauritius, Mozambique, Senegal, Seychelles, South Africa, Uganda, Zimbabwe) ****''Encyrtus barbiger'' is a parasitoid of ''Parasaissetia litorea'' (South Africa) ****''Encyrtus bedfordi'' is a parasitoid of ''Waxiella mimosae'' (South Africa) ****''Encyrtus cotterelli'' is a parasitoid of ''Sahlbergella'' species (Ghana) ****''Encyrtus decorus'' is a parasitoid of ''Pulvinaria'' and ''Saissetia'' species (Zimbabwe) ****''Encyrtus fuliginosus'' is a parasitoid of a range of Coccidae (Eritrea, Ethiopia, Kenya, Madagascar, Mozambique, Namibia, South Africa) ****''Encyrtus hesperus'' (Gambia, Ivory Coast) ****''Encyrtus imitator'' (Cameroon, Gabon, Uganda) ****''Encyrtus infelix'' is a parasitoid of a range of Coccidae (Kenya, Madagascar, Seychelles, Zimbabwe) ****''Encyrtus melas'' is a parasitoid of ''Gascardia'' and ''Tachardina'' species (South Africa) ****''Encyrtus palpator'' ((Cameroon) ****''Encyrtus sacchari'' is a parasitoid of ''Pulvinaria'' species on rice and sugar cane (Benin, Cameroon, Gabon, Gambia, Ivory Coast, Kenya, Nigeria, Senegal, South Africa, Zimbabwe) ****''Encyrtus saliens'' is a parasitoid of ''Pulvinaria'' species (South Africa) ****''Encyrtus signifer'' (Cameroon, Gabon) *23b Mandible tridentate; gonostyli present - [[File:Diversinervus.jpg|thumb|''Diversinervus'' sp., New Zealand]] **'''''Diversinervus''''' Silvestri, 1915 ***iNaturalist has images of ''Diversinervus''.<ref name=iNatDiversinervus>https://www.inaturalist.org/taxa/250172 ''Diversinervus'' photographs on iNaturalist (CC-BY-NC)</ref> ***12 species worldwide; 10 Afrotropical species: ****''Diversinervus cervantesi'' is a parasitoid of Coccidae (South Africa) ****''Diversinervus desantisi'' is a parasitoid of ''Pulvinaria'' species (Eritrea, Ethiopia) ****''Diversinervus elegans'' is a parasitoid of a range of Coccidae (Angola, Eritrea, Ethiopia, Kenya, South Africa) ****''Diversinervus masakaensis'' is a parasitoid of ''Saissetia oleae'' (Uganda) ****''Diversinervus orarius'' is a parasitoid of a ''Ctenochiton'' sp. (South Africa) ****''Diversinervus redactus'' is a parasitoid of a ''Ceroplastes'' sp. (South Africa) ****''Diversinervus scutatus'' is a parasitoid of a ''Ceronema'' sp. (South Africa) ****''Diversinervus silvestrii'' is a parasitoid of ''Coccus'' species (Mauritius, South Africa) ****''Diversinervus smithi'' is a parasitoid of ''Saissetia oleae'' (South Africa) ****''Diversinervus stramineus'' is a parasitoid of ''Coccus alpinus'', ''Coccus celatus'', and ''Saissetia persimilis'' (Kenya, South Africa) ===24 (Wings reduced, scutellar tuft of bristles absent)=== *24a Apterous, or wings represented by a stub - **'''''Metaphycus''''' Mercet, 1917 ***476 species worldwide; 86 Afrotropical species: ****Many pics of winged species on iNaturalist (but not Afrotropical and not apterous) *24b Fore wing reduced in size, but with venation distinct (fig. 17 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) - [[File:Neococcidencyrtus-poutiersi-Mercet-1922-A-Lateral-view-B-Dorsal-view-C W640.jpg|thumb|''Neococcidencyrtus poutiersi'', Iran.]] **'''''Neococcidencyrtus''''' Compere, 1928 ***20 species worldwide; 5 Afrotropical species: ****''Neococcidencyrtus brenhindis'' (Madagascar) ****''Neococcidencyrtus cliradainis'' (Cameroon) ****''Neococcidencyrtus poutiersi'' is a parasitoid of ''Furchadaspis zamiae'', cycad scale (South Africa) Fig. 5. in https://www.researchgate.net/publication/343006453 ****''Neococcidencyrtus pudaspidis'' is a parasitoid of ''Pudaspis newsteadi'' (South Africa) ****''Neococcidencyrtus syndodis'' (South Africa) ==25 Wings not greatly reduced== *25a Dorsum of scutellum with a longitudinal, inconspicuous, median keel - [[File:Encyrtidae iNat 178385702 08.jpg |thumb|''Pentelicus'' sp., South Africa]] **'''''Pentelicus''''' Howard, 1895 ***Head and thorax pitted; antennal club three-segmented, obliquely truncate apically. ***10 species worldwide; ? Afrotropical species: *25b Scutellum without a median keel................26 ===26 (Scutellum without a median keel)=== *26a Head with a horn-like protuberance jutting from middle of face just below antennal Insertions - [[File:Paratetracnemoidea malenotti Fauna iberica (1921).jpg|thumb|Male ''Paratetracnemoidea malenotti'']][[File:Paratetracnemoidea malenotti, head, lateral view.jpg|thumb|''Paratetracnemoidea malenotti'', lateral view of head]] **'''''Paratetracnemoidea''''' Girault , 1915 ***''Rhinoencyrtus'' Mercet, 1918 is a synonym of ''Paratetracnemoidea'' ***Photos at https://www.waspweb.org/chalcidoidea/Encyrtidae/Encyrtinae/Paratetracnemoidea/index.htm ***5 species worldwide; 3 Afrotropical species: ****''Paratetracnemoidea breviventris'' - no associates known (Tanzania) ****''Paratetracnemoidea cornis'' - no associates known (South Africa) ****''Paratetracnemoidea malenotti'' - no associates known (Gambia, Nigeria, Sudan) *26b Head without facial protuberance................ 27 ===27 (Head without facial protuberance)=== *27a Fore wing with stigmal vein branching away before venation reaches cephalic wing margin (figs 18- 22 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); postmarginal vein never reaching cephalic edge of wing................28 *27b Fore wing venation normal, at most marginal vein punctiform (figs 34, 63, 82, 89 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); or rarely, if marginal vein absent, then postmarginal touches edge of wing (fig. 80 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)................32 ==28 Fore wing with stigmal vein branching away before venation reaches cephalic wing margin== *28a Anterior margin of frontovertex produced to form a prominent ridge that overhangs upper limits of scrobes; mandibles diminutive - **''''' Amira ''''' Girault , 1913 *** 3 species worldwide; 1 Afrotropical species: ****''Amira durantae'' is a parasitoid of spiders ''Nephila inaurata'' and ''Nephila madagascarensis'' (Madagascar) *28b Frontovertex rounded on to face, without an anterior ledge; mandibles relatively large, well developed........ 29 ===29 (Frontovertex rounded on to face, without an anterior ledge; mandibles relatively large)=== *29a Antennal scrobes sulcate, impressed on face as an inverted V, their lateral margins sharply angled (fig. 23 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Male and female antennae identical in shape and segmentation; parasitic in Aclerdidae - **''''' Allencyrtus ''''' Annecke and Mynhardt, 1973 *** 1 species worldwide - Afrotropical: ****''Allencyrtus monomorphus'' is a parasitoid of an Aclerdid scale, ''Rhodesaclerda'' sp. (South Africa) ****Description of genus and species: Annecke & Mynhardt (1973) [https://journals.co.za/doi/pdf/10.10520/AJA00128789_3436 PDF]<ref name=>Annecke, DP & Mynhardt, M. J. (1973). New and Iittle known African Encyrtidae, with descriptions of two new genera (Hymenoptera: Chalcidoidea). Journal of the Entomological Society of southern Africa, 36(2), 211-28. [https://journals.co.za/doi/pdf/10.10520/AJA00128789_3436 PDF]</ref> *29b Antennal scrobes not impressed on face as an inverted V with sharply angled lateral margins ....... 30 ===30 (Antennal scrobes not impressed on face as an inverted V with sharply angled lateral margins)=== *30a Antennal club three-segmented; mandible edentate, broadly rounded apically (fig. 24 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); parasitic in Coccidae and Stictococcidae -[[File:Aethognathus afer female Silvestri 1915 with inset.jpg|thumb|''Aethognathus afer'', female; inset shows detail of stigmal and postmarginal veins]] **''''' Aethognathus ''''' Silvestri, 1915 ***5 species worldwide; all Afrotropical: ****''Aethognathus afer'' is a parasitoid of scales, ''Stictococcus diversiseta'' and ''Stictococcus multispinosus'' (Benin, Ghana) ****''Aethognathus bicolor'' is a parasitoid of the scale ''Stictococcus multispinosus'' (Uganda) ****''Aethognathus cavilabris'' is a parasitoid of coccid scales, ''Saissetia''and ''Stictococcus'' spp. (Congo, Uganda) ****''Aethognathus khryzhanovskyi'' - no associates known (Equatorial Guinea) ****''Aethognathus unicolor'' is a parasitoid of scales, ''Stictococcus gowdeyi'' and ''Stictococcus multispinosus'' (Nigeria, Uganda) *30b Antennal club not segmented, obliquely truncate; mandible tridentate; not parasitic in scale insects........ 31 ===31 (Antennal club not segmented, obliquely truncate; mandible tridentate)=== *31a Frontovertex and face with large pits, each with a strong metallic lustre; antennal scape (fig. 25 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) strongly expanded ventrally; parasitic in eggs of spiders - **''''' Proleurocerus ''''' Ferriere, 1935 *** 5 species worldwide; 2 Afrotropical species: ****''Proleurocerus clavatus'' - no associates known (Zimbabwe) ****''Proleurocerus zululandiae'' - no associates known (South Africa) *31b Frontovertex at most finely punctate, non-metallic; antennal scape at most slightly expanded ventrally; parasitic in Neuroptera nymphs - [[File:Isodromus iNat 147864868.jpg |thumb|''Isodromus'' sp., Mexico.]][[File:Isodromus vinulus, male, Spain.jpg|thumb|''Isodromus vinulus'', a parasitic wasp in the family Encyrtidae; male]] **''''' Isodromus''''' Howard, 1887 *** 26 species worldwide; 1 Afrotropical species: ****''Isodromus timberlakei'' is a parasitoid of a ''Chrysopa'' species (South Africa) ==32 Fore wing venation normal, at most marginal vein punctiform; or rarely, if marginal vein absent, then postmarginal touches edge of wing== *32a Scutellum with a semi-erect tuft of bristles, these strong bristles rarely scattered and not forming a distinct tuft................ 33 *32b Scutellum without a tuft of bristles, the setae recumbent, except for one subapical pair which is sometimes present................37 ==33 Scutellum with a semi-erect tuft of bristles== *33a Head elongate in dorsal view, longer than wide or almost so, the greater part of each eye placed dorsally; mesoscutum (fig. 26 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) usually with a tuft of coarse bristles, but this tuft lacking in some species - [[File:Diversinervus.jpg|thumb|''Diversinervus'' sp., New Zealand]] **''''' Diversinervus''''' Silvestri, 1915 ***iNaturalist has images of ''Diversinervus''.<ref name=iNatDiversinervus/> *** 12 species worldwide; 10 Afrotropical species: ****''Diversinervus cervantesi'' is a parasitoid of coccid scales, ''Ceroplastes floridensis'', ''Coccus hesperidum'', ''Pulvinaria'' spp., ''Pulvinariella mesembryanthemi'', ''Saissetia coffeae'', ''Saissetia oleae'' (South Africa) ****''Diversinervus desantisi '' is a parasitoid of coccid scales, ''Pulvinaria'' sp. (Eritrea, Ethiopia) ****''Diversinervus elegans'' is a parasitoid of a wide range of coccid scales (Angola, Eritrea, Ethiopia, Kenya, South Africa) ****''Diversinervus masakaensis'' is a parasitoid of coccid scales, ''Saissetia oleae'' (Uganda) ****''Diversinervus orarius'' is a parasitoid of coccid scales, ''Ctenochiton'' sp. (South Africa) ****''Diversinervus redactus'' is a parasitoid of coccid scales, ''Ceroplastes'' sp. (South Africa) ****''Diversinervus scutatus'' is a parasitoid of coccid scales, ''Ceronema'' sp. (South Africa) ****''Diversinervus silvestrii'' is a parasitoid of coccid scales, ''Coccus'' spp. (Mauritius, South Africa) ****''Diversinervus smithi'' is a parasitoid of coccid scales, ''Saissetia oleae'' (South Africa) ****''Diversinervus stramineus'' is a parasitoid of coccid scales, ''Coccus alpinus'', ''Coccus celatus'', ''Saissetia persimilis'' (Kenya, South Africa) *33b Head not longer than wide, eyes not placed dorsally; mesoscutum never with a tuft of bristles................34 ===34 (Head not longer than wide, eyes not placed dorsally; mesoscutum never with a tuft of bristles)=== *34a Antenna enlarged, flattened, the club two-segmented, very large, almost as long as entire funicle; mandible bidentate; parasitic in Pseudococcidae. Head and body generally smooth and polished, brilliantly metallic in colour - **''''' Chrysoplatycerus''''' Ashmead, 1889 *** 6 species worldwide; 1 Afrotropical species: ****''Chrysoplatycerus splendens'' is a parasitoid of mealybugs, ''Dysmicoccus'' spp., ''Ferrisia virgata'', ''Ferrisiana virgata'', ''Formicococcus njalensis'', ''Planococcoides'' spp., ''Pseudococcus'' spp. (Ghana, South Africa) *34b Antenna not broadened and flattened, the club three-segmented; mandibles not bidentate; not parasitic in mealybugs................ 35 ===35 (Antenna not broadened and flattened, the club three-segmented)=== *35a Mandible edentate (fig. 16 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), broadly rounded apically; gonostyli absent; primary parasitoids of Coccidae - [[File:Encyrtus aurantii iNat 132121027 d.jpg|thumb|''Encyrtus aurantii'', Italy.]][[File:Encyrtus infelix iNat 159262263 a.jpg |thumb|''Encyrtus infelix'', New Zealand.]] **''''' Encyrtus''''' Latreille, 1809 *** 96 species worldwide; 15 Afrotropical species: ****''Encyrtus aquilus'' is a parasitoid of coccid scales, ''Ceroplastes'' sp., ''Gascardia'' sp., ''Gascardia destructor'' (South Africa) ****''Encyrtus aurantii'' is a parasitoid of many different Hemiptera from Aleyrodidae, Coccidae, Diaspididae, Eriococcidae, and Pseudococcidae (Cameroon, Gabon, Ghana, Madagascar, Malawi, Mauritius, Mozambique, Senegal, South Africa, Uganda, Zimbabwe) ****''Encyrtus barbiger'' is a parasitoid of a coccid scale ''Parasaissetia litorea'' (South Africa) ****''Encyrtus bedfordi'' is a parasitoid of a coccid scale ''Waxiella mimosae'' (South Africa) ****''Encyrtus cotterelli'' is a parasitoid of plant bugs, ''Sahlbergella'' spp., Miridae (Ghana) ****''Encyrtus decorus'' is a parasitoid of coccid scales ''Pulvinaria'' sp., ''Saissetia'' sp. (Zimbabwe) ****''Encyrtus fuliginosus'' is a parasitoid of coccid scales ''Coccus'', ''Lichtensia'', ''Pulvinaria'', ''Saissetia'', ''Saissetia oleae'', and ''Udinia'' species. (Eritrea, Ethiopia, Kenya, Madagascar, Mozambique, Namibia, South Africa) ****''Encyrtus hesperus'' - no associates known (Gambia, Ivory Coast) ****''Encyrtus imitator'' - no associates known (Cameroon, Gabon, Uganda) ****''Encyrtus infelix'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Coccus hesperidum'', ''Gascardia madagascariensis'', ''Lecanium hemisphaericum'', ''Protopulvinaria pyriformis'', ''Pulvinaria innumerabilis'', ''Pulvinaria urbicola'', ''Saissetia'' spp. (Kenya, Madagascar, Seychelles, Zimbabwe) ****''Encyrtus melas'' is a parasitoid of coccid scales ''Gascardia'' sp., ''Gascardia tachardiaformis'', and lac scales ''Tachardina'' sp. (South Africa) ****''Encyrtus palpator'' - no associates known (Cameroon) ****''Encyrtus sacchari'' is a parasitoid of coccid scales ''Pulvinaria'' spp. on rice and sugar cane (Benin, Cameroon, Gabon, Gambia, Ivory Coast, Kenya, Nigeria, Senegal, South Africa, Zimbabwe) ****''Encyrtus saliens'' is a parasitoid of coccid scales ''Pulvinaria delottoi'' spp., ''Pulvinariella'' spp. (South Africa) ****''Encyrtus signifer'' - no associates known (Cameroon, Gabon) *35b Mandible not edentate; gonostyli present; usually hyperparasitoids................36 ===36 (Mandible not edentate; gonostyli present; usually hyperparasitoids)=== *36a Ovipositor not or only slightly exserted at apex of metasoma - [[File:Cheiloneurus iNat 90442164 a.jpg|thumb|Male ''Cheiloneurus'' sp., USA]] [[File:Cheiloneurus iNat 47473995.jpg|thumb|Female ''Cheiloneurus'' sp., Canada]] **''''' Cheiloneurus''''' Westwood, 1833 *** 152 species worldwide; 15 Afrotropical species: ****''Cheiloneurus afer'' is a parasitoid or hyperparasitoid from coccid scales ''Pulvinarisca jacksoni'' (Ghana) ****''Cheiloneurus angustifrons'' is a parasitoid or hyperparasitoid from coccid scales ''Ceroplastes mimosae'', ''Waxiella mimosae'' (Sudan) ****''Cheiloneurus caesar'' is a hyperparasitoid of ''Dryinus orophilus'' in a delphacid planthopper (Mozambique) ****''Cheiloneurus carinatus'' is a parasitoid or hyperparasitoid from coccid scales ''Saissetia'' spp. and mealybugs ''Allococcus quaesitus'', ''Delottococcus quaesitus'', ''Ferrisiana virgata'', ''Nipaecoccus'' spp., ''Phenacoccus'' spp., ''Planococcoides'' spp., ''Pseudococcus'' spp. (Central African Republic, Democratic Republic of Congo, Eritrea, Ethiopia, Ghana, Ivory Coast, Kenya, Madagascar, Malawi, South Africa, Tanzania) ****''Cheiloneurus chiaromontei'' is a parasitoid or hyperparasitoid from coccid scales ''Saissetia oleae'' (Eritrea) ****''Cheiloneurus cyanonotus'' is a hyperparasitoid of Encyrtidae ''Epidinocarsis lopezi'', ''Gyranusoidea tebygi'', ''Homalotylus flaminius'' and Eulophidae ''Tetrastichus'' sp. in a variety of beetles, flies and Hemiptera (Cameroon, Congo, Democratic Republic of Congo, Gabon, Gambia, Ghana, Guinea-Bissau, Kenya, Malawi, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Zimbabwe) ****''Cheiloneurus elegans'' is a hyperparasitoid of Encyrtidae ''Epidinocarsis lopezi'' and Platygastridae ''Platygaster zosine'' in a variety of cecidomyiid midges, scales and mealybugs (Nigeria) ****''Cheiloneurus flavoscutatus'' is a parasitoid or hyperparasitoid from mealybugs ''Adelosoma phragmitidis'', ''Chaetococcus phragmitis'' (Ethiopia) ****''Cheiloneurus gonatopodis'' is a hyperparasitoid of pincer wasps ''Echthrodelphax'' sp., ''Pseudogonatopoides mauritianus'', ''Pseudogonatopus'' spp., ''Richardsidryinus'' sp. in delphacid planthoppers on sugar cane (Madagascar, Mauritius) ****''Cheiloneurus kuisebi'' is a parasitoid or hyperparasitoid from a mealybug ''Phenacoccus manihoti'' on cassava (Namibia) ****''Cheiloneurus leptulus'' is a parasitoid or hyperparasitoid from a ''Ceratina'' bee (Tanzania) ****''Cheiloneurus liorhipnusi'' is a parasitoid or hyperparasitoid from a lady beetle ''Chnootriba similis'', and a scentless plant bug ''Corizus hyalinus'' (Kenya, Senegal) ****''Cheiloneurus metallicus'' - no associates known (Madagascar) ****''Cheiloneurus obscurus'' is a parasitoid or hyperparasitoid from coccid scales ''Gascardia brevicauda'', ''Saissetia oleae'' (Eritrea) ****''Cheiloneurus orbitalis'' is a parasitoid or hyperparasitoid from an encyrtid ''Homalotylus'' sp., the coccid scale ''Saissetia oleae'' and green lacewings ''Chrysopa'' sp., ''Mallada handschini'', ''Suarius squamosa'' on citrus (South Africa) *36b Ovipositor protruding strongly, by about one-half length of metasoma. Metasoma usually truncate apically - [[File:Prochiloneurus bolivari, female, Spain.jpg|thumb|''Prochiloneurus bolivari'', female, Spain.]][[File:Prochiloneurus sp fem researchgate 363819988.jpg|thumb|''Prochiloneurus'' sp., Mato Grosso do Sul, Brazil]] **''''' Prochiloneurus''''' Silvestri, 1915 *** 30 species worldwide; 4 Afrotropical species: ****''Prochiloneurus aegyptiacus'' is a parasitoid or hyperparasitoid from Encyrtidae ''Anagyrus'' spp., ''Clausenia purpurea'', ''Epidinocarsis lopezi'', ''Gyranusoidea tebygi'', ''Homalotylus'' spp., ''Leptomastix'' spp., Pteromalidae ''Metastenus'' sp., lady beetles ''Chilocorus bipustulatus'', ''Exochomus flavipes'', ''Hyperaspis aestimabilis'', coccid scales ''Coccus hesperidum'', ''Saissetia coffeae'' and mealybugs ''Ferrisia virgata'', ''Ferrisiana virgata'', ''Maconellicoccus hirsutus'', ''Nipaecoccus vastator'', ''Nipaecoccus viridis'', ''Octococcus africanus'', ''Pedrococcus'' sp., ''Phenacoccus'' spp., ''Planococcoides'', ''Planococcus'' spp., ''Pseudococcus'' spp., ''Rastrococcus invadens'' (Congo, Democratic Republic of Congo, Egypt, Eritrea, Ethiopia, Gabon, Ghana, Ivory Coast, Namibia, Nigeria, South Africa, Tanzania, Togo) ****''Prochiloneurus bolivari'' is a parasitoid or hyperparasitoid from Encyrtidae ''Anagyrus'' sp., ''Blepyrus insularis'', ''Clausenia purpurea'', ''Epidinocarsis lopezi'', ''Leptomastix flava'', Coccidae, Eriococcidae, and Pseudococcidae (Congo, Democratic Republic of Congo, Nigeria, Sao Tomé and Principe, South Africa) ****''Prochiloneurus comperei'' is a parasitoid or hyperparasitoid from Coccidae ''Lecanium viride'', Margarodidae ''Icerya formicarum'', ''Palaeococcus bicolor'', and Pseudococcidae ''Nipaecoccus'' spp., ''Pseudococcus'' sp. (Eritrea, Ethiopia, Malawi, Senegal, South Africa, Tanzania) ****''Prochiloneurus pulchellus'' is a parasitoid or hyperparasitoid from Encyrtidae ''Anagyrus'' spp., ''Epidinocarsis lopezi'', ''Gyranusoidea tebygi'', ''Leptomastix nigrocoxalis'', Diaspididae, Eriococcidae, Margarodidae, and Pseudococcidae (Cameroon, Congo, Democratic Republic of Congo, Eritrea, Ethiopia, Gabon, Gambia, Ghana, Guinea-Bissau, Madagascar, Malawi, Nigeria, Rwanda, Seychelles, South Africa, Togo) ==37 Scutellum without a tuft of bristles== *37a Apex of scutellum with a pair of lamelliform setae (figs 27, 28)........ 38 *37b Scutellum without a pair of lamelliform setae........ 39 ===38 (Apex of scutellum with a pair of lamelliform setae)=== *38a Antenna (fig. 29 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) broadened and flattened, the funicle segments strongly transverse; eyes margined dorsally with white; fronto-occipital margin of head without a pair of lamelliform setae. Parasitic in [[w:Diaspididae|armored scale insects]] - **''''' Comperiella ''''' Howard, 1906 *** Links: [https://www.inaturalist.org/taxa/250283 iNaturalist] *** 11 species worldwide; 6 Afrotropical species: ****''Comperiella apoda'' is a parasitoid of ''Diclavaspis ehretiae'' (Namibia, South Africa) ****''Comperiella bifasciata'' is a parasitoid of many Diaspididae, and the coccid ''Saissetia coffeae'' (Madagascar, Mauritius, South Africa, Swaziland, Zambia, Zimbabwe) ****''Comperiella karoo'' - no associates known (South Africa) ****''Comperiella lemniscata'' is a parasitoid of ''Aonidiella'' spp., ''Chrysomphalus dictyospermi'' (South Africa) ****''Comperiella ponticula'' is a parasitoid of ''Clavaspis pituranthi'' (Namibia, South Africa) ****''Comperiella unifasciata'' is a parasitoid of ''Aonidiella'' spp., ''Aspidiotus'' spp., ''Pseudaonidia'' spp., ''Aleurodicus destructor'', ''Ceroplastes rubens'' (Mauritius) *38b Antenna not broadened and flattened; eyes not margined with white; fronto-occipital margin with a pair of small lamelliform setae. Parasitic in [[w:Diaspididae|armored scale insects]] - [[File:Habrolepis dalmanni Howard 1898 Fig.1.jpg|thumb|Female ''Habrolepis dalmanni'']][[File:Habrolepis dalmanni Howard 1898 Fig.2.jpg|thumb|Female ''Habrolepis dalmanni'']] **''''' Habrolepis ''''' Foerster, 1856 *** Links: [https://www.inaturalist.org/taxa/376512 iNaturalist] *** 17 species worldwide; 12 Afrotropical species: ****''Habrolepis aeruginosa'' - no associates known (Seychelles) ****''Habrolepis algoensis'' is a parasitoid of ''Aspidiotus capensis'' (South Africa) ****''Habrolepis apicalis'' is a parasitoid of ''Chionaspis minor'', ''Pinnaspis temporaria'' (Ghana) ****''Habrolepis dalmanni'' is a parasitoid of pit scale insects ''Asterodiaspis'' spp., ''Asterolecanium'' sp., coccid scale insects ''Didesmococcus'' sp., armored scale insects ''Lepidosaphes ulmi'', ''Melanaspis inopinata'', ''Targionia vitis'', mealybugs ''Pseudococcus'' sp., and moths ''Leucoptera'' sp. (South Africa, Uganda) ****''Habrolepis diaspidi'' is a parasitoid of armored scale insects ''Aonidiella'' spp., ''Chionaspis'' sp., ''Chrysomphalus'' spp., ''Diaspidiotus perniciosus'', ''Diaspis senegalensis'', ''Hemiberlesia lataniae'', ''Parlatoria ziziphi'', ''Pinnaspis strachani'', ''Pudaspis newsteadi'', ''Quadraspidiotus perniciosus'', ''Selenaspidius'' spp., ''Tecaspis visci'', ''Umbaspis regularis'' (Eritrea, Ethiopia, Mozambique, Senegal, South Africa, Zimbabwe) ****''Habrolepis guineensis'' is a parasitoid of armored scale insects ''Duplaspidiotus pavettae'' (Guinea) ****''Habrolepis namibensis'' is a parasitoid of armored scale insects ''Namaquea simplex'' (Namibia) ****''Habrolepis obscura'' is a parasitoid of armored scale insects ''Africaspis chionaspiformis'', ''Aonidiella orientalis'', ''Chionaspis'' sp., ''Diclavaspis ehretiae'', ''Ledaspis distincta'', ''Lindingaspis rossi'', ''Melanaspis corticosa'', ''Quadraspidiotus perniciosus'', ''Separaspis capensis'' (Namibia, Saudi Arabia, South Africa, Zimbabwe) ****''Habrolepis occidua'' is a parasitoid of armored scale insects ''Melanaspis phenax'', ''Morganella phenax'', ''Pseudotargionia'' spp. (Namibia, South Africa) ****''Habrolepis oppugnati'' is a parasitoid of armored scale insects ''Aspidiotus elaeidis'', ''Aspidiotus oppugnatus'' (Eritrea) ****''Habrolepis rouxi'' is a parasitoid of armored scale insects ''Aonidiella'' spp., ''Aspidiotus'' spp., ''Carulaspis minima'', ''Chrysomphalus'' spp., ''Hemiberlesia rapax'', ''Lepidosaphes newsteadi'', ''Parlatoria oleae'', ''Selenaspidius articulatus'' spp. (Kenya, Madagascar, Mozambique, South Africa, Swaziland, Uganda, Zimbabwe) ****''Habrolepis setigera'' is a parasitoid of armored scale insects ''Lindingaspis greeni'' (South Africa) ===39 (Scutellum without a pair of lamelliform setae)=== *39a Submarginal vein of fore wing with a subtriangular expansion (figs 30, 34 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) in its apical one-third, this expansion usually bearing a single strong seta........ 40 *39b Submarginal vein without a triangular expansion................43 ===40 (Submarginal vein of fore wing with a subtriangular expansion in its apical one-third)=== *40a Junction of frontovertex and face forming a transverse ledge above scrobes (fig. 35 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); antennal scape broadly expanded ventrally................41 *40b Frontovertex rounded on to face, not forming a ledge; antenna slender, the scape at most slightly expanded ventrally................42 ===41 (Junction of frontovertex and face forming a transverse ledge above scrobes; antennal scape broadly expanded ventrally)=== *41a Antenna entirely broadened and flattened (fig. 31 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); fore wing with a characteristic pattern of radiating dark bands (fig. 32 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); head and body black with strong metallic refringence; presumed hyperparasitoids of Coccidae - [[File:Cerapterocerus mirabilis, female.jpg|thumb|''Cerapterocerus mirabilis'', female, Spain]][[File:Cerapterocerus celadus inat 194830169 a.jpg|thumb|Adult ''Cerapterocerus celadus'', France]] **''''' Cerapterocerus''''' Westwood, 1833 *** Links: [https://www.inaturalist.org/taxa/250477-Cerapterocerus iNaturalist] *** 17 species worldwide; 1 Afrotropical species: ****''Cerapterocerus mirabilis'' is probably a hyperparasitoid of encyrtid wasps in scale insects (South Africa) *41b Antenna not broadened and flattened except for scape (fig. 33 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); fore wing (fig. 34 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) infuscated, but without distinct patterns as above; head and body dominantly brownish, without strong metallic refringence; primary parasitoids of Asterolecaniidae (pit scales). Head as in fig. 35 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/> - **''''' Mayrencyrtus''''' Hincks, 1944 *** 6 species worldwide; No Afrotropical species in Universal Chalcidoidea Database ===42 (Frontovertex rounded on to face, not forming a ledge; antenna slender, the scape at most slightly expanded ventrally)=== *42a Mesoscutum with incomplete parapsidal sulci (fig. 36 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); maxillary and labial palpi each two-segmented; paratergites present; parasitic in Pseudococcidae - [[File:Coccidoxenoides perminutus Fernandes 2016 a.jpg|thumb|Adult ''Coccidoxenoides perminutus'', Brazil]] **'''''Coccidoxenoides''''' Girault, 1915 ***'' Pauridia'' Timberlake, 1919 is a synonym of ''Coccidoxenoides'' (a monotypic genus) ****''Coccidoxenoides perminutus'' Girault, 1915 is a parasitoid of mealybugs ''Allococcus quaesitus'', ''Allococcus quaestius'', ''Delottococcus quaesitus'', ''Ferrisia virgata'', ''Ferrisiana virgata'', ''Maconellicoccus hirsutus'', ''Phenacoccus madeirensis'', ''Planococcoides'' spp., ''Planococcus citri'' spp., ''Pseudococcus'' spp., ''Spilococcus'' sp. and armored scale insects ''Aspidiotus nerii'', ''Carulaspis minima'', ''Chionaspis striata'' (Ghana, Ivory Coast, Kenya, South Africa) *42b Mesoscutum without parapsidal sulci; maxillary palpi each with four segments, the labial with three; paratergites absent; parasitic in Diaspididae -[[File:Tyndarichus melanacis, female, Spain.jpg|thumb|''Tyndarichus melanacis'', female, Spain]] **'''''Tyndarichus''''' Howard, 1910 ***''Protyndarichus combretae'', ''P. orarius'', ''P. prolatus'', ''P. sparnus'' are a synonyms of the ''Tyndarichus'' species below. *** 24 species worldwide; 4 Afrotropical species: ****''Tyndarichus combretae'' no known associates (Senegal) ****''Tyndarichus orarius'' is a parasitoid of Coccidae, ''Idiosaissetia peringueyi'' (South Africa) ****''Tyndarichus prolatus'' is a parasitoid of Coccidae, ''Ceroplastes elytropappi'' (South Africa) ****''Tyndarichus sparnus'' is a parasitoid of Lecanodiaspididae, ''Lecanodiaspis tarsalis'' (South Africa) ===43 (Submarginal vein without a triangular expansion)=== *43a Mandible with only two acute or subacute teeth (figs 37, 38 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Paratergites (fig. 39 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) usually present, plainly visible in cleared, slide-mounted specimens; speculum of fore wing usually lacking a row of coarse, spine-like setae along outer edge of speculum; cercal plates often advanced to a level near base of metasoma; exclusively parasitic in Pseudococcidae ................ 120 *43b Mandible never with only two pointed teeth ........ 44 ===44 (Mandible never with only two pointed teeth)=== *44a Entire fore wing, or part of it, distinctly [[wikt:infuscate|infuscated]] (with a dark tinge), the infuscation rarely restricted to an area beneath the venation ........ 45 *44b Fore wing entirely [[w:hyaline|hyaline]] (translucent or transparent), or very faintly and inconspicuously infuscated, the infuscation then usually only visible if wing held against a white background ........ 73 ==45 Fore wing, or part of it, distinctly infuscated== *45a Fore wing with a conspicuous incision in cephalic wing margin at distal end of submarginal vein (fig. 40 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) - **''''' Eugahania''''' Mercet, 1926 *** 10 species worldwide; No Afrotropical species in Universal Chalcidoidea Database.<ref name=Noyes2019/> *45b Fore wing without an incision in cephalic margin ................46 ===46 Fore wing without an incision in cephalic margin=== *46a Scutellum with a posterior flange or lamella (fig. 15 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); in profile this flange shows as a thin flat [[wikt:caudal|caudal]] projection of the scutellum................47 *46b Scutellum without a marginal flange, the posterior margin rarely forming a very short lip........ 49 ===47 Scutellum with a posterior flange or lamella=== *47a Antennal [[wikt:clava|club]] white; [[wikt:gonostylus|gonostyli]] absent; [[wikt:clava|club]] large, much longer than the distal three [[wikt:funicle|funicle]] segments together; parasitic in Lepidoptera eggs. Antenna as in fig. 41 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/> - **''''' Hesperencyrtus''''' Annecke, 1971 *** 2 species worldwide; 1 Afrotropical species: ****''Hesperencyrtus lycoenephila'' is a parasitoid of lycaenid butterflies ''Deodorix antalus'', ''Deudorix antalus'', ''Lampides boeticus'' (Senegal) *47b Antennal [[wikt:clava|club]] not white; [[wikt:gonostylus|gonostyli]] present; [[wikt:clava|club]] about as long as the distal three [[wikt:funicle|funicle]] segments together; not parasitic in Lepidoptera........ 48 ===48 Antennal club not white; club about as long as the distal three funicle segments together=== *48a Frontovertex and face with numerous large pits, each brilliantly metallic green in colour - [[File:Discodes arizonensis Smithsonian Institution 2019 CC-BY BOLD CCDB-34079-D12.jpg|thumb|''Discodes arizonensis'', New Mexico, United States]] **''''' Discodes''''' Foerster, 1856 *** 44 species worldwide; 2 Afrotropical species: ****''Discodes discors'' is a parasitoid of felt scales ''Eriococcus'' spp. (South Africa) ****''Discodes melas'' - no associates known (Namibia) *48b Head at most with fine punctations. Orange-brown to dark brown, rarely black, species, at most weakly refringent; fore wing strongly and uniformly infuscated from base to near apex; usually parasitic in Pulvinaria spp. on grasses - [[File:Paraphaenodiscus monawari, female, dorsal view.jpg|thumb|Female ''Paraphaenodiscus monawari'', India]] **''''' Paraphaenodiscus''''' Girault, 1915 *** 20 species worldwide; 10 Afrotropical species: ****''Paraphaenodiscus africanus'' - no associates known (South Africa) ****''Paraphaenodiscus ceroplastodesi'' is a parasitoid of a wax scale ''Ceroplastes'' sp.(Senegal) ****''Paraphaenodiscus chrysocomae'' - no associates known (South Africa) ****''Paraphaenodiscus munroi'' is a parasitoid of a coccid scale ''Pulvinaria iceryi'' (South Africa) ****''Paraphaenodiscus niger'' is a parasitoid of coccid scales ''Pulvinariai'' spp. (South Africa) ****''Paraphaenodiscus paralis'' is a parasitoid associated with the grass ''Plagiochloa uniolae'' (South Africa) ****''Paraphaenodiscus pavoniae'' is a parasitoid of coccid scales ''Ceroplastes'' sp., ''Pulvinaria'' spp. (Senegal, South Africa, Zimbabwe) ****''Paraphaenodiscus pedanus'' is a parasitoid associated with the grass ''Plagiochloa uniolae'' (South Africa) ****''Paraphaenodiscus risbeci'' is a parasitoid of a moth ''Sesamia cretica'' (Senegal, Sudan) ****''Paraphaenodiscus rizicola'' is a parasitoid associated with rice ''Oryza sativa'' (Cameroon, Swaziland, Zimbabwe) ===49 Scutellum without a marginal flange=== *49a Stigmal vein of fore wing placed almost at right angle to postmarginal vein (fig. 42 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Fore wing infuscated with contrasting hyaline patches as in fig. 42<ref name=Prinsloo&Anneke1979/>; parasitic in Lacciferidae and Coccidae - **''''' Ruandella''''' Risbec, 1957 *** 4 species worldwide; 4 Afrotropical species: ****''Ruandella capensis'' is a parasitoid of coccid scales ''Ceroplastes'' sp. ''Saissetia'' sp. (South Africa) ****''Ruandella stigmosa'' is a parasitoid of coccid scales ''Lichtensia'' sp., ''Saissetia'' spp. (South Africa) ****''Ruandella tertia'' is a parasitoid of lac scales ''Tachardina'' spp. (South Africa) ****''Ruandella testacea'' is a parasitoid of a wax scale ''Ceroplastes'' sp. (Rwanda, South Africa) *49b Angle between stigmal and postmarginal veins much less than 90 degrees ........ 50 ===50 Angle between stigmal and postmarginal veins much smaller than right angle=== *50a Mandible with four teeth (fig. 43 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Body somewhat flattened dorsoventrally; head subtriangular in lateral view, the face a little inflexed; parasitic in Diaspididae - [[File:Adelencyrtus inat 31626163.jpg|thumb|''Adelencyrtus'' sp., South Africa]][[File:Adelencyrtus Cipola 2022 EntomoBrasilis 15 e1003 CC-BY.jpg|thumb|Female ''Adelencyrtus'' sp., Brazil]] **''''' Adelencyrtus''''' Ashmead, 1900 *** 45 species worldwide; 10 Afrotropical species: ****''Adelencyrtus antennatus'' is a parasitoid of armored scale insects ''Aspidiotus'' sp. (South Africa) ****''Adelencyrtus aulacaspidis'' is a parasitoid of coccid scales ''Lecanopsis nevesi'', and armored scales ''Aulacaspis difficilis'', ''Aulacaspis rosae'', ''Chionaspis salicis'', ''Dynaspidiotus britannicus'', ''Lepidosaphes cupressi'', ''Pseudaulacaspis pentagona'', ''Quadraspidiotus macroporanus'', ''Unaspis yanonensis'' (Madagascar) ****''Adelencyrtus depressus'' - no associates known (Madagascar) ****''Adelencyrtus flagellatus'' - no associates known (South Africa) ****''Adelencyrtus inglisiae'' is a parasitoid of armored scale insects ''Africaspis''' spp. ''Aspidiotus'' spp., ''Balaspis faurei'', ''Clavaspis'' spp., ''Clavaspis pituranthi'', ''Diaspis echinocacti'', ''Moraspis euphorbiae'', ''Mytilococcus'' spp., ''Quadraspidiotus perniciosus'' (South Africa, Zimbabwe) ****''Adelencyrtus mangiphila'' is a parasitoid of armored scale insects ''Phenacaspis dilatata'' (Madagascar) ****''Adelencyrtus mayurai'' is a parasitoid of armored scale insects ''Aonidiella orientalis'', ''Melanaspis glomerata'' (Mauritania) ****''Adelencyrtus moderatus'' is a parasitoid of whiteflies ''Bemisia tabaci'', armored scales ''Aspidiella hartii'', ''Aspidiella sacchari'', ''Aspidiotus glomeratus'', ''Aulacaspis'' spp., ''Duplachionaspis'' spp., ''Lepidosaphes'' spp., ''Melanaspis glomerata'', and mealybugs ''Saccharicoccus sacchari'' (Ghana, Madagascar, Mauritius, Tanzania, Uganda) ****''Adelencyrtus odonaspidis'' is a parasitoid of armored scales ''Duplachionaspis sansevieriae'', ''Odonaspidis'' sp., ''Odonaspis'' spp., and mealybugs ''Antonina graminis'' (South Africa) ****''Adelencyrtus tibialis'' - no associates known (South Africa) *50b Mandibles do not have four teeth ........ 51 ===51 (Mandibles do not have four teeth)=== *51a Antennal club white, usually obliquely truncate apically................52 *51b Antennal club dark, seldom obliquely truncate apically................55 ===52 Antennal club white, usually obliquely truncate apically=== *52a Antennal club three-segmented; not parasitic in Coleoptera........ 53 *52b Antennal club not segmented, rarely with faint traces of one or two septa on one side of the club; parasitic in Coleoptera........ 54 ===53 Antennal club three-segmented=== *53a Antennal scape expanded ventrally (fig. 44 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); hcad and body strongly metallic in colour, the head and thorax usually covered with silvery-white setae; parasitic in the oothecae of cockroaches - [[File:Comperia Smithsonian Institution 2019 CCDB-34079-D08 CC-BY boldsystems.jpg|thumb|''Comperia'' sp., Illinois, United States]] **''''' Comperia''''' Gomes, 1942 *** 7 species worldwide; 7 Afrotropical species: ****''Comperia alfierii'' is a parasitoid of a cockroach ''Blattella'' sp., and a dance fly ''Phyllodromia'' sp. (Egypt, Kenya, South Africa) ****''Comperia austrina'' - no associates known (South Africa) ****''Comperia clavata'' - no associates known (South Africa) ****''Comperia domestica'' - no associates known (South Africa) ****''Comperia faceta'' - no associates known (South Africa) ****''Comperia hirsuta Annecke'' - no associates known (South Africa) ****''Comperia merceti'' is a parasitoid of a cockroaches ''Blattella germanica'', ''Supella longipalpa'', ''Supella supellectilium'', ''Periplaneta americana'' (Uganda) *53b Antennal scape not or only slightly expanded ventrally (fig. 45 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); head and body without metallic refringence; parasitic in Pseudococcidae - [[File:Aphycus apicalis gbif.org - occurrence - 3905669246 03.png|thumb|''Aphycus apicalis'', Netherlands]] **''''' Aphycus''''' Mayr, 1876 *** 33 species worldwide; 1 Afrotropical species: ****''Aphycus comperei'' is a parasitoid of mealybugs ''Pedrococcus'' sp. (South Africa) ===54 Antennal club not segmented; parasitic in Coleoptera=== *54a Mesoscutum with parapsidal sulci (fig. 46 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); basal one-half or so of tegulae white; antennal scape slender, subcylindrical; primary parasitoids of Coccinellidae -[[File:Homalotylus flaminius, female, Spain.jpg|thumb|''Homalotylus flaminius'', female]][[File:Homalotylus iNat 135531367.jpg|thumb|''Homalotylus'' sp., South Africa]] **''''' Homalotylus''''' Mayr, 1876 *** 68 species worldwide; 6 Afrotropical species: ****''Homalotylus africanus'' is a parasitoid of lady beetles ''Exochomus concavus'', ''Hyperaspis'' spp., ''Lindorus lophanthae'', ''Scymnus ornatulus'' (Democratic Republic of Congo, Ghana, Namibia, Nigeria, Rwanda, South Africa) ****''Homalotylus eytelweinii'' is a parasitoid of lady beetles ''Adonia variegata'', ''Anatis ocellata'', ''Brumoides suturalis'', ''Cheilomenes sexmaculata'', ''Chilocorus'' spp., ''Coccinella septempunctata'', ''Menochilus sexmaculatus'', ''Rodolia'' spp. (Congo, Kenya, Malawi, South Africa, Sudan, Togo) ****''Homalotylus flaminius'' is a parasitoid of lady beetles ''Adalia'' spp., ''Adonia variegata'', ''Anatis ocellata'', ''Brumoides suturalis'', ''Brumus suturalis'', ''Cheilomenes'' spp., ''Chilocorus'' spp., ''Coccinella'' spp., ''Coleomegilla maculata'', ''Cycloneda'' spp., ''Epilachna chrysomelina'', ''Eriopis connexa'', ''Exochomus'' spp., ''Harmonia'' spp., ''Henosepilachna bifasciata'', ''Hippodamia'' spp., ''Hyperaspis'' spp., ''Lioadala flavomaculata'', ''Menochilus sexmaculatus'', ''Neomysia oblongoguttata'', ''Nephus bipunctatus'', ''Orcus'' spp., ''Pharoscymnus'' spp., ''Platynaspis'' sp., ''Rodolia'' spp., ''Scymnus'' spp., ''Thea vigintiduopunctata'', ''Verania frenata'', leaf beetles ''Galeruca calmariensis'', coccid scale insects ''Parthenolecanium corni'', ''Saissetia oleae'', mealybugs ''Nipaecoccus viridis'', ''Planococcus citri'', ''Pseudococcus citri'' (Cameroon, Democratic Republic of Congo, Gambia, Ghana, Guinea-Bissau, Madagascar, Mali, Namibia, Nigeria, Senegal, South Africa, Togo) ****''Homalotylus hemipterinus'' is a parasitoid of lady beetles ''Chilocorus'' spp., ''Chilomenes'' sp., ''Coccinella septempunctata'', ''Cycloneda sanguinea'', ''Menochilus sexmaculatus'', ''Orcus'' sp., stink bugs ''Cantheconidia furcellata'', mealybugs ''Nipaecoccus viridis'', ''Pseudococcus'' sp., gelechiid moths ''Aproaerema modicella'' (Chad, Congo, Democratic Republic of Congo, Kenya, Malawi, South Africa, Sudan, Togo) ****''Homalotylus quaylei'' is a parasitoid of lady beetles ''Hyperaspis'' spp., ''Nephus'' spp., ''Pharoscymnus'' spp., ''Scymnus'' spp., ''Sidis'' sp., coccid scales ''Eulecanium persicae'', mealybugs ''Nipaecoccus viridis'', ''Phenacoccus herreni'', ''Planococcus''; spp. (Gabon, Mauritania) ****''Homalotylus vicinus'' is a parasitoid of lady beetles ''Hyperaspis marmottani'', ''Nephus bipunctatus'', ''Nephus vetustus'', ''Scymnus'' sp. (Eritrea, Ethiopia, Madagascar) *54b Mesoscutum without parapsidal sulci; tegula not white; scape moderately to broadly expanded ventrally; parasitic in Discolomatidae - [[File:Homalotyloidea dahlbomii, female.jpg|thumb|''Homalotyloidea dahlbomii'', female, Spain]] **''''' Homalotyloidea''''' Mercet, 1921 *** 8 species worldwide; 1 Afrotropical species: ****''Homalotyloidea africana'' is a parasitoid of beetles ''Notiophygus piger'' (South Africa) ===55 Antennal club dark, seldom obliquely truncate apically=== *55a Body flattened dorsoventrally, the dorsum of head and thorax almost flat. Parasitic in Diaspididae........ 56 *55b Body not flattened dorsoventrally, the head and thorax more or less convex........ 57 ===56 Body not flattened dorsoventrally, the head and thorax convex=== *56a Antenna entirely broadened and flattened (fig. 29 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); frontovertex with two narrow whitish bands, one each extending along the dorsal eye margins. Fore wing boldly marked -[[File:Cain2565.jpg|thumb| ''Comperiella bifasciata'']] **''''' Comperiella''''' Howard, 1906 *** 11 species worldwide; 6 Afrotropical species: ****''Comperiella apoda'' is a parasitoid of armored scale insects ''Affirmaspis ehretiae'' (Namibia, South Africa) ****''[[w:Comperiella bifasciata|Comperiella bifasciata]]'' is a parasitoid of armored scale insects ''Aonidiella aurantii'', ''Aspidiotus'' spp., ''Chrysomphalus'' spp., ''Clavaspis'' sp., ''Diaspidiotus gigas'', ''Diaspis echinocacti'', ''Dynaspidiotus abietis'', ''Hemiberlesia'' spp., ''Lindingaspis fusca'', ''Morganella longispina'', ''Nuculaspis abietis'', ''Parlatoria pergandii'', ''Pseudaonidia trilobitiformis'', ''Pseudaulacaspis'' spp., ''Quadraspidiotus'' spp., ''Temnaspidiotus destructor'', ''Unaspis yanonensis'', coccid scale insects ''Saissetia coffeae'' (Madagascar, Mauritius, South Africa, Swaziland, Zambia, Zimbabwe) ****''Comperiella karoo'' - no associates known (South Africa) ****''Comperiella lemniscata'' is a parasitoid of armored scale insects ''Aonidiella'' spp., ''Chrysomphalus dictyospermi'' (South Africa) ****''Comperiella ponticula'' is a parasitoid of armored scale insects ''Clavaspis pituranthi'' (Namibia, South Africa) ****''Comperiella unifasciata'' is a parasitoid of armored scale insects ''Aonidiella'' spp., ''Aspidiotus'' spp., ''Pseudaonidia'' spp., whiteflies ''Aleurodicus destructor'', wax scale insects ''Ceroplastes rubens'' (Mauritius) *56b Antenna not broadened and flattened; frontovertex without pale bands - [[File:Habrolepis dalmanni Howard 1898 Fig.1.jpg|thumb|Female ''Habrolepis dalmanni'']][[File:Habrolepis dalmanni Howard 1898 Fig.2.jpg|thumb|Female ''Habrolepis dalmanni'']] **''''' Habrolepis''''' Foerster, 1856 *** 17 species worldwide; 12 Afrotropical species: ****''Habrolepis aeruginosa'' - no associates known (Seychelles) ****''Habrolepis algoensis'' is a parasitoid of armored scale insects ''Aspidiotus capensis'' (South Africa) ****''Habrolepis apicalis'' is a parasitoid of armored scale insects ''Chionaspis minor'', ''Pinnaspis temporaria'' (Ghana) ****''Habrolepis dalmanni'' is a parasitoid of armored scale insects ''Lepidosaphes ulmi'', ''Melanaspis inopinata'', ''Targionia vitis'', pit scales, ''Asterodiaspis'' sp., ''Asterolecanium'' sp., coccid scales ''Didesmococcus'' sp., mealybugs, ''Pseudococcus'' sp., and a moth, ''Leucoptera'' sp. (South Africa, Uganda) ****''Habrolepis diaspidi'' is a parasitoid of armored scale insects ''Aonidiella aurantii'' spp., ''Chionaspis'' sp., ''Chrysomphalus aonidum'' spp., ''Diaspidiotus perniciosus'', ''Diaspis senegalensis'', ''Hemiberlesia lataniae'', ''Parlatoria ziziphi'', ''Pinnaspis strachani'', ''Pudaspis newsteadi'', ''Quadraspidiotus perniciosus'', ''Selenaspidius celastri'' spp., ''Tecaspis visci'', ''Umbaspis regularis'' (Eritrea, Ethiopia, Mozambique, Senegal, South Africa, Zimbabwe) ****''Habrolepis guineensis'' is a parasitoid of armored scale insects ''Duplaspidiotus pavettae'' (Guinea) ****''Habrolepis namibensis'' is a parasitoid of armored scale insects ''Namaquea simplex'' (Namibia) ****''Habrolepis obscura'' is a parasitoid of armored scale insects ''Africaspis chionaspiformis'', ''Aonidiella orientalis'', ''Chionaspis'' sp., ''Diclavaspis ehretiae'', ''Ledaspis distincta'', ''Lindingaspis rossi'', ''Melanaspis corticosa'', ''Quadraspidiotus perniciosus'', ''Separaspis capensis'' (Namibia, South Africa, Zimbabwe) ****''Habrolepis occidua'' is a parasitoid of armored scale insects ''Melanaspis phenax'', ''Morganella phenax'', ''Pseudotargionia'' spp. (Namibia, South Africa) ****''Habrolepis oppugnati'' is a parasitoid of armored scale insects ''Aspidiotus'' spp. (Eritrea) ****''Habrolepis rouxi'' is a parasitoid of armored scale insects ''Aonidiella'' spp., ''Aspidiotus'' spp., ''Carulaspis minima'', ''Chrysomphalus'' spp., ''Hemiberlesia rapax'', ''Lepidosaphes newsteadi'', ''Parlatoria oleae'', ''Selenaspidius'' spp. (Kenya, Madagascar, Mozambique, South Africa, Swaziland, Uganda, Zimbabwe) ****''Habrolepis setigera'' is a parasitoid of armored scale insects ''Lindingaspis greeni'' (South Africa) ===57 Body not flattened, head and thorax convex=== *57a Antenna foliaceously flattened (fig. 47 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); junction of frontovertex and face carinate or at least acutely angled and grooved........ 58 *57b Antenna not flattened except for scape which may be expanded ventrally; head without a facial carina................60 ===58 Antenna flattened, junction of frontovertex and face carinate or acutely angled and grooved=== *58a Frontovertex terminating anteriorly at a transverse groove (fig. 48 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) containing dense, recumbent, silvery-white setae - **''''' Anasemion''''' Annecke, 1967 *** 1 species worldwide; 1 Afrotropical species: ****''Anasemion inutile'' is a parasitoid of wax scales ''Ceroplastes'' spp., ''Waxiella mimosae'' (Kenya, South Africa) *58b Junction of frontovertex and face lacking a transverse row of dense setae - [[File:Anicetus iNat 180762161 g.jpg|thumb|''Anicetus'' sp., South Africa]] **'''''Anicetus''''' Howard, 1896 ***''Paraceraptrocerus'' is a synonym of ''Anicetus''. In the Prinsloo-Annecke key,<ref name=Prinsloo&Anneke1979/> step 59 separated ''Paraceraptrocerus'' and ''Anicetus'' *** 52 species worldwide; 19 Afrotropical species: ****'' Anicetus abyssinicus '' is a parasitoid of coccid scales ''Parasaissetia nigra'' (Eritrea) ****'' Anicetus africanus'' is a parasitoid of wax scales ''Ceroplastes'' spp., ''Waxiella mimosae'' (Egypt, South Africa) ****'' Anicetus anneckei '' is a parasitoid of coccid scales ''Saissetia'' spp. (South Africa) ****'' Anicetus aquilus '' is a parasitoid of wax scales ''Gascardia destructor'' (South Africa) ****'' Anicetus austrinus'' is a parasitoid of wax scales ''Ceroplastes'' spp. (South Africa) ****'' Anicetus calidus'' is a parasitoid of wax scales ''Ceroplastes'' sp. and ''Gascardia'' sp. (South Africa) ****'' Anicetus clivus'' is a parasitoid of wax scales ''Gascardia tachardiaformis'' (South Africa) ****'' Anicetus communis'' is a parasitoid of wax scales ''Ceroplastes'' spp., ''Coccus longulus'', ''Gascardia'' spp., ''Gascardia destructor'', ''Parasaissetia litorea'', ''Waxiella mimosae'' (South Africa) ****'' Anicetus fotsyae'' - no associates known (Madagascar) ****'' Anicetus fuscus'' is a parasitoid of wax scales ''Ceroplastes bipartitus'' (South Africa) ****'' Anicetus graminosus'' is a parasitoid of coccid scales ''Pulvinaria iceryi'' (South Africa) ****'' Anicetus italicus'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Coccus elongatus'', felt scales ''Gossyparia spuria'' (Zimbabwe) ****'' Anicetus nyasicus'' is a parasitoid of coccid scales ''Ceroplastes'' spp. (Malawi, South Africa) ****'' Anicetus parilis'' is a parasitoid of coccid scales ''Gascardia rustica'', ''Lichtensia'' sp. (South Africa) ****'' Anicetus parvus'' is a parasitoid of wax scales ''Ceroplastes'' spp. (Congo, Democratic Republic of Congo, South Africa, Uganda) ****'' Anicetus pattersoni'' is a parasitoid of coccid scales ''Ceroplastes personatus'', ''Vinsonia personata'' (Ghana) ****'' Anicetus russeus'' - no associates known (South Africa) ****'' Anicetus sepis'' is a parasitoid of coccid scales ''Ceroplastes'' sp. (South Africa) ****'' Anicetus taylori'' is a parasitoid of wax scales ''Ceroplastes'' spp. (South Africa) ===59 ''Paraceraptrocerus''=== *In the Prinsloo-Annecke key,<ref name=Prinsloo&Anneke1979/> step 59 separated ''Paraceraptrocerus'' and ''Anicetus''. However, ''Paraceraptrocerus'' is now regarded as a synonym of ''Anicetus'', making this step redundant. ===60 (Antenna not flattened although the scape may be expanded ventrally; no facial carina)=== *60a Ovipositor protruding strongly (fig. 49 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) at apex of metasoma by about one half length of metasoma........ 61 *60b Ovipositor not exserted or slightly exserted; if strongly protruded (rare), then antennal scrobes sulcate, or mandible slender, tridentate, the upper tooth retracted (fig. 50 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 62 ===61 (Ovipositor protruding strongly)=== *61a Head with numerous setigerous pits; fore wing with a single pale cross-band beyond venation; body robust, black in colour; parasitic in Coccidae - **'''''Lombitsikala''''' Risbec, 1957 *** 1 species worldwide; 1 Afrotropical species: ****''Lombitsikala coccidivora'' is a parasitoid of coccid scales ''Gascardia madagascariensis'' (Madagascar) *61b Head at most with minute, indistinct punctations; fore wing without hyaline cross-bands; body more or less slender, usually generally yellowish to brownish; probably hyperparasitoids, usually in mealybugs - [[File:Prochiloneurus sp fem researchgate 363819988.jpg|thumb|Female ''Prochiloneurus'' sp., Mato Grosso do Sul, Brazil]] **''''' Prochiloneurus''''' Silvestri, 1915 *** 30 species worldwide; 4 Afrotropical species: ****'' Prochiloneurus aegyptiacus'' is a parasitoid of mealybugs ''Ferrisia virgata'', ''Ferrisiana virgata'', ''Maconellicoccus hirsutus'', ''Nipaecoccus vastator'', ''Nipaecoccus viridis'', ''Octococcus africanus'', ''Pedrococcus'' sp., ''Phenacoccus'' spp., ''Planococcoides njalensis'', ''Planococcus'' spp., ''Pseudococcus'' spp., ''Rastrococcus invadens'', coccid scales ''Coccus hesperidum'', ''Saissetia coffeae'' and lady beetles ''Chilocorus bipustulatus'', ''Exochomus flavipes'', ''Hyperaspis aestimabilis'' (Congo, Democratic Republic of Congo, Eritrea, Ethiopia, Gabon, Ghana, Ivory Coast, Namibia, Nigeria, South Africa, Tanzania, Togo) ****'' Prochiloneurus bolivari'' is a parasitoid of mealybugs ''Atrococcus'' sp., ''Dysmicoccus multivorus'', ''Ferrisia virgata'', ''Heliococcus bohemicus'', ''Heterococcopsis opertus'', ''Maconellicoccus hirsutus'', ''Naiacoccus serpentinus'', ''Peliococcus'' spp., ''Phenacoccus'' spp., ''Planococcus'' spp., ''Pseudococcus'' spp., ''Puto pilosellae'', ''Spinococcus calluneti'', ''Trionymus'' spp., coccid scales ''Rhizopulvinaria armeniaca'', felt scales ''Acanthococcus desertus'', ''Eriococcus insignis'', ''Neoacanthococcus tamaricicola'' (Congo, Democratic Republic of Congo, Nigeria, Sao Tomé and Principe, South Africa) ****'' Prochiloneurus comperei'' is a parasitoid of mealybugs ''Nipaecoccus'' spp., ''Pseudococcus'' sp., coccid scales ''Lecanium viride'', margarodid scales ''Icerya formicarum'', ''Palaeococcus bicolor'' (Eritrea, Ethiopia, Malawi, Senegal, South Africa, Tanzania) ****'' Prochiloneurus pulchellus'' is a parasitoid of mealybugs ''Centrococcus'' spp., ''Coccidohystrix'' spp., ''Dysmicoccus'' sp., ''Ferrisia virgata'', ''Naiacoccus serpentinus'', ''Nipaecoccus'' spp., ''Octococcus'' sp., ''Oxyacanthus chrysocomae'', ''Paracoccus'' sp., ''Peliococcus mesasiaticus'', ''Phenacoccus'' spp., ''Planococcus'' spp., ''Pseudococcus'' sp., ''Rastrococcus iceryoides'' spp., ''Trabutina crassispinosa'', ''Trabutina leonardii'', armored scale insects ''Chionaspis'' sp., felt scales ''Eriococcus stenoclini'', ''Neoacanthococcus tamaricicola'' (Cameroon, Cape Verde Islands, Congo, Democratic Republic of Congo, Eritrea, Ethiopia, Gabon, Gambia, Ghana, Guinea-Bissau, Madagascar, Malawi, Nigeria, Rwanda, Seychelles, South Africa, Togo) ===62 (Ovipositor not exserted or slightly exserted)=== *62a Antennal scape long and slender, at most slightly expanded ventrally........ 63 *62b Antennal scape moderately to broadly expanded, less than three times as long as its greatest width................70 ==63 Antennal scape long and slender== *63a Fore wing with marginal vein several times longer than stigmal (fig. 51 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); antennal club with four segments, visible only in cleared slide·mounted specimens (fig. 52 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) -[[File:Metaphaenodiscus nemoralis, female, Spain.jpg|thumb|''Metaphaenodiscus nemoralis'', female, Spain.]][[File:Metaphaenodiscus nemoralis, female, lateral view.jpg|thumb|''Metaphaenodiscus nemoralis'', female, lateral view]] **''''' Metaphaenodiscus''''' Mercet, 1921 *** Host species generally unknown, except for ''Metaphaenodiscus umbilicatus'' (Australia) which is known to be a parasitoid of a mealy bug. *** 10 species worldwide; 4 Afrotropical species: ****'' Metaphaenodiscus aethiops'' - no associates known (South Africa, Zimbabwe) ****'' Metaphaenodiscus capensis'', associated with ''Protea aurea'' (South Africa) ****'' Metaphaenodiscus karoo'' - no associates known (South Africa) ****'' Metaphaenodiscus watshami'' - no associates known (South Africa, Zimbabwe) *63b Marginal vein of fore wing shorter than, or subequal to stigmal vein; club with fewer than four segments................64 ===64 (Marginal vein shorter than stigmal vein; antennal club with less than four segments)=== *64a Antennal scrobes sulcate (figs 53 and 54 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), impressed on face as two deep furrows, their lateral margins acutely angled, at least in their basal one-half or so, converging, sometimes confluent dorsally to form an inverted V-shaped impression on face........ 65 *64b Antennal scrobes otherwise................66 ===65 (Antennal scrobes impressed on face as two deep furrows)=== *65a Antennal club not longer than the distal funicle segments together; frontovertex more or less pitted; mandible with two teeth and a broad truncation (fig. 55 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); parasitic in Coccidae - **''''' Aloencyrtus''''' Prinsloo, 1978 *** 20 species worldwide; 19 Afrotropical species: ****'' Aloencyrtus alox'' - no associates known (South Africa) ****'' Aloencyrtus angustifrons'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Gascardia brevicauda'' spp. (South Africa) ****'' Aloencyrtus claripennis'' is a parasitoid of coccid scales ''Inglisia conchiformis'' (South Africa, Uganda) ****'' Aloencyrtus coelops'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Gascardia destructor'', ''Waxiella mimosae'' (Eritrea, Nigeria, South Africa, Uganda) ****'' Aloencyrtus delottoi'' is a parasitoid of coccid scales ''Saissetia opulenta'' (Kenya, South Africa) ****'' Aloencyrtus diaphorocerus'' is a parasitoid of coccid scales ''Saissetia coffeae'' (Mauritius, Seychelles) ****'' Aloencyrtus distinguendus'' is a parasitoid of coccid scales ''Coccus subhemisphaericus'', ''Lecanium'' sp. (Cameroon, Ghana, Nigeria) ****'' Aloencyrtus facetus'' is a parasitoid of coccid scales ''Ceroplastes longicauda'' (South Africa) ****'' Aloencyrtus habrus'' is a parasitoid of coccid scales ''Saissetia coffeae'' (Cameroon) ****'' Aloencyrtus hardii'' is a parasitoid of coccid scales ''Parasaissetia nigra'', ''Saissetia'' spp. (South Africa) ****'' Aloencyrtus johani'' is a parasitoid of coccid scales ''Parasaissetia nigra'' (South Africa) ****'' Aloencyrtus lindae'' is a parasitoid of coccid scales ''Ceroplastes'' sp. (South Africa) ****'' Aloencyrtus nativus'' is a parasitoid of coccid scales ''Coccus longulus'', ''Parthenolecanium persicae'' (Benin, Madagascar, South Africa, Uganda, Zimbabwe) ****'' Aloencyrtus obscuratus'' is a parasitoid of coccid scales ''Lecanium somereni'', ''Saissetia'' spp. (Ghana, Kenya, South Africa) ****'' Aloencyrtus saissetiae'' is a parasitoid of coccid scales ''Ceroplastes'' sp. ''Coccus'' spp. ''Cryptinglisia lounsburyi'', ''Parasaissetia nigra'', ''Saissetia'' spp. (Ivory Coast, Kenya, Malawi, South Africa, Uganda, Zimbabwe) ****'' Aloencyrtus ugandensis'' is a parasitoid of coccid scales ''Ceroplastes'' spp. (Uganda) ****'' Aloencyrtus umbrinus'' is a parasitoid of coccid scales ''Ceroplastes'' spp. (Kenya, ) ****'' Aloencyrtus utilis'' is a parasitoid of coccid scales ''Saissetia oleae'' (South Africa) ****'' Aloencyrtus vivo'' - no associates known (Uganda) *65b Antennal club much longer than the distal three funicle segments together; frontovertex without pits or punctations; mandible with three teeth and a truncation (fig. 56 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Parasitic in Lacciferidae. Male antenna with two smaIl funicle segments and a large, unsegmented banana shaped club (fig. 57 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) - **''''' Erencyrtus''''' Mahdihassan, 1923 *** 6 species worldwide; 4 Afrotropical species: ****'' Erencyrtus ater'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus contrarius'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus fuscus'' is a parasitoid of coccid scales ''Waxiella mimosae'', lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus notialis'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) ===66 (Antennal scrobes not deeply impressed)=== *66a Mandible with three distinct teeth, the upper one sometimes retracted ................ 67 *66b Mandible otherwise ................ 68 ===67 (Mandible with three distinct teeth)=== *67a Antenna (fig. 58 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) slender, not clavate, the funicle segments each longer than wide, the pedicel and funicle subcqual in length; parasitic in Coccidae - **''''' Hadrencyrtus''''' Annecke and Mynhardt, 1973 *** 1 species worldwide; 1 Afrotropical species: ****'' Hadrencyrtus cirritus'' is a parasitoid of mealybugs ''Distichlicoccus'' sp. (South Africa) *67b Antenna (fig. 45 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) clavate, not particularly slender, the basal funicle segment plainly wider than long, small, much shorter than pedicel; parasitic in Pseudococcidae - [[File:Aphycus apicalis gbif.org - occurrence - 3905669246 03.png|thumb|''Aphycus apicalis'', Netherlands]] **''''' Aphycus''''' Mayr , 1876 *** 33 species worldwide; 1 Afrotropical species: ****'' Aphycus comperei'' is a parasitoid of mealybugs ''Pedrococcus'' sp. (South Africa) ===68 (Mandible does not have three distinct teeth)=== *68a Mandible with a single tooth and a broad serrated truncation (fig. 59 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); ovipositor with gonostyli absent; parasitic in Membracidae - [[File:Prionomastix biharensis - Female 01.jpg|thumb|Female ''Prionomastix biharensis'', Bihar, India.]] **''''' Prionomastix''''' Mayr , 1876 *** 30 species worldwide; 7 Afrotropical species: ****'' Prionomastix africana'' - no associates known (South Africa) ****'' Prionomastix capeneri'' is a parasitoid of treehoppers ''Beaufortiana viridis'', ''Leprechaunus cristatus'' (South Africa) ****'' Prionomastix congoensis'' - no associates known (Rwanda) ****'' Prionomastix montana'' is a parasitoid of treehoppers ''Dukeobelus simplex'' (South Africa) ****'' Prionomastix myartsevae'' - no associates known (South Africa) ****'' Prionomastix siccarius'' is a parasitoid of treehoppers ''Gongroneura fasciata'' (South Africa) ****'' Prionomastix wonjeae'' is a parasitoid of leafhoppers ''Coloborrhis corticina'' (Cameroon) *68b Mandible otherwise; gonostyli present; not parasitic in Membracidae................69 ===69 (Mandible does not have three distinct teeth, or a single tooth and a broad serrated truncation)=== *69a Antennal club large, about as long as entire funicle; integument of head and thorax heavily sclerotized, strongly and intricately sculptured with raised, irregular ridges; probably parasitic in Lacciferidae. Fore wing with areas of very coarse discal setae (fig. 60 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) - ** '''Coccopilatus''' Annecke, 1963 *** 4 species worldwide; 1 Afrotropical species: ****'' Coccopilatus judithae'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) *69b Antennal club shorter than funicle; sculpture of head and thorax mostly cellulite-reticulate; parasitic in Diaspididae - [[File:Neococcidencyrtus-poutiersi-Mercet-1922-A-Lateral-view-B-Dorsal-view-C W640.jpg|thumb|''Neococcidencyrtus poutiersi'', Iran]] **'' ' '' Neococcidencyrtus Compere, 1928 *** 20 species worldwide; 5 Afrotropical species: ****'' Neococcidencyrtus brenhindis'' - no associates known (Madagascar) ****'' Neococcidencyrtus cliradainis'' - no associates known (Cameroon) ****'' Neococcidencyrtus poutiersi'' is a parasitoid of armored scales ''Furchadaspis zamiae'' (South Africa) ****'' Neococcidencyrtus pudaspidis'' is a parasitoid of armored scales ''Pudaspis newsteadi'' (South Africa) ****'' Neococcidencyrtus syndodis'' - no associates known (South Africa) ==70 Antennal scape expanded== *70a Antenna with all funicle segments transverse (fig. 61 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); club very large, longer than entire funicle; paratergitcs present; frontovertex pitted; parasitic in mealybugs - [[File:Aenasius 2019 08 25 9470.jpg|thumb|''Aenasius'' sp., South Africa]] **''''' Aenasius''''' Walker, 1846 *** 42 species worldwide; 7 Afrotropical species: ****'' Aenasius abengouroui'' is a parasitoid of mealybugs ''Planococcoides njalensis'', ''Planococcus citri'' (Ghana, Ivory Coast) ****'' Aenasius advena'' is a parasitoid of mealybugs ''Ferrisia'' spp., ''Phenacoccus'' spp., ''Planococcus'' spp., ''Pseudococcus'' spp., ''Spilococcus'' sp. (Congo, Democratic Republic of Congo, South Africa) ****'' Aenasius comperei'' is a parasitoid of mealybugs ''Allococcus quaesitus'', ''Delottococcus'' spp., ''Octococcus'' sp. ''Pseudococcus'' sp. (Kenya, South Africa) ****'' Aenasius flandersi'' is a parasitoid of mealybugs ''Ferrisia virgata'', ''Phenacoccus'' spp. (Democratic Republic of Congo, Senegal) ****'' Aenasius hyettus'' is a parasitoid of mealybugs ''Ferrisia virgata'', ''Phenacoccus'' sp. (Afrotropical) ****'' Aenasius martinii'' is a parasitoid of mealybugs ''Ferrisia virgata'', ''Planococcoides njalensis'', ''Planococcus celtis'' spp., ''Pseudococcus'' sp. (Eritrea, Ethiopia, Ghana, Ivory Coast, Kenya) ****'' Aenasius phenacocci'' is a parasitoid of mealybugs ''Phenacoccus'' spp., ''Planococcoides njalensis'' (Ghana) 70b Funicle segments not all wider than long; club shorter than entire funicle; paratergites absent; frontovertex at most with fine punctations; not parasitic in mealybugs ................ 71 ===71 (Funicle segments not all wider than long; club shorter than entire funicle; frontovertex not markedly pitted)=== *71a Head and thoracic dorsum largely metallic blue-green or cupreous, covered with silvery-white setae; parasitic in the oothecae of cockroaches - [[File:Comperia Smithsonian Institution 2019 CCDB-34079-D08 CC-BY boldsystems.jpg|thumb|''Comperia'' sp., Illinois, United States]] **''''' Comperia''''' Gomes, 1942 *** 7 species worldwide; 7 Afrotropical species: ****'' Comperia alfierii'' is a parasitoid of cockroaches ''Blattella'' sp., ''Phyllodromia'' sp. (Egypt, Kenya, South Africa) ****'' Comperia austrina'' - no associates known (South Africa) ****'' Comperia clavata'' - no associates known (South Africa) ****'' Comperia domestica'' - no associates known (South Africa) ****'' Comperia faceta'' - no associates known (South Africa) ****'' Comperia hirsuta'' - no associates known (South Africa) ****'' Comperia merceti'' is a parasitoid of cockroaches ''Blattella germanica'', ''Supella longipalpa'', ''Supella supellectilium'', ''Periplaneta americana'' (Uganda) *71b Head and body generally yellowish to brownish, without any metallic refringence or white setae; parasitic in Coccoidea ................ 72 ===72 (Head and body yellowish to brownish, not metallic, no white setae)=== *72a Antennal club longer than distal three funicle segments together, usually much wider than funicle segment VI; if rarely shorter, then distal four funicle segments white - [[File:Metaphycus inat 5003180 c.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. *72b Club about as long as the distal three funicle segments together, at most a little wider than distal funicle segment; funicle with at most distal three segments white - [[File:Microterys nietneri female.jpg|thumb|Female ''Microterys nietneri'', New Zealand]][[File:Microterys iN 253517641.jpg|thumb|''Microterys'' sp., South Africa]] **'''''Microterys''''' Thomson, 1876 *** 228 species worldwide; 12 Afrotropical species: ****'' Microterys africa'' is a parasitoid of lac scales ''Tachardia decorella'' (Uganda) ****'' Microterys anneckei'' is a parasitoid of coccid scales ''Filippia'' sp., ''Lichtensia'' sp., ''Parasaissetia litorea'', ''Pulvinaria mesembryanthemi'', ''Saissetia'' sp. (South Africa) ****'' Microterys bizanensis'' is a parasitoid of coccid scales ''Ceronema'' sp., ''Parasaissetia nigra'', ''Saissetia cuneiformis'' (Eritrea) ****'' Microterys capensis'' is a parasitoid of coccid scales ''Pulvinaria'' sp. (South Africa) ****'' Microterys ceroplastae'' is a parasitoid of coccid scales ''Ceroplastes destructor'' (Kenya) ****'' Microterys clauseni'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Metaceronema japonica'' (South Africa) ****'' Microterys haroldi'' is a parasitoid of coccid scales ''Ceroplastes'' sp., ''Messinea plana'' (South Africa) ****'' Microterys kenyaensis'' is a parasitoid of coccid scales ''Ceroplastes'' sp., ''Coccus hesperidum'', ''Lecanium oleae'', ''Saissetia'' spp. (Kenya, South Africa) ****'' Microterys nanus'' is a parasitoid of cerococcid scales ''Cerococcus'' sp., coccid scales ''Ceroplastes'' sp. (South Africa) ****'' Microterys nicholsoni'' is a parasitoid of coccid scales ''Coccus hesperidum'', ''Ceroplastes destructor'', ''Parasaissetia litorea'', ''Parasaissetia nigra'', ''Saissetia'' spp. (Kenya, South Africa, Zimbabwe) ****'' Microterys nietneri'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Chloropulvinaria'' spp., ''Coccus'' spp., ''Eucalymnatus tessellatus'', ''Lecanium'' spp., ''Maacoccus piperis'', ''Parasaissetia'' spp., ''Parasaissetia oleae'', ''Parthenolecanium'' spp., ''Parthenolecanium corni'', ''Protopulvinaria'' spp., ''Pulvinaria'' spp., ''Saissetia'' spp., ''Sphaerolecanium prunastri'', armored scales ''Hemichionaspis theae'', ''Pinnaspis theae'', mealybugs ''Rastrococcus iceryoides'' (South Africa) ****'' Microterys speciosus'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Coccus'' spp. (South Africa) == 73 Fore wing entirely hyaline, or faintly infuscated (any infuscation only visible against a pale background; from 44)== * 73a Gonostyli exserted at apex of metasoma, the exserted parts laterally compressed, usually more or less rounded apically in lateral view........ 74 * 73b Gonostyli, if protruding at apex of metasoma, not flattened laterally, usually having the appearance of two slender, sharp stylets................78 == 74 Gonostyli extend beyond apex of metasoma, laterally compressed and rounded apically == * 74a Scutellum entirely or partly shiny, with a polished appearance, without differentiated sculptural cells; mandibles exceptionally large (fig. 62 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979>Prinsloo, G. L., & Annecke, D. P. (1979). A key to the genera of Encyrtidae from the Ethiopian region, with descriptions of three new genera (Hymenoptera: Chalcidoidea). Journal of the Entomological Society of southern Africa, 42(2), 349-382. [https://journals.co.za/doi/pdf/10.10520/AJA00128789_2641 PDF]</ref>)........ 75 * 74b Scutellum dorsally sculptured, not smooth and polished; mandibles normal................76 === 75 Scutellum shiny; mandibles large=== * 75a Postmarginal vein (fig. 63 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) of fore wing shorter than marginal, not reaching to a level near apex of stigmal; basal triangle of wing disc largely devoid of setae; parasitic in Coleoptera - [[File:Cerchysiella inat 104244416.jpg|thumb|''Cerchysiella'' sp., United States]] **''''' Cerchysiella''''' Girault, 1914 ***''Zeteticontus'' Silvestri, 1915 is a synonym of ''Cerchysiella''. *** 36 species worldwide; 5 Afrotropical species: ****''Cerchysiella abilis'' (Silvestri) (5) ****''Cerchysiella neodypsisae'' (Risbec) (1) ****''Cerchysiella punctiscutellum'' (Subba Rao) (1) ****''Cerchysiella utilis'' (Noyes) (5) ****''Cerchysiella xanthopus'' (Masi) (1) * 75b Postmarginal vein of fore wing subequal to or longer than marginal, reaching to about the level of apex of stigmal; basal triangle of wing disc evenly and densely setose; parasitic in Diptera - [[File:Tachinaephagus iNat 148445032.jpg|thumb|''Tachinaephagus'' sp., South Africa]] **''''' Tachinaephagus''''' Ashmead, 1904 *** 11 species worldwide; 3 Afrotropical species: ****''Tachinaephagus congoensis'' Subba Rao (1) ****''Tachinaephagus stomoxicida'' Subba Rao (3) ****''Tachinaephagus zealandicus'' Ashmead (6) === 76 Scutellum sculptured, not smooth; mandibles not large === * 76a Antennal funicle and club white in colour; antennal scape expanded ventrally, the funicle segments all wider than long; parasitic in Coleoptera. Head with membranous interruptions of sclerotized integument as in fig. 64 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/> - **''''' Chrysomelechthrus''''' Trjapitzin, 1977 *** 1 species worldwide; 1 Afrotropical species: ****''Chrysomelechthrus descampsi'' (Risbec) (3) * 76b Antennal funicle and club dark in colour; scape slender, subcylindrical, the funicle with at least basal four or five segments longer than wide; parasitic in Diptera........ 77 === 77 Antennal funicle and club dark; scape slender, subcylindrical; funicle with more than three segments longer than wide === * 77a Head and body entirely metallic green to blue-green in colour; pedicel shorter than, to about as long as, basal funicle segment; clypeal margin not crenulate - [[File:Cerchysius inat 7295295.jpg|thumb|''Cerchysius'' sp., United States]] **''''' Cerchysius''''' Westwood, 1832 *** 15 species worldwide; 2 Afrotropical species: ****''Cerchysius kilimanjarensis'' Kerrich (1) ****''Cerchysius ugandensis'' Kerrich (4) * 77b Head and body without metallic lustre; pedicel plainly longer than basal funicle segment; clypeal margin with crenulae - **''''' Coccidoctonus''''' Crawford, 1912 ***''Xyphigaster'' Risbec, 1954 is a synonym of '' Coccidoctonus'' *** 8 species worldwide; 1 Afrotropical species: ****''Coccidoctonus pseudococci'' (Risbec) (9) == 78 If gonostyli protrude from apex of metasoma, not flattened laterally == * 78a Head, in frontal view, with eyes large, extending almost to mouth margin, the genae very short. Head and body metallic green in colour, the tegulae partly white; male antenna with four rami, borne on the first four funicle segments; parasitic in Lepidoptera - [[File:Parablastothrix vespertinus male antenna Fauna ibérica p254 BHL10940309.jpg|thumb|Male antenna of ''Parablastothrix vespertinus'', Spain]][[File:Parablastothrix vespertinus female antenna Fauna ibérica p254 BHL10940309.jpg|thumb|Feale antenna of ''Parablastothrix vespertinus'', Spain]] **''''' Parablastothrix''''' Mercet, 1917 *** 16 species worldwide; ? Afrotropical species: ****No Afrotropical records in UCD? * 78b Genae much longer, usually plainly more than one-third longest diameter of eye in frontal view........ 79 === 79 In frontal view genae more than one-third longest diameter of eye === * 79a Mandible with four teeth (figs 43, 65 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 80 * 79b Mandible otherwise................81 === 80 Mandible with four teeth === * 80a Scutellum longitudinally striate (fig. 66 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); dorsum of thorax gently convex, the thorax not dorsoventrally compressed - [[File:Lamennaisia ambigua male p284.jpg|thumb|''Lamennaisia ambigua'', male]] **''''' Lamennaisia''''' Girault, 1922 ***''Mercetencyrtus'' Trjapitzin, 1963 is a synonym of ''Lamennaisia'' *** 5 species worldwide; 1 Afrotropical species: ****''Lamennaisia nobilis'' (Nees) (South Africa) * 80b Scutellum largely cellulate-reticulate, not giving the surface a striated effect; body some what flattened dorsoventrally, the thoracic dorsum flat or almost so - [[File:Adelencyrtus - Japoshvili, G. and Soethof, R. (2022).jpg|thumb|''Adelencyrtus aulacaspidis'', Netherlands]] **''''' Adelencyrtus''''' Ashmead, 1900 *** 45 species worldwide; 10 Afrotropical species: ****''Adelencyrtus antennatus'' is a parasitoid of armored scale insects ''Aspidiotus'' sp. (South Africa) ****''Adelencyrtus aulacaspidis'' is a parasitoid of coccid scales ''Lecanopsis nevesi'', and armored scales ''Aulacaspis difficilis'', ''Aulacaspis rosae'', ''Chionaspis salicis'', ''Dynaspidiotus britannicus'', ''Lepidosaphes cupressi'', ''Pseudaulacaspis pentagona'', ''Quadraspidiotus macroporanus'', ''Unaspis yanonensis'' (Madagascar) ****''Adelencyrtus depressus'' - no associates known (Madagascar) ****''Adelencyrtus flagellatus'' - no associates known (South Africa) ****''Adelencyrtus inglisiae'' is a parasitoid of armored scale insects ''Africaspis''' spp. ''Aspidiotus'' spp., ''Balaspis faurei'', ''Clavaspis'' spp., ''Clavaspis pituranthi'', ''Diaspis echinocacti'', ''Moraspis euphorbiae'', ''Mytilococcus'' spp., ''Quadraspidiotus perniciosus'' (South Africa, Zimbabwe) ****''Adelencyrtus mangiphila'' is a parasitoid of armored scale insects ''Phenacaspis dilatata'' (Madagascar) ****''Adelencyrtus mayurai'' is a parasitoid of armored scale insects ''Aonidiella orientalis'', ''Melanaspis glomerata'' (Mauritania) ****''Adelencyrtus moderatus'' is a parasitoid of whiteflies ''Bemisia tabaci'', armored scales ''Aspidiella hartii'', ''Aspidiella sacchari'', ''Aspidiotus glomeratus'', ''Aulacaspis'' spp., ''Duplachionaspis'' spp., ''Lepidosaphes'' spp., ''Melanaspis glomerata'', and mealybugs ''Saccharicoccus sacchari'' (Ghana, Madagascar, Mauritius, Tanzania, Uganda) ****''Adelencyrtus odonaspidis'' is a parasitoid of armored scales ''Duplachionaspis sansevieriae'', ''Odonaspidis'' sp., ''Odonaspis'' spp., and mealybugs ''Antonina graminis'' (South Africa) ****''Adelencyrtus tibialis'' - no associates known (South Africa) === 81 Mandible does not have four teeth === * 81a Mesoscutum with parapsidal sulci (cf. fig. 46 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 82 * 81b Mesoscutum without parapsidal sulci........ 83 === 82 Mesoscutum with parapsidal sulci=== * 82a Antenna (fig. 67 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) long and slender, the scape subcylindrical, the funicle segments all longer than wide; paratergites present; body entirely black, or black with metasoma yellowish, the latter laterally margined with blackish-brown; head and thorax with a metallic refringence; parasitic in Pseudococcidae - [[File:Charitopus fulviventris male Fig. 218 Mercet (1921) Fauna ibérica.jpg|thumb|Male ''Charitopus fulviventris'']][[File:Charitopus fulviventris female Fig. 220 Mercet (1921) Fauna ibérica.jpg|thumb|Female ''Charitopus fulviventris'']] **''''' Charitopus''''' Foerster, 1856 *** 18 species worldwide; 1 Afrotropical species: ****''Charitopus fulviventris'' - no associates known (South Africa) * 82b Antennal scape moderately to broadly expanded ventrally, the funicle segments not all longer than wide (fig. 68 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); paratergites absent; head and body without a metallic refringence, usually yellowish to brownish in colour; parasitic in Coccoidea other than Pseudococcidae - [[File:Metaphycus inat 4772310 b.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. === 83 Mesoscutum without parapsidal sulci=== * 83a Antennal scape cylindrical or almost so, more than three times as long as its greatest width........ 84 * 83b Scape moderately to broadly expanded ventrally, less than three times as long as wide........ 117 == 84 Antennal scape cylindrical or almost so, much longer than wide== * 84a Antennal sockets placed high on face (fig. 69 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), their lower limits at or above lower eye level. Body black in colour, the frontovertex and face more or less pitted; antennal scrobes usually sulcate; parasitic in Coccidae - **''''' Bothriophryne''''' Compere, 1937 *** 8 species worldwide; 6 Afrotropical species: ****''Bothriophryne acaciae'' (Risbec) (3) ****''Bothriophryne ceroplastae'' Compere (5) ****''Bothriophryne dispar'' Compere (2) ****''Bothriophryne fuscicornis'' Compere (5) ****''Bothriophryne purpurascens'' Compere (3) ****''Bothriophryne velata'' Prinsloo and Annecke (2) * 84b Antennal scrobes placed lower on face, their lower limits well below lower eye level, sometimes almost at mouth margin........ 85 === 85 Antennal scrobes are low on face, lower limits well below bottom of eye=== * 85a Antennal club white........ 86 * 85b Antennal club not white........ 87 === 86 Antennal club white=== * 86a Head and thorax brilliant metallic green in colour; antennal club strongly obliquely truncate apically; mandible (fig. 70 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with two teeth and a broad truncation; parasitic in the oothecae of cockroaches - [[File:Comperia Smithsonian Institution 2019 CCDB-34079-D08 CC-BY boldsystems.jpg|thumb|''Comperia'' sp., Illinois, United States]] **''''' Comperia''''' Gomes, 1942 *** 7 species worldwide; 7 Afrotropical species: ****''Comperia alfierii'' is a parasitoid of a cockroach ''Blattella'' sp., and a dance fly ''Phyllodromia'' sp. (Egypt, Kenya, South Africa) ****''Comperia austrina'' - no associates known (South Africa) ****''Comperia clavata'' - no associates known (South Africa) ****''Comperia domestica'' - no associates known (South Africa) ****''Comperia faceta'' - no associates known (South Africa) ****''Comperia hirsuta'' - no associates known (South Africa) ****''Comperia merceti'' is a parasitoid of a cockroaches ''Blattella germanica'', ''Supella longipalpa'', ''Supella supellectilium'', ''Periplaneta americana'' (Uganda) * 86b Head and body without metallic refringence; club rounded apically; mandible (fig. 50 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with three slender teeth, the dorsal one somewhat retracted; parasitic in Pseudococcidae - **''''' Aphycus''''' Mayr, 1876 *** 33 species worldwide; 1 Afrotropical species: ****''Aphycus comperei'' is a parasitoid of mealybugs ''Pedrococcus'' sp. (South Africa) === 87 Antennal club not white=== * 87a Antenna nine-segmented, the club unsegmented. Polyembryonic parasitoids of Lepidoptera larvae................88 * 87b Antenna eleven-segmented, the club three-segmented................89 === 88 Antenna nine-segmented, the club unsegmented=== * 88a Antennal club obliquely truncate from near base (fig. 71 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); postmarginal vein of fore wing short, shorter than stigmal - [[File:Copidosoma varicorne female.jpg|thumb|''Copidosoma varicorne'', female]][[File:202101 Copidosoma floridanum attack.svg|thumb|''Copidosoma floridanum'']] **''''' Copidosoma''''' Ratzeburg, 1844 *** ''Litomastix'' is a synonym of ''Copidosoma'' *** See also step 109 below *** 212 species worldwide; 8 Afrotropical species: ****''Copidosoma delattrei'' (Ghesquiere) (2) ****''Copidosoma desantisi'' Annecke and Mynhardt (2) ****''Copidosoma floridanum'' is a parasitoid of Lepidoptera (Cape Verde Islands, Ivory Coast, Senegal) ****''Copidosoma koehleri'' Blanchard (17) ****''Copidosoma primulum'' (Mercet) (2) ****''Copidosoma truncatellum'' (Dalman) (2) ****''Copidosoma uruguayensis'' Tachnikawa (3) ****''Copidosoma varicorne'' (Nees) (7) * 88b Antennal club rounded or more or less squarely truncate at apex (fig. 72 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); postmarginal vein (fig. 73 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) unsually long, reaching to a level beyond apex of stigmal vein - [[File:Ageniaspis fuscicollis (Dalman, 1820) Fauna iberica 1921 p337 Fig143.jpg|thumb|Female ''Ageniaspis fuscicollis'']][[File:Ageniaspis fuscicollis (Dalman, 1820) Fauna iberica 1921 p337 Fig145.jpg|thumb|Postmarginal and stigmal veins, ''Ageniaspis fuscicollis'' female fore-wing.]] **''''' Ageniaspis''''' Dahlbom, 1857 *** 21 species worldwide; 2 Afrotropical species: ****''Ageniaspis citricola'' Logvinovskaya (1) ****''Ageniaspis primus'' Prinsloo (1) === 89 Antenna eleven-segmented, the club three-segmented=== * 89a Mandible (fig. 74 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with three distinct teeth and a straight dorsal truncation. Parasitic in Lacciferidae........ 90 * 89b Mandible otherwise........ 91 === 90 === * 90a Abdomen with two interrupted rows of gland-like structures (fig. 75 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), one each on tergum II and VII, head and thorax with rather strong metallic refringence - **''''' Adencyrtus''''' Prinsloo, 1977 *** 3 species worldwide; 3 Afrotropical species: ****''Adencyrtus afer'' Prinsloo (2) ****''Adencyrtus callainus'' Prinsloo (2) ****''Adencyrtus pictus'' Prinsloo (2) * 90b Abdomen without gland-like structures; head and body at most very slightly metallic in parts. Male antenna (fig. 57 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with two small, transverse funicle segments and a long, unsegmented banana-shaped club - **''''' Erencyrtus''''' Mahdihassan, 1923 *** 6 species worldwide; 4 Afrotropical species: ****'' Erencyrtus ater'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus contrarius'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus fuscus'' is a parasitoid of coccid scales ''Waxiella mimosae'', lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus notialis'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) === 91 === * 91a Antennal scrobes sulcate (figs 53, 54, 76), their lateral margins sharply angled, usually impressed on face as an inverted V........ 92 * 91b Scrobes otherwise........ 94 === 92 === * 92a Gonostyli very short and broad (fig. 77 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), subtriangular, densely covered with short, spine-like setae. Body black in colour; male antenna ten-segmented, the club two-segmented; parasitic in Lacciferidae - **'''''Laccacida''''' Prinsloo, 1977 *** 1 species worldwide; 1 Afrotropical species: ****'' Laccacida lacunata'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) * 92b Gonostyli otherwise: elongate and slender, not densely covered with spine-like setae. Antenna of male nine-segmented, the club not segmented........ 93 === 93 === * 93a Mandible (fig. 78 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with three teeth; frontovertex with fine punctations; parasitic in Lacciferidae - **''''' Tachardiaephagus''''' Ashmead, 1904 *** 7 species worldwide; 4 Afrotropical species: ****'' Tachardiaephagus absonus'' Prinsloo (2) ****'' Tachardiaephagus communis'' Prinsloo (2) ****'' Tachardiaephagus gracilis'' Prinsloo (2) ****'' Tachardiaephagus similis'' Prinsloo (2) * 93b Mandible (fig. 55 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with two teeth and a dorsal truncation; frontovertex with large punctations or with pits; parasitic in Coccidae - **''''' Aloencyrtus''''' Prinsloo, 1978 *** 20 species worldwide; 19 Afrotropical species: ****'' Aloencyrtus alox'' - no associates known (South Africa) ****'' Aloencyrtus angustifrons'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Gascardia brevicauda'' spp. (South Africa) ****'' Aloencyrtus claripennis'' is a parasitoid of coccid scales ''Inglisia conchiformis'' (South Africa, Uganda) ****'' Aloencyrtus coelops'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Gascardia destructor'', ''Waxiella mimosae'' (Eritrea, Nigeria, South Africa, Uganda) ****'' Aloencyrtus delottoi'' is a parasitoid of coccid scales ''Saissetia opulenta'' (Kenya, South Africa) ****'' Aloencyrtus diaphorocerus'' is a parasitoid of coccid scales ''Saissetia coffeae'' (Mauritius, Seychelles) ****'' Aloencyrtus distinguendus'' is a parasitoid of coccid scales ''Coccus subhemisphaericus'', ''Lecanium'' sp. (Cameroon, Ghana, Nigeria) ****'' Aloencyrtus facetus'' is a parasitoid of coccid scales ''Ceroplastes longicauda'' (South Africa) ****'' Aloencyrtus habrus'' is a parasitoid of coccid scales ''Saissetia coffeae'' (Cameroon) ****'' Aloencyrtus hardii'' is a parasitoid of coccid scales ''Parasaissetia nigra'', ''Saissetia'' spp. (South Africa) ****'' Aloencyrtus johani'' is a parasitoid of coccid scales ''Parasaissetia nigra'' (South Africa) ****'' Aloencyrtus lindae'' is a parasitoid of coccid scales ''Ceroplastes'' sp. (South Africa) ****'' Aloencyrtus nativus'' is a parasitoid of coccid scales ''Coccus longulus'', ''Parthenolecanium persicae'' (Benin, Madagascar, South Africa, Uganda, Zimbabwe) ****'' Aloencyrtus obscuratus'' is a parasitoid of coccid scales ''Lecanium somereni'', ''Saissetia'' spp. (Ghana, Kenya, South Africa) ****'' Aloencyrtus saissetiae'' is a parasitoid of coccid scales ''Ceroplastes'' sp. ''Coccus'' spp. ''Cryptinglisia lounsburyi'', ''Parasaissetia nigra'', ''Saissetia'' spp. (Ivory Coast, Kenya, Malawi, South Africa, Uganda, Zimbabwe) ****'' Aloencyrtus ugandensis'' is a parasitoid of coccid scales ''Ceroplastes'' spp. (Uganda) ****'' Aloencyrtus umbrinus'' is a parasitoid of coccid scales ''Ceroplastes'' spp. (Kenya, ) ****'' Aloencyrtus utilis'' is a parasitoid of coccid scales ''Saissetia oleae'' (South Africa) ****'' Aloencyrtus vivo'' - no associates known (Uganda) === 94 === * 94a Antennal funicle with contrasting white and black segments........ 95 * 94b Antennal funicle unicolorous or almost so........ 97 === 95 === * 95a Body yellowish to brownish, without a metallic tinge; antennal club rounded apically; primary parasitoids of Coccidae - [[File:Metaphycus inat 4772310 a.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. * 95b Body black, in parts with weak to strong metallic refringence; antennal club obliquely or transversely truncate apically; not parasitic in Coccidae........ 96 === 96 === * 96a Mandible with three distinct teeth; antennal club (fig. 79 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) transversely truncate apically; marginal vein punctiform (fig. 80 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); polyembryonic parasitoids in larvae of Lepidoptera - **'''''Paralitomastix''''' Mercet, 1921 is a synonym of '''''Copidosoma''''' Ratzeburg, 1844 (see step 88) * 96b Mandible with two teeth and a dorsal truncation; antennal club (fig. 81 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) obliquely truncate apically; marginal vein of fore wing (fig. 82 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) well developed; hyperparasitic in Coccidae - **'''''Tremblaya''''' Trjapitzin, 1985 *** ''Silvestria'' Trjapitzin, 1972 is a synonym of ''Tremblaya'' *** 5 species worldwide; 5 Afrotropical species: ****''Tremblaya ceroplastae'' (Risbec) (4) ****''Tremblaya coffeicola'' Noyes (1) ****''Tremblaya minor'' (Silvestri) (6) ****''Tremblaya oleae'' (Silvestri) (5) ****''Tremblaya palaeococci'' (Risbec) (2) === 97 === * 97a All funicle segments plainly wider than long................98 * 97b Funicle segments not all wider than long................102 === 98 All funicle segments plainly wider than long=== * 98a Postmarginal vein (fig. 83 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) of fore wing very long, much longer than marginal, reaching to a level beyond apex of stigmal; paratergites present; mandible with three slender teeth, the middle one longest; parasitic in Pseudococcidae - **'''''Blepyrus''''' Howard, 1898 *** 19 species worldwide; 3 Afrotropical species: ****''Blepyrus insularis'' (Cameron) (11) ****''Blepyrus saccharicola'' Gahan (2) ****''Blepyrus schwarzi'' (Howard) (1) * 98b Fore wing venation otherwise; paratergites absent; mandible otherwise; not parasitic in mealybugs........ 99 === 99 === * 99a Antennal scrobes absent or represented by two very short, shallow furrows, at most hardly longer than the longest diameter of a torulus; the latter placed at or close to mouth margin; parasitic in aculeate Hymenoptera - **'''''Coelopencyrtus''''' Timberlake, 1919 ***31 species worldwide; 7 Afrotropical species: ****''Coelopencyrtus bekiliensis'' (Risbec, 1952) (Madagascar) ****''Coelopencyrtus callainus'' Annecke, 1958 is a parasitoid of ''Xylocopa'' species (Mozambique, South Africa, Zimbabwe) ****''Coelopencyrtus cyprius'' Annecke, 1968 is a parasitoid of ''Xylocopa'' species (Zimbabwe) ****''Coelopencyrtus ivorensis'' (Risbec, 1953) (Ivory Coast) Only this species has reduced wings? ****''Coelopencyrtus nothylaei'' Annecke 1968 is a parasitoid of ''Hylaeus'' species (South Africa) ****''Coelopencyrtus taylori'' (Annecke and Doutt, 1961) is a parasitoid of ''Xylocopa'' species (South Africa) ****''Coelopencyrtus watmoughi'' Annecke, 1968 is a parasitoid of ''Xylocopa flavorufa'' (Zimbabwe). * 99b Antennal scrobes otherwise, usually well developed; antennal sockets placed higher on face, their upper limits usually about level with lower eye margins; not parasitic in aculeate Hymenoptera........ 100 === 100 === * 100a Maxillary palpi each with three segments, the labial with a single segment; small species, about 0,6 mm in length; parasitic in eggs of Coleoptera and Diptera - **''''' Oobius''''' Trjapitzin, 1963 *** 45 species worldwide; 4 Afrotropical species: ****''Oobius abditus'' Annecke (2) ****''Oobius funestus'' Annecke (2) ****''Oobius longoi'' (Siscaro) (4) ****''Oobius striatus'' Annecke (3) * 100b Palpi otherwise; larger species, often more than 1 mm in length; not egg parasitoids........ 101 === 101 === * 101a Head and body dominantly dark blackish-brown to black; antennal club (fig. 84 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) obliquely truncate apically; parasitic in Diptera - **'''''Exoristobia''''' Ashmead, 1904 *** 9 species worldwide; 3 Afrotropical species: ****''Exoristobia dipterae'' (Risbec) (8) ****''Exoristobia macrocerus'' (Masi) (1) ****''Exoristobia ugandensis'' Subba Rao (2) * 101b Head and body dominantly yellowish to brownish-yellow; antennal club rounded apically; parasitic in Coccoidea - [[File:Metaphycus inat 4772310 b.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. *** ''Metaphycus'' keys out at 82, 95, 101, 110, 119 === 102 Funicle segments not all wider than long=== * 102a Small species, at most about 1 mm in length, but usually less than 1 mm; exclusively parasitic in insect eggs, often in those of Lepidoptera, Hemiptera and Coleoptera........ 103 * 102b Larger species, usually more than 1 mm in length; if less than 1 mm in length, then not parasitic in insect eggs, but in the larvae and pupae of insects................104 === 103 === * 103a Antennal club longer than entire funicle; funicle segments I-V transverse; maxillary palpi each with three segments, the labial palpi not segmented - **''''' Oobius''''' Trjapitzin, 1963 *** 45 species worldwide; 4 Afrotropical species (See step 100) * 103b Antennal club shorter than entire funicle; maxillary palpi each with four segments, the labial with three - [[File:Gypsy Moth (Lymantria dispar) Egg Mass Being Parasitized by Ooencyrtus kuvanae - Mississauga, Ontario.jpg|thumb|''Ooencyrtus kuvanae'' on a moth egg mass, Canada]] [[File:Ooencyrtus gravis, female, Spain.jpg|thumb|''Ooencyrtus gravis'', female, Spain.]] **'''''Ooencyrtus''''' Ashmead, 1900 *** 343 species worldwide; 38 Afrotropical species: ****''Ooencyrtus afer'' Prinsloo (1) ****''Ooencyrtus albicrus'' Prinsloo (3) ****''Ooencyrtus angolensis'' Prinsloo (1) ****''Ooencyrtus austrinus'' Prinsloo (1) ****''Ooencyrtus azul'' Prinsloo (1) ****''Ooencyrtus bambeyi'' (Risbec) (2) ****''Ooencyrtus bedfordi'' Prinsloo (1) ****''Ooencyrtus camerounensis'' (Risbec) (4) ****''Ooencyrtus cinctus'' Prinsloo (2) ****''Ooencyrtus cirinae'' Prinsloo (1) ****''Ooencyrtus congensis'' Prinsloo (1) ****''Ooencyrtus cretatus'' Prinsloo (1) ****''Ooencyrtus demodoci'' (Risbec) (4) ****''Ooencyrtus dipterae'' (Risbec) (4) ****''Ooencyrtus distatus'' Prinsloo (1) ****''Ooencyrtus epilachnae'' Annecke (3) ****''Ooencyrtus exallus'' Prinsloo (1) ****''Ooencyrtus guamensis'' Fullaway (6) ****''Ooencyrtus homoeoceri'' (Risbec) (3) ****''Ooencyrtus insignis'' Prinsloo (1) ****''Ooencyrtus jeani'' Noyes and Prinsloo (3) ****''Ooencyrtus kuvanae'' is an egg parasitoid of Lepidoptera and Hemiptera (Nigeria) ****''Ooencyrtus lamborni'' Waterston (11) ****''Ooencyrtus mimus'' Prinsloo (1) ****''Ooencyrtus nanus'' Prinsloo (1) ****''Ooencyrtus pallidipes'' (Ashmead) (2) ****''Ooencyrtus piezodori'' (Risbec) (3) ****''Ooencyrtus polyphagus'' (Risbec) (3) ****''Ooencyrtus puparum'' Prinsloo (1) ****''Ooencyrtus rigemae'' (Risbec) (3) ****''Ooencyrtus risbeci'' Prinsloo (1) ****''Ooencyrtus rufogaster'' (Risbec) (2) ****''Ooencyrtus senegalensis'' (Risbec) (4) ****''Ooencyrtus sesbaniae'' Risbec (1) ****''Ooencyrtus sinis'' Prinsloo (1) ****''Ooencyrtus unicus'' Prinsloo (1) ****''Ooencyrtus utetheisae'' (Risbec) (11) ****''Ooencyrtus ventralis'' (Masi) (1) === 104 === * 104a Antennal scrobes absent or represented by two very short shallow furrows, at most hardly longer than the longest diameter of a torulus; head usually approximately round in outline in frontal view with mouth margin broad, antennal sockets placed close to mouth margin; parasitic in aculeate Hymenoptera - **'''''Coelopencyrtus''''' Walker, 1837 ***31 species worldwide; 7 Afrotropical species: ****''Coelopencyrtus bekiliensis'' (Risbec, 1952) (Madagascar) ****''Coelopencyrtus callainus'' Annecke, 1958 is a parasitoid of ''Xylocopa'' species (Mozambique, South Africa, Zimbabwe) ****''Coelopencyrtus cyprius'' Annecke, 1968 is a parasitoid of ''Xylocopa'' species (Zimbabwe) ****''Coelopencyrtus ivorensis'' (Risbec, 1953) (Ivory Coast) Only this species has reduced wings? ****''Coelopencyrtus nothylaei'' Annecke 1968 is a parasitoid of ''Hylaeus'' species (South Africa) ****''Coelopencyrtus taylori'' (Annecke and Doutt, 1961) is a parasitoid of ''Xylocopa'' species (South Africa) ****''Coelopencyrtus watmoughi'' Annecke, 1968 is a parasitoid of ''Xylocopa flavorufa'' (Zimbabwe). * 104b Scrobes otherwise, usually well developed; other characters different; not parasitic in aculeate Hymenoptera........ 105 === 105 === * 105a Mandible with three acute or subacute teeth (figs 85, 86)........ 106 * 105b Mandible not with three acute or subacute teeth; rarely with three teeth, but then dorsal tooth not acute or subacute, but broad, the apex squarely to roundly truncate (fig. 87 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)................111 === 106 Mandible with three acute or subacute teeth=== * 106a Head and body entirely and brilliantly metallic in colour; parasitic in Aclerdidae - [[File:Mayridia pulchra, female, Spain.jpg|thumb|''Mayridia pulchra'', female, Spain]] **'''''Mayridia''''' Mercet, 1921 ***34 species worldwide; 2 Afrotropical species: ****''Mayridia arida'' Prinsloo and Annecke (3) ****''Mayridia maryae'' Prinsloo (1) * 106b Head and body at most with a faint to moderately strong metallic refringence on frontovertex, face and thorax; not parasitic in Aclerdidae........ 107 === 107 === * 107a Antennal club as long as the distal three funicle segments together; marginal vein or fore wing longer than stigmal; parasitic in dryinid wasps - **'''''Helegonatopus''''' Perkins, 1906 ***13 species worldwide; 1 Afrotropical species: ****''Helegonatopus saotomensis'' Prinsloo (2) * 107b Antennal club longer than funicle segments III-VI; marginal vein at most as long as stigmal; not parasitic in Hymenoptera........ 108 === 108 === * 108a Antennal club obliquely truncate apically. Thoracic dorsum usually with metallic green and purple refringence; polyembryonic parasitoids of Lepidoptera larvae - **'''''Litomastix''''' Thomson, 1876 *** ''Litomastix'' is a synonym of ''Copidosoma'', making this step redundant, although presumably useful for identification of species groups?. * 108b Antennal club rounded apically, or club segments transverse........ 109 === 109 === * 109a Antenna long and slender, the funicle segments all longer than wide; polyembryonic parasitoids of Lepidoptera larvae - [[File:Copidosoma koehleri 03.jpg|thumb|''Copidosoma koehleri'']] **''''' Copidosoma''''' Ratzeburg, 1844 *** See also step 88 (above) *** 212 species worldwide; 8 Afrotropical species: ****''Copidosoma delattrei'' (Ghesquiere) (2) ****''Copidosoma desantisi'' Annecke and Mynhardt (2) ****''Copidosoma floridanum'' (Ashmead) (6) ****''Copidosoma koehleri'' Blanchard (17) ****''Copidosoma primulum'' (Mercet) (2) ****''Copidosoma truncatellum'' (Dalman) (2) ****''Copidosoma uruguayensis'' Tachnikawa (3) ****''Copidosoma varicorne'' (Nees) (7) * 109b Funicle segments not all longer than wide, the antenna not particularly slender; not parasitic in Lepidoptera................110 === 110 === * 110a Marginal and postmarginal veins very short, the latter much shorter than stigmal vein, sometimes punctiform; frontovertex without punctations; usually parasitic in Coccidae - [[File:Metaphycus inat 4772310 a.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. *** ''Metaphycus'' keys out at 82, 95, 101, 110, 119 * 110b Marginal and postmarginal veins well developed, the latter reaching almost to the level of apex of stigmal vein; frontovertex with scattered puncrations; exclusively parasitic in Lacciferidae - **''''' Tachardiaephagus''''' Ashmead, 1904 ***'' Tachardiaephagus'' keys out at 93, 110 *** 7 species worldwide; 4 Afrotropical species: ****'' Tachardiaephagus absonus'' Prinsloo (2) ****'' Tachardiaephagus communis'' Prinsloo (2) ****'' Tachardiaephagus gracilis'' Prinsloo (2) ****'' Tachardiaephagus similis'' Prinsloo (2) === 111 Mandible not with three acute or subacute teeth=== * 111a Tergum II and VII of abdomen each with an interrupted row of gland-like structures (fig. 88 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); Antennal club long, usually about as long as enure funicle; legs usually banded; parasitic in Diaspididae. - **'''''Zaomma''''' Ashmead, 1900 *** 17 species worldwide; 8 Afrotropical species: ****''Zaomma acaciae'' (Risbec) (1) ****''Zaomma carinae'' Prinsloo (2) ****''Zaomma cestus'' Prinsloo (2) ****''Zaomma ficusae'' (Risbec) (1) ****''Zaomma lambinus'' (Walker) (5) ****''Zaomma sitis'' Prinsloo (2) ****''Zaomma vix'' Prinsloo (2) ****''Zaomma xhosa'' Prinsloo (2) * 111b Abdomen without gland-like structures........ 112 === 112 Abdomen without gland-like structures=== * 112a Maxillary palpi each with three segments, the labial each with two; parasitic in Diaspididae. Small species, usually not much more than 1 mm in length; antenna generally slender, the club long - **'''''Coccidencyrtus''''' Ashmead, 1900 *** 36 species worldwide; 3 Afrotropical species: ****''Coccidencyrtus ochraceipes'' Gahan (1) ****''Coccidencyrtus plectroniae'' Risbec (1) ****''Coccidencyrtus punctatus'' Compere and Annecke (1) * 112b Maxillary palpi each with four segments, the labial with three; not parasitic in Diaspididae........ 113 === 113 === * 113a Marginal vein of fore wing relatively long*, broad, dark in colour, about as long as, or longer than, stigmal vein (figs 89, 90); mandible with three well separated teeth, the upper one squarely or roundly truncate (fig. 87 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 114 * 113b Marginal vein punctiform or very short, shorter than stigmal (figs 91, 92); if rarely subequal to stigmal, then mandible with a well separated ventral tooth and a broad dorsal truncation (fig. 93 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 115 === 114 === * 114a Body longer than 1 mm; thorax slender, the scutellum longer than wide; legs usually not banded; primary parasitoids of Syrphidae - [[File:Syrphophagus aphidivorus, female, Spain.jpg|thumb|''Syrphophagus aphidivorus'', female, Spain]][[File:Syrphophagus inat 125775071.jpg|thumb|''Syrphophagus'' sp., Georgia, US.]] **''''' Syrphophagus''''' Ashmead, 1900 *** 85 species worldwide; 6 Afrotropical species: ****''Syrphophagus africanus'' (Gahan) (6) ****''Syrphophagus aphidivorus'' (Mayr) (2) ****''Syrphophagus cassatus'' (Annecke) (6) ****''Syrphophagus coccidicola'' (Gahan) (2) ****''Syrphophagus nigrocyaneus'' Ashmead (2) ****''Syrphophagus similis'' (Prinsloo) (3) * 114b Smaller species, usually about 1 mm in length; scutellum relatively broad, about as long as wide or a little wider than long; legs usually banded; hyperparasitoids of aphids, rarely of psyllids - **''''' Syrphophagus''''' Ashmead, 1900 ***''Aphidencyrtus'' is a synonym of ''Syrphophagus''; this step previously separated ''Aphidencyrtus'' *** 85 species worldwide; 6 Afrotropical species: ****''Syrphophagus africanus'' (Gahan) (6) ****''Syrphophagus aphidivorus'' (Mayr) (2) ****''Syrphophagus cassatus'' (Annecke) (6) ****''Syrphophagus coccidicola'' (Gahan) (2) ****''Syrphophagus nigrocyaneus'' Ashmead (2) ****''Syrphophagus similis'' (Prinsloo) (3) === 115 === * 115a Head and body pale, dominantly yellow in colour, without metallic refringence; parasitic in Coccidae. Male remarkable in colour: orange and brilliant metallic green in parts - **''''' Argutencyrtus''''' Prinsloo and Annecke, 1974<ref name=Prinsloo1974>Prinsloo, G.L. & Annecke, D.P. (1973). A new genus and species of Encyrtidae (Hymenoptera: Chalcidoidea) from South Africa. Journal of the Entomological Society of Southern Africa, 37(2), 345-349. https://journals.co.za/doi/abs/10.10520/AJA00128789_2638</ref> *** 1 species worldwide; 1 Afrotropical species: ****''Argutencyrtus luteolus'' Prinsloo and Annecke, 1974 * 115b Head and body entirely metallic in colour, or black with some parts with faint to moderately strong metallic refringence, or rarely at least head and thorax black; not parasitic in Coccidae........ 116 === 116 === * 116a Usually entirely metallic green or blue-green in colour, rarely with only some parts metallic in colour; parasitic in Psyllidae - [[File:Psyllaephagus inat 165372177 davidfdz b82, some rights reserved (CC-BY).jpg|thumb|''Psyllaephagus'' sp., Córdoba, Spain.]][[File:Psyllaephagus guangxiensis (10.3897-BDJ.9.e63253) Figure 1.jpg|thumb|Female ''Psyllaephagus guangxiensis'', China]] [[File:Psyllaephagus euphyllurae, female, Spain.jpg|thumb|''Psyllaephagus euphyllurae'', female, Spain]] **'''''[[w:Psyllaephagus|Psyllaephagus]]''''' Ashmead, 1900 *** 246 species worldwide; 30 Afrotropical species: ****''Psyllaephagus africanus'' Prinsloo (3) ****''Psyllaephagus albicrus'' Prinsloo (2) ****''Psyllaephagus arytainae'' Prinsloo (2) ****''Psyllaephagus bicolor'' Prinsloo (2) ****''Psyllaephagus blastopsyllae'' Tamesse, Soufo, Tchanatame, Dzokou, Gumovsky and De Coninck (1) ****''Psyllaephagus bliteus'' Riek, 1962 (Australia, introduced to South Africa and also Neotropical and western Palaearctic regions) ****''Psyllaephagus callainus'' Prinsloo (2) ****''Psyllaephagus capeneri'' Prinsloo (2) ****''Psyllaephagus cellulatus'' Waterston (1) ****''Psyllaephagus chianganus'' Prinsloo (3) ****''Psyllaephagus cincticrus'' Prinsloo (2) ****''Psyllaephagus dealbatae'' (Risbec) (1) ****''Psyllaephagus dispar'' Prinsloo (2) ****''Psyllaephagus furvus'' Prinsloo (1) ****''Psyllaephagus hibiscusae'' (Risbec) (1) ****''Psyllaephagus io'' Prinsloo (1) ****''Psyllaephagus lucaris'' Prinsloo (2) ****''Psyllaephagus minor'' Prinsloo (2) ****''Psyllaephagus oleae'' Prinsloo (2) ****''Psyllaephagus ornatus'' Prinsloo (2) ****''Psyllaephagus pauliani'' (Risbec) (1) ****''Psyllaephagus perendinus'' Robinson (1) ****''Psyllaephagus phytolymae'' (Ferriere) (5) ****''Psyllaephagus pulvinatus'' (Waterston) (12) ****''Psyllaephagus rhusae'' Prinsloo (2) ****''Psyllaephagus secus'' Prinsloo (3) ****''Psyllaephagus tessmannii'' Tamesse and Tiyo (1) ****''Psyllaephagus vastus'' Prinsloo (2) ****''Psyllaephagus viridis'' Prinsloo (2) ****''Psyllaephagus yaseeni'' Noyes (Tanzania) * 116b Never entirely metallic in colour, at most the head and thoracic dorsum with weak to moderately strong metallic refringence; parasitic in Syrphidae and Coccinellidae - **'''''Syrphophagus''''' Ashmead, 1900 *** ''Syrphophagus'' keys out at 114a, 114b, 116b, 117a *** 85 species worldwide; 6 Afrotropical species: ****''Syrphophagus africanus'' (Gahan) (6) ****''Syrphophagus aphidivorus'' (Mayr) (2) ****''Syrphophagus cassatus'' (Annecke) (6) ****''Syrphophagus coccidicola'' (Gahan) (2) ****''Syrphophagus nigrocyaneus'' Ashmead (2) ****''Syrphophagus similis'' (Prinsloo) (3) == 117 Scape moderately to broadly expanded ventrally, less than three times as long as wide == * 117a Eyes exceptionally setose (fig. 123 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), the setae long, strongly developed; frontovertex sparsely pitted; antenna (fig. 126 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with scape blackish, the remainder of antenna uniformly paler in colour - [[File:Syrphophagus inat 125775071.jpg|thumb|''Syrphophagus'' sp., Georgia, US.]] **'''''Syrphophagus''''' Ashmead, 1900 *** ''Syrphophagus'' keys out at 114b, 116b, 117a *** 85 species worldwide; 6 Afrotropical species: ****''Syrphophagus africanus'' (Gahan) (6) ****''Syrphophagus aphidivorus'' (Mayr) (2) ****''Syrphophagus cassatus'' (Annecke) (6) ****''Syrphophagus coccidicola'' (Gahan) (2) ****''Syrphophagus nigrocyaneus'' Ashmead (2) ****''Syrphophagus similis'' (Prinsloo) (3) * 117b Eyes sparsely setose, the setae fine; frontovertex at most finely punctate; colour of antenna otherwise........ 118 === 118 Eyes sparsely setose=== * 118a Head tending to opisthognathous, the frontovertex almost horizontal, meeting the inflexed face at an acute angle, so that head is subtriangular in lateral view; parasitic in ticks (Ixodidae). Male sometimes brachypterous, in which case the head has a forked process jutting forward at junction of frontovertex and face - [[File:Ixodiphagus hookeri.jpg|thumb|''Ixodiphagus hookeri'', France]] **'''''Ixodiphagus''''' Howard, 1907 ***''Hunterellus'' Howard, 1908 is a synonym of ''Ixodiphagus'' *** 15 species worldwide; 2 Afrotropical species: ****''Ixodiphagus hookeri'' (Howard) (14) ****''Ixodiphagus theilerae'' (Fiedler) (5) * 118b Head hypognathous, the frontovertex more or less convex, rounded on to face; not parasitic in ticks........ 119 === 119 === * 119a Head and body largely yellowish to brownish, without metallic refringence; antennal scrobes more or less well developed; toruli with lower limits well above clypeal margin; parasitic in Coccoidea - [[File:Metaphycus inat 4772310 b.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. *** ''Metaphycus'' keys out at 82, 95, 101, 110, 119 * 119b Head and body dominantly black, the head and thoracic dorsum with faint to strong metallic refringence; scrobes absent or developed as two very short shallow furrows, hardly longer than the longest diameter of a torulus; toruli placed at or close to mouth margin; polyembryonic parasitoids of aculeate Hymenoptera - **'''''Coelopencyrtus''''' Walker, 1837 ***31 species worldwide; 7 Afrotropical species: ****''Coelopencyrtus bekiliensis'' (Risbec, 1952) (Madagascar) ****''Coelopencyrtus callainus'' Annecke, 1958 is a parasitoid of ''Xylocopa'' species (Mozambique, South Africa, Zimbabwe) ****''Coelopencyrtus cyprius'' Annecke, 1968 is a parasitoid of ''Xylocopa'' species (Zimbabwe) ****''Coelopencyrtus ivorensis'' (Risbec, 1953) (Ivory Coast) Only this species has reduced wings? ****''Coelopencyrtus nothylaei'' Annecke 1968 is a parasitoid of ''Hylaeus'' species (South Africa) ****''Coelopencyrtus taylori'' (Annecke and Doutt, 1961) is a parasitoid of ''Xylocopa'' species (South Africa) ****''Coelopencyrtus watmoughi'' Annecke, 1968 is a parasitoid of ''Xylocopa flavorufa'' (Zimbabwe). == 120 Mandible with only two teeth; paratergites usually present; usually without coarse setae at edge of speculum; cercal plates often advanced. Mealybug parasitoids== [Mandible with only two acute or subacute teeth (figs 37, 38 of the Prinsloo-Annecke key[1]). Paratergites (fig. 39 of the Prinsloo-Annecke key[1]) usually present, plainly visible in cleared, slide-mounted specimens; speculum of fore wing usually lacking a row of coarse, spine-like setae along outer edge of speculum; cercal plates often advanced to a level near base of metasoma; exclusively parasitic in Pseudococcidae (from 43)] * 120a Antennal funicle seven-segmented - **''''' Alamella''''' Agarwal, 1966 *** 5 species worldwide; 1 Afrotropical species: ****''Alamella flava'' - a parasitoid of eriococcids and mealybugs (Angola, Madagascar, Namibia, South Africa) ****Species description: [https://www.ias.ac.in/public/Volumes/secb/063/02/0067-0079.pdf Agarwal (1966)]<ref name=Agarwal1966>Agarwal, M. M. (1966). Three undescribed genera and species of Encyrtidae (Hymenoptera-Chalcidoidea) parasitic on coccids. In Proceedings/Indian Academy of Sciences (Vol. 63, No. 2, pp. 67-79). New Delhi: Springer India.</ref> * 120b Club two-segmented; head and body without metallic lustre; maxillary palpi each with three segments, the labial with two. Funicle with six or fewer segments........ 121 === 121 === * 121a Scutellum with a posterior flange or lamella (cf. fig. 15 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); in profile this flange shows as a thin flat caudal projection of the scutellum. Body often black, the head dark metallic green; antenna long, slender, the scape cylindrical; marginal and postmarginal veins long - [[File:Ericydnus inat 183126807 Mario Bassini.jpg|thumb|''Ericydnus'' sp., Italy]] **''''' Ericydnus''''' Haliday, 1832 *** 33 species worldwide; Afrotropical species? *** ''Ericydnus'' sp. - 2 specimens at ARC-PPRI (https://www.gbif.org/occurrence/search?dataset_key=b2ee8537-2a6c-4b4b-965a-538b47788606&taxon_key=1378896) * 121b Scutellum without a flange........ 122 === 122 === * 122a Head prognathous (fig. 94 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), elongate and flattened in dorsal view, almost as long as thorax (fig. 95 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), the eyes elongate, in dorsal view occupying almost whole of head laterally; antenna (fig. 96 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) extremely large, foliaceously flattened, the club three-segmented - **''''' Monstranusia''''' Trjapitzin, 1964 *** 3 species worldwide; 2 Afrotropical species: ****''Monstranusia antennata'' (Narayanan) (1) ****''Monstranusia mirabilissima'' Trjapitzin (4) * 122b Head otherwise; if antenna foliaceously flattened, then club not segmented................123 === 123 === * 123a Antenna nine-segmented........ 124 * 123b Antenna ten or eleven-segmented........ 126 === 124 === * 124a Fore wing distinctly infuscated with hyaline patches (fig. 97 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Head .and body largely metallic in colour; antenna sometimes foliaceously flattened; ovipositor often strongly protruded at apex of metasoma; male antenna with funicle six-segmented, segments II – V each with a ramus - **''''' Tetracnemus''''' Westwood, 1837 *** 37 species worldwide; 2 Afrotropical species: ****''Tetracnemus'' bifasciatellus (Mercet) (1) ****''Tetracnemus gumilevi'' Pilipjuk and Trjapitzin (1) * 124b Fore wing entirely hyaline........ 125 === 125 === * 125a Head and body entirely metallic green to blue-green in colour; antenna (fig. 111 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) long, the fumcle and club broad, somewhat laterally compressed - **''''' Callaincyrtus''''' Prinsloo & Annecke, 1979 *** 1 species worldwide; 1 Afrotropical species: ****''Callaincyrtus decorus'' - no known associates (South Africa, Zimbabwe) * 125b Head and body at most with faint metallic refringence on frontovertex, face and thoracic dorsum; antenna not particularly slender, the segments not flattened - **''''' Allocerellus''''' Silvestri, 1915<ref name=>Silvestri, F. 1915, Contributo all conoscenza degli insetti dell'olivo dell'Eritrea e dell'Africa meridionalei. Bollettino del Laboratorio di Zoologia Generale e Agraria della R. Scuola Superiore d'Agricoltura, Portici 9:305 [https://www.biodiversitylibrary.org/page/14029132 BHL][https://www.nhm.ac.uk/resources/research-curation/projects/chalcidoids/pdf_X/Silves915.pdf PDF]</ref> *** This genus was reviewed in 1995: Prinsloo, G. L. (1995). The encyrtid genus Allocerellus Silvestri (Hymenoptera: Chalcidoidea), parasitoids of mealybugs (Homoptera: Pseudococcidae). Insect Systematics & Evolution, 26(2), 167-179. *** 12 species worldwide; 12 Afrotropical species: ****'' Allocerellus ater'' Prinsloo (1) ****'' Allocerellus bizonatus'' Annecke and Mynhardt (3) ****'' Allocerellus curtus'' Prinsloo (1) ****'' Allocerellus hortensis'' Annecke and Mynhardt (2) ****'' Allocerellus inquirendus'' Silvestri (2) ****'' Allocerellus mimus'' Prinsloo (1) ****'' Allocerellus notatus'' Prinsloo (1) ****'' Allocerellus orestes'' Annecke and Mynhardt (4) ****'' Allocerellus paulus'' Annecke and Mynhardt (3) ****'' Allocerellus venustus'' Annecke and Mynhardt (4) ****'' Allocerellus vittatus'' Annecke and Mynhardt (4) ****'' Allocerellus zonatus'' Annecke and Mynhardt (4) === 126 === * 126a Antenna ten-segmented, the club with two segments........ 127 * 126b Antenna eleven-segmented, the club three-segmented........ 128 === 127 === * 127a Head and body flatlened dorsoventrally; maxillary palpi each with two segments, the labial not segmented. Small species, weakly sclerotized, usually yellowish, without metallic refringence; marginal and postmarginal veins short or punctiform - [[File:Rhopus nigroclavatus Moravvej 2018 Encyrtidae of Khuzestan in southwestern Iran a.jpg|thumb|''Rhopus nigroclavatus'', Iran]] **'''''Rhopus''''' Foerster, 1856 *** This genus was reviewed in 1989: Prinsloo, G. L. (1989). The southern African species of ''Astymachus'' Howard and ''Rhopus'' Foerster (Hymenoptera: Encyrtidae). Journal of the Entomological Society of southern Africa, 52(1), 129-147. *** 70 species worldwide; 7 Afrotropical species: ****'' Rhopus adustus'' Prinsloo (2) ****'' Rhopus discretus'' Prinsloo (1) ****'' Rhopus geminus'' Prinsloo (2) ****'' Rhopus luridus'' Prinsloo (1) ****'' Rhopus notius'' Prinsloo (2) ****'' Rhopus pilatus'' Prinsloo (1) ****'' Rhopus urbanus'' Prinsloo (2) * 127b Head and body not flattened dorsoventrally; maxillary palpi each with three segments, the labial each with two - **''''' Allocerellus''''' Silvestri, 1915 *** 12 species worldwide; 12 Afrotropical species: ***See step 125 === 128 === * 128a Frontovertex (fig. 98 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) densely pitted, the pits with a metallic green lustre; antennal scape subcylindical. Dominantly black species, the fore wing entirely and strongly infuscated; cephalic margin of fore wing forming an incision at apex of submarginal vein; male antenna with six transverse funicle segments and a long unsegmented banana-shaped club - [[File:Aenasius 2019 08 25 9692.jpg|thumb|''Aenasius'' sp., South Africa]] **''''' Aenasius''''' Walker, 1846 *** ''Chalcaspis'' Howard, 1895 is a synonym of '' Aenasius'' *** 42 species worldwide; 7 Afrotropical species: ****'' Aenasius abengouroui'' (Risbec) (4) ****'' Aenasius advena'' Compere (9) ****'' Aenasius comperei'' (Kerrich) (4) ****'' Aenasius flandersi'' Kerrich (1) ****'' Aenasius hyettus'' (Walker) (1) ****'' Aenasius martinii'' (Compere) (4) ****'' Aenasius phenacocci'' (Ashmead) (1) * 128b Frontovertex at most punctate, the punctations not refringent........ 129 === 129 === * 129a Head and body flattened dorsoventrally; maxillary palpi each with two segments, the labial not segmented. Small species, weakly sclerotized, usually yellowish, without metallic refringence; marginal and postmarginal veins very short or punctiform - [[File:Rhopus nigroclavatus Moravvej 2018 Encyrtidae of Khuzestan in southwestern Iran a.jpg|thumb|''Rhopus nigroclavatus'', Iran]] **''''' Rhopus''''' Foerster, 1856 *** This genus was reviewed in 1989: Prinsloo, G. L. (1989). The southern African species of ''Astymachus'' Howard and ''Rhopus'' Foerster (Hymenoptera: Encyrtidae). Journal of the Entomological Society of southern Africa, 52(1), 129-147. *** 70 species worldwide; 7 Afrotropical species: **** See step 127 * 129b Head and body not flattened dorsoventrally; palpi otherwise........ 130 === 130 === * 130a Maxillary palpi each with three segments, the labial each with two................131 * 130b Maxillary palpi each with four segments, the labial three-segmented........ 132 === 131 === * 131a Antenna (fig. 99 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) long, filiform, the funicle segments all plainly longer than wide; postmarginal vein (fig. 100 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) of fore wing long, extending to a level well beyond apex of stigmal; small species. Fore wing hyaline or partly infuscated - [[File:Leptomastidea abnormis inat 8538894 Jesse Rorabaugh.jpg|thumb|''Leptomastidea abnormis'', California, USA]] **''''' Leptomastidea''''' Mercet, 1916 *** This genus was reviewed in 2001: Prinsloo, G.L. 2001, The aftrotropical species of Leptomastidea Mercet (Hymenoptera: Encyrtidae) parasitoids of mealybugs. Journal of Hymenoptera Research 10(2):158-159. Includes photos of fore wings. *** 23 species worldwide; 8 Afrotropical species: ****'' Leptomastidea abnormis'' (Girault) (12) ****'' Leptomastidea ascia'' Prinsloo (1) ****'' Leptomastidea jeanneli'' Mercet (5) ****'' Leptomastidea lamto'' Prinsloo (1) ****'' Leptomastidea pondo'' Prinsloo (1) ****'' Leptomastidea tecta'' Prinsloo (1) ****'' Leptomastidea turba'' Prinsloo (1) ****'' Leptomastidea usta'' Prinsloo (1) * 131b Antenna (fig. 101 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) not particularly slender, the funicle segments not all longer than wide; postmarginal vein short, shorter than stigmal; larger species - [[File:Anagyrus lopezi.jpg|thumb|''Anagyrus lopezi'']] **''''' Anagyrus''''' Howard, 1896 *** ''Doliphoceras'' Mercet, 1921 is a synonym of '' Anagyrus'' *** 293 species worldwide; 33 Afrotropical species: ****'' Anagyrus aberiae'' Guerrieri (1) ****'' Anagyrus abyssinicus'' Compere (4) ****'' Anagyrus agraensis'' Saraswat (1) ****'' Anagyrus amnicus'' Prinsloo (1) ****'' Anagyrus amoenus'' Compere (5) ****'' Anagyrus antoniae'' Guerrieri (1) ****'' Anagyrus arambourgi'' Risbec (1) ****'' Anagyrus arenaria'' Prinsloo (1) ****'' Anagyrus aurantifrons'' Compere (6) ****'' Anagyrus bambeyi'' Risbec (3) ****'' Anagyrus beneficians'' Compere (7) ****'' Anagyrus bugandaensis'' Compere (5) ****'' Anagyrus diversicornis'' (Howard) (11) ****'' Anagyrus fusciventris'' (Girault) (2) ****'' Anagyrus gracilis'' (Hayat) (3) ****'' Anagyrus greeni'' Howard (1) ****'' Anagyrus haroldi'' Noyes and Hayat (4) ****'' Anagyrus incongruens'' (Masi) (1) ****'' Anagyrus indicus'' (Subba Rao) (1) ****'' Anagyrus kivuensis'' Compere (5) ****'' Anagyrus lopezi'' (De Santis) (92) ****'' Anagyrus mangicola'' Noyes (7) ****'' Anagyrus mirzai'' Agarwal and Alam (3) ****'' Anagyrus nigrescens'' Compere (5) ****'' Anagyrus pseudococci'' (Girault) (10) ****'' Anagyrus pullus'' Compere (7) ****'' Anagyrus rubellus'' (Annecke) (4) ****'' Anagyrus saccharicola'' Timberlake (8) ****'' Anagyrus siccus'' (Prinsloo and Annecke) (3) ****'' Anagyrus subflaviceps'' (Girault) (2) ****'' Anagyrus subnigricornis'' Ishii (1) ****'' Anagyrus subproximus'' (Silvestri) (5) ****'' Anagyrus swezeyi'' Timberlake (2) === 132 === * 132a Antennal funicle with contrasting white and black segments; if rarely unicolorous, then marginal and postmarginal veins very short or punctiform........ 133 * 132b Funicle unicolorous; marginal and postmarginal veins well developed, the latter often very long........ 134 === 133 === * 133a Antennal scape moderately to broadly expanded ventrally (fig. 102 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); fore wing hyaline; frontovertex without punctations - **''''' Anagyrus''''' Howard, 1896 *** 293 species worldwide; 33 Afrotropical species: **** See step 131b * 133b Antennal scape subcylindrical (fig. 121 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); fore wing weakly to strongly infuscated (fig. 119 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), at least in the distal three-fourths or so; frontovertex and face with scattered punctations (fig. 118 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Basal part of fore wing with setation as in fig. 120 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>; male antenna as in fig. 122 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/> - [[File:Apoleptomastix iNat 165108113.jpg|thumb|''Apoleptomastix'' sp., South Africa]] **''''' Apoleptomastix''''' Kerrich, 1982 ***''Xiphomastix'' De Santis, 1972 is a synonym of ''Apoleptomastix'' *** 6 species worldwide; 2 Afrotropical species: ****''Apoleptomastix anneckei'' Pseudococcidae ''Antonina'' sp. (Gambia, South Africa, Zimbabwe) ****''Apoleptomastix bicoloricornis'' Pseudococcidae ''Brevennia rehi'', ''Coccidohystrix insolita'', ''Heterococcus nigeriensis'' (Ethiopia, Gambia, Namibia, Nigeria, South Africa, Zambia, Zimbabwe) === 134 === * 134a Fore wing distinctly infuscated with hyaline patches........ 135 * 134b Fore wing hyaline; if rarely infuscated, then with faint longitudinally infuscated bands........ 136 === 135 === * 135a Head and body dominantly orange-red; fore wing (fig. 103 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) tapering towards apex from the level of apex of venation, the wing disc characteristically maculated as in fig. 103 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>; antenna not particularly slender, the scape somewhat expanded ventrally, about three times as long as its greatest width; wings held horizontal in life - **''''' Yasumatsuiola''''' Trjapitzin, 1977 *** 1 species worldwide; No Afrotropical species? ****''Yasumatsuiola orientalis'' Trjapitzin, 1977 found in Afrotropics? * 135b Colour of head and body otherwise; fore wing (fig. 104 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) long, slender, not tapering towards apex, the latter broadly rounded; wing disc infuscated with hyaline cross-bands or patches; antenna (fig. 105 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) long and slender, filiform, the scape cylindrical, much more than three times as long as wide; wings held erect in life - [[File:Callipteroma sexguttata iNat 150291293.jpg|thumb|''Callipteroma sexguttata'', South Africa]][[File:Mercet 1921 27 Callipteroma 118.jpg|thumb|Male ''Callipteroma sexguttata'', Spain]] **''''' Callipteroma''''' Motschulsky, 1863 *** 6 species worldwide; 3 Afrotropical species: ****''Callipteroma albiclava'' Noyes (1) ****''Callipteroma sexguttata'' Motschulsky (3) ****''Callipteroma testacea'' Motschulsky (2) === 136 === * 136a Scutellum with sculptural cells longitudinally oriented, somewhat raised, giving the disc a striate effect (fig. 114 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Mesoscutum with parapsidal sulci (fig. 114 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); head and body black, shiny, without metallic refringence; male antenna (fig. 117 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with rami, one each on funicle segments II–V - **'''''Neocharitopus''''' Hayat, Alam and Agarwal, 1975 *** ''Insleyia'' Prinsloo and Annecke, 1979 is a synonym of ''Neocharitopus'' *** 3 species worldwide; 2 Afrotropical species: ****''Neocharitopus crassus'' (Prinsloo and Annecke) (3) ****''Neocharitopus solani'' (Risbec) (1) * 136b Sculpture of scutellum otherwise................137 === 137 === * 137a Antennal scape (fig. 106 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) moderately to broadly expanded ventrally, or if only slightly expanded, then the ends cylindrical. General colour yellow to orange, without metallic lustre; thorax covered with fine white setae; postmarginal vein long, reaching to a level beyond apex of stigmal - **''''' Gyranusoidea''''' Compere, 1947 *** 44 species worldwide; 11 Afrotropical species: ****''Gyranusoidea austrina'' Annecke and Mynhardt (4) ****''Gyranusoidea citrina'' (Compere) (6) ****''Gyranusoidea dilatata'' Annecke and Mynhardt (4) ****''Gyranusoidea flava'' Shafee, Alam and Agarwal (1) ****''Gyranusoidea klugei'' Prinsloo and Annecke (3) ****''Gyranusoidea litura'' Prinsloo (3) ****''Gyranusoidea munda'' Annecke (5) ****''Gyranusoidea pauliani'' (Risbec) (2) ****''Gyranusoidea separata'' Prinsloo (3) ****''Gyranusoidea signata'' Annecke and Mynhardt (5) ****''Gyranusoidea tebygi'' Noyes (28) * 137b Antennal scape not or hardly expanded ventrally........ 138 === 138 === * 138a Body always black, with moderate to strong metallic green, blue or purplish refringence. Mesoscutum with incomplete parapsidal sulci; marginal and postmarginal veins long - **''''' Clausenia''''' Ishii, 1923 *** 12 species worldwide; 7 Afrotropical species: ****''Clausenia capensis'' Annecke and Mynhardt (3) ****''Clausenia comperei'' Kerrich (4) ****''Clausenia concinna'' Annecke and Mynhardt (3) ****''Clausenia confusor'' Kerrich (3) ****''Clausenia corrugata'' Kerrich (3) ****''Clausenia guineensis'' Kerrich (3) ****''Clausenia sobrina'' Annecke and Mynhardt (3) * 138b Colour otherwise, if rarely black, then without any metallic refringence........ 139 === 139 === * 139a Antenna filiform, the basal funicle segment longer than pedicel, often very much so; cercal plates advanced to a level near base of metasoma - [[File:Leptomastix inat 153928277.jpg|thumb|''Leptomastix'' sp., South Africa]] **''''' Leptomastix''''' Foerster, 1856 *** 34 species worldwide; 12 Afrotropical species: ****''Leptomastix abyssinica'' Compere (5) ****''Leptomastix africana'' Anga and Noyes (1) ****''Leptomastix dactylopii'' Howard (24) ****''Leptomastix digitariae'' Risbec (1) ****''Leptomastix flava'' Mercet (3) ****''Leptomastix herreni'' Anga and Noyes (1) ****''Leptomastix hibiscusae'' Risbec (3) ****''Leptomastix jonesi'' Noyes (1) ****''Leptomastix nigra'' Compere (6) ****''Leptomastix nigrocincta'' Risbec (4) ****''Leptomastix nigrocoxalis'' Compere (6) ****''Leptomastix tsukumiensis'' Tachikawa (2) * 139b Antenna not filiform, the pedicel longer than basal funicle segment; cecal plates placed near apex of metasoma - **''''' Allocerellus''''' Silvestri, 1915 *** 12 species worldwide; 12 Afrotropical species: ***See step 125 =Other genera known from the Afrotropics= [[File:Achalcerinys lindus faunaibrica Mercet 1921 F112 p270.jpg|thumb|''Achalcerinys lindus'', female, Spain.]][[File:Blastothrix erythrostetha female Fig95 p245.jpg|thumb|''Blastothrix erythrostetha'', female]][[File:Cryptanusia iNat 19192414 magriet b.jpg|thumb|''Cryptanusia'' sp., South Africa]][[File:Mira integralis Fauna iberica (1921) p.554.jpg|thumb|Male ''Mira integralis'']][[File:Mira integralis Fauna iberica (1921) p.556.jpg|thumb|Female ''Mira integralis'']][[File:Trichomasthus cyanifrons, female, Spain.jpg|thumb|''Trichomasthus cyanifrons'', female, Spain]] *Some of these genera have been found in the Afrotropics since the key was created (1979) **'''''Achalcerinys''''' Girault, 1915 ***''Parasyrpophagus'' is a synonym of ''Achalcerinys'' *** 5 species worldwide; 2 Afrotropical species: ****''Achalcerinys gorodkovi'' (Myartseva, 1983) - no known associates (Egypt, Ethiopia) ****''Achalcerinys lindus'' (Mercet, 1921) - a parasitoid of Eriococcidae, Pseudococcidae, Encyrtidae (Ethiopia) **'''''Agarwalencyrtus''''' Hayat, 1981 *** 4 species worldwide; 1 Afrotropical species: ****''Agarwalencyrtus citri'' - a parasitoid or hyperparasitoid in mealybugs; ''Planococcus'' spp. (South Africa, Swaziland, Zimbabwe) ****Photograph of specimen in [https://www.cabidigitallibrary.org/doi/pdf/10.5555/20203576260 Tirunagaru and Sagadai (2020)] **'''''Anomalencyrtus''''' Hayat and Verma, 1980 *** 2 species worldwide; 1 Afrotropical species: ****''Anomalencyrtus longicornis'' - no known associates (Madagascar) **'''''Anomalicornia''''' Mercet, 1921 *** 1 species worldwide; 1 Afrotropical species: ****''Anomalicornia tenuicornis'' - a parasitoid of mealybugs (Burkina Faso, Cameroon, Ivory Coast, Madagascar, Zimbabwe) **'''''Astymachus''''' Howard, 1898 *** 6 species worldwide; 1 Afrotropical species: ****''Astymachus exilis '' - no known associates (South Africa) **'''''Blastothrix ''''' *** 29 species worldwide; 1 Afrotropical species: ****''Blastothrix anthocleistae'' Risbec, 1952 (Madagascar) **'''''Bothriocraera''''' Timberlake, 1916 *** 4 species worldwide; 1 Afrotropical species: ****''Bothriocraera bicolor'' - a parasitoid of mealybugs (Ghana) **'''''Brachyplatycerus''''' De Santis, 1972 *** 1 species worldwide; 1 Afrotropical species: ****''Brachyplatycerus minutum'' - a parasitoid of moths ''Cydia pomonella'' (South Africa) **'''''Brethesiella''''' Porter, 1920 *** 18 species worldwide; 1 Afrotropical species: ****''Brethesiella abnormicornis'' - a parasitoid of Margarodidae ''Icerya'' spp. (Sao Tomé and Principe) **'''''Cladiscodes''''' Subba Rao, 1977 *** 5 species worldwide; 1 Afrotropical species: ****''Cladiscodes incisius'' - no known associates (South Africa) **'''''Cryptanusia''''' Girault , 1917 *** 8 species worldwide; 1 Afrotropical species: ****''Cryptanusia aureiscutellum'' - no known associates (South Africa) **'''''Diaphorencyrtus''''' Hayat, 1981 *** 2 species worldwide; 2 Afrotropical species: ****''Diaphorencyrtus aligarhensis'' (Shafee, Alam and Agarwal) (Réunion, South Africa) ****''Diaphorencyrtus harrisoni'' (Robinson, 1960) (South Africa) **'''''Dionencyrtus''''' De Santis, 1985 *** 2 species worldwide; 1 Afrotropical species: ****''Dionencyrtus cordylomerae'' (Risbec, 1951) (Senegal) **'''''Dusmetia''''' Mercet, 1921 *** 6 species worldwide; 1 Afrotropical species: ****''Dusmetia fuscipennis'' (Noyes & Hayat, 1984) (Zimbabwe) **'''''Ectroma''''' Westwood, 1833 *** 11 species worldwide; 1 Afrotropical species: ****''Ectroma truncatum'' Prinsloo, 1986 (Zimbabwe) **''''' Erencyrtus''''' Mahdihassan, 1923 *** 6 species worldwide; 4 Afrotropical species: ****''Erencyrtus ater'' Annecke and Mynhardt (South Africa) ****''Erencyrtus contrarius'' Prinsloo and Mynhardt (South Africa) ****''Erencyrtus fuscus'' Annecke and Mynhardt (South Africa) ****''Erencyrtus notialis'' Prinsloo and Mynhardt (South Africa) **'''''Hambletonia''''' Compere, 1936 *** 9 species worldwide; 1 Afrotropical species: ****''Hambletonia pseudococcina'' Compere, 1936 (Ghana) **'''''Hemileucoceras''''' Hoffer, 1976 *** 3 species worldwide; 1 Afrotropical species: ****''Hemileucoceras madagascariensis'' (Risbec) (Madagascar) **'''''Holcencyrtus''''' Ashmead, 1900 *** 10 species worldwide; 2 Afrotropical species: ****''Holcencyrtus liriomyzae'' Risbec (Senegal) ****''Holcencyrtus myrmicoides'' (Compere and Zinna) (Ghana) **'''''Homosemion''''' Annecke, 1967 *** 1 species worldwide; 1 Afrotropical species: ****''Homosemion bennetti'' Annecke, 1967 (Sao Tomé and Principe) **'''''Incisencyrtus''''' Prinsloo, 1988 *** 4 species worldwide; 3 Afrotropical species: ****''Incisencyrtus afer'' Prinsloo, 1988 (South Africa, Zimbabwe) ****''Incisencyrtus secus'' Prinsloo, 1988 (Madagascar) ****''Incisencyrtus sirus'' Prinsloo, 1988 (Nigeria) **'''''Lakshaphagus''''' Mahdihassan, 1931 *** 9 species worldwide; 2 Afrotropical species: ****''Lakshaphagus armillatus'' (Annecke, 1969) (South Africa) ****''Lakshaphagus ceroplastae'' (Risbec, 1951) (Senegal) **'''''Manicnemus''''' Hayat, 1981 *** 2 species worldwide; 1 Afrotropical species: ****''Manicnemus'' sp. (Tanzania) <ref name=vanNoort>van Noort, S. (2024). WaspWeb: Hymenoptera of the Afrotropical region. [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Tetracneminae/Manicnemus/Manicnemus_species.htm Manicnemus species] (accessed on 14 March 2024).</ref> **''''' Mahencyrtus''''' Masi, 1917 *** 14 species worldwide; 1 Afrotropical species: ****''Mahencyrtus occultans'' - no associates known (Seychelles) **'''''Mira''''' *** 6 species worldwide; 1 Afrotropical species: ****''Mira integralis'' (Mercet, 1921) (Senegal) **'''''Neastymachus''''' Girault, 1915 *** 21 species worldwide; 1 Afrotropical species: ****''Neastymachus dispar'' Prinsloo, 1996 (South Africa) **'''''Neodusmetia''''' Kerrich, 1964 *** 6 species worldwide; 1 Afrotropical species: ****''Neodusmetia sangwani'' (Subba Rao, 1957) (Kenya, Namibia, South Africa, Zimbabwe) **'''''Parablatticida''''' Girault, 1915 *** 15 species worldwide; 2 Afrotropical species: ****''Parablatticida aphycoides'' (Masi, 1917) (Seychelles) ****''Parablatticida vidua'' (Masi, 1917) (Seychelles) **'''''Pseudococcobius''''' Timberlake, 1916 *** 12 species worldwide; 6 Afrotropical species: ****''Pseudococcobius akares'' Prinsloo, 2003 (South Africa) ****''Pseudococcobius ancylus'' Prinsloo, 2003 (South Africa) ****''Pseudococcobius dolus'' Prinsloo, 2003 (South Africa) ****''Pseudococcobius san'' Prinsloo, 2003 (South Africa) ****''Pseudococcobius vibex'' Prinsloo, 2003 (South Africa) ****''Pseudococcobius vinealis'' Prinsloo, 2003 (South Africa) **'''''Rhytidothorax''''' Ashmead, 1900 *** 20 species worldwide; 2 Afrotropical species: ****''Rhytidothorax ambositrensis'' (Risbec, 1952) (Madagascar) ****''Rhytidothorax latiscapus'' (Prinsloo and Annecke, 1979) (Swaziland, Zimbabwe) **'''''Scotteus''''' Masi, 1917 *** 1 species worldwide; 1 Afrotropical species: ****''Scotteus ochroleucus'' Masi, 1917 (Seychelles) **'''''Spaniopterus''''' Gahan, 1927 *** 1 species worldwide; 1 Afrotropical species: ****''Spaniopterus crucifer'' Gahan, 1927 (Mauritius) **'''''Stemmatosteres''''' Timberlake, 1918 *** 5 species worldwide; 1 Afrotropical species: ****''Stemmatosteres primus'' Prinsloo and Mynhardt, 1981 (South Africa) **'''''Trichomasthus''''' *** 60 species worldwide; 1 Afrotropical species: ****''Trichomasthus portoricensis'' (Crawford, 1913) (Sao Tomé and Principe) **'''''Xenostryxis''''' *** 10 species worldwide; 1 Afrotropical species: ****''Xenostryxis margiscutellum'' Girault, 1920 (South Africa) **'''''Zarhopalus''''' Ashmead, 1900 *** 8 species worldwide; 1 Afrotropical species: ****''Zarhopalus corvinus'' a parasitoid of Pseudococcidae, ''Pseudococcus'' spp. (South Africa) **'''''Zozoros''''' *** 2 species worldwide; 1 Afrotropical species: ****''Zozoros adamsoniae'' (Risbec, 1951) (Senegal) =References= {{Reflist}} [[Category:African Arthropods|Afrotropical Encyrtidae Key]] 7bs8ob0baua3hbblsyo4hgyvfed8lhm 2690109 2690108 2024-12-03T13:08:03Z Alandmanson 1669821 /* 72 (Head and body yellowish to brownish, not metallic, no white setae) */ 2690109 wikitext text/x-wiki Encyrtidae is a large family of parasitic wasps in the Superfamily [[w:Chalcidoidea|Chalcidoidea]]. There are more than 640 described species of [[w:Afrotropical|Afrotropical]] Encyrtidae in about 130 genera. Many encyrtid species are parasitoids of [[w:scale insect|scale insect]]s, some of which are pests that reduce the productivity of agricultural crops across the world.