Wikiversity:Colloquium

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&lt;!-- MESSAGES GO BELOW --&gt;
== Reminder! Vote closing soon to fill vacancies of the first U4C ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Dear all,

The voting period for the Universal Code of Conduct Coordinating Committee (U4C) is closing soon. It is open through 10 August 2024. Read the information on [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Election/2024_Special_Election#Voting|the voting page on Meta-wiki to learn more about voting and voter eligibility]]. If you are eligible to vote and have not voted in this special election, it is important that you vote now.

'''Why should you vote?''' The U4C is a global group dedicated to providing an equitable and consistent implementation of the UCoC. Community input into the committee membership is critical to the success of the UCoC.

Please share this message with members of your community so they can participate as well.

In cooperation with the U4C,&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 15:30, 6 August 2024 (UTC)
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== User group for Wikiversians ==

Was there ever a discussion about the possibility of establishing a user group in the sense of an affiliated organization that would defend the interests of professors and scientists on Wikiversity and possibly actively develop some projects? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:21, 8 August 2024 (UTC)

:Not that I'm aware of. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:20, 8 August 2024 (UTC)
:It's a pleasure to talk to a scientist on Wikiversity. I am a historian of technics and I would like to publish the following biography either on Wikiversity or on Wikipedia: 
:https://en.wikiversity.org/wiki/User:Rbmn/Arthur_Constantin_KREBS_(1850-1935):_Military_engineer,_Automotive_industrialist,_Great_projects_manager
:What would be your advice? [[User:Rbmn|Rbmn]] ([[User talk:Rbmn|discuss]] • [[Special:Contributions/Rbmn|contribs]]) 15:44, 6 October 2024 (UTC)
::The content appears to be largely biographical/encyclopedic, so I think it is likely best suited to Wikipedia. Consider improving/incorporating this content into the existing page: [[w:Arthur Constantin Krebs]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:05, 7 October 2024 (UTC)
::Please do not link to the Wikiversity [[wv:userspace|Userspace]] in Wikipedia articles. You will want to wait until you have a page in the [[wv:mainspace|Wikiversity mainspace]]. You'll also want to use the &lt;code&gt;{{[[:w:Template:Wikiversity|Wikiversity]]}}&lt;/code&gt; template (on Wikipedia) rather than embedding a photo with a link. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:21, 7 October 2