<br> =Key to the genera of Afrotropical Encyrtidae= This key is based on this paper: '''Prinsloo, G. L., & Annecke, D. P. (1979).''' A key to the genera of Encyrtidae from the Ethiopian region, with descriptions of three new genera (Hymenoptera: Chalcidoidea). Journal of the Entomological Society of southern Africa, 42(2), 349-382.<ref name=Prinsloo&Anneke1979>Prinsloo, G. L., & Annecke, D. P. (1979). A key to the genera of Encyrtidae from the Ethiopian region, with descriptions of three new genera (Hymenoptera: Chalcidoidea). Journal of the Entomological Society of southern Africa, 42(2), 349-382. [https://journals.co.za/doi/pdf/10.10520/AJA00128789_2641 PDF]</ref> The Universal Chalcidoidea Database<ref name=Noyes2019/>, WaspWeb<ref name=vanNoort2024>van Noort, S. 2024. WaspWeb: Hymenoptera of the Afrotropical region. https://www.waspweb.org/Chalcidoidea/Encyrtidae/Classification/index.htm (accessed 2023-2024).</ref>, and other on-line sources were used to add details. ==1 Encyrtidae == [[African Arthropods/Encyrtidae|'''Diagnostic features of Encyrtidae''']] include: mesopleuron very enlarged; mid coxae level with middle of mesopleuron in side view; cercal plates advanced; linea calva distinct; mesoscutum transverse and without distinct notauli.<ref name=Pitkin2004>Pitkin, B.R. (2004) Notes on families: Encyrtidae. Universal Chalcidoidea Database. [https://www.nhm.ac.uk/our-science/data/chalcidoids/encyrtidae.html www.nhm.ac.uk]</ref> There are illustrations of these features on another [[African Arthropods/Encyrtidae|page of the '''African Arthropods project''']].<br> 1a Tarsi with four segments ........ 2<br> 1b Tarsi with five segments ........ 3 ==2 Tarsi with four segments== *Marginal cilia of forewing very long (fig. 2 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key] and Prinsloo & Anneke, 1979<ref name=Prinsloo&Anneke1979/>); axillae indistinct (fig. 3 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb]); funicle with five or six segments - **'''''Anthemus''''' <small>HOWARD, 1896</small> ***22 species worldwide; 12 Afrotropical species. ***Photos: [http://ponent.atspace.org/fauna/ins/fam/encyrtidae/anthemus_hab.htm Ponent, Catalonia] ***Paper: Prinsloo, G. L., & Neser, O. C. (1989). A revision of the genus Anthemus Howard (Hymenoptera: Encyrtidae) in the Afrotropical region. Revue de Zoologie Africaine, 103(1), 51-72. *Marginal cilia of forewing short (cf. fig. 4 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key] and Prinsloo & Anneke, 1979<ref name=Prinsloo&Anneke1979/>), the longest cilia never much longer than the setae on the submarginal vein; axillae are distinct and meet medially; funicle with two to four segments - [[File:Mercet 1921 7 Arrenophagus parasite in Alacaspis rosae p54.jpg|thumb|''Arrhenophagus chionaspidis'' before emergence from scale host, Spain.]][[File:Mercet 1921 6 Arrhenophagus chionaspidis female antenna p53.jpg|thumb|''Arrhenophagus chionaspidis'' female antenna]] **'''''Arrhenophagus''''' <small>AURIVILLIUS, 1888</small> ***Photos: [https://www.nhm.ac.uk/our-science/data/chalcidoids/database/media.dsml?IMAGENO=chalc071&VALGENUS=Arrhenophagus&VALSPECIES=albitibiae&isVideo= Universal Chalcidoidea Database] [https://takagi.tenteki.org/%E5%A4%A9%E6%95%B5%E5%9B%B3%E9%91%912/%E3%82%AF%E3%83%AF%E3%82%B7%E3%83%AD%E3%82%AB%E3%82%A4%E3%82%AC%E3%83%A9.htm takagi.tenteki] ***Papers: [https://journals.flvc.org/mundi/article/view/129680 '''Suh S-J. 2021.''' Parasitoids (Hymenoptera: Chalcidoidea) of the white peach scale, Pseudaulacaspis pentagona (Targioni-Tozzetti) (Hemiptera: Diaspididae) on Prunus salicina Lindl. (Rosales: Rosaceae) in South Korea. Insecta Mundi 0885: 1–5.] [http://doi.org/10.5281/zenodo.3697168 '''Suh, Soo-Jung, 2018.''' Parasitoids (Hymenoptera: Chalcidoidea) reared from Pseudaulacaspis cockerelli (Cooley) (Hemiptera: Coccoidea) in the Republic of Korea, Insecta Mundi 612, pp. 1-6 : 3-4] [https://doi.org/10.4308/hjb.19.3.110 '''Muniappan, R., Watson, G. W., Evans, G. A., Rauf, A., & Von Ellenrieder, N. (2012). Cycad aulacaspis scale, a newly introduced insect pest in Indonesia. HAYATI Journal of Biosciences, 19(3), 110-114., R., Watson, G. W., Evans, G. A., Rauf, A., & Von Ellenrieder, N. (2012).''' Cycad aulacaspis scale, a newly introduced insect pest in Indonesia. HAYATI Journal of Biosciences, 19(3), 110-114.] *** 2 species worldwide; 1 Afrotropical species: ****''Arrhenophagus chionaspidis'' (worldwide) ==3 Tarsi five-segmented== *3a Forewing without stigmal, marginal or postmarginal veins, with an infuscated patch (fig. 4 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key]); on the head, the scrobes are moderately deep, in the shape of aninverted V, their confluence is separated medially by a membranous joint that extends to the front of the vertex; a similar membrane runs transversely between the eyes where the fronto-vertex adjoins the face (fig. 5 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key] and figs 1, 13, 20, 24 of Annecke & Mynhardt (1974)<ref name=AnneckeMynhardt1974>Annecke, DP & Mynhardt, M.J., 1974. On some new and described species of arrhenophagine Encyrtidae (Hymenoptera). Journal of the Entomological Society of southern Africa, 37(1), pp.35-47. [https://journals.co.za/doi/abs/10.10520/AJA00128789_2835 DOI] [https://journals.co.za/doi/pdf/10.10520/AJA00128789_2835 PDF]</ref>) - **'''''Arrhenophagoidea''''' <small>Girault, 1915</small><br> ***''Arrhenophagoidea'' and ''Arrhenophagus'' are morphologically similar, except that the tarsi are four-segmented in ''Arrhenophagus'' and five-segmented in ''Arrhenophagoidea''. Species of both genera are very small (body length about 0.5 mm). ***Four Afrotropical species: ****''Arrhenophagoidea chaetacmae'' Annecke & Prinsloo, 1974 (South Africa) ****''Arrhenophagoidea neseri'' Prinsloo, 1974 (South Africa) ****''Arrhenophagoidea rolaspidis'' Annecke & Prinsloo, 1974 (South Africa) ****''Arrhenophagoidea sierra'' Annecke & Prinsloo, 1974 (South Africa) *3b Forewing venation partly or well-developed; head without membranous features above the scrobes ........ 4 ===4 (Fore wing venation at least partly developed; head without membranous interruptions)=== *4a Posterior margin of mesosetum with two round projections, each fitting into an indentation in anterior margin of axillae (fig. 6 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key]); forewing with marginal cilia unusually long along caudal wing margin (fig. 7 of [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Keys/Dichotomus_keys/Encyrtidae_genera.htm waspweb key]); egg parasitoids of Tettigometridae - **'''''Psyllechthrus''''' <small>GHESQUIERE, 1958</small> ***A single species, ''Psyllechthrus oophagus'' is known - from Congo, Democratic Republic of Congo, Kenya, Malawi, Namibia, South Africa, Zimbabwe.<ref name=Noyes2019>Noyes, J.S. 2019. Universal Chalcidoidea Database. The Natural History Museum, London. https://www.nhm.ac.uk/our-science/data/chalcidoids/database/index.dsml</ref> ***''Psyllechthrus oophagus'' has been reared from the eggs of ''Nototettigometra patruelis'', which is thought to be its only host.<ref name=Prinsloo1985>Prinsloo, G.L. 1985, Afrotropical Encyrtidae (Hymenoptera: Chalcidoidea): new records and notes. Journal of Natural History 19:281</ref> ***Photographs of ''Nototettigometra patruelis'' eggs with tiny wasps that are probably ''Psyllechthrus oophagus'': [http://www.biodiversityexplorer.info/bugs/tettigometridae/hilda_patruelis.htm] and [https://www.inaturalist.org/observations/180134054] <gallery mode=packed heights=300> Psyllechthrus oophagus 192741071 a.jpg|''Psyllechthrus oophagus'' Psyllechthrus oophagus 192741071 c.jpg|''Psyllechthrus oophagus'' on eggs of ''Nototettigometra patruelis''. </gallery> *4b Margin of mesoseutum without two round projections fitting into indentations in the anterior margin of the axillae; marginal cilia of forewing not unusually long; not parasites of Tettigometridae ........ 5 ===5 (Posterior margin of mesoscutum without two round projections fitting into the anterior margin of axillae, forewing with marginal cilia not unusually long)=== *5a Fore femur and tibia greatly swollen, the apex of the latter with two blunt spines in addition to the strigil; antenna eleven-segmented, the segments of pedicel, funicle and club similar in shape; head and body hardly encyrtiform (fig. 9 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) **'''''Sanghalia''''' <small>RISBEC, 1955</small> ***A single species from Congo, ''Sanghalia kerandeli'' *5b Fore femur and tibia at most slightly swollen, the latter without spines; antenna otherwise, usually clavate................6 ===6 (Fore femur and tibia not greatly swollen, fore tibia without spines)=== *6a Funicle with less than six segments........ 7 *6b Funicle with six or seven segments........ 16 ==7 Funicle with less than six segments== *7a Antenna (fig. 10 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) extensively flattened and expanded - both scape and flagellum leaf-like; the club is not segmented; the funicle has three to five transverse segments; Pseudococeid parasitoids -[[File:Zaplatycerus fullawayi Timberlake 1925 Plate IX Fig. 1.jpg|thumb|''Zaplatycerus fullawayi''; A. female antenna; B. Male antenna; C. Female mandible frontal view]] **'''''Zaplatycerus''''' Timberlake, 1925 ***Synonyms include: ''Tropidophryne'' Compere, 1931; ''Neoplatycerus'' Subba Rao, 1965; ''Avernes'' Noyes et Woolley, 1994; ''Assamencyrtus'' Singh, 2006.<ref name=Trjapitzin2018>Trjapitzin, V. A. (2018). A Review of the Encyrtid-Wasp Genus ''Zaplatycerus'' Timberlake, 1925 (Hymenoptera, Chalcidoidea: Encyrtidae) of the World Fauna, Parasitoids of Mealybugs (Hemiptera, Pseudococcidae). Entomological Review, 98, 787-792.</ref> ***16 species worldwide; 4 Afrotropical species<ref name=Noyes2019/> ***Description and images of ''Zaplatycerus notialis'' on [https://www.researchgate.net/publication/271666428 Researchgate] Afrotropical species *7b Antenna not extensively flattened, but the scape may be expanded ventrally........ 8 ===8 (Antenna not extensively flattened; scape may be expanded)=== *8a Funicle with four segments ........ 9 *8b Funicle with five segments ........ 10 ===9 (Funicle with four segments)=== *9a Apex of scutellum with two lamelliform (flattened) setae (cf. figs 27 & 28 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>, and ''Habrolepis'', 38b below); forewing distinctly darkened, patterned; body flattened dorsoventrally; parasitoids of armored scale insects - **'''''Caenohomalopoda''''' Tachikawa, 1979 ***11 species worldwide; 1 Afrotropical species: ****''Caenohomalopoda shikokuensis'' a parasitoid of armored scales, ''Froggattiella penicillata'', ''Odonaspis'' spp. (South Africa) ****Description and figures - [https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/9592/1/20(3-4)_p90-96.pdf Tachikawa, 1956]<ref name=Tachikawa1956>Tachikawa, T. (1956). Description of a new species of the genus Pseudhomalopoda Cirault from Japan, with a list of the known species and their hosts of the Habrolepis-like genera (Hymenoptera: Encyrtidae). Insecta matsumurana, 20(3-4), 90-96. https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/9592/1/20(3-4)_p90-96.pdf</ref> *9b Scutellum without scale-like setae; forewing transparent; body not flattened dorsoventrally; parasitoids of bees - **'''''Xylencyrtus''''' Annecke, 1968 ***Two Afrotropical species: ''Xylencyrtus mumifex'', a parasitoid of ''Allodapula melanopus'', is known from South Africa; and ''Xylencyrtus tridens'' is known from Cameroon, Kenya, South Africa, and Uganda and is a parasitoid of several xylocopine bee species (Tribe Allodapini).<ref name=Noyes2019/> ***Description and figures - [https://journals.co.za/doi/pdf/10.10520/AJA00128789_3102 Annecke, 1968]<ref name=Annecke1968>Annecke, D. P. (1968). Records and Descriptions of African Encyrtidae-4 (Hymenoptera: Chalcidoidea). Journal of the Entomological Society of southern Africa, 31(2), 249-264.</ref> ===10 (Funicle with five segments)=== *10a Antennal club not divided (a single segment) - **'''''Trechnites''''' Thomson, 1876 ***The body is blackish, with a metallic green scutellum; marginal and postmarginal veins of forewing punctiform or very short; parapsidal sulci present; ***Parasitoids of psyllids. *** 30 species worldwide; 3 Afrotropical species: ****''Trechnites angolensis'' associated with the legume ''Isoberlinia'' sp. (Angola) ****''Trechnites manaliensis'' a parasitoid of ''Euphyllura eastopi'', ''Euphyllura longiciliata'', ''Psylla hyalina'' (South Africa) ****''Trechnites morulus'' associated with ''Ceroplastes'' sp. (South Africa) *10b The antennal club has two or three segments ........ 11 ===11 (Antennal club with two or three segments)=== *11a Antennal club with two segments. (Maxillary palpi each with two segments, the labial not segmented; mandible tridentate (fig. 11 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), the upper tooth retracted; parasitic in Pseudococcidae) - [[File:Pseudectroma europaeum Fauna ibérica p192 Fig.65.jpg|thumb|Female ''Pseudectroma europaeum'', Spain]] **'''''Pseudectroma''''' Girault , 1915 ***''Timberlakia'' Mercet, 1925 is a synonym<ref name=Noyes2019/> ***16 species worldwide; 3 Afrotropical species: ''Pseudectroma cussoniae'' (Madagascar), ''Pseudectroma gilvum'' (South Africa), ''Pseudectroma signatum'' (Israel, South Africa)<ref name=Noyes2019/> ***Parasitoids - hosts include soft scales (Coccidae) and mealybugs (Pseudococcidae)<ref name=Noyes2019/> *11b Club with three segments ........ 12 ===12 (Antennal club with three segments)=== *12a Ovipositor protruding from the end of the metasoma - **'''''Acerophagus''''' Smith, 1880 ***''Pseudaphycus'' is a synonym of ''Acerophagus'' (see 13 below). ***''Acerophagus'' species are parasitoids of mealybugs (Pseudococcidae). ***iNaturalist has images of ''Acerophagus'' (CC-BY-NC).<ref name=iNatAcerophagus>https://www.inaturalist.org/taxa/250166 ''Acerophagus'' photographs on iNaturalist (CC-BY-NC)</ref> *12b Ovipositor not distinctly protruding from the end of the metasoma ........ 14 ===13 (Ovipositor protruding from the end of the metasoma - ''Acerophagus'')=== *13a Antennal club white; maxillary palpi each with four segments, the labial with three segments - **Afrotropical species of ''Acerophagus'' with a white antennal club (described as ''Pseudaphycus'') include ''A. angelicus'', ''A. dysmicocci'', ''A. ferrisianae'', ''A. maculipennis'', ''A. mundus'', ''A. notativentris '', ''A. perdignus'', ''A. prosopidis''. *13b Antennal club not white; maxillary palpi each with four segments, the labial with two segments - **Afrotropical species of ''Acerophagus'' with an antennal club that is not white (described as ''Acerophagus'') include ''A. coccois'', ''A. pallidus''. ===14 (Ovipositor not protruding or just protruding)=== *14a Mandible with two teeth; maxillary palpi each have two segments, the labial not segmented; paratergites present; Male antenna ramose, rami on funicle segments I-IV - **'''''Tetracnemoidea''''' Howard, 1898 ***''Tetracnemoidea'' species are parasitoids of mealybugs (Pseudococcidae).<ref name=Noyes2019/> ***Afrotropical species: ****''T. brevicornis'' (Girault) (Worldwide; Ghana in Afrotropics) ****''T. coffeicola'' (Kerrich) (Kenya, Uganda) ****''T. peregrina'' (Compere) (Worldwide; Ghana, South Africa in Afrotropics) ****''T. sydneyensis'' (Timberlake) (Worldwide; Ghana in Afrotropics) *14b Mandible with three or more teeth; palpi do not have two segments; no paratergites; not parasitoids of mealybugs ................15 ===15 (Mandible with three or more teeth; palpi do not have two segments; no paratergites; not parasitoids of mealybugs)=== *15a Head and body dark brown to blackish-brown, non-metallic except for frontovertex which may have a very slight metallic tinge; parasitic in aculeate Hymenoptera - **'''''Xylencyrtus''''' Annecke, 1968 ***Afrotropical species: ****''Xylencyrtus mumifex'', a parasitoid of ''Allodapula melanopus'' (South Africa); and ****''Xylencyrtus tridens'' is a parasitoid of several xylocopine bee species (Tribe Allodapini) (Cameroon, Kenya, South Africa, and Uganda).<ref name=Noyes2019/> *15b Head and body predominantly black, the scutellum brilliant metallic green in colour; parasitic in Psyllidae - **'''''Trechnites''''' Thomson, 1876 ***The body is blackish, with a metallic green scutellum; marginal and postmarginal veins of forewing punctiform or very short; parapsidal sulci present; ***Parasitoids of psyllids. ==16 Funicle with six or seven segments== *16a Hind tibia foliaceously flattened (fig. 12 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 17 *16b Hind tibia not or only slightly flattened................ 18 ===17 (Hind tibia foliaceously flattened)=== *17a Antennal club three-segmented or not segmented; parasitoids of Aphrophoridae and Cicadellidae. Male antenna may have six rami (fig. 14 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) - [[File:Neocladia iNat 170580378.jpg|thumb|''Neocladia'' sp., Australia]] **'''''Neocladia''''' Perkins, 1906 ***''Carabunia'' Waterston, 1928 is a synonym of ''Neocladia''<ref name=Noyes2019/> ***iNaturalist has images of ''Neocladia''.<ref name=iNatNeocladia>https://www.inaturalist.org/taxa/253254 ''Neocladia'' photographs on iNaturalist (including some CC-BY)</ref> ***Afrotropical species:<ref name=Noyes2019/> ****''Neocladia gigantica'' is a parasitoid of ''Ptyelus flavescens'', the Yellow Raintree Spittlebug (Uganda). ****''Neocladia senegalensis'' (Senegal, South Africa). ****''Neocladia tibialis'' is a parasitoid of ''Batrachomorphus capeneri'', a leafhopper (South Africa). ===18 (Hind tibia not or only slightly flattened)=== *18a Wings markedly reduced ................19 *18b Wings not greatly reduced ............. 25 ==19 Wings markedly reduced== *19a Scutellum with a flange or lamella (fig. 15 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), in profile this flange shows as a thin, flat, caudal projection of the apex of scutellum................20 *19b Scutellum without a flange................21 ===20 (Wings reduced, scutellum with a flange or lamella)=== *20a Mandible with two acute teeth; parasitoids of bees - [[File:Ericydnus inat 170283716 davidfdz b82, some rights reserved (CC-BY).jpg|thumb|''Ericydnus'' sp., Spain]] **'''''Ericydnus''''' Walker, 1837 *** 33 species worldwide; Afrotropical species? *** ''Ericydnus'' sp. - 2 specimens at ARC-PPRI (https://www.gbif.org/occurrence/search?dataset_key=b2ee8537-2a6c-4b4b-965a-538b47788606&taxon_key=1378896) *20b Mandible with three teeth; parasitoids of Coccidae - [[File:Paraphaenodiscus bicolor Fauna ibérica Ricardo García Mercet 1921.jpg|thumb|Female ''Paraphaenodiscus bicolor'', Spain]] **'''''Paraphaenodiscus''''' Girault, 1915 ***20 species worldwide; 10 Afrotropical species: ***Afrotropical species: ****''Paraphaenodiscus africanus'' Prinsloo (South Africa) ****''Paraphaenodiscus ceroplastodesi'' (Risbec) is a parasitoid of ''Ceroplastes'' species (Senegal) ****''Paraphaenodiscus chrysocomae'' Prinsloo (South Africa) ****''Paraphaenodiscus munroi'' Prinsloo is a parasitoid of ''Pulvinaria iceryi'' (South Africa) ****''Paraphaenodiscus niger'' Prinsloo is a parasitoid of ''Pulvinaria iceryi'' (South Africa) ****''Paraphaenodiscus paralis'' Prinsloo and Mynhardt is a parasitoid of ''Plagiochloa uniolae'' (South Africa) ****''Paraphaenodiscus pavoniae'' Risbec is a parasitoid of ''Ceroplastes'' and ''Pulvinaria'' species (Senegal, South Africa, Zimbabwe) ****''Paraphaenodiscus pedanus'' Prinsloo and Mynhardt is a parasitoid of ''Plagiochloa uniolae'' (South Africa) ****''Paraphaenodiscus risbeci'' Ghesquiere is a parasitoid of the moth ''Sesamia cretica'' (Senegal, Sudan) ****''Paraphaenodiscus rizicola'' (Risbec) has been associated with rice plants (Cameroon, Swaziland, Zimbabwe) ===21 (Wings reduced, scutellum without a flange)=== *21a Antenna nine-segmented, the club not segmented; mandible bidentate; parasitic in Pseudococcidae. Male antenna six-segmented, segments II - V each with a ramus - **'''''Tetracnemus''''' Westwood, 1837 ***iNaturalist has images of ''Tetracnemus''.<ref name=iNatTetracnemus>https://www.inaturalist.org/taxa/250503 ''Tetracnemus'' photographs on iNaturalist (some CC-BY-NC)</ref> ***37 species worldwide; 2 Afrotropical species: ****''Tetracnemus bifasciatellus'' (Mercet) (South Africa) ****''Tetracnemus gumilevi'' Pilipjuk and Trjapitzin (Ethiopia) *21b Antenna eleven-segmented, the club with three segments; mandible otherwise; not parasitic in Pseudococcidae................22 ===22 (Antenna eleven-segmented, the club with three segments)=== *22a Scutellum with a semi-erect tuft of bristles, these strong bristles rarely scattered and not forming a distinct tuft........................23 *22b Scutellar tuft of bristles absent........ 24 ===23 (Wings reduced, scutellum with a semi-erect tuft of bristles)=== *23a Mandible edentate, broadly rounded apically (fig. 16 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); gonostyli (3rd valvulae) absent - **'''''Encyrtus''''' Latreille, 1809 ***96 species worldwide; 15 Afrotropical species: ****''Encyrtus aquilus'' is a parasitoid of Coccidae ''Ceroplastes'' and ''Gascardia'' species (South Africa) ****''Encyrtus aurantii'' is a parasitoid of Hemiptera including Aleyrodidae, Coccidae, Diaspididae, Eriococcidae, Pseudococcidae (Cameroon, Gabon, Ghana, Madagascar, Malawi, Mauritius, Mozambique, Senegal, Seychelles, South Africa, Uganda, Zimbabwe) ****''Encyrtus barbiger'' is a parasitoid of ''Parasaissetia litorea'' (South Africa) ****''Encyrtus bedfordi'' is a parasitoid of ''Waxiella mimosae'' (South Africa) ****''Encyrtus cotterelli'' is a parasitoid of ''Sahlbergella'' species (Ghana) ****''Encyrtus decorus'' is a parasitoid of ''Pulvinaria'' and ''Saissetia'' species (Zimbabwe) ****''Encyrtus fuliginosus'' is a parasitoid of a range of Coccidae (Eritrea, Ethiopia, Kenya, Madagascar, Mozambique, Namibia, South Africa) ****''Encyrtus hesperus'' (Gambia, Ivory Coast) ****''Encyrtus imitator'' (Cameroon, Gabon, Uganda) ****''Encyrtus infelix'' is a parasitoid of a range of Coccidae (Kenya, Madagascar, Seychelles, Zimbabwe) ****''Encyrtus melas'' is a parasitoid of ''Gascardia'' and ''Tachardina'' species (South Africa) ****''Encyrtus palpator'' ((Cameroon) ****''Encyrtus sacchari'' is a parasitoid of ''Pulvinaria'' species on rice and sugar cane (Benin, Cameroon, Gabon, Gambia, Ivory Coast, Kenya, Nigeria, Senegal, South Africa, Zimbabwe) ****''Encyrtus saliens'' is a parasitoid of ''Pulvinaria'' species (South Africa) ****''Encyrtus signifer'' (Cameroon, Gabon) *23b Mandible tridentate; gonostyli present - [[File:Diversinervus.jpg|thumb|''Diversinervus'' sp., New Zealand]] **'''''Diversinervus''''' Silvestri, 1915 ***iNaturalist has images of ''Diversinervus''.<ref name=iNatDiversinervus>https://www.inaturalist.org/taxa/250172 ''Diversinervus'' photographs on iNaturalist (CC-BY-NC)</ref> ***12 species worldwide; 10 Afrotropical species: ****''Diversinervus cervantesi'' is a parasitoid of Coccidae (South Africa) ****''Diversinervus desantisi'' is a parasitoid of ''Pulvinaria'' species (Eritrea, Ethiopia) ****''Diversinervus elegans'' is a parasitoid of a range of Coccidae (Angola, Eritrea, Ethiopia, Kenya, South Africa) ****''Diversinervus masakaensis'' is a parasitoid of ''Saissetia oleae'' (Uganda) ****''Diversinervus orarius'' is a parasitoid of a ''Ctenochiton'' sp. (South Africa) ****''Diversinervus redactus'' is a parasitoid of a ''Ceroplastes'' sp. (South Africa) ****''Diversinervus scutatus'' is a parasitoid of a ''Ceronema'' sp. (South Africa) ****''Diversinervus silvestrii'' is a parasitoid of ''Coccus'' species (Mauritius, South Africa) ****''Diversinervus smithi'' is a parasitoid of ''Saissetia oleae'' (South Africa) ****''Diversinervus stramineus'' is a parasitoid of ''Coccus alpinus'', ''Coccus celatus'', and ''Saissetia persimilis'' (Kenya, South Africa) ===24 (Wings reduced, scutellar tuft of bristles absent)=== *24a Apterous, or wings represented by a stub - **'''''Metaphycus''''' Mercet, 1917 ***476 species worldwide; 86 Afrotropical species: ****Many pics of winged species on iNaturalist (but not Afrotropical and not apterous) *24b Fore wing reduced in size, but with venation distinct (fig. 17 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) - [[File:Neococcidencyrtus-poutiersi-Mercet-1922-A-Lateral-view-B-Dorsal-view-C W640.jpg|thumb|''Neococcidencyrtus poutiersi'', Iran.]] **'''''Neococcidencyrtus''''' Compere, 1928 ***20 species worldwide; 5 Afrotropical species: ****''Neococcidencyrtus brenhindis'' (Madagascar) ****''Neococcidencyrtus cliradainis'' (Cameroon) ****''Neococcidencyrtus poutiersi'' is a parasitoid of ''Furchadaspis zamiae'', cycad scale (South Africa) Fig. 5. in https://www.researchgate.net/publication/343006453 ****''Neococcidencyrtus pudaspidis'' is a parasitoid of ''Pudaspis newsteadi'' (South Africa) ****''Neococcidencyrtus syndodis'' (South Africa) ==25 Wings not greatly reduced== *25a Dorsum of scutellum with a longitudinal, inconspicuous, median keel - [[File:Encyrtidae iNat 178385702 08.jpg |thumb|''Pentelicus'' sp., South Africa]] **'''''Pentelicus''''' Howard, 1895 ***Head and thorax pitted; antennal club three-segmented, obliquely truncate apically. ***10 species worldwide; ? Afrotropical species: *25b Scutellum without a median keel................26 ===26 (Scutellum without a median keel)=== *26a Head with a horn-like protuberance jutting from middle of face just below antennal Insertions - [[File:Paratetracnemoidea malenotti Fauna iberica (1921).jpg|thumb|Male ''Paratetracnemoidea malenotti'']][[File:Paratetracnemoidea malenotti, head, lateral view.jpg|thumb|''Paratetracnemoidea malenotti'', lateral view of head]] **'''''Paratetracnemoidea''''' Girault , 1915 ***''Rhinoencyrtus'' Mercet, 1918 is a synonym of ''Paratetracnemoidea'' ***Photos at https://www.waspweb.org/chalcidoidea/Encyrtidae/Encyrtinae/Paratetracnemoidea/index.htm ***5 species worldwide; 3 Afrotropical species: ****''Paratetracnemoidea breviventris'' - no associates known (Tanzania) ****''Paratetracnemoidea cornis'' - no associates known (South Africa) ****''Paratetracnemoidea malenotti'' - no associates known (Gambia, Nigeria, Sudan) *26b Head without facial protuberance................ 27 ===27 (Head without facial protuberance)=== *27a Fore wing with stigmal vein branching away before venation reaches cephalic wing margin (figs 18- 22 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); postmarginal vein never reaching cephalic edge of wing................28 *27b Fore wing venation normal, at most marginal vein punctiform (figs 34, 63, 82, 89 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); or rarely, if marginal vein absent, then postmarginal touches edge of wing (fig. 80 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)................32 ==28 Fore wing with stigmal vein branching away before venation reaches cephalic wing margin== *28a Anterior margin of frontovertex produced to form a prominent ridge that overhangs upper limits of scrobes; mandibles diminutive - **''''' Amira ''''' Girault , 1913 *** 3 species worldwide; 1 Afrotropical species: ****''Amira durantae'' is a parasitoid of spiders ''Nephila inaurata'' and ''Nephila madagascarensis'' (Madagascar) *28b Frontovertex rounded on to face, without an anterior ledge; mandibles relatively large, well developed........ 29 ===29 (Frontovertex rounded on to face, without an anterior ledge; mandibles relatively large)=== *29a Antennal scrobes sulcate, impressed on face as an inverted V, their lateral margins sharply angled (fig. 23 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Male and female antennae identical in shape and segmentation; parasitic in Aclerdidae - **''''' Allencyrtus ''''' Annecke and Mynhardt, 1973 *** 1 species worldwide - Afrotropical: ****''Allencyrtus monomorphus'' is a parasitoid of an Aclerdid scale, ''Rhodesaclerda'' sp. (South Africa) ****Description of genus and species: Annecke & Mynhardt (1973) [https://journals.co.za/doi/pdf/10.10520/AJA00128789_3436 PDF]<ref name=>Annecke, DP & Mynhardt, M. J. (1973). New and Iittle known African Encyrtidae, with descriptions of two new genera (Hymenoptera: Chalcidoidea). Journal of the Entomological Society of southern Africa, 36(2), 211-28. [https://journals.co.za/doi/pdf/10.10520/AJA00128789_3436 PDF]</ref> *29b Antennal scrobes not impressed on face as an inverted V with sharply angled lateral margins ....... 30 ===30 (Antennal scrobes not impressed on face as an inverted V with sharply angled lateral margins)=== *30a Antennal club three-segmented; mandible edentate, broadly rounded apically (fig. 24 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); parasitic in Coccidae and Stictococcidae -[[File:Aethognathus afer female Silvestri 1915 with inset.jpg|thumb|''Aethognathus afer'', female; inset shows detail of stigmal and postmarginal veins]] **''''' Aethognathus ''''' Silvestri, 1915 ***5 species worldwide; all Afrotropical: ****''Aethognathus afer'' is a parasitoid of scales, ''Stictococcus diversiseta'' and ''Stictococcus multispinosus'' (Benin, Ghana) ****''Aethognathus bicolor'' is a parasitoid of the scale ''Stictococcus multispinosus'' (Uganda) ****''Aethognathus cavilabris'' is a parasitoid of coccid scales, ''Saissetia''and ''Stictococcus'' spp. (Congo, Uganda) ****''Aethognathus khryzhanovskyi'' - no associates known (Equatorial Guinea) ****''Aethognathus unicolor'' is a parasitoid of scales, ''Stictococcus gowdeyi'' and ''Stictococcus multispinosus'' (Nigeria, Uganda) *30b Antennal club not segmented, obliquely truncate; mandible tridentate; not parasitic in scale insects........ 31 ===31 (Antennal club not segmented, obliquely truncate; mandible tridentate)=== *31a Frontovertex and face with large pits, each with a strong metallic lustre; antennal scape (fig. 25 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) strongly expanded ventrally; parasitic in eggs of spiders - **''''' Proleurocerus ''''' Ferriere, 1935 *** 5 species worldwide; 2 Afrotropical species: ****''Proleurocerus clavatus'' - no associates known (Zimbabwe) ****''Proleurocerus zululandiae'' - no associates known (South Africa) *31b Frontovertex at most finely punctate, non-metallic; antennal scape at most slightly expanded ventrally; parasitic in Neuroptera nymphs - [[File:Isodromus iNat 147864868.jpg |thumb|''Isodromus'' sp., Mexico.]][[File:Isodromus vinulus, male, Spain.jpg|thumb|''Isodromus vinulus'', a parasitic wasp in the family Encyrtidae; male]] **''''' Isodromus''''' Howard, 1887 *** 26 species worldwide; 1 Afrotropical species: ****''Isodromus timberlakei'' is a parasitoid of a ''Chrysopa'' species (South Africa) ==32 Fore wing venation normal, at most marginal vein punctiform; or rarely, if marginal vein absent, then postmarginal touches edge of wing== *32a Scutellum with a semi-erect tuft of bristles, these strong bristles rarely scattered and not forming a distinct tuft................ 33 *32b Scutellum without a tuft of bristles, the setae recumbent, except for one subapical pair which is sometimes present................37 ==33 Scutellum with a semi-erect tuft of bristles== *33a Head elongate in dorsal view, longer than wide or almost so, the greater part of each eye placed dorsally; mesoscutum (fig. 26 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) usually with a tuft of coarse bristles, but this tuft lacking in some species - [[File:Diversinervus.jpg|thumb|''Diversinervus'' sp., New Zealand]] **''''' Diversinervus''''' Silvestri, 1915 ***iNaturalist has images of ''Diversinervus''.<ref name=iNatDiversinervus/> *** 12 species worldwide; 10 Afrotropical species: ****''Diversinervus cervantesi'' is a parasitoid of coccid scales, ''Ceroplastes floridensis'', ''Coccus hesperidum'', ''Pulvinaria'' spp., ''Pulvinariella mesembryanthemi'', ''Saissetia coffeae'', ''Saissetia oleae'' (South Africa) ****''Diversinervus desantisi '' is a parasitoid of coccid scales, ''Pulvinaria'' sp. (Eritrea, Ethiopia) ****''Diversinervus elegans'' is a parasitoid of a wide range of coccid scales (Angola, Eritrea, Ethiopia, Kenya, South Africa) ****''Diversinervus masakaensis'' is a parasitoid of coccid scales, ''Saissetia oleae'' (Uganda) ****''Diversinervus orarius'' is a parasitoid of coccid scales, ''Ctenochiton'' sp. (South Africa) ****''Diversinervus redactus'' is a parasitoid of coccid scales, ''Ceroplastes'' sp. (South Africa) ****''Diversinervus scutatus'' is a parasitoid of coccid scales, ''Ceronema'' sp. (South Africa) ****''Diversinervus silvestrii'' is a parasitoid of coccid scales, ''Coccus'' spp. (Mauritius, South Africa) ****''Diversinervus smithi'' is a parasitoid of coccid scales, ''Saissetia oleae'' (South Africa) ****''Diversinervus stramineus'' is a parasitoid of coccid scales, ''Coccus alpinus'', ''Coccus celatus'', ''Saissetia persimilis'' (Kenya, South Africa) *33b Head not longer than wide, eyes not placed dorsally; mesoscutum never with a tuft of bristles................34 ===34 (Head not longer than wide, eyes not placed dorsally; mesoscutum never with a tuft of bristles)=== *34a Antenna enlarged, flattened, the club two-segmented, very large, almost as long as entire funicle; mandible bidentate; parasitic in Pseudococcidae. Head and body generally smooth and polished, brilliantly metallic in colour - **''''' Chrysoplatycerus''''' Ashmead, 1889 *** 6 species worldwide; 1 Afrotropical species: ****''Chrysoplatycerus splendens'' is a parasitoid of mealybugs, ''Dysmicoccus'' spp., ''Ferrisia virgata'', ''Ferrisiana virgata'', ''Formicococcus njalensis'', ''Planococcoides'' spp., ''Pseudococcus'' spp. (Ghana, South Africa) *34b Antenna not broadened and flattened, the club three-segmented; mandibles not bidentate; not parasitic in mealybugs................ 35 ===35 (Antenna not broadened and flattened, the club three-segmented)=== *35a Mandible edentate (fig. 16 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), broadly rounded apically; gonostyli absent; primary parasitoids of Coccidae - [[File:Encyrtus aurantii iNat 132121027 d.jpg|thumb|''Encyrtus aurantii'', Italy.]][[File:Encyrtus infelix iNat 159262263 a.jpg |thumb|''Encyrtus infelix'', New Zealand.]] **''''' Encyrtus''''' Latreille, 1809 *** 96 species worldwide; 15 Afrotropical species: ****''Encyrtus aquilus'' is a parasitoid of coccid scales, ''Ceroplastes'' sp., ''Gascardia'' sp., ''Gascardia destructor'' (South Africa) ****''Encyrtus aurantii'' is a parasitoid of many different Hemiptera from Aleyrodidae, Coccidae, Diaspididae, Eriococcidae, and Pseudococcidae (Cameroon, Gabon, Ghana, Madagascar, Malawi, Mauritius, Mozambique, Senegal, South Africa, Uganda, Zimbabwe) ****''Encyrtus barbiger'' is a parasitoid of a coccid scale ''Parasaissetia litorea'' (South Africa) ****''Encyrtus bedfordi'' is a parasitoid of a coccid scale ''Waxiella mimosae'' (South Africa) ****''Encyrtus cotterelli'' is a parasitoid of plant bugs, ''Sahlbergella'' spp., Miridae (Ghana) ****''Encyrtus decorus'' is a parasitoid of coccid scales ''Pulvinaria'' sp., ''Saissetia'' sp. (Zimbabwe) ****''Encyrtus fuliginosus'' is a parasitoid of coccid scales ''Coccus'', ''Lichtensia'', ''Pulvinaria'', ''Saissetia'', ''Saissetia oleae'', and ''Udinia'' species. (Eritrea, Ethiopia, Kenya, Madagascar, Mozambique, Namibia, South Africa) ****''Encyrtus hesperus'' - no associates known (Gambia, Ivory Coast) ****''Encyrtus imitator'' - no associates known (Cameroon, Gabon, Uganda) ****''Encyrtus infelix'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Coccus hesperidum'', ''Gascardia madagascariensis'', ''Lecanium hemisphaericum'', ''Protopulvinaria pyriformis'', ''Pulvinaria innumerabilis'', ''Pulvinaria urbicola'', ''Saissetia'' spp. (Kenya, Madagascar, Seychelles, Zimbabwe) ****''Encyrtus melas'' is a parasitoid of coccid scales ''Gascardia'' sp., ''Gascardia tachardiaformis'', and lac scales ''Tachardina'' sp. (South Africa) ****''Encyrtus palpator'' - no associates known (Cameroon) ****''Encyrtus sacchari'' is a parasitoid of coccid scales ''Pulvinaria'' spp. on rice and sugar cane (Benin, Cameroon, Gabon, Gambia, Ivory Coast, Kenya, Nigeria, Senegal, South Africa, Zimbabwe) ****''Encyrtus saliens'' is a parasitoid of coccid scales ''Pulvinaria delottoi'' spp., ''Pulvinariella'' spp. (South Africa) ****''Encyrtus signifer'' - no associates known (Cameroon, Gabon) *35b Mandible not edentate; gonostyli present; usually hyperparasitoids................36 ===36 (Mandible not edentate; gonostyli present; usually hyperparasitoids)=== *36a Ovipositor not or only slightly exserted at apex of metasoma - [[File:Cheiloneurus iNat 90442164 a.jpg|thumb|Male ''Cheiloneurus'' sp., USA]] [[File:Cheiloneurus iNat 47473995.jpg|thumb|Female ''Cheiloneurus'' sp., Canada]] **''''' Cheiloneurus''''' Westwood, 1833 *** 152 species worldwide; 15 Afrotropical species: ****''Cheiloneurus afer'' is a parasitoid or hyperparasitoid from coccid scales ''Pulvinarisca jacksoni'' (Ghana) ****''Cheiloneurus angustifrons'' is a parasitoid or hyperparasitoid from coccid scales ''Ceroplastes mimosae'', ''Waxiella mimosae'' (Sudan) ****''Cheiloneurus caesar'' is a hyperparasitoid of ''Dryinus orophilus'' in a delphacid planthopper (Mozambique) ****''Cheiloneurus carinatus'' is a parasitoid or hyperparasitoid from coccid scales ''Saissetia'' spp. and mealybugs ''Allococcus quaesitus'', ''Delottococcus quaesitus'', ''Ferrisiana virgata'', ''Nipaecoccus'' spp., ''Phenacoccus'' spp., ''Planococcoides'' spp., ''Pseudococcus'' spp. (Central African Republic, Democratic Republic of Congo, Eritrea, Ethiopia, Ghana, Ivory Coast, Kenya, Madagascar, Malawi, South Africa, Tanzania) ****''Cheiloneurus chiaromontei'' is a parasitoid or hyperparasitoid from coccid scales ''Saissetia oleae'' (Eritrea) ****''Cheiloneurus cyanonotus'' is a hyperparasitoid of Encyrtidae ''Epidinocarsis lopezi'', ''Gyranusoidea tebygi'', ''Homalotylus flaminius'' and Eulophidae ''Tetrastichus'' sp. in a variety of beetles, flies and Hemiptera (Cameroon, Congo, Democratic Republic of Congo, Gabon, Gambia, Ghana, Guinea-Bissau, Kenya, Malawi, Mali, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Zimbabwe) ****''Cheiloneurus elegans'' is a hyperparasitoid of Encyrtidae ''Epidinocarsis lopezi'' and Platygastridae ''Platygaster zosine'' in a variety of cecidomyiid midges, scales and mealybugs (Nigeria) ****''Cheiloneurus flavoscutatus'' is a parasitoid or hyperparasitoid from mealybugs ''Adelosoma phragmitidis'', ''Chaetococcus phragmitis'' (Ethiopia) ****''Cheiloneurus gonatopodis'' is a hyperparasitoid of pincer wasps ''Echthrodelphax'' sp., ''Pseudogonatopoides mauritianus'', ''Pseudogonatopus'' spp., ''Richardsidryinus'' sp. in delphacid planthoppers on sugar cane (Madagascar, Mauritius) ****''Cheiloneurus kuisebi'' is a parasitoid or hyperparasitoid from a mealybug ''Phenacoccus manihoti'' on cassava (Namibia) ****''Cheiloneurus leptulus'' is a parasitoid or hyperparasitoid from a ''Ceratina'' bee (Tanzania) ****''Cheiloneurus liorhipnusi'' is a parasitoid or hyperparasitoid from a lady beetle ''Chnootriba similis'', and a scentless plant bug ''Corizus hyalinus'' (Kenya, Senegal) ****''Cheiloneurus metallicus'' - no associates known (Madagascar) ****''Cheiloneurus obscurus'' is a parasitoid or hyperparasitoid from coccid scales ''Gascardia brevicauda'', ''Saissetia oleae'' (Eritrea) ****''Cheiloneurus orbitalis'' is a parasitoid or hyperparasitoid from an encyrtid ''Homalotylus'' sp., the coccid scale ''Saissetia oleae'' and green lacewings ''Chrysopa'' sp., ''Mallada handschini'', ''Suarius squamosa'' on citrus (South Africa) *36b Ovipositor protruding strongly, by about one-half length of metasoma. Metasoma usually truncate apically - [[File:Prochiloneurus bolivari, female, Spain.jpg|thumb|''Prochiloneurus bolivari'', female, Spain.]][[File:Prochiloneurus sp fem researchgate 363819988.jpg|thumb|''Prochiloneurus'' sp., Mato Grosso do Sul, Brazil]] **''''' Prochiloneurus''''' Silvestri, 1915 *** 30 species worldwide; 4 Afrotropical species: ****''Prochiloneurus aegyptiacus'' is a parasitoid or hyperparasitoid from Encyrtidae ''Anagyrus'' spp., ''Clausenia purpurea'', ''Epidinocarsis lopezi'', ''Gyranusoidea tebygi'', ''Homalotylus'' spp., ''Leptomastix'' spp., Pteromalidae ''Metastenus'' sp., lady beetles ''Chilocorus bipustulatus'', ''Exochomus flavipes'', ''Hyperaspis aestimabilis'', coccid scales ''Coccus hesperidum'', ''Saissetia coffeae'' and mealybugs ''Ferrisia virgata'', ''Ferrisiana virgata'', ''Maconellicoccus hirsutus'', ''Nipaecoccus vastator'', ''Nipaecoccus viridis'', ''Octococcus africanus'', ''Pedrococcus'' sp., ''Phenacoccus'' spp., ''Planococcoides'', ''Planococcus'' spp., ''Pseudococcus'' spp., ''Rastrococcus invadens'' (Congo, Democratic Republic of Congo, Egypt, Eritrea, Ethiopia, Gabon, Ghana, Ivory Coast, Namibia, Nigeria, South Africa, Tanzania, Togo) ****''Prochiloneurus bolivari'' is a parasitoid or hyperparasitoid from Encyrtidae ''Anagyrus'' sp., ''Blepyrus insularis'', ''Clausenia purpurea'', ''Epidinocarsis lopezi'', ''Leptomastix flava'', Coccidae, Eriococcidae, and Pseudococcidae (Congo, Democratic Republic of Congo, Nigeria, Sao Tomé and Principe, South Africa) ****''Prochiloneurus comperei'' is a parasitoid or hyperparasitoid from Coccidae ''Lecanium viride'', Margarodidae ''Icerya formicarum'', ''Palaeococcus bicolor'', and Pseudococcidae ''Nipaecoccus'' spp., ''Pseudococcus'' sp. (Eritrea, Ethiopia, Malawi, Senegal, South Africa, Tanzania) ****''Prochiloneurus pulchellus'' is a parasitoid or hyperparasitoid from Encyrtidae ''Anagyrus'' spp., ''Epidinocarsis lopezi'', ''Gyranusoidea tebygi'', ''Leptomastix nigrocoxalis'', Diaspididae, Eriococcidae, Margarodidae, and Pseudococcidae (Cameroon, Congo, Democratic Republic of Congo, Eritrea, Ethiopia, Gabon, Gambia, Ghana, Guinea-Bissau, Madagascar, Malawi, Nigeria, Rwanda, Seychelles, South Africa, Togo) ==37 Scutellum without a tuft of bristles== *37a Apex of scutellum with a pair of lamelliform setae (figs 27, 28)........ 38 *37b Scutellum without a pair of lamelliform setae........ 39 ===38 (Apex of scutellum with a pair of lamelliform setae)=== *38a Antenna (fig. 29 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) broadened and flattened, the funicle segments strongly transverse; eyes margined dorsally with white; fronto-occipital margin of head without a pair of lamelliform setae. Parasitic in [[w:Diaspididae|armored scale insects]] - **''''' Comperiella ''''' Howard, 1906 *** Links: [https://www.inaturalist.org/taxa/250283 iNaturalist] *** 11 species worldwide; 6 Afrotropical species: ****''Comperiella apoda'' is a parasitoid of ''Diclavaspis ehretiae'' (Namibia, South Africa) ****''Comperiella bifasciata'' is a parasitoid of many Diaspididae, and the coccid ''Saissetia coffeae'' (Madagascar, Mauritius, South Africa, Swaziland, Zambia, Zimbabwe) ****''Comperiella karoo'' - no associates known (South Africa) ****''Comperiella lemniscata'' is a parasitoid of ''Aonidiella'' spp., ''Chrysomphalus dictyospermi'' (South Africa) ****''Comperiella ponticula'' is a parasitoid of ''Clavaspis pituranthi'' (Namibia, South Africa) ****''Comperiella unifasciata'' is a parasitoid of ''Aonidiella'' spp., ''Aspidiotus'' spp., ''Pseudaonidia'' spp., ''Aleurodicus destructor'', ''Ceroplastes rubens'' (Mauritius) *38b Antenna not broadened and flattened; eyes not margined with white; fronto-occipital margin with a pair of small lamelliform setae. Parasitic in [[w:Diaspididae|armored scale insects]] - [[File:Habrolepis dalmanni Howard 1898 Fig.1.jpg|thumb|Female ''Habrolepis dalmanni'']][[File:Habrolepis dalmanni Howard 1898 Fig.2.jpg|thumb|Female ''Habrolepis dalmanni'']] **''''' Habrolepis ''''' Foerster, 1856 *** Links: [https://www.inaturalist.org/taxa/376512 iNaturalist] *** 17 species worldwide; 12 Afrotropical species: ****''Habrolepis aeruginosa'' - no associates known (Seychelles) ****''Habrolepis algoensis'' is a parasitoid of ''Aspidiotus capensis'' (South Africa) ****''Habrolepis apicalis'' is a parasitoid of ''Chionaspis minor'', ''Pinnaspis temporaria'' (Ghana) ****''Habrolepis dalmanni'' is a parasitoid of pit scale insects ''Asterodiaspis'' spp., ''Asterolecanium'' sp., coccid scale insects ''Didesmococcus'' sp., armored scale insects ''Lepidosaphes ulmi'', ''Melanaspis inopinata'', ''Targionia vitis'', mealybugs ''Pseudococcus'' sp., and moths ''Leucoptera'' sp. (South Africa, Uganda) ****''Habrolepis diaspidi'' is a parasitoid of armored scale insects ''Aonidiella'' spp., ''Chionaspis'' sp., ''Chrysomphalus'' spp., ''Diaspidiotus perniciosus'', ''Diaspis senegalensis'', ''Hemiberlesia lataniae'', ''Parlatoria ziziphi'', ''Pinnaspis strachani'', ''Pudaspis newsteadi'', ''Quadraspidiotus perniciosus'', ''Selenaspidius'' spp., ''Tecaspis visci'', ''Umbaspis regularis'' (Eritrea, Ethiopia, Mozambique, Senegal, South Africa, Zimbabwe) ****''Habrolepis guineensis'' is a parasitoid of armored scale insects ''Duplaspidiotus pavettae'' (Guinea) ****''Habrolepis namibensis'' is a parasitoid of armored scale insects ''Namaquea simplex'' (Namibia) ****''Habrolepis obscura'' is a parasitoid of armored scale insects ''Africaspis chionaspiformis'', ''Aonidiella orientalis'', ''Chionaspis'' sp., ''Diclavaspis ehretiae'', ''Ledaspis distincta'', ''Lindingaspis rossi'', ''Melanaspis corticosa'', ''Quadraspidiotus perniciosus'', ''Separaspis capensis'' (Namibia, Saudi Arabia, South Africa, Zimbabwe) ****''Habrolepis occidua'' is a parasitoid of armored scale insects ''Melanaspis phenax'', ''Morganella phenax'', ''Pseudotargionia'' spp. (Namibia, South Africa) ****''Habrolepis oppugnati'' is a parasitoid of armored scale insects ''Aspidiotus elaeidis'', ''Aspidiotus oppugnatus'' (Eritrea) ****''Habrolepis rouxi'' is a parasitoid of armored scale insects ''Aonidiella'' spp., ''Aspidiotus'' spp., ''Carulaspis minima'', ''Chrysomphalus'' spp., ''Hemiberlesia rapax'', ''Lepidosaphes newsteadi'', ''Parlatoria oleae'', ''Selenaspidius articulatus'' spp. (Kenya, Madagascar, Mozambique, South Africa, Swaziland, Uganda, Zimbabwe) ****''Habrolepis setigera'' is a parasitoid of armored scale insects ''Lindingaspis greeni'' (South Africa) ===39 (Scutellum without a pair of lamelliform setae)=== *39a Submarginal vein of fore wing with a subtriangular expansion (figs 30, 34 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) in its apical one-third, this expansion usually bearing a single strong seta........ 40 *39b Submarginal vein without a triangular expansion................43 ===40 (Submarginal vein of fore wing with a subtriangular expansion in its apical one-third)=== *40a Junction of frontovertex and face forming a transverse ledge above scrobes (fig. 35 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); antennal scape broadly expanded ventrally................41 *40b Frontovertex rounded on to face, not forming a ledge; antenna slender, the scape at most slightly expanded ventrally................42 ===41 (Junction of frontovertex and face forming a transverse ledge above scrobes; antennal scape broadly expanded ventrally)=== *41a Antenna entirely broadened and flattened (fig. 31 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); fore wing with a characteristic pattern of radiating dark bands (fig. 32 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); head and body black with strong metallic refringence; presumed hyperparasitoids of Coccidae - [[File:Cerapterocerus mirabilis, female.jpg|thumb|''Cerapterocerus mirabilis'', female, Spain]][[File:Cerapterocerus celadus inat 194830169 a.jpg|thumb|Adult ''Cerapterocerus celadus'', France]] **''''' Cerapterocerus''''' Westwood, 1833 *** Links: [https://www.inaturalist.org/taxa/250477-Cerapterocerus iNaturalist] *** 17 species worldwide; 1 Afrotropical species: ****''Cerapterocerus mirabilis'' is probably a hyperparasitoid of encyrtid wasps in scale insects (South Africa) *41b Antenna not broadened and flattened except for scape (fig. 33 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); fore wing (fig. 34 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) infuscated, but without distinct patterns as above; head and body dominantly brownish, without strong metallic refringence; primary parasitoids of Asterolecaniidae (pit scales). Head as in fig. 35 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/> - **''''' Mayrencyrtus''''' Hincks, 1944 *** 6 species worldwide; No Afrotropical species in Universal Chalcidoidea Database ===42 (Frontovertex rounded on to face, not forming a ledge; antenna slender, the scape at most slightly expanded ventrally)=== *42a Mesoscutum with incomplete parapsidal sulci (fig. 36 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); maxillary and labial palpi each two-segmented; paratergites present; parasitic in Pseudococcidae - [[File:Coccidoxenoides perminutus Fernandes 2016 a.jpg|thumb|Adult ''Coccidoxenoides perminutus'', Brazil]] **'''''Coccidoxenoides''''' Girault, 1915 ***'' Pauridia'' Timberlake, 1919 is a synonym of ''Coccidoxenoides'' (a monotypic genus) ****''Coccidoxenoides perminutus'' Girault, 1915 is a parasitoid of mealybugs ''Allococcus quaesitus'', ''Allococcus quaestius'', ''Delottococcus quaesitus'', ''Ferrisia virgata'', ''Ferrisiana virgata'', ''Maconellicoccus hirsutus'', ''Phenacoccus madeirensis'', ''Planococcoides'' spp., ''Planococcus citri'' spp., ''Pseudococcus'' spp., ''Spilococcus'' sp. and armored scale insects ''Aspidiotus nerii'', ''Carulaspis minima'', ''Chionaspis striata'' (Ghana, Ivory Coast, Kenya, South Africa) *42b Mesoscutum without parapsidal sulci; maxillary palpi each with four segments, the labial with three; paratergites absent; parasitic in Diaspididae -[[File:Tyndarichus melanacis, female, Spain.jpg|thumb|''Tyndarichus melanacis'', female, Spain]] **'''''Tyndarichus''''' Howard, 1910 ***''Protyndarichus combretae'', ''P. orarius'', ''P. prolatus'', ''P. sparnus'' are a synonyms of the ''Tyndarichus'' species below. *** 24 species worldwide; 4 Afrotropical species: ****''Tyndarichus combretae'' no known associates (Senegal) ****''Tyndarichus orarius'' is a parasitoid of Coccidae, ''Idiosaissetia peringueyi'' (South Africa) ****''Tyndarichus prolatus'' is a parasitoid of Coccidae, ''Ceroplastes elytropappi'' (South Africa) ****''Tyndarichus sparnus'' is a parasitoid of Lecanodiaspididae, ''Lecanodiaspis tarsalis'' (South Africa) ===43 (Submarginal vein without a triangular expansion)=== *43a Mandible with only two acute or subacute teeth (figs 37, 38 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Paratergites (fig. 39 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) usually present, plainly visible in cleared, slide-mounted specimens; speculum of fore wing usually lacking a row of coarse, spine-like setae along outer edge of speculum; cercal plates often advanced to a level near base of metasoma; exclusively parasitic in Pseudococcidae ................ 120 *43b Mandible never with only two pointed teeth ........ 44 ===44 (Mandible never with only two pointed teeth)=== *44a Entire fore wing, or part of it, distinctly [[wikt:infuscate|infuscated]] (with a dark tinge), the infuscation rarely restricted to an area beneath the venation ........ 45 *44b Fore wing entirely [[w:hyaline|hyaline]] (translucent or transparent), or very faintly and inconspicuously infuscated, the infuscation then usually only visible if wing held against a white background ........ 73 ==45 Fore wing, or part of it, distinctly infuscated== *45a Fore wing with a conspicuous incision in cephalic wing margin at distal end of submarginal vein (fig. 40 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) - **''''' Eugahania''''' Mercet, 1926 *** 10 species worldwide; No Afrotropical species in Universal Chalcidoidea Database.<ref name=Noyes2019/> *45b Fore wing without an incision in cephalic margin ................46 ===46 Fore wing without an incision in cephalic margin=== *46a Scutellum with a posterior flange or lamella (fig. 15 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); in profile this flange shows as a thin flat [[wikt:caudal|caudal]] projection of the scutellum................47 *46b Scutellum without a marginal flange, the posterior margin rarely forming a very short lip........ 49 ===47 Scutellum with a posterior flange or lamella=== *47a Antennal [[wikt:clava|club]] white; [[wikt:gonostylus|gonostyli]] absent; [[wikt:clava|club]] large, much longer than the distal three [[wikt:funicle|funicle]] segments together; parasitic in Lepidoptera eggs. Antenna as in fig. 41 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/> - **''''' Hesperencyrtus''''' Annecke, 1971 *** 2 species worldwide; 1 Afrotropical species: ****''Hesperencyrtus lycoenephila'' is a parasitoid of lycaenid butterflies ''Deodorix antalus'', ''Deudorix antalus'', ''Lampides boeticus'' (Senegal) *47b Antennal [[wikt:clava|club]] not white; [[wikt:gonostylus|gonostyli]] present; [[wikt:clava|club]] about as long as the distal three [[wikt:funicle|funicle]] segments together; not parasitic in Lepidoptera........ 48 ===48 Antennal club not white; club about as long as the distal three funicle segments together=== *48a Frontovertex and face with numerous large pits, each brilliantly metallic green in colour - [[File:Discodes arizonensis Smithsonian Institution 2019 CC-BY BOLD CCDB-34079-D12.jpg|thumb|''Discodes arizonensis'', New Mexico, United States]] **''''' Discodes''''' Foerster, 1856 *** 44 species worldwide; 2 Afrotropical species: ****''Discodes discors'' is a parasitoid of felt scales ''Eriococcus'' spp. (South Africa) ****''Discodes melas'' - no associates known (Namibia) *48b Head at most with fine punctations. Orange-brown to dark brown, rarely black, species, at most weakly refringent; fore wing strongly and uniformly infuscated from base to near apex; usually parasitic in Pulvinaria spp. on grasses - [[File:Paraphaenodiscus monawari, female, dorsal view.jpg|thumb|Female ''Paraphaenodiscus monawari'', India]] **''''' Paraphaenodiscus''''' Girault, 1915 *** 20 species worldwide; 10 Afrotropical species: ****''Paraphaenodiscus africanus'' - no associates known (South Africa) ****''Paraphaenodiscus ceroplastodesi'' is a parasitoid of a wax scale ''Ceroplastes'' sp.(Senegal) ****''Paraphaenodiscus chrysocomae'' - no associates known (South Africa) ****''Paraphaenodiscus munroi'' is a parasitoid of a coccid scale ''Pulvinaria iceryi'' (South Africa) ****''Paraphaenodiscus niger'' is a parasitoid of coccid scales ''Pulvinariai'' spp. (South Africa) ****''Paraphaenodiscus paralis'' is a parasitoid associated with the grass ''Plagiochloa uniolae'' (South Africa) ****''Paraphaenodiscus pavoniae'' is a parasitoid of coccid scales ''Ceroplastes'' sp., ''Pulvinaria'' spp. (Senegal, South Africa, Zimbabwe) ****''Paraphaenodiscus pedanus'' is a parasitoid associated with the grass ''Plagiochloa uniolae'' (South Africa) ****''Paraphaenodiscus risbeci'' is a parasitoid of a moth ''Sesamia cretica'' (Senegal, Sudan) ****''Paraphaenodiscus rizicola'' is a parasitoid associated with rice ''Oryza sativa'' (Cameroon, Swaziland, Zimbabwe) ===49 Scutellum without a marginal flange=== *49a Stigmal vein of fore wing placed almost at right angle to postmarginal vein (fig. 42 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Fore wing infuscated with contrasting hyaline patches as in fig. 42<ref name=Prinsloo&Anneke1979/>; parasitic in Lacciferidae and Coccidae - **''''' Ruandella''''' Risbec, 1957 *** 4 species worldwide; 4 Afrotropical species: ****''Ruandella capensis'' is a parasitoid of coccid scales ''Ceroplastes'' sp. ''Saissetia'' sp. (South Africa) ****''Ruandella stigmosa'' is a parasitoid of coccid scales ''Lichtensia'' sp., ''Saissetia'' spp. (South Africa) ****''Ruandella tertia'' is a parasitoid of lac scales ''Tachardina'' spp. (South Africa) ****''Ruandella testacea'' is a parasitoid of a wax scale ''Ceroplastes'' sp. (Rwanda, South Africa) *49b Angle between stigmal and postmarginal veins much less than 90 degrees ........ 50 ===50 Angle between stigmal and postmarginal veins much smaller than right angle=== *50a Mandible with four teeth (fig. 43 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Body somewhat flattened dorsoventrally; head subtriangular in lateral view, the face a little inflexed; parasitic in Diaspididae - [[File:Adelencyrtus inat 31626163.jpg|thumb|''Adelencyrtus'' sp., South Africa]][[File:Adelencyrtus Cipola 2022 EntomoBrasilis 15 e1003 CC-BY.jpg|thumb|Female ''Adelencyrtus'' sp., Brazil]] **''''' Adelencyrtus''''' Ashmead, 1900 *** 45 species worldwide; 10 Afrotropical species: ****''Adelencyrtus antennatus'' is a parasitoid of armored scale insects ''Aspidiotus'' sp. (South Africa) ****''Adelencyrtus aulacaspidis'' is a parasitoid of coccid scales ''Lecanopsis nevesi'', and armored scales ''Aulacaspis difficilis'', ''Aulacaspis rosae'', ''Chionaspis salicis'', ''Dynaspidiotus britannicus'', ''Lepidosaphes cupressi'', ''Pseudaulacaspis pentagona'', ''Quadraspidiotus macroporanus'', ''Unaspis yanonensis'' (Madagascar) ****''Adelencyrtus depressus'' - no associates known (Madagascar) ****''Adelencyrtus flagellatus'' - no associates known (South Africa) ****''Adelencyrtus inglisiae'' is a parasitoid of armored scale insects ''Africaspis''' spp. ''Aspidiotus'' spp., ''Balaspis faurei'', ''Clavaspis'' spp., ''Clavaspis pituranthi'', ''Diaspis echinocacti'', ''Moraspis euphorbiae'', ''Mytilococcus'' spp., ''Quadraspidiotus perniciosus'' (South Africa, Zimbabwe) ****''Adelencyrtus mangiphila'' is a parasitoid of armored scale insects ''Phenacaspis dilatata'' (Madagascar) ****''Adelencyrtus mayurai'' is a parasitoid of armored scale insects ''Aonidiella orientalis'', ''Melanaspis glomerata'' (Mauritania) ****''Adelencyrtus moderatus'' is a parasitoid of whiteflies ''Bemisia tabaci'', armored scales ''Aspidiella hartii'', ''Aspidiella sacchari'', ''Aspidiotus glomeratus'', ''Aulacaspis'' spp., ''Duplachionaspis'' spp., ''Lepidosaphes'' spp., ''Melanaspis glomerata'', and mealybugs ''Saccharicoccus sacchari'' (Ghana, Madagascar, Mauritius, Tanzania, Uganda) ****''Adelencyrtus odonaspidis'' is a parasitoid of armored scales ''Duplachionaspis sansevieriae'', ''Odonaspidis'' sp., ''Odonaspis'' spp., and mealybugs ''Antonina graminis'' (South Africa) ****''Adelencyrtus tibialis'' - no associates known (South Africa) *50b Mandibles do not have four teeth ........ 51 ===51 (Mandibles do not have four teeth)=== *51a Antennal club white, usually obliquely truncate apically................52 *51b Antennal club dark, seldom obliquely truncate apically................55 ===52 Antennal club white, usually obliquely truncate apically=== *52a Antennal club three-segmented; not parasitic in Coleoptera........ 53 *52b Antennal club not segmented, rarely with faint traces of one or two septa on one side of the club; parasitic in Coleoptera........ 54 ===53 Antennal club three-segmented=== *53a Antennal scape expanded ventrally (fig. 44 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); hcad and body strongly metallic in colour, the head and thorax usually covered with silvery-white setae; parasitic in the oothecae of cockroaches - [[File:Comperia Smithsonian Institution 2019 CCDB-34079-D08 CC-BY boldsystems.jpg|thumb|''Comperia'' sp., Illinois, United States]] **''''' Comperia''''' Gomes, 1942 *** 7 species worldwide; 7 Afrotropical species: ****''Comperia alfierii'' is a parasitoid of a cockroach ''Blattella'' sp., and a dance fly ''Phyllodromia'' sp. (Egypt, Kenya, South Africa) ****''Comperia austrina'' - no associates known (South Africa) ****''Comperia clavata'' - no associates known (South Africa) ****''Comperia domestica'' - no associates known (South Africa) ****''Comperia faceta'' - no associates known (South Africa) ****''Comperia hirsuta Annecke'' - no associates known (South Africa) ****''Comperia merceti'' is a parasitoid of a cockroaches ''Blattella germanica'', ''Supella longipalpa'', ''Supella supellectilium'', ''Periplaneta americana'' (Uganda) *53b Antennal scape not or only slightly expanded ventrally (fig. 45 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); head and body without metallic refringence; parasitic in Pseudococcidae - [[File:Aphycus apicalis gbif.org - occurrence - 3905669246 03.png|thumb|''Aphycus apicalis'', Netherlands]] **''''' Aphycus''''' Mayr, 1876 *** 33 species worldwide; 1 Afrotropical species: ****''Aphycus comperei'' is a parasitoid of mealybugs ''Pedrococcus'' sp. (South Africa) ===54 Antennal club not segmented; parasitic in Coleoptera=== *54a Mesoscutum with parapsidal sulci (fig. 46 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); basal one-half or so of tegulae white; antennal scape slender, subcylindrical; primary parasitoids of Coccinellidae -[[File:Homalotylus flaminius, female, Spain.jpg|thumb|''Homalotylus flaminius'', female]][[File:Homalotylus iNat 135531367.jpg|thumb|''Homalotylus'' sp., South Africa]] **''''' Homalotylus''''' Mayr, 1876 *** 68 species worldwide; 6 Afrotropical species: ****''Homalotylus africanus'' is a parasitoid of lady beetles ''Exochomus concavus'', ''Hyperaspis'' spp., ''Lindorus lophanthae'', ''Scymnus ornatulus'' (Democratic Republic of Congo, Ghana, Namibia, Nigeria, Rwanda, South Africa) ****''Homalotylus eytelweinii'' is a parasitoid of lady beetles ''Adonia variegata'', ''Anatis ocellata'', ''Brumoides suturalis'', ''Cheilomenes sexmaculata'', ''Chilocorus'' spp., ''Coccinella septempunctata'', ''Menochilus sexmaculatus'', ''Rodolia'' spp. (Congo, Kenya, Malawi, South Africa, Sudan, Togo) ****''Homalotylus flaminius'' is a parasitoid of lady beetles ''Adalia'' spp., ''Adonia variegata'', ''Anatis ocellata'', ''Brumoides suturalis'', ''Brumus suturalis'', ''Cheilomenes'' spp., ''Chilocorus'' spp., ''Coccinella'' spp., ''Coleomegilla maculata'', ''Cycloneda'' spp., ''Epilachna chrysomelina'', ''Eriopis connexa'', ''Exochomus'' spp., ''Harmonia'' spp., ''Henosepilachna bifasciata'', ''Hippodamia'' spp., ''Hyperaspis'' spp., ''Lioadala flavomaculata'', ''Menochilus sexmaculatus'', ''Neomysia oblongoguttata'', ''Nephus bipunctatus'', ''Orcus'' spp., ''Pharoscymnus'' spp., ''Platynaspis'' sp., ''Rodolia'' spp., ''Scymnus'' spp., ''Thea vigintiduopunctata'', ''Verania frenata'', leaf beetles ''Galeruca calmariensis'', coccid scale insects ''Parthenolecanium corni'', ''Saissetia oleae'', mealybugs ''Nipaecoccus viridis'', ''Planococcus citri'', ''Pseudococcus citri'' (Cameroon, Democratic Republic of Congo, Gambia, Ghana, Guinea-Bissau, Madagascar, Mali, Namibia, Nigeria, Senegal, South Africa, Togo) ****''Homalotylus hemipterinus'' is a parasitoid of lady beetles ''Chilocorus'' spp., ''Chilomenes'' sp., ''Coccinella septempunctata'', ''Cycloneda sanguinea'', ''Menochilus sexmaculatus'', ''Orcus'' sp., stink bugs ''Cantheconidia furcellata'', mealybugs ''Nipaecoccus viridis'', ''Pseudococcus'' sp., gelechiid moths ''Aproaerema modicella'' (Chad, Congo, Democratic Republic of Congo, Kenya, Malawi, South Africa, Sudan, Togo) ****''Homalotylus quaylei'' is a parasitoid of lady beetles ''Hyperaspis'' spp., ''Nephus'' spp., ''Pharoscymnus'' spp., ''Scymnus'' spp., ''Sidis'' sp., coccid scales ''Eulecanium persicae'', mealybugs ''Nipaecoccus viridis'', ''Phenacoccus herreni'', ''Planococcus''; spp. (Gabon, Mauritania) ****''Homalotylus vicinus'' is a parasitoid of lady beetles ''Hyperaspis marmottani'', ''Nephus bipunctatus'', ''Nephus vetustus'', ''Scymnus'' sp. (Eritrea, Ethiopia, Madagascar) *54b Mesoscutum without parapsidal sulci; tegula not white; scape moderately to broadly expanded ventrally; parasitic in Discolomatidae - [[File:Homalotyloidea dahlbomii, female.jpg|thumb|''Homalotyloidea dahlbomii'', female, Spain]] **''''' Homalotyloidea''''' Mercet, 1921 *** 8 species worldwide; 1 Afrotropical species: ****''Homalotyloidea africana'' is a parasitoid of beetles ''Notiophygus piger'' (South Africa) ===55 Antennal club dark, seldom obliquely truncate apically=== *55a Body flattened dorsoventrally, the dorsum of head and thorax almost flat. Parasitic in Diaspididae........ 56 *55b Body not flattened dorsoventrally, the head and thorax more or less convex........ 57 ===56 Body not flattened dorsoventrally, the head and thorax convex=== *56a Antenna entirely broadened and flattened (fig. 29 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); frontovertex with two narrow whitish bands, one each extending along the dorsal eye margins. Fore wing boldly marked -[[File:Cain2565.jpg|thumb| ''Comperiella bifasciata'']] **''''' Comperiella''''' Howard, 1906 *** 11 species worldwide; 6 Afrotropical species: ****''Comperiella apoda'' is a parasitoid of armored scale insects ''Affirmaspis ehretiae'' (Namibia, South Africa) ****''[[w:Comperiella bifasciata|Comperiella bifasciata]]'' is a parasitoid of armored scale insects ''Aonidiella aurantii'', ''Aspidiotus'' spp., ''Chrysomphalus'' spp., ''Clavaspis'' sp., ''Diaspidiotus gigas'', ''Diaspis echinocacti'', ''Dynaspidiotus abietis'', ''Hemiberlesia'' spp., ''Lindingaspis fusca'', ''Morganella longispina'', ''Nuculaspis abietis'', ''Parlatoria pergandii'', ''Pseudaonidia trilobitiformis'', ''Pseudaulacaspis'' spp., ''Quadraspidiotus'' spp., ''Temnaspidiotus destructor'', ''Unaspis yanonensis'', coccid scale insects ''Saissetia coffeae'' (Madagascar, Mauritius, South Africa, Swaziland, Zambia, Zimbabwe) ****''Comperiella karoo'' - no associates known (South Africa) ****''Comperiella lemniscata'' is a parasitoid of armored scale insects ''Aonidiella'' spp., ''Chrysomphalus dictyospermi'' (South Africa) ****''Comperiella ponticula'' is a parasitoid of armored scale insects ''Clavaspis pituranthi'' (Namibia, South Africa) ****''Comperiella unifasciata'' is a parasitoid of armored scale insects ''Aonidiella'' spp., ''Aspidiotus'' spp., ''Pseudaonidia'' spp., whiteflies ''Aleurodicus destructor'', wax scale insects ''Ceroplastes rubens'' (Mauritius) *56b Antenna not broadened and flattened; frontovertex without pale bands - [[File:Habrolepis dalmanni Howard 1898 Fig.1.jpg|thumb|Female ''Habrolepis dalmanni'']][[File:Habrolepis dalmanni Howard 1898 Fig.2.jpg|thumb|Female ''Habrolepis dalmanni'']] **''''' Habrolepis''''' Foerster, 1856 *** 17 species worldwide; 12 Afrotropical species: ****''Habrolepis aeruginosa'' - no associates known (Seychelles) ****''Habrolepis algoensis'' is a parasitoid of armored scale insects ''Aspidiotus capensis'' (South Africa) ****''Habrolepis apicalis'' is a parasitoid of armored scale insects ''Chionaspis minor'', ''Pinnaspis temporaria'' (Ghana) ****''Habrolepis dalmanni'' is a parasitoid of armored scale insects ''Lepidosaphes ulmi'', ''Melanaspis inopinata'', ''Targionia vitis'', pit scales, ''Asterodiaspis'' sp., ''Asterolecanium'' sp., coccid scales ''Didesmococcus'' sp., mealybugs, ''Pseudococcus'' sp., and a moth, ''Leucoptera'' sp. (South Africa, Uganda) ****''Habrolepis diaspidi'' is a parasitoid of armored scale insects ''Aonidiella aurantii'' spp., ''Chionaspis'' sp., ''Chrysomphalus aonidum'' spp., ''Diaspidiotus perniciosus'', ''Diaspis senegalensis'', ''Hemiberlesia lataniae'', ''Parlatoria ziziphi'', ''Pinnaspis strachani'', ''Pudaspis newsteadi'', ''Quadraspidiotus perniciosus'', ''Selenaspidius celastri'' spp., ''Tecaspis visci'', ''Umbaspis regularis'' (Eritrea, Ethiopia, Mozambique, Senegal, South Africa, Zimbabwe) ****''Habrolepis guineensis'' is a parasitoid of armored scale insects ''Duplaspidiotus pavettae'' (Guinea) ****''Habrolepis namibensis'' is a parasitoid of armored scale insects ''Namaquea simplex'' (Namibia) ****''Habrolepis obscura'' is a parasitoid of armored scale insects ''Africaspis chionaspiformis'', ''Aonidiella orientalis'', ''Chionaspis'' sp., ''Diclavaspis ehretiae'', ''Ledaspis distincta'', ''Lindingaspis rossi'', ''Melanaspis corticosa'', ''Quadraspidiotus perniciosus'', ''Separaspis capensis'' (Namibia, South Africa, Zimbabwe) ****''Habrolepis occidua'' is a parasitoid of armored scale insects ''Melanaspis phenax'', ''Morganella phenax'', ''Pseudotargionia'' spp. (Namibia, South Africa) ****''Habrolepis oppugnati'' is a parasitoid of armored scale insects ''Aspidiotus'' spp. (Eritrea) ****''Habrolepis rouxi'' is a parasitoid of armored scale insects ''Aonidiella'' spp., ''Aspidiotus'' spp., ''Carulaspis minima'', ''Chrysomphalus'' spp., ''Hemiberlesia rapax'', ''Lepidosaphes newsteadi'', ''Parlatoria oleae'', ''Selenaspidius'' spp. (Kenya, Madagascar, Mozambique, South Africa, Swaziland, Uganda, Zimbabwe) ****''Habrolepis setigera'' is a parasitoid of armored scale insects ''Lindingaspis greeni'' (South Africa) ===57 Body not flattened, head and thorax convex=== *57a Antenna foliaceously flattened (fig. 47 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); junction of frontovertex and face carinate or at least acutely angled and grooved........ 58 *57b Antenna not flattened except for scape which may be expanded ventrally; head without a facial carina................60 ===58 Antenna flattened, junction of frontovertex and face carinate or acutely angled and grooved=== *58a Frontovertex terminating anteriorly at a transverse groove (fig. 48 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) containing dense, recumbent, silvery-white setae - **''''' Anasemion''''' Annecke, 1967 *** 1 species worldwide; 1 Afrotropical species: ****''Anasemion inutile'' is a parasitoid of wax scales ''Ceroplastes'' spp., ''Waxiella mimosae'' (Kenya, South Africa) *58b Junction of frontovertex and face lacking a transverse row of dense setae - [[File:Anicetus iNat 180762161 g.jpg|thumb|''Anicetus'' sp., South Africa]] **'''''Anicetus''''' Howard, 1896 ***''Paraceraptrocerus'' is a synonym of ''Anicetus''. In the Prinsloo-Annecke key,<ref name=Prinsloo&Anneke1979/> step 59 separated ''Paraceraptrocerus'' and ''Anicetus'' *** 52 species worldwide; 19 Afrotropical species: ****'' Anicetus abyssinicus '' is a parasitoid of coccid scales ''Parasaissetia nigra'' (Eritrea) ****'' Anicetus africanus'' is a parasitoid of wax scales ''Ceroplastes'' spp., ''Waxiella mimosae'' (Egypt, South Africa) ****'' Anicetus anneckei '' is a parasitoid of coccid scales ''Saissetia'' spp. (South Africa) ****'' Anicetus aquilus '' is a parasitoid of wax scales ''Gascardia destructor'' (South Africa) ****'' Anicetus austrinus'' is a parasitoid of wax scales ''Ceroplastes'' spp. (South Africa) ****'' Anicetus calidus'' is a parasitoid of wax scales ''Ceroplastes'' sp. and ''Gascardia'' sp. (South Africa) ****'' Anicetus clivus'' is a parasitoid of wax scales ''Gascardia tachardiaformis'' (South Africa) ****'' Anicetus communis'' is a parasitoid of wax scales ''Ceroplastes'' spp., ''Coccus longulus'', ''Gascardia'' spp., ''Gascardia destructor'', ''Parasaissetia litorea'', ''Waxiella mimosae'' (South Africa) ****'' Anicetus fotsyae'' - no associates known (Madagascar) ****'' Anicetus fuscus'' is a parasitoid of wax scales ''Ceroplastes bipartitus'' (South Africa) ****'' Anicetus graminosus'' is a parasitoid of coccid scales ''Pulvinaria iceryi'' (South Africa) ****'' Anicetus italicus'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Coccus elongatus'', felt scales ''Gossyparia spuria'' (Zimbabwe) ****'' Anicetus nyasicus'' is a parasitoid of coccid scales ''Ceroplastes'' spp. (Malawi, South Africa) ****'' Anicetus parilis'' is a parasitoid of coccid scales ''Gascardia rustica'', ''Lichtensia'' sp. (South Africa) ****'' Anicetus parvus'' is a parasitoid of wax scales ''Ceroplastes'' spp. (Congo, Democratic Republic of Congo, South Africa, Uganda) ****'' Anicetus pattersoni'' is a parasitoid of coccid scales ''Ceroplastes personatus'', ''Vinsonia personata'' (Ghana) ****'' Anicetus russeus'' - no associates known (South Africa) ****'' Anicetus sepis'' is a parasitoid of coccid scales ''Ceroplastes'' sp. (South Africa) ****'' Anicetus taylori'' is a parasitoid of wax scales ''Ceroplastes'' spp. (South Africa) ===59 ''Paraceraptrocerus''=== *In the Prinsloo-Annecke key,<ref name=Prinsloo&Anneke1979/> step 59 separated ''Paraceraptrocerus'' and ''Anicetus''. However, ''Paraceraptrocerus'' is now regarded as a synonym of ''Anicetus'', making this step redundant. ===60 (Antenna not flattened although the scape may be expanded ventrally; no facial carina)=== *60a Ovipositor protruding strongly (fig. 49 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) at apex of metasoma by about one half length of metasoma........ 61 *60b Ovipositor not exserted or slightly exserted; if strongly protruded (rare), then antennal scrobes sulcate, or mandible slender, tridentate, the upper tooth retracted (fig. 50 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 62 ===61 (Ovipositor protruding strongly)=== *61a Head with numerous setigerous pits; fore wing with a single pale cross-band beyond venation; body robust, black in colour; parasitic in Coccidae - **'''''Lombitsikala''''' Risbec, 1957 *** 1 species worldwide; 1 Afrotropical species: ****''Lombitsikala coccidivora'' is a parasitoid of coccid scales ''Gascardia madagascariensis'' (Madagascar) *61b Head at most with minute, indistinct punctations; fore wing without hyaline cross-bands; body more or less slender, usually generally yellowish to brownish; probably hyperparasitoids, usually in mealybugs - [[File:Prochiloneurus sp fem researchgate 363819988.jpg|thumb|Female ''Prochiloneurus'' sp., Mato Grosso do Sul, Brazil]] **''''' Prochiloneurus''''' Silvestri, 1915 *** 30 species worldwide; 4 Afrotropical species: ****'' Prochiloneurus aegyptiacus'' is a parasitoid of mealybugs ''Ferrisia virgata'', ''Ferrisiana virgata'', ''Maconellicoccus hirsutus'', ''Nipaecoccus vastator'', ''Nipaecoccus viridis'', ''Octococcus africanus'', ''Pedrococcus'' sp., ''Phenacoccus'' spp., ''Planococcoides njalensis'', ''Planococcus'' spp., ''Pseudococcus'' spp., ''Rastrococcus invadens'', coccid scales ''Coccus hesperidum'', ''Saissetia coffeae'' and lady beetles ''Chilocorus bipustulatus'', ''Exochomus flavipes'', ''Hyperaspis aestimabilis'' (Congo, Democratic Republic of Congo, Eritrea, Ethiopia, Gabon, Ghana, Ivory Coast, Namibia, Nigeria, South Africa, Tanzania, Togo) ****'' Prochiloneurus bolivari'' is a parasitoid of mealybugs ''Atrococcus'' sp., ''Dysmicoccus multivorus'', ''Ferrisia virgata'', ''Heliococcus bohemicus'', ''Heterococcopsis opertus'', ''Maconellicoccus hirsutus'', ''Naiacoccus serpentinus'', ''Peliococcus'' spp., ''Phenacoccus'' spp., ''Planococcus'' spp., ''Pseudococcus'' spp., ''Puto pilosellae'', ''Spinococcus calluneti'', ''Trionymus'' spp., coccid scales ''Rhizopulvinaria armeniaca'', felt scales ''Acanthococcus desertus'', ''Eriococcus insignis'', ''Neoacanthococcus tamaricicola'' (Congo, Democratic Republic of Congo, Nigeria, Sao Tomé and Principe, South Africa) ****'' Prochiloneurus comperei'' is a parasitoid of mealybugs ''Nipaecoccus'' spp., ''Pseudococcus'' sp., coccid scales ''Lecanium viride'', margarodid scales ''Icerya formicarum'', ''Palaeococcus bicolor'' (Eritrea, Ethiopia, Malawi, Senegal, South Africa, Tanzania) ****'' Prochiloneurus pulchellus'' is a parasitoid of mealybugs ''Centrococcus'' spp., ''Coccidohystrix'' spp., ''Dysmicoccus'' sp., ''Ferrisia virgata'', ''Naiacoccus serpentinus'', ''Nipaecoccus'' spp., ''Octococcus'' sp., ''Oxyacanthus chrysocomae'', ''Paracoccus'' sp., ''Peliococcus mesasiaticus'', ''Phenacoccus'' spp., ''Planococcus'' spp., ''Pseudococcus'' sp., ''Rastrococcus iceryoides'' spp., ''Trabutina crassispinosa'', ''Trabutina leonardii'', armored scale insects ''Chionaspis'' sp., felt scales ''Eriococcus stenoclini'', ''Neoacanthococcus tamaricicola'' (Cameroon, Cape Verde Islands, Congo, Democratic Republic of Congo, Eritrea, Ethiopia, Gabon, Gambia, Ghana, Guinea-Bissau, Madagascar, Malawi, Nigeria, Rwanda, Seychelles, South Africa, Togo) ===62 (Ovipositor not exserted or slightly exserted)=== *62a Antennal scape long and slender, at most slightly expanded ventrally........ 63 *62b Antennal scape moderately to broadly expanded, less than three times as long as its greatest width................70 ==63 Antennal scape long and slender== *63a Fore wing with marginal vein several times longer than stigmal (fig. 51 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); antennal club with four segments, visible only in cleared slide·mounted specimens (fig. 52 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) -[[File:Metaphaenodiscus nemoralis, female, Spain.jpg|thumb|''Metaphaenodiscus nemoralis'', female, Spain.]][[File:Metaphaenodiscus nemoralis, female, lateral view.jpg|thumb|''Metaphaenodiscus nemoralis'', female, lateral view]] **''''' Metaphaenodiscus''''' Mercet, 1921 *** Host species generally unknown, except for ''Metaphaenodiscus umbilicatus'' (Australia) which is known to be a parasitoid of a mealy bug. *** 10 species worldwide; 4 Afrotropical species: ****'' Metaphaenodiscus aethiops'' - no associates known (South Africa, Zimbabwe) ****'' Metaphaenodiscus capensis'', associated with ''Protea aurea'' (South Africa) ****'' Metaphaenodiscus karoo'' - no associates known (South Africa) ****'' Metaphaenodiscus watshami'' - no associates known (South Africa, Zimbabwe) *63b Marginal vein of fore wing shorter than, or subequal to stigmal vein; club with fewer than four segments................64 ===64 (Marginal vein shorter than stigmal vein; antennal club with less than four segments)=== *64a Antennal scrobes sulcate (figs 53 and 54 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), impressed on face as two deep furrows, their lateral margins acutely angled, at least in their basal one-half or so, converging, sometimes confluent dorsally to form an inverted V-shaped impression on face........ 65 *64b Antennal scrobes otherwise................66 ===65 (Antennal scrobes impressed on face as two deep furrows)=== *65a Antennal club not longer than the distal funicle segments together; frontovertex more or less pitted; mandible with two teeth and a broad truncation (fig. 55 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); parasitic in Coccidae - **''''' Aloencyrtus''''' Prinsloo, 1978 *** 20 species worldwide; 19 Afrotropical species: ****'' Aloencyrtus alox'' - no associates known (South Africa) ****'' Aloencyrtus angustifrons'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Gascardia brevicauda'' spp. (South Africa) ****'' Aloencyrtus claripennis'' is a parasitoid of coccid scales ''Inglisia conchiformis'' (South Africa, Uganda) ****'' Aloencyrtus coelops'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Gascardia destructor'', ''Waxiella mimosae'' (Eritrea, Nigeria, South Africa, Uganda) ****'' Aloencyrtus delottoi'' is a parasitoid of coccid scales ''Saissetia opulenta'' (Kenya, South Africa) ****'' Aloencyrtus diaphorocerus'' is a parasitoid of coccid scales ''Saissetia coffeae'' (Mauritius, Seychelles) ****'' Aloencyrtus distinguendus'' is a parasitoid of coccid scales ''Coccus subhemisphaericus'', ''Lecanium'' sp. (Cameroon, Ghana, Nigeria) ****'' Aloencyrtus facetus'' is a parasitoid of coccid scales ''Ceroplastes longicauda'' (South Africa) ****'' Aloencyrtus habrus'' is a parasitoid of coccid scales ''Saissetia coffeae'' (Cameroon) ****'' Aloencyrtus hardii'' is a parasitoid of coccid scales ''Parasaissetia nigra'', ''Saissetia'' spp. (South Africa) ****'' Aloencyrtus johani'' is a parasitoid of coccid scales ''Parasaissetia nigra'' (South Africa) ****'' Aloencyrtus lindae'' is a parasitoid of coccid scales ''Ceroplastes'' sp. (South Africa) ****'' Aloencyrtus nativus'' is a parasitoid of coccid scales ''Coccus longulus'', ''Parthenolecanium persicae'' (Benin, Madagascar, South Africa, Uganda, Zimbabwe) ****'' Aloencyrtus obscuratus'' is a parasitoid of coccid scales ''Lecanium somereni'', ''Saissetia'' spp. (Ghana, Kenya, South Africa) ****'' Aloencyrtus saissetiae'' is a parasitoid of coccid scales ''Ceroplastes'' sp. ''Coccus'' spp. ''Cryptinglisia lounsburyi'', ''Parasaissetia nigra'', ''Saissetia'' spp. (Ivory Coast, Kenya, Malawi, South Africa, Uganda, Zimbabwe) ****'' Aloencyrtus ugandensis'' is a parasitoid of coccid scales ''Ceroplastes'' spp. (Uganda) ****'' Aloencyrtus umbrinus'' is a parasitoid of coccid scales ''Ceroplastes'' spp. (Kenya, ) ****'' Aloencyrtus utilis'' is a parasitoid of coccid scales ''Saissetia oleae'' (South Africa) ****'' Aloencyrtus vivo'' - no associates known (Uganda) *65b Antennal club much longer than the distal three funicle segments together; frontovertex without pits or punctations; mandible with three teeth and a truncation (fig. 56 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Parasitic in Lacciferidae. Male antenna with two smaIl funicle segments and a large, unsegmented banana shaped club (fig. 57 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) - **''''' Erencyrtus''''' Mahdihassan, 1923 *** 6 species worldwide; 4 Afrotropical species: ****'' Erencyrtus ater'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus contrarius'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus fuscus'' is a parasitoid of coccid scales ''Waxiella mimosae'', lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus notialis'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) ===66 (Antennal scrobes not deeply impressed)=== *66a Mandible with three distinct teeth, the upper one sometimes retracted ................ 67 *66b Mandible otherwise ................ 68 ===67 (Mandible with three distinct teeth)=== *67a Antenna (fig. 58 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) slender, not clavate, the funicle segments each longer than wide, the pedicel and funicle subcqual in length; parasitic in Coccidae - **''''' Hadrencyrtus''''' Annecke and Mynhardt, 1973 *** 1 species worldwide; 1 Afrotropical species: ****'' Hadrencyrtus cirritus'' is a parasitoid of mealybugs ''Distichlicoccus'' sp. (South Africa) *67b Antenna (fig. 45 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) clavate, not particularly slender, the basal funicle segment plainly wider than long, small, much shorter than pedicel; parasitic in Pseudococcidae - [[File:Aphycus apicalis gbif.org - occurrence - 3905669246 03.png|thumb|''Aphycus apicalis'', Netherlands]] **''''' Aphycus''''' Mayr , 1876 *** 33 species worldwide; 1 Afrotropical species: ****'' Aphycus comperei'' is a parasitoid of mealybugs ''Pedrococcus'' sp. (South Africa) ===68 (Mandible does not have three distinct teeth)=== *68a Mandible with a single tooth and a broad serrated truncation (fig. 59 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); ovipositor with gonostyli absent; parasitic in Membracidae - [[File:Prionomastix biharensis - Female 01.jpg|thumb|Female ''Prionomastix biharensis'', Bihar, India.]] **''''' Prionomastix''''' Mayr , 1876 *** 30 species worldwide; 7 Afrotropical species: ****'' Prionomastix africana'' - no associates known (South Africa) ****'' Prionomastix capeneri'' is a parasitoid of treehoppers ''Beaufortiana viridis'', ''Leprechaunus cristatus'' (South Africa) ****'' Prionomastix congoensis'' - no associates known (Rwanda) ****'' Prionomastix montana'' is a parasitoid of treehoppers ''Dukeobelus simplex'' (South Africa) ****'' Prionomastix myartsevae'' - no associates known (South Africa) ****'' Prionomastix siccarius'' is a parasitoid of treehoppers ''Gongroneura fasciata'' (South Africa) ****'' Prionomastix wonjeae'' is a parasitoid of leafhoppers ''Coloborrhis corticina'' (Cameroon) *68b Mandible otherwise; gonostyli present; not parasitic in Membracidae................69 ===69 (Mandible does not have three distinct teeth, or a single tooth and a broad serrated truncation)=== *69a Antennal club large, about as long as entire funicle; integument of head and thorax heavily sclerotized, strongly and intricately sculptured with raised, irregular ridges; probably parasitic in Lacciferidae. Fore wing with areas of very coarse discal setae (fig. 60 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) - ** '''Coccopilatus''' Annecke, 1963 *** 4 species worldwide; 1 Afrotropical species: ****'' Coccopilatus judithae'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) *69b Antennal club shorter than funicle; sculpture of head and thorax mostly cellulite-reticulate; parasitic in Diaspididae - [[File:Neococcidencyrtus-poutiersi-Mercet-1922-A-Lateral-view-B-Dorsal-view-C W640.jpg|thumb|''Neococcidencyrtus poutiersi'', Iran]] **'' ' '' Neococcidencyrtus Compere, 1928 *** 20 species worldwide; 5 Afrotropical species: ****'' Neococcidencyrtus brenhindis'' - no associates known (Madagascar) ****'' Neococcidencyrtus cliradainis'' - no associates known (Cameroon) ****'' Neococcidencyrtus poutiersi'' is a parasitoid of armored scales ''Furchadaspis zamiae'' (South Africa) ****'' Neococcidencyrtus pudaspidis'' is a parasitoid of armored scales ''Pudaspis newsteadi'' (South Africa) ****'' Neococcidencyrtus syndodis'' - no associates known (South Africa) ==70 Antennal scape expanded== *70a Antenna with all funicle segments transverse (fig. 61 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); club very large, longer than entire funicle; paratergitcs present; frontovertex pitted; parasitic in mealybugs - [[File:Aenasius 2019 08 25 9470.jpg|thumb|''Aenasius'' sp., South Africa]] **''''' Aenasius''''' Walker, 1846 *** 42 species worldwide; 7 Afrotropical species: ****'' Aenasius abengouroui'' is a parasitoid of mealybugs ''Planococcoides njalensis'', ''Planococcus citri'' (Ghana, Ivory Coast) ****'' Aenasius advena'' is a parasitoid of mealybugs ''Ferrisia'' spp., ''Phenacoccus'' spp., ''Planococcus'' spp., ''Pseudococcus'' spp., ''Spilococcus'' sp. (Congo, Democratic Republic of Congo, South Africa) ****'' Aenasius comperei'' is a parasitoid of mealybugs ''Allococcus quaesitus'', ''Delottococcus'' spp., ''Octococcus'' sp. ''Pseudococcus'' sp. (Kenya, South Africa) ****'' Aenasius flandersi'' is a parasitoid of mealybugs ''Ferrisia virgata'', ''Phenacoccus'' spp. (Democratic Republic of Congo, Senegal) ****'' Aenasius hyettus'' is a parasitoid of mealybugs ''Ferrisia virgata'', ''Phenacoccus'' sp. (Afrotropical) ****'' Aenasius martinii'' is a parasitoid of mealybugs ''Ferrisia virgata'', ''Planococcoides njalensis'', ''Planococcus celtis'' spp., ''Pseudococcus'' sp. (Eritrea, Ethiopia, Ghana, Ivory Coast, Kenya) ****'' Aenasius phenacocci'' is a parasitoid of mealybugs ''Phenacoccus'' spp., ''Planococcoides njalensis'' (Ghana) 70b Funicle segments not all wider than long; club shorter than entire funicle; paratergites absent; frontovertex at most with fine punctations; not parasitic in mealybugs ................ 71 ===71 (Funicle segments not all wider than long; club shorter than entire funicle; frontovertex not markedly pitted)=== *71a Head and thoracic dorsum largely metallic blue-green or cupreous, covered with silvery-white setae; parasitic in the oothecae of cockroaches - [[File:Comperia Smithsonian Institution 2019 CCDB-34079-D08 CC-BY boldsystems.jpg|thumb|''Comperia'' sp., Illinois, United States]] **''''' Comperia''''' Gomes, 1942 *** 7 species worldwide; 7 Afrotropical species: ****'' Comperia alfierii'' is a parasitoid of cockroaches ''Blattella'' sp., ''Phyllodromia'' sp. (Egypt, Kenya, South Africa) ****'' Comperia austrina'' - no associates known (South Africa) ****'' Comperia clavata'' - no associates known (South Africa) ****'' Comperia domestica'' - no associates known (South Africa) ****'' Comperia faceta'' - no associates known (South Africa) ****'' Comperia hirsuta'' - no associates known (South Africa) ****'' Comperia merceti'' is a parasitoid of cockroaches ''Blattella germanica'', ''Supella longipalpa'', ''Supella supellectilium'', ''Periplaneta americana'' (Uganda) *71b Head and body generally yellowish to brownish, without any metallic refringence or white setae; parasitic in Coccoidea ................ 72 ===72 (Head and body yellowish to brownish, not metallic, no white setae)=== *72a Antennal club longer than distal three funicle segments together, usually much wider than funicle segment VI; if rarely shorter, then distal four funicle segments white - [[File:Metaphycus inat 5003180 c.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. *72b Club about as long as the distal three funicle segments together, at most a little wider than distal funicle segment; funicle with at most distal three segments white - [[File:Microterys iN 253517641.jpg|thumb|''Microterys'' sp., South Africa]][[File:Microterys nietneri female.jpg|thumb|Female ''Microterys nietneri'', New Zealand]] **'''''Microterys''''' Thomson, 1876 *** 228 species worldwide; 12 Afrotropical species: ****'' Microterys africa'' is a parasitoid of lac scales ''Tachardia decorella'' (Uganda) ****'' Microterys anneckei'' is a parasitoid of coccid scales ''Filippia'' sp., ''Lichtensia'' sp., ''Parasaissetia litorea'', ''Pulvinaria mesembryanthemi'', ''Saissetia'' sp. (South Africa) ****'' Microterys bizanensis'' is a parasitoid of coccid scales ''Ceronema'' sp., ''Parasaissetia nigra'', ''Saissetia cuneiformis'' (Eritrea) ****'' Microterys capensis'' is a parasitoid of coccid scales ''Pulvinaria'' sp. (South Africa) ****'' Microterys ceroplastae'' is a parasitoid of coccid scales ''Ceroplastes destructor'' (Kenya) ****'' Microterys clauseni'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Metaceronema japonica'' (South Africa) ****'' Microterys haroldi'' is a parasitoid of coccid scales ''Ceroplastes'' sp., ''Messinea plana'' (South Africa) ****'' Microterys kenyaensis'' is a parasitoid of coccid scales ''Ceroplastes'' sp., ''Coccus hesperidum'', ''Lecanium oleae'', ''Saissetia'' spp. (Kenya, South Africa) ****'' Microterys nanus'' is a parasitoid of cerococcid scales ''Cerococcus'' sp., coccid scales ''Ceroplastes'' sp. (South Africa) ****'' Microterys nicholsoni'' is a parasitoid of coccid scales ''Coccus hesperidum'', ''Ceroplastes destructor'', ''Parasaissetia litorea'', ''Parasaissetia nigra'', ''Saissetia'' spp. (Kenya, South Africa, Zimbabwe) ****'' Microterys nietneri'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Chloropulvinaria'' spp., ''Coccus'' spp., ''Eucalymnatus tessellatus'', ''Lecanium'' spp., ''Maacoccus piperis'', ''Parasaissetia'' spp., ''Parasaissetia oleae'', ''Parthenolecanium'' spp., ''Parthenolecanium corni'', ''Protopulvinaria'' spp., ''Pulvinaria'' spp., ''Saissetia'' spp., ''Sphaerolecanium prunastri'', armored scales ''Hemichionaspis theae'', ''Pinnaspis theae'', mealybugs ''Rastrococcus iceryoides'' (South Africa) ****'' Microterys speciosus'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Coccus'' spp. (South Africa) == 73 Fore wing entirely hyaline, or faintly infuscated (any infuscation only visible against a pale background; from 44)== * 73a Gonostyli exserted at apex of metasoma, the exserted parts laterally compressed, usually more or less rounded apically in lateral view........ 74 * 73b Gonostyli, if protruding at apex of metasoma, not flattened laterally, usually having the appearance of two slender, sharp stylets................78 == 74 Gonostyli extend beyond apex of metasoma, laterally compressed and rounded apically == * 74a Scutellum entirely or partly shiny, with a polished appearance, without differentiated sculptural cells; mandibles exceptionally large (fig. 62 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979>Prinsloo, G. L., & Annecke, D. P. (1979). A key to the genera of Encyrtidae from the Ethiopian region, with descriptions of three new genera (Hymenoptera: Chalcidoidea). Journal of the Entomological Society of southern Africa, 42(2), 349-382. [https://journals.co.za/doi/pdf/10.10520/AJA00128789_2641 PDF]</ref>)........ 75 * 74b Scutellum dorsally sculptured, not smooth and polished; mandibles normal................76 === 75 Scutellum shiny; mandibles large=== * 75a Postmarginal vein (fig. 63 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) of fore wing shorter than marginal, not reaching to a level near apex of stigmal; basal triangle of wing disc largely devoid of setae; parasitic in Coleoptera - [[File:Cerchysiella inat 104244416.jpg|thumb|''Cerchysiella'' sp., United States]] **''''' Cerchysiella''''' Girault, 1914 ***''Zeteticontus'' Silvestri, 1915 is a synonym of ''Cerchysiella''. *** 36 species worldwide; 5 Afrotropical species: ****''Cerchysiella abilis'' (Silvestri) (5) ****''Cerchysiella neodypsisae'' (Risbec) (1) ****''Cerchysiella punctiscutellum'' (Subba Rao) (1) ****''Cerchysiella utilis'' (Noyes) (5) ****''Cerchysiella xanthopus'' (Masi) (1) * 75b Postmarginal vein of fore wing subequal to or longer than marginal, reaching to about the level of apex of stigmal; basal triangle of wing disc evenly and densely setose; parasitic in Diptera - [[File:Tachinaephagus iNat 148445032.jpg|thumb|''Tachinaephagus'' sp., South Africa]] **''''' Tachinaephagus''''' Ashmead, 1904 *** 11 species worldwide; 3 Afrotropical species: ****''Tachinaephagus congoensis'' Subba Rao (1) ****''Tachinaephagus stomoxicida'' Subba Rao (3) ****''Tachinaephagus zealandicus'' Ashmead (6) === 76 Scutellum sculptured, not smooth; mandibles not large === * 76a Antennal funicle and club white in colour; antennal scape expanded ventrally, the funicle segments all wider than long; parasitic in Coleoptera. Head with membranous interruptions of sclerotized integument as in fig. 64 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/> - **''''' Chrysomelechthrus''''' Trjapitzin, 1977 *** 1 species worldwide; 1 Afrotropical species: ****''Chrysomelechthrus descampsi'' (Risbec) (3) * 76b Antennal funicle and club dark in colour; scape slender, subcylindrical, the funicle with at least basal four or five segments longer than wide; parasitic in Diptera........ 77 === 77 Antennal funicle and club dark; scape slender, subcylindrical; funicle with more than three segments longer than wide === * 77a Head and body entirely metallic green to blue-green in colour; pedicel shorter than, to about as long as, basal funicle segment; clypeal margin not crenulate - [[File:Cerchysius inat 7295295.jpg|thumb|''Cerchysius'' sp., United States]] **''''' Cerchysius''''' Westwood, 1832 *** 15 species worldwide; 2 Afrotropical species: ****''Cerchysius kilimanjarensis'' Kerrich (1) ****''Cerchysius ugandensis'' Kerrich (4) * 77b Head and body without metallic lustre; pedicel plainly longer than basal funicle segment; clypeal margin with crenulae - **''''' Coccidoctonus''''' Crawford, 1912 ***''Xyphigaster'' Risbec, 1954 is a synonym of '' Coccidoctonus'' *** 8 species worldwide; 1 Afrotropical species: ****''Coccidoctonus pseudococci'' (Risbec) (9) == 78 If gonostyli protrude from apex of metasoma, not flattened laterally == * 78a Head, in frontal view, with eyes large, extending almost to mouth margin, the genae very short. Head and body metallic green in colour, the tegulae partly white; male antenna with four rami, borne on the first four funicle segments; parasitic in Lepidoptera - [[File:Parablastothrix vespertinus male antenna Fauna ibérica p254 BHL10940309.jpg|thumb|Male antenna of ''Parablastothrix vespertinus'', Spain]][[File:Parablastothrix vespertinus female antenna Fauna ibérica p254 BHL10940309.jpg|thumb|Feale antenna of ''Parablastothrix vespertinus'', Spain]] **''''' Parablastothrix''''' Mercet, 1917 *** 16 species worldwide; ? Afrotropical species: ****No Afrotropical records in UCD? * 78b Genae much longer, usually plainly more than one-third longest diameter of eye in frontal view........ 79 === 79 In frontal view genae more than one-third longest diameter of eye === * 79a Mandible with four teeth (figs 43, 65 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 80 * 79b Mandible otherwise................81 === 80 Mandible with four teeth === * 80a Scutellum longitudinally striate (fig. 66 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); dorsum of thorax gently convex, the thorax not dorsoventrally compressed - [[File:Lamennaisia ambigua male p284.jpg|thumb|''Lamennaisia ambigua'', male]] **''''' Lamennaisia''''' Girault, 1922 ***''Mercetencyrtus'' Trjapitzin, 1963 is a synonym of ''Lamennaisia'' *** 5 species worldwide; 1 Afrotropical species: ****''Lamennaisia nobilis'' (Nees) (South Africa) * 80b Scutellum largely cellulate-reticulate, not giving the surface a striated effect; body some what flattened dorsoventrally, the thoracic dorsum flat or almost so - [[File:Adelencyrtus - Japoshvili, G. and Soethof, R. (2022).jpg|thumb|''Adelencyrtus aulacaspidis'', Netherlands]] **''''' Adelencyrtus''''' Ashmead, 1900 *** 45 species worldwide; 10 Afrotropical species: ****''Adelencyrtus antennatus'' is a parasitoid of armored scale insects ''Aspidiotus'' sp. (South Africa) ****''Adelencyrtus aulacaspidis'' is a parasitoid of coccid scales ''Lecanopsis nevesi'', and armored scales ''Aulacaspis difficilis'', ''Aulacaspis rosae'', ''Chionaspis salicis'', ''Dynaspidiotus britannicus'', ''Lepidosaphes cupressi'', ''Pseudaulacaspis pentagona'', ''Quadraspidiotus macroporanus'', ''Unaspis yanonensis'' (Madagascar) ****''Adelencyrtus depressus'' - no associates known (Madagascar) ****''Adelencyrtus flagellatus'' - no associates known (South Africa) ****''Adelencyrtus inglisiae'' is a parasitoid of armored scale insects ''Africaspis''' spp. ''Aspidiotus'' spp., ''Balaspis faurei'', ''Clavaspis'' spp., ''Clavaspis pituranthi'', ''Diaspis echinocacti'', ''Moraspis euphorbiae'', ''Mytilococcus'' spp., ''Quadraspidiotus perniciosus'' (South Africa, Zimbabwe) ****''Adelencyrtus mangiphila'' is a parasitoid of armored scale insects ''Phenacaspis dilatata'' (Madagascar) ****''Adelencyrtus mayurai'' is a parasitoid of armored scale insects ''Aonidiella orientalis'', ''Melanaspis glomerata'' (Mauritania) ****''Adelencyrtus moderatus'' is a parasitoid of whiteflies ''Bemisia tabaci'', armored scales ''Aspidiella hartii'', ''Aspidiella sacchari'', ''Aspidiotus glomeratus'', ''Aulacaspis'' spp., ''Duplachionaspis'' spp., ''Lepidosaphes'' spp., ''Melanaspis glomerata'', and mealybugs ''Saccharicoccus sacchari'' (Ghana, Madagascar, Mauritius, Tanzania, Uganda) ****''Adelencyrtus odonaspidis'' is a parasitoid of armored scales ''Duplachionaspis sansevieriae'', ''Odonaspidis'' sp., ''Odonaspis'' spp., and mealybugs ''Antonina graminis'' (South Africa) ****''Adelencyrtus tibialis'' - no associates known (South Africa) === 81 Mandible does not have four teeth === * 81a Mesoscutum with parapsidal sulci (cf. fig. 46 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 82 * 81b Mesoscutum without parapsidal sulci........ 83 === 82 Mesoscutum with parapsidal sulci=== * 82a Antenna (fig. 67 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) long and slender, the scape subcylindrical, the funicle segments all longer than wide; paratergites present; body entirely black, or black with metasoma yellowish, the latter laterally margined with blackish-brown; head and thorax with a metallic refringence; parasitic in Pseudococcidae - [[File:Charitopus fulviventris male Fig. 218 Mercet (1921) Fauna ibérica.jpg|thumb|Male ''Charitopus fulviventris'']][[File:Charitopus fulviventris female Fig. 220 Mercet (1921) Fauna ibérica.jpg|thumb|Female ''Charitopus fulviventris'']] **''''' Charitopus''''' Foerster, 1856 *** 18 species worldwide; 1 Afrotropical species: ****''Charitopus fulviventris'' - no associates known (South Africa) * 82b Antennal scape moderately to broadly expanded ventrally, the funicle segments not all longer than wide (fig. 68 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); paratergites absent; head and body without a metallic refringence, usually yellowish to brownish in colour; parasitic in Coccoidea other than Pseudococcidae - [[File:Metaphycus inat 4772310 b.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. === 83 Mesoscutum without parapsidal sulci=== * 83a Antennal scape cylindrical or almost so, more than three times as long as its greatest width........ 84 * 83b Scape moderately to broadly expanded ventrally, less than three times as long as wide........ 117 == 84 Antennal scape cylindrical or almost so, much longer than wide== * 84a Antennal sockets placed high on face (fig. 69 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), their lower limits at or above lower eye level. Body black in colour, the frontovertex and face more or less pitted; antennal scrobes usually sulcate; parasitic in Coccidae - **''''' Bothriophryne''''' Compere, 1937 *** 8 species worldwide; 6 Afrotropical species: ****''Bothriophryne acaciae'' (Risbec) (3) ****''Bothriophryne ceroplastae'' Compere (5) ****''Bothriophryne dispar'' Compere (2) ****''Bothriophryne fuscicornis'' Compere (5) ****''Bothriophryne purpurascens'' Compere (3) ****''Bothriophryne velata'' Prinsloo and Annecke (2) * 84b Antennal scrobes placed lower on face, their lower limits well below lower eye level, sometimes almost at mouth margin........ 85 === 85 Antennal scrobes are low on face, lower limits well below bottom of eye=== * 85a Antennal club white........ 86 * 85b Antennal club not white........ 87 === 86 Antennal club white=== * 86a Head and thorax brilliant metallic green in colour; antennal club strongly obliquely truncate apically; mandible (fig. 70 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with two teeth and a broad truncation; parasitic in the oothecae of cockroaches - [[File:Comperia Smithsonian Institution 2019 CCDB-34079-D08 CC-BY boldsystems.jpg|thumb|''Comperia'' sp., Illinois, United States]] **''''' Comperia''''' Gomes, 1942 *** 7 species worldwide; 7 Afrotropical species: ****''Comperia alfierii'' is a parasitoid of a cockroach ''Blattella'' sp., and a dance fly ''Phyllodromia'' sp. (Egypt, Kenya, South Africa) ****''Comperia austrina'' - no associates known (South Africa) ****''Comperia clavata'' - no associates known (South Africa) ****''Comperia domestica'' - no associates known (South Africa) ****''Comperia faceta'' - no associates known (South Africa) ****''Comperia hirsuta'' - no associates known (South Africa) ****''Comperia merceti'' is a parasitoid of a cockroaches ''Blattella germanica'', ''Supella longipalpa'', ''Supella supellectilium'', ''Periplaneta americana'' (Uganda) * 86b Head and body without metallic refringence; club rounded apically; mandible (fig. 50 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with three slender teeth, the dorsal one somewhat retracted; parasitic in Pseudococcidae - **''''' Aphycus''''' Mayr, 1876 *** 33 species worldwide; 1 Afrotropical species: ****''Aphycus comperei'' is a parasitoid of mealybugs ''Pedrococcus'' sp. (South Africa) === 87 Antennal club not white=== * 87a Antenna nine-segmented, the club unsegmented. Polyembryonic parasitoids of Lepidoptera larvae................88 * 87b Antenna eleven-segmented, the club three-segmented................89 === 88 Antenna nine-segmented, the club unsegmented=== * 88a Antennal club obliquely truncate from near base (fig. 71 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); postmarginal vein of fore wing short, shorter than stigmal - [[File:Copidosoma varicorne female.jpg|thumb|''Copidosoma varicorne'', female]][[File:202101 Copidosoma floridanum attack.svg|thumb|''Copidosoma floridanum'']] **''''' Copidosoma''''' Ratzeburg, 1844 *** ''Litomastix'' is a synonym of ''Copidosoma'' *** See also step 109 below *** 212 species worldwide; 8 Afrotropical species: ****''Copidosoma delattrei'' (Ghesquiere) (2) ****''Copidosoma desantisi'' Annecke and Mynhardt (2) ****''Copidosoma floridanum'' is a parasitoid of Lepidoptera (Cape Verde Islands, Ivory Coast, Senegal) ****''Copidosoma koehleri'' Blanchard (17) ****''Copidosoma primulum'' (Mercet) (2) ****''Copidosoma truncatellum'' (Dalman) (2) ****''Copidosoma uruguayensis'' Tachnikawa (3) ****''Copidosoma varicorne'' (Nees) (7) * 88b Antennal club rounded or more or less squarely truncate at apex (fig. 72 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); postmarginal vein (fig. 73 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) unsually long, reaching to a level beyond apex of stigmal vein - [[File:Ageniaspis fuscicollis (Dalman, 1820) Fauna iberica 1921 p337 Fig143.jpg|thumb|Female ''Ageniaspis fuscicollis'']][[File:Ageniaspis fuscicollis (Dalman, 1820) Fauna iberica 1921 p337 Fig145.jpg|thumb|Postmarginal and stigmal veins, ''Ageniaspis fuscicollis'' female fore-wing.]] **''''' Ageniaspis''''' Dahlbom, 1857 *** 21 species worldwide; 2 Afrotropical species: ****''Ageniaspis citricola'' Logvinovskaya (1) ****''Ageniaspis primus'' Prinsloo (1) === 89 Antenna eleven-segmented, the club three-segmented=== * 89a Mandible (fig. 74 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with three distinct teeth and a straight dorsal truncation. Parasitic in Lacciferidae........ 90 * 89b Mandible otherwise........ 91 === 90 === * 90a Abdomen with two interrupted rows of gland-like structures (fig. 75 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), one each on tergum II and VII, head and thorax with rather strong metallic refringence - **''''' Adencyrtus''''' Prinsloo, 1977 *** 3 species worldwide; 3 Afrotropical species: ****''Adencyrtus afer'' Prinsloo (2) ****''Adencyrtus callainus'' Prinsloo (2) ****''Adencyrtus pictus'' Prinsloo (2) * 90b Abdomen without gland-like structures; head and body at most very slightly metallic in parts. Male antenna (fig. 57 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with two small, transverse funicle segments and a long, unsegmented banana-shaped club - **''''' Erencyrtus''''' Mahdihassan, 1923 *** 6 species worldwide; 4 Afrotropical species: ****'' Erencyrtus ater'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus contrarius'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus fuscus'' is a parasitoid of coccid scales ''Waxiella mimosae'', lac scales ''Tachardina'' sp. (South Africa) ****'' Erencyrtus notialis'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) === 91 === * 91a Antennal scrobes sulcate (figs 53, 54, 76), their lateral margins sharply angled, usually impressed on face as an inverted V........ 92 * 91b Scrobes otherwise........ 94 === 92 === * 92a Gonostyli very short and broad (fig. 77 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), subtriangular, densely covered with short, spine-like setae. Body black in colour; male antenna ten-segmented, the club two-segmented; parasitic in Lacciferidae - **'''''Laccacida''''' Prinsloo, 1977 *** 1 species worldwide; 1 Afrotropical species: ****'' Laccacida lacunata'' is a parasitoid of lac scales ''Tachardina'' sp. (South Africa) * 92b Gonostyli otherwise: elongate and slender, not densely covered with spine-like setae. Antenna of male nine-segmented, the club not segmented........ 93 === 93 === * 93a Mandible (fig. 78 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with three teeth; frontovertex with fine punctations; parasitic in Lacciferidae - **''''' Tachardiaephagus''''' Ashmead, 1904 *** 7 species worldwide; 4 Afrotropical species: ****'' Tachardiaephagus absonus'' Prinsloo (2) ****'' Tachardiaephagus communis'' Prinsloo (2) ****'' Tachardiaephagus gracilis'' Prinsloo (2) ****'' Tachardiaephagus similis'' Prinsloo (2) * 93b Mandible (fig. 55 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with two teeth and a dorsal truncation; frontovertex with large punctations or with pits; parasitic in Coccidae - **''''' Aloencyrtus''''' Prinsloo, 1978 *** 20 species worldwide; 19 Afrotropical species: ****'' Aloencyrtus alox'' - no associates known (South Africa) ****'' Aloencyrtus angustifrons'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Gascardia brevicauda'' spp. (South Africa) ****'' Aloencyrtus claripennis'' is a parasitoid of coccid scales ''Inglisia conchiformis'' (South Africa, Uganda) ****'' Aloencyrtus coelops'' is a parasitoid of coccid scales ''Ceroplastes'' spp., ''Gascardia destructor'', ''Waxiella mimosae'' (Eritrea, Nigeria, South Africa, Uganda) ****'' Aloencyrtus delottoi'' is a parasitoid of coccid scales ''Saissetia opulenta'' (Kenya, South Africa) ****'' Aloencyrtus diaphorocerus'' is a parasitoid of coccid scales ''Saissetia coffeae'' (Mauritius, Seychelles) ****'' Aloencyrtus distinguendus'' is a parasitoid of coccid scales ''Coccus subhemisphaericus'', ''Lecanium'' sp. (Cameroon, Ghana, Nigeria) ****'' Aloencyrtus facetus'' is a parasitoid of coccid scales ''Ceroplastes longicauda'' (South Africa) ****'' Aloencyrtus habrus'' is a parasitoid of coccid scales ''Saissetia coffeae'' (Cameroon) ****'' Aloencyrtus hardii'' is a parasitoid of coccid scales ''Parasaissetia nigra'', ''Saissetia'' spp. (South Africa) ****'' Aloencyrtus johani'' is a parasitoid of coccid scales ''Parasaissetia nigra'' (South Africa) ****'' Aloencyrtus lindae'' is a parasitoid of coccid scales ''Ceroplastes'' sp. (South Africa) ****'' Aloencyrtus nativus'' is a parasitoid of coccid scales ''Coccus longulus'', ''Parthenolecanium persicae'' (Benin, Madagascar, South Africa, Uganda, Zimbabwe) ****'' Aloencyrtus obscuratus'' is a parasitoid of coccid scales ''Lecanium somereni'', ''Saissetia'' spp. (Ghana, Kenya, South Africa) ****'' Aloencyrtus saissetiae'' is a parasitoid of coccid scales ''Ceroplastes'' sp. ''Coccus'' spp. ''Cryptinglisia lounsburyi'', ''Parasaissetia nigra'', ''Saissetia'' spp. (Ivory Coast, Kenya, Malawi, South Africa, Uganda, Zimbabwe) ****'' Aloencyrtus ugandensis'' is a parasitoid of coccid scales ''Ceroplastes'' spp. (Uganda) ****'' Aloencyrtus umbrinus'' is a parasitoid of coccid scales ''Ceroplastes'' spp. (Kenya, ) ****'' Aloencyrtus utilis'' is a parasitoid of coccid scales ''Saissetia oleae'' (South Africa) ****'' Aloencyrtus vivo'' - no associates known (Uganda) === 94 === * 94a Antennal funicle with contrasting white and black segments........ 95 * 94b Antennal funicle unicolorous or almost so........ 97 === 95 === * 95a Body yellowish to brownish, without a metallic tinge; antennal club rounded apically; primary parasitoids of Coccidae - [[File:Metaphycus inat 4772310 a.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. * 95b Body black, in parts with weak to strong metallic refringence; antennal club obliquely or transversely truncate apically; not parasitic in Coccidae........ 96 === 96 === * 96a Mandible with three distinct teeth; antennal club (fig. 79 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) transversely truncate apically; marginal vein punctiform (fig. 80 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); polyembryonic parasitoids in larvae of Lepidoptera - **'''''Paralitomastix''''' Mercet, 1921 is a synonym of '''''Copidosoma''''' Ratzeburg, 1844 (see step 88) * 96b Mandible with two teeth and a dorsal truncation; antennal club (fig. 81 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) obliquely truncate apically; marginal vein of fore wing (fig. 82 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) well developed; hyperparasitic in Coccidae - **'''''Tremblaya''''' Trjapitzin, 1985 *** ''Silvestria'' Trjapitzin, 1972 is a synonym of ''Tremblaya'' *** 5 species worldwide; 5 Afrotropical species: ****''Tremblaya ceroplastae'' (Risbec) (4) ****''Tremblaya coffeicola'' Noyes (1) ****''Tremblaya minor'' (Silvestri) (6) ****''Tremblaya oleae'' (Silvestri) (5) ****''Tremblaya palaeococci'' (Risbec) (2) === 97 === * 97a All funicle segments plainly wider than long................98 * 97b Funicle segments not all wider than long................102 === 98 All funicle segments plainly wider than long=== * 98a Postmarginal vein (fig. 83 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) of fore wing very long, much longer than marginal, reaching to a level beyond apex of stigmal; paratergites present; mandible with three slender teeth, the middle one longest; parasitic in Pseudococcidae - **'''''Blepyrus''''' Howard, 1898 *** 19 species worldwide; 3 Afrotropical species: ****''Blepyrus insularis'' (Cameron) (11) ****''Blepyrus saccharicola'' Gahan (2) ****''Blepyrus schwarzi'' (Howard) (1) * 98b Fore wing venation otherwise; paratergites absent; mandible otherwise; not parasitic in mealybugs........ 99 === 99 === * 99a Antennal scrobes absent or represented by two very short, shallow furrows, at most hardly longer than the longest diameter of a torulus; the latter placed at or close to mouth margin; parasitic in aculeate Hymenoptera - **'''''Coelopencyrtus''''' Timberlake, 1919 ***31 species worldwide; 7 Afrotropical species: ****''Coelopencyrtus bekiliensis'' (Risbec, 1952) (Madagascar) ****''Coelopencyrtus callainus'' Annecke, 1958 is a parasitoid of ''Xylocopa'' species (Mozambique, South Africa, Zimbabwe) ****''Coelopencyrtus cyprius'' Annecke, 1968 is a parasitoid of ''Xylocopa'' species (Zimbabwe) ****''Coelopencyrtus ivorensis'' (Risbec, 1953) (Ivory Coast) Only this species has reduced wings? ****''Coelopencyrtus nothylaei'' Annecke 1968 is a parasitoid of ''Hylaeus'' species (South Africa) ****''Coelopencyrtus taylori'' (Annecke and Doutt, 1961) is a parasitoid of ''Xylocopa'' species (South Africa) ****''Coelopencyrtus watmoughi'' Annecke, 1968 is a parasitoid of ''Xylocopa flavorufa'' (Zimbabwe). * 99b Antennal scrobes otherwise, usually well developed; antennal sockets placed higher on face, their upper limits usually about level with lower eye margins; not parasitic in aculeate Hymenoptera........ 100 === 100 === * 100a Maxillary palpi each with three segments, the labial with a single segment; small species, about 0,6 mm in length; parasitic in eggs of Coleoptera and Diptera - **''''' Oobius''''' Trjapitzin, 1963 *** 45 species worldwide; 4 Afrotropical species: ****''Oobius abditus'' Annecke (2) ****''Oobius funestus'' Annecke (2) ****''Oobius longoi'' (Siscaro) (4) ****''Oobius striatus'' Annecke (3) * 100b Palpi otherwise; larger species, often more than 1 mm in length; not egg parasitoids........ 101 === 101 === * 101a Head and body dominantly dark blackish-brown to black; antennal club (fig. 84 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) obliquely truncate apically; parasitic in Diptera - **'''''Exoristobia''''' Ashmead, 1904 *** 9 species worldwide; 3 Afrotropical species: ****''Exoristobia dipterae'' (Risbec) (8) ****''Exoristobia macrocerus'' (Masi) (1) ****''Exoristobia ugandensis'' Subba Rao (2) * 101b Head and body dominantly yellowish to brownish-yellow; antennal club rounded apically; parasitic in Coccoidea - [[File:Metaphycus inat 4772310 b.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. *** ''Metaphycus'' keys out at 82, 95, 101, 110, 119 === 102 Funicle segments not all wider than long=== * 102a Small species, at most about 1 mm in length, but usually less than 1 mm; exclusively parasitic in insect eggs, often in those of Lepidoptera, Hemiptera and Coleoptera........ 103 * 102b Larger species, usually more than 1 mm in length; if less than 1 mm in length, then not parasitic in insect eggs, but in the larvae and pupae of insects................104 === 103 === * 103a Antennal club longer than entire funicle; funicle segments I-V transverse; maxillary palpi each with three segments, the labial palpi not segmented - **''''' Oobius''''' Trjapitzin, 1963 *** 45 species worldwide; 4 Afrotropical species (See step 100) * 103b Antennal club shorter than entire funicle; maxillary palpi each with four segments, the labial with three - [[File:Gypsy Moth (Lymantria dispar) Egg Mass Being Parasitized by Ooencyrtus kuvanae - Mississauga, Ontario.jpg|thumb|''Ooencyrtus kuvanae'' on a moth egg mass, Canada]] [[File:Ooencyrtus gravis, female, Spain.jpg|thumb|''Ooencyrtus gravis'', female, Spain.]] **'''''Ooencyrtus''''' Ashmead, 1900 *** 343 species worldwide; 38 Afrotropical species: ****''Ooencyrtus afer'' Prinsloo (1) ****''Ooencyrtus albicrus'' Prinsloo (3) ****''Ooencyrtus angolensis'' Prinsloo (1) ****''Ooencyrtus austrinus'' Prinsloo (1) ****''Ooencyrtus azul'' Prinsloo (1) ****''Ooencyrtus bambeyi'' (Risbec) (2) ****''Ooencyrtus bedfordi'' Prinsloo (1) ****''Ooencyrtus camerounensis'' (Risbec) (4) ****''Ooencyrtus cinctus'' Prinsloo (2) ****''Ooencyrtus cirinae'' Prinsloo (1) ****''Ooencyrtus congensis'' Prinsloo (1) ****''Ooencyrtus cretatus'' Prinsloo (1) ****''Ooencyrtus demodoci'' (Risbec) (4) ****''Ooencyrtus dipterae'' (Risbec) (4) ****''Ooencyrtus distatus'' Prinsloo (1) ****''Ooencyrtus epilachnae'' Annecke (3) ****''Ooencyrtus exallus'' Prinsloo (1) ****''Ooencyrtus guamensis'' Fullaway (6) ****''Ooencyrtus homoeoceri'' (Risbec) (3) ****''Ooencyrtus insignis'' Prinsloo (1) ****''Ooencyrtus jeani'' Noyes and Prinsloo (3) ****''Ooencyrtus kuvanae'' is an egg parasitoid of Lepidoptera and Hemiptera (Nigeria) ****''Ooencyrtus lamborni'' Waterston (11) ****''Ooencyrtus mimus'' Prinsloo (1) ****''Ooencyrtus nanus'' Prinsloo (1) ****''Ooencyrtus pallidipes'' (Ashmead) (2) ****''Ooencyrtus piezodori'' (Risbec) (3) ****''Ooencyrtus polyphagus'' (Risbec) (3) ****''Ooencyrtus puparum'' Prinsloo (1) ****''Ooencyrtus rigemae'' (Risbec) (3) ****''Ooencyrtus risbeci'' Prinsloo (1) ****''Ooencyrtus rufogaster'' (Risbec) (2) ****''Ooencyrtus senegalensis'' (Risbec) (4) ****''Ooencyrtus sesbaniae'' Risbec (1) ****''Ooencyrtus sinis'' Prinsloo (1) ****''Ooencyrtus unicus'' Prinsloo (1) ****''Ooencyrtus utetheisae'' (Risbec) (11) ****''Ooencyrtus ventralis'' (Masi) (1) === 104 === * 104a Antennal scrobes absent or represented by two very short shallow furrows, at most hardly longer than the longest diameter of a torulus; head usually approximately round in outline in frontal view with mouth margin broad, antennal sockets placed close to mouth margin; parasitic in aculeate Hymenoptera - **'''''Coelopencyrtus''''' Walker, 1837 ***31 species worldwide; 7 Afrotropical species: ****''Coelopencyrtus bekiliensis'' (Risbec, 1952) (Madagascar) ****''Coelopencyrtus callainus'' Annecke, 1958 is a parasitoid of ''Xylocopa'' species (Mozambique, South Africa, Zimbabwe) ****''Coelopencyrtus cyprius'' Annecke, 1968 is a parasitoid of ''Xylocopa'' species (Zimbabwe) ****''Coelopencyrtus ivorensis'' (Risbec, 1953) (Ivory Coast) Only this species has reduced wings? ****''Coelopencyrtus nothylaei'' Annecke 1968 is a parasitoid of ''Hylaeus'' species (South Africa) ****''Coelopencyrtus taylori'' (Annecke and Doutt, 1961) is a parasitoid of ''Xylocopa'' species (South Africa) ****''Coelopencyrtus watmoughi'' Annecke, 1968 is a parasitoid of ''Xylocopa flavorufa'' (Zimbabwe). * 104b Scrobes otherwise, usually well developed; other characters different; not parasitic in aculeate Hymenoptera........ 105 === 105 === * 105a Mandible with three acute or subacute teeth (figs 85, 86)........ 106 * 105b Mandible not with three acute or subacute teeth; rarely with three teeth, but then dorsal tooth not acute or subacute, but broad, the apex squarely to roundly truncate (fig. 87 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)................111 === 106 Mandible with three acute or subacute teeth=== * 106a Head and body entirely and brilliantly metallic in colour; parasitic in Aclerdidae - [[File:Mayridia pulchra, female, Spain.jpg|thumb|''Mayridia pulchra'', female, Spain]] **'''''Mayridia''''' Mercet, 1921 ***34 species worldwide; 2 Afrotropical species: ****''Mayridia arida'' Prinsloo and Annecke (3) ****''Mayridia maryae'' Prinsloo (1) * 106b Head and body at most with a faint to moderately strong metallic refringence on frontovertex, face and thorax; not parasitic in Aclerdidae........ 107 === 107 === * 107a Antennal club as long as the distal three funicle segments together; marginal vein or fore wing longer than stigmal; parasitic in dryinid wasps - **'''''Helegonatopus''''' Perkins, 1906 ***13 species worldwide; 1 Afrotropical species: ****''Helegonatopus saotomensis'' Prinsloo (2) * 107b Antennal club longer than funicle segments III-VI; marginal vein at most as long as stigmal; not parasitic in Hymenoptera........ 108 === 108 === * 108a Antennal club obliquely truncate apically. Thoracic dorsum usually with metallic green and purple refringence; polyembryonic parasitoids of Lepidoptera larvae - **'''''Litomastix''''' Thomson, 1876 *** ''Litomastix'' is a synonym of ''Copidosoma'', making this step redundant, although presumably useful for identification of species groups?. * 108b Antennal club rounded apically, or club segments transverse........ 109 === 109 === * 109a Antenna long and slender, the funicle segments all longer than wide; polyembryonic parasitoids of Lepidoptera larvae - [[File:Copidosoma koehleri 03.jpg|thumb|''Copidosoma koehleri'']] **''''' Copidosoma''''' Ratzeburg, 1844 *** See also step 88 (above) *** 212 species worldwide; 8 Afrotropical species: ****''Copidosoma delattrei'' (Ghesquiere) (2) ****''Copidosoma desantisi'' Annecke and Mynhardt (2) ****''Copidosoma floridanum'' (Ashmead) (6) ****''Copidosoma koehleri'' Blanchard (17) ****''Copidosoma primulum'' (Mercet) (2) ****''Copidosoma truncatellum'' (Dalman) (2) ****''Copidosoma uruguayensis'' Tachnikawa (3) ****''Copidosoma varicorne'' (Nees) (7) * 109b Funicle segments not all longer than wide, the antenna not particularly slender; not parasitic in Lepidoptera................110 === 110 === * 110a Marginal and postmarginal veins very short, the latter much shorter than stigmal vein, sometimes punctiform; frontovertex without punctations; usually parasitic in Coccidae - [[File:Metaphycus inat 4772310 a.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. *** ''Metaphycus'' keys out at 82, 95, 101, 110, 119 * 110b Marginal and postmarginal veins well developed, the latter reaching almost to the level of apex of stigmal vein; frontovertex with scattered puncrations; exclusively parasitic in Lacciferidae - **''''' Tachardiaephagus''''' Ashmead, 1904 ***'' Tachardiaephagus'' keys out at 93, 110 *** 7 species worldwide; 4 Afrotropical species: ****'' Tachardiaephagus absonus'' Prinsloo (2) ****'' Tachardiaephagus communis'' Prinsloo (2) ****'' Tachardiaephagus gracilis'' Prinsloo (2) ****'' Tachardiaephagus similis'' Prinsloo (2) === 111 Mandible not with three acute or subacute teeth=== * 111a Tergum II and VII of abdomen each with an interrupted row of gland-like structures (fig. 88 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); Antennal club long, usually about as long as enure funicle; legs usually banded; parasitic in Diaspididae. - **'''''Zaomma''''' Ashmead, 1900 *** 17 species worldwide; 8 Afrotropical species: ****''Zaomma acaciae'' (Risbec) (1) ****''Zaomma carinae'' Prinsloo (2) ****''Zaomma cestus'' Prinsloo (2) ****''Zaomma ficusae'' (Risbec) (1) ****''Zaomma lambinus'' (Walker) (5) ****''Zaomma sitis'' Prinsloo (2) ****''Zaomma vix'' Prinsloo (2) ****''Zaomma xhosa'' Prinsloo (2) * 111b Abdomen without gland-like structures........ 112 === 112 Abdomen without gland-like structures=== * 112a Maxillary palpi each with three segments, the labial each with two; parasitic in Diaspididae. Small species, usually not much more than 1 mm in length; antenna generally slender, the club long - **'''''Coccidencyrtus''''' Ashmead, 1900 *** 36 species worldwide; 3 Afrotropical species: ****''Coccidencyrtus ochraceipes'' Gahan (1) ****''Coccidencyrtus plectroniae'' Risbec (1) ****''Coccidencyrtus punctatus'' Compere and Annecke (1) * 112b Maxillary palpi each with four segments, the labial with three; not parasitic in Diaspididae........ 113 === 113 === * 113a Marginal vein of fore wing relatively long*, broad, dark in colour, about as long as, or longer than, stigmal vein (figs 89, 90); mandible with three well separated teeth, the upper one squarely or roundly truncate (fig. 87 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 114 * 113b Marginal vein punctiform or very short, shorter than stigmal (figs 91, 92); if rarely subequal to stigmal, then mandible with a well separated ventral tooth and a broad dorsal truncation (fig. 93 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>)........ 115 === 114 === * 114a Body longer than 1 mm; thorax slender, the scutellum longer than wide; legs usually not banded; primary parasitoids of Syrphidae - [[File:Syrphophagus aphidivorus, female, Spain.jpg|thumb|''Syrphophagus aphidivorus'', female, Spain]][[File:Syrphophagus inat 125775071.jpg|thumb|''Syrphophagus'' sp., Georgia, US.]] **''''' Syrphophagus''''' Ashmead, 1900 *** 85 species worldwide; 6 Afrotropical species: ****''Syrphophagus africanus'' (Gahan) (6) ****''Syrphophagus aphidivorus'' (Mayr) (2) ****''Syrphophagus cassatus'' (Annecke) (6) ****''Syrphophagus coccidicola'' (Gahan) (2) ****''Syrphophagus nigrocyaneus'' Ashmead (2) ****''Syrphophagus similis'' (Prinsloo) (3) * 114b Smaller species, usually about 1 mm in length; scutellum relatively broad, about as long as wide or a little wider than long; legs usually banded; hyperparasitoids of aphids, rarely of psyllids - **''''' Syrphophagus''''' Ashmead, 1900 ***''Aphidencyrtus'' is a synonym of ''Syrphophagus''; this step previously separated ''Aphidencyrtus'' *** 85 species worldwide; 6 Afrotropical species: ****''Syrphophagus africanus'' (Gahan) (6) ****''Syrphophagus aphidivorus'' (Mayr) (2) ****''Syrphophagus cassatus'' (Annecke) (6) ****''Syrphophagus coccidicola'' (Gahan) (2) ****''Syrphophagus nigrocyaneus'' Ashmead (2) ****''Syrphophagus similis'' (Prinsloo) (3) === 115 === * 115a Head and body pale, dominantly yellow in colour, without metallic refringence; parasitic in Coccidae. Male remarkable in colour: orange and brilliant metallic green in parts - **''''' Argutencyrtus''''' Prinsloo and Annecke, 1974<ref name=Prinsloo1974>Prinsloo, G.L. & Annecke, D.P. (1973). A new genus and species of Encyrtidae (Hymenoptera: Chalcidoidea) from South Africa. Journal of the Entomological Society of Southern Africa, 37(2), 345-349. https://journals.co.za/doi/abs/10.10520/AJA00128789_2638</ref> *** 1 species worldwide; 1 Afrotropical species: ****''Argutencyrtus luteolus'' Prinsloo and Annecke, 1974 * 115b Head and body entirely metallic in colour, or black with some parts with faint to moderately strong metallic refringence, or rarely at least head and thorax black; not parasitic in Coccidae........ 116 === 116 === * 116a Usually entirely metallic green or blue-green in colour, rarely with only some parts metallic in colour; parasitic in Psyllidae - [[File:Psyllaephagus inat 165372177 davidfdz b82, some rights reserved (CC-BY).jpg|thumb|''Psyllaephagus'' sp., Córdoba, Spain.]][[File:Psyllaephagus guangxiensis (10.3897-BDJ.9.e63253) Figure 1.jpg|thumb|Female ''Psyllaephagus guangxiensis'', China]] [[File:Psyllaephagus euphyllurae, female, Spain.jpg|thumb|''Psyllaephagus euphyllurae'', female, Spain]] **'''''[[w:Psyllaephagus|Psyllaephagus]]''''' Ashmead, 1900 *** 246 species worldwide; 30 Afrotropical species: ****''Psyllaephagus africanus'' Prinsloo (3) ****''Psyllaephagus albicrus'' Prinsloo (2) ****''Psyllaephagus arytainae'' Prinsloo (2) ****''Psyllaephagus bicolor'' Prinsloo (2) ****''Psyllaephagus blastopsyllae'' Tamesse, Soufo, Tchanatame, Dzokou, Gumovsky and De Coninck (1) ****''Psyllaephagus bliteus'' Riek, 1962 (Australia, introduced to South Africa and also Neotropical and western Palaearctic regions) ****''Psyllaephagus callainus'' Prinsloo (2) ****''Psyllaephagus capeneri'' Prinsloo (2) ****''Psyllaephagus cellulatus'' Waterston (1) ****''Psyllaephagus chianganus'' Prinsloo (3) ****''Psyllaephagus cincticrus'' Prinsloo (2) ****''Psyllaephagus dealbatae'' (Risbec) (1) ****''Psyllaephagus dispar'' Prinsloo (2) ****''Psyllaephagus furvus'' Prinsloo (1) ****''Psyllaephagus hibiscusae'' (Risbec) (1) ****''Psyllaephagus io'' Prinsloo (1) ****''Psyllaephagus lucaris'' Prinsloo (2) ****''Psyllaephagus minor'' Prinsloo (2) ****''Psyllaephagus oleae'' Prinsloo (2) ****''Psyllaephagus ornatus'' Prinsloo (2) ****''Psyllaephagus pauliani'' (Risbec) (1) ****''Psyllaephagus perendinus'' Robinson (1) ****''Psyllaephagus phytolymae'' (Ferriere) (5) ****''Psyllaephagus pulvinatus'' (Waterston) (12) ****''Psyllaephagus rhusae'' Prinsloo (2) ****''Psyllaephagus secus'' Prinsloo (3) ****''Psyllaephagus tessmannii'' Tamesse and Tiyo (1) ****''Psyllaephagus vastus'' Prinsloo (2) ****''Psyllaephagus viridis'' Prinsloo (2) ****''Psyllaephagus yaseeni'' Noyes (Tanzania) * 116b Never entirely metallic in colour, at most the head and thoracic dorsum with weak to moderately strong metallic refringence; parasitic in Syrphidae and Coccinellidae - **'''''Syrphophagus''''' Ashmead, 1900 *** ''Syrphophagus'' keys out at 114a, 114b, 116b, 117a *** 85 species worldwide; 6 Afrotropical species: ****''Syrphophagus africanus'' (Gahan) (6) ****''Syrphophagus aphidivorus'' (Mayr) (2) ****''Syrphophagus cassatus'' (Annecke) (6) ****''Syrphophagus coccidicola'' (Gahan) (2) ****''Syrphophagus nigrocyaneus'' Ashmead (2) ****''Syrphophagus similis'' (Prinsloo) (3) == 117 Scape moderately to broadly expanded ventrally, less than three times as long as wide == * 117a Eyes exceptionally setose (fig. 123 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), the setae long, strongly developed; frontovertex sparsely pitted; antenna (fig. 126 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with scape blackish, the remainder of antenna uniformly paler in colour - [[File:Syrphophagus inat 125775071.jpg|thumb|''Syrphophagus'' sp., Georgia, US.]] **'''''Syrphophagus''''' Ashmead, 1900 *** ''Syrphophagus'' keys out at 114b, 116b, 117a *** 85 species worldwide; 6 Afrotropical species: ****''Syrphophagus africanus'' (Gahan) (6) ****''Syrphophagus aphidivorus'' (Mayr) (2) ****''Syrphophagus cassatus'' (Annecke) (6) ****''Syrphophagus coccidicola'' (Gahan) (2) ****''Syrphophagus nigrocyaneus'' Ashmead (2) ****''Syrphophagus similis'' (Prinsloo) (3) * 117b Eyes sparsely setose, the setae fine; frontovertex at most finely punctate; colour of antenna otherwise........ 118 === 118 Eyes sparsely setose=== * 118a Head tending to opisthognathous, the frontovertex almost horizontal, meeting the inflexed face at an acute angle, so that head is subtriangular in lateral view; parasitic in ticks (Ixodidae). Male sometimes brachypterous, in which case the head has a forked process jutting forward at junction of frontovertex and face - [[File:Ixodiphagus hookeri.jpg|thumb|''Ixodiphagus hookeri'', France]] **'''''Ixodiphagus''''' Howard, 1907 ***''Hunterellus'' Howard, 1908 is a synonym of ''Ixodiphagus'' *** 15 species worldwide; 2 Afrotropical species: ****''Ixodiphagus hookeri'' (Howard) (14) ****''Ixodiphagus theilerae'' (Fiedler) (5) * 118b Head hypognathous, the frontovertex more or less convex, rounded on to face; not parasitic in ticks........ 119 === 119 === * 119a Head and body largely yellowish to brownish, without metallic refringence; antennal scrobes more or less well developed; toruli with lower limits well above clypeal margin; parasitic in Coccoidea - [[File:Metaphycus inat 4772310 b.jpg|thumb|''Metaphycus'' sp., California, United States]] **''''' Metaphycus''''' Mercet, 1917 ***''Metaphycus'' spp. are parasitoids of scale insects, mostly Coccidae *** 476 species worldwide; 86 Afrotropical species. *** ''Metaphycus'' keys out at 82, 95, 101, 110, 119 * 119b Head and body dominantly black, the head and thoracic dorsum with faint to strong metallic refringence; scrobes absent or developed as two very short shallow furrows, hardly longer than the longest diameter of a torulus; toruli placed at or close to mouth margin; polyembryonic parasitoids of aculeate Hymenoptera - **'''''Coelopencyrtus''''' Walker, 1837 ***31 species worldwide; 7 Afrotropical species: ****''Coelopencyrtus bekiliensis'' (Risbec, 1952) (Madagascar) ****''Coelopencyrtus callainus'' Annecke, 1958 is a parasitoid of ''Xylocopa'' species (Mozambique, South Africa, Zimbabwe) ****''Coelopencyrtus cyprius'' Annecke, 1968 is a parasitoid of ''Xylocopa'' species (Zimbabwe) ****''Coelopencyrtus ivorensis'' (Risbec, 1953) (Ivory Coast) Only this species has reduced wings? ****''Coelopencyrtus nothylaei'' Annecke 1968 is a parasitoid of ''Hylaeus'' species (South Africa) ****''Coelopencyrtus taylori'' (Annecke and Doutt, 1961) is a parasitoid of ''Xylocopa'' species (South Africa) ****''Coelopencyrtus watmoughi'' Annecke, 1968 is a parasitoid of ''Xylocopa flavorufa'' (Zimbabwe). == 120 Mandible with only two teeth; paratergites usually present; usually without coarse setae at edge of speculum; cercal plates often advanced. Mealybug parasitoids== [Mandible with only two acute or subacute teeth (figs 37, 38 of the Prinsloo-Annecke key[1]). Paratergites (fig. 39 of the Prinsloo-Annecke key[1]) usually present, plainly visible in cleared, slide-mounted specimens; speculum of fore wing usually lacking a row of coarse, spine-like setae along outer edge of speculum; cercal plates often advanced to a level near base of metasoma; exclusively parasitic in Pseudococcidae (from 43)] * 120a Antennal funicle seven-segmented - **''''' Alamella''''' Agarwal, 1966 *** 5 species worldwide; 1 Afrotropical species: ****''Alamella flava'' - a parasitoid of eriococcids and mealybugs (Angola, Madagascar, Namibia, South Africa) ****Species description: [https://www.ias.ac.in/public/Volumes/secb/063/02/0067-0079.pdf Agarwal (1966)]<ref name=Agarwal1966>Agarwal, M. M. (1966). Three undescribed genera and species of Encyrtidae (Hymenoptera-Chalcidoidea) parasitic on coccids. In Proceedings/Indian Academy of Sciences (Vol. 63, No. 2, pp. 67-79). New Delhi: Springer India.</ref> * 120b Club two-segmented; head and body without metallic lustre; maxillary palpi each with three segments, the labial with two. Funicle with six or fewer segments........ 121 === 121 === * 121a Scutellum with a posterior flange or lamella (cf. fig. 15 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); in profile this flange shows as a thin flat caudal projection of the scutellum. Body often black, the head dark metallic green; antenna long, slender, the scape cylindrical; marginal and postmarginal veins long - [[File:Ericydnus inat 183126807 Mario Bassini.jpg|thumb|''Ericydnus'' sp., Italy]] **''''' Ericydnus''''' Haliday, 1832 *** 33 species worldwide; Afrotropical species? *** ''Ericydnus'' sp. - 2 specimens at ARC-PPRI (https://www.gbif.org/occurrence/search?dataset_key=b2ee8537-2a6c-4b4b-965a-538b47788606&taxon_key=1378896) * 121b Scutellum without a flange........ 122 === 122 === * 122a Head prognathous (fig. 94 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), elongate and flattened in dorsal view, almost as long as thorax (fig. 95 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), the eyes elongate, in dorsal view occupying almost whole of head laterally; antenna (fig. 96 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) extremely large, foliaceously flattened, the club three-segmented - **''''' Monstranusia''''' Trjapitzin, 1964 *** 3 species worldwide; 2 Afrotropical species: ****''Monstranusia antennata'' (Narayanan) (1) ****''Monstranusia mirabilissima'' Trjapitzin (4) * 122b Head otherwise; if antenna foliaceously flattened, then club not segmented................123 === 123 === * 123a Antenna nine-segmented........ 124 * 123b Antenna ten or eleven-segmented........ 126 === 124 === * 124a Fore wing distinctly infuscated with hyaline patches (fig. 97 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Head .and body largely metallic in colour; antenna sometimes foliaceously flattened; ovipositor often strongly protruded at apex of metasoma; male antenna with funicle six-segmented, segments II – V each with a ramus - **''''' Tetracnemus''''' Westwood, 1837 *** 37 species worldwide; 2 Afrotropical species: ****''Tetracnemus'' bifasciatellus (Mercet) (1) ****''Tetracnemus gumilevi'' Pilipjuk and Trjapitzin (1) * 124b Fore wing entirely hyaline........ 125 === 125 === * 125a Head and body entirely metallic green to blue-green in colour; antenna (fig. 111 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) long, the fumcle and club broad, somewhat laterally compressed - **''''' Callaincyrtus''''' Prinsloo & Annecke, 1979 *** 1 species worldwide; 1 Afrotropical species: ****''Callaincyrtus decorus'' - no known associates (South Africa, Zimbabwe) * 125b Head and body at most with faint metallic refringence on frontovertex, face and thoracic dorsum; antenna not particularly slender, the segments not flattened - **''''' Allocerellus''''' Silvestri, 1915<ref name=>Silvestri, F. 1915, Contributo all conoscenza degli insetti dell'olivo dell'Eritrea e dell'Africa meridionalei. Bollettino del Laboratorio di Zoologia Generale e Agraria della R. Scuola Superiore d'Agricoltura, Portici 9:305 [https://www.biodiversitylibrary.org/page/14029132 BHL][https://www.nhm.ac.uk/resources/research-curation/projects/chalcidoids/pdf_X/Silves915.pdf PDF]</ref> *** This genus was reviewed in 1995: Prinsloo, G. L. (1995). The encyrtid genus Allocerellus Silvestri (Hymenoptera: Chalcidoidea), parasitoids of mealybugs (Homoptera: Pseudococcidae). Insect Systematics & Evolution, 26(2), 167-179. *** 12 species worldwide; 12 Afrotropical species: ****'' Allocerellus ater'' Prinsloo (1) ****'' Allocerellus bizonatus'' Annecke and Mynhardt (3) ****'' Allocerellus curtus'' Prinsloo (1) ****'' Allocerellus hortensis'' Annecke and Mynhardt (2) ****'' Allocerellus inquirendus'' Silvestri (2) ****'' Allocerellus mimus'' Prinsloo (1) ****'' Allocerellus notatus'' Prinsloo (1) ****'' Allocerellus orestes'' Annecke and Mynhardt (4) ****'' Allocerellus paulus'' Annecke and Mynhardt (3) ****'' Allocerellus venustus'' Annecke and Mynhardt (4) ****'' Allocerellus vittatus'' Annecke and Mynhardt (4) ****'' Allocerellus zonatus'' Annecke and Mynhardt (4) === 126 === * 126a Antenna ten-segmented, the club with two segments........ 127 * 126b Antenna eleven-segmented, the club three-segmented........ 128 === 127 === * 127a Head and body flatlened dorsoventrally; maxillary palpi each with two segments, the labial not segmented. Small species, weakly sclerotized, usually yellowish, without metallic refringence; marginal and postmarginal veins short or punctiform - [[File:Rhopus nigroclavatus Moravvej 2018 Encyrtidae of Khuzestan in southwestern Iran a.jpg|thumb|''Rhopus nigroclavatus'', Iran]] **'''''Rhopus''''' Foerster, 1856 *** This genus was reviewed in 1989: Prinsloo, G. L. (1989). The southern African species of ''Astymachus'' Howard and ''Rhopus'' Foerster (Hymenoptera: Encyrtidae). Journal of the Entomological Society of southern Africa, 52(1), 129-147. *** 70 species worldwide; 7 Afrotropical species: ****'' Rhopus adustus'' Prinsloo (2) ****'' Rhopus discretus'' Prinsloo (1) ****'' Rhopus geminus'' Prinsloo (2) ****'' Rhopus luridus'' Prinsloo (1) ****'' Rhopus notius'' Prinsloo (2) ****'' Rhopus pilatus'' Prinsloo (1) ****'' Rhopus urbanus'' Prinsloo (2) * 127b Head and body not flattened dorsoventrally; maxillary palpi each with three segments, the labial each with two - **''''' Allocerellus''''' Silvestri, 1915 *** 12 species worldwide; 12 Afrotropical species: ***See step 125 === 128 === * 128a Frontovertex (fig. 98 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) densely pitted, the pits with a metallic green lustre; antennal scape subcylindical. Dominantly black species, the fore wing entirely and strongly infuscated; cephalic margin of fore wing forming an incision at apex of submarginal vein; male antenna with six transverse funicle segments and a long unsegmented banana-shaped club - [[File:Aenasius 2019 08 25 9692.jpg|thumb|''Aenasius'' sp., South Africa]] **''''' Aenasius''''' Walker, 1846 *** ''Chalcaspis'' Howard, 1895 is a synonym of '' Aenasius'' *** 42 species worldwide; 7 Afrotropical species: ****'' Aenasius abengouroui'' (Risbec) (4) ****'' Aenasius advena'' Compere (9) ****'' Aenasius comperei'' (Kerrich) (4) ****'' Aenasius flandersi'' Kerrich (1) ****'' Aenasius hyettus'' (Walker) (1) ****'' Aenasius martinii'' (Compere) (4) ****'' Aenasius phenacocci'' (Ashmead) (1) * 128b Frontovertex at most punctate, the punctations not refringent........ 129 === 129 === * 129a Head and body flattened dorsoventrally; maxillary palpi each with two segments, the labial not segmented. Small species, weakly sclerotized, usually yellowish, without metallic refringence; marginal and postmarginal veins very short or punctiform - [[File:Rhopus nigroclavatus Moravvej 2018 Encyrtidae of Khuzestan in southwestern Iran a.jpg|thumb|''Rhopus nigroclavatus'', Iran]] **''''' Rhopus''''' Foerster, 1856 *** This genus was reviewed in 1989: Prinsloo, G. L. (1989). The southern African species of ''Astymachus'' Howard and ''Rhopus'' Foerster (Hymenoptera: Encyrtidae). Journal of the Entomological Society of southern Africa, 52(1), 129-147. *** 70 species worldwide; 7 Afrotropical species: **** See step 127 * 129b Head and body not flattened dorsoventrally; palpi otherwise........ 130 === 130 === * 130a Maxillary palpi each with three segments, the labial each with two................131 * 130b Maxillary palpi each with four segments, the labial three-segmented........ 132 === 131 === * 131a Antenna (fig. 99 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) long, filiform, the funicle segments all plainly longer than wide; postmarginal vein (fig. 100 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) of fore wing long, extending to a level well beyond apex of stigmal; small species. Fore wing hyaline or partly infuscated - [[File:Leptomastidea abnormis inat 8538894 Jesse Rorabaugh.jpg|thumb|''Leptomastidea abnormis'', California, USA]] **''''' Leptomastidea''''' Mercet, 1916 *** This genus was reviewed in 2001: Prinsloo, G.L. 2001, The aftrotropical species of Leptomastidea Mercet (Hymenoptera: Encyrtidae) parasitoids of mealybugs. Journal of Hymenoptera Research 10(2):158-159. Includes photos of fore wings. *** 23 species worldwide; 8 Afrotropical species: ****'' Leptomastidea abnormis'' (Girault) (12) ****'' Leptomastidea ascia'' Prinsloo (1) ****'' Leptomastidea jeanneli'' Mercet (5) ****'' Leptomastidea lamto'' Prinsloo (1) ****'' Leptomastidea pondo'' Prinsloo (1) ****'' Leptomastidea tecta'' Prinsloo (1) ****'' Leptomastidea turba'' Prinsloo (1) ****'' Leptomastidea usta'' Prinsloo (1) * 131b Antenna (fig. 101 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) not particularly slender, the funicle segments not all longer than wide; postmarginal vein short, shorter than stigmal; larger species - [[File:Anagyrus lopezi.jpg|thumb|''Anagyrus lopezi'']] **''''' Anagyrus''''' Howard, 1896 *** ''Doliphoceras'' Mercet, 1921 is a synonym of '' Anagyrus'' *** 293 species worldwide; 33 Afrotropical species: ****'' Anagyrus aberiae'' Guerrieri (1) ****'' Anagyrus abyssinicus'' Compere (4) ****'' Anagyrus agraensis'' Saraswat (1) ****'' Anagyrus amnicus'' Prinsloo (1) ****'' Anagyrus amoenus'' Compere (5) ****'' Anagyrus antoniae'' Guerrieri (1) ****'' Anagyrus arambourgi'' Risbec (1) ****'' Anagyrus arenaria'' Prinsloo (1) ****'' Anagyrus aurantifrons'' Compere (6) ****'' Anagyrus bambeyi'' Risbec (3) ****'' Anagyrus beneficians'' Compere (7) ****'' Anagyrus bugandaensis'' Compere (5) ****'' Anagyrus diversicornis'' (Howard) (11) ****'' Anagyrus fusciventris'' (Girault) (2) ****'' Anagyrus gracilis'' (Hayat) (3) ****'' Anagyrus greeni'' Howard (1) ****'' Anagyrus haroldi'' Noyes and Hayat (4) ****'' Anagyrus incongruens'' (Masi) (1) ****'' Anagyrus indicus'' (Subba Rao) (1) ****'' Anagyrus kivuensis'' Compere (5) ****'' Anagyrus lopezi'' (De Santis) (92) ****'' Anagyrus mangicola'' Noyes (7) ****'' Anagyrus mirzai'' Agarwal and Alam (3) ****'' Anagyrus nigrescens'' Compere (5) ****'' Anagyrus pseudococci'' (Girault) (10) ****'' Anagyrus pullus'' Compere (7) ****'' Anagyrus rubellus'' (Annecke) (4) ****'' Anagyrus saccharicola'' Timberlake (8) ****'' Anagyrus siccus'' (Prinsloo and Annecke) (3) ****'' Anagyrus subflaviceps'' (Girault) (2) ****'' Anagyrus subnigricornis'' Ishii (1) ****'' Anagyrus subproximus'' (Silvestri) (5) ****'' Anagyrus swezeyi'' Timberlake (2) === 132 === * 132a Antennal funicle with contrasting white and black segments; if rarely unicolorous, then marginal and postmarginal veins very short or punctiform........ 133 * 132b Funicle unicolorous; marginal and postmarginal veins well developed, the latter often very long........ 134 === 133 === * 133a Antennal scape moderately to broadly expanded ventrally (fig. 102 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); fore wing hyaline; frontovertex without punctations - **''''' Anagyrus''''' Howard, 1896 *** 293 species worldwide; 33 Afrotropical species: **** See step 131b * 133b Antennal scape subcylindrical (fig. 121 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); fore wing weakly to strongly infuscated (fig. 119 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>), at least in the distal three-fourths or so; frontovertex and face with scattered punctations (fig. 118 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Basal part of fore wing with setation as in fig. 120 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>; male antenna as in fig. 122 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/> - [[File:Apoleptomastix iNat 165108113.jpg|thumb|''Apoleptomastix'' sp., South Africa]] **''''' Apoleptomastix''''' Kerrich, 1982 ***''Xiphomastix'' De Santis, 1972 is a synonym of ''Apoleptomastix'' *** 6 species worldwide; 2 Afrotropical species: ****''Apoleptomastix anneckei'' Pseudococcidae ''Antonina'' sp. (Gambia, South Africa, Zimbabwe) ****''Apoleptomastix bicoloricornis'' Pseudococcidae ''Brevennia rehi'', ''Coccidohystrix insolita'', ''Heterococcus nigeriensis'' (Ethiopia, Gambia, Namibia, Nigeria, South Africa, Zambia, Zimbabwe) === 134 === * 134a Fore wing distinctly infuscated with hyaline patches........ 135 * 134b Fore wing hyaline; if rarely infuscated, then with faint longitudinally infuscated bands........ 136 === 135 === * 135a Head and body dominantly orange-red; fore wing (fig. 103 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) tapering towards apex from the level of apex of venation, the wing disc characteristically maculated as in fig. 103 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>; antenna not particularly slender, the scape somewhat expanded ventrally, about three times as long as its greatest width; wings held horizontal in life - **''''' Yasumatsuiola''''' Trjapitzin, 1977 *** 1 species worldwide; No Afrotropical species? ****''Yasumatsuiola orientalis'' Trjapitzin, 1977 found in Afrotropics? * 135b Colour of head and body otherwise; fore wing (fig. 104 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) long, slender, not tapering towards apex, the latter broadly rounded; wing disc infuscated with hyaline cross-bands or patches; antenna (fig. 105 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) long and slender, filiform, the scape cylindrical, much more than three times as long as wide; wings held erect in life - [[File:Callipteroma sexguttata iNat 150291293.jpg|thumb|''Callipteroma sexguttata'', South Africa]][[File:Mercet 1921 27 Callipteroma 118.jpg|thumb|Male ''Callipteroma sexguttata'', Spain]] **''''' Callipteroma''''' Motschulsky, 1863 *** 6 species worldwide; 3 Afrotropical species: ****''Callipteroma albiclava'' Noyes (1) ****''Callipteroma sexguttata'' Motschulsky (3) ****''Callipteroma testacea'' Motschulsky (2) === 136 === * 136a Scutellum with sculptural cells longitudinally oriented, somewhat raised, giving the disc a striate effect (fig. 114 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>). Mesoscutum with parapsidal sulci (fig. 114 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>); head and body black, shiny, without metallic refringence; male antenna (fig. 117 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) with rami, one each on funicle segments II–V - **'''''Neocharitopus''''' Hayat, Alam and Agarwal, 1975 *** ''Insleyia'' Prinsloo and Annecke, 1979 is a synonym of ''Neocharitopus'' *** 3 species worldwide; 2 Afrotropical species: ****''Neocharitopus crassus'' (Prinsloo and Annecke) (3) ****''Neocharitopus solani'' (Risbec) (1) * 136b Sculpture of scutellum otherwise................137 === 137 === * 137a Antennal scape (fig. 106 of the Prinsloo-Annecke key<ref name=Prinsloo&Anneke1979/>) moderately to broadly expanded ventrally, or if only slightly expanded, then the ends cylindrical. General colour yellow to orange, without metallic lustre; thorax covered with fine white setae; postmarginal vein long, reaching to a level beyond apex of stigmal - **''''' Gyranusoidea''''' Compere, 1947 *** 44 species worldwide; 11 Afrotropical species: ****''Gyranusoidea austrina'' Annecke and Mynhardt (4) ****''Gyranusoidea citrina'' (Compere) (6) ****''Gyranusoidea dilatata'' Annecke and Mynhardt (4) ****''Gyranusoidea flava'' Shafee, Alam and Agarwal (1) ****''Gyranusoidea klugei'' Prinsloo and Annecke (3) ****''Gyranusoidea litura'' Prinsloo (3) ****''Gyranusoidea munda'' Annecke (5) ****''Gyranusoidea pauliani'' (Risbec) (2) ****''Gyranusoidea separata'' Prinsloo (3) ****''Gyranusoidea signata'' Annecke and Mynhardt (5) ****''Gyranusoidea tebygi'' Noyes (28) * 137b Antennal scape not or hardly expanded ventrally........ 138 === 138 === * 138a Body always black, with moderate to strong metallic green, blue or purplish refringence. Mesoscutum with incomplete parapsidal sulci; marginal and postmarginal veins long - **''''' Clausenia''''' Ishii, 1923 *** 12 species worldwide; 7 Afrotropical species: ****''Clausenia capensis'' Annecke and Mynhardt (3) ****''Clausenia comperei'' Kerrich (4) ****''Clausenia concinna'' Annecke and Mynhardt (3) ****''Clausenia confusor'' Kerrich (3) ****''Clausenia corrugata'' Kerrich (3) ****''Clausenia guineensis'' Kerrich (3) ****''Clausenia sobrina'' Annecke and Mynhardt (3) * 138b Colour otherwise, if rarely black, then without any metallic refringence........ 139 === 139 === * 139a Antenna filiform, the basal funicle segment longer than pedicel, often very much so; cercal plates advanced to a level near base of metasoma - [[File:Leptomastix inat 153928277.jpg|thumb|''Leptomastix'' sp., South Africa]] **''''' Leptomastix''''' Foerster, 1856 *** 34 species worldwide; 12 Afrotropical species: ****''Leptomastix abyssinica'' Compere (5) ****''Leptomastix africana'' Anga and Noyes (1) ****''Leptomastix dactylopii'' Howard (24) ****''Leptomastix digitariae'' Risbec (1) ****''Leptomastix flava'' Mercet (3) ****''Leptomastix herreni'' Anga and Noyes (1) ****''Leptomastix hibiscusae'' Risbec (3) ****''Leptomastix jonesi'' Noyes (1) ****''Leptomastix nigra'' Compere (6) ****''Leptomastix nigrocincta'' Risbec (4) ****''Leptomastix nigrocoxalis'' Compere (6) ****''Leptomastix tsukumiensis'' Tachikawa (2) * 139b Antenna not filiform, the pedicel longer than basal funicle segment; cecal plates placed near apex of metasoma - **''''' Allocerellus''''' Silvestri, 1915 *** 12 species worldwide; 12 Afrotropical species: ***See step 125 =Other genera known from the Afrotropics= [[File:Achalcerinys lindus faunaibrica Mercet 1921 F112 p270.jpg|thumb|''Achalcerinys lindus'', female, Spain.]][[File:Blastothrix erythrostetha female Fig95 p245.jpg|thumb|''Blastothrix erythrostetha'', female]][[File:Cryptanusia iNat 19192414 magriet b.jpg|thumb|''Cryptanusia'' sp., South Africa]][[File:Mira integralis Fauna iberica (1921) p.554.jpg|thumb|Male ''Mira integralis'']][[File:Mira integralis Fauna iberica (1921) p.556.jpg|thumb|Female ''Mira integralis'']][[File:Trichomasthus cyanifrons, female, Spain.jpg|thumb|''Trichomasthus cyanifrons'', female, Spain]] *Some of these genera have been found in the Afrotropics since the key was created (1979) **'''''Achalcerinys''''' Girault, 1915 ***''Parasyrpophagus'' is a synonym of ''Achalcerinys'' *** 5 species worldwide; 2 Afrotropical species: ****''Achalcerinys gorodkovi'' (Myartseva, 1983) - no known associates (Egypt, Ethiopia) ****''Achalcerinys lindus'' (Mercet, 1921) - a parasitoid of Eriococcidae, Pseudococcidae, Encyrtidae (Ethiopia) **'''''Agarwalencyrtus''''' Hayat, 1981 *** 4 species worldwide; 1 Afrotropical species: ****''Agarwalencyrtus citri'' - a parasitoid or hyperparasitoid in mealybugs; ''Planococcus'' spp. (South Africa, Swaziland, Zimbabwe) ****Photograph of specimen in [https://www.cabidigitallibrary.org/doi/pdf/10.5555/20203576260 Tirunagaru and Sagadai (2020)] **'''''Anomalencyrtus''''' Hayat and Verma, 1980 *** 2 species worldwide; 1 Afrotropical species: ****''Anomalencyrtus longicornis'' - no known associates (Madagascar) **'''''Anomalicornia''''' Mercet, 1921 *** 1 species worldwide; 1 Afrotropical species: ****''Anomalicornia tenuicornis'' - a parasitoid of mealybugs (Burkina Faso, Cameroon, Ivory Coast, Madagascar, Zimbabwe) **'''''Astymachus''''' Howard, 1898 *** 6 species worldwide; 1 Afrotropical species: ****''Astymachus exilis '' - no known associates (South Africa) **'''''Blastothrix ''''' *** 29 species worldwide; 1 Afrotropical species: ****''Blastothrix anthocleistae'' Risbec, 1952 (Madagascar) **'''''Bothriocraera''''' Timberlake, 1916 *** 4 species worldwide; 1 Afrotropical species: ****''Bothriocraera bicolor'' - a parasitoid of mealybugs (Ghana) **'''''Brachyplatycerus''''' De Santis, 1972 *** 1 species worldwide; 1 Afrotropical species: ****''Brachyplatycerus minutum'' - a parasitoid of moths ''Cydia pomonella'' (South Africa) **'''''Brethesiella''''' Porter, 1920 *** 18 species worldwide; 1 Afrotropical species: ****''Brethesiella abnormicornis'' - a parasitoid of Margarodidae ''Icerya'' spp. (Sao Tomé and Principe) **'''''Cladiscodes''''' Subba Rao, 1977 *** 5 species worldwide; 1 Afrotropical species: ****''Cladiscodes incisius'' - no known associates (South Africa) **'''''Cryptanusia''''' Girault , 1917 *** 8 species worldwide; 1 Afrotropical species: ****''Cryptanusia aureiscutellum'' - no known associates (South Africa) **'''''Diaphorencyrtus''''' Hayat, 1981 *** 2 species worldwide; 2 Afrotropical species: ****''Diaphorencyrtus aligarhensis'' (Shafee, Alam and Agarwal) (Réunion, South Africa) ****''Diaphorencyrtus harrisoni'' (Robinson, 1960) (South Africa) **'''''Dionencyrtus''''' De Santis, 1985 *** 2 species worldwide; 1 Afrotropical species: ****''Dionencyrtus cordylomerae'' (Risbec, 1951) (Senegal) **'''''Dusmetia''''' Mercet, 1921 *** 6 species worldwide; 1 Afrotropical species: ****''Dusmetia fuscipennis'' (Noyes & Hayat, 1984) (Zimbabwe) **'''''Ectroma''''' Westwood, 1833 *** 11 species worldwide; 1 Afrotropical species: ****''Ectroma truncatum'' Prinsloo, 1986 (Zimbabwe) **''''' Erencyrtus''''' Mahdihassan, 1923 *** 6 species worldwide; 4 Afrotropical species: ****''Erencyrtus ater'' Annecke and Mynhardt (South Africa) ****''Erencyrtus contrarius'' Prinsloo and Mynhardt (South Africa) ****''Erencyrtus fuscus'' Annecke and Mynhardt (South Africa) ****''Erencyrtus notialis'' Prinsloo and Mynhardt (South Africa) **'''''Hambletonia''''' Compere, 1936 *** 9 species worldwide; 1 Afrotropical species: ****''Hambletonia pseudococcina'' Compere, 1936 (Ghana) **'''''Hemileucoceras''''' Hoffer, 1976 *** 3 species worldwide; 1 Afrotropical species: ****''Hemileucoceras madagascariensis'' (Risbec) (Madagascar) **'''''Holcencyrtus''''' Ashmead, 1900 *** 10 species worldwide; 2 Afrotropical species: ****''Holcencyrtus liriomyzae'' Risbec (Senegal) ****''Holcencyrtus myrmicoides'' (Compere and Zinna) (Ghana) **'''''Homosemion''''' Annecke, 1967 *** 1 species worldwide; 1 Afrotropical species: ****''Homosemion bennetti'' Annecke, 1967 (Sao Tomé and Principe) **'''''Incisencyrtus''''' Prinsloo, 1988 *** 4 species worldwide; 3 Afrotropical species: ****''Incisencyrtus afer'' Prinsloo, 1988 (South Africa, Zimbabwe) ****''Incisencyrtus secus'' Prinsloo, 1988 (Madagascar) ****''Incisencyrtus sirus'' Prinsloo, 1988 (Nigeria) **'''''Lakshaphagus''''' Mahdihassan, 1931 *** 9 species worldwide; 2 Afrotropical species: ****''Lakshaphagus armillatus'' (Annecke, 1969) (South Africa) ****''Lakshaphagus ceroplastae'' (Risbec, 1951) (Senegal) **'''''Manicnemus''''' Hayat, 1981 *** 2 species worldwide; 1 Afrotropical species: ****''Manicnemus'' sp. (Tanzania) <ref name=vanNoort>van Noort, S. (2024). WaspWeb: Hymenoptera of the Afrotropical region. [https://www.waspweb.org/Chalcidoidea/Encyrtidae/Tetracneminae/Manicnemus/Manicnemus_species.htm Manicnemus species] (accessed on 14 March 2024).</ref> **''''' Mahencyrtus''''' Masi, 1917 *** 14 species worldwide; 1 Afrotropical species: ****''Mahencyrtus occultans'' - no associates known (Seychelles) **'''''Mira''''' *** 6 species worldwide; 1 Afrotropical species: ****''Mira integralis'' (Mercet, 1921) (Senegal) **'''''Neastymachus''''' Girault, 1915 *** 21 species worldwide; 1 Afrotropical species: ****''Neastymachus dispar'' Prinsloo, 1996 (South Africa) **'''''Neodusmetia''''' Kerrich, 1964 *** 6 species worldwide; 1 Afrotropical species: ****''Neodusmetia sangwani'' (Subba Rao, 1957) (Kenya, Namibia, South Africa, Zimbabwe) **'''''Parablatticida''''' Girault, 1915 *** 15 species worldwide; 2 Afrotropical species: ****''Parablatticida aphycoides'' (Masi, 1917) (Seychelles) ****''Parablatticida vidua'' (Masi, 1917) (Seychelles) **'''''Pseudococcobius''''' Timberlake, 1916 *** 12 species worldwide; 6 Afrotropical species: ****''Pseudococcobius akares'' Prinsloo, 2003 (South Africa) ****''Pseudococcobius ancylus'' Prinsloo, 2003 (South Africa) ****''Pseudococcobius dolus'' Prinsloo, 2003 (South Africa) ****''Pseudococcobius san'' Prinsloo, 2003 (South Africa) ****''Pseudococcobius vibex'' Prinsloo, 2003 (South Africa) ****''Pseudococcobius vinealis'' Prinsloo, 2003 (South Africa) **'''''Rhytidothorax''''' Ashmead, 1900 *** 20 species worldwide; 2 Afrotropical species: ****''Rhytidothorax ambositrensis'' (Risbec, 1952) (Madagascar) ****''Rhytidothorax latiscapus'' (Prinsloo and Annecke, 1979) (Swaziland, Zimbabwe) **'''''Scotteus''''' Masi, 1917 *** 1 species worldwide; 1 Afrotropical species: ****''Scotteus ochroleucus'' Masi, 1917 (Seychelles) **'''''Spaniopterus''''' Gahan, 1927 *** 1 species worldwide; 1 Afrotropical species: ****''Spaniopterus crucifer'' Gahan, 1927 (Mauritius) **'''''Stemmatosteres''''' Timberlake, 1918 *** 5 species worldwide; 1 Afrotropical species: ****''Stemmatosteres primus'' Prinsloo and Mynhardt, 1981 (South Africa) **'''''Trichomasthus''''' *** 60 species worldwide; 1 Afrotropical species: ****''Trichomasthus portoricensis'' (Crawford, 1913) (Sao Tomé and Principe) **'''''Xenostryxis''''' *** 10 species worldwide; 1 Afrotropical species: ****''Xenostryxis margiscutellum'' Girault, 1920 (South Africa) **'''''Zarhopalus''''' Ashmead, 1900 *** 8 species worldwide; 1 Afrotropical species: ****''Zarhopalus corvinus'' a parasitoid of Pseudococcidae, ''Pseudococcus'' spp. (South Africa) **'''''Zozoros''''' *** 2 species worldwide; 1 Afrotropical species: ****''Zozoros adamsoniae'' (Risbec, 1951) (Senegal) =References= {{Reflist}} [[Category:African Arthropods|Afrotropical Encyrtidae Key]] itinut2xk4jhed58gcea46v8lle5abw 0 304964 2690175 2677278 2024-12-03T23:38:02Z Watchduck 137431 2690175 wikitext text/x-wiki These articles about Boolean functions use a similar style and terminology. &nbsp; <small style="opacity: .7;">They are created by [[User:Watchduck|Watchduck]] a.k.a. Tilman Piesk.</small> * '''[[Studies of Boolean functions/terminology]]''' * '''[[Studies of Boolean functions/examples]]''' * '''[[Discrete helpers/boolf]]''' * [[Properties of Boolean functions]] and [[Properties of truth tables|of truth tables]] * [[Integer sequences related to Boolean functions]] * [[Linear Boolean functions]] * [[Gender of Boolean functions]] * [[Mentors of Boolean functions]] * [[Principalities and dominions of Boolean functions]] * <small>[[Tesseract and 16-cell faces]]</small> ==[[Studies of Euler diagrams]]== <gallery> File:EuDi; potula (shapes).svg File:EuDi; gilera.svg File:EuDi; nisuke.svg File:EuDi; kimuri.svg File:EuDi; levana flat.svg File:EuDi; medusa.png File:EuDi; batch 5; 5.svg </gallery> ==Zhegalkin indices== [[File:ANF to 1000 1001.svg|thumb|150px|left|ANF to truth table]] [[File:Zhegalkin 256.svg|thumb|717px|right|Zhegalkin matrix]] * [[Algebraic normal form]] * [[Zhegalkin matrix]], [[Zhegalkin twins]] * [[Noble Boolean functions]] * [[Gentle sets of Boolean functions]] * [[Linear and noble Boolean functions]] * [[Smallest Zhegalkin index]] {{clear}} ==Commons== Some topics exist mainly in the form of categories on Commons. Articles here should follow. {| style="text-align: center; background-color: #f8f9fa; border: 1px solid #a2a9b1" |style="padding-right: 20px;"| [[commons:Category:3-ary Zhegalkin indices in octeract matrix; great principalities; with entries on diagonal|3-ary]] <span style="font-size: 70%; opacity: .6;">(4)</span> |style="padding-right: 20px;"| [[commons:Category:4-ary Zhegalkin indices in 16-cube matrix; great principalities; with entries on diagonal|4-ary]] <span style="font-size: 70%; opacity: .6;">(20)</span> |rowspan="2" style="text-align: right; padding-right: 10px;"| great principalities <small>with entries</small> |style="text-align: left; padding-right: 0 20px;"| on diagonal &nbsp; <span style="font-size: 70%; opacity: .6;">(related to patron dominions)</span> |- |style="padding-right: 20px;"| [[commons:Category:3-ary Zhegalkin indices in octeract matrix; great principalities; with entries in top row|3-ary]] <span style="font-size: 70%; opacity: .6;">(4)</span> |style="padding-right: 20px;"| [[commons:Category:4-ary Zhegalkin indices in 16-cube matrix; great principalities; with entries in top row|4-ary]] <span style="font-size: 70%; opacity: .6;">(22)</span> |style="text-align: left; padding-right: 0 20px;"| in top row &nbsp; <span style="font-size: 70%; opacity: .6;">(related to patron principalities)</span> |} {| class="wikitable" style="width: 800px; text-align: center;" | [[commons:Category:2-ary Boolean functions in tesseract matrix; great prefects|2-ary]] {{spaces|3}} [[commons:Category:3-ary Boolean functions in octeract matrix; great prefects|3-ary]] {{spaces|3}} [[commons:Category:4-ary Boolean functions in 16-cube matrix; great prefects|4-ary]] {{spaces|7}} great prefects in hypercube matrix |} {| class="wikitable" style="width: 800px; text-align: center;" | [[commons:Category:2-ary Boolean functions in tesseract matrix; principalities and dominions|2-ary]] {{spaces|3}} [[commons:Category:3-ary Boolean functions in octeract matrix; principalities and dominions|3-ary]] {{spaces|3}} [[commons:Category:4-ary Boolean functions in 16-cube matrix; principalities and dominions|4-ary]] {{spaces|7}} principalities and dominions in hypercube matrix |} * {{Commons catlink|Quadrant colors in hypercube matrices (image set)}} * {{Commons catlink|3-ary Boolean functions in octeract matrix; faction clusters}} * {{Commons catlink|3-ary Boolean functions; graphs of faction clusters}} * {{Commons catlink|Walsh spectra of 3-ary Boolean functions; families}} ==old== These old pages require some updates. * [[3-ary Boolean functions]] * [[4-ary Boolean functions]] * [[Seal (discrete mathematics)]] (subgroups of nimber addition)) [[Category:Studies of Boolean functions]] 5fczhdvdzpgafw9xd5h30cdmnkzfaff 10 305247 2690166 2627397 2024-12-03T22:24:48Z Watchduck 137431 2690166 wikitext text/x-wiki [[commons:Category:{{{1}}}|{{{2|{{{1}}}}}}]]<noinclude> ---- <code><nowiki>{{Commons catlink|Flowers}}</nowiki></code> creates {{Commons catlink|Flowers}} <code><nowiki>{{Commons catlink|Flowers|FLOWERS}}</nowiki></code> creates {{Commons catlink|Flowers|FLOWERS}} [[Category:Interwiki templates]] </noinclude> l0slgbfb5x3orguc32xdgdo27e54x4r 0 306032 2690149 2667862 2024-12-03T19:29:25Z UniBambergIslamicStudies 2987517 2690149 wikitext text/x-wiki '''The Bamberg Introduction to the History of Islam (BIHI)''' provides an overview of the history of Islam by [[User:PaFra|Prof. Dr. Patrick Franke]] across 14 chapters. Franke utilizes this material as the foundation for his lectures at the [[w:University of Bamberg|University of Bamberg]]. As an [[Open Educational Resources|Open Educational Resource]], however, it can be used by other educational institutions or for self-study purposes. The text, which is updated regularly, features links to enlargeable illustrations, maps, digitized materials, selected Wikipedia articles for further reading, and Qur'anic quotes from [[w:Corpus_Coranicum|Corpus Coranicum]] database , thereby giving it an interactive character. Please be aware that not all linked Wikipedia articles meet scholarly quality criteria. Articles supervised from an academic perspective are exclusively those included in the [https://www.uni-bamberg.de/islamwissenschaft/bie/ Bamberg Encyclopedia of Islam]. Please also observe the [https://www.uni-bamberg.de/islamwissenschaft/bie/zitierhinweis/ citation guidelines] provided there. Please note that this page is a translation of Professor Franke’s course, originally published on the German Wikiversity. The content is currently being translated and updated. You can find the complete course on the German Wikiversity under [https://de.wikiversity.org/wiki/Bamberger_Einf%C3%BChrung_in_die_Geschichte_des_Islams_(BEGI) Bamberger Einführung in die Geschichte des Islams (BEGI)]. {| class="wikitable" | 1 ||| [[The_Bamberg_Introduction_to_the_History_of_Islam_(BIHI)_01|Fundamentals, Arabia on the Eve of Islam]] — The first session covers preliminary topics, introduces the lecture's concept, and examines the religious, social, and political landscape of late antique Arabia and its influence on Islam. Special emphasis is placed on the tensions between the various religious cultures that set the stage for the emergence of Ḥanīfism, and subsequently, Islam. || [[File:Wuquf.JPG|80px]] |- | 2 || [[The_Bamberg_Introduction_to_the_History_of_Islam_(BIHI)_02|The Beginnings of the New Religion: Muḥammad in Mecca]] — This session explores Muḥammad's religious development within the Ḥanīfic milieu, his followers, and his confrontations with opponents in Mecca up to the year 622. His early religious message is then reconstructed on the basis of Qur'anic statements. Finally, the new forms of worship that defined the emerging religious community are discussed. || [[File:Intheroadofhiracave.JPG|80px]] |- | 3 || [[The_Bamberg_Introduction_to_the_History_of_Islam_(BIHI)_03|The Prophet of Yathrib and the New Polity (622-630)]] — The center of the new religion shifts to the oasis of Yathrib, with warfare taking center stage. Muḥammad and his followers engage in battles against pagan Mecca and increasingly come into conflict with the Jews of Yathrib, who are ultimately expelled from the oasis. As the leader of the nascent community, Muḥammad implements a series of legal, social, and ritual reforms. || style="text-align:center" |[[File:Dinar, Khusro II, 590, 591-628 AD, year 31 - Bode-Museum - DSC02737.JPG|60px]] |- | 4 || '''The Expansion of the Islamic State and the Early Caliphate (630-656) ''' — The state of Yathrib (Medina) rises to become the most dominant power in Arabia. Though Muḥammad's death in 632 plunged the state into a deep crisis, this challenge was swiftly overcome. With the support of the Arab tribes, an expansionist movement was set in motion, leading to the conquest of the entire Middle East. Notable religious innovations: the reform of the calendar and the codification of the Qur’an. || [[File:The ‘Uthman Qur'an - Kufic.jpg|80px]] |- | 5 || '''The Division of the Ummah: Kharijites and Shiites (656-692) ''' — The tensions that had already become apparent during ʿUthmān's caliphate erupted fully, leading to a significant divide within the Muslim community. The Muslim community splits into various subgroups, each developing its own religious and political doctrines, and clashing with one another. The Umayyads construct the Dome of the Rock as an alternative sacred site to the Kaaba. Muftis and Qur’an exegetes emerge as new religious specialists. || [[File:Palestine-2013(2)-Jerusalem-Temple Mount-Dome of the Rock (SE exposure).jpg|80px]] |- | 6 ||'''The Disintegration of the Jihad State and the Beginnings of Fiqh (692-750)'''— The early Islamic expansionist movement reaches its zenith and decline. Social tensions between Arabs and non-Arabs intensify. Murji'a, Qadarīya, Jahmīya, and Ibādīya emerge as new religious-political parties. In addition, a distinct Islamic normative doctrine, known as fiqh, emerges and is cultivated in various local schools. || [[File:Qusayr Amra.jpg|80px]] |- | 7 ||'''Traditionalism, Rationalism, and the Beginnings of Ismāʿīlīya (750-930) '''— The unity of the Islamic empire disintegrates. The Abbasids and Alids, two families from the Prophet's clan, struggle for power. Two opposing religious cultures emerge with Kalām and Hadith scholarship. The question of the Qur’anic createdness divides Muslims. The Shi'a continues to diversify; the Shi'a Fatimid dynasty rose to power in the west. || [[File:Ghardaia 01.jpg|80px]] |- | 8 ||'''The Shiite Century and the Consolidation of Sunnism (930–1173) ''' — Most Islamic countries are ruled by Shiite dynasties. These dynasties promote not only Shiite scholarship and a memorial culture but also Muʿtazilite theology and philosophy. Beginning around 1050, a "Sunni restoration" commences, despite significant dogmatic differences within the Sunni camp. Islam increasingly spreads to Africa. || [[File:Tin Mal Mosque4 (js).jpg|80px]] |- | 9 || '''The Flourishing of Sufi Orders and Twelver Shia (1173-1517) ''' — The Sufi mystical tradition gains increasing prominence and receives patronage from rulers. The Mongol invasion causes great upheaval but ultimately contributes to the further spread of Islam. The Egyptian Mamluks secure authority over Islam's sacred sites and uphold an Abbasid "shadow caliphate." Twelver Shia is adopted as the state doctrine in Iran. || [[File:Bagdad1258.jpg|80px]] |- | 10 || '''The Ottoman Supremacy and the Rise of the Wahhabis (1517–1813) ''' — Islamization advances in the Balkans and Southeast Asia. The Ottoman Empire rises as the new Islamic superpower, with a definite Sunni-orientation, while the Safavid state emerges as its Shiite counterpart. In the Indian Mughal Empire, efforts to establish a new cross-religious doctrine fail. In Arabia, Wahhabism emerges as a new rigorist branch of Islam. || [[File:Mirror Image of 'Ali wali Allah WDL6788.png|80px]] |- | 11 || '''Development and Peak of Modernist Islam (1813-1924) ''' — The encroachment of European powers into the Islamic world forces Muslims to rethink their beliefs and societal structures. Islamic-modernist schools of thought emerge in Egypt and India under British rule. Pan-Islamism develops as a response to European imperialism. Significant upheavals during this period include the end of the Ottoman Caliphate and the Saudi conquest of the Hejaz.|| [[File:Turkish refugees sumla1877 wiki.jpg|80px]] |- | 12 || '''The Impetus of Secular Ideologies and the "Islamic Revolution" (1924-1979)''' — Secularism, socialism, and nationalism gain increasing numbers of adherents among Muslims. New Islamic movements respond with Daʿwah, the "call to Islam". Saudi Arabia attempts to position itself at the forefront with the Muslim World League. The OIC emerges as a supranational Islamic organization. Revolutionary regimes in Libya and Iran offer alternative models to Saudi Islam.|| [[File:Bundesarchiv Bild 146-1987-004-09A, Amin al Husseini und Adolf Hitler.jpg|80px]] |- | 13 ||''' "Islamic Awakening" among Sunnis and the Birth of al-Qāʿidah (1979-2001) ''' — Shia Iran's attempts to export its revolutionary form of Islam to other countries put Sunni Islamic representatives under pressure. Their responses include the "Islamic Awakening," Salafism, and the jihad in Afghanistan. After 1989, Islam emerges as the adversary of the West, succeeding the Eastern Bloc. Muslim minorities in the West come into greater focus. || [[File:AnschalgInZahran1996 KhobarTower.jpg|80px]] |- | 14 || '''The IS Caliphate and the Rise of Anti-Islamism (2001–2022)''' — The attacks of September 11, 2001, triggers a global wave of anti-Islamism. Militant Islamists initially align themselves with al-Qāʿidah, but after 2014, the leadership of the Jihadist International shifts to the IS organization. Concurrently, various efforts to combat extremism are initiated. The political Islam of the Muslim Brotherhood leads to new polarizations. ''' || [[File:Erdogan gesturing Rabia.jpg|80px]] |} If you have general questions or suggestions for improving BIHI, please leave a message on Prof. Franke's discussion page. [[Category:Islamic Studies]] kdrj6sy6a22pcf4cxmdpjnp4t53dhw4 0 306361 2690150 2689909 2024-12-03T19:44:17Z 152.22.75.23 p diddy !! 2690150 wikitext text/x-wiki <center>[[File:Wikiphilosophers.png|150px|link=]] <span style="color: #333; font-size: 1.4em">The philosopedia for the new generation of thinkers<br></span></center> <br> ---- <br> ''[[Sean "P Diddy" Combs|'''Wikiphilosophers is a project aiming to provide an overview of philosophical ideas from new philosophers and thinkers. On Wikiphilosophers, you can articulate all your philosophical views under the lemma to which they belong. In this way, we collect hundreds of philosophies from today's thinkers! Explore, develop and exchange countless philosophical ideas!''']]'' == '''''[[Socratic Methods|Getting started]]''''' == '''''[[Socratic Methods|What do you think you know for sure? And what assumptions are you making? What are you not quite sure about yet? Try to sort this out for yourself before you get started, by thinking about what philosophical ideas you would like to write about.]]''''' '''''[[Socratic Methods|<br /> What is the topic of your philosophical idea about in one or two words? Once you know this, create a new topic page via the button below or go to the existing topic page if it already exists. <br><br>]]''''' <inputbox> type = create placeholder = Title of the topic, e.g. "Consciousness" or "Free will" buttonlabel = Create a new topic prefix = Wikiphilosophers/ break = no useve = true </inputbox> '''''[[Socratic Methods|<br> After that, you can write out your own philosophical view via <code>Wikiphilosophers/<name of topic>/<username></code>. Preferably as short and concise as possible, so that one does not have to read extensive texts.]]''''' === '''''[[Socratic Methods|Starting dialogues]]''''' === '''''[[Socratic Methods|When reading other people's philosophical views, it is possible to start a dialogue on the discussion page. Ask questions if something is not clear to you, preferably through the Socratic method. This creates the opportunity for the writer to develop his philosophical views more deeply. If you understand each other better, you can additionally get inspiration from each other. Just make sure that you always ask questions and don't try to explain your own philosophical views on the discussion page. Because you can do this on your own page.]]''''' == '''''[[Socratic Methods|Topics]]''''' == === '''''[[Socratic Methods|Epistemology]]''''' === * '''''[[Socratic Methods|Foundational beliefs]]''''' === '''''[[Socratic Methods|Ontology]]''''' === * '''''[[Socratic Methods|What there is]]''''' === '''''[[Socratic Methods|Metaphysics]]''''' === * '''''[[Socratic Methods|Universe]]''''' * '''''[[Socratic Methods|Extraterrestrial life]]''''' * '''''[[Socratic Methods|Paranormality]]''''' * '''''[[Socratic Methods|Past lives]]''''' === '''''[[Socratic Methods|Philosophy of mind]]''''' === * '''''[[Socratic Methods|Consciousness]]''''' * '''''[[Socratic Methods|Free will]]''''' === '''''[[Socratic Methods|Ethics]]''''' === * '''''[[Socratic Methods|Goodness]]''''' * '''''[[Socratic Methods|Meaning of life]]''''' * '''''[[Socratic Methods|Moral Reasoning]]''''' === '''''[[Socratic Methods|Psychology]]''''' === * '''''[[Socratic Methods|Happiness]]''''' * '''''[[Socratic Methods|Self-improvement]]''''' [[Category:Wikiphilosophers| ]] mk8y3gzd8vlsk3otl3fqc7iijoemt0z 2690151 2690150 2024-12-03T19:44:24Z Tres Libras 2993673 Undid edits by [[Special:Contribs/152.22.75.23|152.22.75.23]] ([[User talk:152.22.75.23|talk]]) to last version by Prototyperspective 2690151 wikitext text/x-wiki <center>[[File:Wikiphilosophers.png|150px|link=]] <span style="font-size: 2.6em; font-variant: small-caps">Welcome to Wikiphilosophers!</span><br/> <span style="color: #333; font-size: 1.4em">The philosopedia for the new generation of thinkers<br></span></center> <br> ---- <br> '''Wikiphilosophers''' is a project aiming to provide an overview of philosophical ideas from new philosophers and thinkers. On Wikiphilosophers, you can articulate all your philosophical views under the lemma to which they belong. In this way, we collect hundreds of philosophies from today's thinkers! Explore, develop and exchange countless philosophical ideas! == Getting started == What do you think you know for sure? And what assumptions are you making? What are you not quite sure about yet? Try to sort this out for yourself before you get started, by thinking about what philosophical ideas you would like to write about. What is the topic of your philosophical idea about in one or two words? Once you know this, create a new topic page via the button below or go to the existing topic page if it already exists. <br><br> <inputbox> type = create placeholder = Title of the topic, e.g. "Consciousness" or "Free will" buttonlabel = Create a new topic prefix = Wikiphilosophers/ break = no useve = true </inputbox> <br> After that, you can write out your own philosophical view via <code>Wikiphilosophers/<name of topic>/<username></code>. Preferably as short and concise as possible, so that one does not have to read extensive texts. === Starting dialogues === When reading other people's philosophical views, it is possible to start a dialogue on the discussion page. Ask questions if something is not clear to you, preferably through the [[Socratic Methods|Socratic method]]. This creates the opportunity for the writer to develop his philosophical views more deeply. If you understand each other better, you can additionally get inspiration from each other. Just make sure that you always ask questions and don't try to explain your own philosophical views on the discussion page. Because you can do this on your own page. == Topics == === Epistemology === * [[Wikiphilosophers/Foundationalism|Foundational beliefs]] === Ontology === * [[Wikiphilosophers/What there is|What there is]] === Metaphysics === * [[Wikiphilosophers/Universe|Universe]] * [[Wikiphilosophers/Extraterrestrial life|Extraterrestrial life]] * [[Wikiphilosophers/Paranormality|Paranormality]] * [[Wikiphilosophers/Past lives|Past lives]] === Philosophy of mind === * [[Wikiphilosophers/Consciousness|Consciousness]] * [[Wikiphilosophers/Free will|Free will]] === Ethics === * [[Wikiphilosophers/Goodness|Goodness]] * [[Wikiphilosophers/Meaning of life|Meaning of life]] * [[Wikiphilosophers/Moral Reasoning|Moral Reasoning]] === Psychology === * [[Wikiphilosophers/Happiness|Happiness]] * [[Wikiphilosophers/Self-improvement|Self-improvement]] [[Category:Wikiphilosophers| ]] 7oxotsb8q19n5w872zx154z9e8ief98 2690152 2690151 2024-12-03T19:44:57Z 152.22.75.23 2690152 wikitext text/x-wiki <center>[[File:Sean Combs in 2023.png|223x223px]] <span style="font-size: 2.6em; font-variant: small-caps">Welcome to Diddyphilosophers!</span><br/> <span style="color: #333; font-size: 1.4em">The philosopedia for the new generation of thinkers<br></span></center> <br> ---- <br> '''Wikiphilosophers''' is a project aiming to provide an overview of philosophical ideas from new philosophers and thinkers. On Wikiphilosophers, you can articulate all your philosophical views under the lemma to which they belong. In this way, we collect hundreds of philosophies from today's thinkers! Explore, develop and exchange countless philosophical ideas! == Getting started == What do you think you know for sure? And what assumptions are you making? What are you not quite sure about yet? Try to sort this out for yourself before you get started, by thinking about what philosophical ideas you would like to write about. What is the topic of your philosophical idea about in one or two words? Once you know this, create a new topic page via the button below or go to the existing topic page if it already exists. <br><br> <inputbox> type = create placeholder = Title of the topic, e.g. "Consciousness" or "Free will" buttonlabel = Create a new topic prefix = Wikiphilosophers/ break = no useve = true </inputbox> <br> After that, you can write out your own philosophical view via <code>Wikiphilosophers/<name of topic>/<username></code>. Preferably as short and concise as possible, so that one does not have to read extensive texts. === Starting dialogues === When reading other people's philosophical views, it is possible to start a dialogue on the discussion page. Ask questions if something is not clear to you, preferably through the [[Socratic Methods|Socratic method]]. This creates the opportunity for the writer to develop his philosophical views more deeply. If you understand each other better, you can additionally get inspiration from each other. Just make sure that you always ask questions and don't try to explain your own philosophical views on the discussion page. Because you can do this on your own page. == Topics == === Epistemology === * [[Wikiphilosophers/Foundationalism|Foundational beliefs]] === Ontology === * [[Wikiphilosophers/What there is|What there is]] === Metaphysics === * [[Wikiphilosophers/Universe|Universe]] * [[Wikiphilosophers/Extraterrestrial life|Extraterrestrial life]] * [[Wikiphilosophers/Paranormality|Paranormality]] * [[Wikiphilosophers/Past lives|Past lives]] === Philosophy of mind === * [[Wikiphilosophers/Consciousness|Consciousness]] * [[Wikiphilosophers/Free will|Free will]] === Ethics === * [[Wikiphilosophers/Goodness|Goodness]] * [[Wikiphilosophers/Meaning of life|Meaning of life]] * [[Wikiphilosophers/Moral Reasoning|Moral Reasoning]] === Psychology === * [[Wikiphilosophers/Happiness|Happiness]] * [[Wikiphilosophers/Self-improvement|Self-improvement]] [[Category:Wikiphilosophers| ]] ptkniktzh139yhxdri8cgkcp25z7kx1 2690153 2690152 2024-12-03T19:45:06Z Tres Libras 2993673 Undid edits by [[Special:Contribs/152.22.75.23|152.22.75.23]] ([[User talk:152.22.75.23|talk]]) to last version by Tres Libras 2690153 wikitext text/x-wiki <center>[[File:Wikiphilosophers.png|150px|link=]] <span style="font-size: 2.6em; font-variant: small-caps">Welcome to Wikiphilosophers!</span><br/> <span style="color: #333; font-size: 1.4em">The philosopedia for the new generation of thinkers<br></span></center> <br> ---- <br> '''Wikiphilosophers''' is a project aiming to provide an overview of philosophical ideas from new philosophers and thinkers. On Wikiphilosophers, you can articulate all your philosophical views under the lemma to which they belong. In this way, we collect hundreds of philosophies from today's thinkers! Explore, develop and exchange countless philosophical ideas! == Getting started == What do you think you know for sure? And what assumptions are you making? What are you not quite sure about yet? Try to sort this out for yourself before you get started, by thinking about what philosophical ideas you would like to write about. What is the topic of your philosophical idea about in one or two words? Once you know this, create a new topic page via the button below or go to the existing topic page if it already exists. <br><br> <inputbox> type = create placeholder = Title of the topic, e.g. "Consciousness" or "Free will" buttonlabel = Create a new topic prefix = Wikiphilosophers/ break = no useve = true </inputbox> <br> After that, you can write out your own philosophical view via <code>Wikiphilosophers/<name of topic>/<username></code>. Preferably as short and concise as possible, so that one does not have to read extensive texts. === Starting dialogues === When reading other people's philosophical views, it is possible to start a dialogue on the discussion page. Ask questions if something is not clear to you, preferably through the [[Socratic Methods|Socratic method]]. This creates the opportunity for the writer to develop his philosophical views more deeply. If you understand each other better, you can additionally get inspiration from each other. Just make sure that you always ask questions and don't try to explain your own philosophical views on the discussion page. Because you can do this on your own page. == Topics == === Epistemology === * [[Wikiphilosophers/Foundationalism|Foundational beliefs]] === Ontology === * [[Wikiphilosophers/What there is|What there is]] === Metaphysics === * [[Wikiphilosophers/Universe|Universe]] * [[Wikiphilosophers/Extraterrestrial life|Extraterrestrial life]] * [[Wikiphilosophers/Paranormality|Paranormality]] * [[Wikiphilosophers/Past lives|Past lives]] === Philosophy of mind === * [[Wikiphilosophers/Consciousness|Consciousness]] * [[Wikiphilosophers/Free will|Free will]] === Ethics === * [[Wikiphilosophers/Goodness|Goodness]] * [[Wikiphilosophers/Meaning of life|Meaning of life]] * [[Wikiphilosophers/Moral Reasoning|Moral Reasoning]] === Psychology === * [[Wikiphilosophers/Happiness|Happiness]] * [[Wikiphilosophers/Self-improvement|Self-improvement]] [[Category:Wikiphilosophers| ]] 7oxotsb8q19n5w872zx154z9e8ief98 2690154 2690153 2024-12-03T19:45:23Z 152.22.75.23 2690154 wikitext text/x-wiki <center>[[File:Wikiphilosophers.png|150px|link=]] <span style="font-size: 2.6em; font-variant: small-caps">Welcome to Wikiphilosophers!</span><br/> <span style="color: #333; font-size: 1.4em">The philosopedia for the new generation of thinkers<br></span></center> <br> ---- <Secrecy is the practice of hiding information. 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Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. 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Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information. Secrecy is the practice of hiding information.br> '''Wikiphilosophers''' is a project aiming to provide an overview of philosophical ideas from new philosophers and thinkers. On Wikiphilosophers, you can articulate all your philosophical views under the lemma to which they belong. In this way, we collect hundreds of philosophies from today's thinkers! Explore, develop and exchange countless philosophical ideas! == Getting started == What do you think you know for sure? And what assumptions are you making? What are you not quite sure about yet? Try to sort this out for yourself before you get started, by thinking about what philosophical ideas you would like to write about. What is the topic of your philosophical idea about in one or two words? Once you know this, create a new topic page via the button below or go to the existing topic page if it already exists. <br><br> <inputbox> type = create placeholder = Title of the topic, e.g. "Consciousness" or "Free will" buttonlabel = Create a new topic prefix = Wikiphilosophers/ break = no useve = true </inputbox> <br> After that, you can write out your own philosophical view via <code>Wikiphilosophers/<name of topic>/<username></code>. Preferably as short and concise as possible, so that one does not have to read extensive texts. === Starting dialogues === When reading other people's philosophical views, it is possible to start a dialogue on the discussion page. Ask questions if something is not clear to you, preferably through the [[Socratic Methods|Socratic method]]. This creates the opportunity for the writer to develop his philosophical views more deeply. If you understand each other better, you can additionally get inspiration from each other. Just make sure that you always ask questions and don't try to explain your own philosophical views on the discussion page. Because you can do this on your own page. == Topics == === Epistemology === * [[Wikiphilosophers/Foundationalism|Foundational beliefs]] === Ontology === * [[Wikiphilosophers/What there is|What there is]] === Metaphysics === * [[Wikiphilosophers/Universe|Universe]] * [[Wikiphilosophers/Extraterrestrial life|Extraterrestrial life]] * [[Wikiphilosophers/Paranormality|Paranormality]] * [[Wikiphilosophers/Past lives|Past lives]] === Philosophy of mind === * [[Wikiphilosophers/Consciousness|Consciousness]] * [[Wikiphilosophers/Free will|Free will]] === Ethics === * [[Wikiphilosophers/Goodness|Goodness]] * [[Wikiphilosophers/Meaning of life|Meaning of life]] * [[Wikiphilosophers/Moral Reasoning|Moral Reasoning]] === Psychology === * [[Wikiphilosophers/Happiness|Happiness]] * [[Wikiphilosophers/Self-improvement|Self-improvement]] [[Category:Wikiphilosophers| ]] jt11prq4tdbjbijz27j0vuw4e06ny3f 2690155 2690154 2024-12-03T19:45:27Z Tres Libras 2993673 Undid edits by [[Special:Contribs/152.22.75.23|152.22.75.23]] ([[User talk:152.22.75.23|talk]]) to last version by Tres Libras 2690155 wikitext text/x-wiki <center>[[File:Wikiphilosophers.png|150px|link=]] <span style="font-size: 2.6em; font-variant: small-caps">Welcome to Wikiphilosophers!</span><br/> <span style="color: #333; font-size: 1.4em">The philosopedia for the new generation of thinkers<br></span></center> <br> ---- <br> '''Wikiphilosophers''' is a project aiming to provide an overview of philosophical ideas from new philosophers and thinkers. On Wikiphilosophers, you can articulate all your philosophical views under the lemma to which they belong. In this way, we collect hundreds of philosophies from today's thinkers! Explore, develop and exchange countless philosophical ideas! == Getting started == What do you think you know for sure? And what assumptions are you making? What are you not quite sure about yet? Try to sort this out for yourself before you get started, by thinking about what philosophical ideas you would like to write about. What is the topic of your philosophical idea about in one or two words? Once you know this, create a new topic page via the button below or go to the existing topic page if it already exists. <br><br> <inputbox> type = create placeholder = Title of the topic, e.g. "Consciousness" or "Free will" buttonlabel = Create a new topic prefix = Wikiphilosophers/ break = no useve = true </inputbox> <br> After that, you can write out your own philosophical view via <code>Wikiphilosophers/<name of topic>/<username></code>. Preferably as short and concise as possible, so that one does not have to read extensive texts. === Starting dialogues === When reading other people's philosophical views, it is possible to start a dialogue on the discussion page. Ask questions if something is not clear to you, preferably through the [[Socratic Methods|Socratic method]]. This creates the opportunity for the writer to develop his philosophical views more deeply. If you understand each other better, you can additionally get inspiration from each other. Just make sure that you always ask questions and don't try to explain your own philosophical views on the discussion page. Because you can do this on your own page. == Topics == === Epistemology === * [[Wikiphilosophers/Foundationalism|Foundational beliefs]] === Ontology === * [[Wikiphilosophers/What there is|What there is]] === Metaphysics === * [[Wikiphilosophers/Universe|Universe]] * [[Wikiphilosophers/Extraterrestrial life|Extraterrestrial life]] * [[Wikiphilosophers/Paranormality|Paranormality]] * [[Wikiphilosophers/Past lives|Past lives]] === Philosophy of mind === * [[Wikiphilosophers/Consciousness|Consciousness]] * [[Wikiphilosophers/Free will|Free will]] === Ethics === * [[Wikiphilosophers/Goodness|Goodness]] * [[Wikiphilosophers/Meaning of life|Meaning of life]] * [[Wikiphilosophers/Moral Reasoning|Moral Reasoning]] === Psychology === * [[Wikiphilosophers/Happiness|Happiness]] * [[Wikiphilosophers/Self-improvement|Self-improvement]] [[Category:Wikiphilosophers| ]] 7oxotsb8q19n5w872zx154z9e8ief98 2690156 2690155 2024-12-03T19:47:16Z 152.22.75.23 h 2690156 wikitext text/x-wiki == jjuhybgtfvrdeswdefrtghyunbgtrfderftvyuhnijmk,ol.;/.l,kmjnhubgvfcdxscdrvftbgynhuijmko,pl.koijmnhubygvtfrcdexsazwesxdcrtfvgbynhujimk,opl.[;/.kojhyutfvresxdctfvgbyunhijmk,op.;[/ploikjuhyngtvrfdesxcrtfvbgynhuijmk,olp.,okijmnhuybgtfvrdcesxwazsedrcftvgbyhunjimnhuybgtfvrdcesxwazqzwsxedcrfvtgbyhnujuhnbygtvfrcdesxdcrtfvgbynhujbgyvtfcdrtfvgybhunjimk == === Episten === * [[Wikiphilosophers/Foundationalism|Foundational beliefs]] === Ontology === * [[Wikiphilosophers/What there is|What there is]] === Metaphysics === * [[Wikiphilosophers/Universe|Universe]] * [[Wikiphilosophers/Extraterrestrial life|Extraterrestrial life]] * [[Wikiphilosophers/Paranormality|Paranormality]] * [[Wikiphilosophers/Past lives|Past lives]] === Philosophy of mind === * [[Wikiphilosophers/Consciousness|Consciousness]] * [[Wikiphilosophers/Free will|Free will]] === Ethics === * [[Wikiphilosophers/Goodness|Goodness]] * [[Wikiphilosophers/Meaning of life|Meaning of life]] * [[Wikiphilosophers/Moral Reasoning|Moral Reasoning]] === Psychology === * [[Wikiphilosophers/Happiness|Happiness]] * [[Wikiphilosophers/Self-improvement|Self-improvement]] [[Category:Wikiphilosophers| ]] indc9u7ciak3c5902dqt8fo9rw9gpm0 2690157 2690156 2024-12-03T19:47:20Z Tres Libras 2993673 Undid edits by [[Special:Contribs/152.22.75.23|152.22.75.23]] ([[User talk:152.22.75.23|talk]]) to last version by Tres Libras 2690157 wikitext text/x-wiki <center>[[File:Wikiphilosophers.png|150px|link=]] <span style="font-size: 2.6em; font-variant: small-caps">Welcome to Wikiphilosophers!</span><br/> <span style="color: #333; font-size: 1.4em">The philosopedia for the new generation of thinkers<br></span></center> <br> ---- <br> '''Wikiphilosophers''' is a project aiming to provide an overview of philosophical ideas from new philosophers and thinkers. On Wikiphilosophers, you can articulate all your philosophical views under the lemma to which they belong. In this way, we collect hundreds of philosophies from today's thinkers! Explore, develop and exchange countless philosophical ideas! == Getting started == What do you think you know for sure? And what assumptions are you making? What are you not quite sure about yet? Try to sort this out for yourself before you get started, by thinking about what philosophical ideas you would like to write about. What is the topic of your philosophical idea about in one or two words? Once you know this, create a new topic page via the button below or go to the existing topic page if it already exists. <br><br> <inputbox> type = create placeholder = Title of the topic, e.g. "Consciousness" or "Free will" buttonlabel = Create a new topic prefix = Wikiphilosophers/ break = no useve = true </inputbox> <br> After that, you can write out your own philosophical view via <code>Wikiphilosophers/<name of topic>/<username></code>. Preferably as short and concise as possible, so that one does not have to read extensive texts. === Starting dialogues === When reading other people's philosophical views, it is possible to start a dialogue on the discussion page. Ask questions if something is not clear to you, preferably through the [[Socratic Methods|Socratic method]]. This creates the opportunity for the writer to develop his philosophical views more deeply. If you understand each other better, you can additionally get inspiration from each other. Just make sure that you always ask questions and don't try to explain your own philosophical views on the discussion page. Because you can do this on your own page. == Topics == === Epistemology === * [[Wikiphilosophers/Foundationalism|Foundational beliefs]] === Ontology === * [[Wikiphilosophers/What there is|What there is]] === Metaphysics === * [[Wikiphilosophers/Universe|Universe]] * [[Wikiphilosophers/Extraterrestrial life|Extraterrestrial life]] * [[Wikiphilosophers/Paranormality|Paranormality]] * [[Wikiphilosophers/Past lives|Past lives]] === Philosophy of mind === * [[Wikiphilosophers/Consciousness|Consciousness]] * [[Wikiphilosophers/Free will|Free will]] === Ethics === * [[Wikiphilosophers/Goodness|Goodness]] * [[Wikiphilosophers/Meaning of life|Meaning of life]] * [[Wikiphilosophers/Moral Reasoning|Moral Reasoning]] === Psychology === * [[Wikiphilosophers/Happiness|Happiness]] * [[Wikiphilosophers/Self-improvement|Self-improvement]] [[Category:Wikiphilosophers| ]] 7oxotsb8q19n5w872zx154z9e8ief98 0 306587 2690234 2682768 2024-12-04T08:42:18Z CommonsDelinker 9184 Removing [[:c:File:Disposable-vapes-scaled.jpg|Disposable-vapes-scaled.jpg]], it has been deleted from Commons by [[:c:User:Túrelio|Túrelio]] because: [[:c:COM:L|Copyright violation]]: pic from news September 2023; not uploader's own, is spam https://tine 2690234 wikitext text/x-wiki {{title|E-cigarette use motivation:<br>What motivates starting and continuing vaping of nicotine e-cigarettes?}} {{MECR3|1=https://youtu.be/8S1tFh6TPoA}} __TOC__ == Overview == {{IconBoxLeft}} ;Case study A previously healthy 16-year-old male presented with progressive shortness of breath, cough, and hypoxemia in the setting of several months of daily nicotine and THC-containing e-cigarette use. He had been suffering from a chronic cough and intermittent nausea since he started vaping several months before presentation. His cough worsened 1 week before admission to the hospital, accompanied by vomiting induced by coughing and non-bloody diarrhea. He subsequently developed a fever and was evaluated in an Emergency Department. A chest radiograph showed a right lower lobe pneumonia prompting outpatient treatment with bacterial infection medication ([https://www.sciencedirect.com/science/article/pii/S1546084320301504 Shah et al., 2020]). {{IconBoxClose}} [https://en.wikipedia.org/wiki/Electronic%20cigarette Electronic cigarettes] are electronic devices that use a battery powered heating element to disperse liquid, typically a glycerin and/or propylene glycol solution, into an inhalable aerosol ([https://www.mdpi.com/1660-4601/13/7/661 Wadsworth et al., 2016]). This aerosolized liquid contains flavorings, solvents, and the addictive, dependence-producing drug [https://en.wikipedia.org/wiki/Nicotine nicotine] ([https://nyaspubs.onlinelibrary.wiley.com/doi/full/10.1111/nyas.12977 Breland et al., 2017]). Vaping and smoking prevalence in Australia has been trending upward since 2020, with the Australian population aged 14 and over containing 3.5 million smokers and/or vapers, with current smokers (11.8% of the population) outnumbering current vapers (8.9% of the population) (Wakefield et al., 2023). {| class="wikitable" ! Focus questions |- | What motivates people to vape? |- | What are the physical and mental health implications of e-cigarette use? |- | What psychological theories may be applied to e-cigarette use? |} [[File:CDC_electronic_cigarettes_October_2015_(cropped).png|thumb|'''Figure 2'''. Cigarette and e-cigarettes]] == What motivates people to vape? == There are many factors that contribute to the initiation and maintenance of e-cigarette use behaviour. Below are some of the psychological, social, and biological factors that contribute to this behaviour. ==== Reasons for initiating e-cigarette use ==== The most common reason for initiating e-cigarette use or vaping is to stop or reduce tobacco smoking behaviour ([https://journals.sagepub.com/doi/full/10.1080/08897077.2019.1671937 Kinouani et al., 2017]). However, current evidence regarding the effectiveness of e-cigarette use in smoking cessation is inconclusive, and several longitudinal studies have reported that e-cigarette use is associated with a greater risk of initiating the use of tobacco smoking products among adolescents and young adults ([https://journals.sagepub.com/doi/full/10.1080/08897077.2019.1671937 Kinouani et al., 2017]). Smokers who initiate e-cigarette use for cessation rather than recreation or enjoyment purposes are more likely to have greater nicotine dependence, cigarette consumption, and e-cigarette consumption, however, motivations and use differ and are related to both consumption and dependence on nicotine e-cigarette products ([https://www.sciencedirect.com/science/article/pii/S2211335522002315 Temourian et al., 2022]). A qualitative interview-based study of e-cigarette use motivation in smokers and non-smokers revealed that non-smokers cited social reasons for e-cigarette use, such as peer influence and social norms, whereas, smokers or ex-smokers often cited health reasons for initiating e-cigarette use ([https://onlinelibrary.wiley.com/doi/full/10.1002/hpja.442 Amin et al., 2021]). ==== Socioeconomic status, adverse childhood events and e-cigarette use ==== Smoking and e-cigarette use is unequally distributed between people of different socioeconomic status, with higher smoking prevalence in lower status groups, contributing to health inequities ([https://www.sciencedirect.com/science/article/pii/S2352853219301725 Jahnel et al., 2020]). A study by [https://www.sciencedirect.com/science/article/pii/S2352853219302032 Williams et al., 2020] examined adverse childhood experiences and early initiation of e-cigarette use behaviour in Nevada. Findings suggested a strong positively graded relationship between cumulative adverse childhood experience exposure and early initiation of electronic vapour product use in a middle school aged population. ==== Attitudes and education around e-cigarettes ==== Understanding individuals' perceptions around the relative safety of a behaviour provides a basis for a predictive relationship between perception/attitude and engagement in the behaviour ([https://onlinelibrary.wiley.com/doi/full/10.1111/dar.12984 Erku et al., 2019]). There appears to be a direct relationship between smokers' perception of the relative harm of tobacco cigarettes and nicotine vaping products (NVPs) and the likelihood of switching from smoking to vaping ([https://onlinelibrary.wiley.com/doi/full/10.1111/dar.12984 Erku et al., 2019]). A longitudinal study found that smokers and ex-smokers who perceived NVPs as less harmful were subsequently more likely to try them, however, a considerable portion of interviewed smokers reported a lack of knowledge about the relative safety ([https://onlinelibrary.wiley.com/doi/full/10.1111/dar.12984 Erku et al., 2019]). There are various reasons contributing to the significant rise in adolescent vaping. This includes misconceptions about the safety of e-cigarettes, lower prices than traditional tobacco cigarettes, a variety of flavours such as fruits and candy, and social or peer pressure ([https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9195082/ Javed et al., 2022]). ==== Psychosocial factors relating to e-cigarette use ==== E-cigarette use studies have identified many psychosocial factors associated with the behaviour, such as difficulties with studying, school stress, problems communicating with parents, and generalised trust ([https://www.sciencedirect.com/science/article/pii/S0033350617304031 Lindstrom & Rosvall, 2018]). Other psychosocial factors identified include home use of e-cigarette products, friends' use of and positive attitudes towards usage, and harm perception. These were all found to be strongly positively associated with e-cigarette use behaviour ([https://publications.aap.org/pediatrics/article-abstract/136/2/308/33811/Psychosocial-Factors-Associated-With-Adolescent Barrington-Trimis et al., 2015]). A study of university students attending an Appalachian university stated that the most common motivator for e-cigarette use was stress reduction, followed by the good taste, friends' usage, and wanting to quit cigarettes ([https://www.tandfonline.com/doi/full/10.1080/10826084.2021.1914102 Wattick et al., 2021]). ==== Biological factors and addiction ==== The chemical nicotine, found in e-cigarettes and vapes, interacts with an individual's nicotinic acetylcholine receptors, initiating the release of neurotransmitters ([https://www.mdpi.com/1422-0067/24/19/14570 Sansone et al., 2023]). The predominant neurotransmitters that nicotine consumption releases include dopamine, norepinephrine, acetylcholine, serotonin, GABA, glutamate, and endorphins ([https://www.mdpi.com/1422-0067/24/19/14570 Sansone et al., 2023]). The release of these neurotransmitters induce sensations of pleasure, stimulation, and mood modulation ([https://www.mdpi.com/1422-0067/24/19/14570 Sansone et al., 2023]). Activation of these receptors establishes new neural pathways, and, in conjunction with environmental cues, behavioural conditioning occurs ([https://www.mdpi.com/1422-0067/24/19/14570 Sansone et al., 2023]). Between periods of nicotine consumption, or after discontinuing nicotine use, levels of nicotine in the brain decline, causing reductions in dopamine and other neurotransmitters, and symptoms such as craving and withdrawal ([https://www.mdpi.com/1422-0067/24/19/14570 Sansone et al., 2023]). {{RoundBoxTop|theme=2}} ; Quiz Choose your answers and click "Submit": <quiz display="simple"> {What is the most common motivation for initiating e-cigarette use? |type="(True)"} + Cigarette smoking cessation - Colourful packaging - Sweet and fun flavours </quiz> {{RoundBoxBottom}} ==== Maintenance of e-cigarette use behaviour ==== Little is known about the effects of long-term e-cigarette use, however findings suggest that the risk of relapse to combustible cigarette use is low ([https://www.sciencedirect.com/science/article/pii/S0749379719302156?casa%20token=JgVEZE0sniQAAAAA:%20r9Bmhd7kfGTmD-R5rFDlUKUVaf9qapKnm2vyW-F6HOYUgFEAzksYgYZ-dj8GNwBuwJ2cCUd Du & Fan et al., 2019]). Findings also suggest that e-cigarette dependence remains stable in long-term e-cigarette users ([https://www.sciencedirect.com/science/article/pii/S0749379719302156?casa%20token=JgVEZE0sniQAAAAA:%20r9Bmhd7kfGTmD-R5rFDlUKUVaf9qapKnm2vyW-F6HOYUgFEAzksYgYZ-dj8GNwBuwJ2cCUd Du & Fan, 2019]). Nicotine dependence is a factor of e-cigarette use maintenance and resistance to cessation, however a 2018 study from [https://www.sciencedirect.com/science/article/abs/pii/S0306460317302885 Browne and Todd] suggests that motivations for vaping are less dominated by nicotine delivery ([https://en.wikipedia.org/wiki/Reinforcement negative reinforcement]), and may be driven by [https://en.wikipedia.org/wiki/Reinforcement positive reinforcement] factors. == What are the physical and mental health implications of e-cigarette use? == {{expand}} ===== Physical health effects of e-cigarette use ===== [[File:LungCACXR.PNG|thumb|200px|Figure 3. Lung cancer{{expand}}]] Research on the long-term health effects of the orally-ingested toxicants delivered via aerosolized vapor in e-cigarettes is limited, however, there is rising concern about the health impacts among youth who begin using e-cigarettes at an early age ([https://www.sciencedirect.com/science/article/pii/S2352853219302032 Williams et al., 2020]). Many of the volatile organic compounds found in the saliva and urine samples of e-cigarette users are carcinogenic ([https://publications.aap.org/pediatrics/article-abstract/141/4/e20173557/37730/Adolescent-Exposure-to-Toxic-Volatile-Organic Rubinstein et al., 2018]). From March 2019 to February 2020, The Centers for Disease Control and Prevention stated that more than 2,807 cases of lung injury associated with e-cigarette use were reported ([https://journals.sagepub.com/doi/full/10.1177/0022042620921351?casa_token=WeqPz-sZSEQAAAAA%3AMHaFUe4jh4J09P7TrTVubJbFd8tuYWtAP8cFbPitotUKT8cbYknZS6D-67xmc7kfvGBgYuDhuqM Rocheleau, 2020]). Furthermore, as of 2020, there were 68 deaths associated with e-cigarette use across 29 states in the U.S. ([https://journals.sagepub.com/doi/full/10.1177/0022042620921351?casa_token=WeqPz-sZSEQAAAAA%3AMHaFUe4jh4J09P7TrTVubJbFd8tuYWtAP8cFbPitotUKT8cbYknZS6D-67xmc7kfvGBgYuDhuqM Rocheleau, 2020]) ===== Mental health effects of e-cigarette use ===== Nicotine, the addictive chemical component of e-cigarettes, has been shown to cause severe impairment to the growing brain leading to cognitive and psychiatric issues, such as depression, anxiety, violence, other substance abuse, and suicidality ([https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9195082/ Javed et al., 2022]). In adolescents, depressive symptoms predict an increased likelihood of initiating e-cigarette use, but sustained e-cigarette use is associated with an increase in depressive symptoms, and higher frequency of e-cigarette use is associated with higher rates of depressive symptoms ([https://www.sciencedirect.com/science/article/pii/S0091743516304388?casa%20token=d-o3LzpTib0AAAAA:dB-%20wckQbzxTRH-8qIoHruVLjKkGV3tJyS8SbqjBShfulEuzSQHyZYSwhW-Da5sgs0Mc3fjPd5so Lechner et al., 2017]). Although e-cigarette use has detrimental mental health effects, the prevalence of e-cigarette use is significantly higher amongst adults with serious psychological distress ([https://academic.oup.com/ntr/article/22/10/1875/5819790?login=true Weinberger et al., 2020]). The implications of these findings are crucial for approaches to public health and youth wellbeing, as they identify the demographic factors and predictors of the behaviour and the consequences of the behaviour. ===== Nicotine use in adolescents ===== There is a plethora of epidemiological evidence demonstrating that adolescents are more likely to use nicotine, and that nicotine exposure in adolescents causes a greater risk of long-term nicotine dependency ([https://www.sciencedirect.com/science/article/pii/S0028390808003249 O'Dell, 2009]).Adolescents, compared to adults, experience enhanced short-term positive effects and reduced aversive effects when using nicotine ([https://www.sciencedirect.com/science/article/pii/S0028390808003249 O'Dell, 2009]).{{ic|Peer review comment: The information is good but ensure you expand on it and relate it back to the question, why is the information you've presented useful? Consider the implications more.}} == What psychological theories may be applied to e-cigarette use? == {{expand}} ===== Theory of Planned Behaviour ===== [[File:Theory_of_planned_behavior.png|thumb|300px|Figure 4. Ajzen's theory of planned behaviour]] Ajzen's [https://en.wikipedia.org/wiki/Theory_of_planned_behavior theory of planned behaviour] posits that attitudes, subjective norms, and perceived behavioural control all contribute to intentions to perform behaviours ([https://www.sciencedirect.com/science/article/abs/pii/074959789190020T Ajzen, 1991]). In this context, the performed behaviour is e-cigarette use, and the theory of planned behaviour (TPB) components (attitude, subjective norms, perceived behavioural control) all influence an individual's intention as to whether they will perform this behaviour. A study from the [https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1360-0443.1992.tb02742.x?_gl=1*1ckdt8g*_gcl_au*NTU0Nzg5NTIzLjE3MjE0NDQ5NDA. British Journal of Addiction] found that for adult smokers in the general population, perceived behavioural control, attitudes and subjective norms were contributing to intention regarding cigarette-smoking behaviour ([https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1360-0443.1992.tb02742.x Godin et al., 1992]). The most current version of the TPB proposes that perceived behavioural control moderates the effects of subjective norm and attitude on intention ([https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7909507/ LaBarbera & Ajzen, 2020]). This new theory posits that greater perceived behavioural control tends to strengthen the relative importance of attitude in the prediction of intention, whereas it tends to weaken the relative importance of subjective norm ([https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7909507/ LaBarbera & Ajzen, 2020]) ===== Social Learning Theory ===== [https://en.wikipedia.org/wiki/Social%20learning%20theory Social learning theory], originally proposed by [https://www.simplypsychology.org/bandura.html Albert Bandura], primarily focuses on the importance of interactions one has with others in their peer group ([https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118512449.ch12 Akers & Jennings, 2015]), and posits that people learn through observing, imitating, and modelling others' behaviour ([https://www.researchgate.net/profile/Mohammad-Bijandi/publication/367203768%20Bandura's%20Social%20Learning%20Theory%20Social%20Cognitive%20Learning%20Theory/links/63c6a10bd7e5841e0bd70276/Banduras-Social-Learning-Theory-Social-Cognitive-Learning-Theory.pdf Nabavi, 2012]). Findings from a study utilising a social learning approach to e-cigarette use found that higher levels of peer e-cigarette use contribute to higher odds of personal e-cigarette use ([https://journals.sagepub.com/doi/full/10.1177/0022042620921351 Rocheleau et al., 2020]).{{ic|Peer review comment: Include a section on why people maintain vaping and using e-cigarettes. The chapter speaks well about the initiation of this behaviour but doesn't touch on maintenance enough considering the focus question. Consider adding some more review questions throughout}} == Conclusion == Electronic cigarettes are electronic devices that use a battery powered heating element to disperse liquid, typically a glycerin and/or propylene glycol solution, into an inhalable aerosol (Wadsworth et al.,2016), containing flavourings, solvents, and the addictive, dependence-producing drug nicotine (Breland et al., 2017).{{ic|repetitive of Overview}} The current {{what}} literature suggests that reasons for initiation and maintenance of e-cigarette use behaviour vary, however the most common motivation is cessation {{gr}} cigarette smoking behaviour (Kinouani et al., 2017). Lower socioeconomic status and adverse childhood experiences contribute to higher rates of e-cigarette use (Williams et al., 2020), as well as variations in individual attitudes and e-cigarette education (Erku et al., 2019), as well as psychosocial factors such as such as difficulties with studying, school stress, problems communicating with parents, and generalised trust (Lindstrom & Rosvall, 2018). E-cigarette use is associated with detrimental mental and physical health effects, with adolescents being the demographic most likely to be exposed to, and use, nicotine (O'Dell, 2009). Ajzen's theory of planned behaviour and Bandura's social learning theory are both relevant frameworks for understanding the initiation and maintenance of e-cigarette use behaviour. {{ic|What are the practical, take-home messages?}} == See also == {{ic|Use bullet points as shown in Tutorial 2}} [[Motivation_and_emotion/Book/2013/Nicotine_and_emotion|Nicotine and Emotion: what is the effect of nicotine on emotion?]] (book chapter) [https://en.wikipedia.org/wiki/Electronic_cigarette#Society_and_culture Vaping - Society and Culture] (wiki page) == References == {{Hanging indent|1= Ajzen, I. (1991). The theory of planned behavior. ''Organizational behavior and human decision processes, 50''(2), 179-211. Akers, R. L., & Jennings, W. G. (2015). Social learning theory. ''The handbook of criminological theory'', 230-240. Amin, S., Dunn, A. G., & Laranjo, L. (2021). Why do people start or stop using e‐cigarettes in Australia? A qualitative interview‐based study. ''Health Promotion Journal of Australia, 32'', 358-366. Barrington-Trimis, J. L., Berhane, K., Unger, J. B., Cruz, T. B., Huh, J., Leventhal, A. M., & McConnell, R. (2015). Psychosocial factors associated with adolescent electronic cigarette and cigarette use. Pediatrics, 136(2), 308-317. Breland, A., Soule, E., Lopez, A., Ramôa, C., El‐Hellani, A., & Eissenberg, T. (2017). Electronic cigarettes: what are they and what do they do?. ''Annals of the New York Academy of Sciences, 1394''(1), 5-30. Browne, M., & Todd, D. G. (2018). Then and now: Consumption and dependence in e-cigarette users who formerly smoked cigarettes. Addictive behaviors, 76, 113-121. Du, P., Fan, T., Yingst, J., Veldheer, S., Hrabovsky, S., Chen, C., & Foulds, J. (2019). Changes in e-cigarette use behaviors and dependence in long-term e-cigarette users. American journal of preventive medicine, 57(3), 374-383. Erku, D. A., Gartner, C. E., Tengphakwaen, U., Morphett, K., & Steadman, K. J. (2019). Nicotine vaping product use, harm perception and policy support among pharmacy customers in Brisbane, Australia. ''Drug and Alcohol Review, 38''(6), 703-711. Jahnel, T., Ferguson, S. G., Partos, T., & Brose, L. S. (2020). Socioeconomic differences in the motivation to stop using e-cigarettes and attempts to do so. ''Addictive Behaviors Reports, 11'', 100247. Javed, S., Usmani, S., Sarfraz, Z., Sarfraz, A., Hanif, A., Firoz, A., ... & Ahmed, S. (2022). A scoping review of vaping, e-cigarettes and mental health impact: depression and suicidality. ''Journal of community hospital internal medicine perspectives, 12''(3), 33. Kinouani, S., Leflot, C., Vanderkam, P., Auriacombe, M., Langlois, E., & Tzourio, C. (2020). Motivations for using electronic cigarettes in young adults: A systematic review. ''Substance abuse, 41''(3), 315-322. La Barbera, F., & Ajzen, I. (2020). Control interactions in the theory of planned behavior: Rethinking the role of subjective norm. Europe's Journal of Psychology, 16(3), 401. Lechner, W. V., Janssen, T., Kahler, C. W., Audrain-McGovern, J., & Leventhal, A. M. (2017). Bi-directional associations of electronic and combustible cigarette use onset patterns with depressive symptoms in adolescents. ''Preventive medicine, 96'', 73-78. Lindström, M., & Rosvall, M. (2018). Addictive behaviors, social and psychosocial factors, and electronic cigarette use among adolescents: a population-based study. Public Health, 155, 129-132. Nabavi, R. T. (2012). Bandura’s social learning theory & social cognitive learning theory. ''Theory of Developmental Psychology, 1''(1), 1-24. O'Dell, L. E. (2009). A psychobiological framework of the substrates that mediate nicotine use during adolescence. Neuropharmacology, 56, 263-278. Rocheleau, G. C., Vito, A. G., & Intravia, J. (2020). Peers, perceptions, and e-cigarettes: A social learning approach to explaining e-cigarette use among youth. ''Journal of drug issues, 50''(4), 472-489. Rubinstein, M. L., Delucchi, K., Benowitz, N. L., & Ramo, D. E. (2018). Adolescent exposure to toxic volatile organic chemicals from e-cigarettes. ''Pediatrics, 141''(4). Sansone, L., Milani, F., Fabrizi, R., Belli, M., Cristina, M., Zagà, V., ... & Russo, P. (2023). Nicotine: From discovery to biological effects. International Journal of Molecular Sciences, 24(19), 14570. Shah, J., Mullen, M., & Lu, M. (2020). E-cigarette or vaping product use–associated lung injury: a case study and review of the literature. ''Journal of Radiology Nursing, 39''(4), 305-308. Temourian, A. A., Song, A. V., Halliday, D. M., Gonzalez, M., & Epperson, A. E. (2022). Why do smokers use e-cigarettes? A study on reasons among dual users. ''Preventive Medicine Reports, 29'', 101924. Wadsworth, E., Neale, J., McNeill, A., & Hitchman, S. C. (2016). How and why do smokers start using e-cigarettes? Qualitative study of vapers in London, UK. ''International Journal of Environmental Research and Public Health, 13''(7), 661. Wakefield, M., Haynes, A., Tabbakh, T., Scollo, M., & Durkin, S. (2023). Current vaping and current smoking in the Australian population aged 14+ years: February 2018-March 2023. ''Melbourne: Centre for Behavioural Research in Cancer, Cancer Council Victoria''. Wattick, R. A., Olfert, I. M., & Olfert, M. D. (2021). Psychosocial factors associated with E-cigarette use among young adults in a 4-year university in appalachia. Substance Use & Misuse, 56(8), 1182-1189. Weinberger, A. H., Zhu, J., Barrington-Trimis, J. L., Wyka, K., & Goodwin, R. D. (2020). Cigarette use, e-cigarette use, and dual product use are higher among adults with serious psychological distress in the United States: 2014–2017. Nicotine and Tobacco Research, 22(10), 1875-1882. Williams, L., Clements-Nolle, K., Lensch, T., & Yang, W. (2020). Exposure to adverse childhood experiences and early initiation of electronic vapor product use among middle school students in Nevada. ''Addictive Behaviors Reports, 11'', 100266. }} == External links == {{ic|Use bullet points as shown in Tutorial 2}} [https://www.health.gov.au/give-up-for-good?gad%20source=1&gclid=Cj0KCQjwu-63BhC9ARIsAMMTLXQafvvf8FYKhW19FPvDhuLNCkB1SqSmHLzfsRZyQhubPtdOJLAKEvYaApzBEALw%20wcB&gclsrc=aw.ds Quit Vaping], Australian Government [https://www.health.gov.au/ministers/the-hon-mark-butler-mp/media/new-supports-to-quit-vaping-and-smoking New Supports to Quit Vaping and Smoking], Department of Health and Aged Care [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Drugs/Nicotine]] [[Category:Motivation and emotion/Book/Motivation]] 43b7qso784x9trhundvejn5ovbthq1y 0 306856 2690181 2687944 2024-12-04T01:00:42Z CommonsDelinker 9184 Removing [[:c:File:Washing_Hands.jpg|Washing_Hands.jpg]], it has been deleted from Commons by [[:c:User:Yann|Yann]] because: per [[:c:COM:NETCOPYVIO|]]. 2690181 wikitext text/x-wiki {{title|Disgust and hygiene:<br>How does disgust influence hygiene behaviours and what are the psychological mechanisms involved?}} {{MECR3|1=https://www.youtube.com/watch?v=Qx7rJf87QX4}} __TOC__ ==Overview== {{robelbox|width=30|theme=14|title=Scenario}} <div style="{{Robelbox/pad}}"> Imagine entering a public restroom with many people inside, where you experience the smell of a foul odour. In this scenario, this strong emotion experienced is referred to as disgust. The reaction to this odour may induce behaviours to improve or maintain one's cleanliness or hygiene. </div> {{Robelbox/close}} Disgust is an ancient survival mechanism that is hardwired into our system to protect us from sensed dangers by motivating avoidant behaviour(s). However, disgust is not a general reaction as some people are more sensitive to it than others, leading to different hygiene habits and behaviours (see Obsessive Compulsive Disorder {{ic|add link}}). Disgust shapes an individual's daily decisions, for example, avoiding a sticky subway pole or obsessive wiping down surfaces (Olatunji et al., 2007). This chapter reviews the root of disgust, its role as a protective mechanism, and how it informs hygiene behaviours to emphasise further how this important emotion can be utilised in public health and disease prevention. {{RoundBoxTop|theme=9}} '''Focus questions:''' *How does disgust function as a protective emotional response? *What are the psychological mechanisms linking disgust to hygiene behaviours? *How do individual differences in disgust sensitivity impact hygiene practices? {{RoundBoxBottom}} == Understanding disgust == Disgust is a [https://www.ncbi.nlm.nih.gov/books/NBK559106/ defence mechanism] to keep people safe from toxins and illness. Beyond just physical responses, social and moral disgust also affects our interactions and behaviour. People differ in how sensitive they are to disgust, and this motivates how they choose to avoid perceived contaminants and how they maintain their daily hygiene.<ref>{{Cite journal|last=Oaten|first=Megan|last2=Stevenson|first2=Richard J.|last3=Case|first3=Trevor I.|date=2009|title=Disgust as a disease-avoidance mechanism.|url=http://doi.apa.org/getdoi.cfm?doi=10.1037/a0014823|journal=Psychological Bulletin|language=en|volume=135|issue=2|pages=303–321|doi=10.1037/a0014823|issn=1939-1455}}</ref> === Origin === Disgust is an ancient emotions that protects us from dangerous substances that could ultimately result in death. The feeling of disgust closely relates to the behavioural immune system, which Schaller and Park (2011) defined as a mechanism that includes "psychological mechanisms of the detection and further avoidance of the organisms carrying pathogens.". From an evolutionary perspective, disgust likely developed to avoid ingesting toxic or spoiled food, infectious agents, or other harmful environmental circumstances. Disgust has thus evolved from what may threaten the body to moral and social disgust, in which taboo practices or actions result in similar emotional reactions (Rozin et al., 2008). Most disgust evokes the perception of contamination or violation of body purity. For this reason, disgust can be considered an evolutionarily selected defence mechanism for minimising contact with pathogens.{{f}} === Disgust as a defence mechanism === Disgust has evolved to be an important protective mechanism that humans have against potential sources of sickness. The avoidance behaviours motivated by disgust (for instance avoiding spoiled food and avoiding contact with sick people) play a crucial role in minimising the probability of infection and getting sick (Curtis et al., 2011). This behavioural action reduces contact with carriers of infection agents, especially when those agents would not otherwise be visible or even detectable, as in the cases of bacteria and viruses. The cue for this emotion comes with sensory signals of possible danger such as fluids of the body, decaying flesh and filth. Research has also indicated that disgust is not solely confined to physical contamination but also to social behaviours. For example, some social-interpersonal actions, such as betrayal or any form of social norm violation, may be well reflected in triggering another variant of disgust, namely moral disgust, which is adaptive in maintaining social bonding and preventing destructive behaviour against the members of one's group (Tybur et al., 2009). Hence why, people avoid these physical and social contaminants to avoid falling sick and putting themselves in a given social order{{g}}. == Disgust and Hygiene Behaviours == Disgust is an adaptive mechanism used to avoid illness. It motivates hygienic practices, like hand washing, which are essential for avoiding disease. Disgust can be divided into three domains: moral, sexual, and pathogen{{f}}. Pathogen disgust is strongly associated with preventive measures taken to prevent illness.<ref>{{Cite journal|last=Curtis|first=Valerie|last2=de Barra|first2=Mícheál|last3=Aunger|first3=Robert|date=2011-04-27|title=Disgust as an adaptive system for disease avoidance behaviour|url=https://royalsocietypublishing.org/doi/10.1098/rstb.2011.0002|journal=Philosophical Transactions of the Royal Society B: Biological Sciences|language=en|volume=366|issue=1568|pages=1320–1320|doi=10.1098/rstb.2011.0002|issn=0962-8436|pmc=PMC3061113}}</ref> === How disgust drives hygiene practices === Concerning hygiene behaviours, disgust is a primary motivator, and cleaning, washing, or sanitising would help people avoid contamination{{f}}. Various studies{{f}} found that the more disgusting a person feels, the more he or she is interested in washing his/her hands or refraining from touching a dirty surface (Curtis & Biran, 2001){{expand}}. Most significantly, it manifests itself in health settings in that health workers who perceive disgust sensitivity show more concern for hygiene practices such as washing their hands and wearing gloves (Stevenson et al., 2009). There is a remarkable automatism in the association of disgust and hygiene with the elicitation of a disgust elicitor. For example, dirt or bodily fluids prompting immediate action to remove the contaminant. This is why the disgust-based intervention-public health campaigns using images of germs or dirty hands are a very efficient way of enhancing hygiene behaviours, such as washing hands, in cases of outbreaks of infectious diseases. === The role of disgust in everyday hygiene choices === Disgust controls individual choices regarding standard hygiene behaviours. It might become an obsessive cleaning of items someone touches, washing hands, or simply avoiding sights and places perceived as filthy. Many individuals avoid public restrooms due to their relationship with dirt and germs. Individuals with a high propensity for Disgust also try avoiding food consumption in places perceived as unhygienic (Olatunji et al., 2007). Disgust influences consumer behaviour toward hygiene products such as disinfectants, hand sanitisers, and anti-bacterial soaps. Selling these products often depends on appealing to people's disgust sensitivity by overemphasising that one cannot see most hazards presented by germs and dirt. Thus, people make hygiene choices based on physical cues, such as visible dirt or perceived threats, such as invisible germs.{{f}} == Psychological mechanisms of disgust == {{expand}} === Disgust sensitivity: individual differences === Disgust sensitivity defines the degree to which an individual is disgusted by something. Individuals vary significantly in their susceptibility to disgust; this variation affects their hygiene practices{{f}}. Individuals with high disgust sensitivity would be pretty observant of hygiene practices such as frequently washing hands, avoiding public restrooms, and cleaning the environment (Tybur et al., 2009). Individual differences may be traced to genetic causes and variations in early life experiences{{f}}. One earlier hypothesis was that individuals who grow up in an environment where the perceived threat of contamination is high, for example, poor sanitation, develop heightened disgust sensitivity that extends well into adulthood (Stevenson et al., 2009). === Cognitive and Behavioural Links Between Disgust and Hygiene === The cognitive and behavioural links between disgust and hygiene intervenes to evoke the relationship between disgust and hygiene behaviours through behavioural and cognitive factors{{rewrite}}. Cognitively, it operates on a system of learned associations whereby given stimuli-for instance, dirt and bodily fluids-become associated in the mind with contamination and diseases. These cognitive associations then translate to avoidance behaviours wherein one would be disinclined to touch contaminated things or quickly wash one's hands after touching such things (Olatunji et al., 2007). It appeases the protective mechanisms against harm through behavioural means. The responses include hygiene behaviours like cleaning and disinfection and avoidance of direct contact with unclean surfaces. Hygiene behaviour is habitual over time through continuous learning from past experiences that have reinforced a relationship between disgusting stimuli and hygiene. === Evolutionary Perspective on Disgust and Hygiene === Most likely, Disgust has evolved as a protection against pathogens. Following the evolutionary theory, Disgust as supposed to be an adaptative{{sp}} reaction to avoid contamination: for example, spoiled foods, body fluids, and signs of disease - Schaller & Park, 2011. Immediately, this feeling of Disgust appeals to specific actions - for example, avoiding contaminated objects or cleaning to minimise chances of infection. This view has been instigated further by studies{{f}} pointing out that disgust sensitivity is greater among individuals considering health and cleanliness a priority (Oaten et al., 2009). ==== Neural Mechanisms of Disgust ==== FMRI studies have also localised the activation of disgust to the anterior insula (Figure 2) and basal ganglia, brain regions involved in visceral and motor reactions. In this way, the disgust response can arise from emotive and physical responses, such as washing hands or avoiding objects perceived as contaminated (Calder et al., 2001). [[File:Insular Cortex Sub-regions.png|center|thumb|'''Figure 2''': Imaging of insular cortex, neural area related to disgust.]] === Cognitive-Behavioural Theories of Disgust === Cognitive theories support that feelings of disgust occur when an individual appraises the immediate environment for threats. For instance, Tybur et al. 2013 support that the emotional reactions of disgust include the cognitive appraisal of the risk of contamination; therefore, automated appraisals guide behaviours, including avoiding contact with contaminated objects and washing hands following exposure to unhygienically presented environments{{g}}. === Disgust Sensitivity in Hygiene Behaviours === In {{what}} literature, it has been highlighted that disgust sensitivity could be considered an essential predictor of hygiene behaviour; an individual reacts with greater sensitivity while increasing their engagement in behaviours of a preventive health character: hand washing, avoidance of public restrooms to avoid infectious diseases, etc. (Stevenson et al., 2009). This is true in environments where the perceived risk of contamination is high, such as hospitals or public transportation (Curtis & Biran, 2001). === Disgust as a Multidimensional Emotion === Disgust can be divided into several domains, including: '''Pathogen Disgust:''' It is concerned with contamination and disease avoidance. '''Social Disgust:''' the breach of social norms due to cruelty and deception. '''Sexual Disgust:''' Related to inappropriate or unclean behaviours (Tybur et al., 2013). This is important in the conceptualisation of these domains since different types of disgust variably influence hygiene behaviours. For example, whereas pathogen disgust is directly related to behaviours such as washing one's hands, moral disgust contributes to keeping oneself distant from others or avoiding certain public facilities (Curtis et al., 2011). == Real World Application == {{expand}} === Disgust and Public Health Interventions === Our understanding of disgust has been used in public health communications to promote healthy hygiene behaviours. The disgust created from correct handwashing technique initiatives, either featuring dirty hand images or of contaminated surfaces, makes hygiene practices more probable among the populace, as shown by Reynolds and Seeger (2005){{expand}}. This was particularly important during pandemics, such as the Coronavirus Disease of 2019, when contamination avoidance was a critical factor in public health, as the World Health Organization (World Health Organization, 2020) showed. === Disgust in Educational and Public Spaces === Disgust can be utilised as an educational tool to enhance hygiene behaviour in children and the public. The concept of germs and contamination, combined with graphics that could create a moderate degree of disgust, is successful in hygiene handwashing in schools (Reynolds & Seeger, 2005). Similarly, visual reminders in public places such as bathrooms, airports, or other transportation hubs may also increase hand-washing or the use of hand sanitisers, especially when combined with themes of disgust about dirty hands or contaminated surfaces. === Disgust in Healthcare Settings === In the context of health, disgust serves as a crucial means for healthcare practitioners to act with good hygiene practices. Since they are in frequent contact with potentially contagious substances through bodily fluids, Personal Protective Equipment (PPE) (like gloves, masks, or hand sanitisers) is used. Acting according to proper hygiene guidelines, results in the safety of medical workers and their patients. Over time, health professionals may become somewhat "desensitised" to disgust, whereby hygiene practices over time tend to worsen rather than improve (Davey, 2011). Hence, regular training and intervention programs pointing out the importance of hygiene are also relevant to practice consistency and safety. Public health communications that express the disgusting nature of any infection/contamination have also been shown to increase health care professional's chances of practicing good hygiene. For example, hospitals that employ visual suggestions on the need for good hygiene practices and against contamination (such as through the display of fliers and posters showing pictures of germs) often record heightened levels of compliance to good hygiene practices (Curtis et al., 2011). === Disgust and Hygiene Across Cultures === Not every culture equally perceives disgust hygiene behaviour, for example, in more societies where pathogens are less common, through an exaggerated sense of disgust, people adaptively develop a tendency to avoid infection and therefore, have a likelihood of developing sickness (Stevenson et al., 2009). For instance, it has been highlighted that in cultures where food-borne illnesses are more common, hygiene behaviours regarding food avoid contaminants, such as uncooked or spoiled food are less practiced (Tybur et al., 2013). This also has implications for the public health campaigns themselves: Any promotion of hygiene practices must be framed with an awareness of cultural differences. Besides variation in pathogen disgust, there is also variation in moral and sexual disgust that may indirectly influence hygiene practices. For instance, strict moral codes about purity and cleanliness in some cultures may fire stronger disgust responses and, hence, more frequent, or more elaborate hygiene rituals (Curtis & Biran, 2001). The understanding of such differences in the sensitivity of disgust are of importance for the development of public health programs that effectively promote hygiene behaviour accommodating for different cultures. === Disgust sensitivity in vulnerable populations === Sensitivity can be extreme in certain populations, for example, germaphobes or those afflicted with obsessive-compulsive disorder (OCD). Individuals with OCD often demonstrate a heightened disgust sensitivity, especially to contamination-related stimuli. Such heightened disgust sensitivity might give rise to compulsive cleaning and hand-washing behaviours, which, although, in the short-term alleviating anxiety, might become damaging to relationships, work etc. (Olatunji et al., 2007). For such populations, a clear understanding of the operation of disgust becomes very important for the building of treatments to manage these extreme responses without causing further distress. [[File:Obsessive Compulsive Disorder (8970250666).jpg|thumb|Figure 3: Sorting M&M's{{g}} by colour code is a common Complulsive{{sp}} behaviour{{f}}''' {{Robelbox|width=30|theme={{{theme|3}}}|title=Case Study based on Person with OCD (Kaye, 2021)}} <div style="{{Robelbox/pad}}"> Steve is a 56-year-old male who generally has always felt anxious. Contamination and mistake-related fears over time mounted. Compulsions started, such as repeatedly washing one's hands and checking locks and windows. He develops anxiety about illnesses that he knows are irrational, but he checks and rechecks many things numerous times daily. It interfered with his work life and family life. Symptoms worsened, and John sought treatment. Fortunately, these compulsive behaviours subsided with the help of CBT incorporating ERP, hence helping him get his life back.{{ic|Explain what this has to do with disgust}} </div> {{Robelbox/close}} === Quiz === <quiz display="simple"> What happens when someone has a strong sense of disgust? |type="()"} + They avoid things that seem dirty or dangerous - They become curious about gross things - They ignore hygiene completely - They want to touch everything {Why might people from different countries react differently to the same disgusting thing? |type="()"} - Because everyone has the same experiences + Because {{missing}} of different cultural backgrounds and traditions - Because they all watch the same movies - Because they all live in the same climate </quiz> ==Conclusion== Disgust is an adaptive emotional response developed to prevent individuals from coming into contact with dangerous substances or acquiring infections. According to psychological theories and studies, disgust is an adaptive emotion that fosters cleanliness to help prevent illness (Curtis et al., 2011). The two psychological mechanisms linking disgust to hygiene are through cognitive appraisal leading to avoidance behaviours of perceived contamination. However, such behaviours depend on variations in the degree of sensitivity to disgust. Individuals susceptible to disgust are likely to show frequent hygiene practices, whereas individuals of low sensitivity may require another approach to motivate (Tybur et al., 2013; Olatunji et al., 2007). Appreciation of this function of disgust does have some potential to help health promotion campaigns more effectively respond to individual differences with more effective health promotion. ==See also== [[w:Disgust|Disgust]] (Wikipedia) [[w:Hygiene|Hygiene]] (Wikipedia) [[w:Obsessive_compulsive_disorder|Obsessive-compulsive disorder]] (Wikipedia) ==References== {{Hanging indent|1= Calder, A. 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Biological Sciences, 366(1583), 3453–3465. https://doi.org/10.1098/rstb.2011.0039 Oaten, M., Stevenson, R. J., & Case, T. I. (2009). Disgust as a disease-avoidance mechanism. Psychological Bulletin, 135(2), 303-321. https://doi.org/10.1037/a0014823 Olatunji, B. O., Williams, N. L., Tolin, D. F., Sawchuk, C. N., Abramowitz, J. S., & Lohr, J. M. (2007). The disgust scale: Item analysis, factor structure, and suggestions for refinement. Psychological Assessment, 19(3), 281-297. https://doi.org/10.1037/1040-3590.19.3.281 Reynolds, B., & Seeger, M. W. (2005). Crisis and emergency risk communication as an integrative model. Journal of Health Communication, 10(1), 43–55. https://doi.org/10.1080/10810730590904571 Rozin, P., Haidt, J., & McCauley, C. R. (1999). Disgust: The body and soul emotion. Handbook of Cognition and Emotion, pp. 429, 445. Rozin, P., Haidt, J., & McCauley, C. R. (2008). Disgust: The body and soul emotion in the 21st century. Social Research, 75(4), 757–782. https://www.jstor.org/stable/40972075 Schaller, M., & Park, J. H. (2011). The behavioural immune system (and why it matters). Current Directions in Psychological Science, 20(2), 99-103. https://doi.org/10.1177/0963721411402596 Kaye, J. (2021, June 11). John (obsessive-compulsive disorder) | Society of Clinical Psychology. Society of Clinical Psychology | Division 12 of the American Psychological Association. https://div12.org/case_study/john-obsessive-compulsive-disorder/ Stevenson, R. J., Case, T. I., & Oaten, M. J. (2009). Frequency and recency of infection and their relationship with disgust and contamination sensitivity. Evolution and Human Behavior, 30(5), 363-368. https://doi.org/10.1016/j.evolhumbehav.2009.02.005 Tybur, J. M., Lieberman, D., & Griskevicius, V. (2009). Microbes, mating, and morality: Individual differences in three functional domains of Disgust. Journal of Personality and Social Psychology, 97(1), 103-122. https://doi.org/10.1037/a0015474 Tybur, J. M., Lieberman, D., Kurzban, R., & DeScioli, P. (2013). Disgust: Evolved function and structure. Psychological Review, 120(1), 65-84. https://doi.org/10.1037/a0030778 World Health Organization. (2020). Recommendations to member states to improve hand hygiene practices to help prevent the transmission of the COVID-19 virus. Retrieved from https://www.who.int }} ==External links== [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Disgust]] [[Category:Motivation and emotion/Book/Hygiene]] qobyuski4oqzcxv4lxzuijwvyj0fmff 0 307962 2690119 2690036 2024-12-03T16:45:27Z Scogdill 1331941 2690119 wikitext text/x-wiki =Event= On Monday 28 June 1897, Queen Victoria hosted a garden party at Buckingham Palace, inviting between 5,000 and 6,000 people. This party was the final official event of the London Diamond Jubilee celebrations. The Queen released to the press the names of people invited, which means the newspapers could print some or all of this list. The very long article in the London ''Morning Post'', for example, prints what may be the comprehensive list of those invited, although two columns are illegible in some places. The original newspaper account seems to have been published by the ''Court Circular'', and then the popular newspapers reprinted pieces of that story, many adding contextualizing paragraphs of their own. Some of these later reports are quite long, perhaps 5 or more full columns. Sometimes the newspapers included short descriptions of the women's dresses, suggesting that for the list of people invited, the source was the ''Court Circular'', but the parts of the stories devoted to context, history or fashion might have been written by a reporter present at the event. ==Logistics== * 28 June 1897, Monday, in the gardens at Buckingham Palace, hosted by Queen Victoria. * Between 5,000 and 6,000 guests were invited. * Many visitors from the empire who were in town for the Jubilee celebrations were invited to this garden party. * The weather was fine, having improved since the day before. * The garden party was held in the grounds around Buckingham Palace, and the Palace itself was open and available for guests to visit:<blockquote>Great preparations had been made in the splendid grounds adjoining the Royal Palace for the party, the whole scene presenting a fascinating appearance. The beautifully-kept grounds were partially covered with tents and marquees for the convenience of the many guests, and the lovely lake was really in the hands of the Queen’s bargemen, who had charge of the many boats which had been placed on the extensive ornamental waters for the use of guests. There was also plenty of music, several regimental bands being in attendance, while for those who wished to become acquainted with the valuable pictures and works art which are to be found at the Royal residence, all the State and reception rooms of the Palace were thrown open.<ref name=":2">“The Queen’s Garden Party. Brilliant Scene at Buckingham Palace.” ''Globe'' 29 June 1897, Tuesday: 6 [of 8], Col. 3a–c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001652/18970629/050/0006. Print p. 6.</ref> (6, Col. 3a)</blockquote> *The streets around the entrances to Buckingham Palace were lined with spectators beginning hours before the Queen was to arrive:<blockquote>Although the Garden Party was not timed to commence until after five o’clock, the Mall from Marlborough House to Buckingham Palace was well lined by two o’clock, and an hour afterwards large crowds, for the most part composed of ladies, had taken up their positions. This was also the case along Constitution-hill, where the assembly which had gathered to witness the Queen’s arrival at the Palace from Windsor nad [sic] to a large extent remained. The heat was somewhat oppressive, but the trees along the Mall and the Green Park afforded welcome shelter. Many ladies had evidently come prepared for a long wait, as they had provided themselves with the now familiar camp stool, which is always prominent on these occasions. On the other hand, the police were waging war against the men who frequent such places with stools and forms, and as soon as any of them put in an appearance they were quickly pounced upon by the officers, who at once proceeded to destroy the intended stands before the eyes of the helpless owners. Among the sightseers were several of the Indian visitors in gorgeous coloured coats, tight-fitting trousers, and turbans, as well as some of the Australian and New Zealand troops.<ref name=":2" /> (6, Col. 3a)</blockquote> ==Related Events== This garden party was the culminating event of the official celebrations for Queen Victoria's Diamond Jubilee, and more specific events led up to it: # Trip from Windsor to Paddington Station Queen Victoria and a large retinue traveled by train from Windsor to Paddington Station the day before, preceded on an earlier train by "the royal equipages sent from Buckingham Palace for the use of the Queen and her suite," which were<blockquote>First came the splendied semi-state landau in which the Queen made her now famous journey on June 22d. It was preceded by scarlet-coated outriders, and horsed by four magnificent bays driven by postilions in navy blue and white uniforms. Two similar carriages followed, and these were in turn succeeded by a number of pair-horse clarences for the conveyance of the household and suite, and several breaks and ‘buses for luggage. A captain's escort, furnished by the 2d Life Guards, and commanded by Captain Ellison, clattered along in rear of the carriages, and took up a position opposite the spot where, by prior arrangement, Her Majesty’s saloon was to be brought to a standstill. These magnificent troops, riding their great black horses, and with the sunlight dancing upon their nodding plumes, and reflected by their burnished helmets, cuirasses, and trappings, made a very fine show indeed. The escort did not carry the colour, as it did on the 21st, nor was it accompanied by the regimental trumpets.<ref name=":0">"Jubilee Festivities. The Queen Again in London. Interesting Functions. A Visit to Kensington. The Garden Party." ''North British Daily Mail'' 29 June 1897, Tuesday: 5 [of 8], Col. 3a–7b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002683/18970629/083/0005. Print p. 5.</ref>{{rp|5, Col. 3b}}</blockquote> # Reception at Paddington # Visit to Kensington # Kensington to Buckingham Palace # The Garden Party # Return to Windsor by Way of Paddington === Foreign Admirals === On 29 June 1897, the day after the garden party, the ''North British Daily Mail'' reports that, after the Queen's garden party, the foreign admirals would return to Spithead for a tour around the dockyard and luncheon:<blockquote>THE FLEET AT SPITHEAD<p> The fleet at Spithead was again illuminated last night, the railway companies having duplicated the ordinary train service to bring visitors down. The Koenig Wilhelm was to have sailed on Sunday evening, but her departure has been deferred, and last night her officers gave a private dinner party aboard for the anniversary of the Queen’s Coronation. All the commissioned ships in the harbour were dressed at noon. A royal salute was fired. The [Col. 6c–7a] foreign admirals will return from their visit to London on the occasion of the Queen’s garden party to be conducted round the dockyard to-day, and they will be entertained to luncheon.<ref name=":0" />{{rp|5, Col. 6c–7a}}</blockquote> === Colonial Premiers === The day of the garden party the colonial premiers attended a meeting with Secretary of State for the Colonies, [[Social Victorians/People/Chamberlain|Joseph Chamberlain]]:<blockquote>THE COLONIAL PREMIERS The whole of the Colonial Premiers went to the Colonial Office yesterday for further conference with Mr Chamberlain, who received them in his private room, attended by Mr F. H. Wilson, legal assistant, Mr Reid and the Hon. T. Cochrane, M.P., assistant private secretaries. The conference lasted hours, and was of a strictly private and confidential character, the matters discussed involving several points of high State policy. Premiers will be entertained at Warwick Castle by the Earl and Countess of Warwick on July 15th. On the same occasion the Attorney General of Queensland will present a loving cup from Warwick, in Queensland, to the old county town of Warwick, from which it takes its name. He will be accompanied by the Colonial troopers.<ref name=":0" />{{rp|5, Col. 7a}}</blockquote> For these visitors to London during the Diamond Jubilee, the next major social event was on 15 July, at Warwick Castle, hosted by [[Social Victorians/People/Warwick|Daisy, Countess of Warwick and Francis, 5th Earl of Warwick]], although perhaps some attended the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball]]. == Who Was Present == In the absence of a copy of the report about the garden party in the ''Court Circular'', the newspaper account with the fullest list of names is from the ''Morning Post'', although people further down the list can be impossible to identify, and two full columns are damaged (Col. 7 on p. 4 and Col. 1 on p. 5).<ref name=":1">“The Queen’s Garden Party.” ''Morning Post'' 29 June 1897, Tuesday: 4 [of 12], Cols. 1a–7c [of 7] and 5, Col. 1a–c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0000174/18970629/032/0004 and https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970629/032/0005.</ref> Whenever possible, then, what is here has been amended with other newspaper reports that have names to help decipher the illegible ones in the ''Morning Post'' account. The names in the Morning Post are grouped, mostly by rank and name. === People of Color at This Event === One purpose of a closer look at this event is to get a more precise list of names of people of color from the various countries in the empire, who were not recognized and thus not named in newspaper descriptions of other events. For example, the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball]] was said to include a number of South Asian dignitaries, but because the Duchess did not release to the newspapers the names of those who were invited, those dignitaries went mostly unnamed in the newspaper reports, if their presence was noted at all. Besides the South Asian guests invited to this garden party, some South Asian visitors to London were spectators as well:<blockquote>Among the sightseers were several of the Indian visitors in gorgeous coloured coats, tight-fitting trousers, and turbans, as well as some of the Australian and New Zealand troops.<ref name=":2" /> (6, Col. 3a)</blockquote>In a section on what people — mostly women — wore, the reporter for the ''Daily News'' said,<blockquote>Suffice to say, the modistes had done their best, and that their achievements excited general admiration. Here and there, however, was an Eastern beauty whose golden lace drapery, loosely enveloping a figure that owed nothing to the corset, challenged comparison, we will not say with what success, with the European model. In the almost entire absence of uniforms or Court dress, the costumes of the East Indian notables lent colour to the assemblage, while their pearls and diamonds, the wealth of Ormuz and of Ind, were not allowed to pass unobserved.<ref name=":3" /> (5, Col. 6b)</blockquote> === People Invited === # Queen Victoria, with escort and attendants ## Captain's Escort of the 2nd Life Guards ## The Duchess of Buccleuch, Mistress of the Robes ## The Dowager Lady Churchill, Lady in Waiting ## The Hon. Harriet Phipps, Woman of the Bedchamber ## Maids of Honour in Waiting ### The Hon. Mary Hughes ### The Hon. Aline Majendie ## the Earl of Kintore, Lord in Waiting ## Captain Drummond, Groom in Waiting ## Equerries in Waiting ### Major-General Sir John M'Neill, V.C. ### Lieutenant Colonel Davidson, M.V O. [sic] #Grand Duke and Grand Duchess Serge of Russia #Princess Henry of Battenberg, with attendants ##Miss Minnie Cochrane ##Colonel John Clerk, C.S.I., C.V.O. #Her Imperial Majesty the Empress Frederic, attended by ##the Dowager Lady Ampthill ##Lord Harris ##Colonel S. Waller ##Princess Hatzfeldt Trachenberg ##Count Seckendorff ##Baron and Baroness Reischach #Their Royal Highnesses the Prince and Princess of Wales, with attendants ##Lady Suffield, Lady in Waiting ##Miss Knollys, Woman of the Bedchamber ##Lord Colville of Culross, K.T., G.C.V.O., Chamberlain to the Princess of Wales ##The Earl of Gosford, K.P., Lord in Waiting ##General Sir D. Probyn, G.C.V.O., K.C.B., K.C.S.I., V.C, Comptroller ##Sir Francis Knollys, K.C.M.G., C.B., Groom in Waiting ##Major-General Stanley Clarke, C.M.G., Equerry in Waiting #Princess Victoria of Wales #Their Royal Highnesses Prince and Princess Charles of Denmark #Their Royal Highnesses the Grand Duke and Grand Duchess of Mecklenburg-Strelitz, attended by ##Lady Caroline Cust ##Mr. Hugo Erskine Wemyss ##Count Reventlow Criminil ##Baron von der Wense #Their Royal Highnesses Prince and Princess Christian, attended by ##Baroness von und zu Egloffstein ##Colonel the Hon. Charles Eliot #Her Highness Princess Victoria #His Highness Prince Christian Victor #His Highness Prince Albert of Schleswig-Holstein #Her Royal Highness Princess Louise Marchioness of Lorne and the Marquis of Lorne, attended by ##Lady Sophia Macnamara ##[[Social Victorians/People/Arthur Collins|Colonel Arthur Collins]], M.V.O. #Their Royal Highnesses Prince and Princess Henry of Prussia, attended by ##Admiral of the Fleet Sir Edmund Commerell ##Baron and Baroness Seckendorff ##Count Hahn ##Captain Muller #Their Royal Highnesses the Duke and Duchess of Saxe-Coburg and Gotha, attended by ##The Hon. Mrs. Monson ##His Excellency Herr von Schön ##Captain the Hon. D. J. Mouson [sic, s/b Monson?], M.V.O. ##Mr. A. D. J. Monson ##Captain von Ruxleben #Princess Beatrice of Saxe-Coburg and Gotha #The Hereditary Prince of Saxe-Coburg and Gotha #Their Royal Highnesses the Duke and Duchess of Connaught and Strathearn, attended by ##Colonel and the Hon. Mrs. A. Egerton #Her Royal Highness the Duchess of Albany, attended by ##Sir Robert and Lady Collins ##Miss Potts #Her Royal Highness Princess Frederica of Hanover and Baron von Pawel Raminingen, attended by ##Mr. and Mrs. Charles Wood #His Royal Highness the Duke of Cambridge, attended by ##Colonel A. C. FitzGeorge, C.B. #Her Royal Highness the Duchess of Teck and his Highness the Duke of Teck, attended by ##Lady Katherine Coke ##The Hon. A. Nelson Hood #Her Royal Highness Princess Louise Duchess of Fife and the Duke of Fife #His Highness the Prince and her Royal Highness Princess Frederic Charles of Hesse, attended by ##The Hon. A. Hay ##Fraulein von Tasmund ##Baron von Kotwitz #Their Highnesses Prince and Princess Aribert of Anhalt, attended by ##Miss Deverell ##Major Evan Martin #Her Royal Highness the Hereditary Princess of Saxe-Meiningen and her Serene Highness Princess Feodore of Saxe-Meiningen, attended by ##The Hon. Aubrey FitzClarence ##Miss von Dreskan ##Baron von Roeder #His Serene Highness the Prince of Schaumburg-Lippe #Their Highnesses Prince and Princess Edward of Saxe-Weimar #Her Serene Highness Princess Victor of Hohenlohe #Countess Gleichen (x2) #Their Serene Highnesses Prince and Princess Adolphus of Teck #The Prince Francis and Prince Alexander of Teck #His Highness Prince Augustus Leopold of Saxe-Coburg #Their Serene Highnesses Prince and Princess Blucher von Wahlstatt #Their Serene Highnesses Prince and Princess Joachim Murat #Their Serene Highnesses [[Social Victorians/People/Pless|Prince and Princess Hans Henry Pless]] #Prince and Princess Loewenstein #Their Serene Highnesses the Duke and Duchess of Arenberg #Prince Victor Duleep Singh #Prince Frederick Duleep Singh #Princess Duleep Singh (x2) #ARGENTINE REPUBLIC — M. Florencio Dominguez and M. Carlos Dominguez #BADEN — Herr yon Brauer, Mr. Brook Taylor, and Baron Bohlen Halbach #BAVARIA — His Royal Highness the Prince Rupert, General Sir L. Gardiner, K.C.V.O., C.B., Major Fairholme, Lieutenant-Colonel Emile von le Bret Nucourt, and Captain Othon von Stettin #BELGIUM — His Serene Highness the Prince Charles de Ligne, Princess de Ligne, Madlle. de Ligne, Mr. C. lnnes Ker, Count de Jonghe d'Ardoye, and the Marquis d’Asshe #BOLIVIA — M. Caso, Mr. Conway Seymour, M. Pedro Suarez, Madame Suarez, and M. Adolfo Bolivian #BRAZIL — M. [[Social Victorians/People/Souza Correa|de Souza Correa]] [Corréa?] #BULGARIA — Their Royal Highnesses the Prince and Princess of Bulgaria, Colonel J. R. Slade, C.B., Madame Petrow Tchomakoff, Count Robert de Bourboulon, Lieutenant-Colonel Marcoff, Major Petrew, Captain Stoïanow, and Mr. Martin Furth #CENTRAL AMERICA (Greater Republic) — M. Medina and Miss Medina #CHILI — M. Ramon Subercasseaux and Mr. Raglan Somerset #CHINA — His Excellency Chang Yen Hoon, Colonel Mark Bell, V.C,. Mr. Liang, Mr. Jui, and Mr. Koo #COREA — His Excellency Min Young Hwan, Major A. Cavendish, Mr. Min Young Chan, Mr. Min Shangho, and Mr. von Rautenfeld #COSTA RICA — Senor Don Demetrio Iglesias, Mr. C. Alban Young, Dona Eudoxia Castro, Señorita Maria Iglesias, Don Ricardo Fernandez Guardia, and Dona Christina Castro Keith #DENMARK — His Royal Highness the Prince Waldemar, Major-General Arthur Ellis, C.S.I., M. Charles Rothe, and Captain Evers #EGYPT — Prince Mohammed Ali Pasha, Colonel Larking, Tigrane Pasha, Colonel Aziz Bey, Mr. George Smart, Said Zoulfikar Bey #ECUADOR — M. Navares, Colonel Concha #FRANCE — General Davoust, Duc d'Auerstadt, Duchesse d'Auerstadt, and Madlle. Davoust, Colonel Brabazon, Colonel Dawson, General Hagron, M. Crozier, Colonel Humbert, and Captain Riviers de Mauny #GERMANY — His Royal Highness the Prince Albert of Prussia, Prince Regent of Brunswick, Major-General Sir C. du Piat, K.C.B., Colonel Grierson, Lieutenant-General von Plessen, Colonel von Arnim, Captain Fischel, Count von der Schulenberg (Hofmarschall), Major Freiherr von Stein, Dr. Schreibe, Captain von Unzer #GREECE — M. Rangabi, Mr. R. D. Norton #GUATEMALA — Dr. Cruz, Madlles. Cruz (2), Señor Estrada #HAWAIIAN ISLANDS — Mr. S. M. Damon, Captain the Hon. H. Napier, Major Curtis P. Jaukea #HESSE — Their Royal Highnesses the Grand Duke and Grand Duchess of Hesse, Colonel the Hon. H. Byng, C.B., Baroness de Grancy, Baron Riedesel zu Eisenbach, Baron de Genadius Grancy #ITALY — Their Royal Highnesses the Crown Prince and Princess, the Earl of Clarendon, Colonel Needham, Countess Giulia Trigona, Lieutenant-General Terzaghi, Major Cavaliere Viganoni, Captain Cavaliere Merli Miglietti, Count Romnaldo Trigona, Cavaliere F. Comotto #JAPAN — His Imperial Highness the Prince Arisugawa, Mr. R. F. Synge, Captain Beaumont, R.N., Marquis Ito, Mr. S. Saito, Marquis Kido, Captain Funaki, Lieutenant-Colonel Murata, Lieutenant Kato, Mr. Nabeshima #LIBERIA — Mr. H. Hayman #LUXEMBURG — His Royal Highness the Hereditary Grand Duke of Luxemburg, Colonel H. D. Browne, Baron Ritter yon Grünstein #MECKLENBURG-SCHWERIN — His Excellency Herr D. yon Vietinghoff, Mr. Eyre A. Crowe #MEXICO — Don Antonio Mier y Celis, Mr. Arnold Royle, C.B., Don Francisco R. Gallardo, Don Eustagino dc Escaudon, and Captain Don Ponfirio Diaz #MONTENEGRO — His Highness the Prince Danilo, Major the Hon. C Harbord, Colonel Djurcovitch, and Captain Pejanovitch #NETHERLANDS — Count van Lynden, Countess van Lynden, Mr. Horace West, and Count W. de Bylandt #PARAGUAY — M. E. Machain and Madame Machain #PERSIA — His Imperial Highness the Prince Amir Khan, General Sir Thomas Gordon, K.C.I.E., C.B., C.S.I.[,] Mr. Harry Churchill, General Karim Khan, Mirza Ahmad Khan, Mirza Ohaness Khan, Mirza Mohamad Ali Khan #PERU — Senor Canevaro, Duchesse de Zoagli Canevaro, Dr. Don A. N. Puente, Don Alfredo Elster, and Don Carlos von der Heyde #PORTUGAL — His Royal Highness the Duke of Oporto, Major the Hon. H. C Legge, M.V.O., Colonel Duval Telles, Captain Moreira de Sà, Major d'Albuquerque, and Lieutenant Jose de Melie[?] #ROME — Right Rev. Monsignore Sambucetti, [[Social Victorians/People/Stonor|Hon. Harry Stonor]], Right Rev. Monsignore Belmont, the Right Rev. Monsignore de Vaz, Marchesi and Marchesa Muccioli, of the Noble Guard #ROUMANIA — General Pancovici, Colonel G. P. Georgescu #RUSSIA — Their Imperial Highnesses the Grand Duke Serge and Grand Duchess Feodrowna, the Grand Duke Cyril, Lord Churchill, Lieutenant-Colonel Waters, Countess Olsouffiew, Princess Youssoupoff, Princess Lobanoff de Rostow, General Stépanoff, Colonel Gadon, and Prince Youssoupoff, Colonel Clements, Mr. Alexander Gordon Ross, and Sub-Lieutenant N. Coubé (A.D.C. to Grand Duke Cyril) #SAXE-COBURG — His Royal Highness the Prince Philip of Saxe-Coburg, Captain Walter Campbell, and Herr von Schön #SAXE-WEIMAR — His Highness the Prince Hermann of Saxe-Weimar, Mr. Frederick Campbell, and Count Zeppelin #SAXONY — His Royal Highness the Prince Frederick Augustus, Duke of Saxony, Colonel Howard, Freiherr yon Reitzenstern, First Lieutenant von Metzsch, and Baron von Oppell #SERVIA — M. Mijatovich and Madame Mijatovich #SIAM — His Royal Highness the Crown Prince and the Prince Mahit of Siam, Colonel E. H. Sartorius, V.C., Lieutenant-Colonel Rajavallabha, Lieutenant-Colonel C. Vernon Hume, Colonel Indaraty, Surgeon-Major Yarr #SPAIN — Duke of Sotomayor, Captain the Hon. A. Greville, Señor José Caro, Señor Alfonso Merry del Val, and Señor Benitez al Villar #SWEDEN AND NORWAY — His Royal Highness the Prince Eugène of Sweden and Norway, Captain G. L. Holford, Count G. Gyldenstolpe, Captain Roeder, Captain Baron Cederstrom #TURKEY — Munir Pasha, Major Surtees, Brigadier-General Nassir Pasha, Captain Enver Bey, Colonel Gordon Ponsonby #UNITED STATES — His Excellency the Hon. Whitelaw Reid, Mrs. Whitelaw Reid, Colonel Hallam Parr, Major-General Nelson A. Miles, Mrs. Nelson Miles, Rear-Admiral Joseph N. Miller, Captain M. P. Maus, Mr. Ogden Mills, Mrs. Ogden Mills, Mr. G. Creighton Webb, Mr. Erskine Hewett, Commander W. H. Emory, Lieutenant Philip Andrews, Lieutenant T. S. Rogers #URUGUAY — Dr. Alberto Nin, Madlle. Nin, Don Alfonso Saenz de Zumaran, Don Luis Posadas, Colonel C. Robido #WURTEMBURG— His Royal Highness the Duke Albert of Wurtemburg, Colonel C. Swaine, Lieutenant-General von Bilfinger, First Lieutenant Count von Degenfeld- Schonburg; five officers of the Queen's German Regiment: Major C. R. Burn (in attendance), Lieutenant-Colonel von Falkenhayn, Major von Arnim, First Lieutenant Baron von Moeller-Lilienstern, First Lieutenant von Gerlach, Second Lieutenant von Studnitz #"Native Princes, and gentlemen and ladies accompanying them"<ref name=":1" /> (4, Col. 2b) ##His Highness the Raja of Kaparthala ##His Highness the Thakur Sahib of Morvi, K.C.I.E. ##His Highness the Thakur Sahib of Gondal, C.I., and her Highness the Maharani of Gondal, C.I. ##Colonel Maharaj Dhiraz ##Sir Pratab Singh, K.C.S.I. ##Thakur Hari Singh[,?] ##Kunwar Dhokal Singh ##Rajah Ajit Singh of Khetri, attended by ##Rajkumar Unmaid Singh of Shahpura, attended by ###Colonel Trevor (in attendance upon the Rajah Ajit Singh of Khetri and the Rajkumar Unmaid Singh of Shahpura) ##Bijey Singh ##Sir Jamaetjee Jejeebhoy, Bart., C.S.I., Miss Jejeebhoy, Mr. Jejeebhoy ##Mr. and Mrs. Powrala ##Major J. G. Turner and Mrs. Turner ##Mr. A. R. Wood and Mrs. Wood #The "officers of the Imperial Service Troops, with British officers and ladies"<ref name=":1" /> (4, Col. 2b) ##Captain Mir Hashim Ali Khan Hyderabad-Resaldar ##Major Sunayat Singh, Kashmir ##Commandant Abdul Ganny, Gwalior ##Commandant Gooind, Rao Matkar, Indore ##Commandant Mirza Kurim Beg, Bhopal ##Rai Bahadur Dhunpat Rai, Jeypore ##Commandant Nand Singh, Patiala ##Commandant Rai Bahadur Thakur Dip Sing, Bikanir ##Commandant Chatru Singh, Bhartpur ##Resaldar Abdul Majid Khan, Babawalpur ##Commandant Daud Khan, Ulwar ##Commandant Nazir Khan, Rampur ##Risalda-Major Didar Singh, Sindi ##Risaldar-Major Kishan Singh, Nabha ##Risaldar Hara Singh, Karpurthala ##Risaldar Dhan Singhi, Bhavnagar ##Colonel H. Melliss, C.S.I., and Mrs. Melliss ##Major F. H. R. Drummond and Mrs. Drummond ##Captain F. Angelo ##Lieutenant H. Coape-Smith ##Captain G. F. Chenevix-Trench #The "officers of Native Cavalry Corps with British officers and ladies"<ref name=":1" /> (4, Col. 2b) ##Risaldar-Major Baha-ud-din-Khan ##Sardar Bahadur, A.D.C. to Viceroy ##Risaldar-Major Sayyid Abdul Aziz ##Risaldar-Major Khan Bahadur ##Risaldar-Major Izzat Khan ##Risaldar-Major Hukam Singh ##Risaldar-Major Sher Singh ##Risaldar-Major Husain Khan ##Risaldar-Major Mangal Singh ##Risaldar-Major Kesar Singh ##Risaldar- Major Faiz Khan ##Risaldar-Major Muhammad Umar Khan ##Risaldar-Major Ali Mahomed Khan ##Risaldar-Major Mihrab Ali Khan ##Risaldar Kaddam Khan ##Risaldar Jahanzir Khan ##Risaldar Nadir Khan ##Risaldar Mir Haidar Shah Khan ##Risaldar Makbul Khan ##Risaldar Net Ram ##Ressaidar Gurdatt Singh ##Subadar Muhammed Beg Junadar ##Abdul Karin Khan ##Lieutenant-Colonel J. C. H. Gordon and Mrs. Gordon ##Major A. Phayre and Mrs. Phayre ##Captain C. F. Campbell ##Captain P. Melville, in attendance on his Highness Thakur Sahib of Morvi ##Captain M'Cartney Filgate, in attendance on their Highnesses the Thakur Sahib and Maharani of Gondal ##Mr. Nowroz ##M. Parveez ##Sir M. Mansherjee Bhownaggree, M.P. ##Mr. Percy Armytage and Mrs. Armytage ##Mr. Frank Cook, C.I.E., and Mrs. Frank Cook #The "commanding officers of Colonial contingents, with the ladies accompanying them"<ref name=":1" /> (4, Col. 2b) ##Colonel the Hon. M. and Mrs. Aylmer, Canada ##Colonel and Mrs. Lassetter, New South Wales ##Major Reay, Victoria ##Colonel Pitt, New Zealand ##Major and Miss King, Queensland ##Lieutenant and Mrs. Phillips, Cape of Good Hope ##Lieutenant-Colonel Rowell, South Australia ##Major Strickland, Western Australia ##Captain Shepstone, Natal ##Major and Miss Reeves, Ceylon ##Mr. Badeley, Hong Kong ##Colonel Walker, C.M.G., and Mrs. Walker, Straits Settlements ##Captain Lucie Smith, Jamaica ##Lieutenant-Colonel E. B. M'lnnis, C.M.G., and Mrs. M'lnnis, British Guiana ##Major Rooks, Trinidad ##Captain Bernard, Malta ##Captain Kershaw, Cyprus ##Captain and Mrs. Middlemist, Gold Coast ##Inspector Hook, Lagos ##Captain Blakeney, Sierra Leone ##Lieutenant Festing, Royal Niger Company ##Captain Flint, British North Borneo Company ##The Hon. M. Gifford, Rhodesian Horse ##The following British officers attached: Lieutenant-Colonel Boulton, Lieutenant-Colonel Prior, Lieutenant-Colonel Tucker, Lieutenant-Colonel Domville, Lieutenant-Colonel Gibson, and Lieutenant-Colonel Tyrwhitt #The "gentlemen representing the various races in the Island of Ceylon"<ref name=":1" /> (4, Col. 2c) ##Maha Mudaliyar don Solomon Dias Bandaranaihe ##The Hon. Alexander Dealius Sonewiratne ##M. E. Rowland Goonoratne ##M. Charles de Soysa Dessanayaka ##Panabokko Jikiri Banda ##Nugawela Kuia Banda ##Kobbokeduwe Loku Banda ##M. E. S. W. Senathi rajah [sic] and Mrs. Senathi ##M. J. H. de Saram and Miss de Saram ##M. P. Ramanathan ##M. Saunders and Miss Saunders #The "members of the Corps Diplomatique and other foreigners of distinction"<ref name=":1" /> (4, Col. 2c) ##The Russian Ambassador, Madame de Staal, Madlle. de Staal, Madame de Stoeckl, Princess de San Donato, Madame Yermoloff, Madlle. Yermoloff, the Councillor, three Secretaries, and four Attachés of Embassy ##The German Ambassador, Countess Paul Hatzfeldt-Wildenburg, her Serene Highness Princess Hans Hohenlohe-Oehringen, Baroness yon Eckardtstein, the Councillor, two Secretaries, three Attachés of Embassy, and the Director of the Chancery ##The Austro-Hungarian Ambassador, Countess Deym, Countess Isabella Deym, Countess Clary Aldringen, Baroness Ferstel, the Councillor, two Secretaries, and four Attachés of Embassy ##The French Ambassador, Baroness de Courcel[,] Madlle. de Courcel, Madame Geoffray, the Minister Plenipotentiary, five Secretaries, and three Attachés of Embassy ##The Italian Ambassador, Princess Ruspoli, three Secretaries, and three Attachés of Embassy ##The Spanish Ambassador, Countess de Casa Valencia; Mesdlles. de Alcala Galiano (2), Marquise de Guiria, Donna de Zea Bermudez, Countess de Morella, Donna de Ia Camara y Livermore, three Secretaries, and four Attachés of Embassy ##The Turkish Ambassador, Madame Antbopoulos, the Councillor, and two Secretaries of Embassy ##The United States Ambassador, Mrs. Hay, Miss Hay, Mrs. Henry White, Mrs. Carter, Mrs. Colwell, two Secretaries, one Attaché of Embassy, and the Private Secretary to the Ambassador ##The Argentine Minister, Madame Dominguez, Mesdlles. Dominguez (3), and the Secretary of Legation ##The Persian Minister, and one Secretary of Legation ##The Danish Minister, Madame de Bille, Madame Gosch, and the Secretary of Legation ##The Siamese Minister, Mrs. Verney, Miss Verney, Mrs. Loftus, the Councillor, the Secretary, the Attaché, and the Interpreter to the Legation ##The Liberian Minister ##The Roumanian Minister and the Councillor of the Legation ##The Netherlands Minister, Baroness de Goltstein d'Oldenaller, Baroness Schimmelpenninck van der Oye, and the Councillor of Legation ##The Belgian Minister, the Councillor, and two Secretaries of Legation ##The Mexican Minister, Madame Yturbe, Madame Romero, Madame Farias, Madame Garcia, two Secretaries and three Attachés of Legation ##The Japanese Minister, Madame Kato, two Secretaries, and three Atachés [sic] of Legation ##The Minister for Sweden and Norway, Countess Lewenhaupt, and the Attaché of Legation ##The Chinese Minister, Lady Macartney, the English Secretary, three Secretaries, and four Attachés of Legation ##The Portuguese Minister, Madlle. de Quilinan, three Secretaries, and one Attaché of Legation ##The Swiss Minister, Madame Bourcart, Madame de Salis, the Secretary, and the Attaché of Legation ##The Haytian Chargé d’Affaires ##The Chargé d’Affaires of Greece, Madame Metaxas, and the Attaché ##The Chargé d’Affaires of Chile and Madame Bascunan ##Two Secretaries and one Attaché of the Brazilian Legation ##Count E. van Rosen ##Mr. Hippolyte de Aranjo ##Vice-Admiral Montt ##Mr. Pinto, Mrs. Pinto ##Mr. and Mrs. Scaramanga ##Vicomte de Galard ##Dr. Arnold, and Madlle. von Rappoport ##Mrs. John Meiggs, Miss Meiggs ##Miss Margaret Butler ##Mrs. Henry Morgan ##Hon. Chauncey Depew ##Mr. and Mrs. James Taylor ##Mr. and Mrs. Charles Marshall ##Mr. and Mrs. Edmund Bayliss ##Mrs. Colgate ##Miss Furniss ##Miss Wells ##Miss Harris ##Hon. Levi P. Morton, Mrs. Morton, and the Misses Morton ##The Bishop of Illinois and Mrs. Leonard, Miss Leonard ##The Bishop of Albany and Mrs. Doane ##The Bishop of New York and Mrs. Potter ##the Bishop of Minnesota and Mrs. Whipple ##Mr. and Mrs. Walter Burns ##Mrs. Douglas Grant ##Miss Scott ##Mrs. Grace, Miss Margarita Grace ##Mrs. Wentworth ##Miss van Wart ##M. Valentin de Courcel ##Madame la Marquise de Talleyrand Perigord ##Comte Boson de Perigord ##Vicomte d'Espenilles ##Madame and Madlle. Thierry Delanoue ##Madlle. de la Cherè ##M. Cellerier ##M. and Madame Delawarre ##Madame Evelina Fenzi ##Count A. Zannini ##M. and Madame Jules Cottran ##Chevalier E. Mazzuechi ##Signor A. Tedeschi ##Signor A. Mariotti ##Captain Lucian von Ziegler ##Chevalier Lieutenant von Barry ##Baron Georg Rothschild ##Privy Councillor Count Berchtold ##Baron G. E. Levi, Baroness Levi ##Commander E. Philipson, Mrs. E. Philipson ##The Duke and Duchess of San Germano Calabritto ##The Marquis of San Vito ##Donna Lidia Serramezzana ##Donna Margherita Chigi ##Marchioness Vitelleschi ##Chevalier Elia ##Count de Franqueville ##Count Urbain Chevrau ##M. Marcel Fonquier ##M. Baudon de Mony, Madame Baudon de Mony ##Duchess de Rohan ##Marquis de Lastorgrie, Marchioness de Lastorgrie ##Count de Boisgelin, Countess L. de Boisgelin ##M. Stern, Madame Stern, Madlle. Stern ##Count Charles du Luart ##General de Saucy ##M. E. Seydoux ##Count Jean de Madre ##M. de Monbrison ##Baron de la Chevrelière ##Count de la Villestreux, Countess de la Villestreux ##Count Urbain de Maille, Countess Urbain de Maille ##General Faveret de Kerbrich ##Monsieur de la Haye Jousselin ##Baronne Faveret de Kerbrich ##Colonel Matton ##M. Ferinier Didet ##Madame Ferinier Didet ##Donna Isabella Colonna, Donna Victoria Colonna ##Pom-k-Soh ##Madame Reyntiens ##Marquis de Fuente Hermosa ##Herr Rudolf Swobody ##M. Lauritz Tuxen ##Duchesse de Baiten ##M. de Marcoarti ##Comte de Heeren, Madlle. de Heeren ##Monsieur M. de Mauny Talvande ##Senor Don Nicolas Campero ##Lieutenant Charny ##Lieutenant Sanders ##Madame and Madlle. de Mouni ##Comtesse de Montsoulmin #"Foreign Admirals and Commanding Officers and Staffs"<ref name=":1" /> (4, Col. 3a / Col. 3b) ##Austrian Admiral Baron von Spaun, Commander von Ziegler, Lieutenant Retter yon Barry, Lieutenant Mitchell, R.N. (attached) ##Danish Admiral H. H. Koch, Captain Waudel, Lieutenant Middelboc, Lieutenant Majendie, R.N. (attached) ##French Admiral C. F. E. De Courthille, Captain Germinet, Commander Poidlone, Lieutenant Perdriel, Sub-Lieutenant de Caqueray, Lieutenant Phillimore, R.N. (attached) ##Italian Admiral C. E. Morin, Commander Count Prasca, Lieutenant Lunghetti, Lieutenant Count Morano, Lieutenant Henderson. R.N. (attached) ##German Admiral his Royal Highness Prince Henry of Prussia, Captain Muller, Lieutenant von Spee, Sub-Lieutenant Wittman, Lieutenant Garforth, R.N. (attached) ##Japanese Admiral H.I.H. Prince Arizugawa, Captain Miura, Commander Tsuda, Lieutenant Stewart, R.N. (attached) ##Netherlands Admiral F. K. Englebrecht, Captain de Groot, Lieutenant Baron von Hardenbrock, Lieutenant Woolcombe, R.N. (attached) ##Norwegian Rear-Admiral von Krogh, Captain Muller, Lieutenant Petersen, Lieutenant Kerr Pearse, R.N. (attached) ##Portuguese Captain Barreto de Vascomellos, Captain de Cartillo, Lieutenant Trye, R.N. (attached) ##Russian Admiral Nicholas Skrydloff, Captain Domojiroff, Lieutenant Stetsenkoff, Lieutenant Twisleton Wykeham Fiennes, R.N. (attached) ##Spanish Admiral Don Segismundo Bermijo y Merelo, Captain Don Antonio Eulate y Fery, Lieutenant Don Juan Romero, Lieutenant Don Antonio Romero, Lieutenant Fair, R.N. (attached) ##Swedish Admiral A. F. H. Klintberg, Captain Ingelman, Commander Flack, Lieutenant Alton, R.N. (attached) ##United States Admiral J. N. Miller, Lieutenaut Richmond (attached) ##Captain de Mar E. Guerra ##Captain R. S. D. Cumins #The Lord Lieutenant of Ireland and Countess Cadogan #The Right Hon. the Speaker and Mrs. Gully, Miss Gully, and Miss Shelly Gully #Cardinal Vaughan #Right Hon. the Lord Mayor and Lady Mayoress, and Misses Faudel Phillips (2) #The Gold Stick in Waiting, Silver Stick in Waiting, Silver Stick Adjutant in Waiting #Officer Commanding 1st Life Guards and five officers #Officer Commanding 2nd Life Guards and four officers #Officer Commanding Royal Horse Guards and four officers #Officer Commanding 2nd Dragoons and three officers #Field Officer in Brigade Waiting, Adjutant in Brigade Waiting #Commanding Officer Grenadier Guards #Commanding Officer Coldstream Guards #Commanding Officer Scots Guards, a Regimental Adjutant #Commanding Officer 1st, 2nd, and 3rd Battalions Grenadier Guards and three officers of each Battalion #Commanding Officer 1st and 2nd Battalions Coldstream Guards and three officers of each Battalion #Commanding Officer 1st and 2nd Battalions of Scots Guards and three officers of each Battalion #Commanding Officer Woolwich District and six officers #Commanding Officer R.H.A. Home District and two officers #Commanding Officer R.E. and four officers #Commanding Officer 2nd Battalion Lincolnshire Regiment and three officers #Commanding Officer Royal Marines (Chatham) and four officers #Commanding Officer Royal Marines (Portsmouth) and two officers #Four officers of the Honourable Corps of the Gentlemen at Arms #Archbishops — Canterbury, York, Armagh, Ontario, Rupertsland #Dukes and Duchesses ##The Duke and Duchess of [[Social Victorians/People/Argyll|Argyll]] ##The Duke and Duchess of [[Social Victorians/People/Abercorn|Abercorn]] ##The Duchess of De Baileu ##The Duke and Duchess of [[Social Victorians/People/Buccleuch|Buccleuch]] ##The Duchess of [[Social Victorians/People/Cleveland|Cleveland]] ##The Duke and Duchess of [[Social Victorians/People/Devonshire|Devonshire]] ##The Duchess of [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton|Hamilton]] ##The Duke and Duchess of [[Social Victorians/People/Leeds|Leeds]] ##The Duke and Duchess of [[Social Victorians/People/Marlborough|Marlborough]] ##The Duke and Duchess of [[Social Victorians/People/Manchester|Manchester]] ##The Duke and Duchess of [[Social Victorians/People/Montrose|Montrose]] ##The Duke and Duchess of [[Social Victorians/People/Newcastle|Newcastle]] ##The Duke of [[Social Victorians/People/Norfolk|Norfolk]] ##The Duke of [[Social Victorians/People/Northumberland|Northumberland]] ##The Duke and Duchess of [[Social Victorians/People/Portland|Portland]] ##The Duke of [[Social Victorians/People/Richmond and Gordon|Richmond and Gordon]] ##The Duke and Duchess of [[Social Victorians/People/Roxburghe|Roxburghe]] ##The Duke and Duchess of [[Social Victorians/People/Somerset|Somerset]] ##The Duke and Duchess of [[Social Victorians/People/Sutherland|Sutherland]] ##The Duke and Duchess of St. Albans ##The Duke and Duchess of Wellington ##The Duchess of [[Social Victorians/People/Westminster|Westminster]] #Marquises and Marchionesses ##The Marquis of Abergavenny ##The Marchioness of Ailesbury ##The Marquis and Marchioness of Ailsa ##The Marquis of Anglesey ##The Marquis and Marchioness of [[Social Victorians/People/Breadalbane|Breadalbane]] ##The Marchioness of [[Social Victorians/People/Marlborough#Marchioness of Blandford|Blandford]] ##The Marquis and Marchioness of Bristol ##The Marquis of [[Social Victorians/People/Camden|Camden]] ##The Marquis and Marchioness of Conyngham ##Dowager [Marchioness of] Conyngham ##The Marchioness of Cassar de Sai[n] ##The Marquis and Marchioness of Cholmondeley ##The Marquis of D'Auerstadt ##The Marquis and Marchioness [[Social Victorians/People/Stonor|D'Hautpoul]] ##The Marquis and Marchioness of Downshire ##Dowager [Marchioness of] Downshire ##The Marquis and Marchioness of [[Social Victorians/People/Hamilton Temple Blackwood|Dufferin and Ava]] ##The Marquis and Marchioness of [[Social Victorians/People/Exeter|Exeter]] ##The Marquis and Marchioness of Granby ##The Marchioness of [[Social Victorians/People/Florence Rawdon-Hastings Chetwynd|Hastings]] ##The Marquis and Marchioness of [[Social Victorians/People/Bective|Headfort]] ##The Marquis and Marchioness of Hertford ##The Marquis and Marchioness of Huntly ##The Marquis and Marchioness of [[Social Victorians/People/Abercorn#James Hamilton, Marquess of Hamilton|Hamilton]] ##The Marquis and Marchioness of [[Social Victorians/People/Lansdowne|Lansdowne]] ##The Marquis and Marchioness of Lothian ##Dowager (Marchioness of) [[Social Victorians/People/Londonderry|Londonderry]] ##The Marquis and Marchioness of [[Social Victorians/People/Londonderry|Londonderry]] ##The Marquis and Marchioness of [[Social Victorians/People/Ormonde|Ormonde]] ##The Marchioness of [[Social Victorians/People/Queensberry|Queensberry]] ##The Marquis and Marchioness of [[Social Victorians/People/Ripon|Ripon]] ##The Marquis and Marchioness of [[Social Victorians/People/Salisbury|Salisbury]] ##The Marquis and Marchioness of [[Social Victorians/People/Tweeddale|Tweeddale]] ##Dowager (Marchioness of) [[Social Victorians/People/Tweeddale|Tweeddale]] ##John Stewart-Murray, [[Social Victorians/People/Atholl|Marquess of Tullibardine]] ##Lawrence, [[Social Victorians/People/Zetland|Marquess of Zetland]] and Lilian, [[Social Victorians/People/Zetland|Marchioness of Zetland]] #Earls and Countesses ##Countess of Aberdeen and Dowager Countess of Aberdeen ##Earl and Countess of Albemarle and Dowager Countess of Albemarle ##Earl and Countess of Ancaster ##Earl and Countess of Amherst ##Earl of Ava ##Earl and Countess of Antrim ##Earl and Countess of Aylesford ##Earl and Countess of Annesley ##Earl and Countess of Airlie ##Earl and Countess of Arran ##Earl of Aberdeen ##Earl and Countess of Bandon ##Countess of Bantry ##Earl and Countess of Beauchamp ##Earl and Countess of Bathurst and Dowager Countess of Bathurst ##Countess of Bective ##Earl and Countess of Belmore ##Earl of Bradford ##Countess of Bremer ##Earl and Countess of Brownlow ##Earl and Countess of Buckinghamshire ##Earl of Burford ##Earl and Countess of Cairns ##Earl and Countess of Caledon ##Earl of Camperdown ##Earl of Cardigan ##Earl and Countess of Carnarvon and Dowager Countess of Carnarvon ##Earl of Carnwath ##Earl and Countess of Carrington ##Earl and Countess of Carysfort ##Earl and Countess of Castlestuart ##Earl and Countess of Cathcart ##Earl and Countess of Cavan ##Earl and Countess of Chesterfield ##Earl and Countess of Chichester ##Dowager Countess of Clancarty ##Countess of Clanwilliam ##Earl and Countess of Compton ##Countess of Cottenham ##Earl of Courtown ##Earl and Countess of Cowper ##Earl and Countess of Cranbrook ##Earl and Countess of Craven and Dowager Countess of Craven ##Earl and Countess of Crawford ##Earl of Crewe ##Earl and Countess of Cork and Orrery ##Earl and Countess of Coventry ##Countess of Cromartie and Dowager Countess of Cromartie ##Earl and Countess of Dalkeith ##Earl and Countess of Dartmouth ##Earl and Countess of De Grey ##Dowager Countess of De La Warr ##Earl and Countess of Denbigh ##Earl and Countess of Derby ##Earl and Countess of Donoughmore ##Earl and Countess of Drogheda ##Earl of Ducie ##Earl and Countess of Dudley and Dowager Countess of Dudley ##Earl and Countess of Dundonald ##Earl and Countess of Dunmore ##Earl and Countess of Dunraven ##Earl of Durham ##Earl and Countess of Eglinton and Winton ##Earl of Eldon ##Earl and Countess of Ellesinere ##Earl and Countess of Enniskillen ##Earl and Countess of Erne ##Earl and Countess of Errol ##Earl and Countess of Essex and Dowager Countess of Erroll ##Earl of Euston ##Earl and Countess of Feversham ##Earl and Countess of Fingall ##Earl of Fortescue ##Earl and Countess of Gainsborough ##Earl and Countess of Galloway ##Earl and Countess of Glasgow ##Countess of Gosford ##Earl and Countess of Granard ##Countess of Granville ##Earl and Countess of Grey ##Countess of Grosvenor ##Countess of Guilford ##Earl and Countess of Harewood and Dowager Countess of Harewood ##Earl and Countess of Harrington ##Earl and Countess of Hopetoun ##Earl and Countess of Huntingdon ##Earl and Countess of Harrowby ##Countess of Hohenau ##Countess of Howe ##Earl and Countess of Iddesleigh ##Earl and Countess of Jersey ##Earl and Countess of Kenmare ##Earl of Kerry ##Earl and Countess of Kilmorey ##Earl of Kimberley ##Earl and Countess of Kingston ##Earl of Kinnoull ##Josephine, Countess Kinsky ##Earl and Countess of Kintore ##Countess of Leitrim ##Earl and Countess of Lanesborough ##Countess of Lathom ##Earl and Countess of Lauderdale ##Countess of Leicester ##Earl and Countess of Leven and Melville ##Earl and Countess of Lichfield ##Earl and Countess of Limerick ##Earl and Countess of Lindsay ##Earl and Countess of Lisburne ##Earl and Countess of Listowel ##Earl and Countess of Londesborough ##Earl and Countess of Longford ##Earl and Countess of Lonsdale and Dowager Countess of Lonsdale ##Earl and Countess of Loudoun ##Earl and Countess of Lovelace ##Earl and Countess of Lucan ##Countess of Lytton ##Countess of Macclesfield ##Earl and Countess of Malmesbury and Dowager Countess of Malmesbury ##Earl and Countess of Mar ##Earl and Countess of Mar and Kellie and Dowager Countess of Mar and Kellie ##Earl and Countess of Mayo and Dowager Countess of Mayo ##Countess of Meath ##Countess of Metaxas ##Earl and Countess of Mexborough ##Earl and Countess of Minto ##Earl of De Montalt ##Earl and Countess of Morley ##Earl and Countess of Morton and Dowager Countess of Morton ##Earl of Nelson ##Earl and Countess of Norbury ##Earl of Northbrook ##Earl and Countess of Northesk and Dowager Countess of Northesk ##Earl and Countess of Onslow ##Earl of Orford ##Countess of Oxford ##Earl and Countess of Pembroke ##Countess of Percy ##Earl and Countess of Portarlington ##Earl and Countess of Portsmouth ##Earl and Countess of Powis ##Earl and Countess of Radnor ##Earl and Countess of Ravensworth ##Earl and Countess of Roden ##Earl and Countess of Romney ##Lawrence, [[Social Victorians/People/Zetland|Earl of Ronaldshay]] ##Earl of Rosebery ##Earl and Countess of Rosse ##Earl and Countess of Rosslyn and Dowager Countess of Rosslyn ##Earl of Sandwich ##Earl of Scarbrough ##Earl and Countess of Selborne ##Countess of Selkirk ##Countess of Shaftesbury ##Dowager Countess of Shrewsbury and Talbot ##Earl and Countess of Spencer ##Earl and Countess of Stamford ##Earl and Countess of Stanhope ##Earl and Countess of St. Germans ##Earl of Stradbroke ##Earl of Strafford ##Earl and Countess of Suffolk and Berkshire ##Earl and Countess of Temple (of Stowe) ##Earl and Countess of Verulam ##Earl and Countess of Waldegrave ##Earl and Countess of Warwick ##Earl and Countess of Westmeath ##Earl and Countess of Wharncliffe ##Elizabeth, Dowager Countess of Wilton and Isabella, Dowager Countess of Wilton ##Earl and Countess of Winchilsea and Nottingham ##Earl and Countess of Winterton ##Earl and Countess of Yarborough and Dowager Countess of Yarborough #Viscounts<ref name=":1" /> (4, Col. 3c / Col. 4a) and Viscountesses ##Viscount and Viscountess of Boyne ##Viscountess of Cantelupe ##Viscount and Viscountess of Castlerosse ##Viscount and Viscountess of Chelsea ##Viscount and Viscountess of Chetwynd ##Viscountess of Chewton ##Viscount and Viscountess of Clifden ##Viscount and Viscountess of Cobham ##Viscount and Viscountess of Coke ##Viscount of Corry ##Viscount and Viscountess of Cranborne ##Viscount of Crichton ##Viscount and Viscountess of Cross ##Viscount of Curzon ##Viscount and Viscountess of Dalrymple ##Viscount and Viscountess of Deerhurst ##Viscount and Viscountess of De Vesci ##Viscount and Viscountess of Dillon ##Viscount of Doneraile ##Viscount and Viscountess of Duncannon ##Viscount of Dungarvan ##Viscount and Viscountess of Ebrington ##Viscount and Viscountess of Emlyn ##Viscount of Encombe ##Viscount and Viscountess of Exmouth ##Viscount and Viscountess of Falkland ##Viscount and Viscountess of Falmouth ##Viscount of Fitz Harris ##Viscount and Viscountess of Folkestone ##Viscount and Viscountess of Frankfort de Montmorency ##Viscount and Viscountess of Gage ##Viscount and Viscountess of Galway ##Viscount and Viscountess of Garnock ##Viscount and Viscountess of Gough ##Viscount of Gort ##Viscount and Viscountess of Halifax ##Viscount and Viscountess of Hardinge ##Viscount of Harrington ##Viscount and Viscountess of Hood ##Viscount and Viscountess of Kilcoursie ##Viscount and Viscountess of Knutsford ##Viscount and Viscountess of Lifford ##Viscount of Llandaff ##Viscount and Viscountess of Maitland ##Viscount and Viscountess of Marsham ##Viscount and Viscountess of Massereene and Ferrard ##Viscount and Viscountess of Melville ##Viscount and Viscountess of Midleton ##Viscount and Viscountess of Milton ##Viscount and Viscountess of Monck ##Viscount and Viscountess of Morpeth ##Dowager Viscountess of Mountmorres ##Viscount and Viscountess of Newark ##Viscount and Viscountess of Newport ##Viscount and Viscountess of Oxenbridge ##Viscount of Parker ##Viscount of Peel ##Viscount and Viscountess of Portman ##Viscount and Viscountess of Powerscourt ##Viscount and Viscountess of Raincliffe ##Viscountess of Sherbrooke ##Viscount of Sidmouth ##Viscount of St. Cyres ##Viscount of Southwell ##Viscount of Suirdale ##Viscount and Viscountess of Templetown ##Viscountess of Torrington ##Viscount and Viscountess of Trafalgar ##Viscount and Viscountess of Valentia ##Viscount of Valletort ##Viscount of Villiers ##Viscountess of Wolseley #Bishops — Auckland, Barry, Bath and Wells, British Colombia, Chichester, Durham, Ely, Exeter, Gloucester and Bristol, Gibraltar, Hereford, London, Lichfield, Lincoln, Manchester, Newcastle, Norwich, Oxford, Peterborough, Rochester, Ripon, Stepney, Southwark, St. Albans, Salisbury, Sodor and Man, Southwell, Sydney, Sierra Leone, Worcester, Winchester, Wellington #Baronesses — Burdett-Coutts, Macdonald #Lords and Ladies<ref name=":1" /> (4, Col. 4b / Col. 5a) — ##Lord and Lady Abercromby ##Lord and Lady Aberdare ##Lord Aberdour ##Lady Abinger ##Lady Alexandra Acheson ##Lady Adam ##Lady Adderley ##Lord and Lady Addington ##Lady Adye ##Lady Agnew ##Lady Alderson ##Lord and Lady Alington ##Lady Alison ##Lady Mildred Allsopp ##Lord and Lady Amherst of Hackney ##Lady Heathcoat Amory ##Lord and Lady Ampthill ##Lady Agnes Anderson ##Lady Bertha Anson ##Lady Arbuthnot ##Lady Alice Archer Houblon ##Lord Ardee ##Lord and Lady Ardilaun ##Lady Armstrong ##Lady Arnold ##Lady Arnott ##Lord and Lady Ashbourne ##Lord and Lady Ashburton and Dowager Ashburton ##Lord and Lady Ashcombe ##Lady Alice Ashley ##Lady Edith Ashley ##Lady Ashmead-Bartlett ##Lord and Lady Ashton ##Lord and Lady Ashtown ##Lady Florence Astley ##Lady Gertrude Astley-Corbett ##Lady Austin ##Lord Bagot ##Lady Bailey ##Lady Blanche Baillie ##Lady Baird ##Lady Baker ##Lord Balcarres ##Lord and Lady Balfour of Burleigh, Lady Nina Balfour and Lady Betty Balfour ##Lord Balvaird ##Lord Bangor ##Dowager Lady Barclay ##Lord and Lady Barnard ##Lady Florence Barnardiston ##Lady Constance Barne ##Lady Barran ##Lady Barrington ##Lord and Lady Basing ##Lord and Lady Bateman ##Lady Evelyn Bathurst ##Lord and Lady Battersea ##Lady Steuart Bayley ##Lady Violet Beauchamp ##Lord Osborne Beauclerk and Lady Beauclerk (2) ##Lady A. Beaumont ##Lady Bedford ##Lord and Lady Belhaven and Stenton and Dowager Belhaven and Stenton ##Lord and Lady Bellew and Dowager Bellew ##Lord and Lady Belper ##Lady Charles Beresford ##Lady William Beresford (Lilian Duchess of Marlborough) ##Lady Bergne ##Lord and Lady Bertie and Lady Elizabeth Bertie ##Lady Biddulph, Lady Elizabeth Biddulph and Lady Wilfreda Biddulph ##Lady Bigge ##Lord and Lady Bingham ##Lord and Lady Binning ##Lord Blackwood, Lord Basil Blackwood. Lady Hermione Blackwood and Lord Terence Blackwood ##Lady Bloomfield ##Lady Blythswood ##Lord and Lady Bolton ##Lady Maud Bootle-Wilbraham, Lady Bertha Bootle-Wilbraham and Lady Edith Bootle-Wilbraham ##Lord Borthwick ##Lady Margaret Boscawen ##Lord and Lady Boston ##Lady Boughey ##Lady Albreda Bourke and Lady Florence Bourke ##Lady Bowen ##Lady Bower ##Lady Muriel Boyle and Lady Boyle (2) ##Lady Mary Brabazon ##Lady Brackenbury ##Lady Braddon ##Lady Bramwell ##Lady Bramston ##Lord Brassey, Lady Idina Brassey and Lady Violet Brassey ##Lord and Lady Braye ##Lady Mary Bridgeman ##Lady Eleanor Brodie ##Lady Hilda Brodrick ##Lady De Capel Brooke and Dowager Brooke ##Lady Cunliffe Brooks ##Lord and Lady Brougham and Vaux ##Lord and Lady Ulick Browne, Lady Browne and Lady Crichton Browne ##Lady Brownlow ##Lord and Lady F. Brudenell-Bruce ##Lady Brunner ##Dowager Buchanan-Riddeil ##Lady Audrey Buller ##Lady Burdett ##Lord and Lady Burghclere ##Lord Burghley ##Lady Agnes Burne ##Lady Burrell ##Lord and Lady Burton ##Lady Butler and Lady Butler (2) ##Lord and Lady Arthur Butter ##Lady Buxton and Lady Victoria Buxton ##Lady Susan Byng ##Lord and Calthorpe ##Lady C. Cameron and Lady Margaret Cameron ##Lord and Lady Archibald Campbell and Lady A. Campbell ##Lord and Lady George Campbell ##Lady Campbell-Bannerman ##Lord and Lady Camoys ##Lord and Lady Carbery and Dowager Carbery ##Lady Carbutt ##Lady Cardon ##Lord and Lady Cardross ##Lord and Lady Carew ##Lady Carmichael ##Lord and Lady Carnegie ##Lord and Lady Castlemaine ##Lord and Lady Castletown ##Lady Eva Cathcart and Lady R. Cathcart ##Lady Frederick Cavendish, Lady Myra Cavendish, Lady Evelyn Cavendish and Lady Harriet Cavendish ##Lord Charles Cavendish-Bentinck, Lord and Lady Henry Cavendish-Bentinck, Lord William Cavendish-Bentinck, Lady Ottoline Cavendish-Bentinck ##Lord and Eustace Cecil, Lord Hugh Cecil, Lord and John Cecil, Lord and Edward Cecil, Lord and Lady Robert Cecil, Lord W. Cecil, Lady Gwendolen Cecil, Lady Florence Cecil, Lady William Cecil, Lady Louisa Cecil ##Lady Francis Cecil-Dallas ##Lady Chamberlain ##Lady Chelmsford ##Lord and Lady Chesham ##Lady Chetwode ##Lord Cheylesmore ##Lord and Lady Fitzwarine Chichester ##Lady Chitty ##Lady Cholmeley ##Lady Henry Cholmondeley ##Lady Clements (2) ##Lady Churchill, Lady Randolph Churchill, Dowager Churchill, Lady Spencer Churchill (2) ##Lord Edward Spencer-Churchill, Lady Alfred Spencer-Churchill ##Lord and Lady Churston ##Lord and Lady Clifford of Chudleigh ##Lady Marshal Clarke, Lady E. Clarke ##Lady Isabel Clayton ##Lord and Lady Clinton ##Lord and Lady Clonbrock ##Lord Cloncurry ##Lady Muriel Close ##Lady Evelyn Cobbold ##Lady Cochrane, Lady Gertrude Cochrane, Lady Adela Cochrane ##Lady Coddington ##Lady Mabel Coke ##Lord and Lady Colchester ##Lady Cole (2) ##Lady Colebrooke ##Lord and Lady Coleridge ##Lady Collins ##Lady Colomb ##Lady Colvile, Lady Colville ##Lord and Lady Colville of Culross ##Lady Jane Seymour Combe, Lady Constance Combe ##Lady Commerell ##Lord and Lady Alwyne Compton ##Lady Dowager Congleton ##Lord and Lady Connemara ##Lady Conyers ##Lady Blanche Conyngham ##Lady Cooper ##Lady Evelyn Cotterell ##Lord and Lady Cottesloe ##Lady Couch ##Lord and Lady Courtenay ##Lady Coventry (2) ##Lady Cowell ##Lady Helen Craven ##Lord and Lady Crawshaw ##Lady Evelyn Crichton, Lady Emma Crichton ##Lord Crofton ##Lady Cromer ##Lady Mary Crosse ##Lady Crossley ##Lady Mary Cuffe ##Lady Culme-Seymour ##Lady Cunliffe ##Lady Georgiana Curzon ##Lady Elizabeth Cust ##Lady Ida Dalzell ##Lady Mary Dashwood ##Lord and Lady Davey ##Lady Victoria Dawnay, Lady Evelyn Dawnay, Lady Adelaide Dawnay ##Lady Decies ##Lord and Lady De Freyne ##Lord and Lady De L’Isle and Dudley ##Lord De Manley ##Lady Mildred Denison, Lady Elinor Denison ##Lord Deramore ##Lord and Lady De Ramsey ##Lady Dering ##Lady De Ross ##Lord and Lady De Saumarez ##Lady Des Voeux ##Lady De Trafford, Lady Agnes De Trafford ##Lady De Winton ##Lord and Lady Digby ##Lady Dorchester ##Lady Dorington ##Lady Margaret Douglas, Lady Edith Douglas ##Lady H. Douglas-Hamilton ##Lady Dowell ##Lady Drummond, Lady Edith Drummond ##Lady Du Cane ##Lady Duckworth ##Lady Eva Dugdale ##Lord Dunally ##Lady Florence Duncombe, Lady Ulrica Duncombe, Lady Caroline Duncombe ##Lady Alice Dundas ##Lord and Lady Dunleath ##Lord Dunglass ##Lady Dunn ##Lord Dunsandle and Clanconal ##Lady Durand ##Lord Dynevor ##Lord Ebury ##Lady Edmonstone ##Lady Edwards, Lady J. B. Edwards, Lady Blanche Edwards ##Lady Ernestine Edgcumbe ##Lady Egerton (2) ##Lord Egerton of Tatton ##Lady Grey-Egerton ##Lord and Lady Elcho ##Lord and Lady Elibank ##Lady Ellenborough ##Lady Ellis ##Lord and Lady Elphinstone ##Lady Winifred Cary-Elwes ##Lady Engleheart ##Lord Erskine, Lady Erskine (2), Lady Horatia Erskine, Lady Erskine ##Lord and Lady Esher ##Lady Evans ##Lady Evelyn Ewart, Lady Mary Ewart ##Lady Evelyn Eyre ##Lady Fairbairn ##Lady Fairfax ##Lady Anne Fane, Lady Augusta Fane ##Lady Farquhar ##Lord and Lady Farrer ##Lady Fayrer ##Lady Louisa Feilding ##Lady Helen Munro Ferguson ##Lady Fergusson ##Lady Ffolkes ##Lady Finlay ##Lady Fisher ##Lady Dorothea Fitz-Clarence, Lady Maria Fitz-Clarence, Lady Dorothy Fitzclarence ##Lord and Lady Henry Fitz-Gerald, Lady B. Fitz Gerald, Lady M. FitzGerald, Lord Seymour Fitz-Gerald ##Lady Beatrix Fitzmaurice ##Lord and Lady F. FitzRoy, Lady C. Fitz-Roy ##Lady Mary Fitzwilliam ##Lady FitzWygram ##Lady Fletcher ##Lady Flower, Lady Flower ##Lord Foley, Lady Mary Foley ##Lady Gertrude Foljambe ##Lady Angela Forbes, Lady Forbes (2), Dowager Helen Forbes ##Lord and Lady Forester ##Lady Forrest ##Lady Susan Fortescue ##Lady Forwood ##Lady Foster ##Lady Fowler ##Lady Edith Franklin ##Lady Fremantle, Lady Fremantle ##Lady Frere ##Lady Fulton ##Lady Gardiner, Lady Lynedoch Gardiner ##Lord Garioch ##Lady Galton ##Lady Katharine Gathorne-Hardy ##Lady Garvagh ##Lord and Lady Gerard ##Lady Gilbey ##Lady Gillford ##Lady Susan Gilmour ##Lady Gipps ##Lord and Lady Glamis ##Lord and Lady Glenesk ##Lady Glyn, Lady Mary Carr Glyn ##Lady D'Arcy Godolphin-Osborne ##Lady Gordon ##Lady Margaret Ormsby Gore, Lady Constance Gore ##Lady Gore Langton (2) ##Lord Walter Gordon-Lennox, Lord Algernon Gordon-Lennox ##Lady Evelyn Goschen ##Lord R. S. Gower ##Lady Graham, Lady Margaret Graham, Lady Helen Graham ##Lady Charlotte Graham-Toler ##Lady Grant, Lady Florence Grant ##Lady Grant-Duff ##Lady Green ##Lord Greenock ##Lady Grenfell ##Lady Frances Gresley ##Lady Victoria Grey, Lady Grey ##Lady Jane Grey-Trefusis ##Lady Griffin ##Lady Helen Grimston ##Lord and Lady Arthur Grosvenor, Lady Grosvenor (2) ##Lady Gull ##Lady Haldon ##Lady Haliburton ##Lady Basil Hall ##Lady Halle ##Lord and Lady Halsbury ##Lord and Lady E. Hamilton, Lord F. Hamilton, Lady F. Douglas Hamilton, Lady Alexandra Hamilton, Lady Baillie Hamilton (2), Lady C. Hamilton, Lady Victoria Hamilton, Lady George Hamilton ##Lady Hanson ##Lady Harcourt ##Lady Cicely Hardy, Lady Hardy ##Lady Beatrice Hare ##Lord Harlech ##Lady Constance Harris, Lady Harris ##Lady Harrison, Lady Harriet Harrison ##Lady Hart ##Lady Emily Hart-Dyke ##Lady Dixon-Hartland ##Lady Hartopp ##Lord and Lady Hastings ##Lord and Lady Hatherton ##Lady Alice Havelock-Allan ##Lady Hawke ##Lord and Lady Hawkesbury ##Lady John Hay, Lady Hay ##Lady Blanche Haygarth ##Lady Hayter ##Lady Hely-Hutchinson (2) ##Lady Hemming ##Lord and Lady Heneage ##Lord and Lady Henley ##Lord Henniker ##Lady Beatrix Herbert, Lady Herbert (2) ##Lord and Lady Herries ##Lord and Lady Herschell ##Lord Francis Hervey, Lady Augustus Hervey ##Lady Hervey-Bathurst ##Lady Fermor Hesketh ##Lady Hibbert ##Lady Lucy Hicks-Beach ##Lord and Lady Arthur Hill, Lady Clement Hill, Lady Stock Hill ##Lord and Lady Hillingdon ##Lord and Lady Hindlip ##Lord and Lady Hobhouse ##Lady Norah Hodgson ##Lady Holdich ##Lady Mary Holland ##Lady Beatrix Douglas Home ##Lady Maria Hood ##Lady Hood of Avalon ##Lady Hooker ##Lady Mary Hope ##Lady Hoskins ##Lord and Lady Hotham ##Lord and Lady Hothfield ##Lady Houldsworth ##Lady Eleanor Howard, Lady Agnes Howard, Lady Howard (2), Lady Mabel Howard, Lady Rachel Howard ##Lord and Lady Howard of Glossop ##Lady Howarth ##Lady Mary Hozier ##Lady Florentia Hughes ##Lady Seager Hunt ##Lady Hunter ##Lord Hyde ##Lady Hylton ##Lord and Lady Inchiquin ##Lord Inverurie ##Lord and Lady Iveagh ##Lady Jackson ##Lord James of Hereford ##Lady Margaret Jenkins, Lady Jenkins ##Lady Jenner ##Lady Jephson ##Dowager Jessel, Lady Jessell ##Lady Jeune ##Lady Hill Johnes ##Lady Joicey ##Lady Alice Jolliffe ##Lady Burn Jones ##Lady Caroline Lister Kaye, Lady Beatrice Lister Kaye, Lady Lister Kaye ##Lady Isabella Keane ##Lady Keith-Falconer (2) ##Lord and Lady Kelvin ##Lady Kemball ##Lady Beatrice Kemp ##Lady Kennard ##Lady Kennaway ##Lady Aline Kennedy ##Lady Kennett-Barrington ##Lord Kenyon ##Lady Mabel Kenyon-Slaney ##Lord Kensington ##Lady Mary Stuart Keppel ##Lady Innes-Ker (2) ##Lady Kerr (2) ##Lord Kilmarnock ##Lady King ##Lady Florence King King ##Lady Emily Kingscote ##Lady Edith King-Tenison ##Lord and Lady Kinnaird ##Lady Kitson ##Lady Laking ##Lady Frances Lambart, Lady Ellen Lambart ##Lady Victoria Lambton ##Lady Adela Larking ##Lady Isabel Larnach ##Lady Mary Lascelles ##Lord and Lady Lawrence ##Lady Lawson ##Lord and Lady Leconfield ##Lady Elliott Lees, Lady Lees ##Lady Leese ##Lady Legard ##Lord and Lady Leigh ##Lady Henry Gordon-Lennox, Lady Walter Gordon-Lennox, Lady Algernon Gordon-Lennox, Lady Caroline Gordon-Lennox ##Lady Katharine Le Poer Trench ##Lady Constance Leslie ##Lady Susan Leslie-Melville ##Lady Lewis ##Lady Lilian Liddell ##Lady Lindley ##Lady Harriet Lindsay, Lady Jane Lindsay, Lady Jane Lindsay ##Lord and Lady Lingen ##Lord and Lady Lister ##Lady Gwendolen Little ##Lady Margaret Littleton ##Lord and Lady Llangattock ##Lady Llewelyn ##Lord and Lady Loch ##Lady Lockwood ##Lady Louise Loder ##Lady Catherine Loftus ##Lady Doreen Long ##Lady Longley ##Lady Albertha Lopes ##Lady Loraine ##Lord and Lady Lovat ##Lady Drury Lowe, Lady Lucy Drury Lowe ##Lady Lowry-Corry (2) ##Lady Mary Loyd ##Lady Lubbock ##Lord and Lady Lurgan and Dowager Lurgan ##Lady Lyall ##Lady Lyell ##Lady Mary Lygon ##Lady Lyons ##Lady Lysons ##Lady Lyttelton ##Lady Emily Lytton ##Lady MacCormac ##Lord and Lady Macdonald ##Lady Macgregor, Lady MacGregor, Lady Helen MacGregor ##Lady Mackenzie, Lady Mackenzie ##Lady Mackworth ##Lady Maclean ##Lord and Lady Macnaghten ##Lady Macpherson-Grant ##Lady Caroline Madden, Lady Madden ##Lady Louisa Magenis ##Lady Magheramorne, Dowager Magheramorne ##Lady Nora Maitland ##Lady Margaret Crichton-Maitland ##Lady Margaret Majendie ##Lord Cecil Manners, Lord Edward Manners, Lord Manners, Lady Victoria Manners, Lady Manners ##Lady Blundell Maple ##Lady Mappin ##Lady Marjoribanks ##Lady Markham ##Lady Marriott ##Lady Martin, Lady Martin ##Lady Evelyn Mason ##Lady Maude (2) ##Lady H. Maxwell, Lady Maxwell, Lady Maxwell, Lady Maxwell ##Lady Heron-Maxwell ##Lady M'Clintock ##Lady Evelyn M'Donnell ##Lady Meade (2) ##Lord and Lady Medway ##Lady Methuen ##Lady Meysey-Thompson ##Lord and Lady Middleton, Lady Middleton ##Lady Mary Milbanke ##Lady Miller ##Lady Milner ##Lady Clementina Mitford ##Lady Lady M'lver ##Lady Hilda M'Neile ##Lady Monckton ##Lord Moncreiff, Lady Scott Moncrieff ##Lady Moncreiffe ##Lord and Lady Monkswell ##Lady Monson ##Lord Charles Montagu, Lady Cecil Scott Montagu, Lady S. Montagu, Lady Agneta Montagu ##Lord Montagu of Beaulieu ##Lord and Lady Monteagle ##Lady Edith Montgomerie, Lady Sophia Montgomerie ##Lady Charlotte Montgomery ##Lady More-Molyneux ##Lord and Lady Moreton ##Lady Morgan ##Lord and Lady Morris ##Lady Blanche Morris ##Lady Mary Morrison ##Lady Moseley ##Lord and Lady Mostyn ##Lord and Lady Mowbray and Stourton, Dowager Mowbray and Stourton, Lady Mowbray ##Lord and Lady Muncaster ##Lady Anne Murray ##Lady Murray (2) ##Lady Georgiana Mure, Lady Georgiana Mure [sic] ##Lord and Lady Napier and Ettrick ##Lord and Lady Napier of Magdala and Dowager Napier of Magdala ##Lady Naylor-Leyland ##Lady Nelson ##Lord and Lady Henry Nevill ##Lord and Lady Newton ##Lord and Lady Newtown-Butler ##Lady Nicolson ##Lady Augusta Noel, Lady Agnes Noel ##Lady Norman ##Lord and Lady Norreys ##Lord and Lady North, Lady Muriel North ##Lady Northcote, Lady Northcote (2) ##Lord Norton ##Lady Elizabeth Nugent ##Lady O'Brien, Lady O'Brien [sic] ##Lady O'Hagan ##Lady Olpherts ##Lord and Lady O'Neill ##Lady Gwendoline O'Shee ##Princep [sic] Alice Packe ##Lord and Lady Berkeley Paget ##Lady Alfred Paget ##Lady Paget of Cranmore ##Lady Katherine Pakenham ##Lady Palgrave ##Lady Sophia Palmer, Lady Palmer ##Lady Evelyn Parker ##Lady Parratt ##Lady Maude Parry ##Lady Muriel Parsons ##Lord and Lady Pearson, Lady Pearson ##Lady Peel, Lady Georgiana Peel ##Lady Constance Childe-Pemberton ##Lord and Lady Penrhyn ##Lady Mary Pepys ##Lady Perceval ##Lady Percy (2) ##Lady Petre ##Dowager Lady Peyton ##Lady Phillimore ##Lady William Phipps ##Lord and Lady Pirbright ##Lord and Lady Playfair ##Lady Chichele Plowden ##Lady Anna Chandos-Pole ##Lady Pollock ##Lord and Lady Poltimore ##Lady Pontifex ##Lady Alice Portal ##Lady Powell, Lady Powell [sic] ##Lady Baden-Powell ##Lady Dickson-Poynder ##Lady Poynter ##Lord and Lady George Pratt ##Lady Priestley ##Lady Probyn ##Lady Eva Wyndham-Quin, Lady Wyndham-Quin (2) ##Lord and Lady Raglan, Dowager Raglan ##Lady Ramsay ##Lord and Lady Rathdonnell ##Lady Rathmore ##Lord and Lady Rayleigh, Dowager Rayleigh ##Lord and Lady Reay ##Lady Reid ##Lord and Lady Rendel ##Lord Rendlesham ##Lady Jane Repton ##Lord Revelstoke ##Lord and Lady Ribblesdale ##Lady Laura Ridding ##Lord and Lady Robartes ##Lady O. Roberts ##Lady Roberts of Kandahar ##Lady Robinson ##Lord and Lady Rodney ##Lord Romilly ##Lord and Lady Rookwood ##Lord and Lady Rossmore ##Lord Rowton ##Lady Roxburgh ##Lord and Lady Rothschild ##Lady Victoria Russell, Lady Arthur Russell, Lady G. Russell, Lady W. H. Russell, Lady Alexander Russell ##Lord and Lady Russell of Killowen ##Lord and Lady Ruthven ##Lady Jane Ryan ##Lady Mary Sackville ##Lady Salmon ##Lord and Lady Saltoun ##Lady Samuelson, Lady S. Samuel ##Lady Mary Saurin ##Lord and Lady Savile, Lady Marie Savile ##Lady Savory ##Lord George Scott, Lord Henry Scott, Lord Herbert Scott, Lady Sophie Scott, Lady Charles Scott, Lady Louisa Scott, Lady Scott (2) ##Lord and Lady Seaton ##Lord and Lady Settrington ##Lady Seymour, Lady Albert Seymour, Lady William Seymour, Lady Seymour (2) ##Lord and Lady Shand ##Lady Shaw ##Lady Constance Shaw-Lefevre ##Lady Octavia Shaw-Stewart, Lady Alice Shaw-Stewart ##Lady Mary Shelley ##Lord and Lady Sherborne ##Lady Shippard ##Lady Shute ##Lady Kay-Shuttleworth ##Lady Simeon ##Lady Simmons ##Lady Simpson of Windsor ##Lord and Lady Sinclair ##Lord and Lady Skelmersdale ##Lady Esther Smith, Lady Barbara Smith, Lady Smith, Lady Blanche Smith, Lady Sybil Smith, Lady Euan Smith, Lady D. Smith ##Lady Smyth ##Lady Catherine Somerset, Lady Geraldine Somerset, Lady Henry Somerset ##Lord and Lady Southampton, Dowager Southampton ##Lady Edward Spencer-Churchill ##Lady Margaret Spicer ##Lady Sprigg ##Lady Stafford ##Lord Stalbridge ##Lady Stanhope (2) ##Lord Stanmore ##Lord Stanley, Lady Alice Stanley, Lady Isobel Stanley ##Lady Stansfield ##Lord Stavordale ##Lady Stephenson ##Lady Stevenson ##Lady Helen Stewart, Lady Mary Stewart, Lady Mark Stewart, Lady Stewart, Lady Houston Stewart, Lady Stewart [sic], Lady Isabel Stewart ##Lady Stewart of Grantully ##Lady Edith St. Aubyn ##Lord and Lady St. Levan ##Lady St. Leonards ##Lord and Lady St. Oswald ##Lady Stone ##Lady Charlotte Stopford ##Lord and Lady Stratheden and Campbell ##Lady Mary Stuart-Richardson ##Lord Suffield ##Lady Sutherland ##Lady Evelyn Sutton, Lady Susan Sutton ##Lord and Lady Swansea ##Lady Swinnerton Dyer ##Lady Kathleen Swinnerton-Pilkington ##Lord and Lady E. Talbot, Lady Emma Talbot ##Lady Jane Taylor ##Lady Taylour (2) ##Lady Tatton Sykes ##Lord Herbert Vane-Tempest, Lord Henry Vane-Tempest ##Lord and Lady Templemore ##Lady Tennant ##Lord and Lady Tennyson ##Lady Tenterden ##Lord Tewkesbury ##Lord and Lady Teynham ##Lord and Lady Thring ##Lady E. Thornton ##Lady Thursby ##Lady Ulrica Thynne ##Lord and Lady Tollemache ##Lady Agnes Townshend ##Lady Mary Trefusis ##Lady Tredegar ##Lady Trevelyan, Lady Trevelyan [sic] ##Lord and Lady Trevor ##Lady Troubridge ##Lady Turner ##Lady Henrietta Turnor ##Lady Tuson ##Lord and Lady Tweedmouth ##Lady Tyler ##Lady Emily Van De Weyer ##Lady Jane Van Koughnet ##Lord and Lady Ventry ##Lady Villiers (2), Lady Edith Villiers ##Lady Howard Vincent, Lady Helen Vincent, Lady Vincent ##Lady Vivian, Lady Jane Vivian ##Lady Mary Waldegrave ##Lady F. F. Walker, Lady James Walker ##Lady Walrond ##Lady Clementine Walsh ##Lord Wandsworth ##Lady Wantage ##Lord Warksworth ##Lady Leucha Warner ##Lady Warrender ##Lord and Lady Watson ##Lady Cecilia Webb ##Lady Rose Weigall ##Lord Welby ##Lady Willes ##Lady Willis ##Lady Arthur Wellesley ##Lord and Lady Wenlock ##Lord and Lady Westbury and Dowager Westbury ##Lady Isabella Whitbread ##Lady White ##Lady Whitehead ##Lady Whiteway ##Lady Elizabeth Williamson ##Lady Williams-Wynn ##Lady Willoughby (2) ##Lord Willoughby de Broke ##Lord Willoughby de Eresby ##Lady Willshire ##Lady Wilson, Lady Sarah Gordon Wilson ##Lord and Lady Wimborne ##Lady Windeyer ##Lord and Lady Windsor ##Lady Winnington ##Lady Constance Wodehouse ##Lord and Lady Wolverton ##Lady Julia Wombwell ##Lady Wood, Lady Mary Wood ##Lady Woods ##Lord Wrottesley ##Lady Hugh Wyndham ##Lady Barbara Yeatman ##Lady Lilian Yorke ##Lord Zouche #Right Honourables ##H. H. Asquith ##E. Ashley ##A. H. Dyke Acland ##J. Atkinson ##J. B. Balfour ##Sir G. Bowen ##G. W. Balfour ##Sir Hicks-Beach ##A. J. Balfour ##James Bryce ##Sir H. Campbell-Bannerman ##A. H. Smith-Barry ##E. Carson ##H. Chaplin ##Sir J. Chitty ##Jesse Collings ##Sir R. Couch ##G. N. Curzon ##J. Chamberlain ##L. Courtney ##Sir M. Grant-Duff ##A. Akers-Douglas ##Sir W. Hart Dyke ##Sir H. Elliot ##F. Foljambe ##Sir H. Fowler ##Sir A. B. Forwood ##Sir J. Fergusson ##Herbert Gladstone ##Sir J. Gorst ##G. J. Goschen ##W. E. Gladstone ##Sir G. Grey ##C. H. Hemphill ##Charles Seale-Hayne ##R. W. Hanbury ##Lord George Hamilton ##Staveley Hill ##Sir J. T. Hibbert ##Sir W. Harcourt ##lon Hamilton ##Sir Arthur Hayter ##Sir F. Jeune ##W. L. Jackson ##Sir John Kennaway ##G. Shaw-Lefevre ##W. Lidderdale ##Sir Massey Lopes ##James Lowther ##Sir J. Lubbock ##Sir H. Lopes ##Walter Long ##Sir N. Lindley ##J. W. Mellor ##Sir G. O. Morgan ##John Morley ##Arnold Morley ##Sir J. Mowbray ##A. J. Mundella ##J. H. Macdonald ##F. Max Müller ##Sir W. Marriott ##Graham Murray (the Lord Advocate) ##Sir E. Monson ##Sir P. O'Brien ##Sir A. Otway ##Sir F. Peel ##Sir R. Paget of Cranmore ##W. J. Pirrie ##J. P. Robertson ##Sir. J. Rigby ##C. T. Ritchie ##Sir S. H. Strong ##Sir B. Saunderson ##Sir J. Stansfeld ##Sir A. Smith ##C. R. Spencer ##Sir C. Kay-Shuttleworth ##Sir R. Temple ##Sir R. Thompson ##Sir E. Thornton ##Lord Henry Thynne ##Sir G. O. Trevelyan ##C. P. Villiers ##Sir Algernon West ##Sir C. L. Wyke ##C. B. Stuart-Wortley ##S. J. Way #Honourables<ref name=":1" /> (4, Col. 5a / Col. 5b) and Honourable Ladies<ref name=":1" /> (4, Col. 5b / Col. 5c) ##Mrs. Acland ##Mrs. Alexander ##H. Allsopp, Mrs. Allsopp, George Allsopp ##Mrs. Anstruther ##Mrs. Armytage ##[Hon. Lady] Vere Annesley ##Mrs. Bagot, Mrs. Bagot [sic 2x] ##Mrs. Baillie of Dochfour ##Mrs. Balfour ##[Hon.] Coplestone and [Hon.] Mrs. Bampfylde ##John Baring, Susan Baring, Lilian Baring ##Mrs. Barker ##Mrs. Barlow ##Eric Barrington, Mrs. Barrington ##Mrs. Hamar Bass ##Misses Bateman-Hanbury (2) ##Allen B. Bathurst ##Mrs. Benyon ##[Hon. Lady] Beresford ##[Hon.] R. Chetwynd ##Arthur Chichester ##Lady Biddulph ##C. E. Bingham, Mrs. Bingham, Albert Bingham, Mrs. Bingham [sic x2] ##Lady Birkbeck ##Ivo Bligh, Mrs. Bligh ##Diana Sclater-Booth ##O. Borthwick ##J. Boscawen ##Henry Bourke, Mrs. H. Bourke, Charles Bourke, Terence Bourke, Mrs. T. Bourke, Algernon Bourke, Mrs. A. Bourke, Mrs. E. R. Bourke ##Charles Brand, Arthur Brand, Mrs. Brand, Mrs. T. Brand ##T. Brassey, Mrs. A. Brassey ##Mrs. Stapleton Bretherton ##Reginald Brett, Mrs. Brett ##Mrs. F. Bridgeman, Misses Bridgeman (2) ##Mrs. Britten ##W. St. John Brodrick, Albinia Brodrick ##Emmeline Brownlow ##Mrs. T. C. Bruce, Misses Bruce (2) ##Misses M'Clintock Bunbury (2) ##Mary Byng ##T. J. Byrnes ##Arthur Cadogan, Mrs. A. Cadogan, Mrs. C. Cadogan, Ethel Cadogan ##Mrs. Gough-Calthorpe, Rachel (Gough) Calthorpe, Misses Gough Calthorpe (2) ##Mrs. Candy ##G. H. Campbell, K. Campbell, Hugh Campbell, Mrs. H. Campbell, Mrs. Ronald Campbell, Misses Campbell (2), Mrs. J. B. Campbell, Mildred Campbell ##Mrs. Carington ##Mrs. Carpenter ##Emily Cathcart ##W. Cavendish, Mrs. W. Cavendish, Mrs. Cavendish ##Eleonora Chetwynd, Mrs. R. Chetwynd ##Mrs. A. Chichester, Hilda Chichester ##Mrs. Clowes ##T. H. Cochrane ##Audrey Coleridge ##George Colville ##Mrs. Corbett ##Mrs. H. Corry ##Caroline Courtenay ##Henry Coventry ##Osbert Craven ##Misses Cross ##Mrs. P. Crutchley ##Henry Cubitt, Mrs. Cubitt ##Hamilton Cuffe, Mrs. Otway Cuffe ##Lady Cunningham ##Montagu Curzon, Darea Curzon, Mrs. Curzon ##Hew Dalrymple ##John Dawnay, Eustace Dawnay, W. Dawnay, Mrs. Dawnay (2) ##Misses de Montmorency (2) ##Mrs. H. Dennison ##R. C. Devereux, Mrs. R. C. Devereux ##Mrs. Digby ##Conrad Dillon, Mrs. C. Dillon, Edith Dillon ##Misses Douglas-Pennant (2) ##A. Hay Drummond, Mrs. Hay Drummond, Frances Drummond, Mrs. M. Drummond ##Hubert V. Duncombe, Cecil Duncombe, Mrs. C. Duncombe ##C. T. Dundas, Mrs. C. T. Dundas, W. Dundas, Mrs. W. Dundas, Mrs. John Dundas ##Lady Du Cane ##Herbert Eaton, Mrs. H. Eaton ##F. Egerton, Mrs. A. F. Egerton, Lady Grey Egerton, Tatton Egerton, Mrs. T. Egerton ##Arthur Elliot, Mrs. Arthur Elliot, Lady Elliot, Mrs. Eliot ##Lilian Elphinstone ##Mrs. Ellis ##Muriel Erskine ##H. Escombe, Mrs. Escombe ##Mrs. Evans ##Mrs. C. Keith-Falconer ##Sir S. Ponsonby Fane ##Mrs. W. Farquhar ##Ailwyn Fellowes, Mrs. A. Fellowes ##Mrs. Ferguson of Pitfour ##Everard Fielding ##N. Fitzgerald, Mrs. N. Fitzgerald, Mrs. Fitzgerald, , Mrs. F. G. FitzGerald, Lady FitzGerald ##R. Fitzwilliam, W. H. Fitzwilliam ##Mary Forester ##Sir John Forrest ##Mrs. W. H. Forster ##Mrs. Lionel Fortescue ##Sir C. Fremantle, Mary Fremantle ##Sir Malcolm Fraser, Misses Fraser (2) ##Mrs. Charles Keith-Fraser ##Violet Gibson ##Evelyn Giffard ##Mrs. Henry Gladstone ##Lady Godley ##George Ormsby Gore ##F. Leveson-Gower ##Mrs. Gough ##Mrs. Alaric Grant ##Ronald Greville, Mrs. R. Greville, Louis Greville, Mrs. L. Greville, Sidney Greville, Mrs. A. Greville, Mrs. A. H. F. Greville ##Robert Grosvenor, Algernon Grosvenor, Mrs. A. Grosvenor, Maud Grosvenor, Elizabeth Grosvenor ##Lady Hamilton Gordon, [Hon. Lady] Nevil Gordon ##Misses Guest (2) ##Geoffrey Browne Guthrie ##Mrs. Gye ##Mrs. A. Haig ##Mrs. Halford ##, Misses Hamilton (2) ##Mrs. North Dalrymple-Hamilton ##Mrs. Hobart Hampden ##Mrs. Assheton Harbord, Mrs. C. Harbord, Judith Harbord, Bridget Harbord, Mrs. Harbord ##C. Hardinge, Mrs. C. Hardinge, A. Hardinge ##A. E. Gathorne-Hardy, Nina Gathorne-Hardy ##Misses Hawke (2) ##C. G. Hay ##Misses Heneage (2) ##Helen Henniker, Mrs. Henniker ##Robert Herbert, Sir Robert Herbert, Mrs. R. Herbert, Mrs. Herbert ##A. Holland Hibbert, Mrs. A. Holland Hibbert ##Lady Higginson ##Mrs. Hill ##Lionel Holland, Sydney Holland ##Grosvenor Hood, Dorothy Hood ##Lady Acland-Hood ##Fanny Hood of Avalon ##Mrs. Curzon Howe ##[Hon.] Evelyn Hubbard, Mrs. E. Hubbard, Alice Hubbard ##Mary Hughes ##Mrs. Meynell Ingram ##G. Jolliffe, Sydney H. Jolliffe, Mrs. Jolliffe ##Lady Johnston ##G. Keppel, Mrs. Keppel, Derek Keppel, Mrs. William Keppel ##Mrs. Alfred Ker ##Constance Kerr ##Mrs. Kingscote ##C. C. Kingston ##Lady Knollys ##Bertha Lambart ##F. W. Lambton, Mrs. Lambton ##Mary Lascelles ##Charles Laurence, Herbert Laurence ##Wilfrid Laurier ##Mrs. Lawley ##Mrs. C. Lawrence, Misses Lawrence (2), Mrs. H. Lawrence ##Mrs. Legge ##T. W. Legh, Mrs. Legh, Sybil Legh ##F. D. Leigh, Mrs. F. D. Leigh, E. Chandos Leigh, Mrs. E. C. Leigh, Cordelia Leigh ##C. Hanbury Lennox, Mrs. Hanbury Lennox ##G. W. Leslie ##R. l’Estrange ##Atholl Liddell, Mrs. A. Liddell ##Mrs. H. Gore-Lindsay ##Reginald Lister ##Henry Littleton, Misses Littleton (2) ##Misses Loch (2) ##William Lowther, Mrs. W. Lowther, L. Lowther, Mrs. L. Lowther ##Mrs. E. H. Loyd ##Mrs. Lumley ##Alfred Lyttelton, Mrs. A. Lyttelton, Misses Lyttelton (2), Mrs. Lyttelton ##Flora Macdonald, Lady Macdonald ##Mrs. Mackinnon ##Mrs. Maclagan ##Mrs. Magniac ##Mrs. Maguire ##W. Massey-Mainwaring, Mrs. Massey-Mainwaring ##Mrs. Fuller-Maitland ##Aline Majendie ##Misses Henniker Major (2) ##Mrs. Mallet ##Archibald Marjoribanks ##Misses Constable Maxwell (2) ##Mrs. M'Calmont ##Schomberg M'Donnell ##Charles Mills, Violet Mills, Mrs. Mills ##Mrs. Percy Mitford ##Maud de Moleyns ##Mrs. C. Molyneux ##Annette Monck, Mrs. Monck ##Violet Monckton ##Mrs. Monson ##John Scott Montagu ##[Hon.] Evelyn Moore ##R. Moreton, Mrs. R. Moreton ##Mrs. Mostyn, Misses Mostyn (2) ##Mrs. G. H. Murray, Alice Murray ##Lady Musgrave ##[Hon. Lady] Napier, Emilia Napier, Mrs. Scott Napier ##Mrs. Neeld ##Sir Hugh Nelson ##[Hon.] R. Nevill ##Mrs. Newdigate ##Sir H. S. Northcote ##Misses O'Brien (2) ##Mary O'Hagan ##Mrs. Okeover ##Mrs. Oliphant ##R. Terence O'Neill, Henrietta O'Neill ##Misses Palk (2) ##Cecil Parker, R. Parker, F. Parker, Mrs. F. Parker, Mrs. Parker ##Mabel Parnell ##[Hon.] C. B. Parsons, Mrs. Parsons ##Mrs. W. Paton ##[Hon.] Sydney Peel, Misses Peel (2) ##Mrs. Anderson Pelham ##E. S. Douglas-Pennant, Mrs. E. S. Douglas-Pennant ##Mrs. Heber Percy ##Albert Petre, Mrs. A. Petre ##Harriet Phipps ##Mrs. Pirie ##Thomas Playford ##Horace C. Plunkett ##[Hon.] Ashley Ponsonby, Mrs. Ponsonby, Misses Ponsonby (2) ##H. Orde Powlett, Mrs. Orde-Powlett, Myra Orde-Powlett ##E. W. B. Portman, Mrs. Portman, Mary Portman ##Mrs. Pretyman ##C. Ramsay, Mrs. C. Ramsay ##G. H. Reid ##Misses Rendel (2) ##Misses Rice (2) ##Lady White Ridley ##Mrs. Ritchie ##F. Roberts, Mrs. Phillips Roberts ##Misses Roberts (of Kandahar) (2) ##J. M. Rolls, Eleanor Rolls ##W. Rothschild, Evelina Rothschild ##W. Rowley, Mrs W. Rowley, Lady Thelluson Rowley ##A. Russell, Misses Russell (2) ##Gustavus Hamilton-Russell, Misses Hamilton Russell (2) ##the Master of Ruthven, Mrs. Ruthven ##Mrs. J. D. Ryder ##Sir Saul Samuel ##A. Saumarez, Mrs. A. Saumarez ##Mrs. E. J. Saunderson ##J. Maxwell Scott, Mrs. Maxwell Scott ##R. J. Seddon ##Mary Sidney ##Lady Simeon ##Misses Skeffington (2) ##Sir Donald Smith, Mrs. A. H. Smith, [Hon.] W. F. D. Smith ##Granville Somerset, Mrs. G. Somerset, Arthur Somerset, Mrs. A. Somerset, R. Somerset, Violet Somerset ##Mrs. C. R. Spencer ##Sir J. Gordon Sprigg ##Lyulph Stanley, F. C. Stanley, George Stanley, Mrs. E. J. Stanley, Mrs. Stanley, Mrs. V. A. Stanley, Maude Stanley ##Lady Cowell-Stepney ##Randolph Stewart, Mrs. R. Stewart, FitzRoy Stewart, Mrs. Stewart ##Mabel St. Aubyn ##Misses St. Clair (2) ##Mrs. Stirling ##Horatia Stopford ##[Hon. Lady] Alison Stourton ##Mrs. Strutt, Misses Strutt (2) ##Hilda Sugden ##Alfred Talbot, Mrs. Talbot, Mrs. R. A. J. Talbot ##Sir D. Tennant ##S. R. Thayer ##Misses Thellusson (2) ##Edward Thesiger, Mrs. E. Thesiger, Frederick Thesiger, Mrs. F. Thesiger, Mary Thesiger ##Lady Thorold ##Katharine Thring ##Misses Tollemache (2) ##R. Marsham-Townshend, Mrs. Marsham-Townshend ##Alice Hanbury-Tracy ##Charles Grey Trefusis, Misses Trefusis (2) ##Mrs. Trelawny ##Mrs Tremayne ##Mrs. W. le Poer Trench ##Charles Trevor ##George Hill-Trevor, Marcus Hill-Trevor, Mrs. Hill-Trevor, Misses Hill-Trevor (2) ##Mrs. C. W. Trotter ##Lady Tryon ##Rosamond Tufton ##Sir G. Turner ##Rev. L. Tyrwhitt ##Misses Tyssen Amherst (2) ##Misses Vereker (2) ##R. Greville-Verney, Mrs. R. G. Verney, Misses Verney (2) ##F. Villiers, Mrs. F. Villiers ##Misses Vivian (2) ##Arthur Walsh ##Mrs. P. E. Warburton ##Robert Ward, Mrs. Dudley-Ward ##Mrs. West ##Mrs. Whateley ##Sir W. Whiteway ##F. Bootle-Wilbraham ##Ella Williamson ##Tatton Willoughby ##Lady Wilson ##[Hon.] Armine Wodehouse, Mrs. Wodehouse ##Frances Wolseley ##F. Wood, Misses Wood (2) ##Mrs. G. Wrottesley, Evelyn Wrottesley ##Percy Wyndham, Mrs. P. Wyndham, Misses Wyndham (2) ##Maud Wynn ##Lois Yarde-Buller ##Alex. G. Yorke, Mrs. J. Yorke, Mrs. E. C. Yorke #Sirs<ref name=":1" /> (4, Col. 5c–6a) ##Augustus Adderley ##Edwin Arnold ##John Austin ##George Arthur ##John Heathcoat-Amory ##A. Armstrong ##Andrew Agnew ##Frederick Abel ##Henry Acland ##A. Arnold ##Alexander Arbuthnot ##John Barran ##G. Bower ##J. W. Bonser ##J. Crichton-Browne ##Joseph Bailey ##E. Ashmead-Bartlett ##Henry Barkly ##R. Beauchamp ##Raymond Burrell ##Charles Barrington ##David Baird ##Arthur Birch ##Edward Birkbeck ##W. Cunliffe Brooks ##A. de Capel Brooke ##Courtenay Boyle ##F. Burton ##F. Buxton ##Steuart Bayley ##John Bramston ##John Baker ##H. Bullard ##J. T. Brunner ##H. Bellingham ##Henry Bergne ##Thomas Boughey ##F. J. Bramwell ##E. Burne-Jones ##James Blyth ##Seymour Blane ##Henry Chamberlain ##Roderick Cameron ##Hugh Cholmeley ##John Conroy ##Edward Clarke ##C. Cameron ##E. Carbutt ##W. Coddington ##Marshal Clarke ##Reginald Cathcart ##Savile Crossley ##Edward Colebrooke ##Reginald Cust ##Charles Crosthwaite ##John Colomb ##Daniel Cooper ##F. Astley-Corbett ##Donald Currie ##Henry Cunningham ##Robert Cunliffe ##Henry Cotterell ##T. D. Gibson Carmichael ##F. Curden, ##George Dallas ##James Drummond ##Mortimer Durand ##G. Des Vieux ##Henry Dering ##J. N. Dick ##Dyce Duckworth ##T. Swinnerton Dyer ##E. Hastings Doyle ##John Dorington ##William Dunn ##Humphrey de Trafford ##Charles Dalrymple ##G. Dashwood ##Gardner ##Engleheart ##Francis Evans ##A. Edmonstone ##Whittaker Ellis ##W. H. Flower ##Horace Farquhar ##Joseph Fayrer ##H. Fletcher ##William Ffolkes ##William Fraser ##Bartle Frere ##Gerald Seymour Fitz-Gerald ##Robert Finlay ##B. Walter Foster ##Gerald FitzGerald ##R. FitzGerald ##Maurice FitzGerald ##Forrest Fulton ##William Flower ##Andrew Fairbairn ##John Gilbert ##E. T. Gourley ##Edward Grey ##W. Gull ##Walter Gilbey ##Lepel Griffin ##G. Macpherson-Grant ##Reginald Graham ##Philip Grey Egerton ##Douglas Galton ##R. Glyn ##Arthur Godley ##Charles Grant ##R. Gresley ##Alexander Acland-Hood ##T. G. Fermor Hesketh ##Arthur Haliburton ##Brydges Henniker ##F. Dixon-Hartland ##R. Hanson ##Alfred Hickman ##W. Houldsworth ##Henry Howorth ##F. Seager Hunt ##Charles Hall ##E. W. Hamilton ##Reginald Hardy ##Clement Hill ##Basil Hall ##Joseph Hooker ##Charles Hunter ##Charles Hartopp ##Victor Houlton ##Augustus Hemming ##Henry Irving ##Frederic Johnstone ##W. Jenner ##J. Jenkins ##James Joicey ##Charles Jessell ##Harry Johnston ##Edward Jenkinson ##James Hill Johnes ##John Jackson ##H. Seymour King ##James Kitson ##J. Lister-Kaye ##V. Kennett-Barrington ##George Kekewich ##John Leslie ##Thomas Dick Lander ##T. Villiers Lister ##James Linton ##Charles Lees ##Charles Legard ##Thomas Lea ##Wilfrid Lawson ##Elliott Lees ##A. C. Lyall ##J. T. D. Llewelyn ##Joseph Leese ##Leonard Lyell ##F. Laking ##Godfrey Lushington ##F. Lockwood ##Henry Longley ##George Lewis ##F. Milner ##Herbert Maxwell ##Francis Montefiore ##Graham Montgomery ##Robert Moncreiffe ##Musgrave ##Colin Scott Moncrieff ##Francis Mowatt ##Evan MacGregor ##J. G. Miller ##F. D. Maclean ##J. Blundell Maple ##Allan Mackenzie ##Lewis M'lver ##F. Mappin ##Theodore Martin ##Samuel Montagu ##William MacCormac ##Hubert Miller ##Lewis Morris ##Clements Markham ##A. C. Mackenzie ##John Monckton ##J. Stirling-Maxwell ##J. Heron Maxwell ##Kenneth Matheson ##J. S. Montefiore ##Acquin Martin ##W. Maxwell ##Oswald Moseley ##Arthur Nicolson ##Terence O'Brien ##Reginald Ogilvy ##Herbert Oakeley ##Hush Owen ##G. G. Petre ##Walter Parratt ##Frederick Pollock ##Herbert Perrott ##Douglas Powell ##Weetman Pearson ##Joseph Pease ##Francis S. Powell ##Reginald Palgrave ##W. Priestley ##E. G. Poynter ##G. S. Baden-Powell ##Charles Pontifex ##J. Dickson-Poynder ##James Paget ##C. M. Palmer ##C. Lennox Peel ##James B. Peile ##Westby Perceval ##Charles Pigott ##John Puleston ##W. Plowden ##Richard Quain ##George Russell ##C. Lister Ryan ##W. H. Russell ##J. Ramsay ##Owen Roberts ##R. T. Reid ##Charles Robinson ##J. Thellusson Rowley ##James Reid ##C. Euan-Smith ##J. Barrington Simeon ##J. B. Stone ##M. Shaw-Stewart ##Edward Sieveking ##T. H. Sanderson ##Augustus K. Stephenson ##Thomas Sutherland ##Mark Stewart ##Andrew Scoble ##Joseph Savory ##Douglas Straight ##Charles Shelley ##S. Shippard ##E. Sassoon ##A. Condie Stephen ##E. Sullivan ##Arthur Sullivan ##S. Scott ##H. Simpson ##E. Stafford ##Ernest Satow ##Tatton Sykes ##John Tyler ##Charles Tennant ##John Tenniel ##J. Thorold ##John Thursby ##Thomas Troubridge ##Charles Turner ##H. Meysey-Thompson ##W. Vincent ##Edgar Vincent ##Arthur Vicars ##W. Williams-Wynn ##James Walker ##R. Webster ##George Wombwell ##C. Rivers Wilson ##W. H. Wills ##Donald Mackenzie Wallace ##George Warrender ##F. Winnington ##James Whitehead ##Arthur Willshire ##Henry Wood ##Hugh Wyndham ##W. White ##Sidney Waterlow ##Hedworth Williamson ##Jacob Wilson ##W. Windeyer ##Albert Woods (Garter) ##Allen Young #Chairman of County Council (Dr. Collins) #Counts and Countesses ##Count Cassini ##Count and Countess De Ganay ##Count Gurowski ##Count Hohenau ##Count Theodor Bolesta Koziebrodski ##Count Leon Mniszeek ##Count and Countess Potocki ##Count and Countess Raben #Barons and Baronesses ##Baroness Emile Beaumont d'Erlanger ##Baroness De Brienen ##Baron De Onethau and Baroness D’Onethan [sic] ##Baron and Baroness Alphonse de Rothschild ##Baron Ferdinand Rothschild ##Baron and Baroness Schröder ##Baron and Baroness von Deichmann ##Baron von Heeckeren van Wassenaer ##Baroness von Hügel, Baroness Gertrud von Hügel [sic] ##Baron and Baroness Campbell von Laurentz ##Baroness Wilhelm von Rothschild #Rev. the Moderator of the General Assembly of the Church of Scotland #Deans — Christ Church, St. Paul's, Westminster, Windsor #The Provost of Eton #Master of Trinity (Mr. Butler) #The Sub-Dean of the Chapels Royal #Canons — Blundell, Dalton, Duckworth, Fleming, Hervey, Teignmouth Shore, Wilberforce #Dr. Adler (Chief Rabbi) #Dr. M'Cormick #Chaplain of the Fleet #Chaplain General #Reverend Doctors — Edmund Warre, C. J. Welldon #Reverends — Prebendary Hawkshaw, Albert Baillie, W. H. Bliss, M. Ebrington Bisset, Lord W. Cecil, Lord Charles Fitzroy, J. H. Ellison, H. Haweis, W. R. Jolly, G. J. Martin, Newton Mant, Marquis of Normanby, A. Robins. W. Gunion Rutherford, Clement Smith, Montagu Villiers #Doctors — Lennox Browne, J. V. Bridge, Barlow, Robert Farquharson, J. F. Fox, Surgeon-Major Kilkelly, John Lowe, C. H. H. Parry, G. V. Poore, Dorrien Smith, S. Wilks #Messieurs<ref name=":1" /> (4, Col. 6b–7a), Mesdames (4, Col. 7a–b) and Misses<ref name=":1" /> (4, Col. 7c – 5, Col. 1a) ##Mme Abdy ##Mr C. T. Dyke-Acland, Mme A. H. Dyke Acland, Mme Dyke Acland ##Mme Adair ##Misses Adam (2) ##Mr and Mme Adeane ##Misses Adye [?] (2) ##Mme Agar ##Mr Hamilton Aidé ##Mr John Aird, Misses Aird (2) ##Miss Akers-Douglas ##Mr Edward Alderson ##Mr George Alexander, Mme Alexander, Miss Alexander ##Miss Alison ##Mr and Mme Allhusen ##Mme Alma-Tadema ##Mr W. Ambrose ##Miss Heathcoat-Amory ##Mr R. Anderson, Miss Florence Anderson ##Mr E. H. Anson ##Mr H. T. Anstruther, Miss Rosomond Anstruther ##Mme Antrobus ##Mr Arbuthnot, Miss Arbuthnott [sic] ##Miss Archer-Houblon ##Mme Argles ##Mme Arkwright, Miss Arkwright ##Misses Armytage (2) ##Miss Arnott ##Mr and Mme Ascroft, Miss Ascroft ##Mr Arthur Ash ##Mr A. Asher ##Mme Ashton ##Mme Asquith ##Mr Astor, Mr W. Astor ##Mr B. F. Astley ##Mme Evelyn Atherley ##Mr and Mme Alfred Austin, Misses Austin (2) ##Mr and Mrs C. H. Babington ##Mr and Mrs Bagge ##Mrs Charles Bagot, Mrs J. F. Bagot, Miss Alice Bagot ##Mr James Bailey, Mrs J. Bailey, Mrs Bailey, Misses Bailey (2) ##Mrs Duncan Baillie, Misses Duncan Baillie (2) ##Mr Baillie of Dochfour ##Mr and Mrs W. A. Baillie-Hamilton ##Mr E. Bainbridge ##Mr and Mrs H. R. Baird, Mr and Mrs J. G. A. Baird, Misses Baird (2) ##Mr and Mrs Baldwin ##Mr and Mrs E. Balfour, Mr and Mrs Charles Balfour, Miss Balfour ##Mr and Mrs Banbury, Miss Banbury ##Mr and Mrs S. B. Bancroft [actor "Bancroft and his wife accepted with becoming grace the congratulations with which they were well-nigh overwhelmed"<ref name=":3" /> (5, Col. 6b)] ##Bandanaratke [?] ##Mrs Bankes ##Mr Banks ##Mr and Mrs Walter Baring, Miss Baring ##Miss Barker ##Mr J. Emmott Barlow, Mrs Barlow, Mrs Barlow [sic 2x] ##Misses Barnardiston (2) ##Miss Barne ##Mr and Mrs F. G. Barnes, Mr and Mrs Barnes, Misses Barnes (2) ##Miss Barran (2) ##Mr and Mrs J. Wolfe Barry, Mr and Mrs F. Tress Barry, Mrs A. Barry ##Misses Bartlett (2) ##Mr and Mrs D. P. Barton, Mr and Mrs Barton ##Mr Hamar Bass ##Mrs Bates, Miss Bates ##Mr and Mrs H. Bathurst, Misses Bathurst (2) ##Mr and Mrs Baxendale, Miss Baxendale ##Miss Mariot [?] Bayley ##Mr and Mrs W. W. Beach, Miss Beach ##Misses Hicks-Beach (2) ##Mr R. M. Beachcroft ##Mr and Mrs Wentworth Beaumont, Mr Wentworth B. Beaumont, Mrs Beaumont, Miss Hilda Beaumont ##Mr and Mrs Rupert Beckett, Mr E. W. Beckett ##Mr and Mrs Beer ##Mr and Mrs F. F. Begg ##Mr Charles Bell, Mr and Mrs Bell, Misses Bell (2) ##Miss Bellingham ##Mr and Mrs R. Benson, Mr and Mrs Benson ##Miss Berens ##Mr and Mrs Beresford, Miss Beresford ##Miss Berkeley, Misses Berkeley (2) ##Mr and Mrs Bertier, Miss Bertier ##Mr and Mrs Cosmo Bevan, Mr and Mrs F. Bevan, Miss Bevan ##Mr M. M. Bhownaggree ##Mr and Mrs F. Bibby ##Mr Leonard Biddulph, Mr Biddulph, Mr Victor Biddulph, Mr M. Biddulph, Mrs H. M. Biddulph, Misses Biddulph (2), Miss Biddulph, Miss Freda Biddulph ##Mr and Mrs Bigham ##Mr Bigwood ##Mrs C. Bill, Miss Bill ##Miss Birch ##Mrs Birch-Reynardson, Misses Birch-Reynardson (2) ##Mr A. Birrell, Mrs Birrell ##Mr and Mrs Bischoffsheim ##Mrs Ebrington Bissett ##Misses Blackwood (2) ##Mr and Mrs R. G. Blennerhassett ##Mrs W. H. Bliss ##Mrs Blundell, Miss Blundell ##Misses Blyth (2) ##Mr and Mrs Bolitho, Miss Bolitho ##Mr H. C. O. Bonsor, Mrs Bonsor, Miss Bonsor ##Mrs W. Borsel ##Mrs Griffith-Boscawen ##Mr and Mrs Boulnois ##Miss Bourke ##Mr W. R. Bousfield ##Mrs Bowden-Smith ##Miss Bowen (2) ##Mr T. G. Bowles, Mrs Bowles ##Mr Edmund R. Boyle ##Miss Mabel Brackenbury ##Mrs Bradley, Miss Bradley ##Miss Beryl Bradford ##Miss Braddon ##Miss Bramwell ##Mr H. L. C. Brassey, Mrs H. A. Brassey, Misses Brassey (2), Misses Brassey (2) [sic 2x] ## ##, , , , ,Stapleton Bretherton, F. Stapleton Bretherton, , , , , , , , , , , , , , , G. Bridgman, C. G. O. Bridgeman, , , Sydney Buxton, , A. O. Bruce, , , , , , , , , , , . , , , Buchanan, , J. G. Butcher, , , Brookfield, , Brymer, A. H. Brown, W. Burns, Bucknill, , , , , , , , , , , , , , Brigg, , , , F. C Burnand, , Burges, F. Cavendish-Bentinck, Cavendish-Bentinck, Childe-Pemberton, Shepherd Cross, R. Cox, Cobbold, Richard Combe, Henry Pelham Clinton, J. R. G. Cotterell, C. Tyrall Cavendish, Kinloch Cooke, Compton, V. Seymour Corkran, F. Cawley, J. D. Clark, Croombie, Cooke, F. S. W. Cornwallis, Consett, George Courroux, Purdon Clarke, F. L. Cook, Colston, Cameron, R. K. Causton, Victor Cavendish, Henry Cavendish, Percy Crutchley, Austen Chamberlain, Cecil Chaplin, Ernest Clarke. J. D. Campbell, W. A. Cockerell, DOyly Carte, W. M. Cazalet, Burdett-Coutts, Clowes, C. A. Cripps, Cayzer, Clark, Cory, Clough, Evelyn Cecil, W. W. Carlile, Channing, Ward Cook, J. A. Campbell, Atkinson Clark, B. Cohen, Cavendish, Wentworth Cole, T. B. Cochrane, Crawshay, A. Cross, Daniel Cooper, Cameron Corbett, Cruddas, D. Coghill, Wilfrid Cripps, F. Cazenove, P. H. Calderon, Critchett, C. Kinloch Cooke, Lee Dillon, Louis Davidson, W. E. Denison, W. H. Dudley-Ward, W. de Winton, De Trafford, C. S. Dickson, W. Rees Davies, Coningsby Disraeli, A. Drummond, F. Dugdale, R. Disraeli, Gerard Dicconson, J. de la Cour, W. Bromley-Davenport, G. Drummond, J. Diggle, Ben Davies, de Soria, J. K. Digby, C. B. Dalison, Greville Douglas, Kenelm E. Digby, Darling, Dicken, Vaughan Davies, Doxford, Deverell, Thiselton Dyer, Edwin de Lisle, Du Plat Taylor, F. Elliot, Bevan Edwards, Cary-Elwes, T. H. Elliott, Erskine, W. H. Evans, T. E. Ellis, R. Edgcumb, C. C. Edwards, Eyre, F. Eaton, H. P. Ewart, Maurice Euphrussi, M. Eliot, Fitzgerald, Almeric Fitzroy, Alfred Farquhar, J. N. Farquharson, Farquharson of Invercauld, Cecil Fane, G. H. Fane, Herbert Fisher, H. St. George Foley, Hayes Fisher, Dyafer Fakhry, W. Farquhar, Arnold-Forster, Fardell, Munro-Ferguson, W. S. Foster, Johnson-Ferguson, L. Fry, Farmer, Fielden, Firbank, Fison, Flannery, E. Flower, H. W. Forster, Bevill Fortescue, Fane, F. G. Fitzgerald, E. Farquhar, Franklin, J. S. Forbes, Forbes, John Ford, John Gordon, Henry Graves, George Grossmith ("George Grossmith was not a little lionised by titled ladies"<ref name=":3">“The Queen’s Garden Party. Buckingham Palace Grounds. A Brilliant Scene. The Queen’s Cup of Tea.” ''Daily News'' (London) 29 June 1897, Tuesday: 5 [of 10], Col. 6a [of 7] – 6, Col. 2a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970629/021/0005. Print pp. 5–6.</ref> (5, Col. 6b)), Howard of Greystoke, Hamilton Gatliff, G. P. Goldney, Goelet, Gye, Grifflth-Boscawen, A. Gosling, Geoffrey Drage, Otto Goldsmidt, Frank Gore, F. Graham, S. Hoffnung Goldnung Goldsmid, W. H. Kendal Grimston, Gilliat, Gadson, F. W. Gibbs, V. Gore, Goschen, J. E. Gordon, G. Leveson-Gower, E. A. Goulding, Graham, H. R. Graham, Ernest Gray, Montagu Guest, Garfit [?], H. D. Greene, W. R. Greene, J. A. Gretton, Henry Gladstone, W. H. Grenfell, S. W. Gore, Wilhelm Ganz, Scott Gatty, Charles Gold, Walter Gibson, Gurdon, W. Gillett, Sydney Gedge, Tyrell Giles, C. C. Graham, F. R. Gosset, A. C. Humphreys-Owen, G. M. Hutton, Heseltine, Claude Hay, Halford, E. Hope, Philip Henriques, C. D. Hohler, Hornyold, Carl Haag, Hardcastle, Hanbury, L. V. Harcourt, R. K. Hodgson, Adrian Hope, Beresford-Hope, J. Hozier, E. S. Howard, Horner, Maurice Holzman, A. C. Howard, Cozens-Hardy, Thomas Halsey, Hardy, James Hope, R. Hallett Holt, T. Hare, Hatch, R. B. Haldane, C. Harrison, J. Henniker Heaton, Hermon-Hodge, E. Brodie Hoare, G. Hoare, H. Hobhouse, VV. H. Hornby, R. P. Houston, G. B. Hudson, John Hutton, A. E. Hutton, Lewis Hall, Augustus Hare, George Harwood, G. T. Hertslet, Hartmann, H. Higgins, Hughes, Francis Hamilton, John Hare, Hungerford, Joseph Howard, Hope, R. R. Holmes, H. Howard, Haggard, Cecil Higgins, J. C. Horsley, The Munshi Abdul Hafiz Karim, Wootton Isaacson, E. R. Jenkins, Arthur James, Jacobs, Jebb, A. F. Jeffreys, J. H. Johnstone, Brynmor-Jones, H. C. Jervoise, W. James, Atherley-Jones, Philip Burne Jones, Henry Joslin, George Kemp, Nigel Kingscote, C. Kempe, W. Kenny, A. Kennard, J. Kenyon, Kearley, King King, Lees Knowles, Knowles, Kimber, Kuhe, T. Kingscote, Landon, Reginald Lucas, Letchworth, Lyon, Henry Gore Lindsay, E. H. Loyd, Leonard Lindsey, Drury Lowe, Fairfax Lucy, E. Law, Cecil Lister-Kaye, H. B. Lindsay, H. T. Lopes, J. Grant Lawson, H. Lubbock, W. A. Lindsay, A. K. Loyd, Lecky, W. F. Laurence, Edwin Laurence, J. W. Lowther, Luttrell, Loder, S. Leighton, W. C. F. Luttrell, E. Lloyd, Heathcote Long, L’Estrange, T. C. March, C. J. Murray, Mount, Morrell, R. J. More, Moon, E. P. Monckton, Monk, F. Bingham Mildmay, Beresford Melville, M’Laren, M'Ewan, Martin, H. H. Marks, lan Z. Malcolm, H. L. B. MCalmont, J. W. Maclure, Campbell Munro, J. Maclean, J. C. Macdona, W. G. E. Macartney, Muir Mackenzie, Hugh Morrison, G. H. Murray, P. C. Milbank, Bingham Mildmay, Alpin Macgregor, M. Myther, V. Montagu, Frederick Macmillan, C. M’Neill, Arundel St. John Mildmay, C. Maud, Fuller Maitland, A. Milman, W. A M’Arthur, Marjoribanks, W. H. Myers, F. W. Maude, Muntz, Charles Morley, Murdoch, A. B. F. Mitford, B. Mallet, Mure, Madden, W. J. Mure, R. Maguire, Mackinnon, Montgomerie, Maxwell-Lyte, Mason, Ronald Moncrieffe, Milvain, T. G. Menzies, G. Manners, Nicol, F. A. Newdigate, G. Noel, T. W. Nussey, Charles Orde, R. A. Oswald, M. Oldroyd, J. C. O'Dowd, Oswald, Oppenheim, Arthur Oliphant, C. L. Orr-Ewing, J. L. Pattison, J. Balfour Paul, Paton, A. Peckover, Archibald Peel, Perks, J. Pender, J. Penn, Price, Powell, Paoli, Constantine Phipps[,] Charles Phipps, Leslie Probyn, B. Faudel-Phillips, Wilton Phipps, L. Faudel-Phillips, Joseph Pease, Pollock, Arthur Pease, Roland Protheroe, Walter Peace, J. M. Paulton, Platt-Higgins, Pennefather, Provand, Guy Pym , A. E. Pease, Godfrey Pearse, Algernon Peel, A. V. Pryor, Montagu Price, Phelips, John Ponsonby, Hussey Packe, Wyndham Portal, Henry Petre, Lort Phillips, H. W. Primrose, E. Parkes, Herbert Praed, Heber Percy, Quilter, J. Rankin, Renshaw, J. A. Rentoul, H. C. Richards, Read, T. Richardson, A. T. Phillips Roberts, Hugo von Ruffer, Alexander Ramsay, Alderman and Sheriff Ritchie, Richardson, Rebow, G. L. Ryder, G. A. Redford, G. W. E. Russell, H. J. H. Russell, Pandeli Ralli, John Rutherford, J. Rennell Rodd, Leopold Rothschild, T. W. RusseII, Forbes Robertson, Alfred Rothschild, Brooke Robinson, Edmund Robertson, Repton, James Round, Royds, Henry Raikes, Bowen Rowlands, J. D. Ryder, Sheriff Hargreaves Rogers, Skeffington Smyth, Augustus Spalding, H. H. Shaw, E. Strachey, J. Murray Scott, J. Stern, P. L. Sclater, R. Sassoon, W. Sidebottom, Abel Smith, Louis Sinclair, C. H. Seely, Lucas Shadwell, W. E. T. Sharpe, C. E. Shaw, E. B. Sparke, T. H. Sidebottom, Steward, Stibbert, H. Somerset, H. S. Samuel, J. P. Smith, Horace Seymour, A. H. Smith, H. M. Stanley, J. A. Swettenham, A. Spicer, Stevenson, J. H. Stock, J. Sturgis, H. C. Smith, C. J. Stewart, Leslie Stephen, T. Smith, Senhouse, Eames Storey, Christopher Sykes, H. Seton-Karr, Philip Somers-Cocks, T. Skewes-Cox, Shelley-Bontein, Salting, Leo Schuster, Smith, Arthur Sassoon, G. D. Smith, Shaw, Michael Shaw-Stewart, E. J. Stanley, Albert Sandeman, Scaramanga, Sant, F. Sutton, Dudley Smith, C. E. Tritton. W. E. M. Tomlinson, H. F. Tollemache, A. M. Torrance, Tarleton, Edward Tighe, Alma-Tadema, W. H. Wilson-Todd, P. Thornton, F. Taylor, Beerbohm Tree, Dan Tupper, Montagu Tharp, Abel Thomas, Algernon Turnor, Tudway, C. W. Trotter, H. J. Tennant, J. C. Thynne, H. D. Trelawny, C. E. Thynne, F. J. Thynne, Montagu Thorold, Tremayne, H. Graham Toler, John Taylor, A. J. R. Trendell, Tosti, Christopher Tower, T. Usher, A. Ure, T. Usborne, Chas van Raalte, Graham Vivian, R. C. de Grey Vyner, Hope Vere, F. E. Villiers, Von André, Venning, L. Van Loon, Van De Weyer, Val Prinsep, Walter, Thomas Wayman, Hwfa Williams, Cornwallis West, R. G. Webster, Sackville West, Wanklyn, A. S. Wiison, G. Fleetwood Wilson, A. F. Warr, F. W. Wilson, Piers Egerton Warburton, S. Wombwell, Weigall, Powell Williams, John Welby, Wingfleld, Whitbread, J. W. Wilson, Walton, D’Arcy Wyvill, Wodehouse, Wylie, A. Wilson, John Wilson, C. H. Wilson, Herbert Whiteley, Wynne, Lee Warner, W. West, G. Whiteley, Spencer Walpole, H. C. Woods, M.D., Deputy Inspector-General, Charles Wyndham, J. Humphrey Ward, F. Walker, Whateley, W. Woodall, Wyndham, Godfrey Webb, J. Welby, Charles Waldstein, H. Yorke and Yerburgh #Mesdames<ref name=":1" /> (4, Col. 7a–b) — , , , , , , , , , , , , , , , , , , Browne, , , , Brownrigg, Bridge, , , , , , , , , Butler, , , , Burges, Butler, Brocklehurst, , , , , , F. C. Burnand, , , , , , Bryce, C. G. O. Bridgeman, S. Buxton, , , , , A. C. Bruce, , , . , , Buchanan, Brookfield, A. H. Brown, , , C. E. Buckle, , W. Burns, C. K. Burn, H. Churchill, Crutchley, Curzon, F. Cavendish-Bentinck, W. G. Cavendish-Bentinck, Chamberlain. W. Chetwynd, Dick-Cunynghame, Archibald Calvert, Creignton, Daniel Cooper, Calley, Cox, Kinloch Cooke, Rivett Carnac, C. Kinloch Cooke, Henry Pelham Clinton, Colston, Coghill, Castance, B. F. Clark, Cavaye, Consett, G. D. Clark, A. B. Crosbie, Clerk, Wilfrid Cripps, Chapman, Crawshay, F. Campbell. W. W. Carlile, Channing, Cayzer, F. S. W. Cornwallis, Armar Corry, Cory, Critchett, Craik, W. Campbell, Atkinson Clark, R. Cox, Cruddas, Cavendish, Shepherd Cross, Clive, Crombie, F. L. Cook, C. Tyrall Cavendish, Clifford Corry, Hastings Campbell, Cameron Corbett, Carter, Corroux, Chaloner, Cecil Chapiin, J. D. Campbell, W. A. Cockerell, Compton, D'Oyly Carte, Stanley Clark, Cazalet, Seymour Corkran, Chaine, Carson, Boyd Carpenter, Causton, W. Campbell, Codrington, F. L. Campbell, D. B. O. Campbell, Cuninghame, Stapleton Coton, Coventry, Crabbe, Close, Courtney, E. H. Cooper, Carnegy, Randall Davidson, A. Hay Drummond, G. De Plat Taylor, Dickson, Lawrence Drummond, Louis Davidson, Dicken, Denis Daly, Dalton, R. C. de Grey Vyner, Durnford, W. de Winton, Edwin de Lisle, de Arcos, Drummond, Darling, A. L. Douglas, Doxford, Thiselton Dyer, Vanghan Davies, Denny, Coningsby Disraeli, Geoffrey Drage, Davis, Dundas, R. Disraeli, Dicconson, J. de la Cour, G. Drummond, J. Diggle, Akers-Douglas, Digby, Dunne, Dalbiac, de Salis, C. S. Dickson, Domvile, Ellicott, Edwards, Ellison, C. B. Ewart, Edis, East, Eliot, Egerton, F. Elliot, Floyd, Fenwick, E. Farquhar, Barrington Foote, G. M. Farquhar, Farquarson of Invercauld, Almeric Fitzroy, Lancelot Farmer, FitzGeorge, G. H. Finch, Fenn, Wynne Finch, R. Fitzwilliam, Fanshawe, Fullerton, Fane, Hayes Fisher, Fellowes, Houston French, Arnold-Forster, Fardell, Field, W. H. Foster, H. S. Foster, Johnson Ferguson, Farmer, Fielden, Fison, Firbank, Bevill Fortescue, Farnham, H. Fludyer, S. W. Gore, F. R. Gosset, Gregory, C. C. Graham, Guy-Pym, John Gordon, Gooenough, Henry Graves, Gordon, Garfit [?], S. Gedge, Tyrell Giles, Gilliat, Godson, S. Hoffmung Goldsmid, Kendal Grimston, Goldsworthy, J. E. Gordon, Gunter, W. H. Grenfell, H. Grenfell, G. G. Gordon, Gurney, Goodden, F. Gore, S. Gordon, A Goldsmid, Scott Gatty, Walter Gibson, Gordon, Grant, Goelet, Gye, Gardner, Gladstone, Gore, Green, Goschen, A. Gosling, Hargreaves-Rogers, Staveley Hill, Hanbury. James Hope, Claude Hay, Heneage, Heseltine, E. Hope, Arthur Heath, Philip Henriques, C. D. Hohler, Hornyold, Carl Haag, Marcus Hare, Harford, Hardcastle, Holmes, Beresford Hope, Adrian Hope, Hanbury, Horner, Hammet, Hall, A. C. Howard, Halsey, Hardy, Heath, Hermon Hodge, Brodie Hoare, S. Hoare, H. Hobhouse, W. H. Hornby, G B. Hudson, Platt-Higgins, Hildyard, Lewis Hall, G. M. Hutton, G. Hutton, W. G. G. Hutchinson, Haweis, Hartmann, Higgins, John Hare, Hungerford, Humphreys-Owen, R. W. Hamilton, Hills, Hippisley, Herbert, Hatton, Henderson, Haggard, Hervey, J. Howard, H. Howard, Ian Hamilton, Gathorne-Hardy, Howard, Marcus Hare, Inglefield, Wootton Isaacson, Joicey, Jenkinson, Inigo Jones, Jackson, A. James, Cotton-Jodrell, Jacoby, Jebb, A. F. Jeffreys, Jessel, Brynmor Jones, Pryce Jones, J. E. Jameson, H. C. Jervoise, W. James, Atherley Jones, G. Johnstone, J. H. Johnstone, A. Kennard, Kearley, Kimber, Hegan Kennard, Kitching, Kennion [?], Kennison, Knowles, W. Kenny, Kennedy, Keeley, Kuhe, Kingston, Kilkelly, Colin Keppel, Hanning Lee, A. K. Loyd, Lyon, Long, Lane, Lucas, Lockwood, S. Leighton, Lecky, E. Lawrence, Lawrie, Luck, Lloyd. A. P. Lake, J. W. Lowther, Lowe, Lidderdale, Liddell, Lascelles, Luttrell, H. Lubbock, Leslie, Lucas-Shadwell, Laurier, Naylor Leyland, Langenbach, E. Law, Fairfax Lucy, Lockhart, Lewis, Maxwell-Lyte, F. A. Lucas, G. Manners, Beresford Melville, Morrell, Victor Milward, Marshall, Maclure, J. Maclean, M'Laren, M'Ewan, R. B. Martin, Marks, Markham, J. M'Calmont, F. W. Maude, Napier Miles, M’Neill, Max Muller, Meeking, Manvers Moorson, Arundel St. John Mildmay, Frederick Macmillan, Mount, Muntz, Murdoch, Wyndham Murray, W. J. Mure, Graham Murray, Montefiore, W. C. F. Molyneux, Newton Mant, Millett, Malet, Ashurst Morris, May, Maurice, Milvain, Marjoribanks, J. C. Macdona, Moorhouse, Muir Mackenzie, G. Moncrieff, J. Murray, Montgomery, Milbank, Bingham Mildmay, Mellor, C. Maude, T. G. Menzies, J. M'Donald, W. A. M'Arthur, M'Neile, M'N'eill, Campbell Munro, Mostyn, A. Milman, Majoribanks, Noel, H. F. Nicholson, F. Neville, Nicol, Nevul [?], Nugent, Newhouse, Oppenheim, M. Oldroyd, Charles Orde, H. H. Oldham, R. A. Oswald, Oswald. A. Oliphant, Oakley, J. L Pattison, Price, Perowne, Perks, Constantine Phipps, Peacocke [?], R. Prothero, Powell, Leslie Probyn, Pitman, Upton Prior, Lort Phillips, Primrose, Powlett, Pakenham, Peyton, Parkes, Wyndham Portal, Pipon, Pender, Phillpotts, Pollock, Montagu Price, Phellps, John Ponsonby, Fox Pitt, A. Peel, Aldrich Pelham, J. Pease, Poe, G. Pearse, A. Paget, A. Pease. N. G. Philips, Pirie [?], Dampier Palmer, F. Post, Pakenham, Paget, H. Parr, Wilton[?]-Phipps, Quilter, Rebow, J. C. Russell, Rolfe, Rutherford, I[?]. Richardson. James Ronand, Robins, Rennell Rodd, W. W. Russon[?], Alexander Ramsay, Robinson, J. Rennell Rodd, Redford, Harcourt Rose, Royds, H. Raikes, Carl Rosa, Ronalds, Arrnold Royle [? Royce?], Rice, Leopold Rothschild, Raikes, J. Rankin, Renshaw, F. Russell, Ricardo, Riddel, Robertson, G. Royle, Teignmouth [?] Shore, Sandeman, Stopford, Graham Smith, Salting, Brinsley Sheridan, Salmon [?], Salmond, Edgar Shephard, Sant. A. Sandeman, H. Seymour, H. S. Samuel, St. Clair, AbeI Smith, J. P. Smith, H. M. Stanley, A. Spicer, Stevenson, Swaine, Sullivan, J. H. Stock. E. B. Sparke, J. Sturgis, Louis Sinclair, H. Seton-Karr, Slade, J. Stern, Skefflngton Smyth, P. L. Slater, A. C. Stewart, R. Sassoon, C. Smith, E. Strachey, Napier Sturt, Steward, Eames Storey, Starkie, Senhouse, Bridgman Simpson, Seddon, T. Smith, Leslie Stephen, Settle, Scaramanga [?], Arthur Sassoon, L. Seymour, Shaw. R. F. Synge, T. Skewes-Cox, Stevenson, H. C. Smith, Sterling, T. H. Sidebottom, C. H. Seely, Shelley-Bontem [?], Sandford, Hawley Smart, Sergison [?], Frederick Slade, Scobell, Graves Sawle, Scott, Settle, Smith-Barry, Stewart, J. A. Swettenham, Surtees, Synge, Dudley Smith, Thomson, M. Thorold, H. Graham Toler [?], J. W. Taylor, Christopher Tower, Tosti, Temple, Beerbohm Tree, Dan Tupper, R. T. Thynne, Montagu Tharp, Trotter, Anstruther Thomson, Tupper, Taylor, C. E. Tritton, C. F. Anstruther Thomson, Edward Tighe, F. Taylor, Tillard, Tillbrook, Brook Taylor, Tudway, C. E. Thynne, J. C. Thynne, H. Thomas, Thwaites, Tarleton, A. Ure, Usher, R. Vivian, Val Prinsep, Edmund Vaughan, E. Villiers, C. van Raalte, Von André, Verschoyle, F. E. Villiers, Vance, Hope Vere, Villiers, Venning, Sackviile West, Whatman, Williams Wynn, Watson, Wharton, John Wilson, Williams, Stuart Wortley, Wood, C. H. Wilson, S. J. Way, Walton, H. Whiteley, G. Whiteley, Ellis Williams, Wilson, Weywan, E. F. Wodehouse, John Welby, Wray, Wickham, Whatley, Spencer Walpole, Hwfa Williams. J. Woodford, Charles Wyndham, Wingfield, Charles Wood, Lee Warner, Warre, Humphrey Ward, Wallis, Wilberforce, Wynne, J. Welby, Eardley Wilmot, A. S. Wilson, C. [?] E. Ward, Walter, Warner, R. G. Webster, Wells, Cornwallis-West, F. Charteris Wemyss, Yerburgh #Misses<ref name=":1" /> (4, Col. 7c – 5, Col. 1a) — , , , , , Bowden-Smith (2), Browne (2), Bromley-Davenport, , Burrell (2), , , Brownrigg, , , , , Browne (2), Bruce (2), , , , , Browne (2), Stapleton Bretherton [?] (2), , , Evelyne Burne, , , , Brunner, , , Brodie (2), Brookfield, Brown, , Burns, , Buxton (2), , , Brooke, , , Burdett, Mary Bulteel, Burges (2), , , Rhoda Broughton, , , , , , , Budgett, , Butler, Crutchley (2), Culme-Seymour, Carleton, Chapiin [sic?] (2), Cockerell, Lilah Campbell, Boyd Carpenter (2), Cowell-Stepney, Lucia Creighton, Chrichton-Maitland, Leila Crichton, Campbell, Calvert, Ronald Campbell, Cooper (2), Cochrane, Clarke, Clowes (2), Stanley Clarke, Commerell, Colville, Cayzer, Crosse, Chaning (2), Cunliffe, Chetwode (2), Chetwynd (2), Corry, Clark, J. A. Campbell, Cameron, Colomb, Custance, Clive (2), Grace de Capell-Brooke, Cook, Vera Consett, Cooper, Campbell (2), Cockerell, Cecil, Carlisle, Cholmeley (2), Cruddas (2), Cox, Cowell, Causton, Cust (2), Cuffe, Chitty, Chamberlain (2), Crabbe (2), Edith Chaplin, Corbett, Cameron (2), Chaplin, Cholmondeley, Carden, Cotterell (2), Spencer Churchill, Corkran, Commerell, Edith Drummond, Sybil Dudley-Ward, Gladys Dalgety [?], Drummond (2), Duncombe (2), De Winton, De Trafford, De Perpigna, Dalrymple, Dashwood, Duncombe (2), Dawnay (2), Du Cane  (2), De Brienen (2), La Baronne de Friesen, La Baronne Sirtema de Grovestins [?], Mary Drummond, De Winton, Davey, Digby (2), Dowell, Marion Dunne, Du Chair, De Winton, Domvile [?], Douglas (2), Dunn, Doxford, Deverell, Drummond (2), Digby, Disraeli, Adelizs [?] Drummond, May Dundas, Dillon (2), Bevan Edwards (2), Evans (2), Ellison, Eliot (2), Ellicott, Gertrude Elliot, Egerton (2), Ellis (2), Edis (2), Ellaby, Egerton, Grey Egerton, East (2), Elphinstone (2), Rachel Erskine, Evelyn Ellis, Amelia Farquharson, Henrietta Farquharson, Foster, Farmer, Fielden (2), Fison, Fersuson of Pitfour (2), Fitzwilliam (2), Flower, Keith Falconer (2), Fenwick (2), Forwood (2), Farquharson of Invercauld (2), FitzClarence (2), Olga FitzGeorge, Ethel Fitz-Roy, Fergusson, Dorothy Ffolkes, Finch (2), Fanshawe, Flower, Fullerton (2), Feilding (2), Fardell (2), Fisher (2), Fowler (2), Frere (2), Fitz Gerald, Gold, Graves, Gibbs (2), Gregory, Gough-Calthorpe (2), Helen Gladstone, Goschen (2), Glyn, Godley (2), Gardiner, Gillian [?] (2), Gunter (2), Gilbey, Maud Grenfell, Hamilton Gordon, Gurrney Goodden, Goldsmid, Gardiner, Grant, Victona Grant-Duff, Goelet, Gosling, Gore, Gathorne-Hardy, Gordon (2), Hood (2), Heneage, M. Carew Hunt, Hare (2), Hay  (2), Hickman, Adrian Hope (2), Hare (2), Agnes Beresford Hope, Carl Haag, Hardcastle (2), Heseltine, Hare, Hope, Heron Maxwell (2), Halford (2), Hamilton (2), Hamilton, Howard (2), Hardy (2), Hay (2), Herbert Margaret Acland Hood, Mary Hope, Hill, Hemming (2), Jean Hotham, Hall, Harrison, Gladys Higginson, (Brydges) Henniker, Halsey (2), V. Hanson, (Stock) Hill (2), (Brodie) Hoare (2), Hoare (2), Houldsworth (2), Haig, Hart, Hervey, (Lewis) Hall, Harwood (2), Hutchinson, Hughes (2), Hooker, Hart-Dyke (2), Hervey-Bathurst (2), Louisa Heathcote, Howard, Dora Hanbury, Howard (2), Hornby (2), Satyendra Bala Tagore, Grace Jackson, Jolliffe (2), Helena James, Jenner, Joicey, Cotton-Jodrell, Jenkins (2), Johnstone, Jameson (2), Jessel, Jervoise, S. L. Johnstone, Keith-Falconer (2), Ker (2), Ethel Kenny, Kennedy, Kennard, King King, Kennard (2), Kitson (2), Kerr (2), Kimber, Kennaway (2), Nona Kerr, Keppel, Kemball, C. Lees, Lyson, Gore Lindsay, Linton (2), Lindley (2), Lubbock, Aline Lambton, Lambart (2), Liddell, Alice Loch, Lindsay, Lucas-Shadwell, Hanning Lee (2), Emily Loch, Larking, Leese, Llewelyn, Leighton (2), Lawrence (2), Lopes (2), J. Lawson, Laurie (2), Lyte (2), Lloyd (2), Lyall, Luttrell, Lockwood, Lister, Lidderdale (2), Violet Leigh, Liddell (2), Drury Lowe, Lewis (2), Loftus, Lindsay, Lyell (2), Aimee Lowther, l’Estrange, Graham Murray, Mellor (2), Milward, Monk (2), Maxwell (2), Massey-Mainwaring, Mackworth (2), Markham (2), Macdonald, More-Molyneux, Cicely Monson, Maclure, Lena Milman, Morris (2), Macnaghten, Mowatt (2), Margaret Muir MacKenzie, Murray, Mundella, Mowbray, Ethel Morris, Beatrice Mildmay, May Milbank, Evelyn Moreton, Magniac (2), Mackenzie, M'Clintock, Madden, MacGregor(2) Mount (2), Muntz, Murdoch, Mitford, Montagu (2), Mure, Menzies, Macpherson-Grant, Malet, Moseley (2), Meeking, Macgregor, Mary Moore, Montgomery, St. John Mildmay, Madden (2), Milman (2), Constance Maude, Martyn, Campbell Munro, Nevill (2),Noel (2), Nevill, Nicol, Neville, Nelson (2). Olpherts [?] (2), Oakley, Ogilvy, Humphreys Owen, V. A. Okeover, O’Brien (2), Linda Oppenheim, Phoebe Otway, Alina O'Shee, Anderson Pelham, Pole, Pereira, Peyton, Pattison, Orde Powlett, Powlett, Pelly (2), Perowne, Charlotte Probyn, Julia Ponsonby, Peekover, Peel (2), Penn, Peace, Baden Powell, Powell (2), Pease, Priestley, Palgrave, Post, Parker, Pease, Palmer, Packe (2), Alice Paget, Paget, Paget of Cranmore (2), [?] Phillips, Phipps, Cecilia Peel, Chandos Pole, Pollock Phellps, Parry, Ponsonby, Wilton Phipps, Quain, Quilter (2), Russell of Killowen(2), Ritchie (2), Robins, Sibyl Robertson, Round (2), Royds (2), Russell, Rebow, Jane Ryan, Ramsay, Ricardo (2), Rigby, Russell (2), Lucy Raikes, Rankin, Frances Rod, Beatrix Rice, Russell (2), K. Reiss, Ricardo, Smith, Stafford, Stevenson, Stopford (2), M. Seymour, Kay Shuttleworth [?] (2), Seymour (2), Shaw, Shaw-Stewart, Evelyn Starling[?], Maxwell Scott, Abel Smith, Sartorius (2), Maud S[?]hey, Stewart, Magaret Stanley, Dorrien Smith, Smith (2), [?]-Smith, Saurin, Salmond (2), Sandeman (2), Sant, Dudley Smith[?], Swaine, Stephenson (2), Stewart (2), Dora Stone, Sparkes, [Stanley?], Nita Houston Stewart, Lily Severn, Evelyn Stanley, [Sheppart?], Saumarez Smith, Truda Saunderson, Swinburne, [Sullivan?], Mabel Seymour, Shute, R. Sterling, Stern (2), Sar[?] (2), Sassoon (2), P. L. Sclater, Sparke, Smith (Clement), [Sanderson?], Hilda Stewart, Seddon (2), Shelley, Sprigg (2), [?] Stephen, Ruby Spencer Churchill, Rachel Smith, [?], Tremayne (2), Ellen Terry, Ethel Thomas, Muriel [?], Taylor, Mary Talbot, Tomlinson, G. le M. Tupper, [?], Ella Taylor, Thorold, Taylor (2), E. Tuson, Trelawny [?], Adela[?] Trefusis, Rachel Thynne, Tritton (2), Thomson (2), [?], Thesiger, Thynne, I. C. (2), Thynne (2), Thornton (2), [Temple?], Turner, Talbot, Thynne, Usher, Van de Weyer (2), [Vivian?] (2), Dorothy Villiers, Freda Villiers, Verschoyle, Van [der Byl?], Villiers, Venning, Hilda von Deichmann, Wood[ford?], Fleetwood Wilson, Eardley-Wilmot, Maud Walpole, [?hend?] Wilson, Wilson, Wilberforce, Warren (2), [W?vil?] (2), Wills (2), Warrender (2), Walrond (2), Wynd[ham?] (2), Webster (2), Watson, Wombwell, Whitehead (2), [W?Ieyer?] (2), Evelyn Wellesley, Cornwallis West, Whatman {2), [?] (2), Rachel Weigall, F. Walker, Smart Walker, Wood (2), de la Wood[?], Ward, Wilbraham, Wilberforce (2), Walker, Williams, [Workham?] (2), Yeatman #Admirals of the Fleet [initial large caps, rest sm caps] — Earl of Clanwilliam, Lord John [Hay?], the Hon. Sir H. Keppel #Admirals — H. G. Andoe, C. E. Buckle, Sir F. Bedford, Britten, the Hon. W. Carpenter, H. F. Cleveland, Sir H. Chads, Close, [?], Carr, E. J. Church, Sir W. Dowell, R. G. Douglas, A. L. [?], C. E. Domvile, A. T. Dale, D’Eyncourt, Field, Sir A. [Farquhar?], Fitzgerald, Fellowes, Fanshawe, Sir H. Fairfax, Sir [?] Fisher, C. J. Fane, Fullerton, the Hon. Sir E. Fremantle, [?] FitzGeorge, Woods Pasha, Sir W. Hunt-Grubbe, Sir Anthony [?] Hoskin, Lord Hood of Avalon, Sir Leopold Heath, Sir [?] [F.?] Hotham, Sir Algernon Heneage, R. H. Hamond, the Right Hon. Sir [J.?] Hay, St. G. C. D’Arcy Irvine, Jones, Kennedy, Sir A. [?s], A. P. Lake, R. M. Lloyd, Sir L. Loraine, A. H. Markham, [Sir?] R. More-Molyneux, Sir F. L. M'Clintock, Sir R. Macdonald, [the?] Hon. V. Montagu, Nicholson, Noel, Marquis of Northampton, Sir E. Ommaney [?], Sir Augustus Phillimore, A. T. Powlett, [?], [?. ?.] Rowley, Sir F. Richards, Lord Charles Scott, [? St.? John?], W. H. C. St. Clair, Bowden Smith, Sulivan, E. H. Sey[mour?], H. Stephenson, Sir Nowell Salmon, Sir W. Houston [Stewart?], Sir M. [Cuhne?]-Seymour, E. W. Turnour, E. W. Van[?] Wharton, Sir G. Willes, the Hon. W. J. Ward #Captain, R.N. — W. A. D. Acland, C. J. Barlow, F. R. Board[?], H. Bainbridge, Hon. T. Brand, Bickford, Lord Charles [B?ford?], B. F. Clark, Colville, Carter, Hon. S. Cecil Colville, [?ford?], A. G. Douglas, Sir C. Domville, Hon. A. Hay Dru[?], [?] [W.?] [?] Gordon, Hammet, Hon. Curzon Howe, Hender[?], [?] Ingles, Jellicoe, Jephson, Johnstone, Jeffreys, H. C. [?], Hon. A. Littleton, Hon. Hedworth Lambton, Moore, May, [? Net?], Poe, Pipon [?], Aldrich Pelham, Alfred Paget, [Bi.idcl?], Rolleston, John Sinclair, Bridgeman Simpson, [?], Van Koughnet [?], Burges Watson, Eardley-Wilmot, [?ham, Winsloe, Hon. J. Yorke #[Lieutenants???] — Anson, G. R. Bethell, Blair, Bayley, Cave[?], [?] Cave,Hon. Cecil Cadogan, de Salis, Fraser, Floyd, Hon. [?] [F?], Alaric Grant, Morgan, Moore, Marescaux, [?] Stuart, Tupper, Wells, Williams, G. J. S. Warrender #[Lieutenants?] R.N. — Alton, Murray Aynsley, Boyle, Bather, [?], [R. F.?] Boyle, Chaytor, Sir Charles Cust, G. W. Davy, [?] Wyndham-Fiennes, Fair, Godfrey Faussett, Garforth, [L?]ord Clifford, Hopkinson, Henderson, Keyes, Keppel, [?] Lloyd, Majendie, Mitchell, Morant, Kerr-Pearse, [?] Richmond, Rae, Stewart, Hon. Victor Stanley, [?] [Calta?]-Seymoar, Trye, Thring, Hon. Cyril Ward, W[?], R. E. Wemyss, Woolcombe #[Captain?] Trinity House, Sir J. Sydney Webbe #[Field?] Marshall — Sir F. P. Haines, Sir Lintorn Simmons, Sir [?] Stewart, Lord Roberts of Kandahar, Viscount Wolseley #[Generals?] —Sir J. Ardagh, Sir A. Alison, Sir H. J. Alderson, [?n] Annesley, J. Alleyne, Sir J. M. Adye, Sir C. G. [Arbuth?]not, Sir H. Havelock-Allan, R. Bateson, Sir W. F. [B?er, Sir H. Brackenbury, H. M. Bengough, the Right Hon. [?] Buller, Sir Owen Tador-Burne, H. J. Buchanan, Sir C. H. [Brown?low], Sir S. Browne, Sir M. Biddulph, Viscount Bridport, [?. O.?] Barnard, E. F. Chapman, Lord Clarina, C. F. Clery, the Hon. S. Gough-Calthorpe, E. H. Clive, Godfrey Clerk, Lord [Ch?]sford, the Hon. Sir Andrew Clarke, Sir E. Du Cane, Crutchley [?], Lord de Ros, Sir John Donelly, J. H. Dunne, Sir Martin Dillon, Sir Collingwood Dickson, Sir H. de Bathe, Davis, Sir F. de Winton, Sir T. Dennehy, Sir H. Ewart, Sir J. B. Edwards, C. B. Ewart, Cecil East, Arthur French, Sir T. Fitz-Wygram, the Hon. Sir P. Feilding, Sir T. E. Gallwey, Sir T. Goldsmid, Sir R. Gipps, Sir R. Grant, Sir F. W. Grenfell, Coleridge Grove, Goldsworthy, J. J. H. Gordon, Sir E. A. Holdich, Sir E. W. Higginson, Sir R. J. Hay, Sir R. Harrison, Julian Hall, Earl Howe, the Hon. W. Home, J. Jameson, Sir Arnold Kemball, Kelly-Kenay, Lord Mark Kerr, F. T. Lloyd, Sir D. Lysons, Sir Drury Lowe, G. Luck, J. W. Laurie, F. Marshall, the Hon. R. Monck, Crichton Maitland, Sir J. M'Neill, Montgomery, the Hon. S. Mostyn, G. Moncrieff, E. Markham, Sir W. A. Mackinnon, Bryan Milman [?], H. M’Calmont [?], M'Donnell, W. C. F. Molyneux, Lord [Methuen?], J. F. Maurice, Sir F. Middleton, O. H. Nicolls, Sir E. [?] Newdegate, Sir H. N[orman?], Sir W. Olpherts, F. Peyton [?], G. [?] Upton Prior, T. H. Pakenham, G. W. T. Rich, Lord [?der] Russell, Robinson, Rowlands, J. C. Russell, F. [Russell?], A. C. Stewart, Sir Henry Smyth, Sterling, Sir C. [?] Shute, N. Stevenson, Swaine, Lord William Seymour, [?] [Sahmond?], Sir Frederick Stephenson, Sir John Stokes, Sir R. [?], Sir H. B. Tuson, the Hon. R. A. J. Talbot, G. le M. [Tupper?], Taylor, Hon. C. Thesiger, R. T. Thynne, Upperton, [?]H. Utterson, Sir J. Watson, Sir C. W. Wilson, Sir F. F. Walker, Sir Evelyn Wood, Sir C. Warren, Albert Williams, the Hon. G. Wrottesley, Sir G. H. Willis, Sir H. Wilmot #Colonels — Armytage, Arkwright, Pat Boyle, Burges, the Hon. [?] Byng, H. B. H. Blundell, M. S. Brownrigg, Sir E. Bradford, Sir A. [Blyge? Bigge?], the Hon. F. Bridgeman, Brassey, Lord William Beresford, St. John Barne, N. Barnardiston, Lord Blythswood, [?] Cunynghame, F. H. Custance, Clayton, Sir Henry Colville, [?] Carnac [?], Cavaye, Seymour Corkran, the Hon. Charles [?], W. Campbell, Chaloner, Archibald Calvert, the Hon. [?] Campbell, the Hon. Wenman C. Coke, the Hon. W. [?ton], the Hon. Sir W. Colville, Chaine, A. B. Crosbie, [T.?] [R?] Crosse, Lord Edward Pelham Clinton, the Hon. Henry [C?hton], E. H. Cooper, the Hon. H. Corry, John Clerk, Lord Dorchestcr, C. R. Dease, the Hon, Lewis Dawnay, [the?] Hon. H. Denison, Denny, Dalbiac, A. Davidson, the Hon. Cathbert Edwards, the Right Hon. Sir F. Edwards, [?son], R. Edis, the Hon. Charles Edgecumbe, Aubone Fife, [?], Wynne Finch, Ferguson of Pitfour, Forster, Lancelot [?r] H. Frudyer, Barrington Foote, Goldsmid, Gore, Grenfell, [?n], C. G. Gordon, R. Gunter, Alan Gardner, Hon. G. Gough, [?] [?iton], the Hon. A. Hood, the Earl of Home, Lord Claud [Hamilton?], Harford, Herbert, the Earl of Haddington, Haygarth, G. Hatton [?], Hillyard, Arthur Haig, Sir E. Stock Hill, R. Hennell, Archer Houblon [?], the Hon. Cospatrick Home, the Hon. C. Gathorne-Hardy, Johnstone, Cotton-Jodrell, Hegan, [H?nard], Sir N. Kingscote, H. A. Lascelles, the Hon. Heneage [L?], Hanning Lee, F. A. Lucas, the Hon. H. Lyttelton, Lockwood, L. V. Loyd, C. W. Long, Ronald Lane, Lucas, J. Leslie, the Hon. Caryl [?]Molyneux, John Murray, Sir A. W. Mackworth, J. M'Calmont [?], Milward, the Hon. F. C. Morgan, J. J. Mellor, Meeking, Manvers [?], Moorsom, H. Malet, the Earl of Mount Edgecumbe, the [Earl?] of March, Wyndham Murray, Sir V. Majendie, the Hon. G. [Napper?], H. H. Oldham, L. J. Oliphant, A. Paget, Dampier Palmer, [Earl?] Percy, George Paget, C. D. Patterson, Arthur Peel, [Birch?] [Richardson?], the Hon. F. W. Stopford, Sir W. G. Stirling, E J. [Sanderson?], T. M. Sandys, H. Smith, J. F. Sandeman, Renyon-[Surrey?], C. E Stewart, E. H. Sartorius, the Hon. Walter [Stewart?], L. Seymour, Settle, Stevenson, Starkie, C. H. Seafe, the Hon. Sir W. P. Talbot, J. Du Plat[?] Taylor, H. Thomas, A. W. [T?], the Hon. W. Ie Poer Trench, H. P. Vance, Sir C. E. Howard Vincent, M.P.; R. Vivian, A. P. Vivian, E. Villiers, the Duke of Westminster, the Earl of Wemyss, Lord Wantage, Ward, [Waring?], [Earle?] Welby, Lord Arthur Wellesley, Robert Williams, the Hon. H. L. Wood, Sir W. H. Walroud, F. Smart Walker, A. [Williams?] Wynn, Wardrop #Majors — Anne, Atherley, Ashton, F. H. Bowles, the Hon. [?] R. Bourke, Carnegy, H. Candy, Close, the Hon. F. Colborue, the Hon. Wenman Coke, Lawrence Drummond, Alfred [Edgecombe?], G. Egerton, E. H. Elliot, the Hon. A. Henniker, J. [H?a?h], the Hon. Assheton Harbord, the Hon. North Dalrymple [Hamilton?], Jameson, Pryce Jones, Larnach, the Hon. Osbert [Lumley?], C. Little, Marindin, the Hon. J. Scott Napier, Wyndham Quin, F. C Rasch, the Hon. A. Sidney, the Hon. J. T. St. Aubyn, Sir Edgar Sebright, Stirling, T. E. M. Swinnington-Parkington, [?.] M. Temple, Tillbrook, Anstruther Thomson, [E.?] [L.?] Woodhouse, and the Marquis of Winchester #Captains — O. Ames, J. Acland, Alan Boisragon, Bates, H. M. [Biddulph?], the Hon. Baring, Butler, the Hon. J. Byng, the Hon. [N.?] Yarde-Butler, E. W. Blunt, J. F. Bagot, the Hon. W. Bagot, Seymour Combe, W. Chetwynd, Dundas, Denis Daly, Cecil Drummond, M. Drummond, Ellison, Houston French, Gye, R. G. [Gilmour?], P. Green, W. G. Grice-Hutchinson, Ahmed Hussain, G. [L.?] Holford, Jessel, the Hon. W. Lambton, the Hon. G. H. [L?], Sir H. Naylor-Leyland, G. Lister, Matthews, A. D. Miller, [?],M. M'Neill, C. Norton, Phillpotts, N. G. Philips, Prety[man?], Duncan Pirie, Pitman, Fox Pitt, Petre, Harcourt Rose, [W.?] [J.?] Stopford, Sir Eyre Shaw, H. G. D. Shute, Spicer, the Hon. [?.] St. Aubyn, Sutton, Tillard, Webbe, Wray, and Gordon [Watson?] #Lieutenants — Baun, A. Cowell, the Hon. E. C. Lennox, F. Ponsonby, J. Ponsonby, Vandeleur, the Hon. C. Willoughby, and the Hon. C. S. H. D. Willoughby ===Entertainment=== "The Bands of the 1st Life Guards, Grenadier Guards, and Royal Artillery played a selection of music during the afternoon."<ref name=":1" /> (4, Col. 2c) ==Anthology== ====Quote Intro==== <quote></quote> () == Notes and Questions == # ==References== * <references /> lk7dgzs3l6wo10aj412sdhhpyzbyupl 2690176 2690119 2024-12-03T23:52:39Z Scogdill 1331941 2690176 wikitext text/x-wiki =Event= On Monday 28 June 1897, Queen Victoria hosted a garden party at Buckingham Palace, inviting between 5,000 and 6,000 people. This party was the final official event of the London Diamond Jubilee celebrations. The Queen released to the press the names of people invited, which means the newspapers could print some or all of this list. The very long article in the London ''Morning Post'', for example, prints what may be the comprehensive list of those invited, although two columns are illegible in some places. The original newspaper account seems to have been published by the ''Court Circular'', and then the popular newspapers reprinted pieces of that story, many adding contextualizing paragraphs of their own. Some of these later reports are quite long, perhaps 5 or more full columns. Sometimes the newspapers included short descriptions of the women's dresses, suggesting that for the list of people invited, the source was the ''Court Circular'', but the parts of the stories devoted to context, history or fashion might have been written by a reporter present at the event. ==Logistics== * 28 June 1897, Monday, in the gardens at Buckingham Palace, hosted by Queen Victoria. * Between 5,000 and 6,000 guests were invited. * Many visitors from the empire who were in town for the Jubilee celebrations were invited to this garden party. * The weather was fine, having improved since the day before. * The garden party was held in the grounds around Buckingham Palace, and the Palace itself was open and available for guests to visit:<blockquote>Great preparations had been made in the splendid grounds adjoining the Royal Palace for the party, the whole scene presenting a fascinating appearance. The beautifully-kept grounds were partially covered with tents and marquees for the convenience of the many guests, and the lovely lake was really in the hands of the Queen’s bargemen, who had charge of the many boats which had been placed on the extensive ornamental waters for the use of guests. There was also plenty of music, several regimental bands being in attendance, while for those who wished to become acquainted with the valuable pictures and works art which are to be found at the Royal residence, all the State and reception rooms of the Palace were thrown open.<ref name=":2">“The Queen’s Garden Party. Brilliant Scene at Buckingham Palace.” ''Globe'' 29 June 1897, Tuesday: 6 [of 8], Col. 3a–c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001652/18970629/050/0006. Print p. 6.</ref> (6, Col. 3a)</blockquote> *The streets around the entrances to Buckingham Palace were lined with spectators beginning hours before the Queen was to arrive:<blockquote>Although the Garden Party was not timed to commence until after five o’clock, the Mall from Marlborough House to Buckingham Palace was well lined by two o’clock, and an hour afterwards large crowds, for the most part composed of ladies, had taken up their positions. This was also the case along Constitution-hill, where the assembly which had gathered to witness the Queen’s arrival at the Palace from Windsor nad [sic] to a large extent remained. The heat was somewhat oppressive, but the trees along the Mall and the Green Park afforded welcome shelter. Many ladies had evidently come prepared for a long wait, as they had provided themselves with the now familiar camp stool, which is always prominent on these occasions. On the other hand, the police were waging war against the men who frequent such places with stools and forms, and as soon as any of them put in an appearance they were quickly pounced upon by the officers, who at once proceeded to destroy the intended stands before the eyes of the helpless owners. Among the sightseers were several of the Indian visitors in gorgeous coloured coats, tight-fitting trousers, and turbans, as well as some of the Australian and New Zealand troops.<ref name=":2" /> (6, Col. 3a)</blockquote> ==Related Events== This garden party was the culminating event of the official celebrations for Queen Victoria's Diamond Jubilee, and more specific events led up to it: # Trip from Windsor to Paddington Station Queen Victoria and a large retinue traveled by train from Windsor to Paddington Station the day before, preceded on an earlier train by "the royal equipages sent from Buckingham Palace for the use of the Queen and her suite," which were<blockquote>First came the splendied semi-state landau in which the Queen made her now famous journey on June 22d. It was preceded by scarlet-coated outriders, and horsed by four magnificent bays driven by postilions in navy blue and white uniforms. Two similar carriages followed, and these were in turn succeeded by a number of pair-horse clarences for the conveyance of the household and suite, and several breaks and ‘buses for luggage. A captain's escort, furnished by the 2d Life Guards, and commanded by Captain Ellison, clattered along in rear of the carriages, and took up a position opposite the spot where, by prior arrangement, Her Majesty’s saloon was to be brought to a standstill. These magnificent troops, riding their great black horses, and with the sunlight dancing upon their nodding plumes, and reflected by their burnished helmets, cuirasses, and trappings, made a very fine show indeed. The escort did not carry the colour, as it did on the 21st, nor was it accompanied by the regimental trumpets.<ref name=":0">"Jubilee Festivities. The Queen Again in London. Interesting Functions. A Visit to Kensington. The Garden Party." ''North British Daily Mail'' 29 June 1897, Tuesday: 5 [of 8], Col. 3a–7b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002683/18970629/083/0005. Print p. 5.</ref>{{rp|5, Col. 3b}}</blockquote> # Reception at Paddington # Visit to Kensington # Kensington to Buckingham Palace # The Garden Party # Return to Windsor by Way of Paddington === Foreign Admirals === On 29 June 1897, the day after the garden party, the ''North British Daily Mail'' reports that, after the Queen's garden party, the foreign admirals would return to Spithead for a tour around the dockyard and luncheon:<blockquote>THE FLEET AT SPITHEAD<p> The fleet at Spithead was again illuminated last night, the railway companies having duplicated the ordinary train service to bring visitors down. The Koenig Wilhelm was to have sailed on Sunday evening, but her departure has been deferred, and last night her officers gave a private dinner party aboard for the anniversary of the Queen’s Coronation. All the commissioned ships in the harbour were dressed at noon. A royal salute was fired. The [Col. 6c–7a] foreign admirals will return from their visit to London on the occasion of the Queen’s garden party to be conducted round the dockyard to-day, and they will be entertained to luncheon.<ref name=":0" />{{rp|5, Col. 6c–7a}}</blockquote> === Colonial Premiers === The day of the garden party the colonial premiers attended a meeting with Secretary of State for the Colonies, [[Social Victorians/People/Chamberlain|Joseph Chamberlain]]:<blockquote>THE COLONIAL PREMIERS The whole of the Colonial Premiers went to the Colonial Office yesterday for further conference with Mr Chamberlain, who received them in his private room, attended by Mr F. H. Wilson, legal assistant, Mr Reid and the Hon. T. Cochrane, M.P., assistant private secretaries. The conference lasted hours, and was of a strictly private and confidential character, the matters discussed involving several points of high State policy. Premiers will be entertained at Warwick Castle by the Earl and Countess of Warwick on July 15th. On the same occasion the Attorney General of Queensland will present a loving cup from Warwick, in Queensland, to the old county town of Warwick, from which it takes its name. He will be accompanied by the Colonial troopers.<ref name=":0" />{{rp|5, Col. 7a}}</blockquote> For these visitors to London during the Diamond Jubilee, the next major social event was on 15 July, at Warwick Castle, hosted by [[Social Victorians/People/Warwick|Daisy, Countess of Warwick and Francis, 5th Earl of Warwick]], although perhaps some attended the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball]]. == Who Was Present == In the absence of a copy of the report about the garden party in the ''Court Circular'', the newspaper account with the fullest list of names is from the ''Morning Post'', although people further down the list can be impossible to identify, and two full columns are damaged (Col. 7 on p. 4 and Col. 1 on p. 5).<ref name=":1">“The Queen’s Garden Party.” ''Morning Post'' 29 June 1897, Tuesday: 4 [of 12], Cols. 1a–7c [of 7] and 5, Col. 1a–c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0000174/18970629/032/0004 and https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970629/032/0005.</ref> Whenever possible, then, what is here has been amended with other newspaper reports that have names to help decipher the illegible ones in the ''Morning Post'' account. The names in the Morning Post are grouped, mostly by rank and name. === People of Color at This Event === One purpose of a closer look at this event is to get a more precise list of names of people of color from the various countries in the empire, who were not recognized and thus not named in newspaper descriptions of other events. For example, the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball]] was said to include a number of South Asian dignitaries, but because the Duchess did not release to the newspapers the names of those who were invited, those dignitaries went mostly unnamed in the newspaper reports, if their presence was noted at all. Besides the South Asian guests invited to this garden party, some South Asian visitors to London were spectators as well:<blockquote>Among the sightseers were several of the Indian visitors in gorgeous coloured coats, tight-fitting trousers, and turbans, as well as some of the Australian and New Zealand troops.<ref name=":2" /> (6, Col. 3a)</blockquote>In a section on what people — mostly women — wore, the reporter for the ''Daily News'' said,<blockquote>Suffice to say, the modistes had done their best, and that their achievements excited general admiration. Here and there, however, was an Eastern beauty whose golden lace drapery, loosely enveloping a figure that owed nothing to the corset, challenged comparison, we will not say with what success, with the European model. In the almost entire absence of uniforms or Court dress, the costumes of the East Indian notables lent colour to the assemblage, while their pearls and diamonds, the wealth of Ormuz and of Ind, were not allowed to pass unobserved.<ref name=":3" /> (5, Col. 6b)</blockquote> === People Invited === # Queen Victoria, with escort and attendants ## Captain's Escort of the 2nd Life Guards ## The Duchess of Buccleuch, Mistress of the Robes ## The Dowager Lady Churchill, Lady in Waiting ## The Hon. Harriet Phipps, Woman of the Bedchamber ## Maids of Honour in Waiting ### The Hon. Mary Hughes ### The Hon. Aline Majendie ## the Earl of Kintore, Lord in Waiting ## Captain Drummond, Groom in Waiting ## Equerries in Waiting ### Major-General Sir John M'Neill, V.C. ### Lieutenant Colonel Davidson, M.V O. [sic] #Grand Duke and Grand Duchess Serge of Russia #Princess Henry of Battenberg, with attendants ##Miss Minnie Cochrane ##Colonel John Clerk, C.S.I., C.V.O. #Her Imperial Majesty the Empress Frederic, attended by ##the Dowager Lady Ampthill ##Lord Harris ##Colonel S. Waller ##Princess Hatzfeldt Trachenberg ##Count Seckendorff ##Baron and Baroness Reischach #Their Royal Highnesses the Prince and Princess of Wales, with attendants ##Lady Suffield, Lady in Waiting ##Miss Knollys, Woman of the Bedchamber ##Lord Colville of Culross, K.T., G.C.V.O., Chamberlain to the Princess of Wales ##The Earl of Gosford, K.P., Lord in Waiting ##General Sir D. Probyn, G.C.V.O., K.C.B., K.C.S.I., V.C, Comptroller ##Sir Francis Knollys, K.C.M.G., C.B., Groom in Waiting ##Major-General Stanley Clarke, C.M.G., Equerry in Waiting #Princess Victoria of Wales #Their Royal Highnesses Prince and Princess Charles of Denmark #Their Royal Highnesses the Grand Duke and Grand Duchess of Mecklenburg-Strelitz, attended by ##Lady Caroline Cust ##Mr. Hugo Erskine Wemyss ##Count Reventlow Criminil ##Baron von der Wense #Their Royal Highnesses Prince and Princess Christian, attended by ##Baroness von und zu Egloffstein ##Colonel the Hon. Charles Eliot #Her Highness Princess Victoria #His Highness Prince Christian Victor #His Highness Prince Albert of Schleswig-Holstein #Her Royal Highness Princess Louise Marchioness of Lorne and the Marquis of Lorne, attended by ##Lady Sophia Macnamara ##[[Social Victorians/People/Arthur Collins|Colonel Arthur Collins]], M.V.O. #Their Royal Highnesses Prince and Princess Henry of Prussia, attended by ##Admiral of the Fleet Sir Edmund Commerell ##Baron and Baroness Seckendorff ##Count Hahn ##Captain Muller #Their Royal Highnesses the Duke and Duchess of Saxe-Coburg and Gotha, attended by ##The Hon. Mrs. Monson ##His Excellency Herr von Schön ##Captain the Hon. D. J. Mouson [sic, s/b Monson?], M.V.O. ##Mr. A. D. J. Monson ##Captain von Ruxleben #Princess Beatrice of Saxe-Coburg and Gotha #The Hereditary Prince of Saxe-Coburg and Gotha #Their Royal Highnesses the Duke and Duchess of Connaught and Strathearn, attended by ##Colonel and the Hon. Mrs. A. Egerton #Her Royal Highness the Duchess of Albany, attended by ##Sir Robert and Lady Collins ##Miss Potts #Her Royal Highness Princess Frederica of Hanover and Baron von Pawel Raminingen, attended by ##Mr. and Mrs. Charles Wood #His Royal Highness the Duke of Cambridge, attended by ##Colonel A. C. FitzGeorge, C.B. #Her Royal Highness the Duchess of Teck and his Highness the Duke of Teck, attended by ##Lady Katherine Coke ##The Hon. A. Nelson Hood #Her Royal Highness Princess Louise Duchess of Fife and the Duke of Fife #His Highness the Prince and her Royal Highness Princess Frederic Charles of Hesse, attended by ##The Hon. A. Hay ##Fraulein von Tasmund ##Baron von Kotwitz #Their Highnesses Prince and Princess Aribert of Anhalt, attended by ##Miss Deverell ##Major Evan Martin #Her Royal Highness the Hereditary Princess of Saxe-Meiningen and her Serene Highness Princess Feodore of Saxe-Meiningen, attended by ##The Hon. Aubrey FitzClarence ##Miss von Dreskan ##Baron von Roeder #His Serene Highness the Prince of Schaumburg-Lippe #Their Highnesses Prince and Princess Edward of Saxe-Weimar #Her Serene Highness Princess Victor of Hohenlohe #Countess Gleichen (x2) #Their Serene Highnesses Prince and Princess Adolphus of Teck #The Prince Francis and Prince Alexander of Teck #His Highness Prince Augustus Leopold of Saxe-Coburg #Their Serene Highnesses Prince and Princess Blucher von Wahlstatt #Their Serene Highnesses Prince and Princess Joachim Murat #Their Serene Highnesses [[Social Victorians/People/Pless|Prince and Princess Hans Henry Pless]] #Prince and Princess Loewenstein #Their Serene Highnesses the Duke and Duchess of Arenberg #Prince Victor Duleep Singh #Prince Frederick Duleep Singh #Princess Duleep Singh (x2) #ARGENTINE REPUBLIC — M. Florencio Dominguez and M. Carlos Dominguez #BADEN — Herr yon Brauer, Mr. Brook Taylor, and Baron Bohlen Halbach #BAVARIA — His Royal Highness the Prince Rupert, General Sir L. Gardiner, K.C.V.O., C.B., Major Fairholme, Lieutenant-Colonel Emile von le Bret Nucourt, and Captain Othon von Stettin #BELGIUM — His Serene Highness the Prince Charles de Ligne, Princess de Ligne, Madlle. de Ligne, Mr. C. lnnes Ker, Count de Jonghe d'Ardoye, and the Marquis d’Asshe #BOLIVIA — M. Caso, Mr. Conway Seymour, M. Pedro Suarez, Madame Suarez, and M. Adolfo Bolivian #BRAZIL — M. [[Social Victorians/People/Souza Correa|de Souza Correa]] [Corréa?] #BULGARIA — Their Royal Highnesses the Prince and Princess of Bulgaria, Colonel J. R. Slade, C.B., Madame Petrow Tchomakoff, Count Robert de Bourboulon, Lieutenant-Colonel Marcoff, Major Petrew, Captain Stoïanow, and Mr. Martin Furth #CENTRAL AMERICA (Greater Republic) — M. Medina and Miss Medina #CHILI — M. Ramon Subercasseaux and Mr. Raglan Somerset #CHINA — His Excellency Chang Yen Hoon, Colonel Mark Bell, V.C,. Mr. Liang, Mr. Jui, and Mr. Koo #COREA — His Excellency Min Young Hwan, Major A. Cavendish, Mr. Min Young Chan, Mr. Min Shangho, and Mr. von Rautenfeld #COSTA RICA — Senor Don Demetrio Iglesias, Mr. C. Alban Young, Dona Eudoxia Castro, Señorita Maria Iglesias, Don Ricardo Fernandez Guardia, and Dona Christina Castro Keith #DENMARK — His Royal Highness the Prince Waldemar, Major-General Arthur Ellis, C.S.I., M. Charles Rothe, and Captain Evers #EGYPT — Prince Mohammed Ali Pasha, Colonel Larking, Tigrane Pasha, Colonel Aziz Bey, Mr. George Smart, Said Zoulfikar Bey #ECUADOR — M. Navares, Colonel Concha #FRANCE — General Davoust, Duc d'Auerstadt, Duchesse d'Auerstadt, and Madlle. Davoust, Colonel Brabazon, Colonel Dawson, General Hagron, M. Crozier, Colonel Humbert, and Captain Riviers de Mauny #GERMANY — His Royal Highness the Prince Albert of Prussia, Prince Regent of Brunswick, Major-General Sir C. du Piat, K.C.B., Colonel Grierson, Lieutenant-General von Plessen, Colonel von Arnim, Captain Fischel, Count von der Schulenberg (Hofmarschall), Major Freiherr von Stein, Dr. Schreibe, Captain von Unzer #GREECE — M. Rangabi, Mr. R. D. Norton #GUATEMALA — Dr. Cruz, Madlles. Cruz (2), Señor Estrada #HAWAIIAN ISLANDS — Mr. S. M. Damon, Captain the Hon. H. Napier, Major Curtis P. Jaukea #HESSE — Their Royal Highnesses the Grand Duke and Grand Duchess of Hesse, Colonel the Hon. H. Byng, C.B., Baroness de Grancy, Baron Riedesel zu Eisenbach, Baron de Genadius Grancy #ITALY — Their Royal Highnesses the Crown Prince and Princess, the Earl of Clarendon, Colonel Needham, Countess Giulia Trigona, Lieutenant-General Terzaghi, Major Cavaliere Viganoni, Captain Cavaliere Merli Miglietti, Count Romnaldo Trigona, Cavaliere F. Comotto #JAPAN — His Imperial Highness the Prince Arisugawa, Mr. R. F. Synge, Captain Beaumont, R.N., Marquis Ito, Mr. S. Saito, Marquis Kido, Captain Funaki, Lieutenant-Colonel Murata, Lieutenant Kato, Mr. Nabeshima #LIBERIA — Mr. H. Hayman #LUXEMBURG — His Royal Highness the Hereditary Grand Duke of Luxemburg, Colonel H. D. Browne, Baron Ritter yon Grünstein #MECKLENBURG-SCHWERIN — His Excellency Herr D. yon Vietinghoff, Mr. Eyre A. Crowe #MEXICO — Don Antonio Mier y Celis, Mr. Arnold Royle, C.B., Don Francisco R. Gallardo, Don Eustagino dc Escaudon, and Captain Don Ponfirio Diaz #MONTENEGRO — His Highness the Prince Danilo, Major the Hon. C Harbord, Colonel Djurcovitch, and Captain Pejanovitch #NETHERLANDS — Count van Lynden, Countess van Lynden, Mr. Horace West, and Count W. de Bylandt #PARAGUAY — M. E. Machain and Madame Machain #PERSIA — His Imperial Highness the Prince Amir Khan, General Sir Thomas Gordon, K.C.I.E., C.B., C.S.I.[,] Mr. Harry Churchill, General Karim Khan, Mirza Ahmad Khan, Mirza Ohaness Khan, Mirza Mohamad Ali Khan #PERU — Senor Canevaro, Duchesse de Zoagli Canevaro, Dr. Don A. N. Puente, Don Alfredo Elster, and Don Carlos von der Heyde #PORTUGAL — His Royal Highness the Duke of Oporto, Major the Hon. H. C Legge, M.V.O., Colonel Duval Telles, Captain Moreira de Sà, Major d'Albuquerque, and Lieutenant Jose de Melie[?] #ROME — Right Rev. Monsignore Sambucetti, [[Social Victorians/People/Stonor|Hon. Harry Stonor]], Right Rev. Monsignore Belmont, the Right Rev. Monsignore de Vaz, Marchesi and Marchesa Muccioli, of the Noble Guard #ROUMANIA — General Pancovici, Colonel G. P. Georgescu #RUSSIA — Their Imperial Highnesses the Grand Duke Serge and Grand Duchess Feodrowna, the Grand Duke Cyril, Lord Churchill, Lieutenant-Colonel Waters, Countess Olsouffiew, Princess Youssoupoff, Princess Lobanoff de Rostow, General Stépanoff, Colonel Gadon, and Prince Youssoupoff, Colonel Clements, Mr. Alexander Gordon Ross, and Sub-Lieutenant N. Coubé (A.D.C. to Grand Duke Cyril) #SAXE-COBURG — His Royal Highness the Prince Philip of Saxe-Coburg, Captain Walter Campbell, and Herr von Schön #SAXE-WEIMAR — His Highness the Prince Hermann of Saxe-Weimar, Mr. Frederick Campbell, and Count Zeppelin #SAXONY — His Royal Highness the Prince Frederick Augustus, Duke of Saxony, Colonel Howard, Freiherr yon Reitzenstern, First Lieutenant von Metzsch, and Baron von Oppell #SERVIA — M. Mijatovich and Madame Mijatovich #SIAM — His Royal Highness the Crown Prince and the Prince Mahit of Siam, Colonel E. H. Sartorius, V.C., Lieutenant-Colonel Rajavallabha, Lieutenant-Colonel C. Vernon Hume, Colonel Indaraty, Surgeon-Major Yarr #SPAIN — Duke of Sotomayor, Captain the Hon. A. Greville, Señor José Caro, Señor Alfonso Merry del Val, and Señor Benitez al Villar #SWEDEN AND NORWAY — His Royal Highness the Prince Eugène of Sweden and Norway, Captain G. L. Holford, Count G. Gyldenstolpe, Captain Roeder, Captain Baron Cederstrom #TURKEY — Munir Pasha, Major Surtees, Brigadier-General Nassir Pasha, Captain Enver Bey, Colonel Gordon Ponsonby #UNITED STATES — His Excellency the Hon. Whitelaw Reid, Mrs. Whitelaw Reid, Colonel Hallam Parr, Major-General Nelson A. Miles, Mrs. Nelson Miles, Rear-Admiral Joseph N. Miller, Captain M. P. Maus, Mr. Ogden Mills, Mrs. Ogden Mills, Mr. G. Creighton Webb, Mr. Erskine Hewett, Commander W. H. Emory, Lieutenant Philip Andrews, Lieutenant T. S. Rogers #URUGUAY — Dr. Alberto Nin, Madlle. Nin, Don Alfonso Saenz de Zumaran, Don Luis Posadas, Colonel C. Robido #WURTEMBURG— His Royal Highness the Duke Albert of Wurtemburg, Colonel C. Swaine, Lieutenant-General von Bilfinger, First Lieutenant Count von Degenfeld- Schonburg; five officers of the Queen's German Regiment: Major C. R. Burn (in attendance), Lieutenant-Colonel von Falkenhayn, Major von Arnim, First Lieutenant Baron von Moeller-Lilienstern, First Lieutenant von Gerlach, Second Lieutenant von Studnitz #"Native Princes, and gentlemen and ladies accompanying them"<ref name=":1" /> (4, Col. 2b) ##His Highness the Raja of Kaparthala ##His Highness the Thakur Sahib of Morvi, K.C.I.E. ##His Highness the Thakur Sahib of Gondal, C.I., and her Highness the Maharani of Gondal, C.I. ##Colonel Maharaj Dhiraz ##Sir Pratab Singh, K.C.S.I. ##Thakur Hari Singh[,?] ##Kunwar Dhokal Singh ##Rajah Ajit Singh of Khetri, attended by ##Rajkumar Unmaid Singh of Shahpura, attended by ###Colonel Trevor (in attendance upon the Rajah Ajit Singh of Khetri and the Rajkumar Unmaid Singh of Shahpura) ##Bijey Singh ##Sir Jamaetjee Jejeebhoy, Bart., C.S.I., Miss Jejeebhoy, Mr. Jejeebhoy ##Mr. and Mrs. Powrala ##Major J. G. Turner and Mrs. Turner ##Mr. A. R. Wood and Mrs. Wood #The "officers of the Imperial Service Troops, with British officers and ladies"<ref name=":1" /> (4, Col. 2b) ##Captain Mir Hashim Ali Khan Hyderabad-Resaldar ##Major Sunayat Singh, Kashmir ##Commandant Abdul Ganny, Gwalior ##Commandant Gooind, Rao Matkar, Indore ##Commandant Mirza Kurim Beg, Bhopal ##Rai Bahadur Dhunpat Rai, Jeypore ##Commandant Nand Singh, Patiala ##Commandant Rai Bahadur Thakur Dip Sing, Bikanir ##Commandant Chatru Singh, Bhartpur ##Resaldar Abdul Majid Khan, Babawalpur ##Commandant Daud Khan, Ulwar ##Commandant Nazir Khan, Rampur ##Risalda-Major Didar Singh, Sindi ##Risaldar-Major Kishan Singh, Nabha ##Risaldar Hara Singh, Karpurthala ##Risaldar Dhan Singhi, Bhavnagar ##Colonel H. Melliss, C.S.I., and Mrs. Melliss ##Major F. H. R. Drummond and Mrs. Drummond ##Captain F. Angelo ##Lieutenant H. Coape-Smith ##Captain G. F. Chenevix-Trench #The "officers of Native Cavalry Corps with British officers and ladies"<ref name=":1" /> (4, Col. 2b) ##Risaldar-Major Baha-ud-din-Khan ##Sardar Bahadur, A.D.C. to Viceroy ##Risaldar-Major Sayyid Abdul Aziz ##Risaldar-Major Khan Bahadur ##Risaldar-Major Izzat Khan ##Risaldar-Major Hukam Singh ##Risaldar-Major Sher Singh ##Risaldar-Major Husain Khan ##Risaldar-Major Mangal Singh ##Risaldar-Major Kesar Singh ##Risaldar- Major Faiz Khan ##Risaldar-Major Muhammad Umar Khan ##Risaldar-Major Ali Mahomed Khan ##Risaldar-Major Mihrab Ali Khan ##Risaldar Kaddam Khan ##Risaldar Jahanzir Khan ##Risaldar Nadir Khan ##Risaldar Mir Haidar Shah Khan ##Risaldar Makbul Khan ##Risaldar Net Ram ##Ressaidar Gurdatt Singh ##Subadar Muhammed Beg Junadar ##Abdul Karin Khan ##Lieutenant-Colonel J. C. H. Gordon and Mrs. Gordon ##Major A. Phayre and Mrs. Phayre ##Captain C. F. Campbell ##Captain P. Melville, in attendance on his Highness Thakur Sahib of Morvi ##Captain M'Cartney Filgate, in attendance on their Highnesses the Thakur Sahib and Maharani of Gondal ##Mr. Nowroz ##M. Parveez ##Sir M. Mansherjee Bhownaggree, M.P. ##Mr. Percy Armytage and Mrs. Armytage ##Mr. Frank Cook, C.I.E., and Mrs. Frank Cook #The "commanding officers of Colonial contingents, with the ladies accompanying them"<ref name=":1" /> (4, Col. 2b) ##Colonel the Hon. M. and Mrs. Aylmer, Canada ##Colonel and Mrs. Lassetter, New South Wales ##Major Reay, Victoria ##Colonel Pitt, New Zealand ##Major and Miss King, Queensland ##Lieutenant and Mrs. Phillips, Cape of Good Hope ##Lieutenant-Colonel Rowell, South Australia ##Major Strickland, Western Australia ##Captain Shepstone, Natal ##Major and Miss Reeves, Ceylon ##Mr. Badeley, Hong Kong ##Colonel Walker, C.M.G., and Mrs. Walker, Straits Settlements ##Captain Lucie Smith, Jamaica ##Lieutenant-Colonel E. B. M'lnnis, C.M.G., and Mrs. M'lnnis, British Guiana ##Major Rooks, Trinidad ##Captain Bernard, Malta ##Captain Kershaw, Cyprus ##Captain and Mrs. Middlemist, Gold Coast ##Inspector Hook, Lagos ##Captain Blakeney, Sierra Leone ##Lieutenant Festing, Royal Niger Company ##Captain Flint, British North Borneo Company ##The Hon. M. Gifford, Rhodesian Horse ##The following British officers attached: Lieutenant-Colonel Boulton, Lieutenant-Colonel Prior, Lieutenant-Colonel Tucker, Lieutenant-Colonel Domville, Lieutenant-Colonel Gibson, and Lieutenant-Colonel Tyrwhitt #The "gentlemen representing the various races in the Island of Ceylon"<ref name=":1" /> (4, Col. 2c) ##Maha Mudaliyar don Solomon Dias Bandaranaihe ##The Hon. Alexander Dealius Sonewiratne ##M. E. Rowland Goonoratne ##M. Charles de Soysa Dessanayaka ##Panabokko Jikiri Banda ##Nugawela Kuia Banda ##Kobbokeduwe Loku Banda ##M. E. S. W. Senathi rajah [sic] and Mrs. Senathi ##M. J. H. de Saram and Miss de Saram ##M. P. Ramanathan ##M. Saunders and Miss Saunders #The "members of the Corps Diplomatique and other foreigners of distinction"<ref name=":1" /> (4, Col. 2c) ##The Russian Ambassador, Madame de Staal, Madlle. de Staal, Madame de Stoeckl, Princess de San Donato, Madame Yermoloff, Madlle. Yermoloff, the Councillor, three Secretaries, and four Attachés of Embassy ##The German Ambassador, Countess Paul Hatzfeldt-Wildenburg, her Serene Highness Princess Hans Hohenlohe-Oehringen, Baroness yon Eckardtstein, the Councillor, two Secretaries, three Attachés of Embassy, and the Director of the Chancery ##The Austro-Hungarian Ambassador, Countess Deym, Countess Isabella Deym, Countess Clary Aldringen, Baroness Ferstel, the Councillor, two Secretaries, and four Attachés of Embassy ##The French Ambassador, Baroness de Courcel[,] Madlle. de Courcel, Madame Geoffray, the Minister Plenipotentiary, five Secretaries, and three Attachés of Embassy ##The Italian Ambassador, Princess Ruspoli, three Secretaries, and three Attachés of Embassy ##The Spanish Ambassador, Countess de Casa Valencia; Mesdlles. de Alcala Galiano (2), Marquise de Guiria, Donna de Zea Bermudez, Countess de Morella, Donna de Ia Camara y Livermore, three Secretaries, and four Attachés of Embassy ##The Turkish Ambassador, Madame Antbopoulos, the Councillor, and two Secretaries of Embassy ##The United States Ambassador, Mrs. Hay, Miss Hay, Mrs. Henry White, Mrs. Carter, Mrs. Colwell, two Secretaries, one Attaché of Embassy, and the Private Secretary to the Ambassador ##The Argentine Minister, Madame Dominguez, Mesdlles. Dominguez (3), and the Secretary of Legation ##The Persian Minister, and one Secretary of Legation ##The Danish Minister, Madame de Bille, Madame Gosch, and the Secretary of Legation ##The Siamese Minister, Mrs. Verney, Miss Verney, Mrs. Loftus, the Councillor, the Secretary, the Attaché, and the Interpreter to the Legation ##The Liberian Minister ##The Roumanian Minister and the Councillor of the Legation ##The Netherlands Minister, Baroness de Goltstein d'Oldenaller, Baroness Schimmelpenninck van der Oye, and the Councillor of Legation ##The Belgian Minister, the Councillor, and two Secretaries of Legation ##The Mexican Minister, Madame Yturbe, Madame Romero, Madame Farias, Madame Garcia, two Secretaries and three Attachés of Legation ##The Japanese Minister, Madame Kato, two Secretaries, and three Atachés [sic] of Legation ##The Minister for Sweden and Norway, Countess Lewenhaupt, and the Attaché of Legation ##The Chinese Minister, Lady Macartney, the English Secretary, three Secretaries, and four Attachés of Legation ##The Portuguese Minister, Madlle. de Quilinan, three Secretaries, and one Attaché of Legation ##The Swiss Minister, Madame Bourcart, Madame de Salis, the Secretary, and the Attaché of Legation ##The Haytian Chargé d’Affaires ##The Chargé d’Affaires of Greece, Madame Metaxas, and the Attaché ##The Chargé d’Affaires of Chile and Madame Bascunan ##Two Secretaries and one Attaché of the Brazilian Legation ##Count E. van Rosen ##Mr. Hippolyte de Aranjo ##Vice-Admiral Montt ##Mr. Pinto, Mrs. Pinto ##Mr. and Mrs. Scaramanga ##Vicomte de Galard ##Dr. Arnold, and Madlle. von Rappoport ##Mrs. John Meiggs, Miss Meiggs ##Miss Margaret Butler ##Mrs. Henry Morgan ##Hon. Chauncey Depew ##Mr. and Mrs. James Taylor ##Mr. and Mrs. Charles Marshall ##Mr. and Mrs. Edmund Bayliss ##Mrs. Colgate ##Miss Furniss ##Miss Wells ##Miss Harris ##Hon. Levi P. Morton, Mrs. Morton, and the Misses Morton ##The Bishop of Illinois and Mrs. Leonard, Miss Leonard ##The Bishop of Albany and Mrs. Doane ##The Bishop of New York and Mrs. Potter ##the Bishop of Minnesota and Mrs. Whipple ##Mr. and Mrs. Walter Burns ##Mrs. Douglas Grant ##Miss Scott ##Mrs. Grace, Miss Margarita Grace ##Mrs. Wentworth ##Miss van Wart ##M. Valentin de Courcel ##Madame la Marquise de Talleyrand Perigord ##Comte Boson de Perigord ##Vicomte d'Espenilles ##Madame and Madlle. Thierry Delanoue ##Madlle. de la Cherè ##M. Cellerier ##M. and Madame Delawarre ##Madame Evelina Fenzi ##Count A. Zannini ##M. and Madame Jules Cottran ##Chevalier E. Mazzuechi ##Signor A. Tedeschi ##Signor A. Mariotti ##Captain Lucian von Ziegler ##Chevalier Lieutenant von Barry ##Baron Georg Rothschild ##Privy Councillor Count Berchtold ##Baron G. E. Levi, Baroness Levi ##Commander E. Philipson, Mrs. E. Philipson ##The Duke and Duchess of San Germano Calabritto ##The Marquis of San Vito ##Donna Lidia Serramezzana ##Donna Margherita Chigi ##Marchioness Vitelleschi ##Chevalier Elia ##Count de Franqueville ##Count Urbain Chevrau ##M. Marcel Fonquier ##M. Baudon de Mony, Madame Baudon de Mony ##Duchess de Rohan ##Marquis de Lastorgrie, Marchioness de Lastorgrie ##Count de Boisgelin, Countess L. de Boisgelin ##M. Stern, Madame Stern, Madlle. Stern ##Count Charles du Luart ##General de Saucy ##M. E. Seydoux ##Count Jean de Madre ##M. de Monbrison ##Baron de la Chevrelière ##Count de la Villestreux, Countess de la Villestreux ##Count Urbain de Maille, Countess Urbain de Maille ##General Faveret de Kerbrich ##Monsieur de la Haye Jousselin ##Baronne Faveret de Kerbrich ##Colonel Matton ##M. Ferinier Didet ##Madame Ferinier Didet ##Donna Isabella Colonna, Donna Victoria Colonna ##Pom-k-Soh ##Madame Reyntiens ##Marquis de Fuente Hermosa ##Herr Rudolf Swobody ##M. Lauritz Tuxen ##Duchesse de Baiten ##M. de Marcoarti ##Comte de Heeren, Madlle. de Heeren ##Monsieur M. de Mauny Talvande ##Senor Don Nicolas Campero ##Lieutenant Charny ##Lieutenant Sanders ##Madame and Madlle. de Mouni ##Comtesse de Montsoulmin #"Foreign Admirals and Commanding Officers and Staffs"<ref name=":1" /> (4, Col. 3a / Col. 3b) ##Austrian Admiral Baron von Spaun, Commander von Ziegler, Lieutenant Retter yon Barry, Lieutenant Mitchell, R.N. (attached) ##Danish Admiral H. H. Koch, Captain Waudel, Lieutenant Middelboc, Lieutenant Majendie, R.N. (attached) ##French Admiral C. F. E. De Courthille, Captain Germinet, Commander Poidlone, Lieutenant Perdriel, Sub-Lieutenant de Caqueray, Lieutenant Phillimore, R.N. (attached) ##Italian Admiral C. E. Morin, Commander Count Prasca, Lieutenant Lunghetti, Lieutenant Count Morano, Lieutenant Henderson. R.N. (attached) ##German Admiral his Royal Highness Prince Henry of Prussia, Captain Muller, Lieutenant von Spee, Sub-Lieutenant Wittman, Lieutenant Garforth, R.N. (attached) ##Japanese Admiral H.I.H. Prince Arizugawa, Captain Miura, Commander Tsuda, Lieutenant Stewart, R.N. (attached) ##Netherlands Admiral F. K. Englebrecht, Captain de Groot, Lieutenant Baron von Hardenbrock, Lieutenant Woolcombe, R.N. (attached) ##Norwegian Rear-Admiral von Krogh, Captain Muller, Lieutenant Petersen, Lieutenant Kerr Pearse, R.N. (attached) ##Portuguese Captain Barreto de Vascomellos, Captain de Cartillo, Lieutenant Trye, R.N. (attached) ##Russian Admiral Nicholas Skrydloff, Captain Domojiroff, Lieutenant Stetsenkoff, Lieutenant Twisleton Wykeham Fiennes, R.N. (attached) ##Spanish Admiral Don Segismundo Bermijo y Merelo, Captain Don Antonio Eulate y Fery, Lieutenant Don Juan Romero, Lieutenant Don Antonio Romero, Lieutenant Fair, R.N. (attached) ##Swedish Admiral A. F. H. Klintberg, Captain Ingelman, Commander Flack, Lieutenant Alton, R.N. (attached) ##United States Admiral J. N. Miller, Lieutenaut Richmond (attached) ##Captain de Mar E. Guerra ##Captain R. S. D. Cumins #The Lord Lieutenant of Ireland and Countess Cadogan #The Right Hon. the Speaker and Mrs. Gully, Miss Gully, and Miss Shelly Gully #Cardinal Vaughan #Right Hon. the Lord Mayor and Lady Mayoress, and Misses Faudel Phillips (2) #The Gold Stick in Waiting, Silver Stick in Waiting, Silver Stick Adjutant in Waiting #Officer Commanding 1st Life Guards and five officers #Officer Commanding 2nd Life Guards and four officers #Officer Commanding Royal Horse Guards and four officers #Officer Commanding 2nd Dragoons and three officers #Field Officer in Brigade Waiting, Adjutant in Brigade Waiting #Commanding Officer Grenadier Guards #Commanding Officer Coldstream Guards #Commanding Officer Scots Guards, a Regimental Adjutant #Commanding Officer 1st, 2nd, and 3rd Battalions Grenadier Guards and three officers of each Battalion #Commanding Officer 1st and 2nd Battalions Coldstream Guards and three officers of each Battalion #Commanding Officer 1st and 2nd Battalions of Scots Guards and three officers of each Battalion #Commanding Officer Woolwich District and six officers #Commanding Officer R.H.A. Home District and two officers #Commanding Officer R.E. and four officers #Commanding Officer 2nd Battalion Lincolnshire Regiment and three officers #Commanding Officer Royal Marines (Chatham) and four officers #Commanding Officer Royal Marines (Portsmouth) and two officers #Four officers of the Honourable Corps of the Gentlemen at Arms #Archbishops — Canterbury, York, Armagh, Ontario, Rupertsland #Dukes and Duchesses ##The Duke and Duchess of [[Social Victorians/People/Argyll|Argyll]] ##The Duke and Duchess of [[Social Victorians/People/Abercorn|Abercorn]] ##The Duchess of De Baileu ##The Duke and Duchess of [[Social Victorians/People/Buccleuch|Buccleuch]] ##The Duchess of [[Social Victorians/People/Cleveland|Cleveland]] ##The Duke and Duchess of [[Social Victorians/People/Devonshire|Devonshire]] ##The Duchess of [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton|Hamilton]] ##The Duke and Duchess of [[Social Victorians/People/Leeds|Leeds]] ##The Duke and Duchess of [[Social Victorians/People/Marlborough|Marlborough]] ##The Duke and Duchess of [[Social Victorians/People/Manchester|Manchester]] ##The Duke and Duchess of [[Social Victorians/People/Montrose|Montrose]] ##The Duke and Duchess of [[Social Victorians/People/Newcastle|Newcastle]] ##The Duke of [[Social Victorians/People/Norfolk|Norfolk]] ##The Duke of [[Social Victorians/People/Northumberland|Northumberland]] ##The Duke and Duchess of [[Social Victorians/People/Portland|Portland]] ##The Duke of [[Social Victorians/People/Richmond and Gordon|Richmond and Gordon]] ##The Duke and Duchess of [[Social Victorians/People/Roxburghe|Roxburghe]] ##The Duke and Duchess of [[Social Victorians/People/Somerset|Somerset]] ##The Duke and Duchess of [[Social Victorians/People/Sutherland|Sutherland]] ##The Duke and Duchess of St. Albans ##The Duke and Duchess of Wellington ##The Duchess of [[Social Victorians/People/Westminster|Westminster]] #Marquises and Marchionesses ##The Marquis of Abergavenny ##The Marchioness of Ailesbury ##The Marquis and Marchioness of Ailsa ##The Marquis of Anglesey ##The Marquis and Marchioness of [[Social Victorians/People/Breadalbane|Breadalbane]] ##The Marchioness of [[Social Victorians/People/Marlborough#Marchioness of Blandford|Blandford]] ##The Marquis and Marchioness of Bristol ##The Marquis of [[Social Victorians/People/Camden|Camden]] ##The Marquis and Marchioness of Conyngham ##Dowager [Marchioness of] Conyngham ##The Marchioness of Cassar de Sai[n] ##The Marquis and Marchioness of Cholmondeley ##The Marquis of D'Auerstadt ##The Marquis and Marchioness [[Social Victorians/People/Stonor|D'Hautpoul]] ##The Marquis and Marchioness of Downshire ##Dowager [Marchioness of] Downshire ##The Marquis and Marchioness of [[Social Victorians/People/Hamilton Temple Blackwood|Dufferin and Ava]] ##The Marquis and Marchioness of [[Social Victorians/People/Exeter|Exeter]] ##The Marquis and Marchioness of Granby ##The Marchioness of [[Social Victorians/People/Florence Rawdon-Hastings Chetwynd|Hastings]] ##The Marquis and Marchioness of [[Social Victorians/People/Bective|Headfort]] ##The Marquis and Marchioness of Hertford ##The Marquis and Marchioness of Huntly ##The Marquis and Marchioness of [[Social Victorians/People/Abercorn#James Hamilton, Marquess of Hamilton|Hamilton]] ##The Marquis and Marchioness of [[Social Victorians/People/Lansdowne|Lansdowne]] ##The Marquis and Marchioness of Lothian ##Dowager (Marchioness of) [[Social Victorians/People/Londonderry|Londonderry]] ##The Marquis and Marchioness of [[Social Victorians/People/Londonderry|Londonderry]] ##The Marquis and Marchioness of [[Social Victorians/People/Ormonde|Ormonde]] ##The Marchioness of [[Social Victorians/People/Queensberry|Queensberry]] ##The Marquis and Marchioness of [[Social Victorians/People/Ripon|Ripon]] ##The Marquis and Marchioness of [[Social Victorians/People/Salisbury|Salisbury]] ##The Marquis and Marchioness of [[Social Victorians/People/Tweeddale|Tweeddale]] ##Dowager (Marchioness of) [[Social Victorians/People/Tweeddale|Tweeddale]] ##John Stewart-Murray, [[Social Victorians/People/Atholl|Marquess of Tullibardine]] ##Lawrence, [[Social Victorians/People/Zetland|Marquess of Zetland]] and Lilian, [[Social Victorians/People/Zetland|Marchioness of Zetland]] #Earls and Countesses ##Countess of Aberdeen and Dowager Countess of Aberdeen ##Earl and Countess of Albemarle and Dowager Countess of Albemarle ##Earl and Countess of Ancaster ##Earl and Countess of Amherst ##Earl of Ava ##Earl and Countess of Antrim ##Earl and Countess of Aylesford ##Earl and Countess of Annesley ##Earl and Countess of Airlie ##Earl and Countess of Arran ##Earl of Aberdeen ##Earl and Countess of Bandon ##Countess of Bantry ##Earl and Countess of Beauchamp ##Earl and Countess of Bathurst and Dowager Countess of Bathurst ##Countess of Bective ##Earl and Countess of Belmore ##Earl of Bradford ##Countess of Bremer ##Earl and Countess of Brownlow ##Earl and Countess of Buckinghamshire ##Earl of Burford ##Earl and Countess of Cairns ##Earl and Countess of Caledon ##Earl of Camperdown ##Earl of Cardigan ##Earl and Countess of Carnarvon and Dowager Countess of Carnarvon ##Earl of Carnwath ##Earl and Countess of Carrington ##Earl and Countess of Carysfort ##Earl and Countess of Castlestuart ##Earl and Countess of Cathcart ##Earl and Countess of Cavan ##Earl and Countess of Chesterfield ##Earl and Countess of Chichester ##Dowager Countess of Clancarty ##Countess of Clanwilliam ##Earl and Countess of Compton ##Countess of Cottenham ##Earl of Courtown ##Earl and Countess of Cowper ##Earl and Countess of Cranbrook ##Earl and Countess of Craven and Dowager Countess of Craven ##Earl and Countess of Crawford ##Earl of Crewe ##Earl and Countess of Cork and Orrery ##Earl and Countess of Coventry ##Countess of Cromartie and Dowager Countess of Cromartie ##Earl and Countess of Dalkeith ##Earl and Countess of Dartmouth ##Earl and Countess of De Grey ##Dowager Countess of De La Warr ##Earl and Countess of Denbigh ##Earl and Countess of Derby ##Earl and Countess of Donoughmore ##Earl and Countess of Drogheda ##Earl of Ducie ##Earl and Countess of Dudley and Dowager Countess of Dudley ##Earl and Countess of Dundonald ##Earl and Countess of Dunmore ##Earl and Countess of Dunraven ##Earl of Durham ##Earl and Countess of Eglinton and Winton ##Earl of Eldon ##Earl and Countess of Ellesinere ##Earl and Countess of Enniskillen ##Earl and Countess of Erne ##Earl and Countess of Errol ##Earl and Countess of Essex and Dowager Countess of Erroll ##Earl of Euston ##Earl and Countess of Feversham ##Earl and Countess of Fingall ##Earl of Fortescue ##Earl and Countess of Gainsborough ##Earl and Countess of Galloway ##Earl and Countess of Glasgow ##Countess of Gosford ##Earl and Countess of Granard ##Countess of Granville ##Earl and Countess of Grey ##Countess of Grosvenor ##Countess of Guilford ##Earl and Countess of Harewood and Dowager Countess of Harewood ##Earl and Countess of Harrington ##Earl and Countess of Hopetoun ##Earl and Countess of Huntingdon ##Earl and Countess of Harrowby ##Countess of Hohenau ##Countess of Howe ##Earl and Countess of Iddesleigh ##Earl and Countess of Jersey ##Earl and Countess of Kenmare ##Earl of Kerry ##Earl and Countess of Kilmorey ##Earl of Kimberley ##Earl and Countess of Kingston ##Earl of Kinnoull ##Josephine, Countess Kinsky ##Earl and Countess of Kintore ##Countess of Leitrim ##Earl and Countess of Lanesborough ##Countess of Lathom ##Earl and Countess of Lauderdale ##Countess of Leicester ##Earl and Countess of Leven and Melville ##Earl and Countess of Lichfield ##Earl and Countess of Limerick ##Earl and Countess of Lindsay ##Earl and Countess of Lisburne ##Earl and Countess of Listowel ##Earl and Countess of Londesborough ##Earl and Countess of Longford ##Earl and Countess of Lonsdale and Dowager Countess of Lonsdale ##Earl and Countess of Loudoun ##Earl and Countess of Lovelace ##Earl and Countess of Lucan ##Countess of Lytton ##Countess of Macclesfield ##Earl and Countess of Malmesbury and Dowager Countess of Malmesbury ##Earl and Countess of Mar ##Earl and Countess of Mar and Kellie and Dowager Countess of Mar and Kellie ##Earl and Countess of Mayo and Dowager Countess of Mayo ##Countess of Meath ##Countess of Metaxas ##Earl and Countess of Mexborough ##Earl and Countess of Minto ##Earl of De Montalt ##Earl and Countess of Morley ##Earl and Countess of Morton and Dowager Countess of Morton ##Earl of Nelson ##Earl and Countess of Norbury ##Earl of Northbrook ##Earl and Countess of Northesk and Dowager Countess of Northesk ##Earl and Countess of Onslow ##Earl of Orford ##Countess of Oxford ##Earl and Countess of Pembroke ##Countess of Percy ##Earl and Countess of Portarlington ##Earl and Countess of Portsmouth ##Earl and Countess of Powis ##Earl and Countess of Radnor ##Earl and Countess of Ravensworth ##Earl and Countess of Roden ##Earl and Countess of Romney ##Lawrence, [[Social Victorians/People/Zetland|Earl of Ronaldshay]] ##Earl of Rosebery ##Earl and Countess of Rosse ##Earl and Countess of Rosslyn and Dowager Countess of Rosslyn ##Earl of Sandwich ##Earl of Scarbrough ##Earl and Countess of Selborne ##Countess of Selkirk ##Countess of Shaftesbury ##Dowager Countess of Shrewsbury and Talbot ##Earl and Countess of Spencer ##Earl and Countess of Stamford ##Earl and Countess of Stanhope ##Earl and Countess of St. Germans ##Earl of Stradbroke ##Earl of Strafford ##Earl and Countess of Suffolk and Berkshire ##Earl and Countess of Temple (of Stowe) ##Earl and Countess of Verulam ##Earl and Countess of Waldegrave ##Earl and Countess of Warwick ##Earl and Countess of Westmeath ##Earl and Countess of Wharncliffe ##Elizabeth, Dowager Countess of Wilton and Isabella, Dowager Countess of Wilton ##Earl and Countess of Winchilsea and Nottingham ##Earl and Countess of Winterton ##Earl and Countess of Yarborough and Dowager Countess of Yarborough #Viscounts<ref name=":1" /> (4, Col. 3c / Col. 4a) and Viscountesses ##Viscount and Viscountess of Boyne ##Viscountess of Cantelupe ##Viscount and Viscountess of Castlerosse ##Viscount and Viscountess of Chelsea ##Viscount and Viscountess of Chetwynd ##Viscountess of Chewton ##Viscount and Viscountess of Clifden ##Viscount and Viscountess of Cobham ##Viscount and Viscountess of Coke ##Viscount of Corry ##Viscount and Viscountess of Cranborne ##Viscount of Crichton ##Viscount and Viscountess of Cross ##Viscount of Curzon ##Viscount and Viscountess of Dalrymple ##Viscount and Viscountess of Deerhurst ##Viscount and Viscountess of De Vesci ##Viscount and Viscountess of Dillon ##Viscount of Doneraile ##Viscount and Viscountess of Duncannon ##Viscount of Dungarvan ##Viscount and Viscountess of Ebrington ##Viscount and Viscountess of Emlyn ##Viscount of Encombe ##Viscount and Viscountess of Exmouth ##Viscount and Viscountess of Falkland ##Viscount and Viscountess of Falmouth ##Viscount of Fitz Harris ##Viscount and Viscountess of Folkestone ##Viscount and Viscountess of Frankfort de Montmorency ##Viscount and Viscountess of Gage ##Viscount and Viscountess of Galway ##Viscount and Viscountess of Garnock ##Viscount and Viscountess of Gough ##Viscount of Gort ##Viscount and Viscountess of Halifax ##Viscount and Viscountess of Hardinge ##Viscount of Harrington ##Viscount and Viscountess of Hood ##Viscount and Viscountess of Kilcoursie ##Viscount and Viscountess of Knutsford ##Viscount and Viscountess of Lifford ##Viscount of Llandaff ##Viscount and Viscountess of Maitland ##Viscount and Viscountess of Marsham ##Viscount and Viscountess of Massereene and Ferrard ##Viscount and Viscountess of Melville ##Viscount and Viscountess of Midleton ##Viscount and Viscountess of Milton ##Viscount and Viscountess of Monck ##Viscount and Viscountess of Morpeth ##Dowager Viscountess of Mountmorres ##Viscount and Viscountess of Newark ##Viscount and Viscountess of Newport ##Viscount and Viscountess of Oxenbridge ##Viscount of Parker ##Viscount of Peel ##Viscount and Viscountess of Portman ##Viscount and Viscountess of Powerscourt ##Viscount and Viscountess of Raincliffe ##Viscountess of Sherbrooke ##Viscount of Sidmouth ##Viscount of St. Cyres ##Viscount of Southwell ##Viscount of Suirdale ##Viscount and Viscountess of Templetown ##Viscountess of Torrington ##Viscount and Viscountess of Trafalgar ##Viscount and Viscountess of Valentia ##Viscount of Valletort ##Viscount of Villiers ##Viscountess of Wolseley #Bishops — Auckland, Barry, Bath and Wells, British Colombia, Chichester, Durham, Ely, Exeter, Gloucester and Bristol, Gibraltar, Hereford, London, Lichfield, Lincoln, Manchester, Newcastle, Norwich, Oxford, Peterborough, Rochester, Ripon, Stepney, Southwark, St. Albans, Salisbury, Sodor and Man, Southwell, Sydney, Sierra Leone, Worcester, Winchester, Wellington #Baronesses — Burdett-Coutts, Macdonald #Lords and Ladies<ref name=":1" /> (4, Col. 4b / Col. 5a) — ##Lord and Lady Abercromby ##Lord and Lady Aberdare ##Lord Aberdour ##Lady Abinger ##Lady Alexandra Acheson ##Lady Adam ##Lady Adderley ##Lord and Lady Addington ##Lady Adye ##Lady Agnew ##Lady Alderson ##Lord and Lady Alington ##Lady Alison ##Lady Mildred Allsopp ##Lord and Lady Amherst of Hackney ##Lady Heathcoat Amory ##Lord and Lady Ampthill ##Lady Agnes Anderson ##Lady Bertha Anson ##Lady Arbuthnot ##Lady Alice Archer Houblon ##Lord Ardee ##Lord and Lady Ardilaun ##Lady Armstrong ##Lady Arnold ##Lady Arnott ##Lord and Lady Ashbourne ##Lord and Lady Ashburton and Dowager Ashburton ##Lord and Lady Ashcombe ##Lady Alice Ashley ##Lady Edith Ashley ##Lady Ashmead-Bartlett ##Lord and Lady Ashton ##Lord and Lady Ashtown ##Lady Florence Astley ##Lady Gertrude Astley-Corbett ##Lady Austin ##Lord Bagot ##Lady Bailey ##Lady Blanche Baillie ##Lady Baird ##Lady Baker ##Lord Balcarres ##Lord and Lady Balfour of Burleigh, Lady Nina Balfour and Lady Betty Balfour ##Lord Balvaird ##Lord Bangor ##Dowager Lady Barclay ##Lord and Lady Barnard ##Lady Florence Barnardiston ##Lady Constance Barne ##Lady Barran ##Lady Barrington ##Lord and Lady Basing ##Lord and Lady Bateman ##Lady Evelyn Bathurst ##Lord and Lady Battersea ##Lady Steuart Bayley ##Lady Violet Beauchamp ##Lord Osborne Beauclerk and Lady Beauclerk (2) ##Lady A. Beaumont ##Lady Bedford ##Lord and Lady Belhaven and Stenton and Dowager Belhaven and Stenton ##Lord and Lady Bellew and Dowager Bellew ##Lord and Lady Belper ##Lady Charles Beresford ##Lady William Beresford (Lilian Duchess of Marlborough) ##Lady Bergne ##Lord and Lady Bertie and Lady Elizabeth Bertie ##Lady Biddulph, Lady Elizabeth Biddulph and Lady Wilfreda Biddulph ##Lady Bigge ##Lord and Lady Bingham ##Lord and Lady Binning ##Lord Blackwood, Lord Basil Blackwood. Lady Hermione Blackwood and Lord Terence Blackwood ##Lady Bloomfield ##Lady Blythswood ##Lord and Lady Bolton ##Lady Maud Bootle-Wilbraham, Lady Bertha Bootle-Wilbraham and Lady Edith Bootle-Wilbraham ##Lord Borthwick ##Lady Margaret Boscawen ##Lord and Lady Boston ##Lady Boughey ##Lady Albreda Bourke and Lady Florence Bourke ##Lady Bowen ##Lady Bower ##Lady Muriel Boyle and Lady Boyle (2) ##Lady Mary Brabazon ##Lady Brackenbury ##Lady Braddon ##Lady Bramwell ##Lady Bramston ##Lord Brassey, Lady Idina Brassey and Lady Violet Brassey ##Lord and Lady Braye ##Lady Mary Bridgeman ##Lady Eleanor Brodie ##Lady Hilda Brodrick ##Lady De Capel Brooke and Dowager Brooke ##Lady Cunliffe Brooks ##Lord and Lady Brougham and Vaux ##Lord and Lady Ulick Browne, Lady Browne and Lady Crichton Browne ##Lady Brownlow ##Lord and Lady F. Brudenell-Bruce ##Lady Brunner ##Dowager Buchanan-Riddeil ##Lady Audrey Buller ##Lady Burdett ##Lord and Lady Burghclere ##Lord Burghley ##Lady Agnes Burne ##Lady Burrell ##Lord and Lady Burton ##Lady Butler and Lady Butler (2) ##Lord and Lady Arthur Butter ##Lady Buxton and Lady Victoria Buxton ##Lady Susan Byng ##Lord and Calthorpe ##Lady C. Cameron and Lady Margaret Cameron ##Lord and Lady Archibald Campbell and Lady A. Campbell ##Lord and Lady George Campbell ##Lady Campbell-Bannerman ##Lord and Lady Camoys ##Lord and Lady Carbery and Dowager Carbery ##Lady Carbutt ##Lady Cardon ##Lord and Lady Cardross ##Lord and Lady Carew ##Lady Carmichael ##Lord and Lady Carnegie ##Lord and Lady Castlemaine ##Lord and Lady Castletown ##Lady Eva Cathcart and Lady R. Cathcart ##Lady Frederick Cavendish, Lady Myra Cavendish, Lady Evelyn Cavendish and Lady Harriet Cavendish ##Lord Charles Cavendish-Bentinck, Lord and Lady Henry Cavendish-Bentinck, Lord William Cavendish-Bentinck, Lady Ottoline Cavendish-Bentinck ##Lord and Eustace Cecil, Lord Hugh Cecil, Lord and John Cecil, Lord and Edward Cecil, Lord and Lady Robert Cecil, Lord W. Cecil, Lady Gwendolen Cecil, Lady Florence Cecil, Lady William Cecil, Lady Louisa Cecil ##Lady Francis Cecil-Dallas ##Lady Chamberlain ##Lady Chelmsford ##Lord and Lady Chesham ##Lady Chetwode ##Lord Cheylesmore ##Lord and Lady Fitzwarine Chichester ##Lady Chitty ##Lady Cholmeley ##Lady Henry Cholmondeley ##Lady Clements (2) ##Lady Churchill, Lady Randolph Churchill, Dowager Churchill, Lady Spencer Churchill (2) ##Lord Edward Spencer-Churchill, Lady Alfred Spencer-Churchill ##Lord and Lady Churston ##Lord and Lady Clifford of Chudleigh ##Lady Marshal Clarke, Lady E. Clarke ##Lady Isabel Clayton ##Lord and Lady Clinton ##Lord and Lady Clonbrock ##Lord Cloncurry ##Lady Muriel Close ##Lady Evelyn Cobbold ##Lady Cochrane, Lady Gertrude Cochrane, Lady Adela Cochrane ##Lady Coddington ##Lady Mabel Coke ##Lord and Lady Colchester ##Lady Cole (2) ##Lady Colebrooke ##Lord and Lady Coleridge ##Lady Collins ##Lady Colomb ##Lady Colvile, Lady Colville ##Lord and Lady Colville of Culross ##Lady Jane Seymour Combe, Lady Constance Combe ##Lady Commerell ##Lord and Lady Alwyne Compton ##Lady Dowager Congleton ##Lord and Lady Connemara ##Lady Conyers ##Lady Blanche Conyngham ##Lady Cooper ##Lady Evelyn Cotterell ##Lord and Lady Cottesloe ##Lady Couch ##Lord and Lady Courtenay ##Lady Coventry (2) ##Lady Cowell ##Lady Helen Craven ##Lord and Lady Crawshaw ##Lady Evelyn Crichton, Lady Emma Crichton ##Lord Crofton ##Lady Cromer ##Lady Mary Crosse ##Lady Crossley ##Lady Mary Cuffe ##Lady Culme-Seymour ##Lady Cunliffe ##Lady Georgiana Curzon ##Lady Elizabeth Cust ##Lady Ida Dalzell ##Lady Mary Dashwood ##Lord and Lady Davey ##Lady Victoria Dawnay, Lady Evelyn Dawnay, Lady Adelaide Dawnay ##Lady Decies ##Lord and Lady De Freyne ##Lord and Lady De L’Isle and Dudley ##Lord De Manley ##Lady Mildred Denison, Lady Elinor Denison ##Lord Deramore ##Lord and Lady De Ramsey ##Lady Dering ##Lady De Ross ##Lord and Lady De Saumarez ##Lady Des Voeux ##Lady De Trafford, Lady Agnes De Trafford ##Lady De Winton ##Lord and Lady Digby ##Lady Dorchester ##Lady Dorington ##Lady Margaret Douglas, Lady Edith Douglas ##Lady H. Douglas-Hamilton ##Lady Dowell ##Lady Drummond, Lady Edith Drummond ##Lady Du Cane ##Lady Duckworth ##Lady Eva Dugdale ##Lord Dunally ##Lady Florence Duncombe, Lady Ulrica Duncombe, Lady Caroline Duncombe ##Lady Alice Dundas ##Lord and Lady Dunleath ##Lord Dunglass ##Lady Dunn ##Lord Dunsandle and Clanconal ##Lady Durand ##Lord Dynevor ##Lord Ebury ##Lady Edmonstone ##Lady Edwards, Lady J. B. Edwards, Lady Blanche Edwards ##Lady Ernestine Edgcumbe ##Lady Egerton (2) ##Lord Egerton of Tatton ##Lady Grey-Egerton ##Lord and Lady Elcho ##Lord and Lady Elibank ##Lady Ellenborough ##Lady Ellis ##Lord and Lady Elphinstone ##Lady Winifred Cary-Elwes ##Lady Engleheart ##Lord Erskine, Lady Erskine (2), Lady Horatia Erskine, Lady Erskine ##Lord and Lady Esher ##Lady Evans ##Lady Evelyn Ewart, Lady Mary Ewart ##Lady Evelyn Eyre ##Lady Fairbairn ##Lady Fairfax ##Lady Anne Fane, Lady Augusta Fane ##Lady Farquhar ##Lord and Lady Farrer ##Lady Fayrer ##Lady Louisa Feilding ##Lady Helen Munro Ferguson ##Lady Fergusson ##Lady Ffolkes ##Lady Finlay ##Lady Fisher ##Lady Dorothea Fitz-Clarence, Lady Maria Fitz-Clarence, Lady Dorothy Fitzclarence ##Lord and Lady Henry Fitz-Gerald, Lady B. Fitz Gerald, Lady M. FitzGerald, Lord Seymour Fitz-Gerald ##Lady Beatrix Fitzmaurice ##Lord and Lady F. FitzRoy, Lady C. Fitz-Roy ##Lady Mary Fitzwilliam ##Lady FitzWygram ##Lady Fletcher ##Lady Flower, Lady Flower ##Lord Foley, Lady Mary Foley ##Lady Gertrude Foljambe ##Lady Angela Forbes, Lady Forbes (2), Dowager Helen Forbes ##Lord and Lady Forester ##Lady Forrest ##Lady Susan Fortescue ##Lady Forwood ##Lady Foster ##Lady Fowler ##Lady Edith Franklin ##Lady Fremantle, Lady Fremantle ##Lady Frere ##Lady Fulton ##Lady Gardiner, Lady Lynedoch Gardiner ##Lord Garioch ##Lady Galton ##Lady Katharine Gathorne-Hardy ##Lady Garvagh ##Lord and Lady Gerard ##Lady Gilbey ##Lady Gillford ##Lady Susan Gilmour ##Lady Gipps ##Lord and Lady Glamis ##Lord and Lady Glenesk ##Lady Glyn, Lady Mary Carr Glyn ##Lady D'Arcy Godolphin-Osborne ##Lady Gordon ##Lady Margaret Ormsby Gore, Lady Constance Gore ##Lady Gore Langton (2) ##Lord Walter Gordon-Lennox, Lord Algernon Gordon-Lennox ##Lady Evelyn Goschen ##Lord R. S. Gower ##Lady Graham, Lady Margaret Graham, Lady Helen Graham ##Lady Charlotte Graham-Toler ##Lady Grant, Lady Florence Grant ##Lady Grant-Duff ##Lady Green ##Lord Greenock ##Lady Grenfell ##Lady Frances Gresley ##Lady Victoria Grey, Lady Grey ##Lady Jane Grey-Trefusis ##Lady Griffin ##Lady Helen Grimston ##Lord and Lady Arthur Grosvenor, Lady Grosvenor (2) ##Lady Gull ##Lady Haldon ##Lady Haliburton ##Lady Basil Hall ##Lady Halle ##Lord and Lady Halsbury ##Lord and Lady E. Hamilton, Lord F. Hamilton, Lady F. Douglas Hamilton, Lady Alexandra Hamilton, Lady Baillie Hamilton (2), Lady C. Hamilton, Lady Victoria Hamilton, Lady George Hamilton ##Lady Hanson ##Lady Harcourt ##Lady Cicely Hardy, Lady Hardy ##Lady Beatrice Hare ##Lord Harlech ##Lady Constance Harris, Lady Harris ##Lady Harrison, Lady Harriet Harrison ##Lady Hart ##Lady Emily Hart-Dyke ##Lady Dixon-Hartland ##Lady Hartopp ##Lord and Lady Hastings ##Lord and Lady Hatherton ##Lady Alice Havelock-Allan ##Lady Hawke ##Lord and Lady Hawkesbury ##Lady John Hay, Lady Hay ##Lady Blanche Haygarth ##Lady Hayter ##Lady Hely-Hutchinson (2) ##Lady Hemming ##Lord and Lady Heneage ##Lord and Lady Henley ##Lord Henniker ##Lady Beatrix Herbert, Lady Herbert (2) ##Lord and Lady Herries ##Lord and Lady Herschell ##Lord Francis Hervey, Lady Augustus Hervey ##Lady Hervey-Bathurst ##Lady Fermor Hesketh ##Lady Hibbert ##Lady Lucy Hicks-Beach ##Lord and Lady Arthur Hill, Lady Clement Hill, Lady Stock Hill ##Lord and Lady Hillingdon ##Lord and Lady Hindlip ##Lord and Lady Hobhouse ##Lady Norah Hodgson ##Lady Holdich ##Lady Mary Holland ##Lady Beatrix Douglas Home ##Lady Maria Hood ##Lady Hood of Avalon ##Lady Hooker ##Lady Mary Hope ##Lady Hoskins ##Lord and Lady Hotham ##Lord and Lady Hothfield ##Lady Houldsworth ##Lady Eleanor Howard, Lady Agnes Howard, Lady Howard (2), Lady Mabel Howard, Lady Rachel Howard ##Lord and Lady Howard of Glossop ##Lady Howarth ##Lady Mary Hozier ##Lady Florentia Hughes ##Lady Seager Hunt ##Lady Hunter ##Lord Hyde ##Lady Hylton ##Lord and Lady Inchiquin ##Lord Inverurie ##Lord and Lady Iveagh ##Lady Jackson ##Lord James of Hereford ##Lady Margaret Jenkins, Lady Jenkins ##Lady Jenner ##Lady Jephson ##Dowager Jessel, Lady Jessell ##Lady Jeune ##Lady Hill Johnes ##Lady Joicey ##Lady Alice Jolliffe ##Lady Burn Jones ##Lady Caroline Lister Kaye, Lady Beatrice Lister Kaye, Lady Lister Kaye ##Lady Isabella Keane ##Lady Keith-Falconer (2) ##Lord and Lady Kelvin ##Lady Kemball ##Lady Beatrice Kemp ##Lady Kennard ##Lady Kennaway ##Lady Aline Kennedy ##Lady Kennett-Barrington ##Lord Kenyon ##Lady Mabel Kenyon-Slaney ##Lord Kensington ##Lady Mary Stuart Keppel ##Lady Innes-Ker (2) ##Lady Kerr (2) ##Lord Kilmarnock ##Lady King ##Lady Florence King King ##Lady Emily Kingscote ##Lady Edith King-Tenison ##Lord and Lady Kinnaird ##Lady Kitson ##Lady Laking ##Lady Frances Lambart, Lady Ellen Lambart ##Lady Victoria Lambton ##Lady Adela Larking ##Lady Isabel Larnach ##Lady Mary Lascelles ##Lord and Lady Lawrence ##Lady Lawson ##Lord and Lady Leconfield ##Lady Elliott Lees, Lady Lees ##Lady Leese ##Lady Legard ##Lord and Lady Leigh ##Lady Henry Gordon-Lennox, Lady Walter Gordon-Lennox, Lady Algernon Gordon-Lennox, Lady Caroline Gordon-Lennox ##Lady Katharine Le Poer Trench ##Lady Constance Leslie ##Lady Susan Leslie-Melville ##Lady Lewis ##Lady Lilian Liddell ##Lady Lindley ##Lady Harriet Lindsay, Lady Jane Lindsay, Lady Jane Lindsay ##Lord and Lady Lingen ##Lord and Lady Lister ##Lady Gwendolen Little ##Lady Margaret Littleton ##Lord and Lady Llangattock ##Lady Llewelyn ##Lord and Lady Loch ##Lady Lockwood ##Lady Louise Loder ##Lady Catherine Loftus ##Lady Doreen Long ##Lady Longley ##Lady Albertha Lopes ##Lady Loraine ##Lord and Lady Lovat ##Lady Drury Lowe, Lady Lucy Drury Lowe ##Lady Lowry-Corry (2) ##Lady Mary Loyd ##Lady Lubbock ##Lord and Lady Lurgan and Dowager Lurgan ##Lady Lyall ##Lady Lyell ##Lady Mary Lygon ##Lady Lyons ##Lady Lysons ##Lady Lyttelton ##Lady Emily Lytton ##Lady MacCormac ##Lord and Lady Macdonald ##Lady Macgregor, Lady MacGregor, Lady Helen MacGregor ##Lady Mackenzie, Lady Mackenzie ##Lady Mackworth ##Lady Maclean ##Lord and Lady Macnaghten ##Lady Macpherson-Grant ##Lady Caroline Madden, Lady Madden ##Lady Louisa Magenis ##Lady Magheramorne, Dowager Magheramorne ##Lady Nora Maitland ##Lady Margaret Crichton-Maitland ##Lady Margaret Majendie ##Lord Cecil Manners, Lord Edward Manners, Lord Manners, Lady Victoria Manners, Lady Manners ##Lady Blundell Maple ##Lady Mappin ##Lady Marjoribanks ##Lady Markham ##Lady Marriott ##Lady Martin, Lady Martin ##Lady Evelyn Mason ##Lady Maude (2) ##Lady H. Maxwell, Lady Maxwell, Lady Maxwell, Lady Maxwell ##Lady Heron-Maxwell ##Lady M'Clintock ##Lady Evelyn M'Donnell ##Lady Meade (2) ##Lord and Lady Medway ##Lady Methuen ##Lady Meysey-Thompson ##Lord and Lady Middleton, Lady Middleton ##Lady Mary Milbanke ##Lady Miller ##Lady Milner ##Lady Clementina Mitford ##Lady Lady M'lver ##Lady Hilda M'Neile ##Lady Monckton ##Lord Moncreiff, Lady Scott Moncrieff ##Lady Moncreiffe ##Lord and Lady Monkswell ##Lady Monson ##Lord Charles Montagu, Lady Cecil Scott Montagu, Lady S. Montagu, Lady Agneta Montagu ##Lord Montagu of Beaulieu ##Lord and Lady Monteagle ##Lady Edith Montgomerie, Lady Sophia Montgomerie ##Lady Charlotte Montgomery ##Lady More-Molyneux ##Lord and Lady Moreton ##Lady Morgan ##Lord and Lady Morris ##Lady Blanche Morris ##Lady Mary Morrison ##Lady Moseley ##Lord and Lady Mostyn ##Lord and Lady Mowbray and Stourton, Dowager Mowbray and Stourton, Lady Mowbray ##Lord and Lady Muncaster ##Lady Anne Murray ##Lady Murray (2) ##Lady Georgiana Mure, Lady Georgiana Mure [sic] ##Lord and Lady Napier and Ettrick ##Lord and Lady Napier of Magdala and Dowager Napier of Magdala ##Lady Naylor-Leyland ##Lady Nelson ##Lord and Lady Henry Nevill ##Lord and Lady Newton ##Lord and Lady Newtown-Butler ##Lady Nicolson ##Lady Augusta Noel, Lady Agnes Noel ##Lady Norman ##Lord and Lady Norreys ##Lord and Lady North, Lady Muriel North ##Lady Northcote, Lady Northcote (2) ##Lord Norton ##Lady Elizabeth Nugent ##Lady O'Brien, Lady O'Brien [sic] ##Lady O'Hagan ##Lady Olpherts ##Lord and Lady O'Neill ##Lady Gwendoline O'Shee ##Princep [sic] Alice Packe ##Lord and Lady Berkeley Paget ##Lady Alfred Paget ##Lady Paget of Cranmore ##Lady Katherine Pakenham ##Lady Palgrave ##Lady Sophia Palmer, Lady Palmer ##Lady Evelyn Parker ##Lady Parratt ##Lady Maude Parry ##Lady Muriel Parsons ##Lord and Lady Pearson, Lady Pearson ##Lady Peel, Lady Georgiana Peel ##Lady Constance Childe-Pemberton ##Lord and Lady Penrhyn ##Lady Mary Pepys ##Lady Perceval ##Lady Percy (2) ##Lady Petre ##Dowager Lady Peyton ##Lady Phillimore ##Lady William Phipps ##Lord and Lady Pirbright ##Lord and Lady Playfair ##Lady Chichele Plowden ##Lady Anna Chandos-Pole ##Lady Pollock ##Lord and Lady Poltimore ##Lady Pontifex ##Lady Alice Portal ##Lady Powell, Lady Powell [sic] ##Lady Baden-Powell ##Lady Dickson-Poynder ##Lady Poynter ##Lord and Lady George Pratt ##Lady Priestley ##Lady Probyn ##Lady Eva Wyndham-Quin, Lady Wyndham-Quin (2) ##Lord and Lady Raglan, Dowager Raglan ##Lady Ramsay ##Lord and Lady Rathdonnell ##Lady Rathmore ##Lord and Lady Rayleigh, Dowager Rayleigh ##Lord and Lady Reay ##Lady Reid ##Lord and Lady Rendel ##Lord Rendlesham ##Lady Jane Repton ##Lord Revelstoke ##Lord and Lady Ribblesdale ##Lady Laura Ridding ##Lord and Lady Robartes ##Lady O. Roberts ##Lady Roberts of Kandahar ##Lady Robinson ##Lord and Lady Rodney ##Lord Romilly ##Lord and Lady Rookwood ##Lord and Lady Rossmore ##Lord Rowton ##Lady Roxburgh ##Lord and Lady Rothschild ##Lady Victoria Russell, Lady Arthur Russell, Lady G. Russell, Lady W. H. Russell, Lady Alexander Russell ##Lord and Lady Russell of Killowen ##Lord and Lady Ruthven ##Lady Jane Ryan ##Lady Mary Sackville ##Lady Salmon ##Lord and Lady Saltoun ##Lady Samuelson, Lady S. Samuel ##Lady Mary Saurin ##Lord and Lady Savile, Lady Marie Savile ##Lady Savory ##Lord George Scott, Lord Henry Scott, Lord Herbert Scott, Lady Sophie Scott, Lady Charles Scott, Lady Louisa Scott, Lady Scott (2) ##Lord and Lady Seaton ##Lord and Lady Settrington ##Lady Seymour, Lady Albert Seymour, Lady William Seymour, Lady Seymour (2) ##Lord and Lady Shand ##Lady Shaw ##Lady Constance Shaw-Lefevre ##Lady Octavia Shaw-Stewart, Lady Alice Shaw-Stewart ##Lady Mary Shelley ##Lord and Lady Sherborne ##Lady Shippard ##Lady Shute ##Lady Kay-Shuttleworth ##Lady Simeon ##Lady Simmons ##Lady Simpson of Windsor ##Lord and Lady Sinclair ##Lord and Lady Skelmersdale ##Lady Esther Smith, Lady Barbara Smith, Lady Smith, Lady Blanche Smith, Lady Sybil Smith, Lady Euan Smith, Lady D. Smith ##Lady Smyth ##Lady Catherine Somerset, Lady Geraldine Somerset, Lady Henry Somerset ##Lord and Lady Southampton, Dowager Southampton ##Lady Edward Spencer-Churchill ##Lady Margaret Spicer ##Lady Sprigg ##Lady Stafford ##Lord Stalbridge ##Lady Stanhope (2) ##Lord Stanmore ##Lord Stanley, Lady Alice Stanley, Lady Isobel Stanley ##Lady Stansfield ##Lord Stavordale ##Lady Stephenson ##Lady Stevenson ##Lady Helen Stewart, Lady Mary Stewart, Lady Mark Stewart, Lady Stewart, Lady Houston Stewart, Lady Stewart [sic], Lady Isabel Stewart ##Lady Stewart of Grantully ##Lady Edith St. Aubyn ##Lord and Lady St. Levan ##Lady St. Leonards ##Lord and Lady St. Oswald ##Lady Stone ##Lady Charlotte Stopford ##Lord and Lady Stratheden and Campbell ##Lady Mary Stuart-Richardson ##Lord Suffield ##Lady Sutherland ##Lady Evelyn Sutton, Lady Susan Sutton ##Lord and Lady Swansea ##Lady Swinnerton Dyer ##Lady Kathleen Swinnerton-Pilkington ##Lord and Lady E. Talbot, Lady Emma Talbot ##Lady Jane Taylor ##Lady Taylour (2) ##Lady Tatton Sykes ##Lord Herbert Vane-Tempest, Lord Henry Vane-Tempest ##Lord and Lady Templemore ##Lady Tennant ##Lord and Lady Tennyson ##Lady Tenterden ##Lord Tewkesbury ##Lord and Lady Teynham ##Lord and Lady Thring ##Lady E. Thornton ##Lady Thursby ##Lady Ulrica Thynne ##Lord and Lady Tollemache ##Lady Agnes Townshend ##Lady Mary Trefusis ##Lady Tredegar ##Lady Trevelyan, Lady Trevelyan [sic] ##Lord and Lady Trevor ##Lady Troubridge ##Lady Turner ##Lady Henrietta Turnor ##Lady Tuson ##Lord and Lady Tweedmouth ##Lady Tyler ##Lady Emily Van De Weyer ##Lady Jane Van Koughnet ##Lord and Lady Ventry ##Lady Villiers (2), Lady Edith Villiers ##Lady Howard Vincent, Lady Helen Vincent, Lady Vincent ##Lady Vivian, Lady Jane Vivian ##Lady Mary Waldegrave ##Lady F. F. Walker, Lady James Walker ##Lady Walrond ##Lady Clementine Walsh ##Lord Wandsworth ##Lady Wantage ##Lord Warksworth ##Lady Leucha Warner ##Lady Warrender ##Lord and Lady Watson ##Lady Cecilia Webb ##Lady Rose Weigall ##Lord Welby ##Lady Willes ##Lady Willis ##Lady Arthur Wellesley ##Lord and Lady Wenlock ##Lord and Lady Westbury and Dowager Westbury ##Lady Isabella Whitbread ##Lady White ##Lady Whitehead ##Lady Whiteway ##Lady Elizabeth Williamson ##Lady Williams-Wynn ##Lady Willoughby (2) ##Lord Willoughby de Broke ##Lord Willoughby de Eresby ##Lady Willshire ##Lady Wilson, Lady Sarah Gordon Wilson ##Lord and Lady Wimborne ##Lady Windeyer ##Lord and Lady Windsor ##Lady Winnington ##Lady Constance Wodehouse ##Lord and Lady Wolverton ##Lady Julia Wombwell ##Lady Wood, Lady Mary Wood ##Lady Woods ##Lord Wrottesley ##Lady Hugh Wyndham ##Lady Barbara Yeatman ##Lady Lilian Yorke ##Lord Zouche #Right Honourables ##H. H. Asquith ##E. Ashley ##A. H. Dyke Acland ##J. Atkinson ##J. B. Balfour ##Sir G. Bowen ##G. W. Balfour ##Sir Hicks-Beach ##A. J. Balfour ##James Bryce ##Sir H. Campbell-Bannerman ##A. H. Smith-Barry ##E. Carson ##H. Chaplin ##Sir J. Chitty ##Jesse Collings ##Sir R. Couch ##G. N. Curzon ##J. Chamberlain ##L. Courtney ##Sir M. Grant-Duff ##A. Akers-Douglas ##Sir W. Hart Dyke ##Sir H. Elliot ##F. Foljambe ##Sir H. Fowler ##Sir A. B. Forwood ##Sir J. Fergusson ##Herbert Gladstone ##Sir J. Gorst ##G. J. Goschen ##W. E. Gladstone ##Sir G. Grey ##C. H. Hemphill ##Charles Seale-Hayne ##R. W. Hanbury ##Lord George Hamilton ##Staveley Hill ##Sir J. T. Hibbert ##Sir W. Harcourt ##lon Hamilton ##Sir Arthur Hayter ##Sir F. Jeune ##W. L. Jackson ##Sir John Kennaway ##G. Shaw-Lefevre ##W. Lidderdale ##Sir Massey Lopes ##James Lowther ##Sir J. Lubbock ##Sir H. Lopes ##Walter Long ##Sir N. Lindley ##J. W. Mellor ##Sir G. O. Morgan ##John Morley ##Arnold Morley ##Sir J. Mowbray ##A. J. Mundella ##J. H. Macdonald ##F. Max Müller ##Sir W. Marriott ##Graham Murray (the Lord Advocate) ##Sir E. Monson ##Sir P. O'Brien ##Sir A. Otway ##Sir F. Peel ##Sir R. Paget of Cranmore ##W. J. Pirrie ##J. P. Robertson ##Sir. J. Rigby ##C. T. Ritchie ##Sir S. H. Strong ##Sir B. Saunderson ##Sir J. Stansfeld ##Sir A. Smith ##C. R. Spencer ##Sir C. Kay-Shuttleworth ##Sir R. Temple ##Sir R. Thompson ##Sir E. Thornton ##Lord Henry Thynne ##Sir G. O. Trevelyan ##C. P. Villiers ##Sir Algernon West ##Sir C. L. Wyke ##C. B. Stuart-Wortley ##S. J. Way #Honourables<ref name=":1" /> (4, Col. 5a / Col. 5b) and Honourable Ladies<ref name=":1" /> (4, Col. 5b / Col. 5c) ##Mrs. Acland ##Mrs. Alexander ##H. Allsopp, Mrs. Allsopp, George Allsopp ##Mrs. Anstruther ##Mrs. Armytage ##[Hon. Lady] Vere Annesley ##Mrs. Bagot, Mrs. Bagot [sic 2x] ##Mrs. Baillie of Dochfour ##Mrs. Balfour ##[Hon.] Coplestone and [Hon.] Mrs. Bampfylde ##John Baring, Susan Baring, Lilian Baring ##Mrs. Barker ##Mrs. Barlow ##Eric Barrington, Mrs. Barrington ##Mrs. Hamar Bass ##Misses Bateman-Hanbury (2) ##Allen B. Bathurst ##Mrs. Benyon ##[Hon. Lady] Beresford ##[Hon.] R. Chetwynd ##Arthur Chichester ##Lady Biddulph ##C. E. Bingham, Mrs. Bingham, Albert Bingham, Mrs. Bingham [sic x2] ##Lady Birkbeck ##Ivo Bligh, Mrs. Bligh ##Diana Sclater-Booth ##O. Borthwick ##J. Boscawen ##Henry Bourke, Mrs. H. Bourke, Charles Bourke, Terence Bourke, Mrs. T. Bourke, Algernon Bourke, Mrs. A. Bourke, Mrs. E. R. Bourke ##Charles Brand, Arthur Brand, Mrs. Brand, Mrs. T. Brand ##T. Brassey, Mrs. A. Brassey ##Mrs. Stapleton Bretherton ##Reginald Brett, Mrs. Brett ##Mrs. F. Bridgeman, Misses Bridgeman (2) ##Mrs. Britten ##W. St. John Brodrick, Albinia Brodrick ##Emmeline Brownlow ##Mrs. T. C. Bruce, Misses Bruce (2) ##Misses M'Clintock Bunbury (2) ##Mary Byng ##T. J. Byrnes ##Arthur Cadogan, Mrs. A. Cadogan, Mrs. C. Cadogan, Ethel Cadogan ##Mrs. Gough-Calthorpe, Rachel (Gough) Calthorpe, Misses Gough Calthorpe (2) ##Mrs. Candy ##G. H. Campbell, K. Campbell, Hugh Campbell, Mrs. H. Campbell, Mrs. Ronald Campbell, Misses Campbell (2), Mrs. J. B. Campbell, Mildred Campbell ##Mrs. Carington ##Mrs. Carpenter ##Emily Cathcart ##W. Cavendish, Mrs. W. Cavendish, Mrs. Cavendish ##Eleonora Chetwynd, Mrs. R. Chetwynd ##Mrs. A. Chichester, Hilda Chichester ##Mrs. Clowes ##T. H. Cochrane ##Audrey Coleridge ##George Colville ##Mrs. Corbett ##Mrs. H. Corry ##Caroline Courtenay ##Henry Coventry ##Osbert Craven ##Misses Cross ##Mrs. P. Crutchley ##Henry Cubitt, Mrs. Cubitt ##Hamilton Cuffe, Mrs. Otway Cuffe ##Lady Cunningham ##Montagu Curzon, Darea Curzon, Mrs. Curzon ##Hew Dalrymple ##John Dawnay, Eustace Dawnay, W. Dawnay, Mrs. Dawnay (2) ##Misses de Montmorency (2) ##Mrs. H. Dennison ##R. C. Devereux, Mrs. R. C. Devereux ##Mrs. Digby ##Conrad Dillon, Mrs. C. Dillon, Edith Dillon ##Misses Douglas-Pennant (2) ##A. Hay Drummond, Mrs. Hay Drummond, Frances Drummond, Mrs. M. Drummond ##Hubert V. Duncombe, Cecil Duncombe, Mrs. C. Duncombe ##C. T. Dundas, Mrs. C. T. Dundas, W. Dundas, Mrs. W. Dundas, Mrs. John Dundas ##Lady Du Cane ##Herbert Eaton, Mrs. H. Eaton ##F. Egerton, Mrs. A. F. Egerton, Lady Grey Egerton, Tatton Egerton, Mrs. T. Egerton ##Arthur Elliot, Mrs. Arthur Elliot, Lady Elliot, Mrs. Eliot ##Lilian Elphinstone ##Mrs. Ellis ##Muriel Erskine ##H. Escombe, Mrs. Escombe ##Mrs. Evans ##Mrs. C. Keith-Falconer ##Sir S. Ponsonby Fane ##Mrs. W. Farquhar ##Ailwyn Fellowes, Mrs. A. Fellowes ##Mrs. Ferguson of Pitfour ##Everard Fielding ##N. Fitzgerald, Mrs. N. Fitzgerald, Mrs. Fitzgerald, , Mrs. F. G. FitzGerald, Lady FitzGerald ##R. Fitzwilliam, W. H. Fitzwilliam ##Mary Forester ##Sir John Forrest ##Mrs. W. H. Forster ##Mrs. Lionel Fortescue ##Sir C. Fremantle, Mary Fremantle ##Sir Malcolm Fraser, Misses Fraser (2) ##Mrs. Charles Keith-Fraser ##Violet Gibson ##Evelyn Giffard ##Mrs. Henry Gladstone ##Lady Godley ##George Ormsby Gore ##F. Leveson-Gower ##Mrs. Gough ##Mrs. Alaric Grant ##Ronald Greville, Mrs. R. Greville, Louis Greville, Mrs. L. Greville, Sidney Greville, Mrs. A. Greville, Mrs. A. H. F. Greville ##Robert Grosvenor, Algernon Grosvenor, Mrs. A. Grosvenor, Maud Grosvenor, Elizabeth Grosvenor ##Lady Hamilton Gordon, [Hon. Lady] Nevil Gordon ##Misses Guest (2) ##Geoffrey Browne Guthrie ##Mrs. Gye ##Mrs. A. Haig ##Mrs. Halford ##, Misses Hamilton (2) ##Mrs. North Dalrymple-Hamilton ##Mrs. Hobart Hampden ##Mrs. Assheton Harbord, Mrs. C. Harbord, Judith Harbord, Bridget Harbord, Mrs. Harbord ##C. Hardinge, Mrs. C. Hardinge, A. Hardinge ##A. E. Gathorne-Hardy, Nina Gathorne-Hardy ##Misses Hawke (2) ##C. G. Hay ##Misses Heneage (2) ##Helen Henniker, Mrs. Henniker ##Robert Herbert, Sir Robert Herbert, Mrs. R. Herbert, Mrs. Herbert ##A. Holland Hibbert, Mrs. A. Holland Hibbert ##Lady Higginson ##Mrs. Hill ##Lionel Holland, Sydney Holland ##Grosvenor Hood, Dorothy Hood ##Lady Acland-Hood ##Fanny Hood of Avalon ##Mrs. Curzon Howe ##[Hon.] Evelyn Hubbard, Mrs. E. Hubbard, Alice Hubbard ##Mary Hughes ##Mrs. Meynell Ingram ##G. Jolliffe, Sydney H. Jolliffe, Mrs. Jolliffe ##Lady Johnston ##G. Keppel, Mrs. Keppel, Derek Keppel, Mrs. William Keppel ##Mrs. Alfred Ker ##Constance Kerr ##Mrs. Kingscote ##C. C. Kingston ##Lady Knollys ##Bertha Lambart ##F. W. Lambton, Mrs. Lambton ##Mary Lascelles ##Charles Laurence, Herbert Laurence ##Wilfrid Laurier ##Mrs. Lawley ##Mrs. C. Lawrence, Misses Lawrence (2), Mrs. H. Lawrence ##Mrs. Legge ##T. W. Legh, Mrs. Legh, Sybil Legh ##F. D. Leigh, Mrs. F. D. Leigh, E. Chandos Leigh, Mrs. E. C. Leigh, Cordelia Leigh ##C. Hanbury Lennox, Mrs. Hanbury Lennox ##G. W. Leslie ##R. l’Estrange ##Atholl Liddell, Mrs. A. Liddell ##Mrs. H. Gore-Lindsay ##Reginald Lister ##Henry Littleton, Misses Littleton (2) ##Misses Loch (2) ##William Lowther, Mrs. W. Lowther, L. Lowther, Mrs. L. Lowther ##Mrs. E. H. Loyd ##Mrs. Lumley ##Alfred Lyttelton, Mrs. A. Lyttelton, Misses Lyttelton (2), Mrs. Lyttelton ##Flora Macdonald, Lady Macdonald ##Mrs. Mackinnon ##Mrs. Maclagan ##Mrs. Magniac ##Mrs. Maguire ##W. Massey-Mainwaring, Mrs. Massey-Mainwaring ##Mrs. Fuller-Maitland ##Aline Majendie ##Misses Henniker Major (2) ##Mrs. Mallet ##Archibald Marjoribanks ##Misses Constable Maxwell (2) ##Mrs. M'Calmont ##Schomberg M'Donnell ##Charles Mills, Violet Mills, Mrs. Mills ##Mrs. Percy Mitford ##Maud de Moleyns ##Mrs. C. Molyneux ##Annette Monck, Mrs. Monck ##Violet Monckton ##Mrs. Monson ##John Scott Montagu ##[Hon.] Evelyn Moore ##R. Moreton, Mrs. R. Moreton ##Mrs. Mostyn, Misses Mostyn (2) ##Mrs. G. H. Murray, Alice Murray ##Lady Musgrave ##[Hon. Lady] Napier, Emilia Napier, Mrs. Scott Napier ##Mrs. Neeld ##Sir Hugh Nelson ##[Hon.] R. Nevill ##Mrs. Newdigate ##Sir H. S. Northcote ##Misses O'Brien (2) ##Mary O'Hagan ##Mrs. Okeover ##Mrs. Oliphant ##R. Terence O'Neill, Henrietta O'Neill ##Misses Palk (2) ##Cecil Parker, R. Parker, F. Parker, Mrs. F. Parker, Mrs. Parker ##Mabel Parnell ##[Hon.] C. B. Parsons, Mrs. Parsons ##Mrs. W. Paton ##[Hon.] Sydney Peel, Misses Peel (2) ##Mrs. Anderson Pelham ##E. S. Douglas-Pennant, Mrs. E. S. Douglas-Pennant ##Mrs. Heber Percy ##Albert Petre, Mrs. A. Petre ##Harriet Phipps ##Mrs. Pirie ##Thomas Playford ##Horace C. Plunkett ##[Hon.] Ashley Ponsonby, Mrs. Ponsonby, Misses Ponsonby (2) ##H. Orde Powlett, Mrs. Orde-Powlett, Myra Orde-Powlett ##E. W. B. Portman, Mrs. Portman, Mary Portman ##Mrs. Pretyman ##C. Ramsay, Mrs. C. Ramsay ##G. H. Reid ##Misses Rendel (2) ##Misses Rice (2) ##Lady White Ridley ##Mrs. Ritchie ##F. Roberts, Mrs. Phillips Roberts ##Misses Roberts (of Kandahar) (2) ##J. M. Rolls, Eleanor Rolls ##W. Rothschild, Evelina Rothschild ##W. Rowley, Mrs W. Rowley, Lady Thelluson Rowley ##A. Russell, Misses Russell (2) ##Gustavus Hamilton-Russell, Misses Hamilton Russell (2) ##the Master of Ruthven, Mrs. Ruthven ##Mrs. J. D. Ryder ##Sir Saul Samuel ##A. Saumarez, Mrs. A. Saumarez ##Mrs. E. J. Saunderson ##J. Maxwell Scott, Mrs. Maxwell Scott ##R. J. Seddon ##Mary Sidney ##Lady Simeon ##Misses Skeffington (2) ##Sir Donald Smith, Mrs. A. H. Smith, [Hon.] W. F. D. Smith ##Granville Somerset, Mrs. G. Somerset, Arthur Somerset, Mrs. A. Somerset, R. Somerset, Violet Somerset ##Mrs. C. R. Spencer ##Sir J. Gordon Sprigg ##Lyulph Stanley, F. C. Stanley, George Stanley, Mrs. E. J. Stanley, Mrs. Stanley, Mrs. V. A. Stanley, Maude Stanley ##Lady Cowell-Stepney ##Randolph Stewart, Mrs. R. Stewart, FitzRoy Stewart, Mrs. Stewart ##Mabel St. Aubyn ##Misses St. Clair (2) ##Mrs. Stirling ##Horatia Stopford ##[Hon. Lady] Alison Stourton ##Mrs. Strutt, Misses Strutt (2) ##Hilda Sugden ##Alfred Talbot, Mrs. Talbot, Mrs. R. A. J. Talbot ##Sir D. Tennant ##S. R. Thayer ##Misses Thellusson (2) ##Edward Thesiger, Mrs. E. Thesiger, Frederick Thesiger, Mrs. F. Thesiger, Mary Thesiger ##Lady Thorold ##Katharine Thring ##Misses Tollemache (2) ##R. Marsham-Townshend, Mrs. Marsham-Townshend ##Alice Hanbury-Tracy ##Charles Grey Trefusis, Misses Trefusis (2) ##Mrs. Trelawny ##Mrs Tremayne ##Mrs. W. le Poer Trench ##Charles Trevor ##George Hill-Trevor, Marcus Hill-Trevor, Mrs. Hill-Trevor, Misses Hill-Trevor (2) ##Mrs. C. W. Trotter ##Lady Tryon ##Rosamond Tufton ##Sir G. Turner ##Rev. L. Tyrwhitt ##Misses Tyssen Amherst (2) ##Misses Vereker (2) ##R. Greville-Verney, Mrs. R. G. Verney, Misses Verney (2) ##F. Villiers, Mrs. F. Villiers ##Misses Vivian (2) ##Arthur Walsh ##Mrs. P. E. Warburton ##Robert Ward, Mrs. Dudley-Ward ##Mrs. West ##Mrs. Whateley ##Sir W. Whiteway ##F. Bootle-Wilbraham ##Ella Williamson ##Tatton Willoughby ##Lady Wilson ##[Hon.] Armine Wodehouse, Mrs. Wodehouse ##Frances Wolseley ##F. Wood, Misses Wood (2) ##Mrs. G. Wrottesley, Evelyn Wrottesley ##Percy Wyndham, Mrs. P. Wyndham, Misses Wyndham (2) ##Maud Wynn ##Lois Yarde-Buller ##Alex. G. Yorke, Mrs. J. Yorke, Mrs. E. C. Yorke #Sirs<ref name=":1" /> (4, Col. 5c–6a) ##Augustus Adderley ##Edwin Arnold ##John Austin ##George Arthur ##John Heathcoat-Amory ##A. Armstrong ##Andrew Agnew ##Frederick Abel ##Henry Acland ##A. Arnold ##Alexander Arbuthnot ##John Barran ##G. Bower ##J. W. Bonser ##J. Crichton-Browne ##Joseph Bailey ##E. Ashmead-Bartlett ##Henry Barkly ##R. Beauchamp ##Raymond Burrell ##Charles Barrington ##David Baird ##Arthur Birch ##Edward Birkbeck ##W. Cunliffe Brooks ##A. de Capel Brooke ##Courtenay Boyle ##F. Burton ##F. Buxton ##Steuart Bayley ##John Bramston ##John Baker ##H. Bullard ##J. T. Brunner ##H. Bellingham ##Henry Bergne ##Thomas Boughey ##F. J. Bramwell ##E. Burne-Jones ##James Blyth ##Seymour Blane ##Henry Chamberlain ##Roderick Cameron ##Hugh Cholmeley ##John Conroy ##Edward Clarke ##C. Cameron ##E. Carbutt ##W. Coddington ##Marshal Clarke ##Reginald Cathcart ##Savile Crossley ##Edward Colebrooke ##Reginald Cust ##Charles Crosthwaite ##John Colomb ##Daniel Cooper ##F. Astley-Corbett ##Donald Currie ##Henry Cunningham ##Robert Cunliffe ##Henry Cotterell ##T. D. Gibson Carmichael ##F. Curden, ##George Dallas ##James Drummond ##Mortimer Durand ##G. Des Vieux ##Henry Dering ##J. N. Dick ##Dyce Duckworth ##T. Swinnerton Dyer ##E. Hastings Doyle ##John Dorington ##William Dunn ##Humphrey de Trafford ##Charles Dalrymple ##G. Dashwood ##Gardner ##Engleheart ##Francis Evans ##A. Edmonstone ##Whittaker Ellis ##W. H. Flower ##Horace Farquhar ##Joseph Fayrer ##H. Fletcher ##William Ffolkes ##William Fraser ##Bartle Frere ##Gerald Seymour Fitz-Gerald ##Robert Finlay ##B. Walter Foster ##Gerald FitzGerald ##R. FitzGerald ##Maurice FitzGerald ##Forrest Fulton ##William Flower ##Andrew Fairbairn ##John Gilbert ##E. T. Gourley ##Edward Grey ##W. Gull ##Walter Gilbey ##Lepel Griffin ##G. Macpherson-Grant ##Reginald Graham ##Philip Grey Egerton ##Douglas Galton ##R. Glyn ##Arthur Godley ##Charles Grant ##R. Gresley ##Alexander Acland-Hood ##T. G. Fermor Hesketh ##Arthur Haliburton ##Brydges Henniker ##F. Dixon-Hartland ##R. Hanson ##Alfred Hickman ##W. Houldsworth ##Henry Howorth ##F. Seager Hunt ##Charles Hall ##E. W. Hamilton ##Reginald Hardy ##Clement Hill ##Basil Hall ##Joseph Hooker ##Charles Hunter ##Charles Hartopp ##Victor Houlton ##Augustus Hemming ##Henry Irving ##Frederic Johnstone ##W. Jenner ##J. Jenkins ##James Joicey ##Charles Jessell ##Harry Johnston ##Edward Jenkinson ##James Hill Johnes ##John Jackson ##H. Seymour King ##James Kitson ##J. Lister-Kaye ##V. Kennett-Barrington ##George Kekewich ##John Leslie ##Thomas Dick Lander ##T. Villiers Lister ##James Linton ##Charles Lees ##Charles Legard ##Thomas Lea ##Wilfrid Lawson ##Elliott Lees ##A. C. Lyall ##J. T. D. Llewelyn ##Joseph Leese ##Leonard Lyell ##F. Laking ##Godfrey Lushington ##F. Lockwood ##Henry Longley ##George Lewis ##F. Milner ##Herbert Maxwell ##Francis Montefiore ##Graham Montgomery ##Robert Moncreiffe ##Musgrave ##Colin Scott Moncrieff ##Francis Mowatt ##Evan MacGregor ##J. G. Miller ##F. D. Maclean ##J. Blundell Maple ##Allan Mackenzie ##Lewis M'lver ##F. Mappin ##Theodore Martin ##Samuel Montagu ##William MacCormac ##Hubert Miller ##Lewis Morris ##Clements Markham ##A. C. Mackenzie ##John Monckton ##J. Stirling-Maxwell ##J. Heron Maxwell ##Kenneth Matheson ##J. S. Montefiore ##Acquin Martin ##W. Maxwell ##Oswald Moseley ##Arthur Nicolson ##Terence O'Brien ##Reginald Ogilvy ##Herbert Oakeley ##Hush Owen ##G. G. Petre ##Walter Parratt ##Frederick Pollock ##Herbert Perrott ##Douglas Powell ##Weetman Pearson ##Joseph Pease ##Francis S. Powell ##Reginald Palgrave ##W. Priestley ##E. G. Poynter ##G. S. Baden-Powell ##Charles Pontifex ##J. Dickson-Poynder ##James Paget ##C. M. Palmer ##C. Lennox Peel ##James B. Peile ##Westby Perceval ##Charles Pigott ##John Puleston ##W. Plowden ##Richard Quain ##George Russell ##C. Lister Ryan ##W. H. Russell ##J. Ramsay ##Owen Roberts ##R. T. Reid ##Charles Robinson ##J. Thellusson Rowley ##James Reid ##C. Euan-Smith ##J. Barrington Simeon ##J. B. Stone ##M. Shaw-Stewart ##Edward Sieveking ##T. H. Sanderson ##Augustus K. Stephenson ##Thomas Sutherland ##Mark Stewart ##Andrew Scoble ##Joseph Savory ##Douglas Straight ##Charles Shelley ##S. Shippard ##E. Sassoon ##A. Condie Stephen ##E. Sullivan ##Arthur Sullivan ##S. Scott ##H. Simpson ##E. Stafford ##Ernest Satow ##Tatton Sykes ##John Tyler ##Charles Tennant ##John Tenniel ##J. Thorold ##John Thursby ##Thomas Troubridge ##Charles Turner ##H. Meysey-Thompson ##W. Vincent ##Edgar Vincent ##Arthur Vicars ##W. Williams-Wynn ##James Walker ##R. Webster ##George Wombwell ##C. Rivers Wilson ##W. H. Wills ##Donald Mackenzie Wallace ##George Warrender ##F. Winnington ##James Whitehead ##Arthur Willshire ##Henry Wood ##Hugh Wyndham ##W. White ##Sidney Waterlow ##Hedworth Williamson ##Jacob Wilson ##W. Windeyer ##Albert Woods (Garter) ##Allen Young #Chairman of County Council (Dr. Collins) #Counts and Countesses ##Count Cassini ##Count and Countess De Ganay ##Count Gurowski ##Count Hohenau ##Count Theodor Bolesta Koziebrodski ##Count Leon Mniszeek ##Count and Countess Potocki ##Count and Countess Raben #Barons and Baronesses ##Baroness Emile Beaumont d'Erlanger ##Baroness De Brienen ##Baron De Onethau and Baroness D’Onethan [sic] ##Baron and Baroness Alphonse de Rothschild ##Baron Ferdinand Rothschild ##Baron and Baroness Schröder ##Baron and Baroness von Deichmann ##Baron von Heeckeren van Wassenaer ##Baroness von Hügel, Baroness Gertrud von Hügel [sic] ##Baron and Baroness Campbell von Laurentz ##Baroness Wilhelm von Rothschild #Rev. the Moderator of the General Assembly of the Church of Scotland #Deans — Christ Church, St. Paul's, Westminster, Windsor #The Provost of Eton #Master of Trinity (Mr. Butler) #The Sub-Dean of the Chapels Royal #Canons — Blundell, Dalton, Duckworth, Fleming, Hervey, Teignmouth Shore, Wilberforce #Dr. Adler (Chief Rabbi) #Dr. M'Cormick #Chaplain of the Fleet #Chaplain General #Reverend Doctors — Edmund Warre, C. J. Welldon #Reverends — Prebendary Hawkshaw, Albert Baillie, W. H. Bliss, M. Ebrington Bisset, Lord W. Cecil, Lord Charles Fitzroy, J. H. Ellison, H. Haweis, W. R. Jolly, G. J. Martin, Newton Mant, Marquis of Normanby, A. Robins. W. Gunion Rutherford, Clement Smith, Montagu Villiers #Doctors — Lennox Browne, J. V. Bridge, Barlow, Robert Farquharson, J. F. Fox, Surgeon-Major Kilkelly, John Lowe, C. H. H. Parry, G. V. Poore, Dorrien Smith, S. Wilks #Messieurs<ref name=":1" /> (4, Col. 6b–7a), Mesdames (4, Col. 7a–b) and Misses<ref name=":1" /> (4, Col. 7c – 5, Col. 1a) ##Mme Abdy ##Mr C. T. Dyke-Acland, Mme A. H. Dyke Acland, Mme Dyke Acland ##Mme Adair ##Misses Adam (2) ##Mr and Mme Adeane ##Misses Adye [?] (2) ##Mme Agar ##Mr Hamilton Aidé ##Mr John Aird, Misses Aird (2) ##Miss Akers-Douglas ##Mr Edward Alderson ##Mr George Alexander, Mme Alexander, Miss Alexander ##Miss Alison ##Mr and Mme Allhusen ##Mme Alma-Tadema ##Mr W. Ambrose ##Miss Heathcoat-Amory ##Mr R. Anderson, Miss Florence Anderson ##Mr E. H. Anson ##Mr H. T. Anstruther, Miss Rosomond Anstruther ##Mme Antrobus ##Mr Arbuthnot, Miss Arbuthnott [sic] ##Miss Archer-Houblon ##Mme Argles ##Mme Arkwright, Miss Arkwright ##Misses Armytage (2) ##Miss Arnott ##Mr and Mme Ascroft, Miss Ascroft ##Mr Arthur Ash ##Mr A. Asher ##Mme Ashton ##Mme Asquith ##Mr Astor, Mr W. Astor ##Mr B. F. Astley ##Mme Evelyn Atherley ##Mr and Mme Alfred Austin, Misses Austin (2) ##Mr and Mrs C. H. Babington ##Mr and Mrs Bagge ##Mrs Charles Bagot, Mrs J. F. Bagot, Miss Alice Bagot ##Mr James Bailey, Mrs J. Bailey, Mrs Bailey, Misses Bailey (2) ##Mrs Duncan Baillie, Misses Duncan Baillie (2) ##Mr Baillie of Dochfour ##Mr and Mrs W. A. Baillie-Hamilton ##Mr E. Bainbridge ##Mr and Mrs H. R. Baird, Mr and Mrs J. G. A. Baird, Misses Baird (2) ##Mr and Mrs Baldwin ##Mr and Mrs E. Balfour, Mr and Mrs Charles Balfour, Miss Balfour ##Mr and Mrs Banbury, Miss Banbury ##Mr and Mrs S. B. Bancroft [actor "Bancroft and his wife accepted with becoming grace the congratulations with which they were well-nigh overwhelmed"<ref name=":3" /> (5, Col. 6b)] ##Bandanaratke [?] ##Mrs Bankes ##Mr Banks ##Mr and Mrs Walter Baring, Miss Baring ##Miss Barker ##Mr J. Emmott Barlow, Mrs Barlow, Mrs Barlow [sic 2x] ##Misses Barnardiston (2) ##Miss Barne ##Mr and Mrs F. G. Barnes, Mr and Mrs Barnes, Misses Barnes (2) ##Miss Barran (2) ##Mr and Mrs J. Wolfe Barry, Mr and Mrs F. Tress Barry, Mrs A. Barry ##Misses Bartlett (2) ##Mr and Mrs D. P. Barton, Mr and Mrs Barton ##Mr Hamar Bass ##Mrs Bates, Miss Bates ##Mr and Mrs H. Bathurst, Misses Bathurst (2) ##Mr and Mrs Baxendale, Miss Baxendale ##Miss Mariot [?] Bayley ##Mr and Mrs W. W. Beach, Miss Beach ##Misses Hicks-Beach (2) ##Mr R. M. Beachcroft ##Mr and Mrs Wentworth Beaumont, Mr Wentworth B. Beaumont, Mrs Beaumont, Miss Hilda Beaumont ##Mr and Mrs Rupert Beckett, Mr E. W. Beckett ##Mr and Mrs Beer ##Mr and Mrs F. F. Begg ##Mr Charles Bell, Mr and Mrs Bell, Misses Bell (2) ##Miss Bellingham ##Mr and Mrs R. Benson, Mr and Mrs Benson ##Miss Berens ##Mr and Mrs Beresford, Miss Beresford ##Miss Berkeley, Misses Berkeley (2) ##Mr and Mrs Bertier, Miss Bertier ##Mr and Mrs Cosmo Bevan, Mr and Mrs F. Bevan, Miss Bevan ##Mr M. M. Bhownaggree ##Mr and Mrs F. Bibby ##Mr Leonard Biddulph, Mr Biddulph, Mr Victor Biddulph, Mr M. Biddulph, Mrs H. M. Biddulph, Misses Biddulph (2), Miss Biddulph, Miss Freda Biddulph ##Mr and Mrs Bigham ##Mr Bigwood ##Mrs C. Bill, Miss Bill ##Miss Birch ##Mrs Birch-Reynardson, Misses Birch-Reynardson (2) ##Mr A. Birrell, Mrs Birrell ##Mr and Mrs Bischoffsheim ##Mrs Ebrington Bissett ##Misses Blackwood (2) ##Mr and Mrs R. G. Blennerhassett ##Mrs W. H. Bliss ##Mrs Blundell, Miss Blundell ##Misses Blyth (2) ##Mr and Mrs Bolitho, Miss Bolitho ##Mr H. C. O. Bonsor, Mrs Bonsor, Miss Bonsor ##Mrs W. Borsel ##Mrs Griffith-Boscawen ##Mr and Mrs Boulnois ##Miss Bourke ##Mr W. R. Bousfield ##Mrs Bowden-Smith, Misses Bowden-Smith (2) ##Miss Bowen (2) ##Mr T. G. Bowles, Mrs Bowles ##Mr Edmund R. Boyle ##Miss Mabel Brackenbury ##Mrs Bradley, Miss Bradley ##Miss Beryl Bradford ##Miss Braddon ##Miss Bramwell ##Mr H. L. C. Brassey, Mrs H. A. Brassey, Misses Brassey (2), Misses Brassey (2) [sic 2x] ##Mr Stapleton Bretherton, Misses Stapleton Bretherton (2), Mr F. Stapleton Bretherton ##Mrs Bridge ##Mr G. Bridgman, Mr and Mrs C. G. O. Bridgeman ##Mr Brigg ##Mrs Brocklehurst ##Misses Brodie (2) ##Mr and Mrs Brookfield, Miss Brookfield ##Miss Bromley-Davenport ##Miss Brooke ##Miss Rhoda Broughton ##Mr and Mrs A. H. Brown, Miss Brown ##Mrs Browne, Misses Browne (2), Misses Browne (2) [sic 2x] ##Mrs Brownrigg, Miss Brownrigg ##Mr A. O. Bruce, Mrs A. C. Bruce [sic], Misses Bruce (2) ##Miss Brunner ##Mrs Bryce ##Mr Brymer ##Mr and Mrs Buchanan ##Mrs C. E. Buckle ##Mr Bucknill ##Miss Budgett ##Miss Mary Bulteel ##Miss Burdett ##Mr and Mrs Burges, Misses Burges (2) ##Mrs C. K. Burn ##Mr and Mrs F. C Burnand ##Miss Evelyne Burne ##Mr and Mrs W. Burns, Miss Burns ##Misses Burrell (2) ##Mr J. G. Butcher ##Mrs Butler, Mrs Butler, Miss Butler ##Mr Sydney Buxton, Mrs S. Buxton, Misses Buxton (2) ##Mr P. H. Calderon ##Mrs Calley ##Mrs Archibald Calvert, Miss Calvert ##Mr Cameron, Miss Cameron, Misses Cameron (2) ##Mr and Mrs J. D. Campbell, Mr J. A. Campbell, Miss J. A. Campbell, Mrs F. Campbell, Mrs W. Campbell, Mrs Hastings Campbell, Mrs W. Campbell [sic 2x], Mrs F. L. Campbell, Mrs D. B. O. Campbell, Miss Lilah Campbell, Miss Campbell, Miss Ronald Campbell, Misses Campbell (2) ##Miss Grace de Capell-Brooke ##Miss Carden ##Miss Carleton ##Mr and Mrs W. W. Carlile, Miss Carlisle ##Mrs Rivett Carnac ##Mrs Carnegy ##Mrs Boyd Carpenter, Misses Boyd Carpenter (2) ##Mrs Carson ##Mr and Mrs D'Oyly Carte ##Mrs Carter ##Mrs Castance ##Mr R. K. Causton, Mrs Causton, Miss Causton ##Mrs Cavaye ##Mr and Mrs C. Tyrall Cavendish, Mr Victor Cavendish, Mr Henry Cavendish, Mr Cavendish, Mrs Cavendish ##Mr and Mrs F. Cavendish-Bentinck, Mr Cavendish-Bentinck, Mrs W. G. Cavendish-Bentinck ##Mr F. Cawley ##Mr and Mrs Cayzer, Miss Cayzer ##Mr and Mrs W. M. Cazalet ##Mr F. Cazenove ##Mr Evelyn Cecil, Miss Cecil ##Mrs Chaine ##Mrs Chaloner ##Mr Austen Chamberlain, Mrs Chamberlain, Misses Chamberlain (2) ##Misses Chaning (2) ##Mr and Mrs Channing ##Mr and Mrs Cecil Chaplin, Misses Chaplin (2), Miss Edith Chaplin, Miss Chaplin ##Mrs Chapman ##Misses Chetwode (2) ##Mrs W. Chetwynd, Miss Chetwynd (2) ##Mr Childe-Pemberton ##Miss Chitty ##Miss Leila Crichton ##Miss Cholmeley (2) ##Miss Cholmondeley ##Miss Chrichton-Maitland ##Mrs H. Churchill ##Miss Spencer Churchill ##Mr J. D. Clark, Mr and Mrs Atkinson Clark, Mr Clark, Mrs B. F. Clark, Mrs G. D. Clark, Stanley Clark, Miss Clark ##Mr Purdon Clarke, Mr Ernest Clarke, Miss Clarke, Miss Stanley Clarke ##Mrs Clerk ##Mr and Mrs Henry Pelham Clinton ##Mrs Clive, Misses Clive (2) ##Mrs Close ##Mr Clough ##Mr Clowes, Misses Clowes (2) ##Mr Cobbold ##Mr T. B. Cochrane, Miss Cochrane ##Mr and Mrs W. A. Cockerell, Miss Cockerell, Miss Cockerell [sic 2x] ##Mr and Mrs D. Coghill ##Mr B. Cohen ##Mr Wentworth Cole ##Miss Colomb ##Mr and Mrs Colston ##Miss Colville ##Mr Richard Combe ##Miss Commerell, Miss Commerell [sic 2x] ##Mr and Mrs Compton ##Mr and Mrs Consett, Miss Vera Consett ##Mr and Mrs F. L. Cook, Mr Ward Cook, Miss Cook ##Mr and Mrs Kinloch Cooke, Mr Cooke, Mr and Mrs C. Kinloch Cooke ##Mr and Mrs Daniel Cooper, Mrs E. H. Cooper, Misses Cooper (2), Miss Cooper ##Mr and Mrs Cameron Corbett, Miss Corbett ##Mr and Mrs V. Seymour Corkran, Miss Corkran ##Mr and Mrs F. S. W. Cornwallis ##Mr and Mrs Cory ##Mrs Armar Corry, Mrs Clifford Corry, Miss Corry ##Mr J. R. G. Cotterell, Miss Cotterell (2) ##Mrs Stapleton Coton ##Mr and Mrs George Courroux ##Mrs Courtney ##Mr Burdett-Coutts ##Mrs Coventry ##Miss Cowell ##Miss Cowell-Stepney ##Mr and Mrs R. Cox, Mrs Cox, Miss Cox ##Mrs Crabbe, Misses Crabbe (2) ##Mrs Craik ##Mr and Mrs Crawshay ##Mrs Creignton, Miss Lucia Creighton ##Mr C. A. Cripps, Mr and Mrs Wilfrid Cripps ##Mr and Mrs Critchett ##Mr and Mrs Croombie ##Mrs A. B. Crosbie ##Mr and Mrs Shepherd Cross, Mr A. Cross, Miss Crosse ##Mr and Mrs Cruddas, Misses Cruddas (2) ##Mr and Mrs Percy Crutchley, Misses Crutchley (2) ##Miss Cuffe ##Miss Culme-Seymour ##Mrs Cuninghame ##Miss Cunliffe ##Mrs Dick-Cunynghame ##Mrs Curzon ##Misses Cust (2) ##Miss Custance ##Mrs Dalbiac ##Miss Gladys Dalgety [?] ##Mr C. B. Dalison ##Miss Dalrymple ##Mrs Dalton ##Mrs Denis Daly ##Mr and Mrs Darling ##Miss Dashwood ##Mr W. Bromley-Davenport ##Miss Davey ##Mr and Mrs Louis Davidson, Mrs Randall Davidson ##Mr W. Rees Davies, Mr Ben Davies, Mr and Mrs Vaughan Davies ##Mrs Davis ##Miss Dawnay (2) ##Mrs de Arcos ##Misses De Brienen (2) ##[Miss] La Baronne de Friesen ##Mrs R. C. de Grey Vyner ##[Miss] La Baronne Sirtema de Grovestins [?] ##Mr and Mrs J. de la Cour ##Mr and Mrs Edwin de Lisle ##Mr W. E. Denison ##Mrs Denny ##Miss De Perpigna ##Mrs de Salis ##Mr de Soria ##Mr De Trafford, Miss De Trafford ##Mr Deverell, Miss Deverell ##Mr and Mrs W. de Winton, Miss De Winton ##Mr and Mrs Gerard Dicconson ##Mr and Mrs Dicken ##Mr and Mrs C. S. Dickson, Mrs Dickson ##Mr J. K. Digby, Kenelm E. Digby, Mrs Digby, Misses Digby (2), Miss Digby ##Mr and Mrs J. Diggle ##Mr Lee Dillon, Misses Dillon (2) ##Mr and Mrs Coningsby Disraeli, Mr and Mrs R. Disraeli, Miss Disraeli ##Mrs Domvile, Miss Domvile ##Mr Greville Douglas, Mrs A. L. Douglas, Misses Douglas (2) ##Mrs Akers-Douglas ##Miss Dowell ##Mr and Mrs Doxford, Miss Doxford ##Mrs Geoffrey Drage ##Mr A. Drummond, Mr and Mrs G. Drummond, Mrs A. Hay Drummond, Mrs Lawrence Drummond, Mrs Drummond, Miss Edith Drummond, Misses Drummond (2), Miss Mary Drummond, Miss Adelizs [?] Drummond, Misses Drummond (2) [sic 2x] ##Misses Du Cane (2) ##Miss Du Chair ##Mr W. H. Dudley-Ward, Miss Sybil Dudley-Ward ##Mr F. Dugdale ##Misses Duncombe (2) ##Mrs Dundas, Miss May Dundas ##Miss Dunn ##Mrs Dunne, Miss Marion Dunne ##Mr Du Plat Taylor, Mrs G. Du Plat Taylor ##Mrs Durnford ##Mr and Mrs Thiselton Dyer ##Mrs East, Misses East (2) ##Mr F. Eaton ##Mr R. Edgcumb ##Mrs Edis, Misses Edis (2) ##Mr Bevan Edwards, Miss Bevan Edwards (2), Mr C. C. Edwards, Mrs Edwards ##Mrs Egerton, Miss Egerton (2), Miss Egerton ##Miss Grey Egerton ##Mr and Mrs M. Eliot, Misses Eliot (2) ##Miss Ellaby ##Mrs Ellicott, Miss Ellicott ##Mr and Mrs F. Elliot, Mr T. H. Elliott, Miss Gertrude Elliot ##Mr T. E. Ellis, Miss Ellis (2), Miss Evelyn Ellis ##Mrs Ellison, Miss Ellison ##Misses Elphinstone (2) ##Mr Cary-Elwes ##Mr Erskine, Miss Rachel Erskine ##Mr Maurice Euphrussi ##Mr W. H. Evans, Misses Evans (2) ##Mr H. P. Ewart, Mrs C. B. Ewart ##Mr Eyre ##Mr Cecil Fane, Mr G. H. Fane, Mr Fane ##Mr Dyafer Fakhry ##Misses Keith Falconer (2) ##Mrs Fane ##Mrs Fanshawe, Miss Fanshawe ##Mr and Mrs Fardell, Misses Fardell (2) ##Mr and Mrs Farmer, Mrs Lancelot Farmer, Miss Farmer ##Mrs Farnham ##Mr Alfred Farquhar, Mr W. Farquhar, Mr and Mrs E. Farquhar, Mrs G. M. Farquhar ##Mr J. N. Farquharson, Miss Amelia Farquharson, Miss Henrietta Farquharson ##Mr and Mrs Farquharson of Invercauld, Misses Farquharson of Invercauld (2) ##Misses Feilding (2) ##Mrs Fellowes ##Mrs Fenn ##Mrs Fenwick, Misses Fenwick (2) ##Mr and Mrs Johnson-Ferguson ##Mr Munro-Ferguson ##Misses Ferguson of Pitfour (2) ##Miss Fergusson ##Miss Dorothy Ffolkes ##Mrs Field ##Mr and Mrs Fielden, Misses Fielden (2) ##Mrs G. H. Finch, Mrs Wynne Finch, Misses Finch (2) ##Mr and Mrs Firbank ##Mr Herbert Fisher, Mr and Mrs Hayes Fisher, Misses Fisher (2) ##Mr and Mrs Fison, Miss Fison ##Miss FitzClarence (2) ##Mrs FitzGeorge, Miss Olga FitzGeorge ##Mr Fitzgerald, Mr F. G. Fitzgerald, Miss Fitz Gerald ##Mr and Mrs Almeric Fitzroy, Miss Ethel Fitz-Roy ##Mrs R. Fitzwilliam, Misses Fitzwilliam (2) ##Mr Flannery ##Mr E. Flower, Miss Flower, Miss Flower [sic 2x] ##Mrs Floyd ##Mrs H. Fludyer ##Mr H. St. George Foley ##Mrs Barrington Foote ##Mr J. S. Forbes, Mr Forbes ##Mr John Ford ##Mr H. W. Forster ##Mr and Mrs Arnold-Forster ##Mr and Mrs Bevill Fortescue ##Misses Forwood (2) ##Mr W. S. Foster, Mrs W. H. Foster, Mrs H. S. Foster, Miss Foster ##Misses Fowler (2) ##Mr Franklin ##Mrs Houston French ##Misses Frere (2) ##Mr L. Fry ##Mrs Fullerton, Misses Fullerton (2) ##Mr Gadson ##Mr Wilhelm Ganz ##Miss Gardiner, Miss Gardiner [sic 2x] ##Mrs Gardner ##Mr and Mrs Garfit [?] ##Miss Gathorne-Hardy ##Mr Hamilton Gatliff ##Mr and Mrs Scott Gatty ##Mr and Mrs Sydney Gedge ##Mr Geoffrey Drage [sic; does this belong here?] ##Mr F. W. Gibbs, Misses Gibbs (2) ##Mr and Mrs Walter Gibson ##Miss Gilbey ##Mr and Mrs Tyrell Giles ##Mr W. Gillett ##Mr and Mrs Gilliat, Misses Gilliat (2) ##Mr Henry Gladstone, Mrs Gladstone ##Mr Goelet ##Mr Charles Gold ##Mr G. P. Goldney ##Mr S. Hoffnung Goldnung Goldsmid ##Mr Otto Goldsmidt ##Mr John Gordon, J. E. Gordon ##Mr Frank Gore, V. Gore, S. W. Gore ##Mr Goschen ##Mr A. Gosling ##Mr F. R. Gosset ##Mr E. A. Goulding ##Mr G. Leveson-Gower ##, Henry Graves, George Grossmith ("George Grossmith was not a little lionised by titled ladies"<ref name=":3">“The Queen’s Garden Party. Buckingham Palace Grounds. A Brilliant Scene. The Queen’s Cup of Tea.” ''Daily News'' (London) 29 June 1897, Tuesday: 5 [of 10], Col. 6a [of 7] – 6, Col. 2a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970629/021/0005. Print pp. 5–6.</ref> (5, Col. 6b)), Howard of Greystoke, , , , Gye, Grifflth-Boscawen, , , , , F. Graham, , W. H. Kendal Grimston, , , , , , , , Graham, H. R. Graham, Ernest Gray, Montagu Guest, , H. D. Greene, W. R. Greene, J. A. Gretton, , W. H. Grenfell, , , , , Gurdon, , , , C. C. Graham, , A. C. Humphreys-Owen, G. M. Hutton, Heseltine, Claude Hay, Halford, E. Hope, Philip Henriques, C. D. Hohler, Hornyold, Carl Haag, Hardcastle, Hanbury, L. V. Harcourt, R. K. Hodgson, Adrian Hope, Beresford-Hope, J. Hozier, E. S. Howard, Horner, Maurice Holzman, A. C. Howard, Cozens-Hardy, Thomas Halsey, Hardy, James Hope, R. Hallett Holt, T. Hare, Hatch, R. B. Haldane, C. Harrison, J. Henniker Heaton, Hermon-Hodge, E. Brodie Hoare, G. Hoare, H. Hobhouse, VV. H. Hornby, R. P. Houston, G. B. Hudson, John Hutton, A. E. Hutton, Lewis Hall, Augustus Hare, George Harwood, G. T. Hertslet, Hartmann, H. Higgins, Hughes, Francis Hamilton, John Hare, Hungerford, Joseph Howard, Hope, R. R. Holmes, H. Howard, Haggard, Cecil Higgins, J. C. Horsley, The Munshi Abdul Hafiz Karim, Wootton Isaacson, E. R. Jenkins, Arthur James, Jacobs, Jebb, A. F. Jeffreys, J. H. Johnstone, Brynmor-Jones, H. C. Jervoise, W. James, Atherley-Jones, Philip Burne Jones, Henry Joslin, George Kemp, Nigel Kingscote, C. Kempe, W. Kenny, A. Kennard, J. Kenyon, Kearley, King King, Lees Knowles, Knowles, Kimber, Kuhe, T. Kingscote, Landon, Reginald Lucas, Letchworth, Lyon, Henry Gore Lindsay, E. H. Loyd, Leonard Lindsey, Drury Lowe, Fairfax Lucy, E. Law, Cecil Lister-Kaye, H. B. Lindsay, H. T. Lopes, J. Grant Lawson, H. Lubbock, W. A. Lindsay, A. K. Loyd, Lecky, W. F. Laurence, Edwin Laurence, J. W. Lowther, Luttrell, Loder, S. Leighton, W. C. F. Luttrell, E. Lloyd, Heathcote Long, L’Estrange, T. C. March, C. J. Murray, Mount, Morrell, R. J. More, Moon, E. P. Monckton, Monk, F. Bingham Mildmay, Beresford Melville, M’Laren, M'Ewan, Martin, H. H. Marks, lan Z. Malcolm, H. L. B. MCalmont, J. W. Maclure, Campbell Munro, J. Maclean, J. C. Macdona, W. G. E. Macartney, Muir Mackenzie, Hugh Morrison, G. H. Murray, P. C. Milbank, Bingham Mildmay, Alpin Macgregor, M. Myther, V. Montagu, Frederick Macmillan, C. M’Neill, Arundel St. John Mildmay, C. Maud, Fuller Maitland, A. Milman, W. A M’Arthur, Marjoribanks, W. H. Myers, F. W. Maude, Muntz, Charles Morley, Murdoch, A. B. F. Mitford, B. Mallet, Mure, Madden, W. J. Mure, R. Maguire, Mackinnon, Montgomerie, Maxwell-Lyte, Mason, Ronald Moncrieffe, Milvain, T. G. Menzies, G. Manners, Nicol, F. A. Newdigate, G. Noel, T. W. Nussey, Charles Orde, R. A. Oswald, M. Oldroyd, J. C. O'Dowd, Oswald, Oppenheim, Arthur Oliphant, C. L. Orr-Ewing, J. L. Pattison, J. Balfour Paul, Paton, A. Peckover, Archibald Peel, Perks, J. Pender, J. Penn, Price, Powell, Paoli, Constantine Phipps[,] Charles Phipps, Leslie Probyn, B. Faudel-Phillips, Wilton Phipps, L. Faudel-Phillips, Joseph Pease, Pollock, Arthur Pease, Roland Protheroe, Walter Peace, J. M. Paulton, Platt-Higgins, Pennefather, Provand, Guy Pym , A. E. Pease, Godfrey Pearse, Algernon Peel, A. V. Pryor, Montagu Price, Phelips, John Ponsonby, Hussey Packe, Wyndham Portal, Henry Petre, Lort Phillips, H. W. Primrose, E. Parkes, Herbert Praed, Heber Percy, Quilter, J. Rankin, Renshaw, J. A. Rentoul, H. C. Richards, Read, T. Richardson, A. T. Phillips Roberts, Hugo von Ruffer, Alexander Ramsay, Alderman and Sheriff Ritchie, Richardson, Rebow, G. L. Ryder, G. A. Redford, G. W. E. Russell, H. J. H. Russell, Pandeli Ralli, John Rutherford, J. Rennell Rodd, Leopold Rothschild, T. W. RusseII, Forbes Robertson, Alfred Rothschild, Brooke Robinson, Edmund Robertson, Repton, James Round, Royds, Henry Raikes, Bowen Rowlands, J. D. Ryder, Sheriff Hargreaves Rogers, Skeffington Smyth, Augustus Spalding, H. H. Shaw, E. Strachey, J. Murray Scott, J. Stern, P. L. Sclater, R. Sassoon, W. Sidebottom, Abel Smith, Louis Sinclair, C. H. Seely, Lucas Shadwell, W. E. T. Sharpe, C. E. Shaw, E. B. Sparke, T. H. Sidebottom, Steward, Stibbert, H. Somerset, H. S. Samuel, J. P. Smith, Horace Seymour, A. H. Smith, H. M. Stanley, J. A. Swettenham, A. Spicer, Stevenson, J. H. Stock, J. Sturgis, H. C. Smith, C. J. Stewart, Leslie Stephen, T. Smith, Senhouse, Eames Storey, Christopher Sykes, H. Seton-Karr, Philip Somers-Cocks, T. Skewes-Cox, Shelley-Bontein, Salting, Leo Schuster, Smith, Arthur Sassoon, G. D. Smith, Shaw, Michael Shaw-Stewart, E. J. Stanley, Albert Sandeman, Scaramanga, Sant, F. Sutton, Dudley Smith, C. E. Tritton. W. E. M. Tomlinson, H. F. Tollemache, A. M. Torrance, Tarleton, Edward Tighe, Alma-Tadema, W. H. Wilson-Todd, P. Thornton, F. Taylor, Beerbohm Tree, Dan Tupper, Montagu Tharp, Abel Thomas, Algernon Turnor, Tudway, C. W. Trotter, H. J. Tennant, J. C. Thynne, H. D. Trelawny, C. E. Thynne, F. J. Thynne, Montagu Thorold, Tremayne, H. Graham Toler, John Taylor, A. J. R. Trendell, Tosti, Christopher Tower, T. Usher, A. Ure, T. Usborne, Chas van Raalte, Graham Vivian, R. C. de Grey Vyner, Hope Vere, F. E. Villiers, Von André, Venning, L. Van Loon, Van De Weyer, Val Prinsep, Walter, Thomas Wayman, Hwfa Williams, Cornwallis West, R. G. Webster, Sackville West, Wanklyn, A. S. Wiison, G. Fleetwood Wilson, A. F. Warr, F. W. Wilson, Piers Egerton Warburton, S. Wombwell, Weigall, Powell Williams, John Welby, Wingfleld, Whitbread, J. W. Wilson, Walton, D’Arcy Wyvill, Wodehouse, Wylie, A. Wilson, John Wilson, C. H. Wilson, Herbert Whiteley, Wynne, Lee Warner, W. West, G. Whiteley, Spencer Walpole, H. C. Woods, M.D., Deputy Inspector-General, Charles Wyndham, J. Humphrey Ward, F. Walker, Whateley, W. Woodall, Wyndham, Godfrey Webb, J. Welby, Charles Waldstein, H. Yorke and Yerburgh #Mesdames<ref name=":1" /> (4, Col. 7a–b) — Godson, S. Hoffmung Goldsmid, A Goldsmid, Goldsworthy, Goodden, Goodenough, John Gordon, Gordon, J. E. Gordon, G. G. Gordon, S. Gordon, Gordon, S. W. Gore, F. Gore, F. R. Gosset, , , , , , , , , , , , , , , , , , , , , , , , , Gregory, C. C. Graham, Guy-Pym, Henry Graves, , Kendal Grimston, Gunter, W. H. Grenfell, H. Grenfell, Gurney, Grant, Goelet, Gye, , Gore, Green, Goschen, A. Gosling, Hargreaves-Rogers, Staveley Hill, Hanbury. James Hope, Claude Hay, Heneage, Heseltine, E. Hope, Arthur Heath, Philip Henriques, C. D. Hohler, Hornyold, Carl Haag, Marcus Hare, Harford, Hardcastle, Holmes, Beresford Hope, Adrian Hope, Hanbury, Horner, Hammet, Hall, A. C. Howard, Halsey, Hardy, Heath, Hermon Hodge, Brodie Hoare, S. Hoare, H. Hobhouse, W. H. Hornby, G B. Hudson, Platt-Higgins, Hildyard, Lewis Hall, G. M. Hutton, G. Hutton, W. G. G. Hutchinson, Haweis, Hartmann, Higgins, John Hare, Hungerford, Humphreys-Owen, R. W. Hamilton, Hills, Hippisley, Herbert, Hatton, Henderson, Haggard, Hervey, J. Howard, H. Howard, Ian Hamilton, Gathorne-Hardy, Howard, Marcus Hare, Inglefield, Wootton Isaacson, Joicey, Jenkinson, Inigo Jones, Jackson, A. James, Cotton-Jodrell, Jacoby, Jebb, A. F. Jeffreys, Jessel, Brynmor Jones, Pryce Jones, J. E. Jameson, H. C. Jervoise, W. James, Atherley Jones, G. Johnstone, J. H. Johnstone, A. Kennard, Kearley, Kimber, Hegan Kennard, Kitching, Kennion [?], Kennison, Knowles, W. Kenny, Kennedy, Keeley, Kuhe, Kingston, Kilkelly, Colin Keppel, Hanning Lee, A. K. Loyd, Lyon, Long, Lane, Lucas, Lockwood, S. Leighton, Lecky, E. Lawrence, Lawrie, Luck, Lloyd. A. P. Lake, J. W. Lowther, Lowe, Lidderdale, Liddell, Lascelles, Luttrell, H. Lubbock, Leslie, Lucas-Shadwell, Laurier, Naylor Leyland, Langenbach, E. Law, Fairfax Lucy, Lockhart, Lewis, Maxwell-Lyte, F. A. Lucas, G. Manners, Beresford Melville, Morrell, Victor Milward, Marshall, Maclure, J. Maclean, M'Laren, M'Ewan, R. B. Martin, Marks, Markham, J. M'Calmont, F. W. Maude, Napier Miles, M’Neill, Max Muller, Meeking, Manvers Moorson, Arundel St. John Mildmay, Frederick Macmillan, Mount, Muntz, Murdoch, Wyndham Murray, W. J. Mure, Graham Murray, Montefiore, W. C. F. Molyneux, Newton Mant, Millett, Malet, Ashurst Morris, May, Maurice, Milvain, Marjoribanks, J. C. Macdona, Moorhouse, Muir Mackenzie, G. Moncrieff, J. Murray, Montgomery, Milbank, Bingham Mildmay, Mellor, C. Maude, T. G. Menzies, J. M'Donald, W. A. M'Arthur, M'Neile, M'N'eill, Campbell Munro, Mostyn, A. Milman, Majoribanks, Noel, H. F. Nicholson, F. Neville, Nicol, Nevul [?], Nugent, Newhouse, Oppenheim, M. Oldroyd, Charles Orde, H. H. Oldham, R. A. Oswald, Oswald. A. Oliphant, Oakley, J. L Pattison, Price, Perowne, Perks, Constantine Phipps, Peacocke [?], R. Prothero, Powell, Leslie Probyn, Pitman, Upton Prior, Lort Phillips, Primrose, Powlett, Pakenham, Peyton, Parkes, Wyndham Portal, Pipon, Pender, Phillpotts, Pollock, Montagu Price, Phellps, John Ponsonby, Fox Pitt, A. Peel, Aldrich Pelham, J. Pease, Poe, G. Pearse, A. Paget, A. Pease. N. G. Philips, Pirie [?], Dampier Palmer, F. Post, Pakenham, Paget, H. Parr, Wilton[?]-Phipps, Quilter, Rebow, J. C. Russell, Rolfe, Rutherford, I[?]. Richardson. James Ronand, Robins, Rennell Rodd, W. W. Russon[?], Alexander Ramsay, Robinson, J. Rennell Rodd, Redford, Harcourt Rose, Royds, H. Raikes, Carl Rosa, Ronalds, Arrnold Royle [? Royce?], Rice, Leopold Rothschild, Raikes, J. Rankin, Renshaw, F. Russell, Ricardo, Riddel, Robertson, G. Royle, Teignmouth [?] Shore, Sandeman, Stopford, Graham Smith, Salting, Brinsley Sheridan, Salmon [?], Salmond, Edgar Shephard, Sant. A. Sandeman, H. Seymour, H. S. Samuel, St. Clair, AbeI Smith, J. P. Smith, H. M. Stanley, A. Spicer, Stevenson, Swaine, Sullivan, J. H. Stock. E. B. Sparke, J. Sturgis, Louis Sinclair, H. Seton-Karr, Slade, J. Stern, Skefflngton Smyth, P. L. Slater, A. C. Stewart, R. Sassoon, C. Smith, E. Strachey, Napier Sturt, Steward, Eames Storey, Starkie, Senhouse, Bridgman Simpson, Seddon, T. Smith, Leslie Stephen, Settle, Scaramanga [?], Arthur Sassoon, L. Seymour, Shaw. R. F. Synge, T. Skewes-Cox, Stevenson, H. C. Smith, Sterling, T. H. Sidebottom, C. H. Seely, Shelley-Bontem [?], Sandford, Hawley Smart, Sergison [?], Frederick Slade, Scobell, Graves Sawle, Scott, Settle, Smith-Barry, Stewart, J. A. Swettenham, Surtees, Synge, Dudley Smith, Thomson, M. Thorold, H. Graham Toler [?], J. W. Taylor, Christopher Tower, Tosti, Temple, Beerbohm Tree, Dan Tupper, R. T. Thynne, Montagu Tharp, Trotter, Anstruther Thomson, Tupper, Taylor, C. E. Tritton, C. F. Anstruther Thomson, Edward Tighe, F. Taylor, Tillard, Tillbrook, Brook Taylor, Tudway, C. E. Thynne, J. C. Thynne, H. Thomas, Thwaites, Tarleton, A. Ure, Usher, R. Vivian, Val Prinsep, Edmund Vaughan, E. Villiers, C. van Raalte, Von André, Verschoyle, F. E. Villiers, Vance, Hope Vere, Villiers, Venning, Sackviile West, Whatman, Williams Wynn, Watson, Wharton, John Wilson, Williams, Stuart Wortley, Wood, C. H. Wilson, S. J. Way, Walton, H. Whiteley, G. Whiteley, Ellis Williams, Wilson, Weywan, E. F. Wodehouse, John Welby, Wray, Wickham, Whatley, Spencer Walpole, Hwfa Williams. J. Woodford, Charles Wyndham, Wingfield, Charles Wood, Lee Warner, Warre, Humphrey Ward, Wallis, Wilberforce, Wynne, J. Welby, Eardley Wilmot, A. S. Wilson, C. [?] E. Ward, Walter, Warner, R. G. Webster, Wells, Cornwallis-West, F. Charteris Wemyss, Yerburgh #Misses<ref name=":1" /> (4, Col. 7c – 5, Col. 1a) — , , , , , , , , , , , , , , , , , , , , , , , , , , , Gold, Graves, Gregory, Gough-Calthorpe (2), Helen Gladstone, Goschen (2), Glyn, Godley (2), Gunter (2), Maud Grenfell, Hamilton Gordon, Gurrney Goodden, Goldsmid, Grant, Victona Grant-Duff, Goelet, Gosling, Gore, Gordon (2), Hood (2), Heneage, M. Carew Hunt, Hare (2), Hay  (2), Hickman, Adrian Hope (2), Hare (2), Agnes Beresford Hope, Carl Haag, Hardcastle (2), Heseltine, Hare, Hope, Heron Maxwell (2), Halford (2), Hamilton (2), Hamilton, Howard (2), Hardy (2), Hay (2), Herbert Margaret Acland Hood, Mary Hope, Hill, Hemming (2), Jean Hotham, Hall, Harrison, Gladys Higginson, (Brydges) Henniker, Halsey (2), V. Hanson, (Stock) Hill (2), (Brodie) Hoare (2), Hoare (2), Houldsworth (2), Haig, Hart, Hervey, (Lewis) Hall, Harwood (2), Hutchinson, Hughes (2), Hooker, Hart-Dyke (2), Hervey-Bathurst (2), Louisa Heathcote, Howard, Dora Hanbury, Howard (2), Hornby (2), Satyendra Bala Tagore, Grace Jackson, Jolliffe (2), Helena James, Jenner, Joicey, Cotton-Jodrell, Jenkins (2), Johnstone, Jameson (2), Jessel, Jervoise, S. L. Johnstone, Keith-Falconer (2), Ker (2), Ethel Kenny, Kennedy, Kennard, King King, Kennard (2), Kitson (2), Kerr (2), Kimber, Kennaway (2), Nona Kerr, Keppel, Kemball, C. Lees, Lyson, Gore Lindsay, Linton (2), Lindley (2), Lubbock, Aline Lambton, Lambart (2), Liddell, Alice Loch, Lindsay, Lucas-Shadwell, Hanning Lee (2), Emily Loch, Larking, Leese, Llewelyn, Leighton (2), Lawrence (2), Lopes (2), J. Lawson, Laurie (2), Lyte (2), Lloyd (2), Lyall, Luttrell, Lockwood, Lister, Lidderdale (2), Violet Leigh, Liddell (2), Drury Lowe, Lewis (2), Loftus, Lindsay, Lyell (2), Aimee Lowther, l’Estrange, Graham Murray, Mellor (2), Milward, Monk (2), Maxwell (2), Massey-Mainwaring, Mackworth (2), Markham (2), Macdonald, More-Molyneux, Cicely Monson, Maclure, Lena Milman, Morris (2), Macnaghten, Mowatt (2), Margaret Muir MacKenzie, Murray, Mundella, Mowbray, Ethel Morris, Beatrice Mildmay, May Milbank, Evelyn Moreton, Magniac (2), Mackenzie, M'Clintock, Madden, MacGregor(2) Mount (2), Muntz, Murdoch, Mitford, Montagu (2), Mure, Menzies, Macpherson-Grant, Malet, Moseley (2), Meeking, Macgregor, Mary Moore, Montgomery, St. John Mildmay, Madden (2), Milman (2), Constance Maude, Martyn, Campbell Munro, Nevill (2),Noel (2), Nevill, Nicol, Neville, Nelson (2). Olpherts [?] (2), Oakley, Ogilvy, Humphreys Owen, V. A. Okeover, O’Brien (2), Linda Oppenheim, Phoebe Otway, Alina O'Shee, Anderson Pelham, Pole, Pereira, Peyton, Pattison, Orde Powlett, Powlett, Pelly (2), Perowne, Charlotte Probyn, Julia Ponsonby, Peekover, Peel (2), Penn, Peace, Baden Powell, Powell (2), Pease, Priestley, Palgrave, Post, Parker, Pease, Palmer, Packe (2), Alice Paget, Paget, Paget of Cranmore (2), [?] Phillips, Phipps, Cecilia Peel, Chandos Pole, Pollock Phellps, Parry, Ponsonby, Wilton Phipps, Quain, Quilter (2), Russell of Killowen(2), Ritchie (2), Robins, Sibyl Robertson, Round (2), Royds (2), Russell, Rebow, Jane Ryan, Ramsay, Ricardo (2), Rigby, Russell (2), Lucy Raikes, Rankin, Frances Rod, Beatrix Rice, Russell (2), K. Reiss, Ricardo, Smith, Stafford, Stevenson, Stopford (2), M. Seymour, Kay Shuttleworth [?] (2), Seymour (2), Shaw, Shaw-Stewart, Evelyn Starling[?], Maxwell Scott, Abel Smith, Sartorius (2), Maud S[?]hey, Stewart, Magaret Stanley, Dorrien Smith, Smith (2), [?]-Smith, Saurin, Salmond (2), Sandeman (2), Sant, Dudley Smith[?], Swaine, Stephenson (2), Stewart (2), Dora Stone, Sparkes, [Stanley?], Nita Houston Stewart, Lily Severn, Evelyn Stanley, [Sheppart?], Saumarez Smith, Truda Saunderson, Swinburne, [Sullivan?], Mabel Seymour, Shute, R. Sterling, Stern (2), Sar[?] (2), Sassoon (2), P. L. Sclater, Sparke, Smith (Clement), [Sanderson?], Hilda Stewart, Seddon (2), Shelley, Sprigg (2), [?] Stephen, Ruby Spencer Churchill, Rachel Smith, [?], Tremayne (2), Ellen Terry, Ethel Thomas, Muriel [?], Taylor, Mary Talbot, Tomlinson, G. le M. Tupper, [?], Ella Taylor, Thorold, Taylor (2), E. Tuson, Trelawny [?], Adela[?] Trefusis, Rachel Thynne, Tritton (2), Thomson (2), [?], Thesiger, Thynne, I. C. (2), Thynne (2), Thornton (2), [Temple?], Turner, Talbot, Thynne, Usher, Van de Weyer (2), [Vivian?] (2), Dorothy Villiers, Freda Villiers, Verschoyle, Van [der Byl?], Villiers, Venning, Hilda von Deichmann, Wood[ford?], Fleetwood Wilson, Eardley-Wilmot, Maud Walpole, [?hend?] Wilson, Wilson, Wilberforce, Warren (2), [W?vil?] (2), Wills (2), Warrender (2), Walrond (2), Wynd[ham?] (2), Webster (2), Watson, Wombwell, Whitehead (2), [W?Ieyer?] (2), Evelyn Wellesley, Cornwallis West, Whatman {2), [?] (2), Rachel Weigall, F. Walker, Smart Walker, Wood (2), de la Wood[?], Ward, Wilbraham, Wilberforce (2), Walker, Williams, [Workham?] (2), Yeatman #Admirals of the Fleet [initial large caps, rest sm caps] — Earl of Clanwilliam, Lord John [Hay?], the Hon. Sir H. Keppel #Admirals — H. G. Andoe, C. E. Buckle, Sir F. Bedford, Britten, the Hon. W. Carpenter, H. F. Cleveland, Sir H. Chads, Close, [?], Carr, E. J. Church, Sir W. Dowell, R. G. Douglas, A. L. [?], C. E. Domvile, A. T. Dale, D’Eyncourt, Field, Sir A. [Farquhar?], Fitzgerald, Fellowes, Fanshawe, Sir H. Fairfax, Sir [?] Fisher, C. J. Fane, Fullerton, the Hon. Sir E. Fremantle, [?] FitzGeorge, Woods Pasha, Sir W. Hunt-Grubbe, Sir Anthony [?] Hoskin, Lord Hood of Avalon, Sir Leopold Heath, Sir [?] [F.?] Hotham, Sir Algernon Heneage, R. H. Hamond, the Right Hon. Sir [J.?] Hay, St. G. C. D’Arcy Irvine, Jones, Kennedy, Sir A. [?s], A. P. Lake, R. M. Lloyd, Sir L. Loraine, A. H. Markham, [Sir?] R. More-Molyneux, Sir F. L. M'Clintock, Sir R. Macdonald, [the?] Hon. V. Montagu, Nicholson, Noel, Marquis of Northampton, Sir E. Ommaney [?], Sir Augustus Phillimore, A. T. Powlett, [?], [?. ?.] Rowley, Sir F. Richards, Lord Charles Scott, [? St.? John?], W. H. C. St. Clair, Bowden Smith, Sulivan, E. H. Sey[mour?], H. Stephenson, Sir Nowell Salmon, Sir W. Houston [Stewart?], Sir M. [Cuhne?]-Seymour, E. W. Turnour, E. W. Van[?] Wharton, Sir G. Willes, the Hon. W. J. Ward #Captain, R.N. — W. A. D. Acland, C. J. Barlow, F. R. Board[?], H. Bainbridge, Hon. T. Brand, Bickford, Lord Charles [B?ford?], B. F. Clark, Colville, Carter, Hon. S. Cecil Colville, [?ford?], A. G. Douglas, Sir C. Domville, Hon. A. Hay Dru[?], [?] [W.?] [?] Gordon, Hammet, Hon. Curzon Howe, Hender[?], [?] Ingles, Jellicoe, Jephson, Johnstone, Jeffreys, H. C. [?], Hon. A. Littleton, Hon. Hedworth Lambton, Moore, May, [? Net?], Poe, Pipon [?], Aldrich Pelham, Alfred Paget, [Bi.idcl?], Rolleston, John Sinclair, Bridgeman Simpson, [?], Van Koughnet [?], Burges Watson, Eardley-Wilmot, [?ham, Winsloe, Hon. J. Yorke #[Lieutenants???] — Anson, G. R. Bethell, Blair, Bayley, Cave[?], [?] Cave,Hon. Cecil Cadogan, de Salis, Fraser, Floyd, Hon. [?] [F?], Alaric Grant, Morgan, Moore, Marescaux, [?] Stuart, Tupper, Wells, Williams, G. J. S. Warrender #[Lieutenants?] R.N. — Alton, Murray Aynsley, Boyle, Bather, [?], [R. F.?] Boyle, Chaytor, Sir Charles Cust, G. W. Davy, [?] Wyndham-Fiennes, Fair, Godfrey Faussett, Garforth, [L?]ord Clifford, Hopkinson, Henderson, Keyes, Keppel, [?] Lloyd, Majendie, Mitchell, Morant, Kerr-Pearse, [?] Richmond, Rae, Stewart, Hon. Victor Stanley, [?] [Calta?]-Seymoar, Trye, Thring, Hon. Cyril Ward, W[?], R. E. Wemyss, Woolcombe #[Captain?] Trinity House, Sir J. Sydney Webbe #[Field?] Marshall — Sir F. P. Haines, Sir Lintorn Simmons, Sir [?] Stewart, Lord Roberts of Kandahar, Viscount Wolseley #[Generals?] —Sir J. Ardagh, Sir A. Alison, Sir H. J. Alderson, [?n] Annesley, J. Alleyne, Sir J. M. Adye, Sir C. G. [Arbuth?]not, Sir H. Havelock-Allan, R. Bateson, Sir W. F. [B?er, Sir H. Brackenbury, H. M. Bengough, the Right Hon. [?] Buller, Sir Owen Tador-Burne, H. J. Buchanan, Sir C. H. [Brown?low], Sir S. Browne, Sir M. Biddulph, Viscount Bridport, [?. O.?] Barnard, E. F. Chapman, Lord Clarina, C. F. Clery, the Hon. S. Gough-Calthorpe, E. H. Clive, Godfrey Clerk, Lord [Ch?]sford, the Hon. Sir Andrew Clarke, Sir E. Du Cane, Crutchley [?], Lord de Ros, Sir John Donelly, J. H. Dunne, Sir Martin Dillon, Sir Collingwood Dickson, Sir H. de Bathe, Davis, Sir F. de Winton, Sir T. Dennehy, Sir H. Ewart, Sir J. B. Edwards, C. B. Ewart, Cecil East, Arthur French, Sir T. Fitz-Wygram, the Hon. Sir P. Feilding, Sir T. E. Gallwey, Sir T. Goldsmid, Sir R. Gipps, Sir R. Grant, Sir F. W. Grenfell, Coleridge Grove, Goldsworthy, J. J. H. Gordon, Sir E. A. Holdich, Sir E. W. Higginson, Sir R. J. Hay, Sir R. Harrison, Julian Hall, Earl Howe, the Hon. W. Home, J. Jameson, Sir Arnold Kemball, Kelly-Kenay, Lord Mark Kerr, F. T. Lloyd, Sir D. Lysons, Sir Drury Lowe, G. Luck, J. W. Laurie, F. Marshall, the Hon. R. Monck, Crichton Maitland, Sir J. M'Neill, Montgomery, the Hon. S. Mostyn, G. Moncrieff, E. Markham, Sir W. A. Mackinnon, Bryan Milman [?], H. M’Calmont [?], M'Donnell, W. C. F. Molyneux, Lord [Methuen?], J. F. Maurice, Sir F. Middleton, O. H. Nicolls, Sir E. [?] Newdegate, Sir H. N[orman?], Sir W. Olpherts, F. Peyton [?], G. [?] Upton Prior, T. H. Pakenham, G. W. T. Rich, Lord [?der] Russell, Robinson, Rowlands, J. C. Russell, F. [Russell?], A. C. Stewart, Sir Henry Smyth, Sterling, Sir C. [?] Shute, N. Stevenson, Swaine, Lord William Seymour, [?] [Sahmond?], Sir Frederick Stephenson, Sir John Stokes, Sir R. [?], Sir H. B. Tuson, the Hon. R. A. J. Talbot, G. le M. [Tupper?], Taylor, Hon. C. Thesiger, R. T. Thynne, Upperton, [?]H. Utterson, Sir J. Watson, Sir C. W. Wilson, Sir F. F. Walker, Sir Evelyn Wood, Sir C. Warren, Albert Williams, the Hon. G. Wrottesley, Sir G. H. Willis, Sir H. Wilmot #Colonels — Armytage, Arkwright, Pat Boyle, Burges, the Hon. [?] Byng, H. B. H. Blundell, M. S. Brownrigg, Sir E. Bradford, Sir A. [Blyge? Bigge?], the Hon. F. Bridgeman, Brassey, Lord William Beresford, St. John Barne, N. Barnardiston, Lord Blythswood, [?] Cunynghame, F. H. Custance, Clayton, Sir Henry Colville, [?] Carnac [?], Cavaye, Seymour Corkran, the Hon. Charles [?], W. Campbell, Chaloner, Archibald Calvert, the Hon. [?] Campbell, the Hon. Wenman C. Coke, the Hon. W. [?ton], the Hon. Sir W. Colville, Chaine, A. B. Crosbie, [T.?] [R?] Crosse, Lord Edward Pelham Clinton, the Hon. Henry [C?hton], E. H. Cooper, the Hon. H. Corry, John Clerk, Lord Dorchestcr, C. R. Dease, the Hon, Lewis Dawnay, [the?] Hon. H. Denison, Denny, Dalbiac, A. Davidson, the Hon. Cathbert Edwards, the Right Hon. Sir F. Edwards, [?son], R. Edis, the Hon. Charles Edgecumbe, Aubone Fife, [?], Wynne Finch, Ferguson of Pitfour, Forster, Lancelot [?r] H. Frudyer, Barrington Foote, Goldsmid, Gore, Grenfell, [?n], C. G. Gordon, R. Gunter, Alan Gardner, Hon. G. Gough, [?] [?iton], the Hon. A. Hood, the Earl of Home, Lord Claud [Hamilton?], Harford, Herbert, the Earl of Haddington, Haygarth, G. Hatton [?], Hillyard, Arthur Haig, Sir E. Stock Hill, R. Hennell, Archer Houblon [?], the Hon. Cospatrick Home, the Hon. C. Gathorne-Hardy, Johnstone, Cotton-Jodrell, Hegan, [H?nard], Sir N. Kingscote, H. A. Lascelles, the Hon. Heneage [L?], Hanning Lee, F. A. Lucas, the Hon. H. Lyttelton, Lockwood, L. V. Loyd, C. W. Long, Ronald Lane, Lucas, J. Leslie, the Hon. Caryl [?]Molyneux, John Murray, Sir A. W. Mackworth, J. M'Calmont [?], Milward, the Hon. F. C. Morgan, J. J. Mellor, Meeking, Manvers [?], Moorsom, H. Malet, the Earl of Mount Edgecumbe, the [Earl?] of March, Wyndham Murray, Sir V. Majendie, the Hon. G. [Napper?], H. H. Oldham, L. J. Oliphant, A. Paget, Dampier Palmer, [Earl?] Percy, George Paget, C. D. Patterson, Arthur Peel, [Birch?] [Richardson?], the Hon. F. W. Stopford, Sir W. G. Stirling, E J. [Sanderson?], T. M. Sandys, H. Smith, J. F. Sandeman, Renyon-[Surrey?], C. E Stewart, E. H. Sartorius, the Hon. Walter [Stewart?], L. Seymour, Settle, Stevenson, Starkie, C. H. Seafe, the Hon. Sir W. P. Talbot, J. Du Plat[?] Taylor, H. Thomas, A. W. [T?], the Hon. W. Ie Poer Trench, H. P. Vance, Sir C. E. Howard Vincent, M.P.; R. Vivian, A. P. Vivian, E. Villiers, the Duke of Westminster, the Earl of Wemyss, Lord Wantage, Ward, [Waring?], [Earle?] Welby, Lord Arthur Wellesley, Robert Williams, the Hon. H. L. Wood, Sir W. H. Walroud, F. Smart Walker, A. [Williams?] Wynn, Wardrop #Majors — Anne, Atherley, Ashton, F. H. Bowles, the Hon. [?] R. Bourke, Carnegy, H. Candy, Close, the Hon. F. Colborue, the Hon. Wenman Coke, Lawrence Drummond, Alfred [Edgecombe?], G. Egerton, E. H. Elliot, the Hon. A. Henniker, J. [H?a?h], the Hon. Assheton Harbord, the Hon. North Dalrymple [Hamilton?], Jameson, Pryce Jones, Larnach, the Hon. Osbert [Lumley?], C. Little, Marindin, the Hon. J. Scott Napier, Wyndham Quin, F. C Rasch, the Hon. A. Sidney, the Hon. J. T. St. Aubyn, Sir Edgar Sebright, Stirling, T. E. M. Swinnington-Parkington, [?.] M. Temple, Tillbrook, Anstruther Thomson, [E.?] [L.?] Woodhouse, and the Marquis of Winchester #Captains — O. Ames, J. Acland, Alan Boisragon, Bates, H. M. [Biddulph?], the Hon. Baring, Butler, the Hon. J. Byng, the Hon. [N.?] Yarde-Butler, E. W. Blunt, J. F. Bagot, the Hon. W. Bagot, Seymour Combe, W. Chetwynd, Dundas, Denis Daly, Cecil Drummond, M. Drummond, Ellison, Houston French, Gye, R. G. [Gilmour?], P. Green, W. G. Grice-Hutchinson, Ahmed Hussain, G. [L.?] Holford, Jessel, the Hon. W. Lambton, the Hon. G. H. [L?], Sir H. Naylor-Leyland, G. Lister, Matthews, A. D. Miller, [?],M. M'Neill, C. Norton, Phillpotts, N. G. Philips, Prety[man?], Duncan Pirie, Pitman, Fox Pitt, Petre, Harcourt Rose, [W.?] [J.?] Stopford, Sir Eyre Shaw, H. G. D. Shute, Spicer, the Hon. [?.] St. Aubyn, Sutton, Tillard, Webbe, Wray, and Gordon [Watson?] #Lieutenants — Baun, A. Cowell, the Hon. E. C. Lennox, F. Ponsonby, J. Ponsonby, Vandeleur, the Hon. C. Willoughby, and the Hon. C. S. H. D. Willoughby ===Entertainment=== "The Bands of the 1st Life Guards, Grenadier Guards, and Royal Artillery played a selection of music during the afternoon."<ref name=":1" /> (4, Col. 2c) ==Anthology== ====Quote Intro==== <quote></quote> () == Notes and Questions == # ==References== * <references /> osmtp5jurbd2rad3xbcsf36l9dwixqs 0 308661 2690165 2688683 2024-12-03T21:52:24Z Watchduck 137431 2690165 wikitext text/x-wiki <templatestyles src="Collapsible with classes/style.css" /> <templatestyles src="Boolf EC/style.css" /> __NOTOC__ {{Boolf header}} {| style="float: right;" | {{Properties of Boolean functions}} |- | {{Shortcut|Boolf-soft}} |} The number of [[w:Boolean function|Boolean functions]] with arity <math>n</math> (short for [[Boolf-term|adicity]] <math>\le n</math>) is <math>2^{2^n}</math> ({{oeis|A001146}}). This article is about properties of finite truth tables of Boolean functions, that change with the arity. ==simple== * '''weight:''' number of true places * '''sharpness:''' weight parity &nbsp;&nbsp; '''sharp''': odd weight &nbsp;&nbsp; '''dull:''' even weight ==subsets== * '''[[Noble Boolean functions|noble]]:''' truth tables that are their own [[Zhegalkin twins|twins]] * '''{{w|Symmetric Boolean function|symmetric}}:''' order of inputs does not matter ==equivalence classes based on similarity== <small>see also: [[Extended families and clans of Boolean functions]]</small> ===ultra <small class="heading-details">(extension with half-complement)</small>=== {| class="wikitable" style="float:right; text-align: center;" |colspan="3"| The two families on the left form a super-family.<br> The family on the right is a super-family on its own.<br> Together these two super-families form an ultra-family. |- |colspan="2"| [[File:3-ary Boolean functions; super-family of Zhe 40.svg|200px]] | [[File:3-ary Boolean functions; super-family of Zhe 44.svg|200px]] |- | [[File:Venn 0100 0001.svg|30px]] | [[File:Venn 0111 1101.svg|30px]] | [[File:Venn 0010 0111.svg|30px]] |- | [[File:Boolean functions like 1000 0010.svg|100px]] | [[File:Boolean functions like 1011 1110.svg|100px]] | [[File:Boolean functions like 1110 0100.svg|100px]] |} Each Boolean function has two half-complements. <small>(The truth table is complemented on the left or on the right side.)</small><br> A super-family has a unique half-complement. Merging them gives an ultra-family.<br> As super-clans consist of super-families, they can be extended in the same way.<br> <small style="opacity: .5;">(Factions do not have a unique half-complement, so it does not seem useful to define ultra-factions.)</small> ===={{anchor|ultra-family}} '''ultra-family''' <small class="heading-details">(negation, complement, half-complement)</small>==== The functions in an ultra-family have symmetric positions in a hypercube graph (or the related matrix). See [[commons:Category:3-ary truth tables in octeract matrix; ultra-families|matrices]].<br> <small>This family is a complete ultra-family: [[:File:Boolean functions like 1100 1010.svg|1100 1010]] {{spaces|3}} (better seen in [[:File:3-ary Boolean functions; super-family of Zhe 98.svg|its matrix]])</small> ===={{anchor|ultra-clan}} '''ultra-clan''' <small class="heading-details">(negation, permutation, complement, half-complement)</small>==== An ultra-clan is the merge of a super-clan and its half-complement.<br> It can also be seen as a merge of ultra-families, that are permutations of each other.<br> <small>See [[4-ary Boolean functions#ggbec|here]] for a table of the 39 ultra-families of 4-ary Boolean functions.</small> ==partitions into blocks of equal size== ==={{anchor|consul|consuls}} consul <small>(binary Walsh spectrum)</small>=== <span style="opacity: .5;">The [[w:Hadamard transform|Walsh spectrum]] of a TT is its product with a [[w:Walsh matrix|Walsh matrix]].</span><br> The ''binary'' Walsh spectrum of a TT is its product with a ''binary'' Walsh matrix, using [[w:Finite field|'''F'''₂]] operations ([[w:Modular arithmetic|mod]] 2).<br> It is always a Walsh function, and shall be called '''consul'''. The term is also used for the integer denoting the Walsh function. The consul integer is the Walsh index of the [[Boolf-EC#prefect|prefect]] of the [[Zhegalkin twins|twin]]. <small style="opacity: .7;">The consul is essentially the prefect of the twin, but without the negation.</small><br> <small style="opacity: .5;">(One could also define a sign for the consul, by using a ''negated'' binary Walsh matrix. But the sign would just be the sharpness.)</small> {| style="border: 1px solid lightgray; width: 700px;" |- style="vertical-align: top;" | [[File:Walsh spectra of family 0001 1001.svg|thumb|center|250px|sharp family with consuls 0...7]] | [[File:Walsh spectra of family 1100 1001.svg|thumb|center|250px|dull family with consul 2<br><small>(compare [[c:File:Walsh spectra of family patina.svg|4-ary family with consul 6]])</small>]] |- |colspan="2"| 3-ary [[Boolf-EC#family|families]] with Walsh spectra <small>(integers)</small> and consuls <small>(red backgrounds on the right)</small> |} {{anchor|tribe|tribes}} {{Collapsible START|tribe|collapsed strong}} The consul weight is the binary weight of the consul integer. (E.g. consul 6 has consul weight 2.)<br> Dull TT belong to ultra-clans with a unique consul weight, which belong to a dull tribe denoted by that consul weight.<br> Sharp TT form a tribe on their own. {{Properties of truth tables/tribes}} {{Collapsible END}} <small style="opacity: .5;">[[3-ary_Boolean_functions#Walsh spectrum]], [[4-ary_Boolean_functions#wec]]</small> ===patron=== The [[Noble Boolean functions#patron|patron]] of a truth table is the XOR of itself and its [[Zhegalkin twins|twin]]. It is a noble. &nbsp;&nbsp; <small style="opacity: .7;">[[c:Category:3-ary Boolean functions in octeract matrix; great patrons|(3-ary images)]]</small> ===praetor=== XOR of left and right half of the TT. &nbsp;&nbsp; <small style="opacity: .7;">[[c:Category:3-ary Boolean functions in octeract matrix; great praetors|(3-ary images)]]</small> ===quaestor=== XOR of left and reversed right half of the truth table <small>(i.e. of the coordinates in the Hasse matrix)</small> &nbsp;&nbsp; <small style="opacity: .7;">[[c:Category:3-ary Boolean functions in octeract matrix; great quaestors|(3-ary images)]]</small> [[Category:Studies of Boolean functions]] ==principalities and dominions== :''[[Principalities and dominions of Boolean functions]]'' A principality is a set of ''n''-ary truth tables whose (''n''+1)-ary [[Noble Boolean functions|noble]] equivalents form a {{BF-prop|faction}}. Dominions are closely related. 9cavgzij9ryw3005a8jt4a36t94hswo 2690173 2690165 2024-12-03T23:01:49Z Watchduck 137431 /* principalities and dominions */ 2690173 wikitext text/x-wiki <templatestyles src="Collapsible with classes/style.css" /> <templatestyles src="Boolf EC/style.css" /> __NOTOC__ {{Boolf header}} {| style="float: right;" | {{Properties of Boolean functions}} |- | {{Shortcut|Boolf-soft}} |} The number of [[w:Boolean function|Boolean functions]] with arity <math>n</math> (short for [[Boolf-term|adicity]] <math>\le n</math>) is <math>2^{2^n}</math> ({{oeis|A001146}}). This article is about properties of finite truth tables of Boolean functions, that change with the arity. ==simple== * '''weight:''' number of true places * '''sharpness:''' weight parity &nbsp;&nbsp; '''sharp''': odd weight &nbsp;&nbsp; '''dull:''' even weight ==subsets== * '''[[Noble Boolean functions|noble]]:''' truth tables that are their own [[Zhegalkin twins|twins]] * '''{{w|Symmetric Boolean function|symmetric}}:''' order of inputs does not matter ==equivalence classes based on similarity== <small>see also: [[Extended families and clans of Boolean functions]]</small> ===ultra <small class="heading-details">(extension with half-complement)</small>=== {| class="wikitable" style="float:right; text-align: center;" |colspan="3"| The two families on the left form a super-family.<br> The family on the right is a super-family on its own.<br> Together these two super-families form an ultra-family. |- |colspan="2"| [[File:3-ary Boolean functions; super-family of Zhe 40.svg|200px]] | [[File:3-ary Boolean functions; super-family of Zhe 44.svg|200px]] |- | [[File:Venn 0100 0001.svg|30px]] | [[File:Venn 0111 1101.svg|30px]] | [[File:Venn 0010 0111.svg|30px]] |- | [[File:Boolean functions like 1000 0010.svg|100px]] | [[File:Boolean functions like 1011 1110.svg|100px]] | [[File:Boolean functions like 1110 0100.svg|100px]] |} Each Boolean function has two half-complements. <small>(The truth table is complemented on the left or on the right side.)</small><br> A super-family has a unique half-complement. Merging them gives an ultra-family.<br> As super-clans consist of super-families, they can be extended in the same way.<br> <small style="opacity: .5;">(Factions do not have a unique half-complement, so it does not seem useful to define ultra-factions.)</small> ===={{anchor|ultra-family}} '''ultra-family''' <small class="heading-details">(negation, complement, half-complement)</small>==== The functions in an ultra-family have symmetric positions in a hypercube graph (or the related matrix). See [[commons:Category:3-ary truth tables in octeract matrix; ultra-families|matrices]].<br> <small>This family is a complete ultra-family: [[:File:Boolean functions like 1100 1010.svg|1100 1010]] {{spaces|3}} (better seen in [[:File:3-ary Boolean functions; super-family of Zhe 98.svg|its matrix]])</small> ===={{anchor|ultra-clan}} '''ultra-clan''' <small class="heading-details">(negation, permutation, complement, half-complement)</small>==== An ultra-clan is the merge of a super-clan and its half-complement.<br> It can also be seen as a merge of ultra-families, that are permutations of each other.<br> <small>See [[4-ary Boolean functions#ggbec|here]] for a table of the 39 ultra-families of 4-ary Boolean functions.</small> ==partitions into blocks of equal size== ==={{anchor|consul|consuls}} consul <small>(binary Walsh spectrum)</small>=== <span style="opacity: .5;">The [[w:Hadamard transform|Walsh spectrum]] of a TT is its product with a [[w:Walsh matrix|Walsh matrix]].</span><br> The ''binary'' Walsh spectrum of a TT is its product with a ''binary'' Walsh matrix, using [[w:Finite field|'''F'''₂]] operations ([[w:Modular arithmetic|mod]] 2).<br> It is always a Walsh function, and shall be called '''consul'''. The term is also used for the integer denoting the Walsh function. The consul integer is the Walsh index of the [[Boolf-EC#prefect|prefect]] of the [[Zhegalkin twins|twin]]. <small style="opacity: .7;">The consul is essentially the prefect of the twin, but without the negation.</small><br> <small style="opacity: .5;">(One could also define a sign for the consul, by using a ''negated'' binary Walsh matrix. But the sign would just be the sharpness.)</small> {| style="border: 1px solid lightgray; width: 700px;" |- style="vertical-align: top;" | [[File:Walsh spectra of family 0001 1001.svg|thumb|center|250px|sharp family with consuls 0...7]] | [[File:Walsh spectra of family 1100 1001.svg|thumb|center|250px|dull family with consul 2<br><small>(compare [[c:File:Walsh spectra of family patina.svg|4-ary family with consul 6]])</small>]] |- |colspan="2"| 3-ary [[Boolf-EC#family|families]] with Walsh spectra <small>(integers)</small> and consuls <small>(red backgrounds on the right)</small> |} {{anchor|tribe|tribes}} {{Collapsible START|tribe|collapsed strong}} The consul weight is the binary weight of the consul integer. (E.g. consul 6 has consul weight 2.)<br> Dull TT belong to ultra-clans with a unique consul weight, which belong to a dull tribe denoted by that consul weight.<br> Sharp TT form a tribe on their own. {{Properties of truth tables/tribes}} {{Collapsible END}} <small style="opacity: .5;">[[3-ary_Boolean_functions#Walsh spectrum]], [[4-ary_Boolean_functions#wec]]</small> ===patron=== The [[Noble Boolean functions#patron|patron]] of a truth table is the XOR of itself and its [[Zhegalkin twins|twin]]. It is a noble. &nbsp;&nbsp; <small style="opacity: .7;">[[c:Category:3-ary Boolean functions in octeract matrix; great patrons|(3-ary images)]]</small> ===praetor=== XOR of left and right half of the TT. &nbsp;&nbsp; <small style="opacity: .7;">[[c:Category:3-ary Boolean functions in octeract matrix; great praetors|(3-ary images)]]</small> ===quaestor=== XOR of left and reversed right half of the truth table <small>(i.e. of the coordinates in the Hasse matrix)</small> &nbsp;&nbsp; <small style="opacity: .7;">[[c:Category:3-ary Boolean functions in octeract matrix; great quaestors|(3-ary images)]]</small> [[Category:Studies of Boolean functions]] =={{anchor|principality|dominion}} principalities and dominions== :''[[Principalities and dominions of Boolean functions]]'' A principality is a set of ''n''-ary truth tables whose (''n''+1)-ary [[Noble Boolean functions|noble]] equivalents form a {{BF-prop|faction}}. Dominions are closely related. 0ipr6y361l57arxg1d3r437cln0rphc 0 316507 2690236 2689811 2024-12-04T10:06:16Z Sylvain Ribault 2127778 /* Conformal transformations of flat space */ 2690236 wikitext text/x-wiki == Conformal invariance == === Conformal transformations === On a given space or spacetime <math>M</math> with coordinates <math>x^\mu</math>, distances are defined using a metric <math>g_{\mu\nu}</math>. In particular, the length of an infinitesimal vector <math>v^\mu</math> is <math>\|v\| = \sqrt{g_{\mu\nu}v^\mu v^\nu}</math>. If we know distances, we can also compute angles. The angle <math>\theta</math> between two infinitesimal vectors <math>v^\mu,w^\mu</math> obeys :<math> \cos\theta = \frac{g_{\mu\nu}v^\mu w^\nu}{\sqrt{g_{\mu\nu}v^\mu v^\nu}\sqrt{ g_{\mu\nu}w^\mu w^\nu}} </math> For <math>f:M\to M</math> a diffeomorphism, we define the [[w:pullback]] <math>f^*g</math> of the metric by :<math> (f^*g)_{\mu\nu} = g_{\rho\sigma}(f(x)) \frac{\partial f^\rho}{\partial x^\mu}\frac{\partial f^\sigma}{\partial x^\nu} </math> equivalently <math>(f*g)_{\mu\nu}(x)dx^\mu dx^\nu = g_{\mu\nu}(f)df^\mu df^\nu</math>. A diffeomorphism <math>f:M\to M</math> is called an '''isometry''' if it preserves distances, equivalently if :<math>f^* g = g</math>. It is called a '''conformal transformation''' if it preserves angles. Any isometry is a conformal transformation, but the converse is not true. For any function <math>\lambda:M\to \mathbb{R}</math>, the metrics <math>g_{\mu\nu}</math> and <math>\lambda g_{\mu\nu}</math> define the same angles. So <math>f</math> is a conformal transformation if it preserve the metric up to a scalar factor, :<math> \exists \lambda,\ f^* g = \lambda g </math> The set of conformal transformations is called the '''conformal group''' associated to <math>M,g</math>. Let us indicate how many functions on <math>M</math> are needed to parametrize the objects <math>\lambda, f,g</math>, if <math>d=\dim(M)</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Object ! Number of functions on <math>M</math> |- | Function <math>\lambda:M\to \mathbb{R}</math> | <math>1</math> |- | Diffeomorphism <math>f:M\to M</math> | <math>d</math> |- | Metric <math>g</math> on <math>M</math> | <math>\frac{d(d+1)}{2}</math> |} Therefore, given two metrics <math>g_1,g_2</math>, the condition <math>f^* g_1 = \lambda g_2</math> that they are conformally equivalent involves <math>\frac{d(d+1)}{2}</math> equations for <math>d+1</math> unknowns. For <math>d\leq 2</math>, there is always a solution (under reasonable assumptions): in particular any metric on <math>\mathbb{R}^2</math> is conformally flat. For <math>d\geq 3</math>, two metrics are in general not equivalent modulo rescaling. Similarly, the size of the conformal group depends on the dimension: * For <math>d=1</math>, any diffeomorphism is conformal. * For <math>d\geq 2</math>, the conformal group depends on <math>M,g</math>, with flat space <math>\mathbb{R}^d</math> having the largest possible group <math>SO(d+1,1)</math>. * For <math>d\geq 3</math>, a generic space has only one conformal transformation: the identity. === Conformal transformations of flat space === The conformal group of <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math> first includes isometries: * Translations. * Rotations. There are also conformal transformations that are not isometries: * Dilations <math>x^\mu \mapsto \lambda x^\mu </math> with <math>\lambda \in \mathbb{R}</math>. * The inversion <math>x^\mu \mapsto \frac{x^\mu}{\|x\|^2}</math>. * Special conformal transformations <math>x^\mu \mapsto \frac{x^\mu - a^\mu \|x\|^2}{1-2a_\mu x^\mu +\|a\|^2\|x\|^2}</math>. These transformations generate the conformal group <math>SO(d+1,1)</math>. === Conformal symmetry and gravitation === In a theory of gravitation such as general relativity, the metric is not fixed, it is a dynamical object. We can therefore combine diffeomorphisms with changes of the metric. In particular, if we combine a diffeomorphism <math>f</math> with <math>g\mapsto f^*g</math>, we obtain a '''change of coordinates''', which should leave the physics invariant. By definition, modulo a change of coordinates, a conformal transformation amounts to a '''Weyl transformation''' of the metric <math>g\mapsto \lambda g</math>. For gravitational theories, conformal invariance is equivalent to Weyl invariance. General relativity is Weyl invariant for <math>d=2</math> only. It follows that in <math>d=2</math>, any field theory of quantum gravity must be a conformal field theory. Moreover, since any metric is conformally flat, we may replace the 3 components of the metric <math>g_{\mu\nu}</math> with the conformal factor <math>\lambda</math>: only 1 bosonic field. Einstein's equation for <math>g_{\mu\nu}</math> then reduces to the Liouville equation for <math>\log \lambda</math>. The Liouville equation is the classical equation of motion of [[w:Liouville theory]]: a solvable CFT that we will study in this course. Therefore, we can build field theories of gravity called '''Liouville gravity''' based on Liouville theory. (There are several possible theories, depending on the matter contents.) String theory is a theoretical framework that generalizes quantum field theory, and includes quantum theories of gravity. The basic idea is to describe physics in a spacetime <math>Z</math> using a <math>d=2</math> worldsheet <math>M</math> and an embedding <math>X:M\to Z</math>. The metric on <math>Z</math> induces a metric on <math>M</math>, but it is convenient to allow the worldsheet metric <math>g</math> to be an independent dynamical object, unrelated to the induced metric. Nevertheless, the physics should not depend on <math>g</math>. It is possible to fix 2 of the 3 components of <math>g</math> using a change of coordinates on <math>M</math>, and to get <math>g</math>-independence we also have to take care of the third component, by assuming Weyl invariance. This is why the worldsheet description of string theory uses <math>d=2</math> CFT. String theory provides another motivation for CFT in arbitrary <math>d</math> due to the AdS/CFT correspondence: a holographic relation between a string theory in a <math>d+1</math>-dimensional Anti-de Sitter space, and a CFT in <math>d</math> dimensions. In fact the correspondence can be generalized to non-AdS spaces, which then correspond to non-conformal field theories. Nevertheless, the correspondencs is simplest in the AdS/CFT case. === Conformal transformations in two dimensions === Riemann surfaces, moduli. == Scale invariance and conformal invariance == == Fixed points of the renormalization group == == Applications == == Exercises == === COGS: The conformal group of flat space === Consider the Euclidean space <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math>, and the Minkowski space <math>\mathbb{R}^{d+1,1}</math> with coordinates <math>Y=\left(y^\mu,y^-,y^+\right)</math> with <math>\mu = 1,2,\dots, d</math> and the flat metric <math>\|dY\|^2 = \sum_{\mu=1}^d \left(dy^\mu\right)^2 -dy^-dy^+ </math>. Consider the diffeormorphisms :<math> \varphi:\left\{\begin{array}{ccl} \mathbb{R}^d & \to & \mathbb{R}^{d+1,1} \\ x^\mu &\mapsto & \left(x^\mu,\|x\|^2,1\right) \end{array}\right. \quad , \quad \psi: \left\{\begin{array}{ccl} \mathbb{R}^{d+1,1} & \to & \mathbb{R}^{d+1,1} \\ Y &\mapsto & \frac{1}{y^+}Y = \left(\frac{y^\mu}{y^+},\frac{y^-}{y^+},1\right) \end{array}\right. </math> # Check that <math>\varphi</math> is an isometry. Is <math>\psi</math> an isometry? Is it a conformal transformation? # Show that the restriction of <math>\psi</math> to the light cone <math>\mathcal{L}=\left\{Y\in \mathbb{R}^{d+1,1}\left| \|Y\|^2 = 0\right.\right\}</math> is a conformal transformation. # Let <math>G\in SO(d+1,1)</math> be an isometry of <math>\mathbb{R}^{d+1,1}</math>, in particular <math>G</math> is linear. Show that <math>\varphi^{-1}\circ \psi \circ G\circ \varphi</math> is a conformal transformation of <math>\mathbb{R}^d</math>. Deduce that the conformal group of <math>\mathbb{R}^d</math> includes <math>SO(d+1,1)</math>. # Explicitly write the action of <math>G\in SO(d+1,1)</math> on <math>x^\mu</math>. [[Category: CFT course]] racjue6bsmhuzis6xjtbzaotvujxkny 2690237 2690236 2024-12-04T10:19:16Z Sylvain Ribault 2127778 /* Conformal transformations in two dimensions */ 2690237 wikitext text/x-wiki == Conformal invariance == === Conformal transformations === On a given space or spacetime <math>M</math> with coordinates <math>x^\mu</math>, distances are defined using a metric <math>g_{\mu\nu}</math>. In particular, the length of an infinitesimal vector <math>v^\mu</math> is <math>\|v\| = \sqrt{g_{\mu\nu}v^\mu v^\nu}</math>. If we know distances, we can also compute angles. The angle <math>\theta</math> between two infinitesimal vectors <math>v^\mu,w^\mu</math> obeys :<math> \cos\theta = \frac{g_{\mu\nu}v^\mu w^\nu}{\sqrt{g_{\mu\nu}v^\mu v^\nu}\sqrt{ g_{\mu\nu}w^\mu w^\nu}} </math> For <math>f:M\to M</math> a diffeomorphism, we define the [[w:pullback]] <math>f^*g</math> of the metric by :<math> (f^*g)_{\mu\nu} = g_{\rho\sigma}(f(x)) \frac{\partial f^\rho}{\partial x^\mu}\frac{\partial f^\sigma}{\partial x^\nu} </math> equivalently <math>(f*g)_{\mu\nu}(x)dx^\mu dx^\nu = g_{\mu\nu}(f)df^\mu df^\nu</math>. A diffeomorphism <math>f:M\to M</math> is called an '''isometry''' if it preserves distances, equivalently if :<math>f^* g = g</math>. It is called a '''conformal transformation''' if it preserves angles. Any isometry is a conformal transformation, but the converse is not true. For any function <math>\lambda:M\to \mathbb{R}</math>, the metrics <math>g_{\mu\nu}</math> and <math>\lambda g_{\mu\nu}</math> define the same angles. So <math>f</math> is a conformal transformation if it preserve the metric up to a scalar factor, :<math> \exists \lambda,\ f^* g = \lambda g </math> The set of conformal transformations is called the '''conformal group''' associated to <math>M,g</math>. Let us indicate how many functions on <math>M</math> are needed to parametrize the objects <math>\lambda, f,g</math>, if <math>d=\dim(M)</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Object ! Number of functions on <math>M</math> |- | Function <math>\lambda:M\to \mathbb{R}</math> | <math>1</math> |- | Diffeomorphism <math>f:M\to M</math> | <math>d</math> |- | Metric <math>g</math> on <math>M</math> | <math>\frac{d(d+1)}{2}</math> |} Therefore, given two metrics <math>g_1,g_2</math>, the condition <math>f^* g_1 = \lambda g_2</math> that they are conformally equivalent involves <math>\frac{d(d+1)}{2}</math> equations for <math>d+1</math> unknowns. For <math>d\leq 2</math>, there is always a solution (under reasonable assumptions): in particular any metric on <math>\mathbb{R}^2</math> is conformally flat. For <math>d\geq 3</math>, two metrics are in general not equivalent modulo rescaling. Similarly, the size of the conformal group depends on the dimension: * For <math>d=1</math>, any diffeomorphism is conformal. * For <math>d\geq 2</math>, the conformal group depends on <math>M,g</math>, with flat space <math>\mathbb{R}^d</math> having the largest possible group <math>SO(d+1,1)</math>. * For <math>d\geq 3</math>, a generic space has only one conformal transformation: the identity. === Conformal transformations of flat space === The conformal group of <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math> first includes isometries: * Translations. * Rotations. There are also conformal transformations that are not isometries: * Dilations <math>x^\mu \mapsto \lambda x^\mu </math> with <math>\lambda \in \mathbb{R}</math>. * The inversion <math>x^\mu \mapsto \frac{x^\mu}{\|x\|^2}</math>. * Special conformal transformations <math>x^\mu \mapsto \frac{x^\mu - a^\mu \|x\|^2}{1-2a_\mu x^\mu +\|a\|^2\|x\|^2}</math>. These transformations generate the conformal group <math>SO(d+1,1)</math>. === Conformal symmetry and gravitation === In a theory of gravitation such as general relativity, the metric is not fixed, it is a dynamical object. We can therefore combine diffeomorphisms with changes of the metric. In particular, if we combine a diffeomorphism <math>f</math> with <math>g\mapsto f^*g</math>, we obtain a '''change of coordinates''', which should leave the physics invariant. By definition, modulo a change of coordinates, a conformal transformation amounts to a '''Weyl transformation''' of the metric <math>g\mapsto \lambda g</math>. For gravitational theories, conformal invariance is equivalent to Weyl invariance. General relativity is Weyl invariant for <math>d=2</math> only. It follows that in <math>d=2</math>, any field theory of quantum gravity must be a conformal field theory. Moreover, since any metric is conformally flat, we may replace the 3 components of the metric <math>g_{\mu\nu}</math> with the conformal factor <math>\lambda</math>: only 1 bosonic field. Einstein's equation for <math>g_{\mu\nu}</math> then reduces to the Liouville equation for <math>\log \lambda</math>. The Liouville equation is the classical equation of motion of [[w:Liouville theory]]: a solvable CFT that we will study in this course. Therefore, we can build field theories of gravity called '''Liouville gravity''' based on Liouville theory. (There are several possible theories, depending on the matter contents.) String theory is a theoretical framework that generalizes quantum field theory, and includes quantum theories of gravity. The basic idea is to describe physics in a spacetime <math>Z</math> using a <math>d=2</math> worldsheet <math>M</math> and an embedding <math>X:M\to Z</math>. The metric on <math>Z</math> induces a metric on <math>M</math>, but it is convenient to allow the worldsheet metric <math>g</math> to be an independent dynamical object, unrelated to the induced metric. Nevertheless, the physics should not depend on <math>g</math>. It is possible to fix 2 of the 3 components of <math>g</math> using a change of coordinates on <math>M</math>, and to get <math>g</math>-independence we also have to take care of the third component, by assuming Weyl invariance. This is why the worldsheet description of string theory uses <math>d=2</math> CFT. String theory provides another motivation for CFT in arbitrary <math>d</math> due to the AdS/CFT correspondence: a holographic relation between a string theory in a <math>d+1</math>-dimensional Anti-de Sitter space, and a CFT in <math>d</math> dimensions. In fact the correspondence can be generalized to non-AdS spaces, which then correspond to non-conformal field theories. Nevertheless, the correspondencs is simplest in the AdS/CFT case. === Conformal transformations in two dimensions === Let <math>M</math> be a two-dimensional connected, oriented manifold. A metric <math>g</math> on <math>M</math> is called Riemannian if it is positive definite. Let <math>\bar g</math> be the equivalence class of <math>g</math> modulo conformal transformations, then <math>(M,\bar g)</math> is called a [[w:Riemann surface]]. == Scale invariance and conformal invariance == == Fixed points of the renormalization group == == Applications == == Exercises == === COGS: The conformal group of flat space === Consider the Euclidean space <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math>, and the Minkowski space <math>\mathbb{R}^{d+1,1}</math> with coordinates <math>Y=\left(y^\mu,y^-,y^+\right)</math> with <math>\mu = 1,2,\dots, d</math> and the flat metric <math>\|dY\|^2 = \sum_{\mu=1}^d \left(dy^\mu\right)^2 -dy^-dy^+ </math>. Consider the diffeormorphisms :<math> \varphi:\left\{\begin{array}{ccl} \mathbb{R}^d & \to & \mathbb{R}^{d+1,1} \\ x^\mu &\mapsto & \left(x^\mu,\|x\|^2,1\right) \end{array}\right. \quad , \quad \psi: \left\{\begin{array}{ccl} \mathbb{R}^{d+1,1} & \to & \mathbb{R}^{d+1,1} \\ Y &\mapsto & \frac{1}{y^+}Y = \left(\frac{y^\mu}{y^+},\frac{y^-}{y^+},1\right) \end{array}\right. </math> # Check that <math>\varphi</math> is an isometry. Is <math>\psi</math> an isometry? Is it a conformal transformation? # Show that the restriction of <math>\psi</math> to the light cone <math>\mathcal{L}=\left\{Y\in \mathbb{R}^{d+1,1}\left| \|Y\|^2 = 0\right.\right\}</math> is a conformal transformation. # Let <math>G\in SO(d+1,1)</math> be an isometry of <math>\mathbb{R}^{d+1,1}</math>, in particular <math>G</math> is linear. Show that <math>\varphi^{-1}\circ \psi \circ G\circ \varphi</math> is a conformal transformation of <math>\mathbb{R}^d</math>. Deduce that the conformal group of <math>\mathbb{R}^d</math> includes <math>SO(d+1,1)</math>. # Explicitly write the action of <math>G\in SO(d+1,1)</math> on <math>x^\mu</math>. [[Category: CFT course]] ohyl6fe02bnpj2bihp05q6eu4l6n8bi 2690238 2690237 2024-12-04T10:26:05Z Sylvain Ribault 2127778 /* Conformal transformations in two dimensions */ 2690238 wikitext text/x-wiki == Conformal invariance == === Conformal transformations === On a given space or spacetime <math>M</math> with coordinates <math>x^\mu</math>, distances are defined using a metric <math>g_{\mu\nu}</math>. In particular, the length of an infinitesimal vector <math>v^\mu</math> is <math>\|v\| = \sqrt{g_{\mu\nu}v^\mu v^\nu}</math>. If we know distances, we can also compute angles. The angle <math>\theta</math> between two infinitesimal vectors <math>v^\mu,w^\mu</math> obeys :<math> \cos\theta = \frac{g_{\mu\nu}v^\mu w^\nu}{\sqrt{g_{\mu\nu}v^\mu v^\nu}\sqrt{ g_{\mu\nu}w^\mu w^\nu}} </math> For <math>f:M\to M</math> a diffeomorphism, we define the [[w:pullback]] <math>f^*g</math> of the metric by :<math> (f^*g)_{\mu\nu} = g_{\rho\sigma}(f(x)) \frac{\partial f^\rho}{\partial x^\mu}\frac{\partial f^\sigma}{\partial x^\nu} </math> equivalently <math>(f*g)_{\mu\nu}(x)dx^\mu dx^\nu = g_{\mu\nu}(f)df^\mu df^\nu</math>. A diffeomorphism <math>f:M\to M</math> is called an '''isometry''' if it preserves distances, equivalently if :<math>f^* g = g</math>. It is called a '''conformal transformation''' if it preserves angles. Any isometry is a conformal transformation, but the converse is not true. For any function <math>\lambda:M\to \mathbb{R}</math>, the metrics <math>g_{\mu\nu}</math> and <math>\lambda g_{\mu\nu}</math> define the same angles. So <math>f</math> is a conformal transformation if it preserve the metric up to a scalar factor, :<math> \exists \lambda,\ f^* g = \lambda g </math> The set of conformal transformations is called the '''conformal group''' associated to <math>M,g</math>. Let us indicate how many functions on <math>M</math> are needed to parametrize the objects <math>\lambda, f,g</math>, if <math>d=\dim(M)</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Object ! Number of functions on <math>M</math> |- | Function <math>\lambda:M\to \mathbb{R}</math> | <math>1</math> |- | Diffeomorphism <math>f:M\to M</math> | <math>d</math> |- | Metric <math>g</math> on <math>M</math> | <math>\frac{d(d+1)}{2}</math> |} Therefore, given two metrics <math>g_1,g_2</math>, the condition <math>f^* g_1 = \lambda g_2</math> that they are conformally equivalent involves <math>\frac{d(d+1)}{2}</math> equations for <math>d+1</math> unknowns. For <math>d\leq 2</math>, there is always a solution (under reasonable assumptions): in particular any metric on <math>\mathbb{R}^2</math> is conformally flat. For <math>d\geq 3</math>, two metrics are in general not equivalent modulo rescaling. Similarly, the size of the conformal group depends on the dimension: * For <math>d=1</math>, any diffeomorphism is conformal. * For <math>d\geq 2</math>, the conformal group depends on <math>M,g</math>, with flat space <math>\mathbb{R}^d</math> having the largest possible group <math>SO(d+1,1)</math>. * For <math>d\geq 3</math>, a generic space has only one conformal transformation: the identity. === Conformal transformations of flat space === The conformal group of <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math> first includes isometries: * Translations. * Rotations. There are also conformal transformations that are not isometries: * Dilations <math>x^\mu \mapsto \lambda x^\mu </math> with <math>\lambda \in \mathbb{R}</math>. * The inversion <math>x^\mu \mapsto \frac{x^\mu}{\|x\|^2}</math>. * Special conformal transformations <math>x^\mu \mapsto \frac{x^\mu - a^\mu \|x\|^2}{1-2a_\mu x^\mu +\|a\|^2\|x\|^2}</math>. These transformations generate the conformal group <math>SO(d+1,1)</math>. === Conformal symmetry and gravitation === In a theory of gravitation such as general relativity, the metric is not fixed, it is a dynamical object. We can therefore combine diffeomorphisms with changes of the metric. In particular, if we combine a diffeomorphism <math>f</math> with <math>g\mapsto f^*g</math>, we obtain a '''change of coordinates''', which should leave the physics invariant. By definition, modulo a change of coordinates, a conformal transformation amounts to a '''Weyl transformation''' of the metric <math>g\mapsto \lambda g</math>. For gravitational theories, conformal invariance is equivalent to Weyl invariance. General relativity is Weyl invariant for <math>d=2</math> only. It follows that in <math>d=2</math>, any field theory of quantum gravity must be a conformal field theory. Moreover, since any metric is conformally flat, we may replace the 3 components of the metric <math>g_{\mu\nu}</math> with the conformal factor <math>\lambda</math>: only 1 bosonic field. Einstein's equation for <math>g_{\mu\nu}</math> then reduces to the Liouville equation for <math>\log \lambda</math>. The Liouville equation is the classical equation of motion of [[w:Liouville theory]]: a solvable CFT that we will study in this course. Therefore, we can build field theories of gravity called '''Liouville gravity''' based on Liouville theory. (There are several possible theories, depending on the matter contents.) String theory is a theoretical framework that generalizes quantum field theory, and includes quantum theories of gravity. The basic idea is to describe physics in a spacetime <math>Z</math> using a <math>d=2</math> worldsheet <math>M</math> and an embedding <math>X:M\to Z</math>. The metric on <math>Z</math> induces a metric on <math>M</math>, but it is convenient to allow the worldsheet metric <math>g</math> to be an independent dynamical object, unrelated to the induced metric. Nevertheless, the physics should not depend on <math>g</math>. It is possible to fix 2 of the 3 components of <math>g</math> using a change of coordinates on <math>M</math>, and to get <math>g</math>-independence we also have to take care of the third component, by assuming Weyl invariance. This is why the worldsheet description of string theory uses <math>d=2</math> CFT. String theory provides another motivation for CFT in arbitrary <math>d</math> due to the AdS/CFT correspondence: a holographic relation between a string theory in a <math>d+1</math>-dimensional Anti-de Sitter space, and a CFT in <math>d</math> dimensions. In fact the correspondence can be generalized to non-AdS spaces, which then correspond to non-conformal field theories. Nevertheless, the correspondencs is simplest in the AdS/CFT case. === Conformal transformations in two dimensions === Let <math>M</math> be a two-dimensional connected, oriented manifold. A metric <math>g</math> on <math>M</math> is called Riemannian if it is positive definite. Let <math>\bar g</math> be the equivalence class of <math>g</math> modulo conformal transformations, also called a '''conformal structure'''. Then <math>(M,\bar g)</math> is called a [[w:Riemann surface]]. A Riemann surface is characterized by its topology and its conformal structure. Let us focus on compact Riemann surfaces. == Scale invariance and conformal invariance == == Fixed points of the renormalization group == == Applications == == Exercises == === COGS: The conformal group of flat space === Consider the Euclidean space <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math>, and the Minkowski space <math>\mathbb{R}^{d+1,1}</math> with coordinates <math>Y=\left(y^\mu,y^-,y^+\right)</math> with <math>\mu = 1,2,\dots, d</math> and the flat metric <math>\|dY\|^2 = \sum_{\mu=1}^d \left(dy^\mu\right)^2 -dy^-dy^+ </math>. Consider the diffeormorphisms :<math> \varphi:\left\{\begin{array}{ccl} \mathbb{R}^d & \to & \mathbb{R}^{d+1,1} \\ x^\mu &\mapsto & \left(x^\mu,\|x\|^2,1\right) \end{array}\right. \quad , \quad \psi: \left\{\begin{array}{ccl} \mathbb{R}^{d+1,1} & \to & \mathbb{R}^{d+1,1} \\ Y &\mapsto & \frac{1}{y^+}Y = \left(\frac{y^\mu}{y^+},\frac{y^-}{y^+},1\right) \end{array}\right. </math> # Check that <math>\varphi</math> is an isometry. Is <math>\psi</math> an isometry? Is it a conformal transformation? # Show that the restriction of <math>\psi</math> to the light cone <math>\mathcal{L}=\left\{Y\in \mathbb{R}^{d+1,1}\left| \|Y\|^2 = 0\right.\right\}</math> is a conformal transformation. # Let <math>G\in SO(d+1,1)</math> be an isometry of <math>\mathbb{R}^{d+1,1}</math>, in particular <math>G</math> is linear. Show that <math>\varphi^{-1}\circ \psi \circ G\circ \varphi</math> is a conformal transformation of <math>\mathbb{R}^d</math>. Deduce that the conformal group of <math>\mathbb{R}^d</math> includes <math>SO(d+1,1)</math>. # Explicitly write the action of <math>G\in SO(d+1,1)</math> on <math>x^\mu</math>. [[Category: CFT course]] 022o581f4jtq2vw0np5cf0j92uajjvz 2690240 2690238 2024-12-04T10:38:51Z Sylvain Ribault 2127778 /* Conformal transformations in two dimensions */ 2690240 wikitext text/x-wiki == Conformal invariance == === Conformal transformations === On a given space or spacetime <math>M</math> with coordinates <math>x^\mu</math>, distances are defined using a metric <math>g_{\mu\nu}</math>. In particular, the length of an infinitesimal vector <math>v^\mu</math> is <math>\|v\| = \sqrt{g_{\mu\nu}v^\mu v^\nu}</math>. If we know distances, we can also compute angles. The angle <math>\theta</math> between two infinitesimal vectors <math>v^\mu,w^\mu</math> obeys :<math> \cos\theta = \frac{g_{\mu\nu}v^\mu w^\nu}{\sqrt{g_{\mu\nu}v^\mu v^\nu}\sqrt{ g_{\mu\nu}w^\mu w^\nu}} </math> For <math>f:M\to M</math> a diffeomorphism, we define the [[w:pullback]] <math>f^*g</math> of the metric by :<math> (f^*g)_{\mu\nu} = g_{\rho\sigma}(f(x)) \frac{\partial f^\rho}{\partial x^\mu}\frac{\partial f^\sigma}{\partial x^\nu} </math> equivalently <math>(f*g)_{\mu\nu}(x)dx^\mu dx^\nu = g_{\mu\nu}(f)df^\mu df^\nu</math>. A diffeomorphism <math>f:M\to M</math> is called an '''isometry''' if it preserves distances, equivalently if :<math>f^* g = g</math>. It is called a '''conformal transformation''' if it preserves angles. Any isometry is a conformal transformation, but the converse is not true. For any function <math>\lambda:M\to \mathbb{R}</math>, the metrics <math>g_{\mu\nu}</math> and <math>\lambda g_{\mu\nu}</math> define the same angles. So <math>f</math> is a conformal transformation if it preserve the metric up to a scalar factor, :<math> \exists \lambda,\ f^* g = \lambda g </math> The set of conformal transformations is called the '''conformal group''' associated to <math>M,g</math>. Let us indicate how many functions on <math>M</math> are needed to parametrize the objects <math>\lambda, f,g</math>, if <math>d=\dim(M)</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Object ! Number of functions on <math>M</math> |- | Function <math>\lambda:M\to \mathbb{R}</math> | <math>1</math> |- | Diffeomorphism <math>f:M\to M</math> | <math>d</math> |- | Metric <math>g</math> on <math>M</math> | <math>\frac{d(d+1)}{2}</math> |} Therefore, given two metrics <math>g_1,g_2</math>, the condition <math>f^* g_1 = \lambda g_2</math> that they are conformally equivalent involves <math>\frac{d(d+1)}{2}</math> equations for <math>d+1</math> unknowns. For <math>d\leq 2</math>, there is always a solution (under reasonable assumptions): in particular any metric on <math>\mathbb{R}^2</math> is conformally flat. For <math>d\geq 3</math>, two metrics are in general not equivalent modulo rescaling. Similarly, the size of the conformal group depends on the dimension: * For <math>d=1</math>, any diffeomorphism is conformal. * For <math>d\geq 2</math>, the conformal group depends on <math>M,g</math>, with flat space <math>\mathbb{R}^d</math> having the largest possible group <math>SO(d+1,1)</math>. * For <math>d\geq 3</math>, a generic space has only one conformal transformation: the identity. === Conformal transformations of flat space === The conformal group of <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math> first includes isometries: * Translations. * Rotations. There are also conformal transformations that are not isometries: * Dilations <math>x^\mu \mapsto \lambda x^\mu </math> with <math>\lambda \in \mathbb{R}</math>. * The inversion <math>x^\mu \mapsto \frac{x^\mu}{\|x\|^2}</math>. * Special conformal transformations <math>x^\mu \mapsto \frac{x^\mu - a^\mu \|x\|^2}{1-2a_\mu x^\mu +\|a\|^2\|x\|^2}</math>. These transformations generate the conformal group <math>SO(d+1,1)</math>. === Conformal symmetry and gravitation === In a theory of gravitation such as general relativity, the metric is not fixed, it is a dynamical object. We can therefore combine diffeomorphisms with changes of the metric. In particular, if we combine a diffeomorphism <math>f</math> with <math>g\mapsto f^*g</math>, we obtain a '''change of coordinates''', which should leave the physics invariant. By definition, modulo a change of coordinates, a conformal transformation amounts to a '''Weyl transformation''' of the metric <math>g\mapsto \lambda g</math>. For gravitational theories, conformal invariance is equivalent to Weyl invariance. General relativity is Weyl invariant for <math>d=2</math> only. It follows that in <math>d=2</math>, any field theory of quantum gravity must be a conformal field theory. Moreover, since any metric is conformally flat, we may replace the 3 components of the metric <math>g_{\mu\nu}</math> with the conformal factor <math>\lambda</math>: only 1 bosonic field. Einstein's equation for <math>g_{\mu\nu}</math> then reduces to the Liouville equation for <math>\log \lambda</math>. The Liouville equation is the classical equation of motion of [[w:Liouville theory]]: a solvable CFT that we will study in this course. Therefore, we can build field theories of gravity called '''Liouville gravity''' based on Liouville theory. (There are several possible theories, depending on the matter contents.) String theory is a theoretical framework that generalizes quantum field theory, and includes quantum theories of gravity. The basic idea is to describe physics in a spacetime <math>Z</math> using a <math>d=2</math> worldsheet <math>M</math> and an embedding <math>X:M\to Z</math>. The metric on <math>Z</math> induces a metric on <math>M</math>, but it is convenient to allow the worldsheet metric <math>g</math> to be an independent dynamical object, unrelated to the induced metric. Nevertheless, the physics should not depend on <math>g</math>. It is possible to fix 2 of the 3 components of <math>g</math> using a change of coordinates on <math>M</math>, and to get <math>g</math>-independence we also have to take care of the third component, by assuming Weyl invariance. This is why the worldsheet description of string theory uses <math>d=2</math> CFT. String theory provides another motivation for CFT in arbitrary <math>d</math> due to the AdS/CFT correspondence: a holographic relation between a string theory in a <math>d+1</math>-dimensional Anti-de Sitter space, and a CFT in <math>d</math> dimensions. In fact the correspondence can be generalized to non-AdS spaces, which then correspond to non-conformal field theories. Nevertheless, the correspondencs is simplest in the AdS/CFT case. === Conformal transformations in two dimensions === Let <math>M</math> be a two-dimensional connected, oriented manifold. A metric <math>g</math> on <math>M</math> is called Riemannian if it is positive definite. Let <math>\bar g</math> be the equivalence class of <math>g</math> modulo conformal transformations, also called a '''conformal structure'''. Then <math>(M,\bar g)</math> is called a [[w:Riemann surface]]. A Riemann surface is characterized by its topology and its conformal structure. Let us focus on compact Riemann surfaces. Topologically, a compact Riemann surface is characterize by its '''genus''' <math>h\in \mathbb{N}</math>, the number of holes. {| class="wikitable" style="font-size:small; text-align:center;" |- ! Genus <math>h</math> ! Name ! <math>\dim_\mathbb{C} \mathcal{M}_h</math> ! Conformal group |- | 0 | Riemann sphere | <math>0</math> | <math>PSL_2(\mathbb{C})</math> |- | 1 | Torus | 1 | <math>\left(\mathbb{C}/\mathbb{Z}^2\right)\rtimes \text{finite} </math> |- | <math>\geq 2</math> | | <math>3h-3</math> | finite |} == Scale invariance and conformal invariance == == Fixed points of the renormalization group == == Applications == == Exercises == === COGS: The conformal group of flat space === Consider the Euclidean space <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math>, and the Minkowski space <math>\mathbb{R}^{d+1,1}</math> with coordinates <math>Y=\left(y^\mu,y^-,y^+\right)</math> with <math>\mu = 1,2,\dots, d</math> and the flat metric <math>\|dY\|^2 = \sum_{\mu=1}^d \left(dy^\mu\right)^2 -dy^-dy^+ </math>. Consider the diffeormorphisms :<math> \varphi:\left\{\begin{array}{ccl} \mathbb{R}^d & \to & \mathbb{R}^{d+1,1} \\ x^\mu &\mapsto & \left(x^\mu,\|x\|^2,1\right) \end{array}\right. \quad , \quad \psi: \left\{\begin{array}{ccl} \mathbb{R}^{d+1,1} & \to & \mathbb{R}^{d+1,1} \\ Y &\mapsto & \frac{1}{y^+}Y = \left(\frac{y^\mu}{y^+},\frac{y^-}{y^+},1\right) \end{array}\right. </math> # Check that <math>\varphi</math> is an isometry. Is <math>\psi</math> an isometry? Is it a conformal transformation? # Show that the restriction of <math>\psi</math> to the light cone <math>\mathcal{L}=\left\{Y\in \mathbb{R}^{d+1,1}\left| \|Y\|^2 = 0\right.\right\}</math> is a conformal transformation. # Let <math>G\in SO(d+1,1)</math> be an isometry of <math>\mathbb{R}^{d+1,1}</math>, in particular <math>G</math> is linear. Show that <math>\varphi^{-1}\circ \psi \circ G\circ \varphi</math> is a conformal transformation of <math>\mathbb{R}^d</math>. Deduce that the conformal group of <math>\mathbb{R}^d</math> includes <math>SO(d+1,1)</math>. # Explicitly write the action of <math>G\in SO(d+1,1)</math> on <math>x^\mu</math>. [[Category: CFT course]] fde15vr1ma36jb6vej984e7fuwv0mvy 2690241 2690240 2024-12-04T10:44:18Z Sylvain Ribault 2127778 /* Conformal transformations in two dimensions */ 2690241 wikitext text/x-wiki == Conformal invariance == === Conformal transformations === On a given space or spacetime <math>M</math> with coordinates <math>x^\mu</math>, distances are defined using a metric <math>g_{\mu\nu}</math>. In particular, the length of an infinitesimal vector <math>v^\mu</math> is <math>\|v\| = \sqrt{g_{\mu\nu}v^\mu v^\nu}</math>. If we know distances, we can also compute angles. The angle <math>\theta</math> between two infinitesimal vectors <math>v^\mu,w^\mu</math> obeys :<math> \cos\theta = \frac{g_{\mu\nu}v^\mu w^\nu}{\sqrt{g_{\mu\nu}v^\mu v^\nu}\sqrt{ g_{\mu\nu}w^\mu w^\nu}} </math> For <math>f:M\to M</math> a diffeomorphism, we define the [[w:pullback]] <math>f^*g</math> of the metric by :<math> (f^*g)_{\mu\nu} = g_{\rho\sigma}(f(x)) \frac{\partial f^\rho}{\partial x^\mu}\frac{\partial f^\sigma}{\partial x^\nu} </math> equivalently <math>(f*g)_{\mu\nu}(x)dx^\mu dx^\nu = g_{\mu\nu}(f)df^\mu df^\nu</math>. A diffeomorphism <math>f:M\to M</math> is called an '''isometry''' if it preserves distances, equivalently if :<math>f^* g = g</math>. It is called a '''conformal transformation''' if it preserves angles. Any isometry is a conformal transformation, but the converse is not true. For any function <math>\lambda:M\to \mathbb{R}</math>, the metrics <math>g_{\mu\nu}</math> and <math>\lambda g_{\mu\nu}</math> define the same angles. So <math>f</math> is a conformal transformation if it preserve the metric up to a scalar factor, :<math> \exists \lambda,\ f^* g = \lambda g </math> The set of conformal transformations is called the '''conformal group''' associated to <math>M,g</math>. Let us indicate how many functions on <math>M</math> are needed to parametrize the objects <math>\lambda, f,g</math>, if <math>d=\dim(M)</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Object ! Number of functions on <math>M</math> |- | Function <math>\lambda:M\to \mathbb{R}</math> | <math>1</math> |- | Diffeomorphism <math>f:M\to M</math> | <math>d</math> |- | Metric <math>g</math> on <math>M</math> | <math>\frac{d(d+1)}{2}</math> |} Therefore, given two metrics <math>g_1,g_2</math>, the condition <math>f^* g_1 = \lambda g_2</math> that they are conformally equivalent involves <math>\frac{d(d+1)}{2}</math> equations for <math>d+1</math> unknowns. For <math>d\leq 2</math>, there is always a solution (under reasonable assumptions): in particular any metric on <math>\mathbb{R}^2</math> is conformally flat. For <math>d\geq 3</math>, two metrics are in general not equivalent modulo rescaling. Similarly, the size of the conformal group depends on the dimension: * For <math>d=1</math>, any diffeomorphism is conformal. * For <math>d\geq 2</math>, the conformal group depends on <math>M,g</math>, with flat space <math>\mathbb{R}^d</math> having the largest possible group <math>SO(d+1,1)</math>. * For <math>d\geq 3</math>, a generic space has only one conformal transformation: the identity. === Conformal transformations of flat space === The conformal group of <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math> first includes isometries: * Translations. * Rotations. There are also conformal transformations that are not isometries: * Dilations <math>x^\mu \mapsto \lambda x^\mu </math> with <math>\lambda \in \mathbb{R}</math>. * The inversion <math>x^\mu \mapsto \frac{x^\mu}{\|x\|^2}</math>. * Special conformal transformations <math>x^\mu \mapsto \frac{x^\mu - a^\mu \|x\|^2}{1-2a_\mu x^\mu +\|a\|^2\|x\|^2}</math>. These transformations generate the conformal group <math>SO(d+1,1)</math>. === Conformal symmetry and gravitation === In a theory of gravitation such as general relativity, the metric is not fixed, it is a dynamical object. We can therefore combine diffeomorphisms with changes of the metric. In particular, if we combine a diffeomorphism <math>f</math> with <math>g\mapsto f^*g</math>, we obtain a '''change of coordinates''', which should leave the physics invariant. By definition, modulo a change of coordinates, a conformal transformation amounts to a '''Weyl transformation''' of the metric <math>g\mapsto \lambda g</math>. For gravitational theories, conformal invariance is equivalent to Weyl invariance. General relativity is Weyl invariant for <math>d=2</math> only. It follows that in <math>d=2</math>, any field theory of quantum gravity must be a conformal field theory. Moreover, since any metric is conformally flat, we may replace the 3 components of the metric <math>g_{\mu\nu}</math> with the conformal factor <math>\lambda</math>: only 1 bosonic field. Einstein's equation for <math>g_{\mu\nu}</math> then reduces to the Liouville equation for <math>\log \lambda</math>. The Liouville equation is the classical equation of motion of [[w:Liouville theory]]: a solvable CFT that we will study in this course. Therefore, we can build field theories of gravity called '''Liouville gravity''' based on Liouville theory. (There are several possible theories, depending on the matter contents.) String theory is a theoretical framework that generalizes quantum field theory, and includes quantum theories of gravity. The basic idea is to describe physics in a spacetime <math>Z</math> using a <math>d=2</math> worldsheet <math>M</math> and an embedding <math>X:M\to Z</math>. The metric on <math>Z</math> induces a metric on <math>M</math>, but it is convenient to allow the worldsheet metric <math>g</math> to be an independent dynamical object, unrelated to the induced metric. Nevertheless, the physics should not depend on <math>g</math>. It is possible to fix 2 of the 3 components of <math>g</math> using a change of coordinates on <math>M</math>, and to get <math>g</math>-independence we also have to take care of the third component, by assuming Weyl invariance. This is why the worldsheet description of string theory uses <math>d=2</math> CFT. String theory provides another motivation for CFT in arbitrary <math>d</math> due to the AdS/CFT correspondence: a holographic relation between a string theory in a <math>d+1</math>-dimensional Anti-de Sitter space, and a CFT in <math>d</math> dimensions. In fact the correspondence can be generalized to non-AdS spaces, which then correspond to non-conformal field theories. Nevertheless, the correspondencs is simplest in the AdS/CFT case. === Conformal transformations in two dimensions === Let <math>M</math> be a two-dimensional connected, oriented manifold. A metric <math>g</math> on <math>M</math> is called Riemannian if it is positive definite. Let <math>\bar g</math> be the equivalence class of <math>g</math> modulo conformal transformations, also called a '''conformal structure'''. Then <math>(M,\bar g)</math> is called a [[w:Riemann surface]]. A Riemann surface is characterized by its topology and its conformal structure. Let us focus on compact Riemann surfaces. Topologically, a compact Riemann surface is characterize by its '''genus''' <math>h\in \mathbb{N}</math>, the number of holes. For a given genus, there is a finite-dimensional '''moduli space''' <math>\mathcal{M}_h</math> of Riemann surfaces. Each Riemann surface comes with its own conformal group, which does not depend only on <math>h</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Genus <math>h</math> ! Name ! <math>\dim_\mathbb{C} \mathcal{M}_h</math> ! Conformal group |- | 0 | Riemann sphere | <math>0</math> | <math>PSL_2(\mathbb{C})</math> |- | 1 | Torus | 1 | <math>\left(\mathbb{C}/\mathbb{Z}^2\right)\rtimes \text{finite} </math> |- | <math>\geq 2</math> | | <math>3h-3</math> | finite |} == Scale invariance and conformal invariance == == Fixed points of the renormalization group == == Applications == == Exercises == === COGS: The conformal group of flat space === Consider the Euclidean space <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math>, and the Minkowski space <math>\mathbb{R}^{d+1,1}</math> with coordinates <math>Y=\left(y^\mu,y^-,y^+\right)</math> with <math>\mu = 1,2,\dots, d</math> and the flat metric <math>\|dY\|^2 = \sum_{\mu=1}^d \left(dy^\mu\right)^2 -dy^-dy^+ </math>. Consider the diffeormorphisms :<math> \varphi:\left\{\begin{array}{ccl} \mathbb{R}^d & \to & \mathbb{R}^{d+1,1} \\ x^\mu &\mapsto & \left(x^\mu,\|x\|^2,1\right) \end{array}\right. \quad , \quad \psi: \left\{\begin{array}{ccl} \mathbb{R}^{d+1,1} & \to & \mathbb{R}^{d+1,1} \\ Y &\mapsto & \frac{1}{y^+}Y = \left(\frac{y^\mu}{y^+},\frac{y^-}{y^+},1\right) \end{array}\right. </math> # Check that <math>\varphi</math> is an isometry. Is <math>\psi</math> an isometry? Is it a conformal transformation? # Show that the restriction of <math>\psi</math> to the light cone <math>\mathcal{L}=\left\{Y\in \mathbb{R}^{d+1,1}\left| \|Y\|^2 = 0\right.\right\}</math> is a conformal transformation. # Let <math>G\in SO(d+1,1)</math> be an isometry of <math>\mathbb{R}^{d+1,1}</math>, in particular <math>G</math> is linear. Show that <math>\varphi^{-1}\circ \psi \circ G\circ \varphi</math> is a conformal transformation of <math>\mathbb{R}^d</math>. Deduce that the conformal group of <math>\mathbb{R}^d</math> includes <math>SO(d+1,1)</math>. # Explicitly write the action of <math>G\in SO(d+1,1)</math> on <math>x^\mu</math>. [[Category: CFT course]] h74g1ejbyqb15meaf6u92ygvjsdqo9a 2690242 2690241 2024-12-04T10:45:38Z Sylvain Ribault 2127778 /* Conformal transformations in two dimensions */ 2690242 wikitext text/x-wiki == Conformal invariance == === Conformal transformations === On a given space or spacetime <math>M</math> with coordinates <math>x^\mu</math>, distances are defined using a metric <math>g_{\mu\nu}</math>. In particular, the length of an infinitesimal vector <math>v^\mu</math> is <math>\|v\| = \sqrt{g_{\mu\nu}v^\mu v^\nu}</math>. If we know distances, we can also compute angles. The angle <math>\theta</math> between two infinitesimal vectors <math>v^\mu,w^\mu</math> obeys :<math> \cos\theta = \frac{g_{\mu\nu}v^\mu w^\nu}{\sqrt{g_{\mu\nu}v^\mu v^\nu}\sqrt{ g_{\mu\nu}w^\mu w^\nu}} </math> For <math>f:M\to M</math> a diffeomorphism, we define the [[w:pullback]] <math>f^*g</math> of the metric by :<math> (f^*g)_{\mu\nu} = g_{\rho\sigma}(f(x)) \frac{\partial f^\rho}{\partial x^\mu}\frac{\partial f^\sigma}{\partial x^\nu} </math> equivalently <math>(f*g)_{\mu\nu}(x)dx^\mu dx^\nu = g_{\mu\nu}(f)df^\mu df^\nu</math>. A diffeomorphism <math>f:M\to M</math> is called an '''isometry''' if it preserves distances, equivalently if :<math>f^* g = g</math>. It is called a '''conformal transformation''' if it preserves angles. Any isometry is a conformal transformation, but the converse is not true. For any function <math>\lambda:M\to \mathbb{R}</math>, the metrics <math>g_{\mu\nu}</math> and <math>\lambda g_{\mu\nu}</math> define the same angles. So <math>f</math> is a conformal transformation if it preserve the metric up to a scalar factor, :<math> \exists \lambda,\ f^* g = \lambda g </math> The set of conformal transformations is called the '''conformal group''' associated to <math>M,g</math>. Let us indicate how many functions on <math>M</math> are needed to parametrize the objects <math>\lambda, f,g</math>, if <math>d=\dim(M)</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Object ! Number of functions on <math>M</math> |- | Function <math>\lambda:M\to \mathbb{R}</math> | <math>1</math> |- | Diffeomorphism <math>f:M\to M</math> | <math>d</math> |- | Metric <math>g</math> on <math>M</math> | <math>\frac{d(d+1)}{2}</math> |} Therefore, given two metrics <math>g_1,g_2</math>, the condition <math>f^* g_1 = \lambda g_2</math> that they are conformally equivalent involves <math>\frac{d(d+1)}{2}</math> equations for <math>d+1</math> unknowns. For <math>d\leq 2</math>, there is always a solution (under reasonable assumptions): in particular any metric on <math>\mathbb{R}^2</math> is conformally flat. For <math>d\geq 3</math>, two metrics are in general not equivalent modulo rescaling. Similarly, the size of the conformal group depends on the dimension: * For <math>d=1</math>, any diffeomorphism is conformal. * For <math>d\geq 2</math>, the conformal group depends on <math>M,g</math>, with flat space <math>\mathbb{R}^d</math> having the largest possible group <math>SO(d+1,1)</math>. * For <math>d\geq 3</math>, a generic space has only one conformal transformation: the identity. === Conformal transformations of flat space === The conformal group of <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math> first includes isometries: * Translations. * Rotations. There are also conformal transformations that are not isometries: * Dilations <math>x^\mu \mapsto \lambda x^\mu </math> with <math>\lambda \in \mathbb{R}</math>. * The inversion <math>x^\mu \mapsto \frac{x^\mu}{\|x\|^2}</math>. * Special conformal transformations <math>x^\mu \mapsto \frac{x^\mu - a^\mu \|x\|^2}{1-2a_\mu x^\mu +\|a\|^2\|x\|^2}</math>. These transformations generate the conformal group <math>SO(d+1,1)</math>. === Conformal symmetry and gravitation === In a theory of gravitation such as general relativity, the metric is not fixed, it is a dynamical object. We can therefore combine diffeomorphisms with changes of the metric. In particular, if we combine a diffeomorphism <math>f</math> with <math>g\mapsto f^*g</math>, we obtain a '''change of coordinates''', which should leave the physics invariant. By definition, modulo a change of coordinates, a conformal transformation amounts to a '''Weyl transformation''' of the metric <math>g\mapsto \lambda g</math>. For gravitational theories, conformal invariance is equivalent to Weyl invariance. General relativity is Weyl invariant for <math>d=2</math> only. It follows that in <math>d=2</math>, any field theory of quantum gravity must be a conformal field theory. Moreover, since any metric is conformally flat, we may replace the 3 components of the metric <math>g_{\mu\nu}</math> with the conformal factor <math>\lambda</math>: only 1 bosonic field. Einstein's equation for <math>g_{\mu\nu}</math> then reduces to the Liouville equation for <math>\log \lambda</math>. The Liouville equation is the classical equation of motion of [[w:Liouville theory]]: a solvable CFT that we will study in this course. Therefore, we can build field theories of gravity called '''Liouville gravity''' based on Liouville theory. (There are several possible theories, depending on the matter contents.) String theory is a theoretical framework that generalizes quantum field theory, and includes quantum theories of gravity. The basic idea is to describe physics in a spacetime <math>Z</math> using a <math>d=2</math> worldsheet <math>M</math> and an embedding <math>X:M\to Z</math>. The metric on <math>Z</math> induces a metric on <math>M</math>, but it is convenient to allow the worldsheet metric <math>g</math> to be an independent dynamical object, unrelated to the induced metric. Nevertheless, the physics should not depend on <math>g</math>. It is possible to fix 2 of the 3 components of <math>g</math> using a change of coordinates on <math>M</math>, and to get <math>g</math>-independence we also have to take care of the third component, by assuming Weyl invariance. This is why the worldsheet description of string theory uses <math>d=2</math> CFT. String theory provides another motivation for CFT in arbitrary <math>d</math> due to the AdS/CFT correspondence: a holographic relation between a string theory in a <math>d+1</math>-dimensional Anti-de Sitter space, and a CFT in <math>d</math> dimensions. In fact the correspondence can be generalized to non-AdS spaces, which then correspond to non-conformal field theories. Nevertheless, the correspondencs is simplest in the AdS/CFT case. === Conformal transformations in two dimensions === Let <math>M</math> be a two-dimensional connected, oriented manifold. A metric <math>g</math> on <math>M</math> is called Riemannian if it is positive definite. Let <math>\bar g</math> be the equivalence class of <math>g</math> modulo conformal transformations, also called a '''conformal structure'''. Then <math>(M,\bar g)</math> is called a [[w:Riemann surface]]. A Riemann surface is characterized by its topology and its conformal structure. Let us focus on compact Riemann surfaces. Topologically, a compact Riemann surface is characterize by its '''genus''' <math>h\in \mathbb{N}</math>, the number of holes. For a given genus, there is a finite-dimensional '''moduli space''' <math>\mathcal{M}_h</math> of Riemann surfaces. The conformal group of a Riemann surface depends on <math>h</math> and also on the surface: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Genus <math>h</math> ! Name ! <math>\dim_\mathbb{C} \mathcal{M}_h</math> ! Conformal group |- | 0 | Riemann sphere | <math>0</math> | <math>PSL_2(\mathbb{C})</math> |- | 1 | Torus | 1 | <math>\left(\mathbb{C}/\mathbb{Z}^2\right)\rtimes \text{finite} </math> |- | <math>\geq 2</math> | | <math>3h-3</math> | finite |} == Scale invariance and conformal invariance == == Fixed points of the renormalization group == == Applications == == Exercises == === COGS: The conformal group of flat space === Consider the Euclidean space <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math>, and the Minkowski space <math>\mathbb{R}^{d+1,1}</math> with coordinates <math>Y=\left(y^\mu,y^-,y^+\right)</math> with <math>\mu = 1,2,\dots, d</math> and the flat metric <math>\|dY\|^2 = \sum_{\mu=1}^d \left(dy^\mu\right)^2 -dy^-dy^+ </math>. Consider the diffeormorphisms :<math> \varphi:\left\{\begin{array}{ccl} \mathbb{R}^d & \to & \mathbb{R}^{d+1,1} \\ x^\mu &\mapsto & \left(x^\mu,\|x\|^2,1\right) \end{array}\right. \quad , \quad \psi: \left\{\begin{array}{ccl} \mathbb{R}^{d+1,1} & \to & \mathbb{R}^{d+1,1} \\ Y &\mapsto & \frac{1}{y^+}Y = \left(\frac{y^\mu}{y^+},\frac{y^-}{y^+},1\right) \end{array}\right. </math> # Check that <math>\varphi</math> is an isometry. Is <math>\psi</math> an isometry? Is it a conformal transformation? # Show that the restriction of <math>\psi</math> to the light cone <math>\mathcal{L}=\left\{Y\in \mathbb{R}^{d+1,1}\left| \|Y\|^2 = 0\right.\right\}</math> is a conformal transformation. # Let <math>G\in SO(d+1,1)</math> be an isometry of <math>\mathbb{R}^{d+1,1}</math>, in particular <math>G</math> is linear. Show that <math>\varphi^{-1}\circ \psi \circ G\circ \varphi</math> is a conformal transformation of <math>\mathbb{R}^d</math>. Deduce that the conformal group of <math>\mathbb{R}^d</math> includes <math>SO(d+1,1)</math>. # Explicitly write the action of <math>G\in SO(d+1,1)</math> on <math>x^\mu</math>. [[Category: CFT course]] joii6shi7q4p0nqmubrdnru1grolauh 2690243 2690242 2024-12-04T10:51:06Z Sylvain Ribault 2127778 /* Conformal transformations in two dimensions */ 2690243 wikitext text/x-wiki == Conformal invariance == === Conformal transformations === On a given space or spacetime <math>M</math> with coordinates <math>x^\mu</math>, distances are defined using a metric <math>g_{\mu\nu}</math>. In particular, the length of an infinitesimal vector <math>v^\mu</math> is <math>\|v\| = \sqrt{g_{\mu\nu}v^\mu v^\nu}</math>. If we know distances, we can also compute angles. The angle <math>\theta</math> between two infinitesimal vectors <math>v^\mu,w^\mu</math> obeys :<math> \cos\theta = \frac{g_{\mu\nu}v^\mu w^\nu}{\sqrt{g_{\mu\nu}v^\mu v^\nu}\sqrt{ g_{\mu\nu}w^\mu w^\nu}} </math> For <math>f:M\to M</math> a diffeomorphism, we define the [[w:pullback]] <math>f^*g</math> of the metric by :<math> (f^*g)_{\mu\nu} = g_{\rho\sigma}(f(x)) \frac{\partial f^\rho}{\partial x^\mu}\frac{\partial f^\sigma}{\partial x^\nu} </math> equivalently <math>(f*g)_{\mu\nu}(x)dx^\mu dx^\nu = g_{\mu\nu}(f)df^\mu df^\nu</math>. A diffeomorphism <math>f:M\to M</math> is called an '''isometry''' if it preserves distances, equivalently if :<math>f^* g = g</math>. It is called a '''conformal transformation''' if it preserves angles. Any isometry is a conformal transformation, but the converse is not true. For any function <math>\lambda:M\to \mathbb{R}</math>, the metrics <math>g_{\mu\nu}</math> and <math>\lambda g_{\mu\nu}</math> define the same angles. So <math>f</math> is a conformal transformation if it preserve the metric up to a scalar factor, :<math> \exists \lambda,\ f^* g = \lambda g </math> The set of conformal transformations is called the '''conformal group''' associated to <math>M,g</math>. Let us indicate how many functions on <math>M</math> are needed to parametrize the objects <math>\lambda, f,g</math>, if <math>d=\dim(M)</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Object ! Number of functions on <math>M</math> |- | Function <math>\lambda:M\to \mathbb{R}</math> | <math>1</math> |- | Diffeomorphism <math>f:M\to M</math> | <math>d</math> |- | Metric <math>g</math> on <math>M</math> | <math>\frac{d(d+1)}{2}</math> |} Therefore, given two metrics <math>g_1,g_2</math>, the condition <math>f^* g_1 = \lambda g_2</math> that they are conformally equivalent involves <math>\frac{d(d+1)}{2}</math> equations for <math>d+1</math> unknowns. For <math>d\leq 2</math>, there is always a solution (under reasonable assumptions): in particular any metric on <math>\mathbb{R}^2</math> is conformally flat. For <math>d\geq 3</math>, two metrics are in general not equivalent modulo rescaling. Similarly, the size of the conformal group depends on the dimension: * For <math>d=1</math>, any diffeomorphism is conformal. * For <math>d\geq 2</math>, the conformal group depends on <math>M,g</math>, with flat space <math>\mathbb{R}^d</math> having the largest possible group <math>SO(d+1,1)</math>. * For <math>d\geq 3</math>, a generic space has only one conformal transformation: the identity. === Conformal transformations of flat space === The conformal group of <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math> first includes isometries: * Translations. * Rotations. There are also conformal transformations that are not isometries: * Dilations <math>x^\mu \mapsto \lambda x^\mu </math> with <math>\lambda \in \mathbb{R}</math>. * The inversion <math>x^\mu \mapsto \frac{x^\mu}{\|x\|^2}</math>. * Special conformal transformations <math>x^\mu \mapsto \frac{x^\mu - a^\mu \|x\|^2}{1-2a_\mu x^\mu +\|a\|^2\|x\|^2}</math>. These transformations generate the conformal group <math>SO(d+1,1)</math>. === Conformal symmetry and gravitation === In a theory of gravitation such as general relativity, the metric is not fixed, it is a dynamical object. We can therefore combine diffeomorphisms with changes of the metric. In particular, if we combine a diffeomorphism <math>f</math> with <math>g\mapsto f^*g</math>, we obtain a '''change of coordinates''', which should leave the physics invariant. By definition, modulo a change of coordinates, a conformal transformation amounts to a '''Weyl transformation''' of the metric <math>g\mapsto \lambda g</math>. For gravitational theories, conformal invariance is equivalent to Weyl invariance. General relativity is Weyl invariant for <math>d=2</math> only. It follows that in <math>d=2</math>, any field theory of quantum gravity must be a conformal field theory. Moreover, since any metric is conformally flat, we may replace the 3 components of the metric <math>g_{\mu\nu}</math> with the conformal factor <math>\lambda</math>: only 1 bosonic field. Einstein's equation for <math>g_{\mu\nu}</math> then reduces to the Liouville equation for <math>\log \lambda</math>. The Liouville equation is the classical equation of motion of [[w:Liouville theory]]: a solvable CFT that we will study in this course. Therefore, we can build field theories of gravity called '''Liouville gravity''' based on Liouville theory. (There are several possible theories, depending on the matter contents.) String theory is a theoretical framework that generalizes quantum field theory, and includes quantum theories of gravity. The basic idea is to describe physics in a spacetime <math>Z</math> using a <math>d=2</math> worldsheet <math>M</math> and an embedding <math>X:M\to Z</math>. The metric on <math>Z</math> induces a metric on <math>M</math>, but it is convenient to allow the worldsheet metric <math>g</math> to be an independent dynamical object, unrelated to the induced metric. Nevertheless, the physics should not depend on <math>g</math>. It is possible to fix 2 of the 3 components of <math>g</math> using a change of coordinates on <math>M</math>, and to get <math>g</math>-independence we also have to take care of the third component, by assuming Weyl invariance. This is why the worldsheet description of string theory uses <math>d=2</math> CFT. String theory provides another motivation for CFT in arbitrary <math>d</math> due to the AdS/CFT correspondence: a holographic relation between a string theory in a <math>d+1</math>-dimensional Anti-de Sitter space, and a CFT in <math>d</math> dimensions. In fact the correspondence can be generalized to non-AdS spaces, which then correspond to non-conformal field theories. Nevertheless, the correspondencs is simplest in the AdS/CFT case. === Conformal transformations in two dimensions === Let <math>M</math> be a two-dimensional connected, oriented manifold. A metric <math>g</math> on <math>M</math> is called Riemannian if it is positive definite. Let <math>\bar g</math> be the equivalence class of <math>g</math> modulo conformal transformations, also called a '''conformal structure'''. Then <math>(M,\bar g)</math> is called a [[w:Riemann surface]]. A Riemann surface is characterized by its topology and its conformal structure. Let us focus on compact Riemann surfaces. Topologically, a compact Riemann surface is characterize by its '''genus''' <math>h\in \mathbb{N}</math>, the number of holes. For a given genus, there is a finite-dimensional '''moduli space''' <math>\mathcal{M}_h</math> of Riemann surfaces. The conformal group of a Riemann surface depends on <math>h</math> and also on the surface: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Genus <math>h</math> ! Name ! <math>\dim_\mathbb{C} \mathcal{M}_h</math> ! Conformal group |- | 0 | Riemann sphere | <math>0</math> | <math>PSL_2(\mathbb{C})</math> |- | 1 | Torus | 1 | <math>\left(\mathbb{C}/\mathbb{Z}^2\right)\rtimes \text{finite} </math> |- | <math>\geq 2</math> | | <math>3h-3</math> | finite |} * The Riemann sphere is conveniently parametrized by a complex coordinate <math>z\in\mathbb{C}\cup \{\infty\}</math>. Its moduli space is trivial, i.e. all genus 0 Riemann surfaces are conformally equivalent. The conformal group is the Möbius group <math>PSL_2(\mathbb{C})</math>, which acts as :<math> z\mapsto \frac{az+b}{cz+d} \quad \text{for}\quad \left(\begin{smallmatrix} a & b\\ c& d \end{smallmatrix}\right) \in PSL_2(\mathbb{C}) </math> == Scale invariance and conformal invariance == == Fixed points of the renormalization group == == Applications == == Exercises == === COGS: The conformal group of flat space === Consider the Euclidean space <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math>, and the Minkowski space <math>\mathbb{R}^{d+1,1}</math> with coordinates <math>Y=\left(y^\mu,y^-,y^+\right)</math> with <math>\mu = 1,2,\dots, d</math> and the flat metric <math>\|dY\|^2 = \sum_{\mu=1}^d \left(dy^\mu\right)^2 -dy^-dy^+ </math>. Consider the diffeormorphisms :<math> \varphi:\left\{\begin{array}{ccl} \mathbb{R}^d & \to & \mathbb{R}^{d+1,1} \\ x^\mu &\mapsto & \left(x^\mu,\|x\|^2,1\right) \end{array}\right. \quad , \quad \psi: \left\{\begin{array}{ccl} \mathbb{R}^{d+1,1} & \to & \mathbb{R}^{d+1,1} \\ Y &\mapsto & \frac{1}{y^+}Y = \left(\frac{y^\mu}{y^+},\frac{y^-}{y^+},1\right) \end{array}\right. </math> # Check that <math>\varphi</math> is an isometry. Is <math>\psi</math> an isometry? Is it a conformal transformation? # Show that the restriction of <math>\psi</math> to the light cone <math>\mathcal{L}=\left\{Y\in \mathbb{R}^{d+1,1}\left| \|Y\|^2 = 0\right.\right\}</math> is a conformal transformation. # Let <math>G\in SO(d+1,1)</math> be an isometry of <math>\mathbb{R}^{d+1,1}</math>, in particular <math>G</math> is linear. Show that <math>\varphi^{-1}\circ \psi \circ G\circ \varphi</math> is a conformal transformation of <math>\mathbb{R}^d</math>. Deduce that the conformal group of <math>\mathbb{R}^d</math> includes <math>SO(d+1,1)</math>. # Explicitly write the action of <math>G\in SO(d+1,1)</math> on <math>x^\mu</math>. [[Category: CFT course]] lerzg1qqm9zzueh0ycsguu45tyrspiq 2690244 2690243 2024-12-04T10:51:49Z Sylvain Ribault 2127778 /* Conformal transformations in two dimensions */ 2690244 wikitext text/x-wiki == Conformal invariance == === Conformal transformations === On a given space or spacetime <math>M</math> with coordinates <math>x^\mu</math>, distances are defined using a metric <math>g_{\mu\nu}</math>. In particular, the length of an infinitesimal vector <math>v^\mu</math> is <math>\|v\| = \sqrt{g_{\mu\nu}v^\mu v^\nu}</math>. If we know distances, we can also compute angles. The angle <math>\theta</math> between two infinitesimal vectors <math>v^\mu,w^\mu</math> obeys :<math> \cos\theta = \frac{g_{\mu\nu}v^\mu w^\nu}{\sqrt{g_{\mu\nu}v^\mu v^\nu}\sqrt{ g_{\mu\nu}w^\mu w^\nu}} </math> For <math>f:M\to M</math> a diffeomorphism, we define the [[w:pullback]] <math>f^*g</math> of the metric by :<math> (f^*g)_{\mu\nu} = g_{\rho\sigma}(f(x)) \frac{\partial f^\rho}{\partial x^\mu}\frac{\partial f^\sigma}{\partial x^\nu} </math> equivalently <math>(f*g)_{\mu\nu}(x)dx^\mu dx^\nu = g_{\mu\nu}(f)df^\mu df^\nu</math>. A diffeomorphism <math>f:M\to M</math> is called an '''isometry''' if it preserves distances, equivalently if :<math>f^* g = g</math>. It is called a '''conformal transformation''' if it preserves angles. Any isometry is a conformal transformation, but the converse is not true. For any function <math>\lambda:M\to \mathbb{R}</math>, the metrics <math>g_{\mu\nu}</math> and <math>\lambda g_{\mu\nu}</math> define the same angles. So <math>f</math> is a conformal transformation if it preserve the metric up to a scalar factor, :<math> \exists \lambda,\ f^* g = \lambda g </math> The set of conformal transformations is called the '''conformal group''' associated to <math>M,g</math>. Let us indicate how many functions on <math>M</math> are needed to parametrize the objects <math>\lambda, f,g</math>, if <math>d=\dim(M)</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Object ! Number of functions on <math>M</math> |- | Function <math>\lambda:M\to \mathbb{R}</math> | <math>1</math> |- | Diffeomorphism <math>f:M\to M</math> | <math>d</math> |- | Metric <math>g</math> on <math>M</math> | <math>\frac{d(d+1)}{2}</math> |} Therefore, given two metrics <math>g_1,g_2</math>, the condition <math>f^* g_1 = \lambda g_2</math> that they are conformally equivalent involves <math>\frac{d(d+1)}{2}</math> equations for <math>d+1</math> unknowns. For <math>d\leq 2</math>, there is always a solution (under reasonable assumptions): in particular any metric on <math>\mathbb{R}^2</math> is conformally flat. For <math>d\geq 3</math>, two metrics are in general not equivalent modulo rescaling. Similarly, the size of the conformal group depends on the dimension: * For <math>d=1</math>, any diffeomorphism is conformal. * For <math>d\geq 2</math>, the conformal group depends on <math>M,g</math>, with flat space <math>\mathbb{R}^d</math> having the largest possible group <math>SO(d+1,1)</math>. * For <math>d\geq 3</math>, a generic space has only one conformal transformation: the identity. === Conformal transformations of flat space === The conformal group of <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math> first includes isometries: * Translations. * Rotations. There are also conformal transformations that are not isometries: * Dilations <math>x^\mu \mapsto \lambda x^\mu </math> with <math>\lambda \in \mathbb{R}</math>. * The inversion <math>x^\mu \mapsto \frac{x^\mu}{\|x\|^2}</math>. * Special conformal transformations <math>x^\mu \mapsto \frac{x^\mu - a^\mu \|x\|^2}{1-2a_\mu x^\mu +\|a\|^2\|x\|^2}</math>. These transformations generate the conformal group <math>SO(d+1,1)</math>. === Conformal symmetry and gravitation === In a theory of gravitation such as general relativity, the metric is not fixed, it is a dynamical object. We can therefore combine diffeomorphisms with changes of the metric. In particular, if we combine a diffeomorphism <math>f</math> with <math>g\mapsto f^*g</math>, we obtain a '''change of coordinates''', which should leave the physics invariant. By definition, modulo a change of coordinates, a conformal transformation amounts to a '''Weyl transformation''' of the metric <math>g\mapsto \lambda g</math>. For gravitational theories, conformal invariance is equivalent to Weyl invariance. General relativity is Weyl invariant for <math>d=2</math> only. It follows that in <math>d=2</math>, any field theory of quantum gravity must be a conformal field theory. Moreover, since any metric is conformally flat, we may replace the 3 components of the metric <math>g_{\mu\nu}</math> with the conformal factor <math>\lambda</math>: only 1 bosonic field. Einstein's equation for <math>g_{\mu\nu}</math> then reduces to the Liouville equation for <math>\log \lambda</math>. The Liouville equation is the classical equation of motion of [[w:Liouville theory]]: a solvable CFT that we will study in this course. Therefore, we can build field theories of gravity called '''Liouville gravity''' based on Liouville theory. (There are several possible theories, depending on the matter contents.) String theory is a theoretical framework that generalizes quantum field theory, and includes quantum theories of gravity. The basic idea is to describe physics in a spacetime <math>Z</math> using a <math>d=2</math> worldsheet <math>M</math> and an embedding <math>X:M\to Z</math>. The metric on <math>Z</math> induces a metric on <math>M</math>, but it is convenient to allow the worldsheet metric <math>g</math> to be an independent dynamical object, unrelated to the induced metric. Nevertheless, the physics should not depend on <math>g</math>. It is possible to fix 2 of the 3 components of <math>g</math> using a change of coordinates on <math>M</math>, and to get <math>g</math>-independence we also have to take care of the third component, by assuming Weyl invariance. This is why the worldsheet description of string theory uses <math>d=2</math> CFT. String theory provides another motivation for CFT in arbitrary <math>d</math> due to the AdS/CFT correspondence: a holographic relation between a string theory in a <math>d+1</math>-dimensional Anti-de Sitter space, and a CFT in <math>d</math> dimensions. In fact the correspondence can be generalized to non-AdS spaces, which then correspond to non-conformal field theories. Nevertheless, the correspondencs is simplest in the AdS/CFT case. === Conformal transformations in two dimensions === Let <math>M</math> be a two-dimensional connected, oriented manifold. A metric <math>g</math> on <math>M</math> is called Riemannian if it is positive definite. Let <math>\bar g</math> be the equivalence class of <math>g</math> modulo conformal transformations, also called a '''conformal structure'''. Then <math>(M,\bar g)</math> is called a [[w:Riemann surface]]. A Riemann surface is characterized by its topology and its conformal structure. Let us focus on compact Riemann surfaces. Topologically, a compact Riemann surface is characterize by its '''genus''' <math>h\in \mathbb{N}</math>, the number of holes. For a given genus, there is a finite-dimensional '''moduli space''' <math>\mathcal{M}_h</math> of Riemann surfaces. The conformal group of a Riemann surface depends on <math>h</math> and also on the surface: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Genus <math>h</math> ! Name ! <math>\dim_\mathbb{C} \mathcal{M}_h</math> ! Conformal group |- | 0 | Riemann sphere | <math>0</math> | <math>PSL_2(\mathbb{C})</math> |- | 1 | Torus | 1 | <math>\left(\mathbb{C}/\mathbb{Z}^2\right)\rtimes \text{finite} </math> |- | <math>\geq 2</math> | | <math>3h-3</math> | finite |} * The Riemann sphere is conveniently parametrized by a complex coordinate <math>z\in\mathbb{C}\cup \{\infty\}</math>. Its moduli space is trivial, i.e. all genus 0 Riemann surfaces are conformally equivalent. The conformal group is the Möbius group <math>PSL_2(\mathbb{C})</math>, which acts as :<math> z\mapsto \frac{az+b}{cz+d} \qquad \text{for}\qquad \left(\begin{array}{cc} a & b\\ c& d \end{array}\right) \in PSL_2(\mathbb{C}) </math> == Scale invariance and conformal invariance == == Fixed points of the renormalization group == == Applications == == Exercises == === COGS: The conformal group of flat space === Consider the Euclidean space <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math>, and the Minkowski space <math>\mathbb{R}^{d+1,1}</math> with coordinates <math>Y=\left(y^\mu,y^-,y^+\right)</math> with <math>\mu = 1,2,\dots, d</math> and the flat metric <math>\|dY\|^2 = \sum_{\mu=1}^d \left(dy^\mu\right)^2 -dy^-dy^+ </math>. Consider the diffeormorphisms :<math> \varphi:\left\{\begin{array}{ccl} \mathbb{R}^d & \to & \mathbb{R}^{d+1,1} \\ x^\mu &\mapsto & \left(x^\mu,\|x\|^2,1\right) \end{array}\right. \quad , \quad \psi: \left\{\begin{array}{ccl} \mathbb{R}^{d+1,1} & \to & \mathbb{R}^{d+1,1} \\ Y &\mapsto & \frac{1}{y^+}Y = \left(\frac{y^\mu}{y^+},\frac{y^-}{y^+},1\right) \end{array}\right. </math> # Check that <math>\varphi</math> is an isometry. Is <math>\psi</math> an isometry? Is it a conformal transformation? # Show that the restriction of <math>\psi</math> to the light cone <math>\mathcal{L}=\left\{Y\in \mathbb{R}^{d+1,1}\left| \|Y\|^2 = 0\right.\right\}</math> is a conformal transformation. # Let <math>G\in SO(d+1,1)</math> be an isometry of <math>\mathbb{R}^{d+1,1}</math>, in particular <math>G</math> is linear. Show that <math>\varphi^{-1}\circ \psi \circ G\circ \varphi</math> is a conformal transformation of <math>\mathbb{R}^d</math>. Deduce that the conformal group of <math>\mathbb{R}^d</math> includes <math>SO(d+1,1)</math>. # Explicitly write the action of <math>G\in SO(d+1,1)</math> on <math>x^\mu</math>. [[Category: CFT course]] 61s9bhutghb10sxgjw8xgr4w0d18scc 2690245 2690244 2024-12-04T11:01:22Z Sylvain Ribault 2127778 /* Conformal transformations in two dimensions */ 2690245 wikitext text/x-wiki == Conformal invariance == === Conformal transformations === On a given space or spacetime <math>M</math> with coordinates <math>x^\mu</math>, distances are defined using a metric <math>g_{\mu\nu}</math>. In particular, the length of an infinitesimal vector <math>v^\mu</math> is <math>\|v\| = \sqrt{g_{\mu\nu}v^\mu v^\nu}</math>. If we know distances, we can also compute angles. The angle <math>\theta</math> between two infinitesimal vectors <math>v^\mu,w^\mu</math> obeys :<math> \cos\theta = \frac{g_{\mu\nu}v^\mu w^\nu}{\sqrt{g_{\mu\nu}v^\mu v^\nu}\sqrt{ g_{\mu\nu}w^\mu w^\nu}} </math> For <math>f:M\to M</math> a diffeomorphism, we define the [[w:pullback]] <math>f^*g</math> of the metric by :<math> (f^*g)_{\mu\nu} = g_{\rho\sigma}(f(x)) \frac{\partial f^\rho}{\partial x^\mu}\frac{\partial f^\sigma}{\partial x^\nu} </math> equivalently <math>(f*g)_{\mu\nu}(x)dx^\mu dx^\nu = g_{\mu\nu}(f)df^\mu df^\nu</math>. A diffeomorphism <math>f:M\to M</math> is called an '''isometry''' if it preserves distances, equivalently if :<math>f^* g = g</math>. It is called a '''conformal transformation''' if it preserves angles. Any isometry is a conformal transformation, but the converse is not true. For any function <math>\lambda:M\to \mathbb{R}</math>, the metrics <math>g_{\mu\nu}</math> and <math>\lambda g_{\mu\nu}</math> define the same angles. So <math>f</math> is a conformal transformation if it preserve the metric up to a scalar factor, :<math> \exists \lambda,\ f^* g = \lambda g </math> The set of conformal transformations is called the '''conformal group''' associated to <math>M,g</math>. Let us indicate how many functions on <math>M</math> are needed to parametrize the objects <math>\lambda, f,g</math>, if <math>d=\dim(M)</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Object ! Number of functions on <math>M</math> |- | Function <math>\lambda:M\to \mathbb{R}</math> | <math>1</math> |- | Diffeomorphism <math>f:M\to M</math> | <math>d</math> |- | Metric <math>g</math> on <math>M</math> | <math>\frac{d(d+1)}{2}</math> |} Therefore, given two metrics <math>g_1,g_2</math>, the condition <math>f^* g_1 = \lambda g_2</math> that they are conformally equivalent involves <math>\frac{d(d+1)}{2}</math> equations for <math>d+1</math> unknowns. For <math>d\leq 2</math>, there is always a solution (under reasonable assumptions): in particular any metric on <math>\mathbb{R}^2</math> is conformally flat. For <math>d\geq 3</math>, two metrics are in general not equivalent modulo rescaling. Similarly, the size of the conformal group depends on the dimension: * For <math>d=1</math>, any diffeomorphism is conformal. * For <math>d\geq 2</math>, the conformal group depends on <math>M,g</math>, with flat space <math>\mathbb{R}^d</math> having the largest possible group <math>SO(d+1,1)</math>. * For <math>d\geq 3</math>, a generic space has only one conformal transformation: the identity. === Conformal transformations of flat space === The conformal group of <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math> first includes isometries: * Translations. * Rotations. There are also conformal transformations that are not isometries: * Dilations <math>x^\mu \mapsto \lambda x^\mu </math> with <math>\lambda \in \mathbb{R}</math>. * The inversion <math>x^\mu \mapsto \frac{x^\mu}{\|x\|^2}</math>. * Special conformal transformations <math>x^\mu \mapsto \frac{x^\mu - a^\mu \|x\|^2}{1-2a_\mu x^\mu +\|a\|^2\|x\|^2}</math>. These transformations generate the conformal group <math>SO(d+1,1)</math>. === Conformal symmetry and gravitation === In a theory of gravitation such as general relativity, the metric is not fixed, it is a dynamical object. We can therefore combine diffeomorphisms with changes of the metric. In particular, if we combine a diffeomorphism <math>f</math> with <math>g\mapsto f^*g</math>, we obtain a '''change of coordinates''', which should leave the physics invariant. By definition, modulo a change of coordinates, a conformal transformation amounts to a '''Weyl transformation''' of the metric <math>g\mapsto \lambda g</math>. For gravitational theories, conformal invariance is equivalent to Weyl invariance. General relativity is Weyl invariant for <math>d=2</math> only. It follows that in <math>d=2</math>, any field theory of quantum gravity must be a conformal field theory. Moreover, since any metric is conformally flat, we may replace the 3 components of the metric <math>g_{\mu\nu}</math> with the conformal factor <math>\lambda</math>: only 1 bosonic field. Einstein's equation for <math>g_{\mu\nu}</math> then reduces to the Liouville equation for <math>\log \lambda</math>. The Liouville equation is the classical equation of motion of [[w:Liouville theory]]: a solvable CFT that we will study in this course. Therefore, we can build field theories of gravity called '''Liouville gravity''' based on Liouville theory. (There are several possible theories, depending on the matter contents.) String theory is a theoretical framework that generalizes quantum field theory, and includes quantum theories of gravity. The basic idea is to describe physics in a spacetime <math>Z</math> using a <math>d=2</math> worldsheet <math>M</math> and an embedding <math>X:M\to Z</math>. The metric on <math>Z</math> induces a metric on <math>M</math>, but it is convenient to allow the worldsheet metric <math>g</math> to be an independent dynamical object, unrelated to the induced metric. Nevertheless, the physics should not depend on <math>g</math>. It is possible to fix 2 of the 3 components of <math>g</math> using a change of coordinates on <math>M</math>, and to get <math>g</math>-independence we also have to take care of the third component, by assuming Weyl invariance. This is why the worldsheet description of string theory uses <math>d=2</math> CFT. String theory provides another motivation for CFT in arbitrary <math>d</math> due to the AdS/CFT correspondence: a holographic relation between a string theory in a <math>d+1</math>-dimensional Anti-de Sitter space, and a CFT in <math>d</math> dimensions. In fact the correspondence can be generalized to non-AdS spaces, which then correspond to non-conformal field theories. Nevertheless, the correspondencs is simplest in the AdS/CFT case. === Conformal transformations in two dimensions === Let <math>M</math> be a two-dimensional connected, oriented manifold. A metric <math>g</math> on <math>M</math> is called Riemannian if it is positive definite. Let <math>\bar g</math> be the equivalence class of <math>g</math> modulo conformal transformations, also called a '''conformal structure'''. Then <math>(M,\bar g)</math> is called a [[w:Riemann surface]]. A Riemann surface is characterized by its topology and its conformal structure. Let us focus on compact Riemann surfaces. Topologically, a compact Riemann surface is characterize by its '''genus''' <math>h\in \mathbb{N}</math>, the number of holes. For a given genus, there is a finite-dimensional '''moduli space''' <math>\mathcal{M}_h</math> of Riemann surfaces. The conformal group of a Riemann surface depends on <math>h</math> and also on the surface: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Genus <math>h</math> ! Name ! <math>\dim_\mathbb{C} \mathcal{M}_h</math> ! Conformal group |- | 0 | Riemann sphere | <math>0</math> | <math>PSL_2(\mathbb{C})</math> |- | 1 | Torus | 1 | <math>\left(\mathbb{C}/\mathbb{Z}^2\right)\rtimes \text{finite} </math> |- | <math>\geq 2</math> | | <math>3h-3</math> | finite |} * The Riemann sphere is conveniently parametrized by a complex coordinate <math>z\in\mathbb{C}\cup \{\infty\}</math>. Its moduli space is trivial, i.e. all genus 0 Riemann surfaces are conformally equivalent. The conformal group is the Möbius group <math>PSL_2(\mathbb{C})</math>, which acts as :<math> z\mapsto \frac{az+b}{cz+d} \qquad \text{for}\qquad \left(\begin{array}{cc} a & b\\ c& d \end{array}\right) \in PSL_2(\mathbb{C}) </math> * The torus <math>\mathbb{T} = \frac{\mathbb{C}}{\mathbb{Z}+\tau\mathbb{Z}}</math> is parametrized by a '''modulus''' <math>\tau\in\mathbb{H}\equiv\left\{\tau \in \mathbb{C}|\Im \tau>0\right\}</math>. Two toruses are conformally equivalent if their moduli are related by :<math> \tau\mapsto \frac{a\tau+b}{c\tau+d} \qquad \text{for}\qquad \left(\begin{array}{cc} a & b\\ c& d \end{array}\right) \in PSL_2(\mathbb{Z}) </math> so the moduli space is <math>\mathcal{M}_1 = \mathbb{H}/PSL_2(\mathbb{Z})</math>. The conformal group of <math>\mathbb{T}</math> includes translations, which are parametrized by <math>\mathbb{T}</math> itself or equivalently by <math>\mathbb{C}/\mathbb{Z}^2</math>. Depending on <math>\tau</math>, there may also be a finite number of rotations. == Scale invariance and conformal invariance == == Fixed points of the renormalization group == == Applications == == Exercises == === COGS: The conformal group of flat space === Consider the Euclidean space <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math>, and the Minkowski space <math>\mathbb{R}^{d+1,1}</math> with coordinates <math>Y=\left(y^\mu,y^-,y^+\right)</math> with <math>\mu = 1,2,\dots, d</math> and the flat metric <math>\|dY\|^2 = \sum_{\mu=1}^d \left(dy^\mu\right)^2 -dy^-dy^+ </math>. Consider the diffeormorphisms :<math> \varphi:\left\{\begin{array}{ccl} \mathbb{R}^d & \to & \mathbb{R}^{d+1,1} \\ x^\mu &\mapsto & \left(x^\mu,\|x\|^2,1\right) \end{array}\right. \quad , \quad \psi: \left\{\begin{array}{ccl} \mathbb{R}^{d+1,1} & \to & \mathbb{R}^{d+1,1} \\ Y &\mapsto & \frac{1}{y^+}Y = \left(\frac{y^\mu}{y^+},\frac{y^-}{y^+},1\right) \end{array}\right. </math> # Check that <math>\varphi</math> is an isometry. Is <math>\psi</math> an isometry? Is it a conformal transformation? # Show that the restriction of <math>\psi</math> to the light cone <math>\mathcal{L}=\left\{Y\in \mathbb{R}^{d+1,1}\left| \|Y\|^2 = 0\right.\right\}</math> is a conformal transformation. # Let <math>G\in SO(d+1,1)</math> be an isometry of <math>\mathbb{R}^{d+1,1}</math>, in particular <math>G</math> is linear. Show that <math>\varphi^{-1}\circ \psi \circ G\circ \varphi</math> is a conformal transformation of <math>\mathbb{R}^d</math>. Deduce that the conformal group of <math>\mathbb{R}^d</math> includes <math>SO(d+1,1)</math>. # Explicitly write the action of <math>G\in SO(d+1,1)</math> on <math>x^\mu</math>. [[Category: CFT course]] q9pkrxgjffbew93jtj2derqpwpxw44k 2690246 2690245 2024-12-04T11:06:24Z Sylvain Ribault 2127778 /* Conformal transformations in two dimensions */ 2690246 wikitext text/x-wiki == Conformal invariance == === Conformal transformations === On a given space or spacetime <math>M</math> with coordinates <math>x^\mu</math>, distances are defined using a metric <math>g_{\mu\nu}</math>. In particular, the length of an infinitesimal vector <math>v^\mu</math> is <math>\|v\| = \sqrt{g_{\mu\nu}v^\mu v^\nu}</math>. If we know distances, we can also compute angles. The angle <math>\theta</math> between two infinitesimal vectors <math>v^\mu,w^\mu</math> obeys :<math> \cos\theta = \frac{g_{\mu\nu}v^\mu w^\nu}{\sqrt{g_{\mu\nu}v^\mu v^\nu}\sqrt{ g_{\mu\nu}w^\mu w^\nu}} </math> For <math>f:M\to M</math> a diffeomorphism, we define the [[w:pullback]] <math>f^*g</math> of the metric by :<math> (f^*g)_{\mu\nu} = g_{\rho\sigma}(f(x)) \frac{\partial f^\rho}{\partial x^\mu}\frac{\partial f^\sigma}{\partial x^\nu} </math> equivalently <math>(f*g)_{\mu\nu}(x)dx^\mu dx^\nu = g_{\mu\nu}(f)df^\mu df^\nu</math>. A diffeomorphism <math>f:M\to M</math> is called an '''isometry''' if it preserves distances, equivalently if :<math>f^* g = g</math>. It is called a '''conformal transformation''' if it preserves angles. Any isometry is a conformal transformation, but the converse is not true. For any function <math>\lambda:M\to \mathbb{R}</math>, the metrics <math>g_{\mu\nu}</math> and <math>\lambda g_{\mu\nu}</math> define the same angles. So <math>f</math> is a conformal transformation if it preserve the metric up to a scalar factor, :<math> \exists \lambda,\ f^* g = \lambda g </math> The set of conformal transformations is called the '''conformal group''' associated to <math>M,g</math>. Let us indicate how many functions on <math>M</math> are needed to parametrize the objects <math>\lambda, f,g</math>, if <math>d=\dim(M)</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Object ! Number of functions on <math>M</math> |- | Function <math>\lambda:M\to \mathbb{R}</math> | <math>1</math> |- | Diffeomorphism <math>f:M\to M</math> | <math>d</math> |- | Metric <math>g</math> on <math>M</math> | <math>\frac{d(d+1)}{2}</math> |} Therefore, given two metrics <math>g_1,g_2</math>, the condition <math>f^* g_1 = \lambda g_2</math> that they are conformally equivalent involves <math>\frac{d(d+1)}{2}</math> equations for <math>d+1</math> unknowns. For <math>d\leq 2</math>, there is always a solution (under reasonable assumptions): in particular any metric on <math>\mathbb{R}^2</math> is conformally flat. For <math>d\geq 3</math>, two metrics are in general not equivalent modulo rescaling. Similarly, the size of the conformal group depends on the dimension: * For <math>d=1</math>, any diffeomorphism is conformal. * For <math>d\geq 2</math>, the conformal group depends on <math>M,g</math>, with flat space <math>\mathbb{R}^d</math> having the largest possible group <math>SO(d+1,1)</math>. * For <math>d\geq 3</math>, a generic space has only one conformal transformation: the identity. === Conformal transformations of flat space === The conformal group of <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math> first includes isometries: * Translations. * Rotations. There are also conformal transformations that are not isometries: * Dilations <math>x^\mu \mapsto \lambda x^\mu </math> with <math>\lambda \in \mathbb{R}</math>. * The inversion <math>x^\mu \mapsto \frac{x^\mu}{\|x\|^2}</math>. * Special conformal transformations <math>x^\mu \mapsto \frac{x^\mu - a^\mu \|x\|^2}{1-2a_\mu x^\mu +\|a\|^2\|x\|^2}</math>. These transformations generate the conformal group <math>SO(d+1,1)</math>. === Conformal symmetry and gravitation === In a theory of gravitation such as general relativity, the metric is not fixed, it is a dynamical object. We can therefore combine diffeomorphisms with changes of the metric. In particular, if we combine a diffeomorphism <math>f</math> with <math>g\mapsto f^*g</math>, we obtain a '''change of coordinates''', which should leave the physics invariant. By definition, modulo a change of coordinates, a conformal transformation amounts to a '''Weyl transformation''' of the metric <math>g\mapsto \lambda g</math>. For gravitational theories, conformal invariance is equivalent to Weyl invariance. General relativity is Weyl invariant for <math>d=2</math> only. It follows that in <math>d=2</math>, any field theory of quantum gravity must be a conformal field theory. Moreover, since any metric is conformally flat, we may replace the 3 components of the metric <math>g_{\mu\nu}</math> with the conformal factor <math>\lambda</math>: only 1 bosonic field. Einstein's equation for <math>g_{\mu\nu}</math> then reduces to the Liouville equation for <math>\log \lambda</math>. The Liouville equation is the classical equation of motion of [[w:Liouville theory]]: a solvable CFT that we will study in this course. Therefore, we can build field theories of gravity called '''Liouville gravity''' based on Liouville theory. (There are several possible theories, depending on the matter contents.) String theory is a theoretical framework that generalizes quantum field theory, and includes quantum theories of gravity. The basic idea is to describe physics in a spacetime <math>Z</math> using a <math>d=2</math> worldsheet <math>M</math> and an embedding <math>X:M\to Z</math>. The metric on <math>Z</math> induces a metric on <math>M</math>, but it is convenient to allow the worldsheet metric <math>g</math> to be an independent dynamical object, unrelated to the induced metric. Nevertheless, the physics should not depend on <math>g</math>. It is possible to fix 2 of the 3 components of <math>g</math> using a change of coordinates on <math>M</math>, and to get <math>g</math>-independence we also have to take care of the third component, by assuming Weyl invariance. This is why the worldsheet description of string theory uses <math>d=2</math> CFT. String theory provides another motivation for CFT in arbitrary <math>d</math> due to the AdS/CFT correspondence: a holographic relation between a string theory in a <math>d+1</math>-dimensional Anti-de Sitter space, and a CFT in <math>d</math> dimensions. In fact the correspondence can be generalized to non-AdS spaces, which then correspond to non-conformal field theories. Nevertheless, the correspondencs is simplest in the AdS/CFT case. === Conformal transformations in two dimensions === Let <math>M</math> be a two-dimensional connected, oriented manifold. A metric <math>g</math> on <math>M</math> is called Riemannian if it is positive definite. Let <math>\bar g</math> be the equivalence class of <math>g</math> modulo conformal transformations, also called a '''conformal structure'''. Then <math>(M,\bar g)</math> is called a [[w:Riemann surface]]. A Riemann surface is characterized by its topology and its conformal structure. Let us focus on compact Riemann surfaces. Topologically, a compact Riemann surface is characterize by its '''genus''' <math>h\in \mathbb{N}</math>, the number of holes. For a given genus, there is a finite-dimensional '''moduli space''' <math>\mathcal{M}_h</math> of Riemann surfaces. The conformal group of a Riemann surface depends on <math>h</math> and also on the surface: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Genus <math>h</math> ! Name ! <math>\dim_\mathbb{C} \mathcal{M}_h</math> ! Conformal group |- | 0 | Riemann sphere | <math>0</math> | <math>PSL_2(\mathbb{C})</math> |- | 1 | Torus | 1 | <math>\left(\mathbb{C}/\mathbb{Z}^2\right)\rtimes \text{finite} </math> |- | <math>\geq 2</math> | | <math>3h-3</math> | finite |} * The Riemann sphere is conveniently parametrized by a complex coordinate <math>z\in\mathbb{C}\cup \{\infty\}</math>. Its moduli space is trivial, i.e. all genus 0 Riemann surfaces are conformally equivalent. The conformal group is the Möbius group <math>PSL_2(\mathbb{C})</math>, which acts as :<math> z\mapsto \frac{az+b}{cz+d} \qquad \text{for}\qquad \left(\begin{array}{cc} a & b\\ c& d \end{array}\right) \in PSL_2(\mathbb{C}) </math> * The torus <math>\mathbb{T} = \frac{\mathbb{C}}{\mathbb{Z}+\tau\mathbb{Z}}</math> is parametrized by a '''modulus''' <math>\tau\in\mathbb{H}\equiv\left\{\tau \in \mathbb{C}|\Im \tau>0\right\}</math>. Two toruses are conformally equivalent if their moduli are related by <math>\tau\mapsto \frac{a\tau+b}{c\tau+d}</math> for <math>\left(\begin{array}{cc} a & b\\ c& d \end{array}\right) \in PSL_2(\mathbb{Z})</math> so the moduli space is <math>\mathcal{M}_1 = \mathbb{H}/PSL_2(\mathbb{Z})</math>. The conformal group of <math>\mathbb{T}</math> includes translations, which are parametrized by <math>\mathbb{T}</math> itself or equivalently by <math>\mathbb{C}/\mathbb{Z}^2</math>. Depending on <math>\tau</math>, there may also be a finite number of rotations. == Scale invariance and conformal invariance == == Fixed points of the renormalization group == == Applications == == Exercises == === COGS: The conformal group of flat space === Consider the Euclidean space <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math>, and the Minkowski space <math>\mathbb{R}^{d+1,1}</math> with coordinates <math>Y=\left(y^\mu,y^-,y^+\right)</math> with <math>\mu = 1,2,\dots, d</math> and the flat metric <math>\|dY\|^2 = \sum_{\mu=1}^d \left(dy^\mu\right)^2 -dy^-dy^+ </math>. Consider the diffeormorphisms :<math> \varphi:\left\{\begin{array}{ccl} \mathbb{R}^d & \to & \mathbb{R}^{d+1,1} \\ x^\mu &\mapsto & \left(x^\mu,\|x\|^2,1\right) \end{array}\right. \quad , \quad \psi: \left\{\begin{array}{ccl} \mathbb{R}^{d+1,1} & \to & \mathbb{R}^{d+1,1} \\ Y &\mapsto & \frac{1}{y^+}Y = \left(\frac{y^\mu}{y^+},\frac{y^-}{y^+},1\right) \end{array}\right. </math> # Check that <math>\varphi</math> is an isometry. Is <math>\psi</math> an isometry? Is it a conformal transformation? # Show that the restriction of <math>\psi</math> to the light cone <math>\mathcal{L}=\left\{Y\in \mathbb{R}^{d+1,1}\left| \|Y\|^2 = 0\right.\right\}</math> is a conformal transformation. # Let <math>G\in SO(d+1,1)</math> be an isometry of <math>\mathbb{R}^{d+1,1}</math>, in particular <math>G</math> is linear. Show that <math>\varphi^{-1}\circ \psi \circ G\circ \varphi</math> is a conformal transformation of <math>\mathbb{R}^d</math>. Deduce that the conformal group of <math>\mathbb{R}^d</math> includes <math>SO(d+1,1)</math>. # Explicitly write the action of <math>G\in SO(d+1,1)</math> on <math>x^\mu</math>. [[Category: CFT course]] gg55kcq2ok1sautb9cwzshv0qt7qbz0 2690247 2690246 2024-12-04T11:20:00Z Sylvain Ribault 2127778 /* COGS: The conformal group of flat space */ 2690247 wikitext text/x-wiki == Conformal invariance == === Conformal transformations === On a given space or spacetime <math>M</math> with coordinates <math>x^\mu</math>, distances are defined using a metric <math>g_{\mu\nu}</math>. In particular, the length of an infinitesimal vector <math>v^\mu</math> is <math>\|v\| = \sqrt{g_{\mu\nu}v^\mu v^\nu}</math>. If we know distances, we can also compute angles. The angle <math>\theta</math> between two infinitesimal vectors <math>v^\mu,w^\mu</math> obeys :<math> \cos\theta = \frac{g_{\mu\nu}v^\mu w^\nu}{\sqrt{g_{\mu\nu}v^\mu v^\nu}\sqrt{ g_{\mu\nu}w^\mu w^\nu}} </math> For <math>f:M\to M</math> a diffeomorphism, we define the [[w:pullback]] <math>f^*g</math> of the metric by :<math> (f^*g)_{\mu\nu} = g_{\rho\sigma}(f(x)) \frac{\partial f^\rho}{\partial x^\mu}\frac{\partial f^\sigma}{\partial x^\nu} </math> equivalently <math>(f*g)_{\mu\nu}(x)dx^\mu dx^\nu = g_{\mu\nu}(f)df^\mu df^\nu</math>. A diffeomorphism <math>f:M\to M</math> is called an '''isometry''' if it preserves distances, equivalently if :<math>f^* g = g</math>. It is called a '''conformal transformation''' if it preserves angles. Any isometry is a conformal transformation, but the converse is not true. For any function <math>\lambda:M\to \mathbb{R}</math>, the metrics <math>g_{\mu\nu}</math> and <math>\lambda g_{\mu\nu}</math> define the same angles. So <math>f</math> is a conformal transformation if it preserve the metric up to a scalar factor, :<math> \exists \lambda,\ f^* g = \lambda g </math> The set of conformal transformations is called the '''conformal group''' associated to <math>M,g</math>. Let us indicate how many functions on <math>M</math> are needed to parametrize the objects <math>\lambda, f,g</math>, if <math>d=\dim(M)</math>: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Object ! Number of functions on <math>M</math> |- | Function <math>\lambda:M\to \mathbb{R}</math> | <math>1</math> |- | Diffeomorphism <math>f:M\to M</math> | <math>d</math> |- | Metric <math>g</math> on <math>M</math> | <math>\frac{d(d+1)}{2}</math> |} Therefore, given two metrics <math>g_1,g_2</math>, the condition <math>f^* g_1 = \lambda g_2</math> that they are conformally equivalent involves <math>\frac{d(d+1)}{2}</math> equations for <math>d+1</math> unknowns. For <math>d\leq 2</math>, there is always a solution (under reasonable assumptions): in particular any metric on <math>\mathbb{R}^2</math> is conformally flat. For <math>d\geq 3</math>, two metrics are in general not equivalent modulo rescaling. Similarly, the size of the conformal group depends on the dimension: * For <math>d=1</math>, any diffeomorphism is conformal. * For <math>d\geq 2</math>, the conformal group depends on <math>M,g</math>, with flat space <math>\mathbb{R}^d</math> having the largest possible group <math>SO(d+1,1)</math>. * For <math>d\geq 3</math>, a generic space has only one conformal transformation: the identity. === Conformal transformations of flat space === The conformal group of <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math> first includes isometries: * Translations. * Rotations. There are also conformal transformations that are not isometries: * Dilations <math>x^\mu \mapsto \lambda x^\mu </math> with <math>\lambda \in \mathbb{R}</math>. * The inversion <math>x^\mu \mapsto \frac{x^\mu}{\|x\|^2}</math>. * Special conformal transformations <math>x^\mu \mapsto \frac{x^\mu - a^\mu \|x\|^2}{1-2a_\mu x^\mu +\|a\|^2\|x\|^2}</math>. These transformations generate the conformal group <math>SO(d+1,1)</math>. === Conformal symmetry and gravitation === In a theory of gravitation such as general relativity, the metric is not fixed, it is a dynamical object. We can therefore combine diffeomorphisms with changes of the metric. In particular, if we combine a diffeomorphism <math>f</math> with <math>g\mapsto f^*g</math>, we obtain a '''change of coordinates''', which should leave the physics invariant. By definition, modulo a change of coordinates, a conformal transformation amounts to a '''Weyl transformation''' of the metric <math>g\mapsto \lambda g</math>. For gravitational theories, conformal invariance is equivalent to Weyl invariance. General relativity is Weyl invariant for <math>d=2</math> only. It follows that in <math>d=2</math>, any field theory of quantum gravity must be a conformal field theory. Moreover, since any metric is conformally flat, we may replace the 3 components of the metric <math>g_{\mu\nu}</math> with the conformal factor <math>\lambda</math>: only 1 bosonic field. Einstein's equation for <math>g_{\mu\nu}</math> then reduces to the Liouville equation for <math>\log \lambda</math>. The Liouville equation is the classical equation of motion of [[w:Liouville theory]]: a solvable CFT that we will study in this course. Therefore, we can build field theories of gravity called '''Liouville gravity''' based on Liouville theory. (There are several possible theories, depending on the matter contents.) String theory is a theoretical framework that generalizes quantum field theory, and includes quantum theories of gravity. The basic idea is to describe physics in a spacetime <math>Z</math> using a <math>d=2</math> worldsheet <math>M</math> and an embedding <math>X:M\to Z</math>. The metric on <math>Z</math> induces a metric on <math>M</math>, but it is convenient to allow the worldsheet metric <math>g</math> to be an independent dynamical object, unrelated to the induced metric. Nevertheless, the physics should not depend on <math>g</math>. It is possible to fix 2 of the 3 components of <math>g</math> using a change of coordinates on <math>M</math>, and to get <math>g</math>-independence we also have to take care of the third component, by assuming Weyl invariance. This is why the worldsheet description of string theory uses <math>d=2</math> CFT. String theory provides another motivation for CFT in arbitrary <math>d</math> due to the AdS/CFT correspondence: a holographic relation between a string theory in a <math>d+1</math>-dimensional Anti-de Sitter space, and a CFT in <math>d</math> dimensions. In fact the correspondence can be generalized to non-AdS spaces, which then correspond to non-conformal field theories. Nevertheless, the correspondencs is simplest in the AdS/CFT case. === Conformal transformations in two dimensions === Let <math>M</math> be a two-dimensional connected, oriented manifold. A metric <math>g</math> on <math>M</math> is called Riemannian if it is positive definite. Let <math>\bar g</math> be the equivalence class of <math>g</math> modulo conformal transformations, also called a '''conformal structure'''. Then <math>(M,\bar g)</math> is called a [[w:Riemann surface]]. A Riemann surface is characterized by its topology and its conformal structure. Let us focus on compact Riemann surfaces. Topologically, a compact Riemann surface is characterize by its '''genus''' <math>h\in \mathbb{N}</math>, the number of holes. For a given genus, there is a finite-dimensional '''moduli space''' <math>\mathcal{M}_h</math> of Riemann surfaces. The conformal group of a Riemann surface depends on <math>h</math> and also on the surface: {| class="wikitable" style="font-size:small; text-align:center;" |- ! Genus <math>h</math> ! Name ! <math>\dim_\mathbb{C} \mathcal{M}_h</math> ! Conformal group |- | 0 | Riemann sphere | <math>0</math> | <math>PSL_2(\mathbb{C})</math> |- | 1 | Torus | 1 | <math>\left(\mathbb{C}/\mathbb{Z}^2\right)\rtimes \text{finite} </math> |- | <math>\geq 2</math> | | <math>3h-3</math> | finite |} * The Riemann sphere is conveniently parametrized by a complex coordinate <math>z\in\mathbb{C}\cup \{\infty\}</math>. Its moduli space is trivial, i.e. all genus 0 Riemann surfaces are conformally equivalent. The conformal group is the Möbius group <math>PSL_2(\mathbb{C})</math>, which acts as :<math> z\mapsto \frac{az+b}{cz+d} \qquad \text{for}\qquad \left(\begin{array}{cc} a & b\\ c& d \end{array}\right) \in PSL_2(\mathbb{C}) </math> * The torus <math>\mathbb{T} = \frac{\mathbb{C}}{\mathbb{Z}+\tau\mathbb{Z}}</math> is parametrized by a '''modulus''' <math>\tau\in\mathbb{H}\equiv\left\{\tau \in \mathbb{C}|\Im \tau>0\right\}</math>. Two toruses are conformally equivalent if their moduli are related by <math>\tau\mapsto \frac{a\tau+b}{c\tau+d}</math> for <math>\left(\begin{array}{cc} a & b\\ c& d \end{array}\right) \in PSL_2(\mathbb{Z})</math> so the moduli space is <math>\mathcal{M}_1 = \mathbb{H}/PSL_2(\mathbb{Z})</math>. The conformal group of <math>\mathbb{T}</math> includes translations, which are parametrized by <math>\mathbb{T}</math> itself or equivalently by <math>\mathbb{C}/\mathbb{Z}^2</math>. Depending on <math>\tau</math>, there may also be a finite number of rotations. == Scale invariance and conformal invariance == == Fixed points of the renormalization group == == Applications == == Exercises == === COGS: The conformal group of flat space === Consider the Euclidean space <math>\mathbb{R}^d</math> with the flat metric <math>g_{\mu\nu}=\delta_{\mu\nu}</math>, and the Minkowski space <math>\mathbb{R}^{d+1,1}</math> with coordinates <math>Y=\left(y^\mu,y^-,y^+\right)</math> with <math>\mu = 1,2,\dots, d</math> and the flat metric <math>\|dY\|^2 = \sum_{\mu=1}^d \left(dy^\mu\right)^2 -dy^-dy^+ </math>. Consider the diffeormorphisms :<math> \varphi:\left\{\begin{array}{ccl} \mathbb{R}^d & \to & \mathbb{R}^{d+1,1} \\ x^\mu &\mapsto & \left(x^\mu,\|x\|^2,1\right) \end{array}\right. \quad , \quad \psi: \left\{\begin{array}{ccl} \mathbb{R}^{d+1,1} & \to & \mathbb{R}^{d+1,1} \\ Y &\mapsto & \frac{1}{y^+}Y = \left(\frac{y^\mu}{y^+},\frac{y^-}{y^+},1\right) \end{array}\right. </math> # Check that <math>\varphi</math> is an isometry. Is <math>\psi</math> an isometry? Is it a conformal transformation? # Show that the restriction of <math>\psi</math> to the light cone <math>\mathcal{L}=\left\{Y\in \mathbb{R}^{d+1,1}\left| \|Y\|^2 = 0\right.\right\}</math> is a conformal transformation, and that <math>\varphi(\mathbb{R}^d)\subset \mathcal{L}</math>. # Let <math>G\in SO(d+1,1)</math> be an isometry of <math>\mathbb{R}^{d+1,1}</math>, in particular <math>G</math> is linear. Show that <math>\varphi^{-1}\circ \psi \circ G\circ \varphi</math> is a conformal transformation of <math>\mathbb{R}^d</math>. Deduce that the conformal group of <math>\mathbb{R}^d</math> includes <math>SO(d+1,1)</math>. # Explicitly write the action of <math>G\in SO(d+1,1)</math> on <math>x^\mu</math>. [[Category: CFT course]] r4qlkfttlm03t9v36b16k7s4cjeu34u 2 316552 2690194 2689835 2024-12-04T03:06:05Z Jaredscribe 2906761 /* FAA */ Musk has often complained about the FAA "smothering" innovation, boasting that he can build a rocket faster than the agency can process the "Kafkaesque paperwork" required to make the relevant approvals.[1] 2690194 wikitext text/x-wiki The U.S. [[w:Department of Government Efficiency]]. {{Infobox Organization |name=Department of Government Efficiency |logo=DOGE Logo as of November 14, 2024.jpg |logo_size=150px |logo_caption=Logo on [[Twitter|X]] (formerly Twitter) as of November 14, 2024 |seal= |seal_size= |seal_caption= |formation=Announced on November 12, 2024; yet to be established |abbreviation=DOGE |key_people={{plainlist|[[w:Commissioner of the Department of Government Efficiency|Co-commissioners]]: * [[w:Elon Musk]] * [[w:Vivek Ramaswamy]] }} |website={{URL|https://x.com/DOGE|x.com/DOGE}} }} This "'''Wiki Of Government Efficiency'''" (WOGE) will analyze the [[w:U.S._Federal_budget|U.S. federal budget]], [[User:Jaredscribe/Department of Government Efficiency#Reform the other Government Bureaus and Departments|federal bureaucracy]], and [[User:Jaredscribe/Department of Government Efficiency#Shrink the federal civil service|federal civil service]], in the public interest, and in the context of [[w:Second_presidency_of_Donald_Trump|president-elect Trump']]<nowiki/>s [[w:Agenda_47|Agenda 47]], with non-partisan research, analysis, and criticism of forward-looking proposals on how the '''[[w:Department of Government Efficiency|Department of Government Efficiency]]'''{{Efn|Also referred to as '''Government Efficiency Commission'''}} (DOGE) might fulfill its mission to ''"dismantle government bureaucracy, slash excess regulations, and cut wasteful expenditures and restructure federal agencies"'', in the words of president-elect [[wikipedia:Donald_Trump|Donald Trump]], who called for it to address ''"massive waste and fraud"'' in government spending.<ref name=":1">{{Cite web|url=https://www.bbc.co.uk/news/articles/c93qwn8p0l0o|title=Donald Trump picks Elon Musk for US government cost-cutting role|last1=Faguy|first1=Ana|last2=FitzGerald|first2=James|date=2024-11-13|publisher=BBC News|language=en-GB|access-date=2024-11-13}}</ref> The DOGE will work with through the [[w:Office_of_Management_and_Budget|Office of Management and Budget]] as its "policy vector". Here's [[User:Jaredscribe/Department of Government Efficiency/How to contribute|how to contribute]] to the WOGE. The [[w:U.S._budget_deficit|U.S. Budget deficit]], (C.f. [[w:Government_budget_balance|fiscal deficit]]), and the [[w:National_debt_of_the_United_States|U.S. National debt]], currently $35.7 Trillion as of 10/2024, which is 99% of the [[w:U.S._GDP|U.S. GDP]],<ref>{{Unbulleted list citebundle|{{cite news|newspaper=Financial Post| title= Musk's $2 Trillion of Budget Cuts Would Have These Stocks Moving|url=https://financialpost.com/pmn/business-pmn/musks-2-trillion-of-budget-cuts-would-have-these-stocks-moving|first=Alexandra|last=Semenova|date=November 4, 2024}}|{{cite news|newspaper= New York Times|title=Elon|url=https://nytimes.com/2024/10/29/us/politics/elon-musk-trump-economy-hardship.html}}|{{Cite web |date=September 5, 2024 |title=Trump says he'd create a government efficiency commission led by Elon Musk |url=https://apnews.com/article/donald-trump-elon-musk-government-efficiency-commission-e831ed5dc2f6a56999e1a70bb0a4eaeb |publisher=AP News}}|{{cite web|first=Jenn|last=Brice|title=How Elon Musk's $130 million investment in Trump's victory could reap a huge payoff for Tesla and the rest of his business empire|url=https://fortune.com/2024/11/06/elon-musk-donald-trump-tesla-spacex-xai-boring-neuralink|website=Fortune}}|{{cite web|url=https://axios.com/2024/11/07/elon-musk-government-efficiency-trump|title=Musk will bring his Twitter management style to government reform}}|{{cite news| access-date =November 9, 2024|work=Reuters|date=September 6, 2024|first1=Helen|first2=Gram|last1=Coster| last2=Slattery|title=Trump says he will tap Musk to lead government efficiency commission if elected| url= https://reuters.com/world/us/trump-adopt-musks-proposal-government-efficiency-commission-wsj-reports-2024-09-05}}|{{cite web|title=Trump says Musk could head 'government efficiency' force|url= https://bbc.com/news/articles/c74lgwkrmrpo|publisher=BBC}}|{{cite web|date =November 5, 2024|title=How Elon Musk could gut the government under Trump|url=https://independent.co.uk/news/world/americas/us-politics/elon-musk-donald-trump-economy-job-cuts-b2641644.html|website= The Independent}}}}</ref> and expected to grow to 134% of GDP by 2034 if current laws remain unchanged, according to the [[w:Congressional_Budget_Office|Congressional Budget Office]]. The DOGE will be a [[wikipedia:Presidential_commission_(United_States)|presidential advisory commission]] led by the billionaire businessmen [[wikipedia:Elon_Musk|Elon Musk]] and [[wikipedia:Vivek_Ramaswamy|Vivek Ramaswamy]], and possibly [[w:Ron_Paul|Ron Paul]]<ref>{{Cite web|url=https://thehill.com/video/ron-paul-vows-to-join-elon-musk-help-eliminate-government-waste-in-a-trump-admin/10191375|title=Ron Paul vows to join Elon Musk, help eliminate government waste in a Trump admin|date=November 5, 2024|website=The Hill}}</ref><ref>{{Cite web|url=https://usatoday.com/story/business/2024/10/28/patricia-healy-elon-musk-highlights-need-for-government-efficiency/75798556007|title=Elon Musk puts spotlight on ... Department of Government Efficiency? {{!}} Cumberland Comment|last=Healy|first=Patricia|website=USA TODAY|language=en-US|access-date=November 9, 2024}}</ref>. Musk stated his belief that DOGE could remove US$2 trillion from the [[w:United_States_federal_budget|U.S. federal budget]],<ref>{{Cite web|url=https://www.youtube.com/live/HysDMs2a-iM?si=92I5LD1FY2PAsSuG&t=15822|title=WATCH LIVE: Trump holds campaign rally at Madison Square Garden in New York|date=October 28, 2024|website=youtube.com|publisher=[[PBS NewsHour]]|language=en|format=video}}</ref> without specifying whether these savings would be made over a single year or a longer period.<ref>{{Cite web|url=https://www.bbc.co.uk/news/articles/cdj38mekdkgo|title=Can Elon Musk cut $2 trillion from US government spending?|last=Chu|first=Ben|date=2024-11-13|website=BBC News|language=en-GB|access-date=2024-11-14}}</ref> [[File:2023_US_Federal_Budget_Infographic.png|thumb|An infographic on outlays and revenues in the 2023 [[United States federal budget|U.S. federal budget]]]] DOGE could also streamline permitting with “categorical exclusions” from environmental reviews under the National Environmental Policy Act. {{sidebar with collapsible lists|name=U.S. deficit and debt topics|namestyle=background:#bf0a30;|style=width:22.0em; border: 4px double #d69d36; background:var(--background-color-base, #FFFFFF);|bodyclass=vcard|pretitle='''<span class="skin-invert">This article is part of [[:Category:United States|a series]] on the</span>'''|title=[[United States federal budget|<span style="color:var(--color-base, #000000);">Budget and debt in the<br/>United States of America</span>]]|image=[[File:Seal of the United States Congress.svg|90px]] [[File:Seal of the United States Department of the Treasury.svg|90px]]|titlestyle=background:var(--background-color-base, #002868); background-clip:padding-box;|headingstyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff);|listtitlestyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff); text-align:center;|expanded={{{expanded|{{{1|}}}}}}|list1name=dimensions|list1title=Major dimensions|list1class=hlist skin-invert|list1=* [[Economy of the United States|Economy]] * [[Expenditures in the United States federal budget|Expenditures]] * [[United States federal budget|Federal budget]] * [[Financial position of the United States|Financial position]] * [[Military budget of the United States|Military budget]] * [[National debt of the United States|Public debt]] * [[Taxation in the United States|Taxation]] * [[Unemployment in the United States|Unemployment]] * [[Government_spending_in_the_United_States|Gov't spending]]|list2name=programs|list2title=Programs|list2class=hlist skin-invert|list2=* [[Medicare (United States)|Medicare]] * [[Social programs in the United States|Social programs]] * [[Social Security (United States)|Social Security]]|list3name=issues|list3title=Contemporary issues|list3class=skin-invert|list3=<div style="margin-bottom:0.5em"> [[National Commission on Fiscal Responsibility and Reform|Bowles–Simpson Commission]] {{flatlist}} * <!--Bu--> [[Bush tax cuts]] * <!--Deb--> [[United States debt ceiling|Debt ceiling]] ** [[History of the United States debt ceiling|history]] * <!--Def--> [[Deficit reduction in the United States|Deficit reduction]] * <!--F--> [[United States fiscal cliff|Fiscal cliff]] * <!--H--> [[Healthcare reform in the United States|Healthcare reform]] * <!--P--> [[Political debates about the United States federal budget|Political debates]] * <!--So--> [[Social Security debate in the United States|Social Security debate]] * <!--St--> "[[Starve the beast]]" * <!--Su--> [[Subprime mortgage crisis]] {{endflatlist}} </div> [[2007–2008 financial crisis]] {{flatlist}} * <!--D--> [[United States debt-ceiling crisis (disambiguation)|Debt-ceiling crises]] ** [[2011 United States debt-ceiling crisis|2011]] ** [[2013 United States debt-ceiling crisis|2013]] ** [[2023 United States debt-ceiling crisis|2023]] {{endflatlist}} [[2013 United States budget sequestration|2013 budget sequestration]] {{flatlist}} * <!--G--> [[Government shutdowns in the United States|Government shutdowns]] ** [[1980 United States federal government shutdown|1980]] ** [[1981, 1984, and 1986 U.S. federal government shutdowns|1981, 1984, 1986]] ** [[1990 United States federal government shutdown|1990]] ** [[1995–1996 United States federal government shutdowns|1995–1996]] ** [[2013 United States federal government shutdown|2013]] ** [[January 2018 United States federal government shutdown|Jan 2018]] ** [[2018–2019 United States federal government shutdown|2018–2019]] {{endflatlist}} Related events {{flatlist}} *<!--E-->[[Removal of Kevin McCarthy as Speaker of the House|2023 Removal of Kevin McCarthy]] {{endflatlist}}|list4name=terminology|list4title=Terminology|list4class=hlist skin-invert|list4=Cumulative [[Government budget balance|deficit]] + [[National debt of the United States#Debates|Interest]] ≈ [[Government debt|Debt]] * [[Balance of payments]] * [[Inflation]] * [[Continuing resolution]]}} [[w:Deficit_reduction_in_the_United_States|Deficit reduction in the United States]] == Deregulate the Economy == The legal theory that this can be done through the executive branch is found in the U.S. Supreme Court’s ''[[w:West_Virginia_v._EPA|West Virginia v. EPA]]'' and ''[[w:Loper_Bright|Loper Bright]]'' rulings, which rein in the administrative state and mean that much of what the federal government now does is illegal.<ref>{{cite web|url=https://www.wsj.com/opinion/department-of-government-efficiency-elon-musk-vivek-ramaswamy-donald-trump-1e086dab|website=[[w:Wall Street Journal]]|title=The Musk-Ramaswamy Project Could Be Trump’s Best Idea}}</ref> Mr. Trump has set a goal of eliminating 10 regulations for every new one. The [[w:Competitive_Enterprise_Institute|Competitive Enterprise Institute]]’s Wayne Crews says 217,565 rules have been issued since the [[w:Federal_Register|Federal Register]] first began itemizing them in 1976, with 89,368 pages added last year. [https://sgp.fas.org/crs/misc/R43056.pdf 3,000-4,500 rules are added each year]. DOGE’s first order will be to pause enforcement of overreaching rules while starting the process to roll them back. Mr. Trump and DOGE could direct agencies to settle legal challenges to Biden rules by vacating them. This could ease the laborious process of undoing them by rule-making through the [[w:Administrative_Procedure_Act|Administrative Procedure Act]]. A source tells the WSJ they’ll do whatever they think they legally can without the APA. The [[w:Congressional_Review_Act|Congressional Review Act]]—which allows Congress to overturn recently issued agency regulations—had been used only once, prior to [[w:First_presidency_of_Donald_Trump|Trump's first term]]. While in office, he and the Republican Congress used it on 16 rules. This time, there will be more than 56 regulatory actions recent enough to be repealed. The [[w:Chevron_deference|''Chevron'' deference]] had required federal courts to defer to agencies’ interpretations of ambiguous statutes, but this was overturned in 2024. Taken together, with some other recent [[w:SCOTUS|SCOTUS]] rulings, we now have, says the WSJ, the biggest opportunity to cut regulatory red tape in more than 40 years.<ref>[https://www.wsj.com/opinion/let-the-trump-deregulation-begin-us-chamber-of-commerce-second-term-economic-growth-73f24387?cx_testId=3&cx_testVariant=cx_166&cx_artPos=0]</ref><blockquote>"Most legal edicts aren’t laws enacted by Congress but “rules and regulations” promulgated by unelected bureaucrats—tens of thousands of them each year. Most government enforcement decisions and discretionary expenditures aren’t made by the democratically elected president or even his political appointees but by millions of unelected, unappointed civil servants within government agencies who view themselves as immune from firing thanks to civil-service protections." "This is antidemocratic and antithetical to the Founders’ vision. It imposes massive direct and indirect costs on taxpayers." "When the president nullifies thousands of such regulations, critics will allege executive overreach. In fact, it will be ''correcting'' the executive overreach of thousands of regulations promulgated by administrative fiat that were never authorized by Congress. The president owes lawmaking deference to Congress, not to bureaucrats deep within federal agencies. The use of executive orders to substitute for lawmaking by adding burdensome new rules is a constitutional affront, but the use of executive orders to roll back regulations that wrongly bypassed Congress is legitimate and necessary to comply with the Supreme Court’s recent mandates. And after those regulations are fully rescinded, a future president couldn’t simply flip the switch and revive them but would instead have to ask Congress to do so" Mssrs. [https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Musk and Ramaswamy, WSJ, 11/20/2024]</blockquote> == Shrink the federal civil service == The government has around three million [[w:United_States_federal_civil_service|federal civil service]] employees, with an average salary of $106,000. Dr. Anthony Fauci made $481,000 in 2022. The federal head count has ballooned by 120,800 during the Biden years. Civil service and union protections make it hard to fire workers. Mr. Trump intends to quickly resurrect the [[w:Schedule_F|Schedule F]] reform that he sought to implement at the end of his first term but was scrapped by Mr. Biden. These would high-level federal employees to be removed like political appointees, by eliminating their job protections. WSJ proposals[https://www.wsj.com/opinion/the-doge-cheat-sheet-elon-musk-vivek-ramaswamy-department-of-government-efficiency-1c231783#cxrecs_s] The [[w:Administrative_Procedures_Act|Administrative Procedures Act]] statute protects federal employees from political retaliation, but allows for “reductions in force” that don’t target specific employees. The statute further empowers the president to “prescribe rules governing the competitive service.” The Supreme Court has held—in ''[[w:Franklin_v._Massachusetts|Franklin v. Massachusetts]]'' (1992) and ''[[w:Collins_v._Yellen|Collins v. Yellen]]'' (2021) that when revious presidents have used this power to amend the civil service rules by executive order, they weren’t constrained by the APA when they did so. Mr. Trump can, with this authority, implement any number of “rules governing the competitive service” that would curtail administrative overgrowth, from large-scale firings to relocation of federal agencies out of the Washington area. The DOGE welcomes voluntary terminations once the President begins requiring federal employees to come to the office five days a week, because American taxpayers shouldn’t pay federal employees for the Covid-era privilege of staying home.<ref>[https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Elon Musk and Vivek Ramaswamy: The DOGE Plan to Reform Government: Following the Supreme Court’s guidance, we’ll reverse a decadeslong executive power grab. Musk & Ramaswamy 11/20/2024]</ref> == Reduce the deficit and debt by impounding appropriated funds == === Impound appropriated funds === Reports suggest that president-elect Trump intends to override Congress’s power of the purse by [[w:Impoundment_of_appropriated_funds|impoundment of appropriated funds]], that is, refusing to spend them. the president may [[wikipedia:Rescission_bill|propose rescission]] of specific funds, but that rescission must be approved by both the [[wikipedia:United_States_House_of_Representatives|House of Representatives]] and [[wikipedia:United_States_Senate|Senate]] within 45 days. [[w:Thomas_Jefferson|Thomas Jefferson]] was the first president to exercise the power of impoundment in 1801, which power was available to all presidents up to and including [[wikipedia:Richard_Nixon|Richard Nixon]], and was regarded as a power inherent to the office, although one with limits. He may ask Congress to repeal The [[w:Congressional_Budget_and_Impoundment_Control_Act_of_1974|Congressional Budget and Impoundment Control Act of 1974]], which was passed in response to Nixon's abuses.<ref>{{Cite web|url=http://democrats-budget.house.gov/resources/reports/impoundment-control-act-1974-what-it-why-does-it-matter|title=The Impoundment Control Act of 1974: What Is It? Why Does It Matter? {{!}} House Budget Committee Democrats|date=2019-10-23|website=democrats-budget.house.gov|language=en|access-date=2024-05-19}}</ref> If Congress refuses to do so, president Trump may impound funds anyway and argue in court that the 1974 law is unconstitutional. The matter would likely end up at the Supreme Court, which would have to do more than simply hold the 1974 act unconstitutional in order for Mr. Trump to prevail. The court would also have to overrule [[w:Train_v._City_of_New_York_(1975)|''Train v. City of New York'' (1975)]], which held that impoundment is illegal unless the underlying legislation specifically authorizes it. === Reduce the budget deficit === [[wikipedia:U.S. federal budget|U.S. federal budget]] The [[wikipedia:Fiscal_year|fiscal year]], beginning October 1 and ending on September 30 of the year following. Congress is the body required by law to pass appropriations annually and to submit funding bills passed by both houses to the President for signature. Congressional decisions are governed by rules and legislation regarding the [[wikipedia:United_States_budget_process|federal budget process]]. Budget committees set spending limits for the House and Senate committees and for Appropriations subcommittees, which then approve individual [[wikipedia:Appropriations_bill_(United_States)|appropriations bills]] to During FY2022, the federal government spent $6.3 trillion. Spending as % of GDP is 25.1%, almost 2 percentage points greater than the average over the past 50 years. Major categories of FY 2022 spending included: Medicare and Medicaid ($1.339T or 5.4% of GDP), Social Security ($1.2T or 4.8% of GDP), non-defense discretionary spending used to run federal Departments and Agencies ($910B or 3.6% of GDP), Defense Department ($751B or 3.0% of GDP), and net interest ($475B or 1.9% of GDP).<ref name="CBO_2022">[https://www.cbo.gov/publication/58888 The Federal Budget in Fiscal Year 2022: An Infographic]</ref> CBO projects a federal budget deficit of $1.6 trillion for 2024. In the agency’s projections, deficits generally increase over the coming years; the shortfall in 2034 is $2.6 trillion. The deficit amounts to 5.6 percent of gross domestic product (GDP) in 2024, swells to 6.1 percent of GDP in 2025, and then declines in the two years that follow. After 2027, deficits increase again, reaching 6.1 percent of GDP in 2034.<ref name="CBO_budgetOutlook2024">{{cite web|url=https://www.cbo.gov/publication/59710|title=The Budget and Economic Outlook: 2024 to 2034|date=February 7, 2024|publisher=CBO|access-date=February 7, 2024}}</ref> The following table summarizes several budgetary statistics for the fiscal year 2015-2021 periods as a percent of GDP, including federal tax revenue, outlays or spending, deficits (revenue – outlays), and [[wikipedia:National_debt_of_the_United_States|debt held by the public]]. The historical average for 1969-2018 is also shown. With U.S. GDP of about $21 trillion in 2019, 1% of GDP is about $210 billion.<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> Statistics for 2020-2022 are from the CBO Monthly Budget Review for FY 2022.<ref name="CBO_MBRFY2022">{{cite web|url=https://www.cbo.gov/publication/58592|title=Monthly Budget Review: Summary for Fiscal Year 2022|date=November 8, 2022|publisher=CBO|access-date=December 10, 2022}}</ref> {| class="wikitable" !Variable As % GDP !2015 !2016 !2017 !2018 !2019 !2020 !2021 !2022 !Hist Avg |- !Revenue<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> |18.0% |17.6% |17.2% |16.4% |16.4% |16.2% |17.9% |19.6% |17.4% |- !Outlays<ref name="CBO_Hist_20" /> |20.4% |20.8% |20.6% |20.2% |21.0% |31.1% |30.1% |25.1% |21.0% |- !Budget Deficit<ref name="CBO_Hist_20" /> | -2.4% | -3.2% | -3.5% | -3.8% | -4.6% | -14.9% | -12.3% | -5.5% | -3.6% |- !Debt Held by Public<ref name="CBO_Hist_20" /> |72.5% |76.4% |76.2% |77.6% |79.4% |100.3% |99.6% |94.7% | |} The [[wikipedia:U.S._Constitution|U.S. Constitution]] ([[wikipedia:Article_One_of_the_United_States_Constitution|Article I]], section 9, clause 7) states that "No money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of Receipts and Expenditures of all public Money shall be published from time to time." Each year, the President of the United States submits a budget request to Congress for the following fiscal year as required by the [[wikipedia:Budget_and_Accounting_Act_of_1921|Budget and Accounting Act of 1921]]. Current law ({{UnitedStatesCode|31|1105}}(a)) requires the president to submit a budget no earlier than the first Monday in January, and no later than the first Monday in February. Typically, presidents submit budgets on the first Monday in February. The budget submission has been delayed, however, in some new presidents' first year when the previous president belonged to a different party. === Reduce the National debt === == Reform Entitlements == === Healthcare and Medicare === [[w:ObamaCare|ObamaCare]] started as a plausible scheme for universal, cost-effective health insurance with subsidies for the needy. Only the subsidies survive because the ObamaCare policies actually delivered are so overpriced nobody would buy them without a subsidy.<ref>[https://www.wsj.com/opinion/elons-real-trump-mission-protect-growth-department-of-government-efficiency-appointments-cabinet-9e7e62b2]</ref> See below: Department of Health and Human Services === Social Security === Even FDR was aware of its flaw: it discourages working and saving. == Strategic Foreign Policy and Military reform == === Department of State === {{Main article|w:Second_presidency_of_Donald_Trump#Prospective_foreign_policy|w:State Department}} === U.S. Department of Defense === The president-elect is reportedly considering a draft executive order that establishes a “warrior board” of retired senior military personnel with the power to review three- and four-star officers “on leadership capability, strategic readiness, and commitment to military excellence," and to recommend removals of any deemed unfit for leadership. This would fast-track the removal of generals and admirals found to be “lacking in requisite leadership qualities,” consistent with his earlier vow to fire “woke” military leaders.<ref>[https://www.wsj.com/politics/national-security/trump-draft-executive-order-would-create-board-to-purge-generals-7ebaa606<nowiki> Trump draft executive order would create a board to purge generals 11/12/2024]</nowiki></ref> There are legal obstacles. The law prohibits the firing of commissioned officers except by “sentence of a general court-martial,” as a “commutation of a sentence of a general court-martial,” or “in time of war, by order of the president.” A commissioned officer who believes he’s been wrongfully dismissed has the right to seek a trial by court-martial, which may find the dismissal baseless. <ref>[https://www.wsj.com/opinion/trump-tests-the-constitutions-limits-checks-balances-government-policy-law-78d0d0f1<nowiki> Trump test the constitutions limits 11/19/2024]</nowiki></ref> Musk said, "Some idiots are still building manned fighter jets like the F-35," and later added: "Manned fighter jets are outdated in the age of drones and only put pilots' lives at risk." [[w:Bernie_Sanders|Bernie Sanders]] wrote on X: "Elon Musk is right. The Pentagon, with a budget of $886 billion, just failed its 7th audit in a row. It's lost track of billions. Last year, only 13 senators voted against the Military Industrial Complex and a defense budget full of waste and fraud. That must change."<ref>{{Cite web|url=https://www.newsweek.com/bernie-sanders-finds-new-common-ground-elon-musk-1993820|title=Bernie Sanders finds new common ground with Elon Musk|last=Reporter|first=Mandy Taheri Weekend|date=2024-12-01|website=Newsweek|language=en|access-date=2024-12-02}}</ref> Failed its fifth audit in June 2023.<ref>{{Cite web|url=https://www.newsweek.com/fox-news-host-confronts-gop-senator-pentagons-fifth-failed-audit-1804379|title=Fox News host confronts GOP Senator on Pentagon's fifth failed audit|last=Writer|first=Fatma Khaled Staff|date=2023-06-04|website=Newsweek|language=en|access-date=2024-12-02}}</ref> == Reform the other Government Bureaus and Departments == === Department of Education === [[w:United_States_Department_of_Education|w:Department of Education]] has 4,400 employees – the smallest staff of the Cabinet agencies<ref>{{Cite web|url=https://www2.ed.gov/about/overview/fed/role.html|title=Federal Role in Education|date=2021-06-15|website=www2.ed.gov|language=en|access-date=2022-04-28}}</ref> – and a 2024 budget of $238 billion.<ref name="DOE-mission">{{Cite web|url=https://www.usaspending.gov/agency/department-of-education?fy=2024|title=Agency Profile {{!}} U.S. Department of Education|website=www2.ed.gov|access-date=2024-11-14}}</ref> The 2023 Budget was $274 billion, which included funding for children with disabilities ([[wikipedia:Individuals_with_Disabilities_Education_Act|IDEA]]), pandemic recovery, early childhood education, [[wikipedia:Pell_Grant|Pell Grants]], [[wikipedia:Elementary_and_Secondary_Education_Act|Title I]], work assistance, among other programs. This budget was down from $637.7 billion in 2022.<ref>{{Cite web|url=https://www.future-ed.org/what-the-new-pisa-results-really-say-about-u-s-schools/|title=What the New PISA Results Really Say About U.S. Schools|date=2021-06-15|website=future-ed.com|language=en|access-date=2024-11-14}}</ref> The WSJ proposes that the Civil Rights division be absorbed into the Department of Justice, and that its outstanding loan portolio be handled by the Department of the Treasury. Despite the redundancies, its unlikely that it will be abolished, which would require congressional action and buy-in from Democrats in the Senate; Republicans don’t have enough votes to do it alone. A republican appointee is expected to push back against federal education overreach and progressive policies like DEI. <ref>[https://www.wsj.com/opinion/trump-can-teach-the-education-department-a-lesson-nominee-needs-boldness-back-school-choice-oppose-woke-indoctrination-ddf6a38d<nowiki> Trump can teach the Education Department a Lesson. WSJ 11/20/2024]</nowiki></ref> === U.S. Department of Health and Human Services === [[w:U.S._Department_of_Health_and_Human_Services|U.S. Department of Health and Human Services]] was authorized a budget for [[w:2020_United_States_federal_budget|fiscal year 2020]] of $1.293 trillion. It has 13 operating divisions, 10 of which constitute the [[w:United_States_Public_Health_Service|Public Health Services]], whose budget authorization is broken down as follows:<ref name="hhs_budget_fy2020">{{cite web|url=https://www.hhs.gov/about/budget/fy2020/index.html|title=HHS FY 2020 Budget in Brief|date=October 5, 2019|website=HHS Budget & Performance|publisher=United States Department of Health & Human Services|page=7|access-date=May 9, 2020}}</ref> {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Food and Drug Administration|Food and Drug Administration]] (FDA) |$3,329 MM |- |[[w:Health Resources and Services Administration|Health Resources and Services Administration]] (HRSA) |$11,004 |- |[[w:Indian Health Service|Indian Health Service]] (IHS) |$6,104 |- |[[w:Centers for Disease Control and Prevention|Centers for Disease Control and Prevention]] (CDC) |$6,767 |- |[[w:National Institutes of Health|National Institutes of Health]] (NIH) |$33,669 |- |[[w:Substance Abuse and Mental Health Services Administration|Substance Abuse and Mental Health Services Administration]] (SAMHSA) |$5,535 |- |[[w:Agency for Healthcare Research and Quality|Agency for Healthcare Research and Quality]] (AHRQ) |$0 |- |[[w:Centers for Medicare & Medicaid Services|Centers for Medicare & Medicaid Services]] (CMMS) |$1,169,091 |- |[[w:Administration for Children and Families|Administration for Children and Families]] (ACF) |$52,121 |- |[[w:Administration for Community Living|Administration for Community Living]] (ACL) |$1,997 |- |} {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Departmental Management|Departmental Management]] |$340 |- |Non-Recurring Expense Fund |$-400 |- |[[w:Office of Medicare Hearings and Appeals|Office of Medicare Hearings and Appeals]] |$186 |- |[[w:Office of the National Coordinator|Office of the National Coordinator]] |$43 |- |[[w:Office for Civil Rights|Office for Civil Rights]] |$30 |- |[[w:Office of Inspector General|Office of Inspector General]] |$82 |- |[[w:Public Health and Social Services Emergency Fund|Public Health and Social Services Emergency Fund]] |$2,667 |- |[[w:Program Support Center|Program Support Center]] |$749 |- |Offsetting Collections |$-629 |- |Other Collections |$-163 |- |'''TOTAL''' |'''$1,292,523''' |} The FY2020 budget included a $1.276 billion budget decrease for the Centers for Disease Control, and a $4.533 billion budget decrease for the National Institutes of Health. These budget cuts, along with other changes since 2019, comprised a total decrease of over $24 billion in revised discretionary budget authority across the entire Department of Health and Human Services for Fiscal Year 2020.<ref name="hhs_budget_fy2020" /> Additional details of the budgeted outlays, budget authority, and detailed budgets for other years, can be found at the HHS Budget website.<ref>{{cite web|url=http://WWW.HHS.GOV/BUDGET|title=Health and Human Services: Budget and Performance|publisher=United States Department of Health & Human Services|access-date=May 9, 2020}}</ref> [[w:Robert_F._Kennedy_Jr.|Robert F. Kennedy Jr.]] has been nominated as [[w:United_States_Secretary_of_Health_and_Human_Services|United_States_Secretary_of_Health_and_Human_Services]] He is an American politician, [[Environmental law|environmental lawyer]], [[anti-vaccine activist]], and anti-packaged food industry activist, anti-pharmaceutical industry activist, who will be nominated to serve as [[United States Secretary of Health and Human Services]],<ref name="v502">{{cite web|url=https://www.forbes.com/sites/saradorn/2024/11/14/rfk-jr-launches-independent-2024-run-here-are-all-the-conspiracies-he-promotes-from-vaccines-to-mass-shootings/|title=Trump Taps RFK Jr. As Secretary Of Health And Human Services: Here Are All The Conspiracies He's Promoted|last=Dorn|first=Sara|date=2024-11-14|website=Forbes|access-date=2024-11-15}}</ref> with the mission of "Making America Healthy Again". He is the chairman and founder of [[Children's Health Defense]], an anti-vaccine advocacy group and proponent of [[COVID-19 vaccine misinformation|dubious COVID-19 vaccine information]].<ref name="Smith_12/15/2021" /><ref name="KW" /> == CPB, PBS, NPR == [[w:Howard_Husock|Howard Husock]] suggest that instead of zeroing its $535 million budget, Republicans reform the [[w:Public_Broadcasting_Act|Public Broadcasting Act]] to eliminate bias and improve local journalism.<ref>https://www.wsj.com/opinion/the-conservative-case-for-public-broadcasting-media-policy-2d4c3c9f?page=1</ref> == NASA == In September 2026, NASA's [[w:Artemis_program|Artemis program]], established in 2017 via [[wikipedia:Space_Policy_Directive_1|Space Policy Directive 1]], is intended to reestablish a human presence on the Moon for the first time since the [[wikipedia:Apollo_17|Apollo 17]] mission in 1972. The program's stated long-term goal is to establish a [[wikipedia:Moonbase|permanent base on the Moon]] to facilitate [[wikipedia:Human_mission_to_Mars|human missions to Mars]]. The [[w:U.S._National_Academies_of_Sciences,_Engineering,_and_Medicine|U.S. National Academies of Sciences, Engineering, and Medicine]] in October, put out a report titled "NASA at a Crossroads," which identified myriad issues at the agency, including out-of-date infrastructure, pressures to prioritize short-term objectives and inefficient management practices. NASA's costly [[w:Space_Launch_System|Space Launch System]] (SLS) is the cornerstone of the Artemis program. has a price tag of around $4.1 billion per launch, and is a single-use rocket that can only launch every two years, having debuted in 2022 with the uncrewed [[w:Artemis_1_mission|Artemis 1 mission]] to the moon. In contrast, SpaceX is working to reduce the cost of a single Starship flight to under $10 million. NASA Associate Administrator Jim Free urged the incoming administration to maintain the current plans, in a symposium with the [[w:American_Astronautical_Society|American Astronautical Society]] saying "We need that consistency in purpose. That has not happened since Apollo. If we lose that, I believe we will fall apart and we will wander, and other people in this world will pass us by." NASA has already asked both [[w:SpaceX|SpaceX]] and also Jeff Bezos' [[w:Blue_Origin|Blue Origin]], to develop cargo landers for its Artemis missions and to deliver heavy equipment on them to the Moon by 2033. "Having two lunar lander providers with different approaches for crew and cargo landing capability provides mission flexibility while ensuring a regular cadence of moon landings for continued discovery and scientific opportunity," Stephen D. Creech, NASA's assistant deputy associate administrator for the moon to Mars program, said in an announcement about the partnership. "For all of the money we are spending, NASA should NOT be talking about going to the Moon - We did that 50 years ago. They should be focused on the much bigger things we are doing, including Mars (of which the Moon is a part), Defense and Science!" Trump wrote in a post on X in 2019. Trump has said he would create a [[w:Space_National_Guard|Space National Guard]], an idea that lawmakers in Congress have been proposing since 2021. Critics agree that a focus on spaceflight could come at the expense of "Earth and atmospheric sciences at NASA and the [[w:National_Oceanic_and_Atmospheric_Administration|National Oceanic and Atmospheric Administration]] (NOAA), which have been cut during the Biden era."<ref>{{Cite web|url=https://www.newsweek.com/elon-musk-donald-trump-nasa-space-policy-1990599|title=Donald Trump and Elon Musk could radically reshape NASA. Here's how|last=Reporter|first=Martha McHardy US News|date=2024-11-27|website=Newsweek|language=en|access-date=2024-12-02}}</ref> == [[w:Federal_Aviation_Administration|Federal Aviation Administration]] == Musk has often complained about the FAA "smothering" innovation, boasting that he can build a rocket faster than the agency can process the "Kafkaesque paperwork" required to make the relevant approvals.<ref>{{Cite news|url=https://www.economist.com/briefing/2024/11/21/elon-musk-and-donald-trump-seem-besotted-where-is-their-bromance-headed|title=Elon Musk and Donald Trump seem besotted. Where is their bromance headed?|work=The Economist|access-date=2024-12-04|issn=0013-0613}}</ref> == History and Miscellaneous facts == See also: [[w:Department_of_Government_Efficiency#History|Department of Government Efficiency — History]] DOGE's work will "conclude" no later than July 4, 2026, the 250th anniversary of the signing of the [[United States Declaration of Independence|U.S. Declaration of Independence]],<ref>{{Cite web|url=https://thehill.com/policy/4987402-trump-musk-advisory-group-spending/|title=Elon Musk, Vivek Ramaswamy to lead Trump's Department of Government Efficiency (DOGE)|last=Nazzaro|first=Miranda|date=November 13, 2024|website=The Hill|language=en-US|access-date=November 13, 2024}}</ref> also coinciding with America's [[United States Semiquincentennial|semiquincentennial]] celebrations and a proposed "Great American Fair". Despite its name it is not expected to be a [[wikipedia:United_States_federal_executive_departments|federal executive department]], but rather may operate under the [[Federal Advisory Committee Act]],<ref>{{Cite web|url=https://www.cbsnews.com/news/trump-department-of-government-efficiency-doge-elon-musk-ramaswamy/|title=What to know about Trump's Department of Government Efficiency, led by Elon Musk and Vivek Ramaswamy - CBS News|last=Picchi|first=Aimee|date=2024-11-14|website=www.cbsnews.com|language=en-US|access-date=2024-11-14}}</ref> so its formation is not expected to require approval from the [[wikipedia:United_States_Congress|U.S. Congress]]. NYT argues that records of its meetings must be made public.{{Cn}} Musk has stated that he believes such a commission could reduce the [[wikipedia:United_States_federal_budget|U.S. federal budget]] by $2 trillion, which would be a reduction of almost one third from its 2023 total. [[Maya MacGuineas]] of the [[Committee for a Responsible Federal Budget]] has said that this saving is "absolutely doable" over a period of 10 years, but it would be difficult to do in a single year "without compromising some of the fundamental objectives of the government that are widely agreed upon".<ref>{{Cite web|url=https://thehill.com/business/4966789-elon-musk-skepticism-2-trillion-spending-cuts/|title=Elon Musk draws skepticism with call for $2 trillion in spending cuts|last=Folley|first=Aris|date=2024-11-03|website=The Hill|language=en-US|access-date=2024-11-14}}</ref> [[wikipedia:Jamie_Dimon|Jamie Dimon]], the chief executive officer of [[wikipedia:JPMorgan_Chase|JPMorgan Chase]], has supported the idea. Some commentators questioned whether DOGE is a conflict of interest for Musk given that his companies are contractors to the federal government. The body is "unlikely to have any regulatory teeth on its own, but there's little doubt that it can have influence on the incoming administration and how it will determine its budgets".<ref>{{Cite web|url=https://www.vox.com/policy/384904/trumps-department-of-government-efficiency-sounds-like-a-joke-it-isnt|title=Trump tapped Musk to co-lead the "Department of Government Efficiency." What the heck is that?|last=Fayyad|first=Abdallah|date=2024-11-13|website=Vox|language=en-US|access-date=2024-11-14}}</ref> Elon Musk had called [[w:Federico_Sturzenegger|Federico Sturzenegger]], Argentina's [[Minister of Deregulation and Transformation of the State]] ([[w:es:Ministerio_de_Desregulación_y_Transformación_del_Estado|es]]), to discuss imitating his ministry's model.<ref>{{Cite web|url=https://www.infobae.com/economia/2024/11/08/milei-brindo-un-nuevo-apoyo-a-sturzenegger-y-afirmo-que-elon-musk-imitara-su-gestion-en-eeuu/|title=Milei brindó un nuevo apoyo a Sturzenegger y afirmó que Elon Musk imitará su gestión en EEUU|date=November 8, 2024|website=infobae|language=es-ES|access-date=November 13, 2024}}</ref> == Reception and Criticism == See also: [[w:Department_of_Government_Efficiency#Reception|w:Department of Government Efficiency — Reception]] The WSJ reports that Tesla's Texas facility dumped toxic wastewater into the public sewer system, into a lagoon, and into a local river, violated Texas environmental regulations, and fired an employee who attempted to comply with the law.{{Cn}} == See also == * [[w:Second_presidential_transition_of_Donald_Trump|Second presidential transition of Donald Trump]] * [[w:United_States_federal_budget#Deficits_and_debt|United States federal budget - Deficits and debt]] * [[w:United_States_Bureau_of_Efficiency|United States Bureau of Efficiency]] – United States federal government bureau from 1916 to 1933 * [[w:Brownlow_Committee|Brownlow Committee]] – 1937 commission recommending United States federal government reforms * [[w:Grace_Commission|Grace Commission]] – Investigation to eliminate inefficiency in the United States federal government * [[w:Hoover_Commission|Hoover Commission]] – United States federal commission in 1947 advising on executive reform * [[w:Keep_Commission|Keep Commission]] * [[w:Project_on_National_Security_Reform|Project on National Security Reform]] == Reference Notes == <references group="lower-alpha" /> c0u3qj1mj034fk80ilpma7sozyszdhb 2690198 2690194 2024-12-04T03:19:19Z Jaredscribe 2906761 sfn 2690198 wikitext text/x-wiki The U.S. [[w:Department of Government Efficiency]]. {{Infobox Organization |name=Department of Government Efficiency |logo=DOGE Logo as of November 14, 2024.jpg |logo_size=150px |logo_caption=Logo on [[Twitter|X]] (formerly Twitter) as of November 14, 2024 |seal= |seal_size= |seal_caption= |formation=Announced on November 12, 2024; yet to be established |abbreviation=DOGE |key_people={{plainlist|[[w:Commissioner of the Department of Government Efficiency|Co-commissioners]]: * [[w:Elon Musk]] * [[w:Vivek Ramaswamy]] }} |website={{URL|https://x.com/DOGE|x.com/DOGE}} }} This "'''Wiki Of Government Efficiency'''" (WOGE) will analyze the [[w:U.S._Federal_budget|U.S. federal budget]], [[User:Jaredscribe/Department of Government Efficiency#Reform the other Government Bureaus and Departments|federal bureaucracy]], and [[User:Jaredscribe/Department of Government Efficiency#Shrink the federal civil service|federal civil service]], in the public interest, and in the context of [[w:Second_presidency_of_Donald_Trump|president-elect Trump']]<nowiki/>s [[w:Agenda_47|Agenda 47]], with non-partisan research, analysis, and criticism of forward-looking proposals on how the '''[[w:Department of Government Efficiency|Department of Government Efficiency]]'''{{Efn|Also referred to as '''Government Efficiency Commission'''}} (DOGE) might fulfill its mission to ''"dismantle government bureaucracy, slash excess regulations, and cut wasteful expenditures and restructure federal agencies"'', in the words of president-elect [[wikipedia:Donald_Trump|Donald Trump]], who called for it to address ''"massive waste and fraud"'' in government spending.<ref name=":1">{{Cite web|url=https://www.bbc.co.uk/news/articles/c93qwn8p0l0o|title=Donald Trump picks Elon Musk for US government cost-cutting role|last1=Faguy|first1=Ana|last2=FitzGerald|first2=James|date=2024-11-13|publisher=BBC News|language=en-GB|access-date=2024-11-13}}</ref> The DOGE will work with through the [[w:Office_of_Management_and_Budget|Office of Management and Budget]] as its "policy vector". Here's [[User:Jaredscribe/Department of Government Efficiency/How to contribute|how to contribute]] to the WOGE. The [[w:U.S._budget_deficit|U.S. Budget deficit]], (C.f. [[w:Government_budget_balance|fiscal deficit]]), and the [[w:National_debt_of_the_United_States|U.S. National debt]], currently $35.7 Trillion as of 10/2024, which is 99% of the [[w:U.S._GDP|U.S. GDP]],<ref>{{Unbulleted list citebundle|{{cite news|newspaper=Financial Post| title= Musk's $2 Trillion of Budget Cuts Would Have These Stocks Moving|url=https://financialpost.com/pmn/business-pmn/musks-2-trillion-of-budget-cuts-would-have-these-stocks-moving|first=Alexandra|last=Semenova|date=November 4, 2024}}|{{cite news|newspaper= New York Times|title=Elon|url=https://nytimes.com/2024/10/29/us/politics/elon-musk-trump-economy-hardship.html}}|{{Cite web |date=September 5, 2024 |title=Trump says he'd create a government efficiency commission led by Elon Musk |url=https://apnews.com/article/donald-trump-elon-musk-government-efficiency-commission-e831ed5dc2f6a56999e1a70bb0a4eaeb |publisher=AP News}}|{{cite web|first=Jenn|last=Brice|title=How Elon Musk's $130 million investment in Trump's victory could reap a huge payoff for Tesla and the rest of his business empire|url=https://fortune.com/2024/11/06/elon-musk-donald-trump-tesla-spacex-xai-boring-neuralink|website=Fortune}}|{{cite web|url=https://axios.com/2024/11/07/elon-musk-government-efficiency-trump|title=Musk will bring his Twitter management style to government reform}}|{{cite news| access-date =November 9, 2024|work=Reuters|date=September 6, 2024|first1=Helen|first2=Gram|last1=Coster| last2=Slattery|title=Trump says he will tap Musk to lead government efficiency commission if elected| url= https://reuters.com/world/us/trump-adopt-musks-proposal-government-efficiency-commission-wsj-reports-2024-09-05}}|{{cite web|title=Trump says Musk could head 'government efficiency' force|url= https://bbc.com/news/articles/c74lgwkrmrpo|publisher=BBC}}|{{cite web|date =November 5, 2024|title=How Elon Musk could gut the government under Trump|url=https://independent.co.uk/news/world/americas/us-politics/elon-musk-donald-trump-economy-job-cuts-b2641644.html|website= The Independent}}}}</ref> and expected to grow to 134% of GDP by 2034 if current laws remain unchanged, according to the [[w:Congressional_Budget_Office|Congressional Budget Office]]. The DOGE will be a [[wikipedia:Presidential_commission_(United_States)|presidential advisory commission]] led by the billionaire businessmen [[wikipedia:Elon_Musk|Elon Musk]] and [[wikipedia:Vivek_Ramaswamy|Vivek Ramaswamy]], and possibly [[w:Ron_Paul|Ron Paul]]<ref>{{Cite web|url=https://thehill.com/video/ron-paul-vows-to-join-elon-musk-help-eliminate-government-waste-in-a-trump-admin/10191375|title=Ron Paul vows to join Elon Musk, help eliminate government waste in a Trump admin|date=November 5, 2024|website=The Hill}}</ref><ref>{{Cite web|url=https://usatoday.com/story/business/2024/10/28/patricia-healy-elon-musk-highlights-need-for-government-efficiency/75798556007|title=Elon Musk puts spotlight on ... Department of Government Efficiency? {{!}} Cumberland Comment|last=Healy|first=Patricia|website=USA TODAY|language=en-US|access-date=November 9, 2024}}</ref>. Musk stated his belief that DOGE could remove US$2 trillion from the [[w:United_States_federal_budget|U.S. federal budget]],<ref>{{Cite web|url=https://www.youtube.com/live/HysDMs2a-iM?si=92I5LD1FY2PAsSuG&t=15822|title=WATCH LIVE: Trump holds campaign rally at Madison Square Garden in New York|date=October 28, 2024|website=youtube.com|publisher=[[PBS NewsHour]]|language=en|format=video}}</ref> without specifying whether these savings would be made over a single year or a longer period.<ref>{{Cite web|url=https://www.bbc.co.uk/news/articles/cdj38mekdkgo|title=Can Elon Musk cut $2 trillion from US government spending?|last=Chu|first=Ben|date=2024-11-13|website=BBC News|language=en-GB|access-date=2024-11-14}}</ref> [[File:2023_US_Federal_Budget_Infographic.png|thumb|An infographic on outlays and revenues in the 2023 [[United States federal budget|U.S. federal budget]]]] DOGE could also streamline permitting with “categorical exclusions” from environmental reviews under the National Environmental Policy Act. {{sidebar with collapsible lists|name=U.S. deficit and debt topics|namestyle=background:#bf0a30;|style=width:22.0em; border: 4px double #d69d36; background:var(--background-color-base, #FFFFFF);|bodyclass=vcard|pretitle='''<span class="skin-invert">This article is part of [[:Category:United States|a series]] on the</span>'''|title=[[United States federal budget|<span style="color:var(--color-base, #000000);">Budget and debt in the<br/>United States of America</span>]]|image=[[File:Seal of the United States Congress.svg|90px]] [[File:Seal of the United States Department of the Treasury.svg|90px]]|titlestyle=background:var(--background-color-base, #002868); background-clip:padding-box;|headingstyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff);|listtitlestyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff); text-align:center;|expanded={{{expanded|{{{1|}}}}}}|list1name=dimensions|list1title=Major dimensions|list1class=hlist skin-invert|list1=* [[Economy of the United States|Economy]] * [[Expenditures in the United States federal budget|Expenditures]] * [[United States federal budget|Federal budget]] * [[Financial position of the United States|Financial position]] * [[Military budget of the United States|Military budget]] * [[National debt of the United States|Public debt]] * [[Taxation in the United States|Taxation]] * [[Unemployment in the United States|Unemployment]] * [[Government_spending_in_the_United_States|Gov't spending]]|list2name=programs|list2title=Programs|list2class=hlist skin-invert|list2=* [[Medicare (United States)|Medicare]] * [[Social programs in the United States|Social programs]] * [[Social Security (United States)|Social Security]]|list3name=issues|list3title=Contemporary issues|list3class=skin-invert|list3=<div style="margin-bottom:0.5em"> [[National Commission on Fiscal Responsibility and Reform|Bowles–Simpson Commission]] {{flatlist}} * <!--Bu--> [[Bush tax cuts]] * <!--Deb--> [[United States debt ceiling|Debt ceiling]] ** [[History of the United States debt ceiling|history]] * <!--Def--> [[Deficit reduction in the United States|Deficit reduction]] * <!--F--> [[United States fiscal cliff|Fiscal cliff]] * <!--H--> [[Healthcare reform in the United States|Healthcare reform]] * <!--P--> [[Political debates about the United States federal budget|Political debates]] * <!--So--> [[Social Security debate in the United States|Social Security debate]] * <!--St--> "[[Starve the beast]]" * <!--Su--> [[Subprime mortgage crisis]] {{endflatlist}} </div> [[2007–2008 financial crisis]] {{flatlist}} * <!--D--> [[United States debt-ceiling crisis (disambiguation)|Debt-ceiling crises]] ** [[2011 United States debt-ceiling crisis|2011]] ** [[2013 United States debt-ceiling crisis|2013]] ** [[2023 United States debt-ceiling crisis|2023]] {{endflatlist}} [[2013 United States budget sequestration|2013 budget sequestration]] {{flatlist}} * <!--G--> [[Government shutdowns in the United States|Government shutdowns]] ** [[1980 United States federal government shutdown|1980]] ** [[1981, 1984, and 1986 U.S. federal government shutdowns|1981, 1984, 1986]] ** [[1990 United States federal government shutdown|1990]] ** [[1995–1996 United States federal government shutdowns|1995–1996]] ** [[2013 United States federal government shutdown|2013]] ** [[January 2018 United States federal government shutdown|Jan 2018]] ** [[2018–2019 United States federal government shutdown|2018–2019]] {{endflatlist}} Related events {{flatlist}} *<!--E-->[[Removal of Kevin McCarthy as Speaker of the House|2023 Removal of Kevin McCarthy]] {{endflatlist}}|list4name=terminology|list4title=Terminology|list4class=hlist skin-invert|list4=Cumulative [[Government budget balance|deficit]] + [[National debt of the United States#Debates|Interest]] ≈ [[Government debt|Debt]] * [[Balance of payments]] * [[Inflation]] * [[Continuing resolution]]}} [[w:Deficit_reduction_in_the_United_States|Deficit reduction in the United States]] == Deregulate the Economy == The legal theory that this can be done through the executive branch is found in the U.S. Supreme Court’s ''[[w:West_Virginia_v._EPA|West Virginia v. EPA]]'' and ''[[w:Loper_Bright|Loper Bright]]'' rulings, which rein in the administrative state and mean that much of what the federal government now does is illegal.<ref>{{cite web|url=https://www.wsj.com/opinion/department-of-government-efficiency-elon-musk-vivek-ramaswamy-donald-trump-1e086dab|website=[[w:Wall Street Journal]]|title=The Musk-Ramaswamy Project Could Be Trump’s Best Idea}}</ref> Mr. Trump has set a goal of eliminating 10 regulations for every new one. The [[w:Competitive_Enterprise_Institute|Competitive Enterprise Institute]]’s Wayne Crews says 217,565 rules have been issued since the [[w:Federal_Register|Federal Register]] first began itemizing them in 1976, with 89,368 pages added last year. [https://sgp.fas.org/crs/misc/R43056.pdf 3,000-4,500 rules are added each year]. DOGE’s first order will be to pause enforcement of overreaching rules while starting the process to roll them back. Mr. Trump and DOGE could direct agencies to settle legal challenges to Biden rules by vacating them. This could ease the laborious process of undoing them by rule-making through the [[w:Administrative_Procedure_Act|Administrative Procedure Act]]. A source tells the WSJ they’ll do whatever they think they legally can without the APA. The [[w:Congressional_Review_Act|Congressional Review Act]]—which allows Congress to overturn recently issued agency regulations—had been used only once, prior to [[w:First_presidency_of_Donald_Trump|Trump's first term]]. While in office, he and the Republican Congress used it on 16 rules. This time, there will be more than 56 regulatory actions recent enough to be repealed. The [[w:Chevron_deference|''Chevron'' deference]] had required federal courts to defer to agencies’ interpretations of ambiguous statutes, but this was overturned in 2024. Taken together, with some other recent [[w:SCOTUS|SCOTUS]] rulings, we now have, says the WSJ, the biggest opportunity to cut regulatory red tape in more than 40 years.<ref>[https://www.wsj.com/opinion/let-the-trump-deregulation-begin-us-chamber-of-commerce-second-term-economic-growth-73f24387?cx_testId=3&cx_testVariant=cx_166&cx_artPos=0]</ref><blockquote>"Most legal edicts aren’t laws enacted by Congress but “rules and regulations” promulgated by unelected bureaucrats—tens of thousands of them each year. Most government enforcement decisions and discretionary expenditures aren’t made by the democratically elected president or even his political appointees but by millions of unelected, unappointed civil servants within government agencies who view themselves as immune from firing thanks to civil-service protections." "This is antidemocratic and antithetical to the Founders’ vision. It imposes massive direct and indirect costs on taxpayers." "When the president nullifies thousands of such regulations, critics will allege executive overreach. In fact, it will be ''correcting'' the executive overreach of thousands of regulations promulgated by administrative fiat that were never authorized by Congress. The president owes lawmaking deference to Congress, not to bureaucrats deep within federal agencies. The use of executive orders to substitute for lawmaking by adding burdensome new rules is a constitutional affront, but the use of executive orders to roll back regulations that wrongly bypassed Congress is legitimate and necessary to comply with the Supreme Court’s recent mandates. And after those regulations are fully rescinded, a future president couldn’t simply flip the switch and revive them but would instead have to ask Congress to do so" Mssrs. [https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Musk and Ramaswamy, WSJ, 11/20/2024]</blockquote> == Shrink the federal civil service == The government has around three million [[w:United_States_federal_civil_service|federal civil service]] employees, with an average salary of $106,000. Dr. Anthony Fauci made $481,000 in 2022. The federal head count has ballooned by 120,800 during the Biden years. Civil service and union protections make it hard to fire workers. Mr. Trump intends to quickly resurrect the [[w:Schedule_F|Schedule F]] reform that he sought to implement at the end of his first term but was scrapped by Mr. Biden. These would high-level federal employees to be removed like political appointees, by eliminating their job protections. WSJ proposals[https://www.wsj.com/opinion/the-doge-cheat-sheet-elon-musk-vivek-ramaswamy-department-of-government-efficiency-1c231783#cxrecs_s] The [[w:Administrative_Procedures_Act|Administrative Procedures Act]] statute protects federal employees from political retaliation, but allows for “reductions in force” that don’t target specific employees. The statute further empowers the president to “prescribe rules governing the competitive service.” The Supreme Court has held—in ''[[w:Franklin_v._Massachusetts|Franklin v. Massachusetts]]'' (1992) and ''[[w:Collins_v._Yellen|Collins v. Yellen]]'' (2021) that when revious presidents have used this power to amend the civil service rules by executive order, they weren’t constrained by the APA when they did so. Mr. Trump can, with this authority, implement any number of “rules governing the competitive service” that would curtail administrative overgrowth, from large-scale firings to relocation of federal agencies out of the Washington area. The DOGE welcomes voluntary terminations once the President begins requiring federal employees to come to the office five days a week, because American taxpayers shouldn’t pay federal employees for the Covid-era privilege of staying home.<ref>[https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Elon Musk and Vivek Ramaswamy: The DOGE Plan to Reform Government: Following the Supreme Court’s guidance, we’ll reverse a decadeslong executive power grab. Musk & Ramaswamy 11/20/2024]</ref> == Reduce the deficit and debt by impounding appropriated funds == === Impound appropriated funds === Reports suggest that president-elect Trump intends to override Congress’s power of the purse by [[w:Impoundment_of_appropriated_funds|impoundment of appropriated funds]], that is, refusing to spend them. the president may [[wikipedia:Rescission_bill|propose rescission]] of specific funds, but that rescission must be approved by both the [[wikipedia:United_States_House_of_Representatives|House of Representatives]] and [[wikipedia:United_States_Senate|Senate]] within 45 days. [[w:Thomas_Jefferson|Thomas Jefferson]] was the first president to exercise the power of impoundment in 1801, which power was available to all presidents up to and including [[wikipedia:Richard_Nixon|Richard Nixon]], and was regarded as a power inherent to the office, although one with limits. He may ask Congress to repeal The [[w:Congressional_Budget_and_Impoundment_Control_Act_of_1974|Congressional Budget and Impoundment Control Act of 1974]], which was passed in response to Nixon's abuses.<ref>{{Cite web|url=http://democrats-budget.house.gov/resources/reports/impoundment-control-act-1974-what-it-why-does-it-matter|title=The Impoundment Control Act of 1974: What Is It? Why Does It Matter? {{!}} House Budget Committee Democrats|date=2019-10-23|website=democrats-budget.house.gov|language=en|access-date=2024-05-19}}</ref> If Congress refuses to do so, president Trump may impound funds anyway and argue in court that the 1974 law is unconstitutional. The matter would likely end up at the Supreme Court, which would have to do more than simply hold the 1974 act unconstitutional in order for Mr. Trump to prevail. The court would also have to overrule [[w:Train_v._City_of_New_York_(1975)|''Train v. City of New York'' (1975)]], which held that impoundment is illegal unless the underlying legislation specifically authorizes it. === Reduce the budget deficit === [[wikipedia:U.S. federal budget|U.S. federal budget]] The [[wikipedia:Fiscal_year|fiscal year]], beginning October 1 and ending on September 30 of the year following. Congress is the body required by law to pass appropriations annually and to submit funding bills passed by both houses to the President for signature. Congressional decisions are governed by rules and legislation regarding the [[wikipedia:United_States_budget_process|federal budget process]]. Budget committees set spending limits for the House and Senate committees and for Appropriations subcommittees, which then approve individual [[wikipedia:Appropriations_bill_(United_States)|appropriations bills]] to During FY2022, the federal government spent $6.3 trillion. Spending as % of GDP is 25.1%, almost 2 percentage points greater than the average over the past 50 years. Major categories of FY 2022 spending included: Medicare and Medicaid ($1.339T or 5.4% of GDP), Social Security ($1.2T or 4.8% of GDP), non-defense discretionary spending used to run federal Departments and Agencies ($910B or 3.6% of GDP), Defense Department ($751B or 3.0% of GDP), and net interest ($475B or 1.9% of GDP).<ref name="CBO_2022">[https://www.cbo.gov/publication/58888 The Federal Budget in Fiscal Year 2022: An Infographic]</ref> CBO projects a federal budget deficit of $1.6 trillion for 2024. In the agency’s projections, deficits generally increase over the coming years; the shortfall in 2034 is $2.6 trillion. The deficit amounts to 5.6 percent of gross domestic product (GDP) in 2024, swells to 6.1 percent of GDP in 2025, and then declines in the two years that follow. After 2027, deficits increase again, reaching 6.1 percent of GDP in 2034.<ref name="CBO_budgetOutlook2024">{{cite web|url=https://www.cbo.gov/publication/59710|title=The Budget and Economic Outlook: 2024 to 2034|date=February 7, 2024|publisher=CBO|access-date=February 7, 2024}}</ref> The following table summarizes several budgetary statistics for the fiscal year 2015-2021 periods as a percent of GDP, including federal tax revenue, outlays or spending, deficits (revenue – outlays), and [[wikipedia:National_debt_of_the_United_States|debt held by the public]]. The historical average for 1969-2018 is also shown. With U.S. GDP of about $21 trillion in 2019, 1% of GDP is about $210 billion.<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> Statistics for 2020-2022 are from the CBO Monthly Budget Review for FY 2022.<ref name="CBO_MBRFY2022">{{cite web|url=https://www.cbo.gov/publication/58592|title=Monthly Budget Review: Summary for Fiscal Year 2022|date=November 8, 2022|publisher=CBO|access-date=December 10, 2022}}</ref> {| class="wikitable" !Variable As % GDP !2015 !2016 !2017 !2018 !2019 !2020 !2021 !2022 !Hist Avg |- !Revenue<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> |18.0% |17.6% |17.2% |16.4% |16.4% |16.2% |17.9% |19.6% |17.4% |- !Outlays<ref name="CBO_Hist_20" /> |20.4% |20.8% |20.6% |20.2% |21.0% |31.1% |30.1% |25.1% |21.0% |- !Budget Deficit<ref name="CBO_Hist_20" /> | -2.4% | -3.2% | -3.5% | -3.8% | -4.6% | -14.9% | -12.3% | -5.5% | -3.6% |- !Debt Held by Public<ref name="CBO_Hist_20" /> |72.5% |76.4% |76.2% |77.6% |79.4% |100.3% |99.6% |94.7% | |} The [[wikipedia:U.S._Constitution|U.S. Constitution]] ([[wikipedia:Article_One_of_the_United_States_Constitution|Article I]], section 9, clause 7) states that "No money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of Receipts and Expenditures of all public Money shall be published from time to time." Each year, the President of the United States submits a budget request to Congress for the following fiscal year as required by the [[wikipedia:Budget_and_Accounting_Act_of_1921|Budget and Accounting Act of 1921]]. Current law ({{UnitedStatesCode|31|1105}}(a)) requires the president to submit a budget no earlier than the first Monday in January, and no later than the first Monday in February. Typically, presidents submit budgets on the first Monday in February. The budget submission has been delayed, however, in some new presidents' first year when the previous president belonged to a different party. === Reduce the National debt === == Reform Entitlements == === Healthcare and Medicare === [[w:ObamaCare|ObamaCare]] started as a plausible scheme for universal, cost-effective health insurance with subsidies for the needy. Only the subsidies survive because the ObamaCare policies actually delivered are so overpriced nobody would buy them without a subsidy.<ref>[https://www.wsj.com/opinion/elons-real-trump-mission-protect-growth-department-of-government-efficiency-appointments-cabinet-9e7e62b2]</ref> See below: Department of Health and Human Services === Social Security === Even FDR was aware of its flaw: it discourages working and saving. == Strategic Foreign Policy and Military reform == === Department of State === {{Main article|w:Second_presidency_of_Donald_Trump#Prospective_foreign_policy|w:State Department}} === U.S. Department of Defense === The president-elect is reportedly considering a draft executive order that establishes a “warrior board” of retired senior military personnel with the power to review three- and four-star officers “on leadership capability, strategic readiness, and commitment to military excellence," and to recommend removals of any deemed unfit for leadership. This would fast-track the removal of generals and admirals found to be “lacking in requisite leadership qualities,” consistent with his earlier vow to fire “woke” military leaders.<ref>[https://www.wsj.com/politics/national-security/trump-draft-executive-order-would-create-board-to-purge-generals-7ebaa606<nowiki> Trump draft executive order would create a board to purge generals 11/12/2024]</nowiki></ref> There are legal obstacles. The law prohibits the firing of commissioned officers except by “sentence of a general court-martial,” as a “commutation of a sentence of a general court-martial,” or “in time of war, by order of the president.” A commissioned officer who believes he’s been wrongfully dismissed has the right to seek a trial by court-martial, which may find the dismissal baseless. <ref>[https://www.wsj.com/opinion/trump-tests-the-constitutions-limits-checks-balances-government-policy-law-78d0d0f1<nowiki> Trump test the constitutions limits 11/19/2024]</nowiki></ref> Musk said, "Some idiots are still building manned fighter jets like the F-35," and later added: "Manned fighter jets are outdated in the age of drones and only put pilots' lives at risk." [[w:Bernie_Sanders|Bernie Sanders]] wrote on X: "Elon Musk is right. The Pentagon, with a budget of $886 billion, just failed its 7th audit in a row. It's lost track of billions. Last year, only 13 senators voted against the Military Industrial Complex and a defense budget full of waste and fraud. That must change."<ref>{{Cite web|url=https://www.newsweek.com/bernie-sanders-finds-new-common-ground-elon-musk-1993820|title=Bernie Sanders finds new common ground with Elon Musk|last=Reporter|first=Mandy Taheri Weekend|date=2024-12-01|website=Newsweek|language=en|access-date=2024-12-02}}</ref> Failed its fifth audit in June 2023.<ref>{{Cite web|url=https://www.newsweek.com/fox-news-host-confronts-gop-senator-pentagons-fifth-failed-audit-1804379|title=Fox News host confronts GOP Senator on Pentagon's fifth failed audit|last=Writer|first=Fatma Khaled Staff|date=2023-06-04|website=Newsweek|language=en|access-date=2024-12-02}}</ref> == Reform the other Government Bureaus and Departments == === Department of Education === [[w:United_States_Department_of_Education|w:Department of Education]] has 4,400 employees – the smallest staff of the Cabinet agencies<ref>{{Cite web|url=https://www2.ed.gov/about/overview/fed/role.html|title=Federal Role in Education|date=2021-06-15|website=www2.ed.gov|language=en|access-date=2022-04-28}}</ref> – and a 2024 budget of $238 billion.<ref name="DOE-mission">{{Cite web|url=https://www.usaspending.gov/agency/department-of-education?fy=2024|title=Agency Profile {{!}} U.S. Department of Education|website=www2.ed.gov|access-date=2024-11-14}}</ref> The 2023 Budget was $274 billion, which included funding for children with disabilities ([[wikipedia:Individuals_with_Disabilities_Education_Act|IDEA]]), pandemic recovery, early childhood education, [[wikipedia:Pell_Grant|Pell Grants]], [[wikipedia:Elementary_and_Secondary_Education_Act|Title I]], work assistance, among other programs. This budget was down from $637.7 billion in 2022.<ref>{{Cite web|url=https://www.future-ed.org/what-the-new-pisa-results-really-say-about-u-s-schools/|title=What the New PISA Results Really Say About U.S. Schools|date=2021-06-15|website=future-ed.com|language=en|access-date=2024-11-14}}</ref> The WSJ proposes that the Civil Rights division be absorbed into the Department of Justice, and that its outstanding loan portolio be handled by the Department of the Treasury. Despite the redundancies, its unlikely that it will be abolished, which would require congressional action and buy-in from Democrats in the Senate; Republicans don’t have enough votes to do it alone. A republican appointee is expected to push back against federal education overreach and progressive policies like DEI. <ref>[https://www.wsj.com/opinion/trump-can-teach-the-education-department-a-lesson-nominee-needs-boldness-back-school-choice-oppose-woke-indoctrination-ddf6a38d<nowiki> Trump can teach the Education Department a Lesson. WSJ 11/20/2024]</nowiki></ref> === U.S. Department of Health and Human Services === [[w:U.S._Department_of_Health_and_Human_Services|U.S. Department of Health and Human Services]] was authorized a budget for [[w:2020_United_States_federal_budget|fiscal year 2020]] of $1.293 trillion. It has 13 operating divisions, 10 of which constitute the [[w:United_States_Public_Health_Service|Public Health Services]], whose budget authorization is broken down as follows:<ref name="hhs_budget_fy2020">{{cite web|url=https://www.hhs.gov/about/budget/fy2020/index.html|title=HHS FY 2020 Budget in Brief|date=October 5, 2019|website=HHS Budget & Performance|publisher=United States Department of Health & Human Services|page=7|access-date=May 9, 2020}}</ref> {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Food and Drug Administration|Food and Drug Administration]] (FDA) |$3,329 MM |- |[[w:Health Resources and Services Administration|Health Resources and Services Administration]] (HRSA) |$11,004 |- |[[w:Indian Health Service|Indian Health Service]] (IHS) |$6,104 |- |[[w:Centers for Disease Control and Prevention|Centers for Disease Control and Prevention]] (CDC) |$6,767 |- |[[w:National Institutes of Health|National Institutes of Health]] (NIH) |$33,669 |- |[[w:Substance Abuse and Mental Health Services Administration|Substance Abuse and Mental Health Services Administration]] (SAMHSA) |$5,535 |- |[[w:Agency for Healthcare Research and Quality|Agency for Healthcare Research and Quality]] (AHRQ) |$0 |- |[[w:Centers for Medicare & Medicaid Services|Centers for Medicare & Medicaid Services]] (CMMS) |$1,169,091 |- |[[w:Administration for Children and Families|Administration for Children and Families]] (ACF) |$52,121 |- |[[w:Administration for Community Living|Administration for Community Living]] (ACL) |$1,997 |- |} {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Departmental Management|Departmental Management]] |$340 |- |Non-Recurring Expense Fund |$-400 |- |[[w:Office of Medicare Hearings and Appeals|Office of Medicare Hearings and Appeals]] |$186 |- |[[w:Office of the National Coordinator|Office of the National Coordinator]] |$43 |- |[[w:Office for Civil Rights|Office for Civil Rights]] |$30 |- |[[w:Office of Inspector General|Office of Inspector General]] |$82 |- |[[w:Public Health and Social Services Emergency Fund|Public Health and Social Services Emergency Fund]] |$2,667 |- |[[w:Program Support Center|Program Support Center]] |$749 |- |Offsetting Collections |$-629 |- |Other Collections |$-163 |- |'''TOTAL''' |'''$1,292,523''' |} The FY2020 budget included a $1.276 billion budget decrease for the Centers for Disease Control, and a $4.533 billion budget decrease for the National Institutes of Health. These budget cuts, along with other changes since 2019, comprised a total decrease of over $24 billion in revised discretionary budget authority across the entire Department of Health and Human Services for Fiscal Year 2020.<ref name="hhs_budget_fy2020" /> Additional details of the budgeted outlays, budget authority, and detailed budgets for other years, can be found at the HHS Budget website.<ref>{{cite web|url=http://WWW.HHS.GOV/BUDGET|title=Health and Human Services: Budget and Performance|publisher=United States Department of Health & Human Services|access-date=May 9, 2020}}</ref> [[w:Robert_F._Kennedy_Jr.|Robert F. Kennedy Jr.]] has been nominated as [[w:United_States_Secretary_of_Health_and_Human_Services|United_States_Secretary_of_Health_and_Human_Services]] He is an American politician, [[Environmental law|environmental lawyer]], [[anti-vaccine activist]], and anti-packaged food industry activist, anti-pharmaceutical industry activist, who will be nominated to serve as [[United States Secretary of Health and Human Services]],<ref name="v502">{{cite web|url=https://www.forbes.com/sites/saradorn/2024/11/14/rfk-jr-launches-independent-2024-run-here-are-all-the-conspiracies-he-promotes-from-vaccines-to-mass-shootings/|title=Trump Taps RFK Jr. As Secretary Of Health And Human Services: Here Are All The Conspiracies He's Promoted|last=Dorn|first=Sara|date=2024-11-14|website=Forbes|access-date=2024-11-15}}</ref> with the mission of "Making America Healthy Again". He is the chairman and founder of [[Children's Health Defense]], an anti-vaccine advocacy group and proponent of [[COVID-19 vaccine misinformation|dubious COVID-19 vaccine information]].<ref name="Smith_12/15/2021" /><ref name="KW" /> == CPB, PBS, NPR == [[w:Howard_Husock|Howard Husock]] suggest that instead of zeroing its $535 million budget, Republicans reform the [[w:Public_Broadcasting_Act|Public Broadcasting Act]] to eliminate bias and improve local journalism.<ref>https://www.wsj.com/opinion/the-conservative-case-for-public-broadcasting-media-policy-2d4c3c9f?page=1</ref> == NASA == In September 2026, NASA's [[w:Artemis_program|Artemis program]], established in 2017 via [[wikipedia:Space_Policy_Directive_1|Space Policy Directive 1]], is intended to reestablish a human presence on the Moon for the first time since the [[wikipedia:Apollo_17|Apollo 17]] mission in 1972. The program's stated long-term goal is to establish a [[wikipedia:Moonbase|permanent base on the Moon]] to facilitate [[wikipedia:Human_mission_to_Mars|human missions to Mars]]. The [[w:U.S._National_Academies_of_Sciences,_Engineering,_and_Medicine|U.S. National Academies of Sciences, Engineering, and Medicine]] in October, put out a report titled "NASA at a Crossroads," which identified myriad issues at the agency, including out-of-date infrastructure, pressures to prioritize short-term objectives and inefficient management practices. NASA's costly [[w:Space_Launch_System|Space Launch System]] (SLS) is the cornerstone of the Artemis program. has a price tag of around $4.1 billion per launch, and is a single-use rocket that can only launch every two years, having debuted in 2022 with the uncrewed [[w:Artemis_1_mission|Artemis 1 mission]] to the moon. In contrast, SpaceX is working to reduce the cost of a single Starship flight to under $10 million. NASA Associate Administrator Jim Free urged the incoming administration to maintain the current plans, in a symposium with the [[w:American_Astronautical_Society|American Astronautical Society]] saying "We need that consistency in purpose. That has not happened since Apollo. If we lose that, I believe we will fall apart and we will wander, and other people in this world will pass us by." NASA has already asked both [[w:SpaceX|SpaceX]] and also Jeff Bezos' [[w:Blue_Origin|Blue Origin]], to develop cargo landers for its Artemis missions and to deliver heavy equipment on them to the Moon by 2033. "Having two lunar lander providers with different approaches for crew and cargo landing capability provides mission flexibility while ensuring a regular cadence of moon landings for continued discovery and scientific opportunity," Stephen D. Creech, NASA's assistant deputy associate administrator for the moon to Mars program, said in an announcement about the partnership. "For all of the money we are spending, NASA should NOT be talking about going to the Moon - We did that 50 years ago. They should be focused on the much bigger things we are doing, including Mars (of which the Moon is a part), Defense and Science!" Trump wrote in a post on X in 2019. Trump has said he would create a [[w:Space_National_Guard|Space National Guard]], an idea that lawmakers in Congress have been proposing since 2021. Critics agree that a focus on spaceflight could come at the expense of "Earth and atmospheric sciences at NASA and the [[w:National_Oceanic_and_Atmospheric_Administration|National Oceanic and Atmospheric Administration]] (NOAA), which have been cut during the Biden era."<ref>{{Cite web|url=https://www.newsweek.com/elon-musk-donald-trump-nasa-space-policy-1990599|title=Donald Trump and Elon Musk could radically reshape NASA. Here's how|last=Reporter|first=Martha McHardy US News|date=2024-11-27|website=Newsweek|language=en|access-date=2024-12-02}}</ref> == [[w:Federal_Aviation_Administration|Federal Aviation Administration]] == Musk has often complained about the FAA "smothering" innovation, boasting that he can build a rocket faster than the agency can process the "Kafkaesque paperwork" required to make the relevant approvals.{{sfn|Economist 11/23|2024}} == History and Miscellaneous facts == See also: [[w:Department_of_Government_Efficiency#History|Department of Government Efficiency — History]] DOGE's work will "conclude" no later than July 4, 2026, the 250th anniversary of the signing of the [[United States Declaration of Independence|U.S. Declaration of Independence]],<ref>{{Cite web|url=https://thehill.com/policy/4987402-trump-musk-advisory-group-spending/|title=Elon Musk, Vivek Ramaswamy to lead Trump's Department of Government Efficiency (DOGE)|last=Nazzaro|first=Miranda|date=November 13, 2024|website=The Hill|language=en-US|access-date=November 13, 2024}}</ref> also coinciding with America's [[United States Semiquincentennial|semiquincentennial]] celebrations and a proposed "Great American Fair". Despite its name it is not expected to be a [[wikipedia:United_States_federal_executive_departments|federal executive department]], but rather may operate under the [[Federal Advisory Committee Act]],<ref>{{Cite web|url=https://www.cbsnews.com/news/trump-department-of-government-efficiency-doge-elon-musk-ramaswamy/|title=What to know about Trump's Department of Government Efficiency, led by Elon Musk and Vivek Ramaswamy - CBS News|last=Picchi|first=Aimee|date=2024-11-14|website=www.cbsnews.com|language=en-US|access-date=2024-11-14}}</ref> so its formation is not expected to require approval from the [[wikipedia:United_States_Congress|U.S. Congress]]. NYT argues that records of its meetings must be made public.{{Cn}} Musk has stated that he believes such a commission could reduce the [[wikipedia:United_States_federal_budget|U.S. federal budget]] by $2 trillion, which would be a reduction of almost one third from its 2023 total. [[Maya MacGuineas]] of the [[Committee for a Responsible Federal Budget]] has said that this saving is "absolutely doable" over a period of 10 years, but it would be difficult to do in a single year "without compromising some of the fundamental objectives of the government that are widely agreed upon".<ref>{{Cite web|url=https://thehill.com/business/4966789-elon-musk-skepticism-2-trillion-spending-cuts/|title=Elon Musk draws skepticism with call for $2 trillion in spending cuts|last=Folley|first=Aris|date=2024-11-03|website=The Hill|language=en-US|access-date=2024-11-14}}</ref> [[wikipedia:Jamie_Dimon|Jamie Dimon]], the chief executive officer of [[wikipedia:JPMorgan_Chase|JPMorgan Chase]], has supported the idea. Some commentators questioned whether DOGE is a conflict of interest for Musk given that his companies are contractors to the federal government. The body is "unlikely to have any regulatory teeth on its own, but there's little doubt that it can have influence on the incoming administration and how it will determine its budgets".<ref>{{Cite web|url=https://www.vox.com/policy/384904/trumps-department-of-government-efficiency-sounds-like-a-joke-it-isnt|title=Trump tapped Musk to co-lead the "Department of Government Efficiency." What the heck is that?|last=Fayyad|first=Abdallah|date=2024-11-13|website=Vox|language=en-US|access-date=2024-11-14}}</ref> Elon Musk had called [[w:Federico_Sturzenegger|Federico Sturzenegger]], Argentina's [[Minister of Deregulation and Transformation of the State]] ([[w:es:Ministerio_de_Desregulación_y_Transformación_del_Estado|es]]), to discuss imitating his ministry's model.<ref>{{Cite web|url=https://www.infobae.com/economia/2024/11/08/milei-brindo-un-nuevo-apoyo-a-sturzenegger-y-afirmo-que-elon-musk-imitara-su-gestion-en-eeuu/|title=Milei brindó un nuevo apoyo a Sturzenegger y afirmó que Elon Musk imitará su gestión en EEUU|date=November 8, 2024|website=infobae|language=es-ES|access-date=November 13, 2024}}</ref> == Reception and Criticism == See also: [[w:Department_of_Government_Efficiency#Reception|w:Department of Government Efficiency — Reception]] The WSJ reports that Tesla's Texas facility dumped toxic wastewater into the public sewer system, into a lagoon, and into a local river, violated Texas environmental regulations, and fired an employee who attempted to comply with the law.{{Cn}} == See also == * [[w:Second_presidential_transition_of_Donald_Trump|Second presidential transition of Donald Trump]] * [[w:United_States_federal_budget#Deficits_and_debt|United States federal budget - Deficits and debt]] * [[w:United_States_Bureau_of_Efficiency|United States Bureau of Efficiency]] – United States federal government bureau from 1916 to 1933 * [[w:Brownlow_Committee|Brownlow Committee]] – 1937 commission recommending United States federal government reforms * [[w:Grace_Commission|Grace Commission]] – Investigation to eliminate inefficiency in the United States federal government * [[w:Hoover_Commission|Hoover Commission]] – United States federal commission in 1947 advising on executive reform * [[w:Keep_Commission|Keep Commission]] * [[w:Project_on_National_Security_Reform|Project on National Security Reform]] == Notes == {{reflist}} == References == {{refbegin}} * {{Cite news|url=https://www.economist.com/briefing/2024/11/21/elon-musk-and-donald-trump-seem-besotted-where-is-their-bromance-headed|title=Elon Musk and Donald Trump seem besotted. Where is their bromance headed?|work=The Economist|access-date=2024-12-04|issn=0013-0613 |ref={{harvid|Economist 11/23|2024}} }} <references group="lower-alpha" /> {{refend}} rnr37x059oi7otym4fa16lz7aky8msd 2690199 2690198 2024-12-04T03:21:08Z Jaredscribe 2906761 2690199 wikitext text/x-wiki The U.S. [[w:Department of Government Efficiency]]. {{Infobox Organization |name=Department of Government Efficiency |logo=DOGE Logo as of November 14, 2024.jpg |logo_size=150px |logo_caption=Logo on [[Twitter|X]] (formerly Twitter) as of November 14, 2024 |seal= |seal_size= |seal_caption= |formation=Announced on November 12, 2024; yet to be established |abbreviation=DOGE |key_people={{plainlist|[[w:Commissioner of the Department of Government Efficiency|Co-commissioners]]: * [[w:Elon Musk]] * [[w:Vivek Ramaswamy]] }} |website={{URL|https://x.com/DOGE|x.com/DOGE}} }} This "'''Wiki Of Government Efficiency'''" (WOGE) will analyze the [[w:U.S._Federal_budget|U.S. federal budget]], [[User:Jaredscribe/Department of Government Efficiency#Reform the other Government Bureaus and Departments|federal bureaucracy]], and [[User:Jaredscribe/Department of Government Efficiency#Shrink the federal civil service|federal civil service]], in the public interest, and in the context of [[w:Second_presidency_of_Donald_Trump|president-elect Trump']]<nowiki/>s [[w:Agenda_47|Agenda 47]], with non-partisan research, analysis, and criticism of forward-looking proposals on how the '''[[w:Department of Government Efficiency|Department of Government Efficiency]]'''{{Efn|Also referred to as '''Government Efficiency Commission'''}} (DOGE) might fulfill its mission to ''"dismantle government bureaucracy, slash excess regulations, and cut wasteful expenditures and restructure federal agencies"'', in the words of president-elect [[wikipedia:Donald_Trump|Donald Trump]], who called for it to address ''"massive waste and fraud"'' in government spending.<ref name=":1">{{Cite web|url=https://www.bbc.co.uk/news/articles/c93qwn8p0l0o|title=Donald Trump picks Elon Musk for US government cost-cutting role|last1=Faguy|first1=Ana|last2=FitzGerald|first2=James|date=2024-11-13|publisher=BBC News|language=en-GB|access-date=2024-11-13}}</ref> The DOGE will work with through the [[w:Office_of_Management_and_Budget|Office of Management and Budget]] as its "policy vector". Here's [[User:Jaredscribe/Department of Government Efficiency/How to contribute|how to contribute]] to the WOGE. The [[w:U.S._budget_deficit|U.S. Budget deficit]], (C.f. [[w:Government_budget_balance|fiscal deficit]]), and the [[w:National_debt_of_the_United_States|U.S. National debt]], currently $35.7 Trillion as of 10/2024, which is 99% of the [[w:U.S._GDP|U.S. GDP]],<ref>{{Unbulleted list citebundle|{{cite news|newspaper=Financial Post| title= Musk's $2 Trillion of Budget Cuts Would Have These Stocks Moving|url=https://financialpost.com/pmn/business-pmn/musks-2-trillion-of-budget-cuts-would-have-these-stocks-moving|first=Alexandra|last=Semenova|date=November 4, 2024}}|{{cite news|newspaper= New York Times|title=Elon|url=https://nytimes.com/2024/10/29/us/politics/elon-musk-trump-economy-hardship.html}}|{{Cite web |date=September 5, 2024 |title=Trump says he'd create a government efficiency commission led by Elon Musk |url=https://apnews.com/article/donald-trump-elon-musk-government-efficiency-commission-e831ed5dc2f6a56999e1a70bb0a4eaeb |publisher=AP News}}|{{cite web|first=Jenn|last=Brice|title=How Elon Musk's $130 million investment in Trump's victory could reap a huge payoff for Tesla and the rest of his business empire|url=https://fortune.com/2024/11/06/elon-musk-donald-trump-tesla-spacex-xai-boring-neuralink|website=Fortune}}|{{cite web|url=https://axios.com/2024/11/07/elon-musk-government-efficiency-trump|title=Musk will bring his Twitter management style to government reform}}|{{cite news| access-date =November 9, 2024|work=Reuters|date=September 6, 2024|first1=Helen|first2=Gram|last1=Coster| last2=Slattery|title=Trump says he will tap Musk to lead government efficiency commission if elected| url= https://reuters.com/world/us/trump-adopt-musks-proposal-government-efficiency-commission-wsj-reports-2024-09-05}}|{{cite web|title=Trump says Musk could head 'government efficiency' force|url= https://bbc.com/news/articles/c74lgwkrmrpo|publisher=BBC}}|{{cite web|date =November 5, 2024|title=How Elon Musk could gut the government under Trump|url=https://independent.co.uk/news/world/americas/us-politics/elon-musk-donald-trump-economy-job-cuts-b2641644.html|website= The Independent}}}}</ref> and expected to grow to 134% of GDP by 2034 if current laws remain unchanged, according to the [[w:Congressional_Budget_Office|Congressional Budget Office]]. The DOGE will be a [[wikipedia:Presidential_commission_(United_States)|presidential advisory commission]] led by the billionaire businessmen [[wikipedia:Elon_Musk|Elon Musk]] and [[wikipedia:Vivek_Ramaswamy|Vivek Ramaswamy]], and possibly [[w:Ron_Paul|Ron Paul]]<ref>{{Cite web|url=https://thehill.com/video/ron-paul-vows-to-join-elon-musk-help-eliminate-government-waste-in-a-trump-admin/10191375|title=Ron Paul vows to join Elon Musk, help eliminate government waste in a Trump admin|date=November 5, 2024|website=The Hill}}</ref><ref>{{Cite web|url=https://usatoday.com/story/business/2024/10/28/patricia-healy-elon-musk-highlights-need-for-government-efficiency/75798556007|title=Elon Musk puts spotlight on ... Department of Government Efficiency? {{!}} Cumberland Comment|last=Healy|first=Patricia|website=USA TODAY|language=en-US|access-date=November 9, 2024}}</ref>. Musk stated his belief that DOGE could remove US$2 trillion from the [[w:United_States_federal_budget|U.S. federal budget]],<ref>{{Cite web|url=https://www.youtube.com/live/HysDMs2a-iM?si=92I5LD1FY2PAsSuG&t=15822|title=WATCH LIVE: Trump holds campaign rally at Madison Square Garden in New York|date=October 28, 2024|website=youtube.com|publisher=[[PBS NewsHour]]|language=en|format=video}}</ref> without specifying whether these savings would be made over a single year or a longer period.<ref>{{Cite web|url=https://www.bbc.co.uk/news/articles/cdj38mekdkgo|title=Can Elon Musk cut $2 trillion from US government spending?|last=Chu|first=Ben|date=2024-11-13|website=BBC News|language=en-GB|access-date=2024-11-14}}</ref> [[File:2023_US_Federal_Budget_Infographic.png|thumb|An infographic on outlays and revenues in the 2023 [[United States federal budget|U.S. federal budget]]]] DOGE could also streamline permitting with “categorical exclusions” from environmental reviews under the National Environmental Policy Act. {{sidebar with collapsible lists|name=U.S. deficit and debt topics|namestyle=background:#bf0a30;|style=width:22.0em; border: 4px double #d69d36; background:var(--background-color-base, #FFFFFF);|bodyclass=vcard|pretitle='''<span class="skin-invert">This article is part of [[:Category:United States|a series]] on the</span>'''|title=[[United States federal budget|<span style="color:var(--color-base, #000000);">Budget and debt in the<br/>United States of America</span>]]|image=[[File:Seal of the United States Congress.svg|90px]] [[File:Seal of the United States Department of the Treasury.svg|90px]]|titlestyle=background:var(--background-color-base, #002868); background-clip:padding-box;|headingstyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff);|listtitlestyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff); text-align:center;|expanded={{{expanded|{{{1|}}}}}}|list1name=dimensions|list1title=Major dimensions|list1class=hlist skin-invert|list1=* [[Economy of the United States|Economy]] * [[Expenditures in the United States federal budget|Expenditures]] * [[United States federal budget|Federal budget]] * [[Financial position of the United States|Financial position]] * [[Military budget of the United States|Military budget]] * [[National debt of the United States|Public debt]] * [[Taxation in the United States|Taxation]] * [[Unemployment in the United States|Unemployment]] * [[Government_spending_in_the_United_States|Gov't spending]]|list2name=programs|list2title=Programs|list2class=hlist skin-invert|list2=* [[Medicare (United States)|Medicare]] * [[Social programs in the United States|Social programs]] * [[Social Security (United States)|Social Security]]|list3name=issues|list3title=Contemporary issues|list3class=skin-invert|list3=<div style="margin-bottom:0.5em"> [[National Commission on Fiscal Responsibility and Reform|Bowles–Simpson Commission]] {{flatlist}} * <!--Bu--> [[Bush tax cuts]] * <!--Deb--> [[United States debt ceiling|Debt ceiling]] ** [[History of the United States debt ceiling|history]] * <!--Def--> [[Deficit reduction in the United States|Deficit reduction]] * <!--F--> [[United States fiscal cliff|Fiscal cliff]] * <!--H--> [[Healthcare reform in the United States|Healthcare reform]] * <!--P--> [[Political debates about the United States federal budget|Political debates]] * <!--So--> [[Social Security debate in the United States|Social Security debate]] * <!--St--> "[[Starve the beast]]" * <!--Su--> [[Subprime mortgage crisis]] {{endflatlist}} </div> [[2007–2008 financial crisis]] {{flatlist}} * <!--D--> [[United States debt-ceiling crisis (disambiguation)|Debt-ceiling crises]] ** [[2011 United States debt-ceiling crisis|2011]] ** [[2013 United States debt-ceiling crisis|2013]] ** [[2023 United States debt-ceiling crisis|2023]] {{endflatlist}} [[2013 United States budget sequestration|2013 budget sequestration]] {{flatlist}} * <!--G--> [[Government shutdowns in the United States|Government shutdowns]] ** [[1980 United States federal government shutdown|1980]] ** [[1981, 1984, and 1986 U.S. federal government shutdowns|1981, 1984, 1986]] ** [[1990 United States federal government shutdown|1990]] ** [[1995–1996 United States federal government shutdowns|1995–1996]] ** [[2013 United States federal government shutdown|2013]] ** [[January 2018 United States federal government shutdown|Jan 2018]] ** [[2018–2019 United States federal government shutdown|2018–2019]] {{endflatlist}} Related events {{flatlist}} *<!--E-->[[Removal of Kevin McCarthy as Speaker of the House|2023 Removal of Kevin McCarthy]] {{endflatlist}}|list4name=terminology|list4title=Terminology|list4class=hlist skin-invert|list4=Cumulative [[Government budget balance|deficit]] + [[National debt of the United States#Debates|Interest]] ≈ [[Government debt|Debt]] * [[Balance of payments]] * [[Inflation]] * [[Continuing resolution]]}} [[w:Deficit_reduction_in_the_United_States|Deficit reduction in the United States]] == Deregulate the Economy == The legal theory that this can be done through the executive branch is found in the U.S. Supreme Court’s ''[[w:West_Virginia_v._EPA|West Virginia v. EPA]]'' and ''[[w:Loper_Bright|Loper Bright]]'' rulings, which rein in the administrative state and mean that much of what the federal government now does is illegal.<ref>{{cite web|url=https://www.wsj.com/opinion/department-of-government-efficiency-elon-musk-vivek-ramaswamy-donald-trump-1e086dab|website=[[w:Wall Street Journal]]|title=The Musk-Ramaswamy Project Could Be Trump’s Best Idea}}</ref> Mr. Trump has set a goal of eliminating 10 regulations for every new one. The [[w:Competitive_Enterprise_Institute|Competitive Enterprise Institute]]’s Wayne Crews says 217,565 rules have been issued since the [[w:Federal_Register|Federal Register]] first began itemizing them in 1976, with 89,368 pages added last year. [https://sgp.fas.org/crs/misc/R43056.pdf 3,000-4,500 rules are added each year]. DOGE’s first order will be to pause enforcement of overreaching rules while starting the process to roll them back. Mr. Trump and DOGE could direct agencies to settle legal challenges to Biden rules by vacating them. This could ease the laborious process of undoing them by rule-making through the [[w:Administrative_Procedure_Act|Administrative Procedure Act]]. A source tells the WSJ they’ll do whatever they think they legally can without the APA. The [[w:Congressional_Review_Act|Congressional Review Act]]—which allows Congress to overturn recently issued agency regulations—had been used only once, prior to [[w:First_presidency_of_Donald_Trump|Trump's first term]]. While in office, he and the Republican Congress used it on 16 rules. This time, there will be more than 56 regulatory actions recent enough to be repealed. The [[w:Chevron_deference|''Chevron'' deference]] had required federal courts to defer to agencies’ interpretations of ambiguous statutes, but this was overturned in 2024. Taken together, with some other recent [[w:SCOTUS|SCOTUS]] rulings, we now have, says the WSJ, the biggest opportunity to cut regulatory red tape in more than 40 years.<ref>[https://www.wsj.com/opinion/let-the-trump-deregulation-begin-us-chamber-of-commerce-second-term-economic-growth-73f24387?cx_testId=3&cx_testVariant=cx_166&cx_artPos=0]</ref><blockquote>"Most legal edicts aren’t laws enacted by Congress but “rules and regulations” promulgated by unelected bureaucrats—tens of thousands of them each year. Most government enforcement decisions and discretionary expenditures aren’t made by the democratically elected president or even his political appointees but by millions of unelected, unappointed civil servants within government agencies who view themselves as immune from firing thanks to civil-service protections." "This is antidemocratic and antithetical to the Founders’ vision. It imposes massive direct and indirect costs on taxpayers." "When the president nullifies thousands of such regulations, critics will allege executive overreach. In fact, it will be ''correcting'' the executive overreach of thousands of regulations promulgated by administrative fiat that were never authorized by Congress. The president owes lawmaking deference to Congress, not to bureaucrats deep within federal agencies. The use of executive orders to substitute for lawmaking by adding burdensome new rules is a constitutional affront, but the use of executive orders to roll back regulations that wrongly bypassed Congress is legitimate and necessary to comply with the Supreme Court’s recent mandates. And after those regulations are fully rescinded, a future president couldn’t simply flip the switch and revive them but would instead have to ask Congress to do so" Mssrs. [https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Musk and Ramaswamy, WSJ, 11/20/2024]</blockquote> == Shrink the federal civil service == The government has around three million [[w:United_States_federal_civil_service|federal civil service]] employees, with an average salary of $106,000. Dr. Anthony Fauci made $481,000 in 2022. The federal head count has ballooned by 120,800 during the Biden years. Civil service and union protections make it hard to fire workers. Mr. Trump intends to quickly resurrect the [[w:Schedule_F|Schedule F]] reform that he sought to implement at the end of his first term but was scrapped by Mr. Biden. These would high-level federal employees to be removed like political appointees, by eliminating their job protections. WSJ proposals[https://www.wsj.com/opinion/the-doge-cheat-sheet-elon-musk-vivek-ramaswamy-department-of-government-efficiency-1c231783#cxrecs_s] The [[w:Administrative_Procedures_Act|Administrative Procedures Act]] statute protects federal employees from political retaliation, but allows for “reductions in force” that don’t target specific employees. The statute further empowers the president to “prescribe rules governing the competitive service.” The Supreme Court has held—in ''[[w:Franklin_v._Massachusetts|Franklin v. Massachusetts]]'' (1992) and ''[[w:Collins_v._Yellen|Collins v. Yellen]]'' (2021) that when revious presidents have used this power to amend the civil service rules by executive order, they weren’t constrained by the APA when they did so. Mr. Trump can, with this authority, implement any number of “rules governing the competitive service” that would curtail administrative overgrowth, from large-scale firings to relocation of federal agencies out of the Washington area. The DOGE welcomes voluntary terminations once the President begins requiring federal employees to come to the office five days a week, because American taxpayers shouldn’t pay federal employees for the Covid-era privilege of staying home.<ref>[https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Elon Musk and Vivek Ramaswamy: The DOGE Plan to Reform Government: Following the Supreme Court’s guidance, we’ll reverse a decadeslong executive power grab. Musk & Ramaswamy 11/20/2024]</ref> == Reduce the deficit and debt by impounding appropriated funds == === Impound appropriated funds === Reports suggest that president-elect Trump intends to override Congress’s power of the purse by [[w:Impoundment_of_appropriated_funds|impoundment of appropriated funds]], that is, refusing to spend them. the president may [[wikipedia:Rescission_bill|propose rescission]] of specific funds, but that rescission must be approved by both the [[wikipedia:United_States_House_of_Representatives|House of Representatives]] and [[wikipedia:United_States_Senate|Senate]] within 45 days. [[w:Thomas_Jefferson|Thomas Jefferson]] was the first president to exercise the power of impoundment in 1801, which power was available to all presidents up to and including [[wikipedia:Richard_Nixon|Richard Nixon]], and was regarded as a power inherent to the office, although one with limits. He may ask Congress to repeal The [[w:Congressional_Budget_and_Impoundment_Control_Act_of_1974|Congressional Budget and Impoundment Control Act of 1974]], which was passed in response to Nixon's abuses.<ref>{{Cite web|url=http://democrats-budget.house.gov/resources/reports/impoundment-control-act-1974-what-it-why-does-it-matter|title=The Impoundment Control Act of 1974: What Is It? Why Does It Matter? {{!}} House Budget Committee Democrats|date=2019-10-23|website=democrats-budget.house.gov|language=en|access-date=2024-05-19}}</ref> If Congress refuses to do so, president Trump may impound funds anyway and argue in court that the 1974 law is unconstitutional. The matter would likely end up at the Supreme Court, which would have to do more than simply hold the 1974 act unconstitutional in order for Mr. Trump to prevail. The court would also have to overrule [[w:Train_v._City_of_New_York_(1975)|''Train v. City of New York'' (1975)]], which held that impoundment is illegal unless the underlying legislation specifically authorizes it. === Reduce the budget deficit === [[wikipedia:U.S. federal budget|U.S. federal budget]] The [[wikipedia:Fiscal_year|fiscal year]], beginning October 1 and ending on September 30 of the year following. Congress is the body required by law to pass appropriations annually and to submit funding bills passed by both houses to the President for signature. Congressional decisions are governed by rules and legislation regarding the [[wikipedia:United_States_budget_process|federal budget process]]. Budget committees set spending limits for the House and Senate committees and for Appropriations subcommittees, which then approve individual [[wikipedia:Appropriations_bill_(United_States)|appropriations bills]] to During FY2022, the federal government spent $6.3 trillion. Spending as % of GDP is 25.1%, almost 2 percentage points greater than the average over the past 50 years. Major categories of FY 2022 spending included: Medicare and Medicaid ($1.339T or 5.4% of GDP), Social Security ($1.2T or 4.8% of GDP), non-defense discretionary spending used to run federal Departments and Agencies ($910B or 3.6% of GDP), Defense Department ($751B or 3.0% of GDP), and net interest ($475B or 1.9% of GDP).<ref name="CBO_2022">[https://www.cbo.gov/publication/58888 The Federal Budget in Fiscal Year 2022: An Infographic]</ref> CBO projects a federal budget deficit of $1.6 trillion for 2024. In the agency’s projections, deficits generally increase over the coming years; the shortfall in 2034 is $2.6 trillion. The deficit amounts to 5.6 percent of gross domestic product (GDP) in 2024, swells to 6.1 percent of GDP in 2025, and then declines in the two years that follow. After 2027, deficits increase again, reaching 6.1 percent of GDP in 2034.<ref name="CBO_budgetOutlook2024">{{cite web|url=https://www.cbo.gov/publication/59710|title=The Budget and Economic Outlook: 2024 to 2034|date=February 7, 2024|publisher=CBO|access-date=February 7, 2024}}</ref> The following table summarizes several budgetary statistics for the fiscal year 2015-2021 periods as a percent of GDP, including federal tax revenue, outlays or spending, deficits (revenue – outlays), and [[wikipedia:National_debt_of_the_United_States|debt held by the public]]. The historical average for 1969-2018 is also shown. With U.S. GDP of about $21 trillion in 2019, 1% of GDP is about $210 billion.<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> Statistics for 2020-2022 are from the CBO Monthly Budget Review for FY 2022.<ref name="CBO_MBRFY2022">{{cite web|url=https://www.cbo.gov/publication/58592|title=Monthly Budget Review: Summary for Fiscal Year 2022|date=November 8, 2022|publisher=CBO|access-date=December 10, 2022}}</ref> {| class="wikitable" !Variable As % GDP !2015 !2016 !2017 !2018 !2019 !2020 !2021 !2022 !Hist Avg |- !Revenue<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> |18.0% |17.6% |17.2% |16.4% |16.4% |16.2% |17.9% |19.6% |17.4% |- !Outlays<ref name="CBO_Hist_20" /> |20.4% |20.8% |20.6% |20.2% |21.0% |31.1% |30.1% |25.1% |21.0% |- !Budget Deficit<ref name="CBO_Hist_20" /> | -2.4% | -3.2% | -3.5% | -3.8% | -4.6% | -14.9% | -12.3% | -5.5% | -3.6% |- !Debt Held by Public<ref name="CBO_Hist_20" /> |72.5% |76.4% |76.2% |77.6% |79.4% |100.3% |99.6% |94.7% | |} The [[wikipedia:U.S._Constitution|U.S. Constitution]] ([[wikipedia:Article_One_of_the_United_States_Constitution|Article I]], section 9, clause 7) states that "No money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of Receipts and Expenditures of all public Money shall be published from time to time." Each year, the President of the United States submits a budget request to Congress for the following fiscal year as required by the [[wikipedia:Budget_and_Accounting_Act_of_1921|Budget and Accounting Act of 1921]]. Current law ({{UnitedStatesCode|31|1105}}(a)) requires the president to submit a budget no earlier than the first Monday in January, and no later than the first Monday in February. Typically, presidents submit budgets on the first Monday in February. The budget submission has been delayed, however, in some new presidents' first year when the previous president belonged to a different party. === Reduce the National debt === == Reform Entitlements == === Healthcare and Medicare === [[w:ObamaCare|ObamaCare]] started as a plausible scheme for universal, cost-effective health insurance with subsidies for the needy. Only the subsidies survive because the ObamaCare policies actually delivered are so overpriced nobody would buy them without a subsidy.<ref>[https://www.wsj.com/opinion/elons-real-trump-mission-protect-growth-department-of-government-efficiency-appointments-cabinet-9e7e62b2]</ref> See below: Department of Health and Human Services === Social Security === Even FDR was aware of its flaw: it discourages working and saving. == Strategic Foreign Policy and Military reform == === Department of State === {{Main article|w:Second_presidency_of_Donald_Trump#Prospective_foreign_policy|w:State Department}} === U.S. Department of Defense === The president-elect is reportedly considering a draft executive order that establishes a “warrior board” of retired senior military personnel with the power to review three- and four-star officers “on leadership capability, strategic readiness, and commitment to military excellence," and to recommend removals of any deemed unfit for leadership. This would fast-track the removal of generals and admirals found to be “lacking in requisite leadership qualities,” consistent with his earlier vow to fire “woke” military leaders.<ref>[https://www.wsj.com/politics/national-security/trump-draft-executive-order-would-create-board-to-purge-generals-7ebaa606<nowiki> Trump draft executive order would create a board to purge generals 11/12/2024]</nowiki></ref> There are legal obstacles. The law prohibits the firing of commissioned officers except by “sentence of a general court-martial,” as a “commutation of a sentence of a general court-martial,” or “in time of war, by order of the president.” A commissioned officer who believes he’s been wrongfully dismissed has the right to seek a trial by court-martial, which may find the dismissal baseless. <ref>[https://www.wsj.com/opinion/trump-tests-the-constitutions-limits-checks-balances-government-policy-law-78d0d0f1<nowiki> Trump test the constitutions limits 11/19/2024]</nowiki></ref> Musk said, "Some idiots are still building manned fighter jets like the F-35," and later added: "Manned fighter jets are outdated in the age of drones and only put pilots' lives at risk." [[w:Bernie_Sanders|Bernie Sanders]] wrote on X: "Elon Musk is right. The Pentagon, with a budget of $886 billion, just failed its 7th audit in a row. It's lost track of billions. Last year, only 13 senators voted against the Military Industrial Complex and a defense budget full of waste and fraud. That must change."{{sfn|Newsweek 12/02|2024}} == Reform the other Government Bureaus and Departments == === Department of Education === [[w:United_States_Department_of_Education|w:Department of Education]] has 4,400 employees – the smallest staff of the Cabinet agencies<ref>{{Cite web|url=https://www2.ed.gov/about/overview/fed/role.html|title=Federal Role in Education|date=2021-06-15|website=www2.ed.gov|language=en|access-date=2022-04-28}}</ref> – and a 2024 budget of $238 billion.<ref name="DOE-mission">{{Cite web|url=https://www.usaspending.gov/agency/department-of-education?fy=2024|title=Agency Profile {{!}} U.S. Department of Education|website=www2.ed.gov|access-date=2024-11-14}}</ref> The 2023 Budget was $274 billion, which included funding for children with disabilities ([[wikipedia:Individuals_with_Disabilities_Education_Act|IDEA]]), pandemic recovery, early childhood education, [[wikipedia:Pell_Grant|Pell Grants]], [[wikipedia:Elementary_and_Secondary_Education_Act|Title I]], work assistance, among other programs. This budget was down from $637.7 billion in 2022.<ref>{{Cite web|url=https://www.future-ed.org/what-the-new-pisa-results-really-say-about-u-s-schools/|title=What the New PISA Results Really Say About U.S. Schools|date=2021-06-15|website=future-ed.com|language=en|access-date=2024-11-14}}</ref> The WSJ proposes that the Civil Rights division be absorbed into the Department of Justice, and that its outstanding loan portolio be handled by the Department of the Treasury. Despite the redundancies, its unlikely that it will be abolished, which would require congressional action and buy-in from Democrats in the Senate; Republicans don’t have enough votes to do it alone. A republican appointee is expected to push back against federal education overreach and progressive policies like DEI. <ref>[https://www.wsj.com/opinion/trump-can-teach-the-education-department-a-lesson-nominee-needs-boldness-back-school-choice-oppose-woke-indoctrination-ddf6a38d<nowiki> Trump can teach the Education Department a Lesson. WSJ 11/20/2024]</nowiki></ref> === U.S. Department of Health and Human Services === [[w:U.S._Department_of_Health_and_Human_Services|U.S. Department of Health and Human Services]] was authorized a budget for [[w:2020_United_States_federal_budget|fiscal year 2020]] of $1.293 trillion. It has 13 operating divisions, 10 of which constitute the [[w:United_States_Public_Health_Service|Public Health Services]], whose budget authorization is broken down as follows:<ref name="hhs_budget_fy2020">{{cite web|url=https://www.hhs.gov/about/budget/fy2020/index.html|title=HHS FY 2020 Budget in Brief|date=October 5, 2019|website=HHS Budget & Performance|publisher=United States Department of Health & Human Services|page=7|access-date=May 9, 2020}}</ref> {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Food and Drug Administration|Food and Drug Administration]] (FDA) |$3,329 MM |- |[[w:Health Resources and Services Administration|Health Resources and Services Administration]] (HRSA) |$11,004 |- |[[w:Indian Health Service|Indian Health Service]] (IHS) |$6,104 |- |[[w:Centers for Disease Control and Prevention|Centers for Disease Control and Prevention]] (CDC) |$6,767 |- |[[w:National Institutes of Health|National Institutes of Health]] (NIH) |$33,669 |- |[[w:Substance Abuse and Mental Health Services Administration|Substance Abuse and Mental Health Services Administration]] (SAMHSA) |$5,535 |- |[[w:Agency for Healthcare Research and Quality|Agency for Healthcare Research and Quality]] (AHRQ) |$0 |- |[[w:Centers for Medicare & Medicaid Services|Centers for Medicare & Medicaid Services]] (CMMS) |$1,169,091 |- |[[w:Administration for Children and Families|Administration for Children and Families]] (ACF) |$52,121 |- |[[w:Administration for Community Living|Administration for Community Living]] (ACL) |$1,997 |- |} {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Departmental Management|Departmental Management]] |$340 |- |Non-Recurring Expense Fund |$-400 |- |[[w:Office of Medicare Hearings and Appeals|Office of Medicare Hearings and Appeals]] |$186 |- |[[w:Office of the National Coordinator|Office of the National Coordinator]] |$43 |- |[[w:Office for Civil Rights|Office for Civil Rights]] |$30 |- |[[w:Office of Inspector General|Office of Inspector General]] |$82 |- |[[w:Public Health and Social Services Emergency Fund|Public Health and Social Services Emergency Fund]] |$2,667 |- |[[w:Program Support Center|Program Support Center]] |$749 |- |Offsetting Collections |$-629 |- |Other Collections |$-163 |- |'''TOTAL''' |'''$1,292,523''' |} The FY2020 budget included a $1.276 billion budget decrease for the Centers for Disease Control, and a $4.533 billion budget decrease for the National Institutes of Health. These budget cuts, along with other changes since 2019, comprised a total decrease of over $24 billion in revised discretionary budget authority across the entire Department of Health and Human Services for Fiscal Year 2020.<ref name="hhs_budget_fy2020" /> Additional details of the budgeted outlays, budget authority, and detailed budgets for other years, can be found at the HHS Budget website.<ref>{{cite web|url=http://WWW.HHS.GOV/BUDGET|title=Health and Human Services: Budget and Performance|publisher=United States Department of Health & Human Services|access-date=May 9, 2020}}</ref> [[w:Robert_F._Kennedy_Jr.|Robert F. Kennedy Jr.]] has been nominated as [[w:United_States_Secretary_of_Health_and_Human_Services|United_States_Secretary_of_Health_and_Human_Services]] He is an American politician, [[Environmental law|environmental lawyer]], [[anti-vaccine activist]], and anti-packaged food industry activist, anti-pharmaceutical industry activist, who will be nominated to serve as [[United States Secretary of Health and Human Services]],<ref name="v502">{{cite web|url=https://www.forbes.com/sites/saradorn/2024/11/14/rfk-jr-launches-independent-2024-run-here-are-all-the-conspiracies-he-promotes-from-vaccines-to-mass-shootings/|title=Trump Taps RFK Jr. As Secretary Of Health And Human Services: Here Are All The Conspiracies He's Promoted|last=Dorn|first=Sara|date=2024-11-14|website=Forbes|access-date=2024-11-15}}</ref> with the mission of "Making America Healthy Again". He is the chairman and founder of [[Children's Health Defense]], an anti-vaccine advocacy group and proponent of [[COVID-19 vaccine misinformation|dubious COVID-19 vaccine information]].<ref name="Smith_12/15/2021" /><ref name="KW" /> == CPB, PBS, NPR == [[w:Howard_Husock|Howard Husock]] suggest that instead of zeroing its $535 million budget, Republicans reform the [[w:Public_Broadcasting_Act|Public Broadcasting Act]] to eliminate bias and improve local journalism.<ref>https://www.wsj.com/opinion/the-conservative-case-for-public-broadcasting-media-policy-2d4c3c9f?page=1</ref> == NASA == In September 2026, NASA's [[w:Artemis_program|Artemis program]], established in 2017 via [[wikipedia:Space_Policy_Directive_1|Space Policy Directive 1]], is intended to reestablish a human presence on the Moon for the first time since the [[wikipedia:Apollo_17|Apollo 17]] mission in 1972. The program's stated long-term goal is to establish a [[wikipedia:Moonbase|permanent base on the Moon]] to facilitate [[wikipedia:Human_mission_to_Mars|human missions to Mars]]. The [[w:U.S._National_Academies_of_Sciences,_Engineering,_and_Medicine|U.S. National Academies of Sciences, Engineering, and Medicine]] in October, put out a report titled "NASA at a Crossroads," which identified myriad issues at the agency, including out-of-date infrastructure, pressures to prioritize short-term objectives and inefficient management practices. NASA's costly [[w:Space_Launch_System|Space Launch System]] (SLS) is the cornerstone of the Artemis program. has a price tag of around $4.1 billion per launch, and is a single-use rocket that can only launch every two years, having debuted in 2022 with the uncrewed [[w:Artemis_1_mission|Artemis 1 mission]] to the moon. In contrast, SpaceX is working to reduce the cost of a single Starship flight to under $10 million. NASA Associate Administrator Jim Free urged the incoming administration to maintain the current plans, in a symposium with the [[w:American_Astronautical_Society|American Astronautical Society]] saying "We need that consistency in purpose. That has not happened since Apollo. If we lose that, I believe we will fall apart and we will wander, and other people in this world will pass us by." NASA has already asked both [[w:SpaceX|SpaceX]] and also Jeff Bezos' [[w:Blue_Origin|Blue Origin]], to develop cargo landers for its Artemis missions and to deliver heavy equipment on them to the Moon by 2033. "Having two lunar lander providers with different approaches for crew and cargo landing capability provides mission flexibility while ensuring a regular cadence of moon landings for continued discovery and scientific opportunity," Stephen D. Creech, NASA's assistant deputy associate administrator for the moon to Mars program, said in an announcement about the partnership. "For all of the money we are spending, NASA should NOT be talking about going to the Moon - We did that 50 years ago. They should be focused on the much bigger things we are doing, including Mars (of which the Moon is a part), Defense and Science!" Trump wrote in a post on X in 2019. Trump has said he would create a [[w:Space_National_Guard|Space National Guard]], an idea that lawmakers in Congress have been proposing since 2021. Critics agree that a focus on spaceflight could come at the expense of "Earth and atmospheric sciences at NASA and the [[w:National_Oceanic_and_Atmospheric_Administration|National Oceanic and Atmospheric Administration]] (NOAA), which have been cut during the Biden era."<ref>{{Cite web|url=https://www.newsweek.com/elon-musk-donald-trump-nasa-space-policy-1990599|title=Donald Trump and Elon Musk could radically reshape NASA. Here's how|last=Reporter|first=Martha McHardy US News|date=2024-11-27|website=Newsweek|language=en|access-date=2024-12-02}}</ref> == [[w:Federal_Aviation_Administration|Federal Aviation Administration]] == Musk has often complained about the FAA "smothering" innovation, boasting that he can build a rocket faster than the agency can process the "Kafkaesque paperwork" required to make the relevant approvals.{{sfn|Economist 11/23|2024}} == History and Miscellaneous facts == See also: [[w:Department_of_Government_Efficiency#History|Department of Government Efficiency — History]] DOGE's work will "conclude" no later than July 4, 2026, the 250th anniversary of the signing of the [[United States Declaration of Independence|U.S. Declaration of Independence]],<ref>{{Cite web|url=https://thehill.com/policy/4987402-trump-musk-advisory-group-spending/|title=Elon Musk, Vivek Ramaswamy to lead Trump's Department of Government Efficiency (DOGE)|last=Nazzaro|first=Miranda|date=November 13, 2024|website=The Hill|language=en-US|access-date=November 13, 2024}}</ref> also coinciding with America's [[United States Semiquincentennial|semiquincentennial]] celebrations and a proposed "Great American Fair". Despite its name it is not expected to be a [[wikipedia:United_States_federal_executive_departments|federal executive department]], but rather may operate under the [[Federal Advisory Committee Act]],<ref>{{Cite web|url=https://www.cbsnews.com/news/trump-department-of-government-efficiency-doge-elon-musk-ramaswamy/|title=What to know about Trump's Department of Government Efficiency, led by Elon Musk and Vivek Ramaswamy - CBS News|last=Picchi|first=Aimee|date=2024-11-14|website=www.cbsnews.com|language=en-US|access-date=2024-11-14}}</ref> so its formation is not expected to require approval from the [[wikipedia:United_States_Congress|U.S. Congress]]. NYT argues that records of its meetings must be made public.{{Cn}} Musk has stated that he believes such a commission could reduce the [[wikipedia:United_States_federal_budget|U.S. federal budget]] by $2 trillion, which would be a reduction of almost one third from its 2023 total. [[Maya MacGuineas]] of the [[Committee for a Responsible Federal Budget]] has said that this saving is "absolutely doable" over a period of 10 years, but it would be difficult to do in a single year "without compromising some of the fundamental objectives of the government that are widely agreed upon".<ref>{{Cite web|url=https://thehill.com/business/4966789-elon-musk-skepticism-2-trillion-spending-cuts/|title=Elon Musk draws skepticism with call for $2 trillion in spending cuts|last=Folley|first=Aris|date=2024-11-03|website=The Hill|language=en-US|access-date=2024-11-14}}</ref> [[wikipedia:Jamie_Dimon|Jamie Dimon]], the chief executive officer of [[wikipedia:JPMorgan_Chase|JPMorgan Chase]], has supported the idea. Some commentators questioned whether DOGE is a conflict of interest for Musk given that his companies are contractors to the federal government. The body is "unlikely to have any regulatory teeth on its own, but there's little doubt that it can have influence on the incoming administration and how it will determine its budgets".<ref>{{Cite web|url=https://www.vox.com/policy/384904/trumps-department-of-government-efficiency-sounds-like-a-joke-it-isnt|title=Trump tapped Musk to co-lead the "Department of Government Efficiency." What the heck is that?|last=Fayyad|first=Abdallah|date=2024-11-13|website=Vox|language=en-US|access-date=2024-11-14}}</ref> Elon Musk had called [[w:Federico_Sturzenegger|Federico Sturzenegger]], Argentina's [[Minister of Deregulation and Transformation of the State]] ([[w:es:Ministerio_de_Desregulación_y_Transformación_del_Estado|es]]), to discuss imitating his ministry's model.<ref>{{Cite web|url=https://www.infobae.com/economia/2024/11/08/milei-brindo-un-nuevo-apoyo-a-sturzenegger-y-afirmo-que-elon-musk-imitara-su-gestion-en-eeuu/|title=Milei brindó un nuevo apoyo a Sturzenegger y afirmó que Elon Musk imitará su gestión en EEUU|date=November 8, 2024|website=infobae|language=es-ES|access-date=November 13, 2024}}</ref> == Reception and Criticism == See also: [[w:Department_of_Government_Efficiency#Reception|w:Department of Government Efficiency — Reception]] The WSJ reports that Tesla's Texas facility dumped toxic wastewater into the public sewer system, into a lagoon, and into a local river, violated Texas environmental regulations, and fired an employee who attempted to comply with the law.{{Cn}} == See also == * [[w:Second_presidential_transition_of_Donald_Trump|Second presidential transition of Donald Trump]] * [[w:United_States_federal_budget#Deficits_and_debt|United States federal budget - Deficits and debt]] * [[w:United_States_Bureau_of_Efficiency|United States Bureau of Efficiency]] – United States federal government bureau from 1916 to 1933 * [[w:Brownlow_Committee|Brownlow Committee]] – 1937 commission recommending United States federal government reforms * [[w:Grace_Commission|Grace Commission]] – Investigation to eliminate inefficiency in the United States federal government * [[w:Hoover_Commission|Hoover Commission]] – United States federal commission in 1947 advising on executive reform * [[w:Keep_Commission|Keep Commission]] * [[w:Project_on_National_Security_Reform|Project on National Security Reform]] == Notes == {{reflist}} == References == {{refbegin}} * {{Cite web|url=https://www.newsweek.com/bernie-sanders-finds-new-common-ground-elon-musk-1993820|title=Bernie Sanders finds new common ground with Elon Musk|last=Reporter|first=Mandy Taheri Weekend|date=2024-12-01|website=Newsweek|language=en|access-date=2024-12-02}}</ref> Failed its fifth audit in June 2023.<ref>{{Cite web|url=https://www.newsweek.com/fox-news-host-confronts-gop-senator-pentagons-fifth-failed-audit-1804379|title=Fox News host confronts GOP Senator on Pentagon's fifth failed audit|last=Writer|first=Fatma Khaled Staff|date=2023-06-04|website=Newsweek|language=en|access-date=2024-12-02}} * {{Cite news|url=https://www.economist.com/briefing/2024/11/21/elon-musk-and-donald-trump-seem-besotted-where-is-their-bromance-headed|title=Elon Musk and Donald Trump seem besotted. Where is their bromance headed?|work=The Economist|access-date=2024-12-04|issn=0013-0613 |ref={{harvid|Economist 11/23|2024}} }} <references group="lower-alpha" /> {{refend}} h9ehvyo0hs4zl7j4kscp5prp1vvkfus 2690200 2690199 2024-12-04T03:37:39Z Jaredscribe 2906761 /* History and Miscellaneous facts */ 2690200 wikitext text/x-wiki The U.S. [[w:Department of Government Efficiency]]. {{Infobox Organization |name=Department of Government Efficiency |logo=DOGE Logo as of November 14, 2024.jpg |logo_size=150px |logo_caption=Logo on [[Twitter|X]] (formerly Twitter) as of November 14, 2024 |seal= |seal_size= |seal_caption= |formation=Announced on November 12, 2024; yet to be established |abbreviation=DOGE |key_people={{plainlist|[[w:Commissioner of the Department of Government Efficiency|Co-commissioners]]: * [[w:Elon Musk]] * [[w:Vivek Ramaswamy]] }} |website={{URL|https://x.com/DOGE|x.com/DOGE}} }} This "'''Wiki Of Government Efficiency'''" (WOGE) will analyze the [[w:U.S._Federal_budget|U.S. federal budget]], [[User:Jaredscribe/Department of Government Efficiency#Reform the other Government Bureaus and Departments|federal bureaucracy]], and [[User:Jaredscribe/Department of Government Efficiency#Shrink the federal civil service|federal civil service]], in the public interest, and in the context of [[w:Second_presidency_of_Donald_Trump|president-elect Trump']]<nowiki/>s [[w:Agenda_47|Agenda 47]], with non-partisan research, analysis, and criticism of forward-looking proposals on how the '''[[w:Department of Government Efficiency|Department of Government Efficiency]]'''{{Efn|Also referred to as '''Government Efficiency Commission'''}} (DOGE) might fulfill its mission to ''"dismantle government bureaucracy, slash excess regulations, and cut wasteful expenditures and restructure federal agencies"'', in the words of president-elect [[wikipedia:Donald_Trump|Donald Trump]], who called for it to address ''"massive waste and fraud"'' in government spending.<ref name=":1">{{Cite web|url=https://www.bbc.co.uk/news/articles/c93qwn8p0l0o|title=Donald Trump picks Elon Musk for US government cost-cutting role|last1=Faguy|first1=Ana|last2=FitzGerald|first2=James|date=2024-11-13|publisher=BBC News|language=en-GB|access-date=2024-11-13}}</ref> The DOGE will work with through the [[w:Office_of_Management_and_Budget|Office of Management and Budget]] as its "policy vector". Here's [[User:Jaredscribe/Department of Government Efficiency/How to contribute|how to contribute]] to the WOGE. The [[w:U.S._budget_deficit|U.S. Budget deficit]], (C.f. [[w:Government_budget_balance|fiscal deficit]]), and the [[w:National_debt_of_the_United_States|U.S. National debt]], currently $35.7 Trillion as of 10/2024, which is 99% of the [[w:U.S._GDP|U.S. GDP]],<ref>{{Unbulleted list citebundle|{{cite news|newspaper=Financial Post| title= Musk's $2 Trillion of Budget Cuts Would Have These Stocks Moving|url=https://financialpost.com/pmn/business-pmn/musks-2-trillion-of-budget-cuts-would-have-these-stocks-moving|first=Alexandra|last=Semenova|date=November 4, 2024}}|{{cite news|newspaper= New York Times|title=Elon|url=https://nytimes.com/2024/10/29/us/politics/elon-musk-trump-economy-hardship.html}}|{{Cite web |date=September 5, 2024 |title=Trump says he'd create a government efficiency commission led by Elon Musk |url=https://apnews.com/article/donald-trump-elon-musk-government-efficiency-commission-e831ed5dc2f6a56999e1a70bb0a4eaeb |publisher=AP News}}|{{cite web|first=Jenn|last=Brice|title=How Elon Musk's $130 million investment in Trump's victory could reap a huge payoff for Tesla and the rest of his business empire|url=https://fortune.com/2024/11/06/elon-musk-donald-trump-tesla-spacex-xai-boring-neuralink|website=Fortune}}|{{cite web|url=https://axios.com/2024/11/07/elon-musk-government-efficiency-trump|title=Musk will bring his Twitter management style to government reform}}|{{cite news| access-date =November 9, 2024|work=Reuters|date=September 6, 2024|first1=Helen|first2=Gram|last1=Coster| last2=Slattery|title=Trump says he will tap Musk to lead government efficiency commission if elected| url= https://reuters.com/world/us/trump-adopt-musks-proposal-government-efficiency-commission-wsj-reports-2024-09-05}}|{{cite web|title=Trump says Musk could head 'government efficiency' force|url= https://bbc.com/news/articles/c74lgwkrmrpo|publisher=BBC}}|{{cite web|date =November 5, 2024|title=How Elon Musk could gut the government under Trump|url=https://independent.co.uk/news/world/americas/us-politics/elon-musk-donald-trump-economy-job-cuts-b2641644.html|website= The Independent}}}}</ref> and expected to grow to 134% of GDP by 2034 if current laws remain unchanged, according to the [[w:Congressional_Budget_Office|Congressional Budget Office]]. The DOGE will be a [[wikipedia:Presidential_commission_(United_States)|presidential advisory commission]] led by the billionaire businessmen [[wikipedia:Elon_Musk|Elon Musk]] and [[wikipedia:Vivek_Ramaswamy|Vivek Ramaswamy]], and possibly [[w:Ron_Paul|Ron Paul]]<ref>{{Cite web|url=https://thehill.com/video/ron-paul-vows-to-join-elon-musk-help-eliminate-government-waste-in-a-trump-admin/10191375|title=Ron Paul vows to join Elon Musk, help eliminate government waste in a Trump admin|date=November 5, 2024|website=The Hill}}</ref><ref>{{Cite web|url=https://usatoday.com/story/business/2024/10/28/patricia-healy-elon-musk-highlights-need-for-government-efficiency/75798556007|title=Elon Musk puts spotlight on ... Department of Government Efficiency? {{!}} Cumberland Comment|last=Healy|first=Patricia|website=USA TODAY|language=en-US|access-date=November 9, 2024}}</ref>. Musk stated his belief that DOGE could remove US$2 trillion from the [[w:United_States_federal_budget|U.S. federal budget]],<ref>{{Cite web|url=https://www.youtube.com/live/HysDMs2a-iM?si=92I5LD1FY2PAsSuG&t=15822|title=WATCH LIVE: Trump holds campaign rally at Madison Square Garden in New York|date=October 28, 2024|website=youtube.com|publisher=[[PBS NewsHour]]|language=en|format=video}}</ref> without specifying whether these savings would be made over a single year or a longer period.<ref>{{Cite web|url=https://www.bbc.co.uk/news/articles/cdj38mekdkgo|title=Can Elon Musk cut $2 trillion from US government spending?|last=Chu|first=Ben|date=2024-11-13|website=BBC News|language=en-GB|access-date=2024-11-14}}</ref> [[File:2023_US_Federal_Budget_Infographic.png|thumb|An infographic on outlays and revenues in the 2023 [[United States federal budget|U.S. federal budget]]]] DOGE could also streamline permitting with “categorical exclusions” from environmental reviews under the National Environmental Policy Act. {{sidebar with collapsible lists|name=U.S. deficit and debt topics|namestyle=background:#bf0a30;|style=width:22.0em; border: 4px double #d69d36; background:var(--background-color-base, #FFFFFF);|bodyclass=vcard|pretitle='''<span class="skin-invert">This article is part of [[:Category:United States|a series]] on the</span>'''|title=[[United States federal budget|<span style="color:var(--color-base, #000000);">Budget and debt in the<br/>United States of America</span>]]|image=[[File:Seal of the United States Congress.svg|90px]] [[File:Seal of the United States Department of the Treasury.svg|90px]]|titlestyle=background:var(--background-color-base, #002868); background-clip:padding-box;|headingstyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff);|listtitlestyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff); text-align:center;|expanded={{{expanded|{{{1|}}}}}}|list1name=dimensions|list1title=Major dimensions|list1class=hlist skin-invert|list1=* [[Economy of the United States|Economy]] * [[Expenditures in the United States federal budget|Expenditures]] * [[United States federal budget|Federal budget]] * [[Financial position of the United States|Financial position]] * [[Military budget of the United States|Military budget]] * [[National debt of the United States|Public debt]] * [[Taxation in the United States|Taxation]] * [[Unemployment in the United States|Unemployment]] * [[Government_spending_in_the_United_States|Gov't spending]]|list2name=programs|list2title=Programs|list2class=hlist skin-invert|list2=* [[Medicare (United States)|Medicare]] * [[Social programs in the United States|Social programs]] * [[Social Security (United States)|Social Security]]|list3name=issues|list3title=Contemporary issues|list3class=skin-invert|list3=<div style="margin-bottom:0.5em"> [[National Commission on Fiscal Responsibility and Reform|Bowles–Simpson Commission]] {{flatlist}} * <!--Bu--> [[Bush tax cuts]] * <!--Deb--> [[United States debt ceiling|Debt ceiling]] ** [[History of the United States debt ceiling|history]] * <!--Def--> [[Deficit reduction in the United States|Deficit reduction]] * <!--F--> [[United States fiscal cliff|Fiscal cliff]] * <!--H--> [[Healthcare reform in the United States|Healthcare reform]] * <!--P--> [[Political debates about the United States federal budget|Political debates]] * <!--So--> [[Social Security debate in the United States|Social Security debate]] * <!--St--> "[[Starve the beast]]" * <!--Su--> [[Subprime mortgage crisis]] {{endflatlist}} </div> [[2007–2008 financial crisis]] {{flatlist}} * <!--D--> [[United States debt-ceiling crisis (disambiguation)|Debt-ceiling crises]] ** [[2011 United States debt-ceiling crisis|2011]] ** [[2013 United States debt-ceiling crisis|2013]] ** [[2023 United States debt-ceiling crisis|2023]] {{endflatlist}} [[2013 United States budget sequestration|2013 budget sequestration]] {{flatlist}} * <!--G--> [[Government shutdowns in the United States|Government shutdowns]] ** [[1980 United States federal government shutdown|1980]] ** [[1981, 1984, and 1986 U.S. federal government shutdowns|1981, 1984, 1986]] ** [[1990 United States federal government shutdown|1990]] ** [[1995–1996 United States federal government shutdowns|1995–1996]] ** [[2013 United States federal government shutdown|2013]] ** [[January 2018 United States federal government shutdown|Jan 2018]] ** [[2018–2019 United States federal government shutdown|2018–2019]] {{endflatlist}} Related events {{flatlist}} *<!--E-->[[Removal of Kevin McCarthy as Speaker of the House|2023 Removal of Kevin McCarthy]] {{endflatlist}}|list4name=terminology|list4title=Terminology|list4class=hlist skin-invert|list4=Cumulative [[Government budget balance|deficit]] + [[National debt of the United States#Debates|Interest]] ≈ [[Government debt|Debt]] * [[Balance of payments]] * [[Inflation]] * [[Continuing resolution]]}} [[w:Deficit_reduction_in_the_United_States|Deficit reduction in the United States]] == Deregulate the Economy == The legal theory that this can be done through the executive branch is found in the U.S. Supreme Court’s ''[[w:West_Virginia_v._EPA|West Virginia v. EPA]]'' and ''[[w:Loper_Bright|Loper Bright]]'' rulings, which rein in the administrative state and mean that much of what the federal government now does is illegal.<ref>{{cite web|url=https://www.wsj.com/opinion/department-of-government-efficiency-elon-musk-vivek-ramaswamy-donald-trump-1e086dab|website=[[w:Wall Street Journal]]|title=The Musk-Ramaswamy Project Could Be Trump’s Best Idea}}</ref> Mr. Trump has set a goal of eliminating 10 regulations for every new one. The [[w:Competitive_Enterprise_Institute|Competitive Enterprise Institute]]’s Wayne Crews says 217,565 rules have been issued since the [[w:Federal_Register|Federal Register]] first began itemizing them in 1976, with 89,368 pages added last year. [https://sgp.fas.org/crs/misc/R43056.pdf 3,000-4,500 rules are added each year]. DOGE’s first order will be to pause enforcement of overreaching rules while starting the process to roll them back. Mr. Trump and DOGE could direct agencies to settle legal challenges to Biden rules by vacating them. This could ease the laborious process of undoing them by rule-making through the [[w:Administrative_Procedure_Act|Administrative Procedure Act]]. A source tells the WSJ they’ll do whatever they think they legally can without the APA. The [[w:Congressional_Review_Act|Congressional Review Act]]—which allows Congress to overturn recently issued agency regulations—had been used only once, prior to [[w:First_presidency_of_Donald_Trump|Trump's first term]]. While in office, he and the Republican Congress used it on 16 rules. This time, there will be more than 56 regulatory actions recent enough to be repealed. The [[w:Chevron_deference|''Chevron'' deference]] had required federal courts to defer to agencies’ interpretations of ambiguous statutes, but this was overturned in 2024. Taken together, with some other recent [[w:SCOTUS|SCOTUS]] rulings, we now have, says the WSJ, the biggest opportunity to cut regulatory red tape in more than 40 years.<ref>[https://www.wsj.com/opinion/let-the-trump-deregulation-begin-us-chamber-of-commerce-second-term-economic-growth-73f24387?cx_testId=3&cx_testVariant=cx_166&cx_artPos=0]</ref><blockquote>"Most legal edicts aren’t laws enacted by Congress but “rules and regulations” promulgated by unelected bureaucrats—tens of thousands of them each year. Most government enforcement decisions and discretionary expenditures aren’t made by the democratically elected president or even his political appointees but by millions of unelected, unappointed civil servants within government agencies who view themselves as immune from firing thanks to civil-service protections." "This is antidemocratic and antithetical to the Founders’ vision. It imposes massive direct and indirect costs on taxpayers." "When the president nullifies thousands of such regulations, critics will allege executive overreach. In fact, it will be ''correcting'' the executive overreach of thousands of regulations promulgated by administrative fiat that were never authorized by Congress. The president owes lawmaking deference to Congress, not to bureaucrats deep within federal agencies. The use of executive orders to substitute for lawmaking by adding burdensome new rules is a constitutional affront, but the use of executive orders to roll back regulations that wrongly bypassed Congress is legitimate and necessary to comply with the Supreme Court’s recent mandates. And after those regulations are fully rescinded, a future president couldn’t simply flip the switch and revive them but would instead have to ask Congress to do so" Mssrs. [https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Musk and Ramaswamy, WSJ, 11/20/2024]</blockquote> == Shrink the federal civil service == The government has around three million [[w:United_States_federal_civil_service|federal civil service]] employees, with an average salary of $106,000. Dr. Anthony Fauci made $481,000 in 2022. The federal head count has ballooned by 120,800 during the Biden years. Civil service and union protections make it hard to fire workers. Mr. Trump intends to quickly resurrect the [[w:Schedule_F|Schedule F]] reform that he sought to implement at the end of his first term but was scrapped by Mr. Biden. These would high-level federal employees to be removed like political appointees, by eliminating their job protections. WSJ proposals[https://www.wsj.com/opinion/the-doge-cheat-sheet-elon-musk-vivek-ramaswamy-department-of-government-efficiency-1c231783#cxrecs_s] The [[w:Administrative_Procedures_Act|Administrative Procedures Act]] statute protects federal employees from political retaliation, but allows for “reductions in force” that don’t target specific employees. The statute further empowers the president to “prescribe rules governing the competitive service.” The Supreme Court has held—in ''[[w:Franklin_v._Massachusetts|Franklin v. Massachusetts]]'' (1992) and ''[[w:Collins_v._Yellen|Collins v. Yellen]]'' (2021) that when revious presidents have used this power to amend the civil service rules by executive order, they weren’t constrained by the APA when they did so. Mr. Trump can, with this authority, implement any number of “rules governing the competitive service” that would curtail administrative overgrowth, from large-scale firings to relocation of federal agencies out of the Washington area. The DOGE welcomes voluntary terminations once the President begins requiring federal employees to come to the office five days a week, because American taxpayers shouldn’t pay federal employees for the Covid-era privilege of staying home.<ref>[https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Elon Musk and Vivek Ramaswamy: The DOGE Plan to Reform Government: Following the Supreme Court’s guidance, we’ll reverse a decadeslong executive power grab. Musk & Ramaswamy 11/20/2024]</ref> == Reduce the deficit and debt by impounding appropriated funds == === Impound appropriated funds === Reports suggest that president-elect Trump intends to override Congress’s power of the purse by [[w:Impoundment_of_appropriated_funds|impoundment of appropriated funds]], that is, refusing to spend them. the president may [[wikipedia:Rescission_bill|propose rescission]] of specific funds, but that rescission must be approved by both the [[wikipedia:United_States_House_of_Representatives|House of Representatives]] and [[wikipedia:United_States_Senate|Senate]] within 45 days. [[w:Thomas_Jefferson|Thomas Jefferson]] was the first president to exercise the power of impoundment in 1801, which power was available to all presidents up to and including [[wikipedia:Richard_Nixon|Richard Nixon]], and was regarded as a power inherent to the office, although one with limits. He may ask Congress to repeal The [[w:Congressional_Budget_and_Impoundment_Control_Act_of_1974|Congressional Budget and Impoundment Control Act of 1974]], which was passed in response to Nixon's abuses.<ref>{{Cite web|url=http://democrats-budget.house.gov/resources/reports/impoundment-control-act-1974-what-it-why-does-it-matter|title=The Impoundment Control Act of 1974: What Is It? Why Does It Matter? {{!}} House Budget Committee Democrats|date=2019-10-23|website=democrats-budget.house.gov|language=en|access-date=2024-05-19}}</ref> If Congress refuses to do so, president Trump may impound funds anyway and argue in court that the 1974 law is unconstitutional. The matter would likely end up at the Supreme Court, which would have to do more than simply hold the 1974 act unconstitutional in order for Mr. Trump to prevail. The court would also have to overrule [[w:Train_v._City_of_New_York_(1975)|''Train v. City of New York'' (1975)]], which held that impoundment is illegal unless the underlying legislation specifically authorizes it. === Reduce the budget deficit === [[wikipedia:U.S. federal budget|U.S. federal budget]] The [[wikipedia:Fiscal_year|fiscal year]], beginning October 1 and ending on September 30 of the year following. Congress is the body required by law to pass appropriations annually and to submit funding bills passed by both houses to the President for signature. Congressional decisions are governed by rules and legislation regarding the [[wikipedia:United_States_budget_process|federal budget process]]. Budget committees set spending limits for the House and Senate committees and for Appropriations subcommittees, which then approve individual [[wikipedia:Appropriations_bill_(United_States)|appropriations bills]] to During FY2022, the federal government spent $6.3 trillion. Spending as % of GDP is 25.1%, almost 2 percentage points greater than the average over the past 50 years. Major categories of FY 2022 spending included: Medicare and Medicaid ($1.339T or 5.4% of GDP), Social Security ($1.2T or 4.8% of GDP), non-defense discretionary spending used to run federal Departments and Agencies ($910B or 3.6% of GDP), Defense Department ($751B or 3.0% of GDP), and net interest ($475B or 1.9% of GDP).<ref name="CBO_2022">[https://www.cbo.gov/publication/58888 The Federal Budget in Fiscal Year 2022: An Infographic]</ref> CBO projects a federal budget deficit of $1.6 trillion for 2024. In the agency’s projections, deficits generally increase over the coming years; the shortfall in 2034 is $2.6 trillion. The deficit amounts to 5.6 percent of gross domestic product (GDP) in 2024, swells to 6.1 percent of GDP in 2025, and then declines in the two years that follow. After 2027, deficits increase again, reaching 6.1 percent of GDP in 2034.<ref name="CBO_budgetOutlook2024">{{cite web|url=https://www.cbo.gov/publication/59710|title=The Budget and Economic Outlook: 2024 to 2034|date=February 7, 2024|publisher=CBO|access-date=February 7, 2024}}</ref> The following table summarizes several budgetary statistics for the fiscal year 2015-2021 periods as a percent of GDP, including federal tax revenue, outlays or spending, deficits (revenue – outlays), and [[wikipedia:National_debt_of_the_United_States|debt held by the public]]. The historical average for 1969-2018 is also shown. With U.S. GDP of about $21 trillion in 2019, 1% of GDP is about $210 billion.<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> Statistics for 2020-2022 are from the CBO Monthly Budget Review for FY 2022.<ref name="CBO_MBRFY2022">{{cite web|url=https://www.cbo.gov/publication/58592|title=Monthly Budget Review: Summary for Fiscal Year 2022|date=November 8, 2022|publisher=CBO|access-date=December 10, 2022}}</ref> {| class="wikitable" !Variable As % GDP !2015 !2016 !2017 !2018 !2019 !2020 !2021 !2022 !Hist Avg |- !Revenue<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> |18.0% |17.6% |17.2% |16.4% |16.4% |16.2% |17.9% |19.6% |17.4% |- !Outlays<ref name="CBO_Hist_20" /> |20.4% |20.8% |20.6% |20.2% |21.0% |31.1% |30.1% |25.1% |21.0% |- !Budget Deficit<ref name="CBO_Hist_20" /> | -2.4% | -3.2% | -3.5% | -3.8% | -4.6% | -14.9% | -12.3% | -5.5% | -3.6% |- !Debt Held by Public<ref name="CBO_Hist_20" /> |72.5% |76.4% |76.2% |77.6% |79.4% |100.3% |99.6% |94.7% | |} The [[wikipedia:U.S._Constitution|U.S. Constitution]] ([[wikipedia:Article_One_of_the_United_States_Constitution|Article I]], section 9, clause 7) states that "No money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of Receipts and Expenditures of all public Money shall be published from time to time." Each year, the President of the United States submits a budget request to Congress for the following fiscal year as required by the [[wikipedia:Budget_and_Accounting_Act_of_1921|Budget and Accounting Act of 1921]]. Current law ({{UnitedStatesCode|31|1105}}(a)) requires the president to submit a budget no earlier than the first Monday in January, and no later than the first Monday in February. Typically, presidents submit budgets on the first Monday in February. The budget submission has been delayed, however, in some new presidents' first year when the previous president belonged to a different party. === Reduce the National debt === == Reform Entitlements == === Healthcare and Medicare === [[w:ObamaCare|ObamaCare]] started as a plausible scheme for universal, cost-effective health insurance with subsidies for the needy. Only the subsidies survive because the ObamaCare policies actually delivered are so overpriced nobody would buy them without a subsidy.<ref>[https://www.wsj.com/opinion/elons-real-trump-mission-protect-growth-department-of-government-efficiency-appointments-cabinet-9e7e62b2]</ref> See below: Department of Health and Human Services === Social Security === Even FDR was aware of its flaw: it discourages working and saving. == Strategic Foreign Policy and Military reform == === Department of State === {{Main article|w:Second_presidency_of_Donald_Trump#Prospective_foreign_policy|w:State Department}} === U.S. Department of Defense === The president-elect is reportedly considering a draft executive order that establishes a “warrior board” of retired senior military personnel with the power to review three- and four-star officers “on leadership capability, strategic readiness, and commitment to military excellence," and to recommend removals of any deemed unfit for leadership. This would fast-track the removal of generals and admirals found to be “lacking in requisite leadership qualities,” consistent with his earlier vow to fire “woke” military leaders.<ref>[https://www.wsj.com/politics/national-security/trump-draft-executive-order-would-create-board-to-purge-generals-7ebaa606<nowiki> Trump draft executive order would create a board to purge generals 11/12/2024]</nowiki></ref> There are legal obstacles. The law prohibits the firing of commissioned officers except by “sentence of a general court-martial,” as a “commutation of a sentence of a general court-martial,” or “in time of war, by order of the president.” A commissioned officer who believes he’s been wrongfully dismissed has the right to seek a trial by court-martial, which may find the dismissal baseless. <ref>[https://www.wsj.com/opinion/trump-tests-the-constitutions-limits-checks-balances-government-policy-law-78d0d0f1<nowiki> Trump test the constitutions limits 11/19/2024]</nowiki></ref> Musk said, "Some idiots are still building manned fighter jets like the F-35," and later added: "Manned fighter jets are outdated in the age of drones and only put pilots' lives at risk." [[w:Bernie_Sanders|Bernie Sanders]] wrote on X: "Elon Musk is right. The Pentagon, with a budget of $886 billion, just failed its 7th audit in a row. It's lost track of billions. Last year, only 13 senators voted against the Military Industrial Complex and a defense budget full of waste and fraud. That must change."{{sfn|Newsweek 12/02|2024}} == Reform the other Government Bureaus and Departments == === Department of Education === [[w:United_States_Department_of_Education|w:Department of Education]] has 4,400 employees – the smallest staff of the Cabinet agencies<ref>{{Cite web|url=https://www2.ed.gov/about/overview/fed/role.html|title=Federal Role in Education|date=2021-06-15|website=www2.ed.gov|language=en|access-date=2022-04-28}}</ref> – and a 2024 budget of $238 billion.<ref name="DOE-mission">{{Cite web|url=https://www.usaspending.gov/agency/department-of-education?fy=2024|title=Agency Profile {{!}} U.S. Department of Education|website=www2.ed.gov|access-date=2024-11-14}}</ref> The 2023 Budget was $274 billion, which included funding for children with disabilities ([[wikipedia:Individuals_with_Disabilities_Education_Act|IDEA]]), pandemic recovery, early childhood education, [[wikipedia:Pell_Grant|Pell Grants]], [[wikipedia:Elementary_and_Secondary_Education_Act|Title I]], work assistance, among other programs. This budget was down from $637.7 billion in 2022.<ref>{{Cite web|url=https://www.future-ed.org/what-the-new-pisa-results-really-say-about-u-s-schools/|title=What the New PISA Results Really Say About U.S. Schools|date=2021-06-15|website=future-ed.com|language=en|access-date=2024-11-14}}</ref> The WSJ proposes that the Civil Rights division be absorbed into the Department of Justice, and that its outstanding loan portolio be handled by the Department of the Treasury. Despite the redundancies, its unlikely that it will be abolished, which would require congressional action and buy-in from Democrats in the Senate; Republicans don’t have enough votes to do it alone. A republican appointee is expected to push back against federal education overreach and progressive policies like DEI. <ref>[https://www.wsj.com/opinion/trump-can-teach-the-education-department-a-lesson-nominee-needs-boldness-back-school-choice-oppose-woke-indoctrination-ddf6a38d<nowiki> Trump can teach the Education Department a Lesson. WSJ 11/20/2024]</nowiki></ref> === U.S. Department of Health and Human Services === [[w:U.S._Department_of_Health_and_Human_Services|U.S. Department of Health and Human Services]] was authorized a budget for [[w:2020_United_States_federal_budget|fiscal year 2020]] of $1.293 trillion. It has 13 operating divisions, 10 of which constitute the [[w:United_States_Public_Health_Service|Public Health Services]], whose budget authorization is broken down as follows:<ref name="hhs_budget_fy2020">{{cite web|url=https://www.hhs.gov/about/budget/fy2020/index.html|title=HHS FY 2020 Budget in Brief|date=October 5, 2019|website=HHS Budget & Performance|publisher=United States Department of Health & Human Services|page=7|access-date=May 9, 2020}}</ref> {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Food and Drug Administration|Food and Drug Administration]] (FDA) |$3,329 MM |- |[[w:Health Resources and Services Administration|Health Resources and Services Administration]] (HRSA) |$11,004 |- |[[w:Indian Health Service|Indian Health Service]] (IHS) |$6,104 |- |[[w:Centers for Disease Control and Prevention|Centers for Disease Control and Prevention]] (CDC) |$6,767 |- |[[w:National Institutes of Health|National Institutes of Health]] (NIH) |$33,669 |- |[[w:Substance Abuse and Mental Health Services Administration|Substance Abuse and Mental Health Services Administration]] (SAMHSA) |$5,535 |- |[[w:Agency for Healthcare Research and Quality|Agency for Healthcare Research and Quality]] (AHRQ) |$0 |- |[[w:Centers for Medicare & Medicaid Services|Centers for Medicare & Medicaid Services]] (CMMS) |$1,169,091 |- |[[w:Administration for Children and Families|Administration for Children and Families]] (ACF) |$52,121 |- |[[w:Administration for Community Living|Administration for Community Living]] (ACL) |$1,997 |- |} {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Departmental Management|Departmental Management]] |$340 |- |Non-Recurring Expense Fund |$-400 |- |[[w:Office of Medicare Hearings and Appeals|Office of Medicare Hearings and Appeals]] |$186 |- |[[w:Office of the National Coordinator|Office of the National Coordinator]] |$43 |- |[[w:Office for Civil Rights|Office for Civil Rights]] |$30 |- |[[w:Office of Inspector General|Office of Inspector General]] |$82 |- |[[w:Public Health and Social Services Emergency Fund|Public Health and Social Services Emergency Fund]] |$2,667 |- |[[w:Program Support Center|Program Support Center]] |$749 |- |Offsetting Collections |$-629 |- |Other Collections |$-163 |- |'''TOTAL''' |'''$1,292,523''' |} The FY2020 budget included a $1.276 billion budget decrease for the Centers for Disease Control, and a $4.533 billion budget decrease for the National Institutes of Health. These budget cuts, along with other changes since 2019, comprised a total decrease of over $24 billion in revised discretionary budget authority across the entire Department of Health and Human Services for Fiscal Year 2020.<ref name="hhs_budget_fy2020" /> Additional details of the budgeted outlays, budget authority, and detailed budgets for other years, can be found at the HHS Budget website.<ref>{{cite web|url=http://WWW.HHS.GOV/BUDGET|title=Health and Human Services: Budget and Performance|publisher=United States Department of Health & Human Services|access-date=May 9, 2020}}</ref> [[w:Robert_F._Kennedy_Jr.|Robert F. Kennedy Jr.]] has been nominated as [[w:United_States_Secretary_of_Health_and_Human_Services|United_States_Secretary_of_Health_and_Human_Services]] He is an American politician, [[Environmental law|environmental lawyer]], [[anti-vaccine activist]], and anti-packaged food industry activist, anti-pharmaceutical industry activist, who will be nominated to serve as [[United States Secretary of Health and Human Services]],<ref name="v502">{{cite web|url=https://www.forbes.com/sites/saradorn/2024/11/14/rfk-jr-launches-independent-2024-run-here-are-all-the-conspiracies-he-promotes-from-vaccines-to-mass-shootings/|title=Trump Taps RFK Jr. As Secretary Of Health And Human Services: Here Are All The Conspiracies He's Promoted|last=Dorn|first=Sara|date=2024-11-14|website=Forbes|access-date=2024-11-15}}</ref> with the mission of "Making America Healthy Again". He is the chairman and founder of [[Children's Health Defense]], an anti-vaccine advocacy group and proponent of [[COVID-19 vaccine misinformation|dubious COVID-19 vaccine information]].<ref name="Smith_12/15/2021" /><ref name="KW" /> == CPB, PBS, NPR == [[w:Howard_Husock|Howard Husock]] suggest that instead of zeroing its $535 million budget, Republicans reform the [[w:Public_Broadcasting_Act|Public Broadcasting Act]] to eliminate bias and improve local journalism.<ref>https://www.wsj.com/opinion/the-conservative-case-for-public-broadcasting-media-policy-2d4c3c9f?page=1</ref> == NASA == In September 2026, NASA's [[w:Artemis_program|Artemis program]], established in 2017 via [[wikipedia:Space_Policy_Directive_1|Space Policy Directive 1]], is intended to reestablish a human presence on the Moon for the first time since the [[wikipedia:Apollo_17|Apollo 17]] mission in 1972. The program's stated long-term goal is to establish a [[wikipedia:Moonbase|permanent base on the Moon]] to facilitate [[wikipedia:Human_mission_to_Mars|human missions to Mars]]. The [[w:U.S._National_Academies_of_Sciences,_Engineering,_and_Medicine|U.S. National Academies of Sciences, Engineering, and Medicine]] in October, put out a report titled "NASA at a Crossroads," which identified myriad issues at the agency, including out-of-date infrastructure, pressures to prioritize short-term objectives and inefficient management practices. NASA's costly [[w:Space_Launch_System|Space Launch System]] (SLS) is the cornerstone of the Artemis program. has a price tag of around $4.1 billion per launch, and is a single-use rocket that can only launch every two years, having debuted in 2022 with the uncrewed [[w:Artemis_1_mission|Artemis 1 mission]] to the moon. In contrast, SpaceX is working to reduce the cost of a single Starship flight to under $10 million. NASA Associate Administrator Jim Free urged the incoming administration to maintain the current plans, in a symposium with the [[w:American_Astronautical_Society|American Astronautical Society]] saying "We need that consistency in purpose. That has not happened since Apollo. If we lose that, I believe we will fall apart and we will wander, and other people in this world will pass us by." NASA has already asked both [[w:SpaceX|SpaceX]] and also Jeff Bezos' [[w:Blue_Origin|Blue Origin]], to develop cargo landers for its Artemis missions and to deliver heavy equipment on them to the Moon by 2033. "Having two lunar lander providers with different approaches for crew and cargo landing capability provides mission flexibility while ensuring a regular cadence of moon landings for continued discovery and scientific opportunity," Stephen D. Creech, NASA's assistant deputy associate administrator for the moon to Mars program, said in an announcement about the partnership. "For all of the money we are spending, NASA should NOT be talking about going to the Moon - We did that 50 years ago. They should be focused on the much bigger things we are doing, including Mars (of which the Moon is a part), Defense and Science!" Trump wrote in a post on X in 2019. Trump has said he would create a [[w:Space_National_Guard|Space National Guard]], an idea that lawmakers in Congress have been proposing since 2021. Critics agree that a focus on spaceflight could come at the expense of "Earth and atmospheric sciences at NASA and the [[w:National_Oceanic_and_Atmospheric_Administration|National Oceanic and Atmospheric Administration]] (NOAA), which have been cut during the Biden era."<ref>{{Cite web|url=https://www.newsweek.com/elon-musk-donald-trump-nasa-space-policy-1990599|title=Donald Trump and Elon Musk could radically reshape NASA. Here's how|last=Reporter|first=Martha McHardy US News|date=2024-11-27|website=Newsweek|language=en|access-date=2024-12-02}}</ref> == [[w:Federal_Aviation_Administration|Federal Aviation Administration]] == Musk has often complained about the FAA "smothering" innovation, boasting that he can build a rocket faster than the agency can process the "Kafkaesque paperwork" required to make the relevant approvals.{{sfn|Economist 11/23|2024}} == History and Miscellaneous facts == See also: [[w:Department_of_Government_Efficiency#History|Department of Government Efficiency — History]] DOGE's work will "conclude" no later than July 4, 2026, the 250th anniversary of the signing of the [[United States Declaration of Independence|U.S. Declaration of Independence]],<ref>{{Cite web|url=https://thehill.com/policy/4987402-trump-musk-advisory-group-spending/|title=Elon Musk, Vivek Ramaswamy to lead Trump's Department of Government Efficiency (DOGE)|last=Nazzaro|first=Miranda|date=November 13, 2024|website=The Hill|language=en-US|access-date=November 13, 2024}}</ref> also coinciding with America's [[United States Semiquincentennial|semiquincentennial]] celebrations and a proposed "Great American Fair". Despite its name it is not expected to be a [[wikipedia:United_States_federal_executive_departments|federal executive department]], but rather may operate under the [[Federal Advisory Committee Act]],<ref>{{Cite web|url=https://www.cbsnews.com/news/trump-department-of-government-efficiency-doge-elon-musk-ramaswamy/|title=What to know about Trump's Department of Government Efficiency, led by Elon Musk and Vivek Ramaswamy - CBS News|last=Picchi|first=Aimee|date=2024-11-14|website=www.cbsnews.com|language=en-US|access-date=2024-11-14}}</ref> so its formation is not expected to require approval from the [[wikipedia:United_States_Congress|U.S. Congress]]. NYT argues that records of its meetings must be made public.{{Cn}} As an advisor rather than a government employee, Mr. Musk will not be subject to various ethics rules.{{sfn|Economist 11/23}} Musk has stated that he believes such a commission could reduce the [[wikipedia:United_States_federal_budget|U.S. federal budget]] by $2 trillion, which would be a reduction of almost one third from its 2023 total. [[Maya MacGuineas]] of the [[Committee for a Responsible Federal Budget]] has said that this saving is "absolutely doable" over a period of 10 years, but it would be difficult to do in a single year "without compromising some of the fundamental objectives of the government that are widely agreed upon".<ref>{{Cite web|url=https://thehill.com/business/4966789-elon-musk-skepticism-2-trillion-spending-cuts/|title=Elon Musk draws skepticism with call for $2 trillion in spending cuts|last=Folley|first=Aris|date=2024-11-03|website=The Hill|language=en-US|access-date=2024-11-14}}</ref> [[wikipedia:Jamie_Dimon|Jamie Dimon]], the chief executive officer of [[wikipedia:JPMorgan_Chase|JPMorgan Chase]], has supported the idea. Some commentators questioned whether DOGE is a conflict of interest for Musk given that his companies are contractors to the federal government. The body is "unlikely to have any regulatory teeth on its own, but there's little doubt that it can have influence on the incoming administration and how it will determine its budgets".<ref>{{Cite web|url=https://www.vox.com/policy/384904/trumps-department-of-government-efficiency-sounds-like-a-joke-it-isnt|title=Trump tapped Musk to co-lead the "Department of Government Efficiency." What the heck is that?|last=Fayyad|first=Abdallah|date=2024-11-13|website=Vox|language=en-US|access-date=2024-11-14}}</ref> Elon Musk had called [[w:Federico_Sturzenegger|Federico Sturzenegger]], Argentina's [[Minister of Deregulation and Transformation of the State]] ([[w:es:Ministerio_de_Desregulación_y_Transformación_del_Estado|es]]), to discuss imitating his ministry's model.<ref>{{Cite web|url=https://www.infobae.com/economia/2024/11/08/milei-brindo-un-nuevo-apoyo-a-sturzenegger-y-afirmo-que-elon-musk-imitara-su-gestion-en-eeuu/|title=Milei brindó un nuevo apoyo a Sturzenegger y afirmó que Elon Musk imitará su gestión en EEUU|date=November 8, 2024|website=infobae|language=es-ES|access-date=November 13, 2024}}</ref> == Reception and Criticism == See also: [[w:Department_of_Government_Efficiency#Reception|w:Department of Government Efficiency — Reception]] The WSJ reports that Tesla's Texas facility dumped toxic wastewater into the public sewer system, into a lagoon, and into a local river, violated Texas environmental regulations, and fired an employee who attempted to comply with the law.{{Cn}} The Economist estimates that 10% of Mr. Musk's $360bn personal fortune is derived from contracts and benefits from the federal government, and 15% from the Chinese market.{{sfn|Economist 11/23}} == See also == * [[w:Second_presidential_transition_of_Donald_Trump|Second presidential transition of Donald Trump]] * [[w:United_States_federal_budget#Deficits_and_debt|United States federal budget - Deficits and debt]] * [[w:United_States_Bureau_of_Efficiency|United States Bureau of Efficiency]] – United States federal government bureau from 1916 to 1933 * [[w:Brownlow_Committee|Brownlow Committee]] – 1937 commission recommending United States federal government reforms * [[w:Grace_Commission|Grace Commission]] – Investigation to eliminate inefficiency in the United States federal government * [[w:Hoover_Commission|Hoover Commission]] – United States federal commission in 1947 advising on executive reform * [[w:Keep_Commission|Keep Commission]] * [[w:Project_on_National_Security_Reform|Project on National Security Reform]] == Notes == {{reflist}} == References == {{refbegin}} * {{Cite web|url=https://www.newsweek.com/bernie-sanders-finds-new-common-ground-elon-musk-1993820|title=Bernie Sanders finds new common ground with Elon Musk|last=Reporter|first=Mandy Taheri Weekend|date=2024-12-01|website=Newsweek|language=en|access-date=2024-12-02}}</ref> Failed its fifth audit in June 2023.<ref>{{Cite web|url=https://www.newsweek.com/fox-news-host-confronts-gop-senator-pentagons-fifth-failed-audit-1804379|title=Fox News host confronts GOP Senator on Pentagon's fifth failed audit|last=Writer|first=Fatma Khaled Staff|date=2023-06-04|website=Newsweek|language=en|access-date=2024-12-02}} * {{Cite news|url=https://www.economist.com/briefing/2024/11/21/elon-musk-and-donald-trump-seem-besotted-where-is-their-bromance-headed|title=Elon Musk and Donald Trump seem besotted. Where is their bromance headed?|work=The Economist|access-date=2024-12-04|issn=0013-0613 |ref={{harvid|Economist 11/23|2024}} }} <references group="lower-alpha" /> {{refend}} slbwjhxi6u15vmnq60io8n793uvdwyh 2690202 2690200 2024-12-04T03:41:07Z Jaredscribe 2906761 /* References */ 2690202 wikitext text/x-wiki The U.S. [[w:Department of Government Efficiency]]. {{Infobox Organization |name=Department of Government Efficiency |logo=DOGE Logo as of November 14, 2024.jpg |logo_size=150px |logo_caption=Logo on [[Twitter|X]] (formerly Twitter) as of November 14, 2024 |seal= |seal_size= |seal_caption= |formation=Announced on November 12, 2024; yet to be established |abbreviation=DOGE |key_people={{plainlist|[[w:Commissioner of the Department of Government Efficiency|Co-commissioners]]: * [[w:Elon Musk]] * [[w:Vivek Ramaswamy]] }} |website={{URL|https://x.com/DOGE|x.com/DOGE}} }} This "'''Wiki Of Government Efficiency'''" (WOGE) will analyze the [[w:U.S._Federal_budget|U.S. federal budget]], [[User:Jaredscribe/Department of Government Efficiency#Reform the other Government Bureaus and Departments|federal bureaucracy]], and [[User:Jaredscribe/Department of Government Efficiency#Shrink the federal civil service|federal civil service]], in the public interest, and in the context of [[w:Second_presidency_of_Donald_Trump|president-elect Trump']]<nowiki/>s [[w:Agenda_47|Agenda 47]], with non-partisan research, analysis, and criticism of forward-looking proposals on how the '''[[w:Department of Government Efficiency|Department of Government Efficiency]]'''{{Efn|Also referred to as '''Government Efficiency Commission'''}} (DOGE) might fulfill its mission to ''"dismantle government bureaucracy, slash excess regulations, and cut wasteful expenditures and restructure federal agencies"'', in the words of president-elect [[wikipedia:Donald_Trump|Donald Trump]], who called for it to address ''"massive waste and fraud"'' in government spending.<ref name=":1">{{Cite web|url=https://www.bbc.co.uk/news/articles/c93qwn8p0l0o|title=Donald Trump picks Elon Musk for US government cost-cutting role|last1=Faguy|first1=Ana|last2=FitzGerald|first2=James|date=2024-11-13|publisher=BBC News|language=en-GB|access-date=2024-11-13}}</ref> The DOGE will work with through the [[w:Office_of_Management_and_Budget|Office of Management and Budget]] as its "policy vector". Here's [[User:Jaredscribe/Department of Government Efficiency/How to contribute|how to contribute]] to the WOGE. The [[w:U.S._budget_deficit|U.S. Budget deficit]], (C.f. [[w:Government_budget_balance|fiscal deficit]]), and the [[w:National_debt_of_the_United_States|U.S. National debt]], currently $35.7 Trillion as of 10/2024, which is 99% of the [[w:U.S._GDP|U.S. GDP]],<ref>{{Unbulleted list citebundle|{{cite news|newspaper=Financial Post| title= Musk's $2 Trillion of Budget Cuts Would Have These Stocks Moving|url=https://financialpost.com/pmn/business-pmn/musks-2-trillion-of-budget-cuts-would-have-these-stocks-moving|first=Alexandra|last=Semenova|date=November 4, 2024}}|{{cite news|newspaper= New York Times|title=Elon|url=https://nytimes.com/2024/10/29/us/politics/elon-musk-trump-economy-hardship.html}}|{{Cite web |date=September 5, 2024 |title=Trump says he'd create a government efficiency commission led by Elon Musk |url=https://apnews.com/article/donald-trump-elon-musk-government-efficiency-commission-e831ed5dc2f6a56999e1a70bb0a4eaeb |publisher=AP News}}|{{cite web|first=Jenn|last=Brice|title=How Elon Musk's $130 million investment in Trump's victory could reap a huge payoff for Tesla and the rest of his business empire|url=https://fortune.com/2024/11/06/elon-musk-donald-trump-tesla-spacex-xai-boring-neuralink|website=Fortune}}|{{cite web|url=https://axios.com/2024/11/07/elon-musk-government-efficiency-trump|title=Musk will bring his Twitter management style to government reform}}|{{cite news| access-date =November 9, 2024|work=Reuters|date=September 6, 2024|first1=Helen|first2=Gram|last1=Coster| last2=Slattery|title=Trump says he will tap Musk to lead government efficiency commission if elected| url= https://reuters.com/world/us/trump-adopt-musks-proposal-government-efficiency-commission-wsj-reports-2024-09-05}}|{{cite web|title=Trump says Musk could head 'government efficiency' force|url= https://bbc.com/news/articles/c74lgwkrmrpo|publisher=BBC}}|{{cite web|date =November 5, 2024|title=How Elon Musk could gut the government under Trump|url=https://independent.co.uk/news/world/americas/us-politics/elon-musk-donald-trump-economy-job-cuts-b2641644.html|website= The Independent}}}}</ref> and expected to grow to 134% of GDP by 2034 if current laws remain unchanged, according to the [[w:Congressional_Budget_Office|Congressional Budget Office]]. The DOGE will be a [[wikipedia:Presidential_commission_(United_States)|presidential advisory commission]] led by the billionaire businessmen [[wikipedia:Elon_Musk|Elon Musk]] and [[wikipedia:Vivek_Ramaswamy|Vivek Ramaswamy]], and possibly [[w:Ron_Paul|Ron Paul]]<ref>{{Cite web|url=https://thehill.com/video/ron-paul-vows-to-join-elon-musk-help-eliminate-government-waste-in-a-trump-admin/10191375|title=Ron Paul vows to join Elon Musk, help eliminate government waste in a Trump admin|date=November 5, 2024|website=The Hill}}</ref><ref>{{Cite web|url=https://usatoday.com/story/business/2024/10/28/patricia-healy-elon-musk-highlights-need-for-government-efficiency/75798556007|title=Elon Musk puts spotlight on ... Department of Government Efficiency? {{!}} Cumberland Comment|last=Healy|first=Patricia|website=USA TODAY|language=en-US|access-date=November 9, 2024}}</ref>. Musk stated his belief that DOGE could remove US$2 trillion from the [[w:United_States_federal_budget|U.S. federal budget]],<ref>{{Cite web|url=https://www.youtube.com/live/HysDMs2a-iM?si=92I5LD1FY2PAsSuG&t=15822|title=WATCH LIVE: Trump holds campaign rally at Madison Square Garden in New York|date=October 28, 2024|website=youtube.com|publisher=[[PBS NewsHour]]|language=en|format=video}}</ref> without specifying whether these savings would be made over a single year or a longer period.<ref>{{Cite web|url=https://www.bbc.co.uk/news/articles/cdj38mekdkgo|title=Can Elon Musk cut $2 trillion from US government spending?|last=Chu|first=Ben|date=2024-11-13|website=BBC News|language=en-GB|access-date=2024-11-14}}</ref> [[File:2023_US_Federal_Budget_Infographic.png|thumb|An infographic on outlays and revenues in the 2023 [[United States federal budget|U.S. federal budget]]]] DOGE could also streamline permitting with “categorical exclusions” from environmental reviews under the National Environmental Policy Act. {{sidebar with collapsible lists|name=U.S. deficit and debt topics|namestyle=background:#bf0a30;|style=width:22.0em; border: 4px double #d69d36; background:var(--background-color-base, #FFFFFF);|bodyclass=vcard|pretitle='''<span class="skin-invert">This article is part of [[:Category:United States|a series]] on the</span>'''|title=[[United States federal budget|<span style="color:var(--color-base, #000000);">Budget and debt in the<br/>United States of America</span>]]|image=[[File:Seal of the United States Congress.svg|90px]] [[File:Seal of the United States Department of the Treasury.svg|90px]]|titlestyle=background:var(--background-color-base, #002868); background-clip:padding-box;|headingstyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff);|listtitlestyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff); text-align:center;|expanded={{{expanded|{{{1|}}}}}}|list1name=dimensions|list1title=Major dimensions|list1class=hlist skin-invert|list1=* [[Economy of the United States|Economy]] * [[Expenditures in the United States federal budget|Expenditures]] * [[United States federal budget|Federal budget]] * [[Financial position of the United States|Financial position]] * [[Military budget of the United States|Military budget]] * [[National debt of the United States|Public debt]] * [[Taxation in the United States|Taxation]] * [[Unemployment in the United States|Unemployment]] * [[Government_spending_in_the_United_States|Gov't spending]]|list2name=programs|list2title=Programs|list2class=hlist skin-invert|list2=* [[Medicare (United States)|Medicare]] * [[Social programs in the United States|Social programs]] * [[Social Security (United States)|Social Security]]|list3name=issues|list3title=Contemporary issues|list3class=skin-invert|list3=<div style="margin-bottom:0.5em"> [[National Commission on Fiscal Responsibility and Reform|Bowles–Simpson Commission]] {{flatlist}} * <!--Bu--> [[Bush tax cuts]] * <!--Deb--> [[United States debt ceiling|Debt ceiling]] ** [[History of the United States debt ceiling|history]] * <!--Def--> [[Deficit reduction in the United States|Deficit reduction]] * <!--F--> [[United States fiscal cliff|Fiscal cliff]] * <!--H--> [[Healthcare reform in the United States|Healthcare reform]] * <!--P--> [[Political debates about the United States federal budget|Political debates]] * <!--So--> [[Social Security debate in the United States|Social Security debate]] * <!--St--> "[[Starve the beast]]" * <!--Su--> [[Subprime mortgage crisis]] {{endflatlist}} </div> [[2007–2008 financial crisis]] {{flatlist}} * <!--D--> [[United States debt-ceiling crisis (disambiguation)|Debt-ceiling crises]] ** [[2011 United States debt-ceiling crisis|2011]] ** [[2013 United States debt-ceiling crisis|2013]] ** [[2023 United States debt-ceiling crisis|2023]] {{endflatlist}} [[2013 United States budget sequestration|2013 budget sequestration]] {{flatlist}} * <!--G--> [[Government shutdowns in the United States|Government shutdowns]] ** [[1980 United States federal government shutdown|1980]] ** [[1981, 1984, and 1986 U.S. federal government shutdowns|1981, 1984, 1986]] ** [[1990 United States federal government shutdown|1990]] ** [[1995–1996 United States federal government shutdowns|1995–1996]] ** [[2013 United States federal government shutdown|2013]] ** [[January 2018 United States federal government shutdown|Jan 2018]] ** [[2018–2019 United States federal government shutdown|2018–2019]] {{endflatlist}} Related events {{flatlist}} *<!--E-->[[Removal of Kevin McCarthy as Speaker of the House|2023 Removal of Kevin McCarthy]] {{endflatlist}}|list4name=terminology|list4title=Terminology|list4class=hlist skin-invert|list4=Cumulative [[Government budget balance|deficit]] + [[National debt of the United States#Debates|Interest]] ≈ [[Government debt|Debt]] * [[Balance of payments]] * [[Inflation]] * [[Continuing resolution]]}} [[w:Deficit_reduction_in_the_United_States|Deficit reduction in the United States]] == Deregulate the Economy == The legal theory that this can be done through the executive branch is found in the U.S. Supreme Court’s ''[[w:West_Virginia_v._EPA|West Virginia v. EPA]]'' and ''[[w:Loper_Bright|Loper Bright]]'' rulings, which rein in the administrative state and mean that much of what the federal government now does is illegal.<ref>{{cite web|url=https://www.wsj.com/opinion/department-of-government-efficiency-elon-musk-vivek-ramaswamy-donald-trump-1e086dab|website=[[w:Wall Street Journal]]|title=The Musk-Ramaswamy Project Could Be Trump’s Best Idea}}</ref> Mr. Trump has set a goal of eliminating 10 regulations for every new one. The [[w:Competitive_Enterprise_Institute|Competitive Enterprise Institute]]’s Wayne Crews says 217,565 rules have been issued since the [[w:Federal_Register|Federal Register]] first began itemizing them in 1976, with 89,368 pages added last year. [https://sgp.fas.org/crs/misc/R43056.pdf 3,000-4,500 rules are added each year]. DOGE’s first order will be to pause enforcement of overreaching rules while starting the process to roll them back. Mr. Trump and DOGE could direct agencies to settle legal challenges to Biden rules by vacating them. This could ease the laborious process of undoing them by rule-making through the [[w:Administrative_Procedure_Act|Administrative Procedure Act]]. A source tells the WSJ they’ll do whatever they think they legally can without the APA. The [[w:Congressional_Review_Act|Congressional Review Act]]—which allows Congress to overturn recently issued agency regulations—had been used only once, prior to [[w:First_presidency_of_Donald_Trump|Trump's first term]]. While in office, he and the Republican Congress used it on 16 rules. This time, there will be more than 56 regulatory actions recent enough to be repealed. The [[w:Chevron_deference|''Chevron'' deference]] had required federal courts to defer to agencies’ interpretations of ambiguous statutes, but this was overturned in 2024. Taken together, with some other recent [[w:SCOTUS|SCOTUS]] rulings, we now have, says the WSJ, the biggest opportunity to cut regulatory red tape in more than 40 years.<ref>[https://www.wsj.com/opinion/let-the-trump-deregulation-begin-us-chamber-of-commerce-second-term-economic-growth-73f24387?cx_testId=3&cx_testVariant=cx_166&cx_artPos=0]</ref><blockquote>"Most legal edicts aren’t laws enacted by Congress but “rules and regulations” promulgated by unelected bureaucrats—tens of thousands of them each year. Most government enforcement decisions and discretionary expenditures aren’t made by the democratically elected president or even his political appointees but by millions of unelected, unappointed civil servants within government agencies who view themselves as immune from firing thanks to civil-service protections." "This is antidemocratic and antithetical to the Founders’ vision. It imposes massive direct and indirect costs on taxpayers." "When the president nullifies thousands of such regulations, critics will allege executive overreach. In fact, it will be ''correcting'' the executive overreach of thousands of regulations promulgated by administrative fiat that were never authorized by Congress. The president owes lawmaking deference to Congress, not to bureaucrats deep within federal agencies. The use of executive orders to substitute for lawmaking by adding burdensome new rules is a constitutional affront, but the use of executive orders to roll back regulations that wrongly bypassed Congress is legitimate and necessary to comply with the Supreme Court’s recent mandates. And after those regulations are fully rescinded, a future president couldn’t simply flip the switch and revive them but would instead have to ask Congress to do so" Mssrs. [https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Musk and Ramaswamy, WSJ, 11/20/2024]</blockquote> == Shrink the federal civil service == The government has around three million [[w:United_States_federal_civil_service|federal civil service]] employees, with an average salary of $106,000. Dr. Anthony Fauci made $481,000 in 2022. The federal head count has ballooned by 120,800 during the Biden years. Civil service and union protections make it hard to fire workers. Mr. Trump intends to quickly resurrect the [[w:Schedule_F|Schedule F]] reform that he sought to implement at the end of his first term but was scrapped by Mr. Biden. These would high-level federal employees to be removed like political appointees, by eliminating their job protections. WSJ proposals[https://www.wsj.com/opinion/the-doge-cheat-sheet-elon-musk-vivek-ramaswamy-department-of-government-efficiency-1c231783#cxrecs_s] The [[w:Administrative_Procedures_Act|Administrative Procedures Act]] statute protects federal employees from political retaliation, but allows for “reductions in force” that don’t target specific employees. The statute further empowers the president to “prescribe rules governing the competitive service.” The Supreme Court has held—in ''[[w:Franklin_v._Massachusetts|Franklin v. Massachusetts]]'' (1992) and ''[[w:Collins_v._Yellen|Collins v. Yellen]]'' (2021) that when revious presidents have used this power to amend the civil service rules by executive order, they weren’t constrained by the APA when they did so. Mr. Trump can, with this authority, implement any number of “rules governing the competitive service” that would curtail administrative overgrowth, from large-scale firings to relocation of federal agencies out of the Washington area. The DOGE welcomes voluntary terminations once the President begins requiring federal employees to come to the office five days a week, because American taxpayers shouldn’t pay federal employees for the Covid-era privilege of staying home.<ref>[https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Elon Musk and Vivek Ramaswamy: The DOGE Plan to Reform Government: Following the Supreme Court’s guidance, we’ll reverse a decadeslong executive power grab. Musk & Ramaswamy 11/20/2024]</ref> == Reduce the deficit and debt by impounding appropriated funds == === Impound appropriated funds === Reports suggest that president-elect Trump intends to override Congress’s power of the purse by [[w:Impoundment_of_appropriated_funds|impoundment of appropriated funds]], that is, refusing to spend them. the president may [[wikipedia:Rescission_bill|propose rescission]] of specific funds, but that rescission must be approved by both the [[wikipedia:United_States_House_of_Representatives|House of Representatives]] and [[wikipedia:United_States_Senate|Senate]] within 45 days. [[w:Thomas_Jefferson|Thomas Jefferson]] was the first president to exercise the power of impoundment in 1801, which power was available to all presidents up to and including [[wikipedia:Richard_Nixon|Richard Nixon]], and was regarded as a power inherent to the office, although one with limits. He may ask Congress to repeal The [[w:Congressional_Budget_and_Impoundment_Control_Act_of_1974|Congressional Budget and Impoundment Control Act of 1974]], which was passed in response to Nixon's abuses.<ref>{{Cite web|url=http://democrats-budget.house.gov/resources/reports/impoundment-control-act-1974-what-it-why-does-it-matter|title=The Impoundment Control Act of 1974: What Is It? Why Does It Matter? {{!}} House Budget Committee Democrats|date=2019-10-23|website=democrats-budget.house.gov|language=en|access-date=2024-05-19}}</ref> If Congress refuses to do so, president Trump may impound funds anyway and argue in court that the 1974 law is unconstitutional. The matter would likely end up at the Supreme Court, which would have to do more than simply hold the 1974 act unconstitutional in order for Mr. Trump to prevail. The court would also have to overrule [[w:Train_v._City_of_New_York_(1975)|''Train v. City of New York'' (1975)]], which held that impoundment is illegal unless the underlying legislation specifically authorizes it. === Reduce the budget deficit === [[wikipedia:U.S. federal budget|U.S. federal budget]] The [[wikipedia:Fiscal_year|fiscal year]], beginning October 1 and ending on September 30 of the year following. Congress is the body required by law to pass appropriations annually and to submit funding bills passed by both houses to the President for signature. Congressional decisions are governed by rules and legislation regarding the [[wikipedia:United_States_budget_process|federal budget process]]. Budget committees set spending limits for the House and Senate committees and for Appropriations subcommittees, which then approve individual [[wikipedia:Appropriations_bill_(United_States)|appropriations bills]] to During FY2022, the federal government spent $6.3 trillion. Spending as % of GDP is 25.1%, almost 2 percentage points greater than the average over the past 50 years. Major categories of FY 2022 spending included: Medicare and Medicaid ($1.339T or 5.4% of GDP), Social Security ($1.2T or 4.8% of GDP), non-defense discretionary spending used to run federal Departments and Agencies ($910B or 3.6% of GDP), Defense Department ($751B or 3.0% of GDP), and net interest ($475B or 1.9% of GDP).<ref name="CBO_2022">[https://www.cbo.gov/publication/58888 The Federal Budget in Fiscal Year 2022: An Infographic]</ref> CBO projects a federal budget deficit of $1.6 trillion for 2024. In the agency’s projections, deficits generally increase over the coming years; the shortfall in 2034 is $2.6 trillion. The deficit amounts to 5.6 percent of gross domestic product (GDP) in 2024, swells to 6.1 percent of GDP in 2025, and then declines in the two years that follow. After 2027, deficits increase again, reaching 6.1 percent of GDP in 2034.<ref name="CBO_budgetOutlook2024">{{cite web|url=https://www.cbo.gov/publication/59710|title=The Budget and Economic Outlook: 2024 to 2034|date=February 7, 2024|publisher=CBO|access-date=February 7, 2024}}</ref> The following table summarizes several budgetary statistics for the fiscal year 2015-2021 periods as a percent of GDP, including federal tax revenue, outlays or spending, deficits (revenue – outlays), and [[wikipedia:National_debt_of_the_United_States|debt held by the public]]. The historical average for 1969-2018 is also shown. With U.S. GDP of about $21 trillion in 2019, 1% of GDP is about $210 billion.<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> Statistics for 2020-2022 are from the CBO Monthly Budget Review for FY 2022.<ref name="CBO_MBRFY2022">{{cite web|url=https://www.cbo.gov/publication/58592|title=Monthly Budget Review: Summary for Fiscal Year 2022|date=November 8, 2022|publisher=CBO|access-date=December 10, 2022}}</ref> {| class="wikitable" !Variable As % GDP !2015 !2016 !2017 !2018 !2019 !2020 !2021 !2022 !Hist Avg |- !Revenue<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> |18.0% |17.6% |17.2% |16.4% |16.4% |16.2% |17.9% |19.6% |17.4% |- !Outlays<ref name="CBO_Hist_20" /> |20.4% |20.8% |20.6% |20.2% |21.0% |31.1% |30.1% |25.1% |21.0% |- !Budget Deficit<ref name="CBO_Hist_20" /> | -2.4% | -3.2% | -3.5% | -3.8% | -4.6% | -14.9% | -12.3% | -5.5% | -3.6% |- !Debt Held by Public<ref name="CBO_Hist_20" /> |72.5% |76.4% |76.2% |77.6% |79.4% |100.3% |99.6% |94.7% | |} The [[wikipedia:U.S._Constitution|U.S. Constitution]] ([[wikipedia:Article_One_of_the_United_States_Constitution|Article I]], section 9, clause 7) states that "No money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of Receipts and Expenditures of all public Money shall be published from time to time." Each year, the President of the United States submits a budget request to Congress for the following fiscal year as required by the [[wikipedia:Budget_and_Accounting_Act_of_1921|Budget and Accounting Act of 1921]]. Current law ({{UnitedStatesCode|31|1105}}(a)) requires the president to submit a budget no earlier than the first Monday in January, and no later than the first Monday in February. Typically, presidents submit budgets on the first Monday in February. The budget submission has been delayed, however, in some new presidents' first year when the previous president belonged to a different party. === Reduce the National debt === == Reform Entitlements == === Healthcare and Medicare === [[w:ObamaCare|ObamaCare]] started as a plausible scheme for universal, cost-effective health insurance with subsidies for the needy. Only the subsidies survive because the ObamaCare policies actually delivered are so overpriced nobody would buy them without a subsidy.<ref>[https://www.wsj.com/opinion/elons-real-trump-mission-protect-growth-department-of-government-efficiency-appointments-cabinet-9e7e62b2]</ref> See below: Department of Health and Human Services === Social Security === Even FDR was aware of its flaw: it discourages working and saving. == Strategic Foreign Policy and Military reform == === Department of State === {{Main article|w:Second_presidency_of_Donald_Trump#Prospective_foreign_policy|w:State Department}} === U.S. Department of Defense === The president-elect is reportedly considering a draft executive order that establishes a “warrior board” of retired senior military personnel with the power to review three- and four-star officers “on leadership capability, strategic readiness, and commitment to military excellence," and to recommend removals of any deemed unfit for leadership. This would fast-track the removal of generals and admirals found to be “lacking in requisite leadership qualities,” consistent with his earlier vow to fire “woke” military leaders.<ref>[https://www.wsj.com/politics/national-security/trump-draft-executive-order-would-create-board-to-purge-generals-7ebaa606<nowiki> Trump draft executive order would create a board to purge generals 11/12/2024]</nowiki></ref> There are legal obstacles. The law prohibits the firing of commissioned officers except by “sentence of a general court-martial,” as a “commutation of a sentence of a general court-martial,” or “in time of war, by order of the president.” A commissioned officer who believes he’s been wrongfully dismissed has the right to seek a trial by court-martial, which may find the dismissal baseless. <ref>[https://www.wsj.com/opinion/trump-tests-the-constitutions-limits-checks-balances-government-policy-law-78d0d0f1<nowiki> Trump test the constitutions limits 11/19/2024]</nowiki></ref> Musk said, "Some idiots are still building manned fighter jets like the F-35," and later added: "Manned fighter jets are outdated in the age of drones and only put pilots' lives at risk." [[w:Bernie_Sanders|Bernie Sanders]] wrote on X: "Elon Musk is right. The Pentagon, with a budget of $886 billion, just failed its 7th audit in a row. It's lost track of billions. Last year, only 13 senators voted against the Military Industrial Complex and a defense budget full of waste and fraud. That must change."{{sfn|Newsweek 12/02|2024}} == Reform the other Government Bureaus and Departments == === Department of Education === [[w:United_States_Department_of_Education|w:Department of Education]] has 4,400 employees – the smallest staff of the Cabinet agencies<ref>{{Cite web|url=https://www2.ed.gov/about/overview/fed/role.html|title=Federal Role in Education|date=2021-06-15|website=www2.ed.gov|language=en|access-date=2022-04-28}}</ref> – and a 2024 budget of $238 billion.<ref name="DOE-mission">{{Cite web|url=https://www.usaspending.gov/agency/department-of-education?fy=2024|title=Agency Profile {{!}} U.S. Department of Education|website=www2.ed.gov|access-date=2024-11-14}}</ref> The 2023 Budget was $274 billion, which included funding for children with disabilities ([[wikipedia:Individuals_with_Disabilities_Education_Act|IDEA]]), pandemic recovery, early childhood education, [[wikipedia:Pell_Grant|Pell Grants]], [[wikipedia:Elementary_and_Secondary_Education_Act|Title I]], work assistance, among other programs. This budget was down from $637.7 billion in 2022.<ref>{{Cite web|url=https://www.future-ed.org/what-the-new-pisa-results-really-say-about-u-s-schools/|title=What the New PISA Results Really Say About U.S. Schools|date=2021-06-15|website=future-ed.com|language=en|access-date=2024-11-14}}</ref> The WSJ proposes that the Civil Rights division be absorbed into the Department of Justice, and that its outstanding loan portolio be handled by the Department of the Treasury. Despite the redundancies, its unlikely that it will be abolished, which would require congressional action and buy-in from Democrats in the Senate; Republicans don’t have enough votes to do it alone. A republican appointee is expected to push back against federal education overreach and progressive policies like DEI. <ref>[https://www.wsj.com/opinion/trump-can-teach-the-education-department-a-lesson-nominee-needs-boldness-back-school-choice-oppose-woke-indoctrination-ddf6a38d<nowiki> Trump can teach the Education Department a Lesson. WSJ 11/20/2024]</nowiki></ref> === U.S. Department of Health and Human Services === [[w:U.S._Department_of_Health_and_Human_Services|U.S. Department of Health and Human Services]] was authorized a budget for [[w:2020_United_States_federal_budget|fiscal year 2020]] of $1.293 trillion. It has 13 operating divisions, 10 of which constitute the [[w:United_States_Public_Health_Service|Public Health Services]], whose budget authorization is broken down as follows:<ref name="hhs_budget_fy2020">{{cite web|url=https://www.hhs.gov/about/budget/fy2020/index.html|title=HHS FY 2020 Budget in Brief|date=October 5, 2019|website=HHS Budget & Performance|publisher=United States Department of Health & Human Services|page=7|access-date=May 9, 2020}}</ref> {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Food and Drug Administration|Food and Drug Administration]] (FDA) |$3,329 MM |- |[[w:Health Resources and Services Administration|Health Resources and Services Administration]] (HRSA) |$11,004 |- |[[w:Indian Health Service|Indian Health Service]] (IHS) |$6,104 |- |[[w:Centers for Disease Control and Prevention|Centers for Disease Control and Prevention]] (CDC) |$6,767 |- |[[w:National Institutes of Health|National Institutes of Health]] (NIH) |$33,669 |- |[[w:Substance Abuse and Mental Health Services Administration|Substance Abuse and Mental Health Services Administration]] (SAMHSA) |$5,535 |- |[[w:Agency for Healthcare Research and Quality|Agency for Healthcare Research and Quality]] (AHRQ) |$0 |- |[[w:Centers for Medicare & Medicaid Services|Centers for Medicare & Medicaid Services]] (CMMS) |$1,169,091 |- |[[w:Administration for Children and Families|Administration for Children and Families]] (ACF) |$52,121 |- |[[w:Administration for Community Living|Administration for Community Living]] (ACL) |$1,997 |- |} {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Departmental Management|Departmental Management]] |$340 |- |Non-Recurring Expense Fund |$-400 |- |[[w:Office of Medicare Hearings and Appeals|Office of Medicare Hearings and Appeals]] |$186 |- |[[w:Office of the National Coordinator|Office of the National Coordinator]] |$43 |- |[[w:Office for Civil Rights|Office for Civil Rights]] |$30 |- |[[w:Office of Inspector General|Office of Inspector General]] |$82 |- |[[w:Public Health and Social Services Emergency Fund|Public Health and Social Services Emergency Fund]] |$2,667 |- |[[w:Program Support Center|Program Support Center]] |$749 |- |Offsetting Collections |$-629 |- |Other Collections |$-163 |- |'''TOTAL''' |'''$1,292,523''' |} The FY2020 budget included a $1.276 billion budget decrease for the Centers for Disease Control, and a $4.533 billion budget decrease for the National Institutes of Health. These budget cuts, along with other changes since 2019, comprised a total decrease of over $24 billion in revised discretionary budget authority across the entire Department of Health and Human Services for Fiscal Year 2020.<ref name="hhs_budget_fy2020" /> Additional details of the budgeted outlays, budget authority, and detailed budgets for other years, can be found at the HHS Budget website.<ref>{{cite web|url=http://WWW.HHS.GOV/BUDGET|title=Health and Human Services: Budget and Performance|publisher=United States Department of Health & Human Services|access-date=May 9, 2020}}</ref> [[w:Robert_F._Kennedy_Jr.|Robert F. Kennedy Jr.]] has been nominated as [[w:United_States_Secretary_of_Health_and_Human_Services|United_States_Secretary_of_Health_and_Human_Services]] He is an American politician, [[Environmental law|environmental lawyer]], [[anti-vaccine activist]], and anti-packaged food industry activist, anti-pharmaceutical industry activist, who will be nominated to serve as [[United States Secretary of Health and Human Services]],<ref name="v502">{{cite web|url=https://www.forbes.com/sites/saradorn/2024/11/14/rfk-jr-launches-independent-2024-run-here-are-all-the-conspiracies-he-promotes-from-vaccines-to-mass-shootings/|title=Trump Taps RFK Jr. As Secretary Of Health And Human Services: Here Are All The Conspiracies He's Promoted|last=Dorn|first=Sara|date=2024-11-14|website=Forbes|access-date=2024-11-15}}</ref> with the mission of "Making America Healthy Again". He is the chairman and founder of [[Children's Health Defense]], an anti-vaccine advocacy group and proponent of [[COVID-19 vaccine misinformation|dubious COVID-19 vaccine information]].<ref name="Smith_12/15/2021" /><ref name="KW" /> == CPB, PBS, NPR == [[w:Howard_Husock|Howard Husock]] suggest that instead of zeroing its $535 million budget, Republicans reform the [[w:Public_Broadcasting_Act|Public Broadcasting Act]] to eliminate bias and improve local journalism.<ref>https://www.wsj.com/opinion/the-conservative-case-for-public-broadcasting-media-policy-2d4c3c9f?page=1</ref> == NASA == In September 2026, NASA's [[w:Artemis_program|Artemis program]], established in 2017 via [[wikipedia:Space_Policy_Directive_1|Space Policy Directive 1]], is intended to reestablish a human presence on the Moon for the first time since the [[wikipedia:Apollo_17|Apollo 17]] mission in 1972. The program's stated long-term goal is to establish a [[wikipedia:Moonbase|permanent base on the Moon]] to facilitate [[wikipedia:Human_mission_to_Mars|human missions to Mars]]. The [[w:U.S._National_Academies_of_Sciences,_Engineering,_and_Medicine|U.S. National Academies of Sciences, Engineering, and Medicine]] in October, put out a report titled "NASA at a Crossroads," which identified myriad issues at the agency, including out-of-date infrastructure, pressures to prioritize short-term objectives and inefficient management practices. NASA's costly [[w:Space_Launch_System|Space Launch System]] (SLS) is the cornerstone of the Artemis program. has a price tag of around $4.1 billion per launch, and is a single-use rocket that can only launch every two years, having debuted in 2022 with the uncrewed [[w:Artemis_1_mission|Artemis 1 mission]] to the moon. In contrast, SpaceX is working to reduce the cost of a single Starship flight to under $10 million. NASA Associate Administrator Jim Free urged the incoming administration to maintain the current plans, in a symposium with the [[w:American_Astronautical_Society|American Astronautical Society]] saying "We need that consistency in purpose. That has not happened since Apollo. If we lose that, I believe we will fall apart and we will wander, and other people in this world will pass us by." NASA has already asked both [[w:SpaceX|SpaceX]] and also Jeff Bezos' [[w:Blue_Origin|Blue Origin]], to develop cargo landers for its Artemis missions and to deliver heavy equipment on them to the Moon by 2033. "Having two lunar lander providers with different approaches for crew and cargo landing capability provides mission flexibility while ensuring a regular cadence of moon landings for continued discovery and scientific opportunity," Stephen D. Creech, NASA's assistant deputy associate administrator for the moon to Mars program, said in an announcement about the partnership. "For all of the money we are spending, NASA should NOT be talking about going to the Moon - We did that 50 years ago. They should be focused on the much bigger things we are doing, including Mars (of which the Moon is a part), Defense and Science!" Trump wrote in a post on X in 2019. Trump has said he would create a [[w:Space_National_Guard|Space National Guard]], an idea that lawmakers in Congress have been proposing since 2021. Critics agree that a focus on spaceflight could come at the expense of "Earth and atmospheric sciences at NASA and the [[w:National_Oceanic_and_Atmospheric_Administration|National Oceanic and Atmospheric Administration]] (NOAA), which have been cut during the Biden era."<ref>{{Cite web|url=https://www.newsweek.com/elon-musk-donald-trump-nasa-space-policy-1990599|title=Donald Trump and Elon Musk could radically reshape NASA. Here's how|last=Reporter|first=Martha McHardy US News|date=2024-11-27|website=Newsweek|language=en|access-date=2024-12-02}}</ref> == [[w:Federal_Aviation_Administration|Federal Aviation Administration]] == Musk has often complained about the FAA "smothering" innovation, boasting that he can build a rocket faster than the agency can process the "Kafkaesque paperwork" required to make the relevant approvals.{{sfn|Economist 11/23|2024}} == History and Miscellaneous facts == See also: [[w:Department_of_Government_Efficiency#History|Department of Government Efficiency — History]] DOGE's work will "conclude" no later than July 4, 2026, the 250th anniversary of the signing of the [[United States Declaration of Independence|U.S. Declaration of Independence]],<ref>{{Cite web|url=https://thehill.com/policy/4987402-trump-musk-advisory-group-spending/|title=Elon Musk, Vivek Ramaswamy to lead Trump's Department of Government Efficiency (DOGE)|last=Nazzaro|first=Miranda|date=November 13, 2024|website=The Hill|language=en-US|access-date=November 13, 2024}}</ref> also coinciding with America's [[United States Semiquincentennial|semiquincentennial]] celebrations and a proposed "Great American Fair". Despite its name it is not expected to be a [[wikipedia:United_States_federal_executive_departments|federal executive department]], but rather may operate under the [[Federal Advisory Committee Act]],<ref>{{Cite web|url=https://www.cbsnews.com/news/trump-department-of-government-efficiency-doge-elon-musk-ramaswamy/|title=What to know about Trump's Department of Government Efficiency, led by Elon Musk and Vivek Ramaswamy - CBS News|last=Picchi|first=Aimee|date=2024-11-14|website=www.cbsnews.com|language=en-US|access-date=2024-11-14}}</ref> so its formation is not expected to require approval from the [[wikipedia:United_States_Congress|U.S. Congress]]. NYT argues that records of its meetings must be made public.{{Cn}} As an advisor rather than a government employee, Mr. Musk will not be subject to various ethics rules.{{sfn|Economist 11/23}} Musk has stated that he believes such a commission could reduce the [[wikipedia:United_States_federal_budget|U.S. federal budget]] by $2 trillion, which would be a reduction of almost one third from its 2023 total. [[Maya MacGuineas]] of the [[Committee for a Responsible Federal Budget]] has said that this saving is "absolutely doable" over a period of 10 years, but it would be difficult to do in a single year "without compromising some of the fundamental objectives of the government that are widely agreed upon".<ref>{{Cite web|url=https://thehill.com/business/4966789-elon-musk-skepticism-2-trillion-spending-cuts/|title=Elon Musk draws skepticism with call for $2 trillion in spending cuts|last=Folley|first=Aris|date=2024-11-03|website=The Hill|language=en-US|access-date=2024-11-14}}</ref> [[wikipedia:Jamie_Dimon|Jamie Dimon]], the chief executive officer of [[wikipedia:JPMorgan_Chase|JPMorgan Chase]], has supported the idea. Some commentators questioned whether DOGE is a conflict of interest for Musk given that his companies are contractors to the federal government. The body is "unlikely to have any regulatory teeth on its own, but there's little doubt that it can have influence on the incoming administration and how it will determine its budgets".<ref>{{Cite web|url=https://www.vox.com/policy/384904/trumps-department-of-government-efficiency-sounds-like-a-joke-it-isnt|title=Trump tapped Musk to co-lead the "Department of Government Efficiency." What the heck is that?|last=Fayyad|first=Abdallah|date=2024-11-13|website=Vox|language=en-US|access-date=2024-11-14}}</ref> Elon Musk had called [[w:Federico_Sturzenegger|Federico Sturzenegger]], Argentina's [[Minister of Deregulation and Transformation of the State]] ([[w:es:Ministerio_de_Desregulación_y_Transformación_del_Estado|es]]), to discuss imitating his ministry's model.<ref>{{Cite web|url=https://www.infobae.com/economia/2024/11/08/milei-brindo-un-nuevo-apoyo-a-sturzenegger-y-afirmo-que-elon-musk-imitara-su-gestion-en-eeuu/|title=Milei brindó un nuevo apoyo a Sturzenegger y afirmó que Elon Musk imitará su gestión en EEUU|date=November 8, 2024|website=infobae|language=es-ES|access-date=November 13, 2024}}</ref> == Reception and Criticism == See also: [[w:Department_of_Government_Efficiency#Reception|w:Department of Government Efficiency — Reception]] The WSJ reports that Tesla's Texas facility dumped toxic wastewater into the public sewer system, into a lagoon, and into a local river, violated Texas environmental regulations, and fired an employee who attempted to comply with the law.{{Cn}} The Economist estimates that 10% of Mr. Musk's $360bn personal fortune is derived from contracts and benefits from the federal government, and 15% from the Chinese market.{{sfn|Economist 11/23}} == See also == * [[w:Second_presidential_transition_of_Donald_Trump|Second presidential transition of Donald Trump]] * [[w:United_States_federal_budget#Deficits_and_debt|United States federal budget - Deficits and debt]] * [[w:United_States_Bureau_of_Efficiency|United States Bureau of Efficiency]] – United States federal government bureau from 1916 to 1933 * [[w:Brownlow_Committee|Brownlow Committee]] – 1937 commission recommending United States federal government reforms * [[w:Grace_Commission|Grace Commission]] – Investigation to eliminate inefficiency in the United States federal government * [[w:Hoover_Commission|Hoover Commission]] – United States federal commission in 1947 advising on executive reform * [[w:Keep_Commission|Keep Commission]] * [[w:Project_on_National_Security_Reform|Project on National Security Reform]] == Notes == {{reflist}} == References == {{refbegin}} * {{Cite web|url=https://www.newsweek.com/bernie-sanders-finds-new-common-ground-elon-musk-1993820|title=Bernie Sanders finds new common ground with Elon Musk|last=Reporter|first=Mandy Taheri Weekend|date=2024-12-01|website=Newsweek|language=en|access-date=2024-12-02 |ref={{harvid|Newsweek 12/01|2024}} }} * Failed its fifth audit in June 2023.<ref>{{Cite web|url=https://www.newsweek.com/fox-news-host-confronts-gop-senator-pentagons-fifth-failed-audit-1804379|title=Fox News host confronts GOP Senator on Pentagon's fifth failed audit|last=Writer|first=Fatma Khaled Staff|date=2023-06-04|website=Newsweek|language=en|access-date=2024-12-02}} * {{Cite news|url=https://www.economist.com/briefing/2024/11/21/elon-musk-and-donald-trump-seem-besotted-where-is-their-bromance-headed|title=Elon Musk and Donald Trump seem besotted. Where is their bromance headed?|work=The Economist|access-date=2024-12-04|issn=0013-0613 |ref={{harvid|Economist 11/23|2024}} }} <references group="lower-alpha" /> {{refend}} e696i3uoprof9ys6ocaffudhx9zwjd4 2690203 2690202 2024-12-04T03:43:44Z Jaredscribe 2906761 2690203 wikitext text/x-wiki The U.S. [[w:Department of Government Efficiency]]. {{Infobox Organization |name=Department of Government Efficiency |logo=DOGE Logo as of November 14, 2024.jpg |logo_size=150px |logo_caption=Logo on [[Twitter|X]] (formerly Twitter) as of November 14, 2024 |seal= |seal_size= |seal_caption= |formation=Announced on November 12, 2024; yet to be established |abbreviation=DOGE |key_people={{plainlist|[[w:Commissioner of the Department of Government Efficiency|Co-commissioners]]: * [[w:Elon Musk]] * [[w:Vivek Ramaswamy]] }} |website={{URL|https://x.com/DOGE|x.com/DOGE}} }} This "'''Wiki Of Government Efficiency'''" (WOGE) will analyze the [[w:U.S._Federal_budget|U.S. federal budget]], [[User:Jaredscribe/Department of Government Efficiency#Reform the other Government Bureaus and Departments|federal bureaucracy]], and [[User:Jaredscribe/Department of Government Efficiency#Shrink the federal civil service|federal civil service]], in the public interest, and in the context of [[w:Second_presidency_of_Donald_Trump|president-elect Trump']]<nowiki/>s [[w:Agenda_47|Agenda 47]], with non-partisan research, analysis, and criticism of forward-looking proposals on how the '''[[w:Department of Government Efficiency|Department of Government Efficiency]]'''{{Efn|Also referred to as '''Government Efficiency Commission'''}} (DOGE) might fulfill its mission to ''"dismantle government bureaucracy, slash excess regulations, and cut wasteful expenditures and restructure federal agencies"'', in the words of president-elect [[wikipedia:Donald_Trump|Donald Trump]], who called for it to address ''"massive waste and fraud"'' in government spending.<ref name=":1">{{Cite web|url=https://www.bbc.co.uk/news/articles/c93qwn8p0l0o|title=Donald Trump picks Elon Musk for US government cost-cutting role|last1=Faguy|first1=Ana|last2=FitzGerald|first2=James|date=2024-11-13|publisher=BBC News|language=en-GB|access-date=2024-11-13}}</ref> The DOGE will work with through the [[w:Office_of_Management_and_Budget|Office of Management and Budget]] as its "policy vector". Here's [[User:Jaredscribe/Department of Government Efficiency/How to contribute|how to contribute]] to the WOGE. The [[w:U.S._budget_deficit|U.S. Budget deficit]], (C.f. [[w:Government_budget_balance|fiscal deficit]]), and the [[w:National_debt_of_the_United_States|U.S. National debt]], currently $35.7 Trillion as of 10/2024, which is 99% of the [[w:U.S._GDP|U.S. GDP]],<ref>{{Unbulleted list citebundle|{{cite news|newspaper=Financial Post| title= Musk's $2 Trillion of Budget Cuts Would Have These Stocks Moving|url=https://financialpost.com/pmn/business-pmn/musks-2-trillion-of-budget-cuts-would-have-these-stocks-moving|first=Alexandra|last=Semenova|date=November 4, 2024}}|{{cite news|newspaper= New York Times|title=Elon|url=https://nytimes.com/2024/10/29/us/politics/elon-musk-trump-economy-hardship.html}}|{{Cite web |date=September 5, 2024 |title=Trump says he'd create a government efficiency commission led by Elon Musk |url=https://apnews.com/article/donald-trump-elon-musk-government-efficiency-commission-e831ed5dc2f6a56999e1a70bb0a4eaeb |publisher=AP News}}|{{cite web|first=Jenn|last=Brice|title=How Elon Musk's $130 million investment in Trump's victory could reap a huge payoff for Tesla and the rest of his business empire|url=https://fortune.com/2024/11/06/elon-musk-donald-trump-tesla-spacex-xai-boring-neuralink|website=Fortune}}|{{cite web|url=https://axios.com/2024/11/07/elon-musk-government-efficiency-trump|title=Musk will bring his Twitter management style to government reform}}|{{cite news| access-date =November 9, 2024|work=Reuters|date=September 6, 2024|first1=Helen|first2=Gram|last1=Coster| last2=Slattery|title=Trump says he will tap Musk to lead government efficiency commission if elected| url= https://reuters.com/world/us/trump-adopt-musks-proposal-government-efficiency-commission-wsj-reports-2024-09-05}}|{{cite web|title=Trump says Musk could head 'government efficiency' force|url= https://bbc.com/news/articles/c74lgwkrmrpo|publisher=BBC}}|{{cite web|date =November 5, 2024|title=How Elon Musk could gut the government under Trump|url=https://independent.co.uk/news/world/americas/us-politics/elon-musk-donald-trump-economy-job-cuts-b2641644.html|website= The Independent}}}}</ref> and expected to grow to 134% of GDP by 2034 if current laws remain unchanged, according to the [[w:Congressional_Budget_Office|Congressional Budget Office]]. The DOGE will be a [[wikipedia:Presidential_commission_(United_States)|presidential advisory commission]] led by the billionaire businessmen [[wikipedia:Elon_Musk|Elon Musk]] and [[wikipedia:Vivek_Ramaswamy|Vivek Ramaswamy]], and possibly [[w:Ron_Paul|Ron Paul]]<ref>{{Cite web|url=https://thehill.com/video/ron-paul-vows-to-join-elon-musk-help-eliminate-government-waste-in-a-trump-admin/10191375|title=Ron Paul vows to join Elon Musk, help eliminate government waste in a Trump admin|date=November 5, 2024|website=The Hill}}</ref><ref>{{Cite web|url=https://usatoday.com/story/business/2024/10/28/patricia-healy-elon-musk-highlights-need-for-government-efficiency/75798556007|title=Elon Musk puts spotlight on ... Department of Government Efficiency? {{!}} Cumberland Comment|last=Healy|first=Patricia|website=USA TODAY|language=en-US|access-date=November 9, 2024}}</ref>. Musk stated his belief that DOGE could remove US$2 trillion from the [[w:United_States_federal_budget|U.S. federal budget]],<ref>{{Cite web|url=https://www.youtube.com/live/HysDMs2a-iM?si=92I5LD1FY2PAsSuG&t=15822|title=WATCH LIVE: Trump holds campaign rally at Madison Square Garden in New York|date=October 28, 2024|website=youtube.com|publisher=[[PBS NewsHour]]|language=en|format=video}}</ref> without specifying whether these savings would be made over a single year or a longer period.<ref>{{Cite web|url=https://www.bbc.co.uk/news/articles/cdj38mekdkgo|title=Can Elon Musk cut $2 trillion from US government spending?|last=Chu|first=Ben|date=2024-11-13|website=BBC News|language=en-GB|access-date=2024-11-14}}</ref> [[File:2023_US_Federal_Budget_Infographic.png|thumb|An infographic on outlays and revenues in the 2023 [[United States federal budget|U.S. federal budget]]]] DOGE could also streamline permitting with “categorical exclusions” from environmental reviews under the National Environmental Policy Act. {{sidebar with collapsible lists|name=U.S. deficit and debt topics|namestyle=background:#bf0a30;|style=width:22.0em; border: 4px double #d69d36; background:var(--background-color-base, #FFFFFF);|bodyclass=vcard|pretitle='''<span class="skin-invert">This article is part of [[:Category:United States|a series]] on the</span>'''|title=[[United States federal budget|<span style="color:var(--color-base, #000000);">Budget and debt in the<br/>United States of America</span>]]|image=[[File:Seal of the United States Congress.svg|90px]] [[File:Seal of the United States Department of the Treasury.svg|90px]]|titlestyle=background:var(--background-color-base, #002868); background-clip:padding-box;|headingstyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff);|listtitlestyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff); text-align:center;|expanded={{{expanded|{{{1|}}}}}}|list1name=dimensions|list1title=Major dimensions|list1class=hlist skin-invert|list1=* [[Economy of the United States|Economy]] * [[Expenditures in the United States federal budget|Expenditures]] * [[United States federal budget|Federal budget]] * [[Financial position of the United States|Financial position]] * [[Military budget of the United States|Military budget]] * [[National debt of the United States|Public debt]] * [[Taxation in the United States|Taxation]] * [[Unemployment in the United States|Unemployment]] * [[Government_spending_in_the_United_States|Gov't spending]]|list2name=programs|list2title=Programs|list2class=hlist skin-invert|list2=* [[Medicare (United States)|Medicare]] * [[Social programs in the United States|Social programs]] * [[Social Security (United States)|Social Security]]|list3name=issues|list3title=Contemporary issues|list3class=skin-invert|list3=<div style="margin-bottom:0.5em"> [[National Commission on Fiscal Responsibility and Reform|Bowles–Simpson Commission]] {{flatlist}} * <!--Bu--> [[Bush tax cuts]] * <!--Deb--> [[United States debt ceiling|Debt ceiling]] ** [[History of the United States debt ceiling|history]] * <!--Def--> [[Deficit reduction in the United States|Deficit reduction]] * <!--F--> [[United States fiscal cliff|Fiscal cliff]] * <!--H--> [[Healthcare reform in the United States|Healthcare reform]] * <!--P--> [[Political debates about the United States federal budget|Political debates]] * <!--So--> [[Social Security debate in the United States|Social Security debate]] * <!--St--> "[[Starve the beast]]" * <!--Su--> [[Subprime mortgage crisis]] {{endflatlist}} </div> [[2007–2008 financial crisis]] {{flatlist}} * <!--D--> [[United States debt-ceiling crisis (disambiguation)|Debt-ceiling crises]] ** [[2011 United States debt-ceiling crisis|2011]] ** [[2013 United States debt-ceiling crisis|2013]] ** [[2023 United States debt-ceiling crisis|2023]] {{endflatlist}} [[2013 United States budget sequestration|2013 budget sequestration]] {{flatlist}} * <!--G--> [[Government shutdowns in the United States|Government shutdowns]] ** [[1980 United States federal government shutdown|1980]] ** [[1981, 1984, and 1986 U.S. federal government shutdowns|1981, 1984, 1986]] ** [[1990 United States federal government shutdown|1990]] ** [[1995–1996 United States federal government shutdowns|1995–1996]] ** [[2013 United States federal government shutdown|2013]] ** [[January 2018 United States federal government shutdown|Jan 2018]] ** [[2018–2019 United States federal government shutdown|2018–2019]] {{endflatlist}} Related events {{flatlist}} *<!--E-->[[Removal of Kevin McCarthy as Speaker of the House|2023 Removal of Kevin McCarthy]] {{endflatlist}}|list4name=terminology|list4title=Terminology|list4class=hlist skin-invert|list4=Cumulative [[Government budget balance|deficit]] + [[National debt of the United States#Debates|Interest]] ≈ [[Government debt|Debt]] * [[Balance of payments]] * [[Inflation]] * [[Continuing resolution]]}} [[w:Deficit_reduction_in_the_United_States|Deficit reduction in the United States]] == Deregulate the Economy == The legal theory that this can be done through the executive branch is found in the U.S. Supreme Court’s ''[[w:West_Virginia_v._EPA|West Virginia v. EPA]]'' and ''[[w:Loper_Bright|Loper Bright]]'' rulings, which rein in the administrative state and mean that much of what the federal government now does is illegal.<ref>{{cite web|url=https://www.wsj.com/opinion/department-of-government-efficiency-elon-musk-vivek-ramaswamy-donald-trump-1e086dab|website=[[w:Wall Street Journal]]|title=The Musk-Ramaswamy Project Could Be Trump’s Best Idea}}</ref> Mr. Trump has set a goal of eliminating 10 regulations for every new one. The [[w:Competitive_Enterprise_Institute|Competitive Enterprise Institute]]’s Wayne Crews says 217,565 rules have been issued since the [[w:Federal_Register|Federal Register]] first began itemizing them in 1976, with 89,368 pages added last year. [https://sgp.fas.org/crs/misc/R43056.pdf 3,000-4,500 rules are added each year]. DOGE’s first order will be to pause enforcement of overreaching rules while starting the process to roll them back. Mr. Trump and DOGE could direct agencies to settle legal challenges to Biden rules by vacating them. This could ease the laborious process of undoing them by rule-making through the [[w:Administrative_Procedure_Act|Administrative Procedure Act]]. A source tells the WSJ they’ll do whatever they think they legally can without the APA. The [[w:Congressional_Review_Act|Congressional Review Act]]—which allows Congress to overturn recently issued agency regulations—had been used only once, prior to [[w:First_presidency_of_Donald_Trump|Trump's first term]]. While in office, he and the Republican Congress used it on 16 rules. This time, there will be more than 56 regulatory actions recent enough to be repealed. The [[w:Chevron_deference|''Chevron'' deference]] had required federal courts to defer to agencies’ interpretations of ambiguous statutes, but this was overturned in 2024. Taken together, with some other recent [[w:SCOTUS|SCOTUS]] rulings, we now have, says the WSJ, the biggest opportunity to cut regulatory red tape in more than 40 years.<ref>[https://www.wsj.com/opinion/let-the-trump-deregulation-begin-us-chamber-of-commerce-second-term-economic-growth-73f24387?cx_testId=3&cx_testVariant=cx_166&cx_artPos=0]</ref><blockquote>"Most legal edicts aren’t laws enacted by Congress but “rules and regulations” promulgated by unelected bureaucrats—tens of thousands of them each year. Most government enforcement decisions and discretionary expenditures aren’t made by the democratically elected president or even his political appointees but by millions of unelected, unappointed civil servants within government agencies who view themselves as immune from firing thanks to civil-service protections." "This is antidemocratic and antithetical to the Founders’ vision. It imposes massive direct and indirect costs on taxpayers." "When the president nullifies thousands of such regulations, critics will allege executive overreach. In fact, it will be ''correcting'' the executive overreach of thousands of regulations promulgated by administrative fiat that were never authorized by Congress. The president owes lawmaking deference to Congress, not to bureaucrats deep within federal agencies. The use of executive orders to substitute for lawmaking by adding burdensome new rules is a constitutional affront, but the use of executive orders to roll back regulations that wrongly bypassed Congress is legitimate and necessary to comply with the Supreme Court’s recent mandates. And after those regulations are fully rescinded, a future president couldn’t simply flip the switch and revive them but would instead have to ask Congress to do so" Mssrs. [https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Musk and Ramaswamy, WSJ, 11/20/2024]</blockquote> == Shrink the federal civil service == The government has around three million [[w:United_States_federal_civil_service|federal civil service]] employees, with an average salary of $106,000. Dr. Anthony Fauci made $481,000 in 2022. The federal head count has ballooned by 120,800 during the Biden years. Civil service and union protections make it hard to fire workers. Mr. Trump intends to quickly resurrect the [[w:Schedule_F|Schedule F]] reform that he sought to implement at the end of his first term but was scrapped by Mr. Biden. These would high-level federal employees to be removed like political appointees, by eliminating their job protections. WSJ proposals[https://www.wsj.com/opinion/the-doge-cheat-sheet-elon-musk-vivek-ramaswamy-department-of-government-efficiency-1c231783#cxrecs_s] The [[w:Administrative_Procedures_Act|Administrative Procedures Act]] statute protects federal employees from political retaliation, but allows for “reductions in force” that don’t target specific employees. The statute further empowers the president to “prescribe rules governing the competitive service.” The Supreme Court has held—in ''[[w:Franklin_v._Massachusetts|Franklin v. Massachusetts]]'' (1992) and ''[[w:Collins_v._Yellen|Collins v. Yellen]]'' (2021) that when revious presidents have used this power to amend the civil service rules by executive order, they weren’t constrained by the APA when they did so. Mr. Trump can, with this authority, implement any number of “rules governing the competitive service” that would curtail administrative overgrowth, from large-scale firings to relocation of federal agencies out of the Washington area. The DOGE welcomes voluntary terminations once the President begins requiring federal employees to come to the office five days a week, because American taxpayers shouldn’t pay federal employees for the Covid-era privilege of staying home.<ref>[https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Elon Musk and Vivek Ramaswamy: The DOGE Plan to Reform Government: Following the Supreme Court’s guidance, we’ll reverse a decadeslong executive power grab. Musk & Ramaswamy 11/20/2024]</ref> == Reduce the deficit and debt by impounding appropriated funds == === Impound appropriated funds === Reports suggest that president-elect Trump intends to override Congress’s power of the purse by [[w:Impoundment_of_appropriated_funds|impoundment of appropriated funds]], that is, refusing to spend them. the president may [[wikipedia:Rescission_bill|propose rescission]] of specific funds, but that rescission must be approved by both the [[wikipedia:United_States_House_of_Representatives|House of Representatives]] and [[wikipedia:United_States_Senate|Senate]] within 45 days. [[w:Thomas_Jefferson|Thomas Jefferson]] was the first president to exercise the power of impoundment in 1801, which power was available to all presidents up to and including [[wikipedia:Richard_Nixon|Richard Nixon]], and was regarded as a power inherent to the office, although one with limits. He may ask Congress to repeal The [[w:Congressional_Budget_and_Impoundment_Control_Act_of_1974|Congressional Budget and Impoundment Control Act of 1974]], which was passed in response to Nixon's abuses.<ref>{{Cite web|url=http://democrats-budget.house.gov/resources/reports/impoundment-control-act-1974-what-it-why-does-it-matter|title=The Impoundment Control Act of 1974: What Is It? Why Does It Matter? {{!}} House Budget Committee Democrats|date=2019-10-23|website=democrats-budget.house.gov|language=en|access-date=2024-05-19}}</ref> If Congress refuses to do so, president Trump may impound funds anyway and argue in court that the 1974 law is unconstitutional. The matter would likely end up at the Supreme Court, which would have to do more than simply hold the 1974 act unconstitutional in order for Mr. Trump to prevail. The court would also have to overrule [[w:Train_v._City_of_New_York_(1975)|''Train v. City of New York'' (1975)]], which held that impoundment is illegal unless the underlying legislation specifically authorizes it. === Reduce the budget deficit === [[wikipedia:U.S. federal budget|U.S. federal budget]] The [[wikipedia:Fiscal_year|fiscal year]], beginning October 1 and ending on September 30 of the year following. Congress is the body required by law to pass appropriations annually and to submit funding bills passed by both houses to the President for signature. Congressional decisions are governed by rules and legislation regarding the [[wikipedia:United_States_budget_process|federal budget process]]. Budget committees set spending limits for the House and Senate committees and for Appropriations subcommittees, which then approve individual [[wikipedia:Appropriations_bill_(United_States)|appropriations bills]] to During FY2022, the federal government spent $6.3 trillion. Spending as % of GDP is 25.1%, almost 2 percentage points greater than the average over the past 50 years. Major categories of FY 2022 spending included: Medicare and Medicaid ($1.339T or 5.4% of GDP), Social Security ($1.2T or 4.8% of GDP), non-defense discretionary spending used to run federal Departments and Agencies ($910B or 3.6% of GDP), Defense Department ($751B or 3.0% of GDP), and net interest ($475B or 1.9% of GDP).<ref name="CBO_2022">[https://www.cbo.gov/publication/58888 The Federal Budget in Fiscal Year 2022: An Infographic]</ref> CBO projects a federal budget deficit of $1.6 trillion for 2024. In the agency’s projections, deficits generally increase over the coming years; the shortfall in 2034 is $2.6 trillion. The deficit amounts to 5.6 percent of gross domestic product (GDP) in 2024, swells to 6.1 percent of GDP in 2025, and then declines in the two years that follow. After 2027, deficits increase again, reaching 6.1 percent of GDP in 2034.<ref name="CBO_budgetOutlook2024">{{cite web|url=https://www.cbo.gov/publication/59710|title=The Budget and Economic Outlook: 2024 to 2034|date=February 7, 2024|publisher=CBO|access-date=February 7, 2024}}</ref> The following table summarizes several budgetary statistics for the fiscal year 2015-2021 periods as a percent of GDP, including federal tax revenue, outlays or spending, deficits (revenue – outlays), and [[wikipedia:National_debt_of_the_United_States|debt held by the public]]. The historical average for 1969-2018 is also shown. With U.S. GDP of about $21 trillion in 2019, 1% of GDP is about $210 billion.<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> Statistics for 2020-2022 are from the CBO Monthly Budget Review for FY 2022.<ref name="CBO_MBRFY2022">{{cite web|url=https://www.cbo.gov/publication/58592|title=Monthly Budget Review: Summary for Fiscal Year 2022|date=November 8, 2022|publisher=CBO|access-date=December 10, 2022}}</ref> {| class="wikitable" !Variable As % GDP !2015 !2016 !2017 !2018 !2019 !2020 !2021 !2022 !Hist Avg |- !Revenue<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> |18.0% |17.6% |17.2% |16.4% |16.4% |16.2% |17.9% |19.6% |17.4% |- !Outlays<ref name="CBO_Hist_20" /> |20.4% |20.8% |20.6% |20.2% |21.0% |31.1% |30.1% |25.1% |21.0% |- !Budget Deficit<ref name="CBO_Hist_20" /> | -2.4% | -3.2% | -3.5% | -3.8% | -4.6% | -14.9% | -12.3% | -5.5% | -3.6% |- !Debt Held by Public<ref name="CBO_Hist_20" /> |72.5% |76.4% |76.2% |77.6% |79.4% |100.3% |99.6% |94.7% | |} The [[wikipedia:U.S._Constitution|U.S. Constitution]] ([[wikipedia:Article_One_of_the_United_States_Constitution|Article I]], section 9, clause 7) states that "No money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of Receipts and Expenditures of all public Money shall be published from time to time." Each year, the President of the United States submits a budget request to Congress for the following fiscal year as required by the [[wikipedia:Budget_and_Accounting_Act_of_1921|Budget and Accounting Act of 1921]]. Current law ({{UnitedStatesCode|31|1105}}(a)) requires the president to submit a budget no earlier than the first Monday in January, and no later than the first Monday in February. Typically, presidents submit budgets on the first Monday in February. The budget submission has been delayed, however, in some new presidents' first year when the previous president belonged to a different party. === Reduce the National debt === == Reform Entitlements == === Healthcare and Medicare === [[w:ObamaCare|ObamaCare]] started as a plausible scheme for universal, cost-effective health insurance with subsidies for the needy. Only the subsidies survive because the ObamaCare policies actually delivered are so overpriced nobody would buy them without a subsidy.<ref>[https://www.wsj.com/opinion/elons-real-trump-mission-protect-growth-department-of-government-efficiency-appointments-cabinet-9e7e62b2]</ref> See below: Department of Health and Human Services === Social Security === Even FDR was aware of its flaw: it discourages working and saving. == Strategic Foreign Policy and Military reform == === Department of State === {{Main article|w:Second_presidency_of_Donald_Trump#Prospective_foreign_policy|w:State Department}} === U.S. Department of Defense === The president-elect is reportedly considering a draft executive order that establishes a “warrior board” of retired senior military personnel with the power to review three- and four-star officers “on leadership capability, strategic readiness, and commitment to military excellence," and to recommend removals of any deemed unfit for leadership. This would fast-track the removal of generals and admirals found to be “lacking in requisite leadership qualities,” consistent with his earlier vow to fire “woke” military leaders.<ref>[https://www.wsj.com/politics/national-security/trump-draft-executive-order-would-create-board-to-purge-generals-7ebaa606<nowiki> Trump draft executive order would create a board to purge generals 11/12/2024]</nowiki></ref> There are legal obstacles. The law prohibits the firing of commissioned officers except by “sentence of a general court-martial,” as a “commutation of a sentence of a general court-martial,” or “in time of war, by order of the president.” A commissioned officer who believes he’s been wrongfully dismissed has the right to seek a trial by court-martial, which may find the dismissal baseless. <ref>[https://www.wsj.com/opinion/trump-tests-the-constitutions-limits-checks-balances-government-policy-law-78d0d0f1<nowiki> Trump test the constitutions limits 11/19/2024]</nowiki></ref> Musk said, "Some idiots are still building manned fighter jets like the F-35," and later added: "Manned fighter jets are outdated in the age of drones and only put pilots' lives at risk." [[w:Bernie_Sanders|Bernie Sanders]] wrote on X: "Elon Musk is right. The Pentagon, with a budget of $886 billion, just failed its 7th audit in a row. It's lost track of billions. Last year, only 13 senators voted against the Military Industrial Complex and a defense budget full of waste and fraud. That must change."{{sfn|Newsweek 12/02|2024}}. It failed its fifth audit in June 2023.<ref>{{Cite web|url=https://www.newsweek.com/fox-news-host-confronts-gop-senator-pentagons-fifth-failed-audit-1804379|title=Fox News host confronts GOP Senator on Pentagon's fifth failed audit|last=Writer|first=Fatma Khaled Staff|date=2023-06-04|website=Newsweek|language=en|access-date=2024-12-02}} == Reform the other Government Bureaus and Departments == === Department of Education === [[w:United_States_Department_of_Education|w:Department of Education]] has 4,400 employees – the smallest staff of the Cabinet agencies<ref>{{Cite web|url=https://www2.ed.gov/about/overview/fed/role.html|title=Federal Role in Education|date=2021-06-15|website=www2.ed.gov|language=en|access-date=2022-04-28}}</ref> – and a 2024 budget of $238 billion.<ref name="DOE-mission">{{Cite web|url=https://www.usaspending.gov/agency/department-of-education?fy=2024|title=Agency Profile {{!}} U.S. Department of Education|website=www2.ed.gov|access-date=2024-11-14}}</ref> The 2023 Budget was $274 billion, which included funding for children with disabilities ([[wikipedia:Individuals_with_Disabilities_Education_Act|IDEA]]), pandemic recovery, early childhood education, [[wikipedia:Pell_Grant|Pell Grants]], [[wikipedia:Elementary_and_Secondary_Education_Act|Title I]], work assistance, among other programs. This budget was down from $637.7 billion in 2022.<ref>{{Cite web|url=https://www.future-ed.org/what-the-new-pisa-results-really-say-about-u-s-schools/|title=What the New PISA Results Really Say About U.S. Schools|date=2021-06-15|website=future-ed.com|language=en|access-date=2024-11-14}}</ref> The WSJ proposes that the Civil Rights division be absorbed into the Department of Justice, and that its outstanding loan portolio be handled by the Department of the Treasury. Despite the redundancies, its unlikely that it will be abolished, which would require congressional action and buy-in from Democrats in the Senate; Republicans don’t have enough votes to do it alone. A republican appointee is expected to push back against federal education overreach and progressive policies like DEI. <ref>[https://www.wsj.com/opinion/trump-can-teach-the-education-department-a-lesson-nominee-needs-boldness-back-school-choice-oppose-woke-indoctrination-ddf6a38d<nowiki> Trump can teach the Education Department a Lesson. WSJ 11/20/2024]</nowiki></ref> === U.S. Department of Health and Human Services === [[w:U.S._Department_of_Health_and_Human_Services|U.S. Department of Health and Human Services]] was authorized a budget for [[w:2020_United_States_federal_budget|fiscal year 2020]] of $1.293 trillion. It has 13 operating divisions, 10 of which constitute the [[w:United_States_Public_Health_Service|Public Health Services]], whose budget authorization is broken down as follows:<ref name="hhs_budget_fy2020">{{cite web|url=https://www.hhs.gov/about/budget/fy2020/index.html|title=HHS FY 2020 Budget in Brief|date=October 5, 2019|website=HHS Budget & Performance|publisher=United States Department of Health & Human Services|page=7|access-date=May 9, 2020}}</ref> {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Food and Drug Administration|Food and Drug Administration]] (FDA) |$3,329 MM |- |[[w:Health Resources and Services Administration|Health Resources and Services Administration]] (HRSA) |$11,004 |- |[[w:Indian Health Service|Indian Health Service]] (IHS) |$6,104 |- |[[w:Centers for Disease Control and Prevention|Centers for Disease Control and Prevention]] (CDC) |$6,767 |- |[[w:National Institutes of Health|National Institutes of Health]] (NIH) |$33,669 |- |[[w:Substance Abuse and Mental Health Services Administration|Substance Abuse and Mental Health Services Administration]] (SAMHSA) |$5,535 |- |[[w:Agency for Healthcare Research and Quality|Agency for Healthcare Research and Quality]] (AHRQ) |$0 |- |[[w:Centers for Medicare & Medicaid Services|Centers for Medicare & Medicaid Services]] (CMMS) |$1,169,091 |- |[[w:Administration for Children and Families|Administration for Children and Families]] (ACF) |$52,121 |- |[[w:Administration for Community Living|Administration for Community Living]] (ACL) |$1,997 |- |} {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Departmental Management|Departmental Management]] |$340 |- |Non-Recurring Expense Fund |$-400 |- |[[w:Office of Medicare Hearings and Appeals|Office of Medicare Hearings and Appeals]] |$186 |- |[[w:Office of the National Coordinator|Office of the National Coordinator]] |$43 |- |[[w:Office for Civil Rights|Office for Civil Rights]] |$30 |- |[[w:Office of Inspector General|Office of Inspector General]] |$82 |- |[[w:Public Health and Social Services Emergency Fund|Public Health and Social Services Emergency Fund]] |$2,667 |- |[[w:Program Support Center|Program Support Center]] |$749 |- |Offsetting Collections |$-629 |- |Other Collections |$-163 |- |'''TOTAL''' |'''$1,292,523''' |} The FY2020 budget included a $1.276 billion budget decrease for the Centers for Disease Control, and a $4.533 billion budget decrease for the National Institutes of Health. These budget cuts, along with other changes since 2019, comprised a total decrease of over $24 billion in revised discretionary budget authority across the entire Department of Health and Human Services for Fiscal Year 2020.<ref name="hhs_budget_fy2020" /> Additional details of the budgeted outlays, budget authority, and detailed budgets for other years, can be found at the HHS Budget website.<ref>{{cite web|url=http://WWW.HHS.GOV/BUDGET|title=Health and Human Services: Budget and Performance|publisher=United States Department of Health & Human Services|access-date=May 9, 2020}}</ref> [[w:Robert_F._Kennedy_Jr.|Robert F. Kennedy Jr.]] has been nominated as [[w:United_States_Secretary_of_Health_and_Human_Services|United_States_Secretary_of_Health_and_Human_Services]] He is an American politician, [[Environmental law|environmental lawyer]], [[anti-vaccine activist]], and anti-packaged food industry activist, anti-pharmaceutical industry activist, who will be nominated to serve as [[United States Secretary of Health and Human Services]],<ref name="v502">{{cite web|url=https://www.forbes.com/sites/saradorn/2024/11/14/rfk-jr-launches-independent-2024-run-here-are-all-the-conspiracies-he-promotes-from-vaccines-to-mass-shootings/|title=Trump Taps RFK Jr. As Secretary Of Health And Human Services: Here Are All The Conspiracies He's Promoted|last=Dorn|first=Sara|date=2024-11-14|website=Forbes|access-date=2024-11-15}}</ref> with the mission of "Making America Healthy Again". He is the chairman and founder of [[Children's Health Defense]], an anti-vaccine advocacy group and proponent of [[COVID-19 vaccine misinformation|dubious COVID-19 vaccine information]].<ref name="Smith_12/15/2021" /><ref name="KW" /> == CPB, PBS, NPR == [[w:Howard_Husock|Howard Husock]] suggest that instead of zeroing its $535 million budget, Republicans reform the [[w:Public_Broadcasting_Act|Public Broadcasting Act]] to eliminate bias and improve local journalism.<ref>https://www.wsj.com/opinion/the-conservative-case-for-public-broadcasting-media-policy-2d4c3c9f?page=1</ref> == NASA == In September 2026, NASA's [[w:Artemis_program|Artemis program]], established in 2017 via [[wikipedia:Space_Policy_Directive_1|Space Policy Directive 1]], is intended to reestablish a human presence on the Moon for the first time since the [[wikipedia:Apollo_17|Apollo 17]] mission in 1972. The program's stated long-term goal is to establish a [[wikipedia:Moonbase|permanent base on the Moon]] to facilitate [[wikipedia:Human_mission_to_Mars|human missions to Mars]]. The [[w:U.S._National_Academies_of_Sciences,_Engineering,_and_Medicine|U.S. National Academies of Sciences, Engineering, and Medicine]] in October, put out a report titled "NASA at a Crossroads," which identified myriad issues at the agency, including out-of-date infrastructure, pressures to prioritize short-term objectives and inefficient management practices. NASA's costly [[w:Space_Launch_System|Space Launch System]] (SLS) is the cornerstone of the Artemis program. has a price tag of around $4.1 billion per launch, and is a single-use rocket that can only launch every two years, having debuted in 2022 with the uncrewed [[w:Artemis_1_mission|Artemis 1 mission]] to the moon. In contrast, SpaceX is working to reduce the cost of a single Starship flight to under $10 million. NASA Associate Administrator Jim Free urged the incoming administration to maintain the current plans, in a symposium with the [[w:American_Astronautical_Society|American Astronautical Society]] saying "We need that consistency in purpose. That has not happened since Apollo. If we lose that, I believe we will fall apart and we will wander, and other people in this world will pass us by." NASA has already asked both [[w:SpaceX|SpaceX]] and also Jeff Bezos' [[w:Blue_Origin|Blue Origin]], to develop cargo landers for its Artemis missions and to deliver heavy equipment on them to the Moon by 2033. "Having two lunar lander providers with different approaches for crew and cargo landing capability provides mission flexibility while ensuring a regular cadence of moon landings for continued discovery and scientific opportunity," Stephen D. Creech, NASA's assistant deputy associate administrator for the moon to Mars program, said in an announcement about the partnership. "For all of the money we are spending, NASA should NOT be talking about going to the Moon - We did that 50 years ago. They should be focused on the much bigger things we are doing, including Mars (of which the Moon is a part), Defense and Science!" Trump wrote in a post on X in 2019. Trump has said he would create a [[w:Space_National_Guard|Space National Guard]], an idea that lawmakers in Congress have been proposing since 2021. Critics agree that a focus on spaceflight could come at the expense of "Earth and atmospheric sciences at NASA and the [[w:National_Oceanic_and_Atmospheric_Administration|National Oceanic and Atmospheric Administration]] (NOAA), which have been cut during the Biden era."<ref>{{Cite web|url=https://www.newsweek.com/elon-musk-donald-trump-nasa-space-policy-1990599|title=Donald Trump and Elon Musk could radically reshape NASA. Here's how|last=Reporter|first=Martha McHardy US News|date=2024-11-27|website=Newsweek|language=en|access-date=2024-12-02}}</ref> == [[w:Federal_Aviation_Administration|Federal Aviation Administration]] == Musk has often complained about the FAA "smothering" innovation, boasting that he can build a rocket faster than the agency can process the "Kafkaesque paperwork" required to make the relevant approvals.{{sfn|Economist 11/23|2024}} == History and Miscellaneous facts == See also: [[w:Department_of_Government_Efficiency#History|Department of Government Efficiency — History]] DOGE's work will "conclude" no later than July 4, 2026, the 250th anniversary of the signing of the [[United States Declaration of Independence|U.S. Declaration of Independence]],<ref>{{Cite web|url=https://thehill.com/policy/4987402-trump-musk-advisory-group-spending/|title=Elon Musk, Vivek Ramaswamy to lead Trump's Department of Government Efficiency (DOGE)|last=Nazzaro|first=Miranda|date=November 13, 2024|website=The Hill|language=en-US|access-date=November 13, 2024}}</ref> also coinciding with America's [[United States Semiquincentennial|semiquincentennial]] celebrations and a proposed "Great American Fair". Despite its name it is not expected to be a [[wikipedia:United_States_federal_executive_departments|federal executive department]], but rather may operate under the [[Federal Advisory Committee Act]],<ref>{{Cite web|url=https://www.cbsnews.com/news/trump-department-of-government-efficiency-doge-elon-musk-ramaswamy/|title=What to know about Trump's Department of Government Efficiency, led by Elon Musk and Vivek Ramaswamy - CBS News|last=Picchi|first=Aimee|date=2024-11-14|website=www.cbsnews.com|language=en-US|access-date=2024-11-14}}</ref> so its formation is not expected to require approval from the [[wikipedia:United_States_Congress|U.S. Congress]]. NYT argues that records of its meetings must be made public.{{Cn}} As an advisor rather than a government employee, Mr. Musk will not be subject to various ethics rules.{{sfn|Economist 11/23}} Musk has stated that he believes such a commission could reduce the [[wikipedia:United_States_federal_budget|U.S. federal budget]] by $2 trillion, which would be a reduction of almost one third from its 2023 total. [[Maya MacGuineas]] of the [[Committee for a Responsible Federal Budget]] has said that this saving is "absolutely doable" over a period of 10 years, but it would be difficult to do in a single year "without compromising some of the fundamental objectives of the government that are widely agreed upon".<ref>{{Cite web|url=https://thehill.com/business/4966789-elon-musk-skepticism-2-trillion-spending-cuts/|title=Elon Musk draws skepticism with call for $2 trillion in spending cuts|last=Folley|first=Aris|date=2024-11-03|website=The Hill|language=en-US|access-date=2024-11-14}}</ref> [[wikipedia:Jamie_Dimon|Jamie Dimon]], the chief executive officer of [[wikipedia:JPMorgan_Chase|JPMorgan Chase]], has supported the idea. Some commentators questioned whether DOGE is a conflict of interest for Musk given that his companies are contractors to the federal government. The body is "unlikely to have any regulatory teeth on its own, but there's little doubt that it can have influence on the incoming administration and how it will determine its budgets".<ref>{{Cite web|url=https://www.vox.com/policy/384904/trumps-department-of-government-efficiency-sounds-like-a-joke-it-isnt|title=Trump tapped Musk to co-lead the "Department of Government Efficiency." What the heck is that?|last=Fayyad|first=Abdallah|date=2024-11-13|website=Vox|language=en-US|access-date=2024-11-14}}</ref> Elon Musk had called [[w:Federico_Sturzenegger|Federico Sturzenegger]], Argentina's [[Minister of Deregulation and Transformation of the State]] ([[w:es:Ministerio_de_Desregulación_y_Transformación_del_Estado|es]]), to discuss imitating his ministry's model.<ref>{{Cite web|url=https://www.infobae.com/economia/2024/11/08/milei-brindo-un-nuevo-apoyo-a-sturzenegger-y-afirmo-que-elon-musk-imitara-su-gestion-en-eeuu/|title=Milei brindó un nuevo apoyo a Sturzenegger y afirmó que Elon Musk imitará su gestión en EEUU|date=November 8, 2024|website=infobae|language=es-ES|access-date=November 13, 2024}}</ref> == Reception and Criticism == See also: [[w:Department_of_Government_Efficiency#Reception|w:Department of Government Efficiency — Reception]] The WSJ reports that Tesla's Texas facility dumped toxic wastewater into the public sewer system, into a lagoon, and into a local river, violated Texas environmental regulations, and fired an employee who attempted to comply with the law.{{Cn}} The Economist estimates that 10% of Mr. Musk's $360bn personal fortune is derived from contracts and benefits from the federal government, and 15% from the Chinese market.{{sfn|Economist 11/23}} == See also == * [[w:Second_presidential_transition_of_Donald_Trump|Second presidential transition of Donald Trump]] * [[w:United_States_federal_budget#Deficits_and_debt|United States federal budget - Deficits and debt]] * [[w:United_States_Bureau_of_Efficiency|United States Bureau of Efficiency]] – United States federal government bureau from 1916 to 1933 * [[w:Brownlow_Committee|Brownlow Committee]] – 1937 commission recommending United States federal government reforms * [[w:Grace_Commission|Grace Commission]] – Investigation to eliminate inefficiency in the United States federal government * [[w:Hoover_Commission|Hoover Commission]] – United States federal commission in 1947 advising on executive reform * [[w:Keep_Commission|Keep Commission]] * [[w:Project_on_National_Security_Reform|Project on National Security Reform]] == Notes == {{reflist}} == References == {{refbegin}} * {{Cite web|url=https://www.newsweek.com/bernie-sanders-finds-new-common-ground-elon-musk-1993820|title=Bernie Sanders finds new common ground with Elon Musk|last=Reporter|first=Mandy Taheri Weekend|date=2024-12-01|website=Newsweek|language=en|access-date=2024-12-02 |ref={{harvid|Newsweek 12/01|2024}} }} * {{Cite news|url=https://www.economist.com/briefing/2024/11/21/elon-musk-and-donald-trump-seem-besotted-where-is-their-bromance-headed|title=Elon Musk and Donald Trump seem besotted. Where is their bromance headed?|work=The Economist|access-date=2024-12-04|issn=0013-0613 |ref={{harvid|Economist 11/23|2024}} }} <references group="lower-alpha" /> {{refend}} sw91rsy8gir0c7jub9m8ylw00scp6fa 2690204 2690203 2024-12-04T03:46:46Z Jaredscribe 2906761 /* NASA */ 2690204 wikitext text/x-wiki The U.S. [[w:Department of Government Efficiency]]. {{Infobox Organization |name=Department of Government Efficiency |logo=DOGE Logo as of November 14, 2024.jpg |logo_size=150px |logo_caption=Logo on [[Twitter|X]] (formerly Twitter) as of November 14, 2024 |seal= |seal_size= |seal_caption= |formation=Announced on November 12, 2024; yet to be established |abbreviation=DOGE |key_people={{plainlist|[[w:Commissioner of the Department of Government Efficiency|Co-commissioners]]: * [[w:Elon Musk]] * [[w:Vivek Ramaswamy]] }} |website={{URL|https://x.com/DOGE|x.com/DOGE}} }} This "'''Wiki Of Government Efficiency'''" (WOGE) will analyze the [[w:U.S._Federal_budget|U.S. federal budget]], [[User:Jaredscribe/Department of Government Efficiency#Reform the other Government Bureaus and Departments|federal bureaucracy]], and [[User:Jaredscribe/Department of Government Efficiency#Shrink the federal civil service|federal civil service]], in the public interest, and in the context of [[w:Second_presidency_of_Donald_Trump|president-elect Trump']]<nowiki/>s [[w:Agenda_47|Agenda 47]], with non-partisan research, analysis, and criticism of forward-looking proposals on how the '''[[w:Department of Government Efficiency|Department of Government Efficiency]]'''{{Efn|Also referred to as '''Government Efficiency Commission'''}} (DOGE) might fulfill its mission to ''"dismantle government bureaucracy, slash excess regulations, and cut wasteful expenditures and restructure federal agencies"'', in the words of president-elect [[wikipedia:Donald_Trump|Donald Trump]], who called for it to address ''"massive waste and fraud"'' in government spending.<ref name=":1">{{Cite web|url=https://www.bbc.co.uk/news/articles/c93qwn8p0l0o|title=Donald Trump picks Elon Musk for US government cost-cutting role|last1=Faguy|first1=Ana|last2=FitzGerald|first2=James|date=2024-11-13|publisher=BBC News|language=en-GB|access-date=2024-11-13}}</ref> The DOGE will work with through the [[w:Office_of_Management_and_Budget|Office of Management and Budget]] as its "policy vector". Here's [[User:Jaredscribe/Department of Government Efficiency/How to contribute|how to contribute]] to the WOGE. The [[w:U.S._budget_deficit|U.S. Budget deficit]], (C.f. [[w:Government_budget_balance|fiscal deficit]]), and the [[w:National_debt_of_the_United_States|U.S. National debt]], currently $35.7 Trillion as of 10/2024, which is 99% of the [[w:U.S._GDP|U.S. GDP]],<ref>{{Unbulleted list citebundle|{{cite news|newspaper=Financial Post| title= Musk's $2 Trillion of Budget Cuts Would Have These Stocks Moving|url=https://financialpost.com/pmn/business-pmn/musks-2-trillion-of-budget-cuts-would-have-these-stocks-moving|first=Alexandra|last=Semenova|date=November 4, 2024}}|{{cite news|newspaper= New York Times|title=Elon|url=https://nytimes.com/2024/10/29/us/politics/elon-musk-trump-economy-hardship.html}}|{{Cite web |date=September 5, 2024 |title=Trump says he'd create a government efficiency commission led by Elon Musk |url=https://apnews.com/article/donald-trump-elon-musk-government-efficiency-commission-e831ed5dc2f6a56999e1a70bb0a4eaeb |publisher=AP News}}|{{cite web|first=Jenn|last=Brice|title=How Elon Musk's $130 million investment in Trump's victory could reap a huge payoff for Tesla and the rest of his business empire|url=https://fortune.com/2024/11/06/elon-musk-donald-trump-tesla-spacex-xai-boring-neuralink|website=Fortune}}|{{cite web|url=https://axios.com/2024/11/07/elon-musk-government-efficiency-trump|title=Musk will bring his Twitter management style to government reform}}|{{cite news| access-date =November 9, 2024|work=Reuters|date=September 6, 2024|first1=Helen|first2=Gram|last1=Coster| last2=Slattery|title=Trump says he will tap Musk to lead government efficiency commission if elected| url= https://reuters.com/world/us/trump-adopt-musks-proposal-government-efficiency-commission-wsj-reports-2024-09-05}}|{{cite web|title=Trump says Musk could head 'government efficiency' force|url= https://bbc.com/news/articles/c74lgwkrmrpo|publisher=BBC}}|{{cite web|date =November 5, 2024|title=How Elon Musk could gut the government under Trump|url=https://independent.co.uk/news/world/americas/us-politics/elon-musk-donald-trump-economy-job-cuts-b2641644.html|website= The Independent}}}}</ref> and expected to grow to 134% of GDP by 2034 if current laws remain unchanged, according to the [[w:Congressional_Budget_Office|Congressional Budget Office]]. The DOGE will be a [[wikipedia:Presidential_commission_(United_States)|presidential advisory commission]] led by the billionaire businessmen [[wikipedia:Elon_Musk|Elon Musk]] and [[wikipedia:Vivek_Ramaswamy|Vivek Ramaswamy]], and possibly [[w:Ron_Paul|Ron Paul]]<ref>{{Cite web|url=https://thehill.com/video/ron-paul-vows-to-join-elon-musk-help-eliminate-government-waste-in-a-trump-admin/10191375|title=Ron Paul vows to join Elon Musk, help eliminate government waste in a Trump admin|date=November 5, 2024|website=The Hill}}</ref><ref>{{Cite web|url=https://usatoday.com/story/business/2024/10/28/patricia-healy-elon-musk-highlights-need-for-government-efficiency/75798556007|title=Elon Musk puts spotlight on ... Department of Government Efficiency? {{!}} Cumberland Comment|last=Healy|first=Patricia|website=USA TODAY|language=en-US|access-date=November 9, 2024}}</ref>. Musk stated his belief that DOGE could remove US$2 trillion from the [[w:United_States_federal_budget|U.S. federal budget]],<ref>{{Cite web|url=https://www.youtube.com/live/HysDMs2a-iM?si=92I5LD1FY2PAsSuG&t=15822|title=WATCH LIVE: Trump holds campaign rally at Madison Square Garden in New York|date=October 28, 2024|website=youtube.com|publisher=[[PBS NewsHour]]|language=en|format=video}}</ref> without specifying whether these savings would be made over a single year or a longer period.<ref>{{Cite web|url=https://www.bbc.co.uk/news/articles/cdj38mekdkgo|title=Can Elon Musk cut $2 trillion from US government spending?|last=Chu|first=Ben|date=2024-11-13|website=BBC News|language=en-GB|access-date=2024-11-14}}</ref> [[File:2023_US_Federal_Budget_Infographic.png|thumb|An infographic on outlays and revenues in the 2023 [[United States federal budget|U.S. federal budget]]]] DOGE could also streamline permitting with “categorical exclusions” from environmental reviews under the National Environmental Policy Act. {{sidebar with collapsible lists|name=U.S. deficit and debt topics|namestyle=background:#bf0a30;|style=width:22.0em; border: 4px double #d69d36; background:var(--background-color-base, #FFFFFF);|bodyclass=vcard|pretitle='''<span class="skin-invert">This article is part of [[:Category:United States|a series]] on the</span>'''|title=[[United States federal budget|<span style="color:var(--color-base, #000000);">Budget and debt in the<br/>United States of America</span>]]|image=[[File:Seal of the United States Congress.svg|90px]] [[File:Seal of the United States Department of the Treasury.svg|90px]]|titlestyle=background:var(--background-color-base, #002868); background-clip:padding-box;|headingstyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff);|listtitlestyle=background:var(--background-color-base, #bf0a30); color:var(--color-base, #fff); text-align:center;|expanded={{{expanded|{{{1|}}}}}}|list1name=dimensions|list1title=Major dimensions|list1class=hlist skin-invert|list1=* [[Economy of the United States|Economy]] * [[Expenditures in the United States federal budget|Expenditures]] * [[United States federal budget|Federal budget]] * [[Financial position of the United States|Financial position]] * [[Military budget of the United States|Military budget]] * [[National debt of the United States|Public debt]] * [[Taxation in the United States|Taxation]] * [[Unemployment in the United States|Unemployment]] * [[Government_spending_in_the_United_States|Gov't spending]]|list2name=programs|list2title=Programs|list2class=hlist skin-invert|list2=* [[Medicare (United States)|Medicare]] * [[Social programs in the United States|Social programs]] * [[Social Security (United States)|Social Security]]|list3name=issues|list3title=Contemporary issues|list3class=skin-invert|list3=<div style="margin-bottom:0.5em"> [[National Commission on Fiscal Responsibility and Reform|Bowles–Simpson Commission]] {{flatlist}} * <!--Bu--> [[Bush tax cuts]] * <!--Deb--> [[United States debt ceiling|Debt ceiling]] ** [[History of the United States debt ceiling|history]] * <!--Def--> [[Deficit reduction in the United States|Deficit reduction]] * <!--F--> [[United States fiscal cliff|Fiscal cliff]] * <!--H--> [[Healthcare reform in the United States|Healthcare reform]] * <!--P--> [[Political debates about the United States federal budget|Political debates]] * <!--So--> [[Social Security debate in the United States|Social Security debate]] * <!--St--> "[[Starve the beast]]" * <!--Su--> [[Subprime mortgage crisis]] {{endflatlist}} </div> [[2007–2008 financial crisis]] {{flatlist}} * <!--D--> [[United States debt-ceiling crisis (disambiguation)|Debt-ceiling crises]] ** [[2011 United States debt-ceiling crisis|2011]] ** [[2013 United States debt-ceiling crisis|2013]] ** [[2023 United States debt-ceiling crisis|2023]] {{endflatlist}} [[2013 United States budget sequestration|2013 budget sequestration]] {{flatlist}} * <!--G--> [[Government shutdowns in the United States|Government shutdowns]] ** [[1980 United States federal government shutdown|1980]] ** [[1981, 1984, and 1986 U.S. federal government shutdowns|1981, 1984, 1986]] ** [[1990 United States federal government shutdown|1990]] ** [[1995–1996 United States federal government shutdowns|1995–1996]] ** [[2013 United States federal government shutdown|2013]] ** [[January 2018 United States federal government shutdown|Jan 2018]] ** [[2018–2019 United States federal government shutdown|2018–2019]] {{endflatlist}} Related events {{flatlist}} *<!--E-->[[Removal of Kevin McCarthy as Speaker of the House|2023 Removal of Kevin McCarthy]] {{endflatlist}}|list4name=terminology|list4title=Terminology|list4class=hlist skin-invert|list4=Cumulative [[Government budget balance|deficit]] + [[National debt of the United States#Debates|Interest]] ≈ [[Government debt|Debt]] * [[Balance of payments]] * [[Inflation]] * [[Continuing resolution]]}} [[w:Deficit_reduction_in_the_United_States|Deficit reduction in the United States]] == Deregulate the Economy == The legal theory that this can be done through the executive branch is found in the U.S. Supreme Court’s ''[[w:West_Virginia_v._EPA|West Virginia v. EPA]]'' and ''[[w:Loper_Bright|Loper Bright]]'' rulings, which rein in the administrative state and mean that much of what the federal government now does is illegal.<ref>{{cite web|url=https://www.wsj.com/opinion/department-of-government-efficiency-elon-musk-vivek-ramaswamy-donald-trump-1e086dab|website=[[w:Wall Street Journal]]|title=The Musk-Ramaswamy Project Could Be Trump’s Best Idea}}</ref> Mr. Trump has set a goal of eliminating 10 regulations for every new one. The [[w:Competitive_Enterprise_Institute|Competitive Enterprise Institute]]’s Wayne Crews says 217,565 rules have been issued since the [[w:Federal_Register|Federal Register]] first began itemizing them in 1976, with 89,368 pages added last year. [https://sgp.fas.org/crs/misc/R43056.pdf 3,000-4,500 rules are added each year]. DOGE’s first order will be to pause enforcement of overreaching rules while starting the process to roll them back. Mr. Trump and DOGE could direct agencies to settle legal challenges to Biden rules by vacating them. This could ease the laborious process of undoing them by rule-making through the [[w:Administrative_Procedure_Act|Administrative Procedure Act]]. A source tells the WSJ they’ll do whatever they think they legally can without the APA. The [[w:Congressional_Review_Act|Congressional Review Act]]—which allows Congress to overturn recently issued agency regulations—had been used only once, prior to [[w:First_presidency_of_Donald_Trump|Trump's first term]]. While in office, he and the Republican Congress used it on 16 rules. This time, there will be more than 56 regulatory actions recent enough to be repealed. The [[w:Chevron_deference|''Chevron'' deference]] had required federal courts to defer to agencies’ interpretations of ambiguous statutes, but this was overturned in 2024. Taken together, with some other recent [[w:SCOTUS|SCOTUS]] rulings, we now have, says the WSJ, the biggest opportunity to cut regulatory red tape in more than 40 years.<ref>[https://www.wsj.com/opinion/let-the-trump-deregulation-begin-us-chamber-of-commerce-second-term-economic-growth-73f24387?cx_testId=3&cx_testVariant=cx_166&cx_artPos=0]</ref><blockquote>"Most legal edicts aren’t laws enacted by Congress but “rules and regulations” promulgated by unelected bureaucrats—tens of thousands of them each year. Most government enforcement decisions and discretionary expenditures aren’t made by the democratically elected president or even his political appointees but by millions of unelected, unappointed civil servants within government agencies who view themselves as immune from firing thanks to civil-service protections." "This is antidemocratic and antithetical to the Founders’ vision. It imposes massive direct and indirect costs on taxpayers." "When the president nullifies thousands of such regulations, critics will allege executive overreach. In fact, it will be ''correcting'' the executive overreach of thousands of regulations promulgated by administrative fiat that were never authorized by Congress. The president owes lawmaking deference to Congress, not to bureaucrats deep within federal agencies. The use of executive orders to substitute for lawmaking by adding burdensome new rules is a constitutional affront, but the use of executive orders to roll back regulations that wrongly bypassed Congress is legitimate and necessary to comply with the Supreme Court’s recent mandates. And after those regulations are fully rescinded, a future president couldn’t simply flip the switch and revive them but would instead have to ask Congress to do so" Mssrs. [https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Musk and Ramaswamy, WSJ, 11/20/2024]</blockquote> == Shrink the federal civil service == The government has around three million [[w:United_States_federal_civil_service|federal civil service]] employees, with an average salary of $106,000. Dr. Anthony Fauci made $481,000 in 2022. The federal head count has ballooned by 120,800 during the Biden years. Civil service and union protections make it hard to fire workers. Mr. Trump intends to quickly resurrect the [[w:Schedule_F|Schedule F]] reform that he sought to implement at the end of his first term but was scrapped by Mr. Biden. These would high-level federal employees to be removed like political appointees, by eliminating their job protections. WSJ proposals[https://www.wsj.com/opinion/the-doge-cheat-sheet-elon-musk-vivek-ramaswamy-department-of-government-efficiency-1c231783#cxrecs_s] The [[w:Administrative_Procedures_Act|Administrative Procedures Act]] statute protects federal employees from political retaliation, but allows for “reductions in force” that don’t target specific employees. The statute further empowers the president to “prescribe rules governing the competitive service.” The Supreme Court has held—in ''[[w:Franklin_v._Massachusetts|Franklin v. Massachusetts]]'' (1992) and ''[[w:Collins_v._Yellen|Collins v. Yellen]]'' (2021) that when revious presidents have used this power to amend the civil service rules by executive order, they weren’t constrained by the APA when they did so. Mr. Trump can, with this authority, implement any number of “rules governing the competitive service” that would curtail administrative overgrowth, from large-scale firings to relocation of federal agencies out of the Washington area. The DOGE welcomes voluntary terminations once the President begins requiring federal employees to come to the office five days a week, because American taxpayers shouldn’t pay federal employees for the Covid-era privilege of staying home.<ref>[https://www.wsj.com/opinion/musk-and-ramaswamy-the-doge-plan-to-reform-government-supreme-court-guidance-end-executive-power-grab-fa51c020?cx_testId=3&cx_testVariant=cx_165&cx_artPos=5 Elon Musk and Vivek Ramaswamy: The DOGE Plan to Reform Government: Following the Supreme Court’s guidance, we’ll reverse a decadeslong executive power grab. Musk & Ramaswamy 11/20/2024]</ref> == Reduce the deficit and debt by impounding appropriated funds == === Impound appropriated funds === Reports suggest that president-elect Trump intends to override Congress’s power of the purse by [[w:Impoundment_of_appropriated_funds|impoundment of appropriated funds]], that is, refusing to spend them. the president may [[wikipedia:Rescission_bill|propose rescission]] of specific funds, but that rescission must be approved by both the [[wikipedia:United_States_House_of_Representatives|House of Representatives]] and [[wikipedia:United_States_Senate|Senate]] within 45 days. [[w:Thomas_Jefferson|Thomas Jefferson]] was the first president to exercise the power of impoundment in 1801, which power was available to all presidents up to and including [[wikipedia:Richard_Nixon|Richard Nixon]], and was regarded as a power inherent to the office, although one with limits. He may ask Congress to repeal The [[w:Congressional_Budget_and_Impoundment_Control_Act_of_1974|Congressional Budget and Impoundment Control Act of 1974]], which was passed in response to Nixon's abuses.<ref>{{Cite web|url=http://democrats-budget.house.gov/resources/reports/impoundment-control-act-1974-what-it-why-does-it-matter|title=The Impoundment Control Act of 1974: What Is It? Why Does It Matter? {{!}} House Budget Committee Democrats|date=2019-10-23|website=democrats-budget.house.gov|language=en|access-date=2024-05-19}}</ref> If Congress refuses to do so, president Trump may impound funds anyway and argue in court that the 1974 law is unconstitutional. The matter would likely end up at the Supreme Court, which would have to do more than simply hold the 1974 act unconstitutional in order for Mr. Trump to prevail. The court would also have to overrule [[w:Train_v._City_of_New_York_(1975)|''Train v. City of New York'' (1975)]], which held that impoundment is illegal unless the underlying legislation specifically authorizes it. === Reduce the budget deficit === [[wikipedia:U.S. federal budget|U.S. federal budget]] The [[wikipedia:Fiscal_year|fiscal year]], beginning October 1 and ending on September 30 of the year following. Congress is the body required by law to pass appropriations annually and to submit funding bills passed by both houses to the President for signature. Congressional decisions are governed by rules and legislation regarding the [[wikipedia:United_States_budget_process|federal budget process]]. Budget committees set spending limits for the House and Senate committees and for Appropriations subcommittees, which then approve individual [[wikipedia:Appropriations_bill_(United_States)|appropriations bills]] to During FY2022, the federal government spent $6.3 trillion. Spending as % of GDP is 25.1%, almost 2 percentage points greater than the average over the past 50 years. Major categories of FY 2022 spending included: Medicare and Medicaid ($1.339T or 5.4% of GDP), Social Security ($1.2T or 4.8% of GDP), non-defense discretionary spending used to run federal Departments and Agencies ($910B or 3.6% of GDP), Defense Department ($751B or 3.0% of GDP), and net interest ($475B or 1.9% of GDP).<ref name="CBO_2022">[https://www.cbo.gov/publication/58888 The Federal Budget in Fiscal Year 2022: An Infographic]</ref> CBO projects a federal budget deficit of $1.6 trillion for 2024. In the agency’s projections, deficits generally increase over the coming years; the shortfall in 2034 is $2.6 trillion. The deficit amounts to 5.6 percent of gross domestic product (GDP) in 2024, swells to 6.1 percent of GDP in 2025, and then declines in the two years that follow. After 2027, deficits increase again, reaching 6.1 percent of GDP in 2034.<ref name="CBO_budgetOutlook2024">{{cite web|url=https://www.cbo.gov/publication/59710|title=The Budget and Economic Outlook: 2024 to 2034|date=February 7, 2024|publisher=CBO|access-date=February 7, 2024}}</ref> The following table summarizes several budgetary statistics for the fiscal year 2015-2021 periods as a percent of GDP, including federal tax revenue, outlays or spending, deficits (revenue – outlays), and [[wikipedia:National_debt_of_the_United_States|debt held by the public]]. The historical average for 1969-2018 is also shown. With U.S. GDP of about $21 trillion in 2019, 1% of GDP is about $210 billion.<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> Statistics for 2020-2022 are from the CBO Monthly Budget Review for FY 2022.<ref name="CBO_MBRFY2022">{{cite web|url=https://www.cbo.gov/publication/58592|title=Monthly Budget Review: Summary for Fiscal Year 2022|date=November 8, 2022|publisher=CBO|access-date=December 10, 2022}}</ref> {| class="wikitable" !Variable As % GDP !2015 !2016 !2017 !2018 !2019 !2020 !2021 !2022 !Hist Avg |- !Revenue<ref name="CBO_Hist_20">[https://www.cbo.gov/about/products/budget-economic-data#2 CBO-Historical Budget Data-Retrieved January 28, 2020]</ref> |18.0% |17.6% |17.2% |16.4% |16.4% |16.2% |17.9% |19.6% |17.4% |- !Outlays<ref name="CBO_Hist_20" /> |20.4% |20.8% |20.6% |20.2% |21.0% |31.1% |30.1% |25.1% |21.0% |- !Budget Deficit<ref name="CBO_Hist_20" /> | -2.4% | -3.2% | -3.5% | -3.8% | -4.6% | -14.9% | -12.3% | -5.5% | -3.6% |- !Debt Held by Public<ref name="CBO_Hist_20" /> |72.5% |76.4% |76.2% |77.6% |79.4% |100.3% |99.6% |94.7% | |} The [[wikipedia:U.S._Constitution|U.S. Constitution]] ([[wikipedia:Article_One_of_the_United_States_Constitution|Article I]], section 9, clause 7) states that "No money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of Receipts and Expenditures of all public Money shall be published from time to time." Each year, the President of the United States submits a budget request to Congress for the following fiscal year as required by the [[wikipedia:Budget_and_Accounting_Act_of_1921|Budget and Accounting Act of 1921]]. Current law ({{UnitedStatesCode|31|1105}}(a)) requires the president to submit a budget no earlier than the first Monday in January, and no later than the first Monday in February. Typically, presidents submit budgets on the first Monday in February. The budget submission has been delayed, however, in some new presidents' first year when the previous president belonged to a different party. === Reduce the National debt === == Reform Entitlements == === Healthcare and Medicare === [[w:ObamaCare|ObamaCare]] started as a plausible scheme for universal, cost-effective health insurance with subsidies for the needy. Only the subsidies survive because the ObamaCare policies actually delivered are so overpriced nobody would buy them without a subsidy.<ref>[https://www.wsj.com/opinion/elons-real-trump-mission-protect-growth-department-of-government-efficiency-appointments-cabinet-9e7e62b2]</ref> See below: Department of Health and Human Services === Social Security === Even FDR was aware of its flaw: it discourages working and saving. == Strategic Foreign Policy and Military reform == === Department of State === {{Main article|w:Second_presidency_of_Donald_Trump#Prospective_foreign_policy|w:State Department}} === U.S. Department of Defense === The president-elect is reportedly considering a draft executive order that establishes a “warrior board” of retired senior military personnel with the power to review three- and four-star officers “on leadership capability, strategic readiness, and commitment to military excellence," and to recommend removals of any deemed unfit for leadership. This would fast-track the removal of generals and admirals found to be “lacking in requisite leadership qualities,” consistent with his earlier vow to fire “woke” military leaders.<ref>[https://www.wsj.com/politics/national-security/trump-draft-executive-order-would-create-board-to-purge-generals-7ebaa606<nowiki> Trump draft executive order would create a board to purge generals 11/12/2024]</nowiki></ref> There are legal obstacles. The law prohibits the firing of commissioned officers except by “sentence of a general court-martial,” as a “commutation of a sentence of a general court-martial,” or “in time of war, by order of the president.” A commissioned officer who believes he’s been wrongfully dismissed has the right to seek a trial by court-martial, which may find the dismissal baseless. <ref>[https://www.wsj.com/opinion/trump-tests-the-constitutions-limits-checks-balances-government-policy-law-78d0d0f1<nowiki> Trump test the constitutions limits 11/19/2024]</nowiki></ref> Musk said, "Some idiots are still building manned fighter jets like the F-35," and later added: "Manned fighter jets are outdated in the age of drones and only put pilots' lives at risk." [[w:Bernie_Sanders|Bernie Sanders]] wrote on X: "Elon Musk is right. The Pentagon, with a budget of $886 billion, just failed its 7th audit in a row. It's lost track of billions. Last year, only 13 senators voted against the Military Industrial Complex and a defense budget full of waste and fraud. That must change."{{sfn|Newsweek 12/02|2024}}. It failed its fifth audit in June 2023.<ref>{{Cite web|url=https://www.newsweek.com/fox-news-host-confronts-gop-senator-pentagons-fifth-failed-audit-1804379|title=Fox News host confronts GOP Senator on Pentagon's fifth failed audit|last=Writer|first=Fatma Khaled Staff|date=2023-06-04|website=Newsweek|language=en|access-date=2024-12-02}} == Reform the other Government Bureaus and Departments == === Department of Education === [[w:United_States_Department_of_Education|w:Department of Education]] has 4,400 employees – the smallest staff of the Cabinet agencies<ref>{{Cite web|url=https://www2.ed.gov/about/overview/fed/role.html|title=Federal Role in Education|date=2021-06-15|website=www2.ed.gov|language=en|access-date=2022-04-28}}</ref> – and a 2024 budget of $238 billion.<ref name="DOE-mission">{{Cite web|url=https://www.usaspending.gov/agency/department-of-education?fy=2024|title=Agency Profile {{!}} U.S. Department of Education|website=www2.ed.gov|access-date=2024-11-14}}</ref> The 2023 Budget was $274 billion, which included funding for children with disabilities ([[wikipedia:Individuals_with_Disabilities_Education_Act|IDEA]]), pandemic recovery, early childhood education, [[wikipedia:Pell_Grant|Pell Grants]], [[wikipedia:Elementary_and_Secondary_Education_Act|Title I]], work assistance, among other programs. This budget was down from $637.7 billion in 2022.<ref>{{Cite web|url=https://www.future-ed.org/what-the-new-pisa-results-really-say-about-u-s-schools/|title=What the New PISA Results Really Say About U.S. Schools|date=2021-06-15|website=future-ed.com|language=en|access-date=2024-11-14}}</ref> The WSJ proposes that the Civil Rights division be absorbed into the Department of Justice, and that its outstanding loan portolio be handled by the Department of the Treasury. Despite the redundancies, its unlikely that it will be abolished, which would require congressional action and buy-in from Democrats in the Senate; Republicans don’t have enough votes to do it alone. A republican appointee is expected to push back against federal education overreach and progressive policies like DEI. <ref>[https://www.wsj.com/opinion/trump-can-teach-the-education-department-a-lesson-nominee-needs-boldness-back-school-choice-oppose-woke-indoctrination-ddf6a38d<nowiki> Trump can teach the Education Department a Lesson. WSJ 11/20/2024]</nowiki></ref> === U.S. Department of Health and Human Services === [[w:U.S._Department_of_Health_and_Human_Services|U.S. Department of Health and Human Services]] was authorized a budget for [[w:2020_United_States_federal_budget|fiscal year 2020]] of $1.293 trillion. It has 13 operating divisions, 10 of which constitute the [[w:United_States_Public_Health_Service|Public Health Services]], whose budget authorization is broken down as follows:<ref name="hhs_budget_fy2020">{{cite web|url=https://www.hhs.gov/about/budget/fy2020/index.html|title=HHS FY 2020 Budget in Brief|date=October 5, 2019|website=HHS Budget & Performance|publisher=United States Department of Health & Human Services|page=7|access-date=May 9, 2020}}</ref> {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Food and Drug Administration|Food and Drug Administration]] (FDA) |$3,329 MM |- |[[w:Health Resources and Services Administration|Health Resources and Services Administration]] (HRSA) |$11,004 |- |[[w:Indian Health Service|Indian Health Service]] (IHS) |$6,104 |- |[[w:Centers for Disease Control and Prevention|Centers for Disease Control and Prevention]] (CDC) |$6,767 |- |[[w:National Institutes of Health|National Institutes of Health]] (NIH) |$33,669 |- |[[w:Substance Abuse and Mental Health Services Administration|Substance Abuse and Mental Health Services Administration]] (SAMHSA) |$5,535 |- |[[w:Agency for Healthcare Research and Quality|Agency for Healthcare Research and Quality]] (AHRQ) |$0 |- |[[w:Centers for Medicare & Medicaid Services|Centers for Medicare & Medicaid Services]] (CMMS) |$1,169,091 |- |[[w:Administration for Children and Families|Administration for Children and Families]] (ACF) |$52,121 |- |[[w:Administration for Community Living|Administration for Community Living]] (ACL) |$1,997 |- |} {| class="wikitable sortable" !Program !2020 Budget !2024 Budget ! employees !2025 Budget !2026 Budget |- |[[w:Departmental Management|Departmental Management]] |$340 |- |Non-Recurring Expense Fund |$-400 |- |[[w:Office of Medicare Hearings and Appeals|Office of Medicare Hearings and Appeals]] |$186 |- |[[w:Office of the National Coordinator|Office of the National Coordinator]] |$43 |- |[[w:Office for Civil Rights|Office for Civil Rights]] |$30 |- |[[w:Office of Inspector General|Office of Inspector General]] |$82 |- |[[w:Public Health and Social Services Emergency Fund|Public Health and Social Services Emergency Fund]] |$2,667 |- |[[w:Program Support Center|Program Support Center]] |$749 |- |Offsetting Collections |$-629 |- |Other Collections |$-163 |- |'''TOTAL''' |'''$1,292,523''' |} The FY2020 budget included a $1.276 billion budget decrease for the Centers for Disease Control, and a $4.533 billion budget decrease for the National Institutes of Health. These budget cuts, along with other changes since 2019, comprised a total decrease of over $24 billion in revised discretionary budget authority across the entire Department of Health and Human Services for Fiscal Year 2020.<ref name="hhs_budget_fy2020" /> Additional details of the budgeted outlays, budget authority, and detailed budgets for other years, can be found at the HHS Budget website.<ref>{{cite web|url=http://WWW.HHS.GOV/BUDGET|title=Health and Human Services: Budget and Performance|publisher=United States Department of Health & Human Services|access-date=May 9, 2020}}</ref> [[w:Robert_F._Kennedy_Jr.|Robert F. Kennedy Jr.]] has been nominated as [[w:United_States_Secretary_of_Health_and_Human_Services|United_States_Secretary_of_Health_and_Human_Services]] He is an American politician, [[Environmental law|environmental lawyer]], [[anti-vaccine activist]], and anti-packaged food industry activist, anti-pharmaceutical industry activist, who will be nominated to serve as [[United States Secretary of Health and Human Services]],<ref name="v502">{{cite web|url=https://www.forbes.com/sites/saradorn/2024/11/14/rfk-jr-launches-independent-2024-run-here-are-all-the-conspiracies-he-promotes-from-vaccines-to-mass-shootings/|title=Trump Taps RFK Jr. As Secretary Of Health And Human Services: Here Are All The Conspiracies He's Promoted|last=Dorn|first=Sara|date=2024-11-14|website=Forbes|access-date=2024-11-15}}</ref> with the mission of "Making America Healthy Again". He is the chairman and founder of [[Children's Health Defense]], an anti-vaccine advocacy group and proponent of [[COVID-19 vaccine misinformation|dubious COVID-19 vaccine information]].<ref name="Smith_12/15/2021" /><ref name="KW" /> == CPB, PBS, NPR == [[w:Howard_Husock|Howard Husock]] suggest that instead of zeroing its $535 million budget, Republicans reform the [[w:Public_Broadcasting_Act|Public Broadcasting Act]] to eliminate bias and improve local journalism.<ref>https://www.wsj.com/opinion/the-conservative-case-for-public-broadcasting-media-policy-2d4c3c9f?page=1</ref> == NASA == In September 2026, NASA's [[w:Artemis_program|Artemis program]], established in 2017 via [[wikipedia:Space_Policy_Directive_1|Space Policy Directive 1]], is intended to reestablish a human presence on the Moon for the first time since the [[wikipedia:Apollo_17|Apollo 17]] mission in 1972. The program's stated long-term goal is to establish a [[wikipedia:Moonbase|permanent base on the Moon]] to facilitate [[wikipedia:Human_mission_to_Mars|human missions to Mars]]. The [[w:U.S._National_Academies_of_Sciences,_Engineering,_and_Medicine|U.S. National Academies of Sciences, Engineering, and Medicine]] in October, put out a report titled "NASA at a Crossroads," which identified myriad issues at the agency, including out-of-date infrastructure, pressures to prioritize short-term objectives and inefficient management practices. NASA's costly [[w:Space_Launch_System|Space Launch System]] (SLS) is the cornerstone of the Artemis program. has a price tag of around $4.1 billion per launch, and is a single-use rocket that can only launch every two years, having debuted in 2022 with the uncrewed [[w:Artemis_1_mission|Artemis 1 mission]] to the moon. In contrast, SpaceX is working to reduce the cost of a single Starship flight to under $10 million. NASA Associate Administrator Jim Free urged the incoming administration to maintain the current plans, in a symposium with the [[w:American_Astronautical_Society|American Astronautical Society]] saying "We need that consistency in purpose. That has not happened since Apollo. If we lose that, I believe we will fall apart and we will wander, and other people in this world will pass us by." NASA has already asked both [[w:SpaceX|SpaceX]] and also Jeff Bezos' [[w:Blue_Origin|Blue Origin]], to develop cargo landers for its Artemis missions and to deliver heavy equipment on them to the Moon by 2033. "Having two lunar lander providers with different approaches for crew and cargo landing capability provides mission flexibility while ensuring a regular cadence of moon landings for continued discovery and scientific opportunity," Stephen D. Creech, NASA's assistant deputy associate administrator for the moon to Mars program, said in an announcement about the partnership. "For all of the money we are spending, NASA should NOT be talking about going to the Moon - We did that 50 years ago. They should be focused on the much bigger things we are doing, including Mars (of which the Moon is a part), Defense and Science!" Trump wrote in a post on X in 2019. Trump has said he would create a [[w:Space_National_Guard|Space National Guard]], an idea that lawmakers in Congress have been proposing since 2021. Critics agree that a focus on spaceflight could come at the expense of "Earth and atmospheric sciences at NASA and the [[w:National_Oceanic_and_Atmospheric_Administration|National Oceanic and Atmospheric Administration]] (NOAA), which have been cut during the Biden era."<ref>{{Cite web|url=https://www.newsweek.com/elon-musk-donald-trump-nasa-space-policy-1990599|title=Donald Trump and Elon Musk could radically reshape NASA. Here's how|last=Reporter|first=Martha McHardy US News|date=2024-11-27|website=Newsweek|language=en|access-date=2024-12-02}}</ref> Regarding his goal and SpaceX's corporate mission of colonising Mars, Mr. Musk has stated that "The DOGE is the only path to extending life beyond earth"{{sfn|Economist 11/23|2024}} == [[w:Federal_Aviation_Administration|Federal Aviation Administration]] == Musk has often complained about the FAA "smothering" innovation, boasting that he can build a rocket faster than the agency can process the "Kafkaesque paperwork" required to make the relevant approvals.{{sfn|Economist 11/23|2024}} == History and Miscellaneous facts == See also: [[w:Department_of_Government_Efficiency#History|Department of Government Efficiency — History]] DOGE's work will "conclude" no later than July 4, 2026, the 250th anniversary of the signing of the [[United States Declaration of Independence|U.S. Declaration of Independence]],<ref>{{Cite web|url=https://thehill.com/policy/4987402-trump-musk-advisory-group-spending/|title=Elon Musk, Vivek Ramaswamy to lead Trump's Department of Government Efficiency (DOGE)|last=Nazzaro|first=Miranda|date=November 13, 2024|website=The Hill|language=en-US|access-date=November 13, 2024}}</ref> also coinciding with America's [[United States Semiquincentennial|semiquincentennial]] celebrations and a proposed "Great American Fair". Despite its name it is not expected to be a [[wikipedia:United_States_federal_executive_departments|federal executive department]], but rather may operate under the [[Federal Advisory Committee Act]],<ref>{{Cite web|url=https://www.cbsnews.com/news/trump-department-of-government-efficiency-doge-elon-musk-ramaswamy/|title=What to know about Trump's Department of Government Efficiency, led by Elon Musk and Vivek Ramaswamy - CBS News|last=Picchi|first=Aimee|date=2024-11-14|website=www.cbsnews.com|language=en-US|access-date=2024-11-14}}</ref> so its formation is not expected to require approval from the [[wikipedia:United_States_Congress|U.S. Congress]]. NYT argues that records of its meetings must be made public.{{Cn}} As an advisor rather than a government employee, Mr. Musk will not be subject to various ethics rules.{{sfn|Economist 11/23}} Musk has stated that he believes such a commission could reduce the [[wikipedia:United_States_federal_budget|U.S. federal budget]] by $2 trillion, which would be a reduction of almost one third from its 2023 total. [[Maya MacGuineas]] of the [[Committee for a Responsible Federal Budget]] has said that this saving is "absolutely doable" over a period of 10 years, but it would be difficult to do in a single year "without compromising some of the fundamental objectives of the government that are widely agreed upon".<ref>{{Cite web|url=https://thehill.com/business/4966789-elon-musk-skepticism-2-trillion-spending-cuts/|title=Elon Musk draws skepticism with call for $2 trillion in spending cuts|last=Folley|first=Aris|date=2024-11-03|website=The Hill|language=en-US|access-date=2024-11-14}}</ref> [[wikipedia:Jamie_Dimon|Jamie Dimon]], the chief executive officer of [[wikipedia:JPMorgan_Chase|JPMorgan Chase]], has supported the idea. Some commentators questioned whether DOGE is a conflict of interest for Musk given that his companies are contractors to the federal government. The body is "unlikely to have any regulatory teeth on its own, but there's little doubt that it can have influence on the incoming administration and how it will determine its budgets".<ref>{{Cite web|url=https://www.vox.com/policy/384904/trumps-department-of-government-efficiency-sounds-like-a-joke-it-isnt|title=Trump tapped Musk to co-lead the "Department of Government Efficiency." What the heck is that?|last=Fayyad|first=Abdallah|date=2024-11-13|website=Vox|language=en-US|access-date=2024-11-14}}</ref> Elon Musk had called [[w:Federico_Sturzenegger|Federico Sturzenegger]], Argentina's [[Minister of Deregulation and Transformation of the State]] ([[w:es:Ministerio_de_Desregulación_y_Transformación_del_Estado|es]]), to discuss imitating his ministry's model.<ref>{{Cite web|url=https://www.infobae.com/economia/2024/11/08/milei-brindo-un-nuevo-apoyo-a-sturzenegger-y-afirmo-que-elon-musk-imitara-su-gestion-en-eeuu/|title=Milei brindó un nuevo apoyo a Sturzenegger y afirmó que Elon Musk imitará su gestión en EEUU|date=November 8, 2024|website=infobae|language=es-ES|access-date=November 13, 2024}}</ref> == Reception and Criticism == See also: [[w:Department_of_Government_Efficiency#Reception|w:Department of Government Efficiency — Reception]] The WSJ reports that Tesla's Texas facility dumped toxic wastewater into the public sewer system, into a lagoon, and into a local river, violated Texas environmental regulations, and fired an employee who attempted to comply with the law.{{Cn}} The Economist estimates that 10% of Mr. Musk's $360bn personal fortune is derived from contracts and benefits from the federal government, and 15% from the Chinese market.{{sfn|Economist 11/23}} == See also == * [[w:Second_presidential_transition_of_Donald_Trump|Second presidential transition of Donald Trump]] * [[w:United_States_federal_budget#Deficits_and_debt|United States federal budget - Deficits and debt]] * [[w:United_States_Bureau_of_Efficiency|United States Bureau of Efficiency]] – United States federal government bureau from 1916 to 1933 * [[w:Brownlow_Committee|Brownlow Committee]] – 1937 commission recommending United States federal government reforms * [[w:Grace_Commission|Grace Commission]] – Investigation to eliminate inefficiency in the United States federal government * [[w:Hoover_Commission|Hoover Commission]] – United States federal commission in 1947 advising on executive reform * [[w:Keep_Commission|Keep Commission]] * [[w:Project_on_National_Security_Reform|Project on National Security Reform]] == Notes == {{reflist}} == References == {{refbegin}} * {{Cite web|url=https://www.newsweek.com/bernie-sanders-finds-new-common-ground-elon-musk-1993820|title=Bernie Sanders finds new common ground with Elon Musk|last=Reporter|first=Mandy Taheri Weekend|date=2024-12-01|website=Newsweek|language=en|access-date=2024-12-02 |ref={{harvid|Newsweek 12/01|2024}} }} * {{Cite news|url=https://www.economist.com/briefing/2024/11/21/elon-musk-and-donald-trump-seem-besotted-where-is-their-bromance-headed|title=Elon Musk and Donald Trump seem besotted. Where is their bromance headed?|work=The Economist|access-date=2024-12-04|issn=0013-0613 |ref={{harvid|Economist 11/23|2024}} }} <references group="lower-alpha" /> {{refend}} 2dqnd6j2w3imx54whwulngw673trq44 0 316821 2690139 2689415 2024-12-03T18:06:54Z Bocardodarapti 289675 2690139 wikitext text/x-wiki {{ Mathematical section{{{opt|}}} |Content= {{ inputdefinition |Subgroup/Normal subgroup/Definition|| }} For a normal subgroup, it is not necessary to distinguish between left cosets and right cosets; we just talk about {{Keyword|cosets|pm=.}} Instead of {{ Mathcor|term1= xH |or|term2= Hx |pm=, }} we write usually {{mat|term= [x] |pm=.}} The equality {{ Relationchain |xH ||Hx || || || |pm= }} does {{Emphasize|term=not|pm=}} mean that {{ Relationchain | xh || hx || || || |pm= }} for all {{ Relationchain | h |\in| H || || || |pm=; }} it only means that for every {{ Relationchain | h |\in| H || || || |pm=, }} there exists a {{ Relationchain | \tilde{h} |\in| H || || || |pm= }} fulfilling {{ Relationchain | xh ||\tilde{h}x || || || |pm=. }} {{ inputfactproof |Normal subgroup/Characterization/Fact|Lemma|| }} {{ inputexample |Permutation group S3/Subgroups and normal subgroup/Example|| }} {{ inputfactproof |Group homomorphism/Kernel/Normal subgroup/Fact|Lemma|| }} |Textform=Section |Category= |}} f34x0fe6hclas52qpyec2sz85nzy7is 6 316883 2690207 2689819 2024-12-04T04:19:15Z Young1lim 21186 /* Summary */ 2690207 wikitext text/x-wiki == Summary == {{Information |Description=LIB.1A: Static Libraries (20241202 - 20241130) |Source={{own|Young1lim}} |Date=2024-12-02 |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}} 241jmno5h7o8ho7ikt5wfi6kix0iod4 2690208 2690207 2024-12-04T04:19:52Z Young1lim 21186 /* Summary */ 2690208 wikitext text/x-wiki == Summary == {{Information |Description=LIB.1A: Shared Libraries (20241202 - 20241130) |Source={{own|Young1lim}} |Date=2024-12-02 |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}} dbg4je2gi83owubx1pym685yap4y5oq 2690210 2690208 2024-12-04T04:20:34Z Young1lim 21186 /* Summary */ 2690210 wikitext text/x-wiki == Summary == {{Information |Description=LIB.2A: Shared Libraries (20241202 - 20241130) |Source={{own|Young1lim}} |Date=2024-12-02 |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}} rj4y04mwoy20n31fn29w0v3noo4n8dd 6 316884 2690220 2689821 2024-12-04T04:25:39Z Young1lim 21186 /* Summary */ 2690220 wikitext text/x-wiki == Summary == {{Information |Description=LCal.8A: Combinator (20241202 - 20241130) |Source={{own|Young1lim}} |Date=2024-12-02 |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}} qwrriv1fqrscpqud3rnj2quwrrw8mni 6 316885 2690229 2689823 2024-12-04T07:20:46Z Young1lim 21186 /* Summary */ 2690229 wikitext text/x-wiki == Summary == {{Information |Description=ARM.2ASM: Branch and Return Methods (20241202 - 20241130) |Source={{own|Young1lim}} |Date=2024-12-02 |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}} 2z4yg2zy82bxtvighls5j2p98c45id5 102 316903 2690183 2689970 2024-12-04T02:04:02Z Jason M. C., Han 2696291 adding up new contents 2690183 wikitext text/x-wiki [[File:SUMMER played by piano student ZeyuCui.wav|thumb|Boy Fruit's "Summer Love" expressed to his kindness mother and soldier father]] '''Storys and Comments''' As piano pupils from childhood, we all knew: 'Summer', composed by Jeo Hishashi, is very famous in piano classroom. More information regarding with this piece of piano music Boy fruit played, please refer to Kikujiro (Wikipedia: https://en.m.wikipedia.org/wiki/Kikujiro ). Zeyu,Cui (Fruit) is my piano student - a little boy named Zeyu Cui is a little expert in its performance. He played it in many situations- in classroom, in life and somewhere traveling with piano. In his heart-music,you can hear: a piano boy's growing day after day and year after year, a tender expression of his love to mother and father, and a desire of happily playing with his companies in school, etc. Let's listen to him! Further information and story,I will add up soon both here and Wikiversity. [[File:Butterfly Lovers （Piano Music）played by piano student Shengran, Ma.wav ⅠthumbⅠHao Hao played a piano musical tune transformed from the famous Chinese tranditional music - Liangzhu (Butterfly Lovers) in piano classroom.]] '''Storys and comments''' I thought the emotional expressions as the dialogues between butterfly lovers one hand by the other、the detailed technique-treatments such as the arpegio-accompanyment、the eighth-chords exactness, and the top-part arms-force...were trained very fluent, comfortable and excellent. Therefore, as a piano teacher, I felt very pleased to introduce it to the public listening. Further technique&art-comments and studying storys I will up-send soon 5uhs3uqw71klpit5wvyvfg9f26xvyec 2690184 2690183 2024-12-04T02:11:46Z Jason M. C., Han 2696291 2690184 wikitext text/x-wiki [[File:SUMMER played by piano student ZeyuCui.wav|thumb|Boy Fruit's "Summer Love" expressed to his kindness mother and soldier father]] '''Storys and Comments''' As piano pupils from childhood, we all knew: 'Summer', composed by Jeo Hishashi, is very famous in piano classroom. More information regarding with this piece of piano music Boy fruit played, please refer to Kikujiro (Wikipedia: https://en.m.wikipedia.org/wiki/Kikujiro ). Zeyu,Cui (Fruit) is my piano student - a little boy named Zeyu Cui is a little expert in its performance. He played it in many situations- in classroom, in life and somewhere traveling with piano. In his heart-music,you can hear: a piano boy's growing day after day and year after year, a tender expression of his love to mother and father, and a desire of happily playing with his companies in school, etc. Let's listen to him! Further information and story,I will add up soon both here and Wikiversity. [[File:Butterfly Lovers （Piano Music）played by piano student Shengran, Ma.wavⅠthumbⅠHao Hao played a piano musical tune transformed from the famous Chinese tranditional music - Liangzhu (Butterfly Lovers) in piano classroom.]] '''Storys and comments''' I thought the emotional expressions as the dialogues between butterfly lovers one hand by the other、the detailed technique-treatments such as the arpegio-accompanyment、the eighth-chords exactness, and the top-part arms-force...were trained very fluent, comfortable and excellent. Therefore, as a piano teacher, I felt very pleased to introduce it to the public listening. Further technique&art-comments and studying storys I will up-send soon b2h3w53sl1e8ivp340hy3hfz19n7hqv 2690187 2690184 2024-12-04T02:20:54Z Jason M. C., Han 2696291 2690187 wikitext text/x-wiki [[File:SUMMER played by piano student ZeyuCui.wav|thumb|Boy Fruit's "Summer Love" expressed to his kindness mother and soldier father]] '''Storys and Comments''' As piano pupils from childhood, we all knew: 'Summer', composed by Jeo Hishashi, is very famous in piano classroom. More information regarding with this piece of piano music Boy fruit played, please refer to Kikujiro (Wikipedia: https://en.m.wikipedia.org/wiki/Kikujiro ). Zeyu,Cui (Fruit) is my piano student - a little boy named Zeyu Cui is a little expert in its performance. He played it in many situations- in classroom, in life and somewhere traveling with piano. In his heart-music,you can hear: a piano boy's growing day after day and year after year, a tender expression of his love to mother and father, and a desire of happily playing with his companies in school, etc. Let's listen to him! Further information and story,I will add up soon both here and Wikiversity. [[File:Butterfly Lovers （Piano Music）played by piano student Shengran, Ma.wavⅠthumbⅠHao Hao played a piano musical tune transformed from the famous Chinese tranditional music - Liangzhu (Butterfly Lovers) in piano classroom.]] '''Storys and comments''' I thought the emotional expressions as the dialogues between butterfly lovers one hand by the other、the detailed technique-treatments such as the arpegio-accompanyment、the eighth-chords exactness, and the top-part arms-force...were trained very fluent, comfortable and excellent. Therefore, as a piano teacher, I felt very pleased to introduce it to the public listening. Further technique&art-comments and studying storys I will up-send soon [[File:Little Trumpet (Piano Music) played by piano student Chen, Cao.wav|thumb|Little Trumpet (Piano Music) played by piano student Chen, Cao.wav]] cgjk0o7m3uio8bbri4k0fpuprk9zv0m 2690190 2690187 2024-12-04T02:24:22Z Jason M. C., Han 2696291 changing citing formation to make right 2690190 wikitext text/x-wiki [[File:SUMMER played by piano student ZeyuCui.wav|thumb|Boy Fruit's "Summer Love" expressed to his kindness mother and soldier father]] '''Storys and Comments''' As piano pupils from childhood, we all knew: 'Summer', composed by Jeo Hishashi, is very famous in piano classroom. More information regarding with this piece of piano music Boy fruit played, please refer to Kikujiro (Wikipedia: https://en.m.wikipedia.org/wiki/Kikujiro ). Zeyu,Cui (Fruit) is my piano student - a little boy named Zeyu Cui is a little expert in its performance. He played it in many situations- in classroom, in life and somewhere traveling with piano. In his heart-music,you can hear: a piano boy's growing day after day and year after year, a tender expression of his love to mother and father, and a desire of happily playing with his companies in school, etc. Let's listen to him! Further information and story,I will add up soon both here and Wikiversity. [[File:Butterfly Lovers （Piano Music）played by piano student Shengran, Ma.wav|thumb|Hao Hao played a piano musical tune transformed from the famous Chinese tranditional music - Liangzhu (Butterfly Lovers) in piano classroom.]] '''Storys and comments''' I thought the emotional expressions as the dialogues between butterfly lovers one hand by the other、the detailed technique-treatments such as the arpegio-accompanyment、the eighth-chords exactness, and the top-part arms-force...were trained very fluent, comfortable and excellent. Therefore, as a piano teacher, I felt very pleased to introduce it to the public listening. Further technique&art-comments and studying storys I will up-send soon [[File:Little Trumpet (Piano Music) played by piano student Chen, Cao.wav|thumb|Little Trumpet (Piano Music) played by piano student Chen, Cao.wav]] 8d85x8av9jkucp3bcpojifrcr4pxufp 2690191 2690190 2024-12-04T02:36:45Z Jason M. C., Han 2696291 adding up new content from another piano student 2690191 wikitext text/x-wiki [[File:SUMMER played by piano student ZeyuCui.wav|thumb|Boy Fruit's "Summer Love" expressed to his kindness mother and soldier father]] '''Storys and Comments''' As piano pupils from childhood, we all knew: 'Summer', composed by Jeo Hishashi, is very famous in piano classroom. More information regarding with this piece of piano music Boy fruit played, please refer to Kikujiro (Wikipedia: https://en.m.wikipedia.org/wiki/Kikujiro ). Zeyu,Cui (Fruit) is my piano student - a little boy named Zeyu Cui is a little expert in its performance. He played it in many situations- in classroom, in life and somewhere traveling with piano. In his heart-music,you can hear: a piano boy's growing day after day and year after year, a tender expression of his love to mother and father, and a desire of happily playing with his companies in school, etc. Let's listen to him! Further information and story,I will add up soon both here and Wikiversity. [[File:Butterfly Lovers （Piano Music）played by piano student Shengran, Ma.wav|thumb|Hao Hao played a piano musical tune transformed from the famous Chinese tranditional music - Liangzhu (Butterfly Lovers) in piano classroom.]] '''Storys and comments''' I thought the emotional expressions as the dialogues between butterfly lovers one hand by the other、the detailed technique-treatments such as the arpegio-accompanyment、the eighth-chords exactness, and the top-part arms-force...were trained very fluent, comfortable and excellent. Therefore, as a piano teacher, I felt very pleased to introduce it to the public listening. Further technique&art-comments and studying storys I will up-send soon [[File:Little Trumpet (Piano Music) played by piano student Chen, Cao.wav|thumb|Little Trumpet (Piano Music) played by piano student Chen, Cao. ]] '''Storys and Comments''' The naught and clever boy played it as in his own personality. After many exercises, you can hear it looks like a smart fingering game from the nature of childhood, such as the situation in the break time between classes on the playground. That's fine, thereby, I would like to introduce it that musical (piano) education's true purpose was located in - studying happily from nature. Let's listen to him! 2n74k8ki7io5yobe6j2cknm7hdfw1yi 1 316904 2690111 2689979 2024-12-03T13:40:25Z Eyoungstrom 1933979 /* Please do not speedy delete! */ Reply 2690111 wikitext text/x-wiki == Please do not speedy delete! == Hi! This page is intended to be an area where resources can be shared to help educate and disseminate information about research in mental and behavioral health and allied disciplines. The vision is to have a set of pages that are linked back to this as the top of the page pile, using it to organize information about scales, benchmarks for clinical application, and links to OSF repositories with code and deidentified data. There is an overlapping set of tools that have been built out in the EBA and OTOPS sections of Wikiversity that are already in use at Nationwide Children's Hospital. Having a set of Wikiversity pages (not Wikipedia!) creates helpful interstitial material for organization and linking. There is obvious potential COI for me editing pages on Wikipedia about NCH or OSU, as I am now employed by them, so I invite people to watch these pages and help maintain NPOV. Having Wikiversity pages as a staging area also creates an opportunity to have new, demographically diverse and clinically sophisticated editors join the community and learn how to make contributions to Wiki platforms, while sharing more aspects of their work with a larger audience in an open science and teaching framework. [[User:Eyoungstrom|Eyoungstrom]] ([[User talk:Eyoungstrom|discuss]] • [[Special:Contributions/Eyoungstrom|contribs]]) 14:43, 2 December 2024 (UTC) :Hello {{ping|Eyoungstrom}} there was a reason why I personally did not act upon the speedy requests. It seems to have been done by a user who is not native to English Wikiversity, so they may not be familiar with what is allowed/what is not allowed on this project. I'm sure the user had good intentions, but Wikiversity's content is quite unique to other Wikimedia projects - and what may seem as "advertisements" on other wikis, are perfectly fine here as long as there is a clear [[Wikiversity:Learning resources|learning objective]] (which you've demonstrated). I'm inclined to remove the speedy requests, but I am currently on vacation at the moment. When I return, I will be removing the speedy deletion requests per your rationale and [[Wikiversity:What is Wikiversity?]]. Thanks! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 15:08, 2 December 2024 (UTC) ::Much appreciated! If any additional information would be helpful from us, just let me know. Meanwhile, have a wonderful vacation! [[User:Eyoungstrom|Eyoungstrom]] ([[User talk:Eyoungstrom|discuss]] • [[Special:Contributions/Eyoungstrom|contribs]]) 13:40, 3 December 2024 (UTC) ni2g86hs5nx94c5sz5euxwbpazcu80v 0 316906 2690201 2689996 2024-12-04T03:39:40Z Atcovi 276019 /* Module 14.2 - Social Dynamics of Organizations */ 2690201 wikitext text/x-wiki '''Organizational Theory, Dynamics, and Change''' ==Module 14.1 - Conceptual & Theoretical Foundations of Organizations== '''Organization''': A group of people who band together for a common goal and follow a number of procedures to develop these products & services. They need ''strategic planning'' (buying from/selling to the unorganized). These organizations are a "way of life". Successful organizations are able to integrate several organizing forces (HR, finance, marketing, production) smoothly. === Classic Organizational Theory === '''Classic organizational theory''' proposes that organizations should emphasize architecture of organization rather than the processes of operation. Bureaucracy is the ideal way. The following are methods for describing an organization: * Division of labor * Delegation of authority * Structure * Span of control The theory assumes there was one best configuration for an organization, and assumes that organizations affect the behaviour of their members, but not the other way around. === Human Relations Theory === The '''human relations theory''' adds a human element to the study of organizations. '''McGregor's Theory X & Theory Y''' goes as the following: * '''Theory X:''' Managers believe subordinate behavior must be controlled. * '''Theory Y:''' Managers believe subordinates are active members of the organization, and responsible for their own behavior. The ''growth perspective of Argyris'' suggests there is natural developmental sequence in humans that can either be improved or destroyed by an organization. The proposed growth is a natural & healthy experience for an individual. === Contingency Theories === 3 organization types are described: * Small batch organization * Large batch & mass production organization * Continuous process organization The span of control varies systematically by the organization type. Introduces technology. ==== Lawrence & Lorsch ==== Lawrence & Lorsch came up with: # '''Mechanistic organizations''': Depend on formal rules & regulations, small span of control # '''Organic organizations''': Less formal procedures, larger span of control. They also identified the department as an "important level" for understanding organizations. ==== Mintzberg ==== 6 forms of coordination: # Mutual adjustments based in informal communication. # Direct supervision # Standardization of work processes # Standardization of KSAOs necessary for production # Standardization of outputs # Standardization of norms ==== Tavistock Institute's Sociotechnical approach ==== This uncovered a number of dramatic changes in social patterns of work that accompany technological change. This includes joint consideration of technology & social patterns. === Recent Approaches & Conclusion === # '''Pfeffer's resource theory''': An organization must be viewed in context of connections to other organizations. He states that the key to organizational survival is the ability to acquire and maintain resources. The conclusion of the theories of organization is that motivation metaphors can be applied to organizational theories. == Module 14.2 - Social Dynamics of Organizations == === Climate & Culture === Brief history of climate consists of [https://www.mindtools.com/aieezpa/lewins-leadership-styles-framework Lewin's autocratic vs. democratic climate]. Recent investigations have found that multiple climates may exist with any organization (service climate and safety climate, for example). The word '''culture''' was introduced to address issues regarding value & meaning of actions taken place in organizations that were not encompassed in climate. The ''Organizational Culture Inventory (OCI)'' measures culture in organizations. When looking at climate vs. culture, basically... * '''Climate''' is about context in which actions take place (created at lower levels of organization). * '''Culture''' is about the meaning intended by these actions (created and conveyed from higher levels of organization) ''What about when cultures clash?'' For multinational corporations, acknowledging the existence of different cultures is key. The following models operate sufficiently under ethnocentrism, polycentrism, regiocentrism, and geocentrism. === Socialization & Concept of Person-Organization (P-O) Fit === '''Organizational socialization''': the process by which a new employee becomes aware of values & organizational procedures. Recruitment is seen as socialization, as seen from research findings. '''Socialization & P-O fit models''': the extent to which skills, abilities, & interests of individual are compatible with the job demands (person-job fit). These are broadened to include fit between the person and the organization (P-O fit). See also the [https://marcr.net/marcr-for-career-professionals/career-theory/career-theories-and-theorists/work-adjustment-theory-dawis-lofquist/ work adjustment model]. === Three Stages of Socialization === # '''Anticipatory Socialization''': Getting in (learning about prospective organizations). # '''The Encounter Stage''': Breaking in (first encounters with the new organization). # '''The Metamorphosis Stage''': Settling in (making full entry into the organization) === Schneider's ASA model === '''ASA''' --> Attraction-Selection-Attrition (ASA) model: Organizations attempt to ''ATTRACT'' and ''SELECT'' particular types of people. ''ATTRITION'' occurs through direct/indirect actions. == Module 14.3 - Organizational Development & Change (slide 28) == 26v4w7sg73ezw1znyhtg69furubp5l3 6 316910 2690206 2690041 2024-12-04T04:18:44Z Young1lim 21186 /* Summary */ 2690206 wikitext text/x-wiki == Summary == {{Information |Description=LIB.1A: Static Libraries (20241203 - 20241202) |Source={{own|Young1lim}} |Date=2024-12-03 |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}} dyw9c57tok1rtmmofmoh0yapdm6oogi 2690209 2690206 2024-12-04T04:20:17Z Young1lim 21186 /* Summary */ 2690209 wikitext text/x-wiki == Summary == {{Information |Description=LIB.2A: Shared Libraries (20241203 - 20241202) |Source={{own|Young1lim}} |Date=2024-12-03 |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}} l7yeverqn5abrcsvo72qofw6q4hp60d 6 316911 2690219 2690053 2024-12-04T04:25:14Z Young1lim 21186 /* Summary */ 2690219 wikitext text/x-wiki == Summary == {{Information |Description=LCal.8A: Combinator (20241203 - 20241202) |Source={{own|Young1lim}} |Date=2024-12-03 |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}} f1eb8ifdufm8v3lnmtu1dei3c78wezk 6 316912 2690216 2690054 2024-12-04T04:24:39Z Young1lim 21186 /* Summary */ 2690216 wikitext text/x-wiki == Summary == {{Information |Description=LCal.9A: Recursion (20241203 - 20240418) |Source={{own|Young1lim}} |Date=2024-12-02 |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}} pa6g3n8v2n94odr9pp6z4zk86d403mb 2690218 2690216 2024-12-04T04:24:59Z Young1lim 21186 /* Summary */ 2690218 wikitext text/x-wiki == Summary == {{Information |Description=LCal.9A: Recursion (20241203 - 20240418) |Source={{own|Young1lim}} |Date=2024-12-03 |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}} nlyp0npgh6i7m9wupl0i0axekhxuber 6 316913 2690228 2690056 2024-12-04T07:20:25Z Young1lim 21186 /* Summary */ 2690228 wikitext text/x-wiki == Summary == {{Information |Description=ARM.2ASM: Branch and Return Methods (20241203 - 20241202) |Source={{own|Young1lim}} |Date=2024-12-03 |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}} l3ya2hj5kph0lopwijqbgcztni9j30k 0 316923 2690117 2024-12-03T16:42:35Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Definition |Text= {{:Subgroup/Situation|pm=.}} We set {{ Relationchain |x | \sim_H|y || || || |pm= }} {{ Extra/Bracket |text=and say that {{mat|term= x |pm=}} and {{mat|term= y |pm=}} are equivalent |pm= }} if {{ Relationchain | x^{-1}y |\in| H || || || |pm=. }} |Textform=Definition |Category= |Word of definition=Equivalence relation for a subgroup }}" 2690117 wikitext text/x-wiki {{ Mathematical text/Definition |Text= {{:Subgroup/Situation|pm=.}} We set {{ Relationchain |x | \sim_H|y || || || |pm= }} {{ Extra/Bracket |text=and say that {{mat|term= x |pm=}} and {{mat|term= y |pm=}} are equivalent |pm= }} if {{ Relationchain | x^{-1}y |\in| H || || || |pm=. }} |Textform=Definition |Category= |Word of definition=Equivalence relation for a subgroup }} 4qv2gyj6msxr0p3f3xgiqtm0ch52f5y 0 316924 2690118 2024-12-03T16:44:41Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Situation{{{opt|}}} |Text= Let {{mat|term={{{G|G}}} |}} be a {{ Definitionlink |group| |pm=, }} and let {{ relationchain | {{{H|H}}} |\subseteq | {{{G|G}}} || || || }} be a {{ Definitionlink |subgroup| |pm={{{pm|}}} }} |Textform=Situation |}}" 2690118 wikitext text/x-wiki {{ Mathematical text/Situation{{{opt|}}} |Text= Let {{mat|term={{{G|G}}} |}} be a {{ Definitionlink |group| |pm=, }} and let {{ relationchain | {{{H|H}}} |\subseteq | {{{G|G}}} || || || }} be a {{ Definitionlink |subgroup| |pm={{{pm|}}} }} |Textform=Situation |}} rg3scxcfymd12naxyk78x3zc8rmh6y8 0 316925 2690120 2024-12-03T16:55:40Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Example |Text= In an {{ Extra/Bracket |text=additively written| |Ipm=|Epm= }} {{ Definitionlink |commutative group| |Context=| |pm= }} like {{mat|term= \Z |pm=}} or a {{ Definitionlink |vector space| |Context=| |pm= }} {{mat|term= V |pm=,}} and of a given {{ Definitionlink |subgroup| |Context=| |pm= }} {{mat|term= H |pm=,}} the equivalence relation {{ Relationchain |x |\sim_H|y || || || |pm= }} means {{ Relationchain | y-x |\in| H || || || |pm=,..." 2690120 wikitext text/x-wiki {{ Mathematical text/Example |Text= In an {{ Extra/Bracket |text=additively written| |Ipm=|Epm= }} {{ Definitionlink |commutative group| |Context=| |pm= }} like {{mat|term= \Z |pm=}} or a {{ Definitionlink |vector space| |Context=| |pm= }} {{mat|term= V |pm=,}} and of a given {{ Definitionlink |subgroup| |Context=| |pm= }} {{mat|term= H |pm=,}} the equivalence relation {{ Relationchain |x |\sim_H|y || || || |pm= }} means {{ Relationchain | y-x |\in| H || || || |pm=, }} that is, there exists a {{ Relationchain | h |\in| H || || || |pm= }} such that {{ Relationchain/display |y ||x+h || || || |pm=. }} The {{ Definitionlink |equivalence classes| |Context=| |pm= }} are of the form {{ Relationchain | x+H || {{Setcond|x+h|h \in H}} || || || |pm=. }} In case {{ Relationchain |H || \Z d |\subseteq|\Z || || |pm= }} with a fixed {{mat|term= d |pm=,}} the equivalence classes have the form {{ Math/display|term= H=\Z d, \, 1+H=\{\ldots, 1 -d, 1,1+d,1+2d, \ldots \}, \, 2+H=\{\ldots, 2-d, 2, 2+d,2+2d, \ldots \}, \ldots |pm=. }} These classes encompass those integer numbers that have, upon division by {{mat|term= d |pm=,}} the remainder {{mat|term= 0 |pm=,}} or {{mat|term= 1 |pm=,}} or {{mat|term= 2 |pm=,}} etc. They form a partition of {{mat|term= \Z|pm=.}} {{ inputimage |ParalleleGeradenEbene|png|230px {{!}} right {{!}} |Text=The equivalence classes of a linear subspace. |User=Mgausmann |Domain= |License=CC-by-sa 4.0 }} If {{ Relationchain |H ||U |\subseteq|V || || |pm= }} is a {{ Definitionlink |linear subspace| |Context=| |pm=, }} then the equivalence classes have the form {{ Relationchain | v+U || {{Setcond|v+u|u \in U}} || || || |pm= }} for a vector {{ Relationchain | v |\in| V || || || |pm=. }} This is ther {{ Definitionlink |affine space| |Context=| |pm= }} with starting point {{mat|term= v |pm=}} and the translating space {{mat|term= U |pm=}} {{ Extra/Bracket |text=in the sense of {{ Definitionlink |definition| |Context=| Definitionname=Affine subspace/Translated linear subspace/Definition |pm= }} |Ipm=|Epm=. }} The equivalence classes form a family of affine subspaces parallel to each other. |Textform=Example |Category= }} 8e2x9brq7i7d8p3jizao848er8z7ru6 0 316926 2690121 2024-12-03T17:00:02Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Fact |Text= {{ Factstructure |Situation={{:Subgroup/Situation||pm=.}} Let {{ Relationchain | x,y |\in| G || || || |pm= }} be elements. |Condition= |Segue= |Conclusion= Then the following statements are equivalent. {{ Enumeration7 |{{ Relationchain | x |\in|yH || || || |pm=. }} |{{ Relationchain | y |\in| xH || || || |pm=. }} |{{ Relationchain | y^{-1}x |\in| H || || || |pm=. }} |{{ Relationchain | x^{-1}y |\in| H || || || |pm=. }} |{{ Relationcha..." 2690121 wikitext text/x-wiki {{ Mathematical text/Fact |Text= {{ Factstructure |Situation={{:Subgroup/Situation||pm=.}} Let {{ Relationchain | x,y |\in| G || || || |pm= }} be elements. |Condition= |Segue= |Conclusion= Then the following statements are equivalent. {{ Enumeration7 |{{ Relationchain | x |\in|yH || || || |pm=. }} |{{ Relationchain | y |\in| xH || || || |pm=. }} |{{ Relationchain | y^{-1}x |\in| H || || || |pm=. }} |{{ Relationchain | x^{-1}y |\in| H || || || |pm=. }} |{{ Relationchain | xH \cap yH |\neq| \emptyset || || || |pm=. }} |{{ Relationchain |x |\sim_H|y || || || |pm=. }} |{{ Relationchain |xH ||yH || || || |pm=. }} }} |Extra= }} |Textform=Fact |Category= |Factname= }} 2rwk3u1ivutpmp7x3iyolfpaq5oby7n 0 316927 2690122 2024-12-03T17:13:31Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= The equivalence between {{mat|term= (1) |pm=}} and {{mat|term= (3) |pm=}} {{ Extra/Bracket |text=and between {{mat|term= (2) |pm=}} and {{mat|term= (4) |pm=}}| |pm= }} follows by multiplication with {{mat|term= y^{-1} |pm=}} and with {{mat|term= y |pm=.}} The equivalence between {{mat|term= (3) |pm=}} and {{mat|term= (4) |pm=}} follows by going to the inverse elements. From {{mat|term= (1)..." 2690122 wikitext text/x-wiki {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= The equivalence between {{mat|term= (1) |pm=}} and {{mat|term= (3) |pm=}} {{ Extra/Bracket |text=and between {{mat|term= (2) |pm=}} and {{mat|term= (4) |pm=}}| |pm= }} follows by multiplication with {{mat|term= y^{-1} |pm=}} and with {{mat|term= y |pm=.}} The equivalence between {{mat|term= (3) |pm=}} and {{mat|term= (4) |pm=}} follows by going to the inverse elements. From {{mat|term= (1) |pm=}} we get {{mat|term= (5) |pm=}} because of {{ Relationchain | 1 |\in| H || || || |pm=. }} If {{mat|term= (5) |pm=}} holds, then this means that {{ Relationchain |xh_1 ||yh_2 || || || |pm= }} holds with certain {{ Relationchain | h_1,h_2 |\in| H || || || |pm=. }} Therefore, {{ Relationchain | x || yh_2h_1^{-1} || || || |pm=, }} and {{mat|term= (1) |pm=}} is satisfied. (4) and (6) are equivalent due to the {{ Definitionlink |definition| |Definitionname=Group theory/Subgroup/Equivalence relation/Definition |pm=. }} Since the left cosets are the {{ Definitionlink |equivalence classes| |Context=| |pm=, }} the equivalence between (5) and (7) follows. |Closure= }} |Textform=Proof |Category=See }} 7hiyz1l1h523mjjz7ky0kss239gr7qp 0 316928 2690123 2024-12-03T17:16:53Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Definition |Text= {{:Subgroup/Situation|pm=.}} For every {{ Relationchain | x |\in| G || || || |pm=, }} the subset {{ Relationchain/display | xH || {{Setcond|xh|h \in H}} || || || |pm= }} is called the {{Word of definition|left coset of|pm=}} {{mat|term= x |pm=}} in {{mat|term= G |pm=}} with respect to {{mat|term= H |pm=.}} Every subset of this form is called a {{Word of definition|left coset|pm=.}} Accordingly, a set of the form {{ Relationchain/dis..." 2690123 wikitext text/x-wiki {{ Mathematical text/Definition |Text= {{:Subgroup/Situation|pm=.}} For every {{ Relationchain | x |\in| G || || || |pm=, }} the subset {{ Relationchain/display | xH || {{Setcond|xh|h \in H}} || || || |pm= }} is called the {{Word of definition|left coset of|pm=}} {{mat|term= x |pm=}} in {{mat|term= G |pm=}} with respect to {{mat|term= H |pm=.}} Every subset of this form is called a {{Word of definition|left coset|pm=.}} Accordingly, a set of the form {{ Relationchain/display | Hx || {{Setcond|hx|h \in H}} || || || |pm= }} is called the {{Word of definition|right coset|pm=}} {{ Extra/Bracket |text=of {{mat|term= x |pm=}}| |Ipm=|Epm=. }} |Textform=Definition |Category= |Word of definition=coset }} 8emhogkvgyl2jq3xm9kcarsc5mr62j8 0 316929 2690124 2024-12-03T17:23:44Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Fact |Text= {{ Factstructure |Situation={{:Finite group/Situation|pm=,}} and let {{ Relationchain |H |\subseteq|G || || || |pm= }} denote a {{ Definitionlink |subgroup| |pm= }} of {{mat|term= G |pm=.}} |Condition= |Segue= |Conclusion= Then the cardinality {{mat|term= {{op:Number|H}} |pm=}} divides the cardinality {{mat|term= {{op:Number|G}} |pm=.}} }} |Textform=Fact |Category= |Factname=Lagrange's theorem }}" 2690124 wikitext text/x-wiki {{ Mathematical text/Fact |Text= {{ Factstructure |Situation={{:Finite group/Situation|pm=,}} and let {{ Relationchain |H |\subseteq|G || || || |pm= }} denote a {{ Definitionlink |subgroup| |pm= }} of {{mat|term= G |pm=.}} |Condition= |Segue= |Conclusion= Then the cardinality {{mat|term= {{op:Number|H}} |pm=}} divides the cardinality {{mat|term= {{op:Number|G}} |pm=.}} }} |Textform=Fact |Category= |Factname=Lagrange's theorem }} 0t4hovsk3pozm8xjyfr2v5nuk8vbkmv 0 316930 2690125 2024-12-03T17:24:15Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Situation{{{opt|}}} |Text= Let {{mat|term= G |pm=}} be a finite {{ Definitionlink |Premath= |group| |Context=| |pm={{{pm|}}} }} |Textform=Situation |}}" 2690125 wikitext text/x-wiki {{ Mathematical text/Situation{{{opt|}}} |Text= Let {{mat|term= G |pm=}} be a finite {{ Definitionlink |Premath= |group| |Context=| |pm={{{pm|}}} }} |Textform=Situation |}} 47whgj7dp7w842fy12pv5iwipt2r2mw 0 316931 2690126 2024-12-03T17:29:28Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= We consider the {{ Definitionlink |left cosets| |pm= }} {{ Relationchain |gH | {{defeq|}} |{{Setcond| gh | h \in H }} || || || |pm= }} for all {{ Relationchain | g |\in| G || || || |pm=. }} The mapping {{ Mapping/display |name= |H|gH |h|gh |pm=, }} is a bijection between {{ Mathcor|term1= H |and|term2= gH |pm=, }} so that all cosets have the same number of elements {{ Extra/Bracket |text=..." 2690126 wikitext text/x-wiki {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= We consider the {{ Definitionlink |left cosets| |pm= }} {{ Relationchain |gH | {{defeq|}} |{{Setcond| gh | h \in H }} || || || |pm= }} for all {{ Relationchain | g |\in| G || || || |pm=. }} The mapping {{ Mapping/display |name= |H|gH |h|gh |pm=, }} is a bijection between {{ Mathcor|term1= H |and|term2= gH |pm=, }} so that all cosets have the same number of elements {{ Extra/Bracket |text=namely {{mat|term= {{op:Number|H}} |pm=}} | |pm=. }} The cosets form {{ Extra/Bracket |text=as they are the equivalence classes| |Ipm=|Epm= }} a {{ Definitionlink |partition| |Context=set| |pm= }} of {{mat|term= G |pm=.}} Hence, {{mat|term= {{op:Number|G|}} |pm=}} is a multiple of {{mat|term= {{op:Number|H|}} |pm=.}} |Closure= }} |Textform=Proof |Category=See }} es8qap9l1zeplxgq9zrm1mlv5crgvm6 0 316932 2690127 2024-12-03T17:37:44Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Fact |Text= {{ Factstructure |Situation= Let {{mat|term= G |pm=}} be a finite {{ Definitionlink |group| |pm=, }} and let {{ Relationchain | g |\in| G |pm= }} denote an element. |Condition= |Segue= |Conclusion= Then the {{ Definitionlink |order of {{mat|term= g |pm=}}| |Definitionname=Group theory/Elementordnung/Definition |pm= }} divides the {{ Definitionlink |group order| |pm=. }} |Extra= }} |Textform=Fact |Factname=Lagrange's theorem (order of a..." 2690127 wikitext text/x-wiki {{ Mathematical text/Fact |Text= {{ Factstructure |Situation= Let {{mat|term= G |pm=}} be a finite {{ Definitionlink |group| |pm=, }} and let {{ Relationchain | g |\in| G |pm= }} denote an element. |Condition= |Segue= |Conclusion= Then the {{ Definitionlink |order of {{mat|term= g |pm=}}| |Definitionname=Group theory/Elementordnung/Definition |pm= }} divides the {{ Definitionlink |group order| |pm=. }} |Extra= }} |Textform=Fact |Factname=Lagrange's theorem (order of a group element) |Request= }} r3qsp7fqjyotc3sqos2tfck2un2iguo 0 316933 2690128 2024-12-03T17:39:54Z Adnanyounis123 2986816 i have created a page called internet engineering added two chapters in it 1.introduction to telecommunications 2. wiring and telephone office exchanges 2690128 wikitext text/x-wiki ==== 1.Introduction to telecommunications. ==== ==== 2. wiring and telephone office exchanges. ==== sstx44hs3u3fe68n7qsbv4a6s6rh1n2 2690131 2690128 2024-12-03T17:42:19Z Adnanyounis123 2986816 i included a third chapter integration and ethernet protocol 2690131 wikitext text/x-wiki ==== 1.Introduction to telecommunications. ==== ==== 2. wiring and telephone office exchanges. ==== ==== 3. Integration and ethernet protocol. ==== ka1bwtow5fila8qabgoxcb1tdmk1972 2690134 2690131 2024-12-03T17:43:53Z Adnanyounis123 2986816 i included a third chapter integration and ethernet protocol 2690134 wikitext text/x-wiki ==== 1.Introduction to telecommunications. ==== ==== 2. wiring and telephone office exchanges. ==== ==== [[Integration and ethernet protocol|3. Integration and ethernet protocol.]] ==== dmdq0qcflj3ruhwbfrdmkf7iy2y4xn5 2690136 2690134 2024-12-03T17:45:53Z Adnanyounis123 2986816 /* 1.Introduction to telecommunications. */ i appended the struggle of nationalists 2690136 wikitext text/x-wiki ==== 1.Introduction to telecommunications: the struggle of nationalists. ==== ==== 2. wiring and telephone office exchanges. ==== ==== [[Integration and ethernet protocol|3. Integration and ethernet protocol.]] ==== l8u8uawy6ypytw9elr2gk6zlig3hlrh 2690141 2690136 2024-12-03T18:24:35Z Adnanyounis123 2986816 i included link for first chapter introduction to telecommunications 2690141 wikitext text/x-wiki ==== [[Introduction to telecommunications: the struggle of nationalists|1.Introduction to telecommunications: the struggle of nationalists.]] ==== ==== 2. wiring and telephone office exchanges. ==== ==== [[Integration and ethernet protocol|3. Integration and ethernet protocol.]] ==== bm82y0wegi6z5mag7hm1zcdj0440807 0 316934 2690129 2024-12-03T17:41:48Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Proof{{{opt|}}} |Text= {{ Proofstructure |Strategy= |Notation= |Proof= {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Let {{mat|term= H |pm=}} be the subgroup generated by {{mat|term= g |pm=.}} Due to {{ Factlink |Factname= Group theory/Finite/Order/Different/Fact |pm=, }} we have {{ Relationchain/display | {{op:Group element order|g|}} || {{op:Group order/ord|H|}} || || || |pm=. }} Therefore, due to {{ Factlink |..." 2690129 wikitext text/x-wiki {{ Mathematical text/Proof{{{opt|}}} |Text= {{ Proofstructure |Strategy= |Notation= |Proof= {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Let {{mat|term= H |pm=}} be the subgroup generated by {{mat|term= g |pm=.}} Due to {{ Factlink |Factname= Group theory/Finite/Order/Different/Fact |pm=, }} we have {{ Relationchain/display | {{op:Group element order|g|}} || {{op:Group order/ord|H|}} || || || |pm=. }} Therefore, due to {{ Factlink |Factname= Group theory (algebra)/Lagrange's theorem/Fact |Refname= Fakt |pm=, }} this number divides the group order of {{mat|term= G |pm=.}} |Closure= }} |Textform=Proof |Category=See }} |Closure= }} |Textform=Proof |}} gt5q5uuwfchkv65p4r9anzy9c09ff29 2690130 2690129 2024-12-03T17:42:09Z Bocardodarapti 289675 2690130 wikitext text/x-wiki {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Let {{mat|term= H |pm=}} be the subgroup generated by {{mat|term= g |pm=.}} Due to {{ Factlink |Factname= Group theory/Finite/Order/Different/Fact |pm=, }} we have {{ Relationchain/display | {{op:Group element order|g|}} || {{op:Group order/ord|H|}} || || || |pm=. }} Therefore, due to {{ Factlink |Factname= Group theory (algebra)/Lagrange's theorem/Fact |Refname= Fakt |pm=, }} this number divides the group order of {{mat|term= G |pm=.}} |Closure= }} |Textform=Proof |Category=See }} qvujf048unytr55mppwd1u3mkrg4evn 10 316935 2690132 2024-12-03T17:42:27Z Bocardodarapti 289675 New resource with "<includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex=\operatorname{ord} \, ({{{1}}}) |#default =\operatorname{ord} \, ({{{1}}}) }}</includeonly><noinclude>{{Semantic template|}}</noinclude>" 2690132 wikitext text/x-wiki <includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex=\operatorname{ord} \, ({{{1}}}) |#default =\operatorname{ord} \, ({{{1}}}) }}</includeonly><noinclude>{{Semantic template|}}</noinclude> 28t1qcirdvym9nfv6qwxkjwgfze40j5 10 316936 2690133 2024-12-03T17:43:12Z Bocardodarapti 289675 New resource with "<includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex=\operatorname{ord} \, ({{{1}}}) |#default =\operatorname{ord} \, ({{{1}}}) }}</includeonly><noinclude>{{Semantic template|}}</noinclude>" 2690133 wikitext text/x-wiki <includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex=\operatorname{ord} \, ({{{1}}}) |#default =\operatorname{ord} \, ({{{1}}}) }}</includeonly><noinclude>{{Semantic template|}}</noinclude> 28t1qcirdvym9nfv6qwxkjwgfze40j5 0 316937 2690135 2024-12-03T17:45:30Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Definition |Text= For a {{ Definitionlink |subgroup| |pm= }} {{ Relationchain |H |\subseteq|G || || || |pm=, }} the cardinality of the {{ Extra/Bracket |text=left- or right-| |Ipm=-|Epm= }}{{ Definitionlink |cosets| |pm= }} is called the {{Word of definition|index|pm=}} of {{mat|term= H |pm=}} in {{mat|term= G |pm=,}} denoted as {{ Math/display|term= {{op:Group index|H|G}} |pm=. }} |Textform=Definition |Category= |Word of definition=Index (subgr..." 2690135 wikitext text/x-wiki {{ Mathematical text/Definition |Text= For a {{ Definitionlink |subgroup| |pm= }} {{ Relationchain |H |\subseteq|G || || || |pm=, }} the cardinality of the {{ Extra/Bracket |text=left- or right-| |Ipm=-|Epm= }}{{ Definitionlink |cosets| |pm= }} is called the {{Word of definition|index|pm=}} of {{mat|term= H |pm=}} in {{mat|term= G |pm=,}} denoted as {{ Math/display|term= {{op:Group index|H|G}} |pm=. }} |Textform=Definition |Category= |Word of definition=Index (subgroup) }} ck6tp191mmbvluuhlcqoci080wuh2n4 0 316938 2690137 2024-12-03T17:51:25Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Fact{{{opt|}}} |Text= {{ Factstructure|typ= |Situation= Let {{mat|term= G |}} be a finite {{ Definitionlink |group| |pm=. }} |Condition= |Segue= |Conclusion= Then every element {{ Relationchain | g |\in| G |SZ= }} has finite {{ Definitionlink |order| |Context=Group element |pm=. }} |Extra= The powers {{ Math/display|term= g^0=e_G,\, g^1=g,\, g^2 {{commadots|}} g^{ {{op:Group element order|g}}-1} }} are all different. }} |Textform=Fact |Category=..." 2690137 wikitext text/x-wiki {{ Mathematical text/Fact{{{opt|}}} |Text= {{ Factstructure|typ= |Situation= Let {{mat|term= G |}} be a finite {{ Definitionlink |group| |pm=. }} |Condition= |Segue= |Conclusion= Then every element {{ Relationchain | g |\in| G |SZ= }} has finite {{ Definitionlink |order| |Context=Group element |pm=. }} |Extra= The powers {{ Math/display|term= g^0=e_G,\, g^1=g,\, g^2 {{commadots|}} g^{ {{op:Group element order|g}}-1} }} are all different. }} |Textform=Fact |Category= |Factname= }} tfc8ib33mt5nvrihudmolvoiiw52ytm 0 316939 2690138 2024-12-03T17:55:46Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Definition{{{opt|}}} |Text= For a finite {{ Definitionlink |group| }} {{mat|term= G |pm=,}} its cardinality is called the {{Word of definition|group order|pm=,}} written as {{ Relationchain/display | {{op:Group order/ord|G}} || {{op:Number|G}} || || || |pm=. }} |Textform=Definition |Word of definition=Group order |}}" 2690138 wikitext text/x-wiki {{ Mathematical text/Definition{{{opt|}}} |Text= For a finite {{ Definitionlink |group| }} {{mat|term= G |pm=,}} its cardinality is called the {{Word of definition|group order|pm=,}} written as {{ Relationchain/display | {{op:Group order/ord|G}} || {{op:Number|G}} || || || |pm=. }} |Textform=Definition |Word of definition=Group order |}} 2hjxxifvfw0tuwok90r4eefiymig68z 0 316940 2690140 2024-12-03T18:23:06Z Adnanyounis123 2986816 i included two paragraph i will include more information in the pages 2690140 wikitext text/x-wiki == Introduction to telecommunications == My name is adnan younis. i am muslim and baloch from the khosa tribe. i have lived in Qatar for 22 years . i have written this course on telecommunications so that anybody can become telecom engineer. ok first of all in this course i will not explain old technologies like 3g mobile networks. only new technologies will be built like 5g and multi-gig networks. == The Nationalist Dream == As a baloch nationalist its my job to provide baloch nation all happiness. the real reason of writing this course is because baloch nation dont have internet . they dont even have 3g service. so all these years i read books from electronics to microprocessor to operating systems and trying to understand them and now i am writing all this information so that one day the baloch nation has internet. so this is my dream to built internet for them. == A Wrong Act == 08fqubo7czabk37k3f5is8nnp3x7d9t 6 316941 2690143 2024-12-03T18:34:28Z Young1lim 21186 {{Information |Description=Carry Flags (20241202 - 20241130) |Source={{own|Young1lim}} |Date=2024-12-03 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2690143 wikitext text/x-wiki == Summary == {{Information |Description=Carry Flags (20241202 - 20241130) |Source={{own|Young1lim}} |Date=2024-12-03 |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}} ipn2cmmhxfuw9y8jabhakhnj0f1tulk 6 316942 2690145 2024-12-03T18:35:23Z Young1lim 21186 {{Information |Description=Carry Flags (20241203 - 20241202) |Source={{own|Young1lim}} |Date=2024-12-03 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2690145 wikitext text/x-wiki == Summary == {{Information |Description=Carry Flags (20241203 - 20241202) |Source={{own|Young1lim}} |Date=2024-12-03 |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}} 6fjsjmc30wrdcrs74qrcu3ft9mwa4rx 1 316943 2690147 2024-12-03T19:07:17Z 88.212.19.72 /* Correctness */ new section 2690147 wikitext text/x-wiki == Correctness == Which version of Firefox was this tested on? I currently use 133.0 and the moz_favicons table is in completely different database, not in the places.sqlite [[Special:Contributions/88.212.19.72|88.212.19.72]] ([[User talk:88.212.19.72|discuss]]) 19:07, 3 December 2024 (UTC) atel4yt4qjkf7il5jk8h31sc397gjjx 0 316944 2690148 2024-12-03T19:26:28Z UniBambergIslamicStudies 2987517 New resource with "[[The Bamberg Introduction to the History of Islam (BIHI) 02|2 <<<]] — [[The Bamberg Introduction to the History of Islam (BIHI) 04|>>> 4]] = 3. The Prophet of Yathrib and the New Polity (622-630) = The center of the new religion shifts to the oasis of Yathrib, with warfare taking center stage. Muḥammad and his followers engage in battles against pagan Mecca and increasingly come into conflict with the Jews of Yathrib, who are ultimately expelled from the oasis. As..." 2690148 wikitext text/x-wiki [[The Bamberg Introduction to the History of Islam (BIHI) 02|2 <<<]] — [[The Bamberg Introduction to the History of Islam (BIHI) 04|>>> 4]] = 3. The Prophet of Yathrib and the New Polity (622-630) = The center of the new religion shifts to the oasis of Yathrib, with warfare taking center stage. Muḥammad and his followers engage in battles against pagan Mecca and increasingly come into conflict with the Jews of Yathrib, who are ultimately expelled from the oasis. As the leader of the nascent community, Muḥammad implements a series of legal, social, and ritual reforms. gw2a29lbk8v9mijtw505qgl306sq70v 10 316945 2690167 2024-12-03T22:50:01Z Watchduck 137431 New resource with "{| class="wikitable" style="text-align: center;" !colspan="5"| 3-ary !colspan="2" rowspan="2" style="border-left: 3px solid black;"| 4-ary noble |- !colspan="3"| truth tables !colspan="2" style="color: #a37a51; border-left: 2px solid gray;"| Ж |- | 0001 0000 | 8 | [[File:Venn 0001 0000.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 136 | [[File:Venn 0001 0001.svg|25px]] |style="border-left: 3px solid black;"| 0000 0001 0001 0000 | 2176 |- | 0000 0100..." 2690167 wikitext text/x-wiki {| class="wikitable" style="text-align: center;" !colspan="5"| 3-ary !colspan="2" rowspan="2" style="border-left: 3px solid black;"| 4-ary noble |- !colspan="3"| truth tables !colspan="2" style="color: #a37a51; border-left: 2px solid gray;"| Ж |- | 0001 0000 | 8 | [[File:Venn 0001 0000.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 136 | [[File:Venn 0001 0001.svg|25px]] |style="border-left: 3px solid black;"| 0000 0001 0001 0000 | 2176 |- | 0000 0100 | 32 | [[File:Venn 0000 0100.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 160 | [[File:Venn 0000 0101.svg|25px]] |style="border-left: 3px solid black;"| 0000 0001 0000 0100 | 8320 |- | 0000 0010 | 64 | [[File:Venn 0000 0010.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 192 | [[File:Venn 0000 0011.svg|25px]] |style="border-left: 3px solid black;"| 0000 0001 0000 0010 | 16512 |- |style="border-top: 2px solid gray;"| 0001 0100 |style="border-top: 2px solid gray;"| 40 |style="border-top: 2px solid gray;"| [[File:Venn 0001 0100.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray; border-top: 2px solid gray;"| 40 |style="border-top: 2px solid gray;"| [[File:Venn 0001 0100.svg|25px]] |style="border-left: 3px solid black;"| 0000 0000 0001 0100 | 10240 |- | 0001 0010 | 72 | [[File:Venn 0001 0010.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 72 | [[File:Venn 0001 0010.svg|25px]] |style="border-left: 3px solid black;"| 0000 0000 0001 0010 | 18432 |- | 0000 0110 | 96 | [[File:Venn 0000 0110.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 96 | [[File:Venn 0000 0110.svg|25px]] |style="border-left: 3px solid black;"| 0000 0000 0000 0110 | 24576 |}<noinclude> [[Category:Studies of Boolean functions]] </noinclude> j7irfjnx1pndm3zoue6941c80uo5rma 2690168 2690167 2024-12-03T22:50:31Z Watchduck 137431 2690168 wikitext text/x-wiki {| class="wikitable" style="text-align: center;" !colspan="5"| 3-ary !colspan="2" rowspan="2" style="border-left: 3px solid black;"| 4-ary noble |- !colspan="3"| truth tables !colspan="2" style="color: #a37a51; border-left: 2px solid gray;"| Ж |- | 0001 0000 | 8 | [[File:Venn 0001 0000.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 136 | [[File:Venn 0001 0001.svg|25px]] |style="border-left: 3px solid black;"| 0000 0001 0001 0000 | 2176 |- | 0000 0100 | 32 | [[File:Venn 0000 0100.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 160 | [[File:Venn 0000 0101.svg|25px]] |style="border-left: 3px solid black;"| 0000 0001 0000 0100 | 8320 |- | 0000 0010 | 64 | [[File:Venn 0000 0010.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 192 | [[File:Venn 0000 0011.svg|25px]] |style="border-left: 3px solid black;"| 0000 0001 0000 0010 | 16512 |- |style="border-top: 2px solid gray;"| 0001 0100 |style="border-top: 2px solid gray;"| 40 |style="border-top: 2px solid gray;"| [[File:Venn 0001 0100.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray; border-top: 2px solid gray;"| 40 |style="border-top: 2px solid gray;"| [[File:Venn 0001 0100.svg|25px]] |style="border-left: 3px solid black;"| 0000 0000 0001 0100 | 10240 |- | 0001 0010 | 72 | [[File:Venn 0001 0010.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 72 | [[File:Venn 0001 0010.svg|25px]] |style="border-left: 3px solid black;"| 0000 0000 0001 0010 | 18432 |- | 0000 0110 | 96 | [[File:Venn 0000 0110.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 96 | [[File:Venn 0000 0110.svg|25px]] |style="border-left: 3px solid black;"| 0000 0000 0000 0110 | 24576 |}<noinclude> [[Category:Principalities and dominions of Boolean functions]] </noinclude> 8wkilyc7w7jdjqx0wubzxony98j9man 2690170 2690168 2024-12-03T22:51:22Z Watchduck 137431 Watchduck moved page [[Template:Principalities and dominions of Boolean functions/example table king index 8]] to [[Template:Principalities and dominions/example table king index 8]] 2690168 wikitext text/x-wiki {| class="wikitable" style="text-align: center;" !colspan="5"| 3-ary !colspan="2" rowspan="2" style="border-left: 3px solid black;"| 4-ary noble |- !colspan="3"| truth tables !colspan="2" style="color: #a37a51; border-left: 2px solid gray;"| Ж |- | 0001 0000 | 8 | [[File:Venn 0001 0000.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 136 | [[File:Venn 0001 0001.svg|25px]] |style="border-left: 3px solid black;"| 0000 0001 0001 0000 | 2176 |- | 0000 0100 | 32 | [[File:Venn 0000 0100.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 160 | [[File:Venn 0000 0101.svg|25px]] |style="border-left: 3px solid black;"| 0000 0001 0000 0100 | 8320 |- | 0000 0010 | 64 | [[File:Venn 0000 0010.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 192 | [[File:Venn 0000 0011.svg|25px]] |style="border-left: 3px solid black;"| 0000 0001 0000 0010 | 16512 |- |style="border-top: 2px solid gray;"| 0001 0100 |style="border-top: 2px solid gray;"| 40 |style="border-top: 2px solid gray;"| [[File:Venn 0001 0100.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray; border-top: 2px solid gray;"| 40 |style="border-top: 2px solid gray;"| [[File:Venn 0001 0100.svg|25px]] |style="border-left: 3px solid black;"| 0000 0000 0001 0100 | 10240 |- | 0001 0010 | 72 | [[File:Venn 0001 0010.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 72 | [[File:Venn 0001 0010.svg|25px]] |style="border-left: 3px solid black;"| 0000 0000 0001 0010 | 18432 |- | 0000 0110 | 96 | [[File:Venn 0000 0110.svg|25px]] |style="color: #a37a51; border-left: 2px solid gray;"| 96 | [[File:Venn 0000 0110.svg|25px]] |style="border-left: 3px solid black;"| 0000 0000 0000 0110 | 24576 |}<noinclude> [[Category:Principalities and dominions of Boolean functions]] </noinclude> 8wkilyc7w7jdjqx0wubzxony98j9man 14 316946 2690169 2024-12-03T22:50:34Z Watchduck 137431 New resource with "[[Category:Studies of Boolean functions]]" 2690169 wikitext text/x-wiki [[Category:Studies of Boolean functions]] 8d5h2ie6o1p539musn2sgcl9fe7uy0v 10 316947 2690171 2024-12-03T22:51:22Z Watchduck 137431 Watchduck moved page [[Template:Principalities and dominions of Boolean functions/example table king index 8]] to [[Template:Principalities and dominions/example table king index 8]] 2690171 wikitext text/x-wiki #REDIRECT [[Template:Principalities and dominions/example table king index 8]] 5b9e07133n7vqpspy09h0q8e47h0yqj 0 316948 2690172 2024-12-03T22:51:37Z Watchduck 137431 New resource with "{{Boolf header}} {| class="wikitable" style="float: right;" ! ! truth tables ! Zhegalkin indices |- ! principality | [[File:3T principality; faction size 6; king index 8.svg|200px]] | [[File:3Z principality; faction size 6; king index 8.svg|200px]] |- ! dominion | [[File:3T dominion; faction size 6; king index 8.svg|200px]] | [[File:3Z dominion; faction size 6; king index 8.svg|200px]] |} A principality is a set of ''n''-ary truth tables whose (''n''+1)-ary Noble Boo..." 2690172 wikitext text/x-wiki {{Boolf header}} {| class="wikitable" style="float: right;" ! ! truth tables ! Zhegalkin indices |- ! principality | [[File:3T principality; faction size 6; king index 8.svg|200px]] | [[File:3Z principality; faction size 6; king index 8.svg|200px]] |- ! dominion | [[File:3T dominion; faction size 6; king index 8.svg|200px]] | [[File:3Z dominion; faction size 6; king index 8.svg|200px]] |} A principality is a set of ''n''-ary truth tables whose (''n''+1)-ary [[Noble Boolean functions|noble]] equivalents form a {{BF-prop|faction}}.<br> Dominions are closely related to them. The reversed truth tables of the principalities are the Zhegalkin indices of the dominion. The following table shows the six members of the red principality, which are also shown in the matrices on the right.<br> <small style="opacity: .5;">A representative of the 4-ary noble faction can be seen in the bottom left corner of [[:commons:File:Representatives of 4-ary royal factions.svg|this]] image.<br><small>(It is easily seen, that this tetrahedron can be permuted into six different positions.)</small></small> {{Principalities and dominions/example table king index 8}} '''Overviews on Commons:''' {{Commons catlink|2-ary Boolean functions in tesseract matrix; principalities and dominions|2-ary}}, {{Commons catlink|3-ary Boolean functions in octeract matrix; principalities and dominions|3-ary}}, {{Commons catlink|4-ary Boolean functions in 16-cube matrix; principalities and dominions|4-ary}}<br> <small>Interesting subsets are those with entries [[commons:Category:3-ary Zhegalkin indices in octeract matrix; great principalities; with entries on diagonal|on the diagonal]] and [[commons:Category:3-ary Zhegalkin indices in octeract matrix; great principalities; with entries in top row|in the top row]] of the matrix of Zhegalkin indices.</small> [[Category:Principalities and dominions of Boolean functions]] d4mab38rcrvhj70kvsjcs2tsu09dj8v 2690174 2690172 2024-12-03T23:26:14Z Watchduck 137431 2690174 wikitext text/x-wiki {{Boolf header}} {| class="wikitable" style="float: right;" ! ! truth tables ! Zhegalkin indices |- ! principality | [[File:3T principality; faction size 6; king index 8.svg|200px]] | [[File:3Z principality; faction size 6; king index 8.svg|200px]] |- ! dominion | [[File:3T dominion; faction size 6; king index 8.svg|200px]] | [[File:3Z dominion; faction size 6; king index 8.svg|200px]] |} A principality is a set of ''n''-ary truth tables whose (''n''+1)-ary [[Noble Boolean functions|noble]] equivalents form a {{BF-prop|faction}}.<br> Dominions are closely related to them. The reversed truth tables of the principalities are the Zhegalkin indices of the dominion. The following table shows the six members of the red principality, which are also shown in the matrices on the right.<br> <small style="opacity: .5;">A representative of the 4-ary noble faction can be seen in the bottom left corner of [[:commons:File:Representatives of 4-ary royal factions.svg|this]] image.<br><small>(It is easily seen, that this tetrahedron can be permuted into six different positions.)</small></small> {{Principalities and dominions/example table king index 8}} '''Overviews on Commons:''' {{Commons catlink|2-ary Boolean functions in tesseract matrix; principalities and dominions|2-ary}}, {{Commons catlink|3-ary Boolean functions in octeract matrix; principalities and dominions|3-ary}}, {{Commons catlink|4-ary Boolean functions in 16-cube matrix; principalities and dominions|4-ary}}<br> <small>Interesting subsets are those with entries [[commons:Category:3-ary Zhegalkin indices in octeract matrix; great principalities; with entries on diagonal|on the diagonal]] and [[commons:Category:3-ary Zhegalkin indices in octeract matrix; great principalities; with entries in top row|in the top row]] of the matrix of Zhegalkin indices.</small> ---- Principalities follow directly from the concept of [[Noble Boolean functions|nobles]]. Dominions are less obvious, but arguably more important. The [[Boolf-soft#quaestor|quaestors]] of each [[Boolf-hard#faction|faction]] form a dominion. Many factions with the same quadrant belong to the same dominion.<br> Take 0100 1011 [[File:Venn 0100 1011.svg|25px]] {{zhe|26}} as an example. <small>(It has quadrant 2)</small>.<br> For arity 3 the quaestors are {3, 5, 9} <small>(yellow in [[:File:2T dominion; faction size 3; king index 2.svg|this]] file)</small> and for arity 4 they are {15, 51, 85, 153, 165, 195} <small>(yellow in [[:File:3T dominion; faction size 6; king index 8.svg|this]] file, also shown above in the bottom left corner)</small>. [[Category:Principalities and dominions of Boolean functions]] i4ngkindzs55tpo2mpd1jipl43weqg4 0 316949 2690196 2024-12-04T03:17:09Z Lucasrbrown23 2994536 Joshua chapter one 2690196 wikitext text/x-wiki < <bdi>[[Bible]]</bdi> | <bdi>[[Bible/King James|King James]]</bdi> | <bdi>[[Bible/King James/Documentary Hypothesis|Documentary Hypothesis]]</bdi> According to the documentary hypothesis, Deuteronomy is composed from a number of originally independent sources joined by a redactor. There follows the text of Deuteronomy in the King James Version, with sources highlighted according to the documentary hypothesis. Further subdivisions of the main sources are viewable by reading the individual source pages. * The [[wikipedia:Jahwist|"Jahwist Source"]] is highlighted in {{font|color=#000088|navy blue}} <small>([[Bible, English, King James, Documentary Hypothesis, Deuteronomist source|view in isolation]])</small> * The [[wikipedia:Elohist|"Elohist source"]] is highlighted in {{font|color=#008888|teal blueish grey}}y <small>([[Bible, English, King James, Documentary Hypothesis, JE source, Elohist source|view in isolation]])</small> * The [[wikipedia:Priestly_source|"Priestly source"]] is highlighted in {{font|color=#888800|olive yellow}} <small>([[Bible, English, King James, Documentary Hypothesis, Priestly source|view in isolation]])</small> * The "Additions by the Redactor and other late insertions" are highlighted in {{font|color=#880000|maroon red}} == Chapter 1 == ¹Now after the death of Moses the servant of the LORD it came to pass, that the LORD spake unto Joshua the son of Nun, Moses' minister, saying, ² Moses my servant is dead; now therefore arise, go over this Jordan, thou, and all this people, unto the land which I do give to them, even to the children of Israel. ³ Every place that the sole of your foot shall tread upon, that have I given unto you, as I said unto Moses. ⁴ From the wilderness and this Lebanon even unto the great river, the river Euphrates, all the land of the Hittites, and unto the great sea toward the going down of the sun, shall be your coast. ⁵ There shall not any man be able to stand before thee all the days of thy life: as I was with Moses, so I will be with thee: I will not fail thee, nor forsake thee. ⁶ Be strong and of a good courage: for unto this people shalt thou divide for an inheritance the land, which I sware unto their fathers to give them. ⁷ Only be thou strong and very courageous, that thou mayest observe to do according to all the law, which Moses my servant commanded thee: turn not from it ''to'' the right hand or ''to'' the left, that thou mayest prosper whithersoever thou goest. ⁸ This book of the law shall not depart out of thy mouth; but thou shalt meditate therein day and night, that thou mayest observe to do according to all that is written therein: for then thou shalt make thy way prosperous, and then thou shalt have good success. ⁹ Have not I commanded thee? Be strong and of a good courage; be not afraid, neither be thou dismayed: for the LORD thy God is with thee whithersoever thou goest. ¹⁰ Then Joshua commanded the officers of the people, saying, ¹¹ Pass through the host, and command the people, saying, Prepare you victuals; for within three days ye shall pass over this Jordan, to go in to possess the land, which the LORD your God giveth you to possess it. ¹² And to the Reubenites, and to the Gadites, and to half the tribe of Manasseh, spake Joshua, saying, ¹³ Remember the word which Moses the servant of the LORD commanded you, saying, The LORD your God hath given you rest, and hath given you this land. ¹⁴ Your wives, your little ones, and your cattle, shall remain in the land which Moses gave you on this side Jordan; but ye shall pass before your brethren armed, all the mighty men of valour, and help them; ¹⁵ Until the LORD have given your brethren rest, as he hath given you, and they also have possessed the land which the LORD your God giveth them: then ye shall return unto the land of your possession, and enjoy it, which Moses the LORD's servant gave you on this side Jordan toward the sunrising. ¹⁶ And they answered Joshua, saying, All that thou commandest us we will do, and whithersoever thou sendest us, we will go. ¹⁷ According as we hearkened unto Moses in all things, so will we hearken unto thee: only the LORD thy God be with thee, as he was with Moses. ¹⁸ Whosoever he be that doth rebel against thy commandment, and will not hearken unto thy words in all that thou commandest him, he shall be put to death: only be strong and of a good courage. m9ij05sp9c6rxfs59czn378s7420mlw 6 316950 2690211 2024-12-04T04:21:23Z Young1lim 21186 {{Information |Description=LIB.2A: Shared Libraries (20241204 - 20241203) |Source={{own|Young1lim}} |Date=2024-12-04 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2690211 wikitext text/x-wiki == Summary == {{Information |Description=LIB.2A: Shared Libraries (20241204 - 20241203) |Source={{own|Young1lim}} |Date=2024-12-04 |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}} f9knzjct4vw6wqkgvdsytn0dv26twbd 0 316951 2690222 2024-12-04T05:16:46Z Ekbreckenridge 2994477 Created introduction to electrical resistance 2690222 wikitext text/x-wiki The '''electrical resistance''' of an object is a measure of its opposition to the flow of electric current. The reciprocal/opposite electrical property is Conductance. Resistance is measured in ohms, symbolized by the Greek letter omega (Ω), named after Georg Simon Ohm. There is a material science behind what makes a good electrical conductor (things like aluminum and copper, which are good at transmitting electricity), and resistors (things like rubber, wood and plastics, which do not like to transmit electricity). There are items like heating elements and items like [[Electronics/Resistors]] that have a fixed resistance value. Resistance is used to ensure the current and voltage after the item causing the resistance is at a specified value. If the resistor is the only path of electrical current flow (series circuit), there will be a voltage drop after the resistance item. If there are multiple path of electrical current flow (parallel circuit), there will be a current drop where the parallel path meets. dmb2lt1yqcucvyktxtte2l1k05c417b 2690223 2690222 2024-12-04T05:22:21Z Ekbreckenridge 2994477 Added Ohms Law relationships 2690223 wikitext text/x-wiki The '''electrical resistance''' of an object is a measure of its opposition to the flow of electric current. The reciprocal/opposite electrical property is Conductance. Resistance is measured in ohms, symbolized by the Greek letter omega (Ω), named after Georg Simon Ohm. There is a material science behind what makes a good electrical conductor (things like aluminum and copper, which are good at transmitting electricity), and resistors (things like rubber, wood and plastics, which do not like to transmit electricity). There are items like heating elements and items like [[Electronics/Resistors]] that have a fixed resistance value. Resistance is used to ensure the current and voltage after the item causing the resistance is at a specified value. If the resistor is the only path of electrical current flow (series circuit), there will be a voltage drop after the resistance item. If there are multiple path of electrical current flow (parallel circuit), there will be a current drop where the parallel path meets. === Ohms Law: === With some of the other electrical properties, the resistance of an object can be calculated. <math>Ohms = Volts^2/Watts</math> <math>Ohms = Watts/Amps^2 </math> <math>Ohms=Volts/Amps</math> b6lh0ynsdpq39zltax76so830luco34 6 316952 2690226 2024-12-04T06:20:30Z Young1lim 21186 {{Information |Description=LCal.9A: Recursion (20241204 - 20241203) |Source={{own|Young1lim}} |Date=2024-12-04 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2690226 wikitext text/x-wiki == Summary == {{Information |Description=LCal.9A: Recursion (20241204 - 20241203) |Source={{own|Young1lim}} |Date=2024-12-04 |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}} mfyrd7ec5mhbn0bjxceiwhzxdttwpqu 6 316953 2690230 2024-12-04T07:22:04Z Young1lim 21186 {{Information |Description=ARM.2ASM: Branch and Return Methods (20241204 - 20241203) |Source={{own|Young1lim}} |Date=2024-12-04 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2690230 wikitext text/x-wiki == Summary == {{Information |Description=ARM.2ASM: Branch and Return Methods (20241204 - 20241203) |Source={{own|Young1lim}} |Date=2024-12-04 |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}} pz4lwjrzl8k7wirjyjd9oxfeltnn02s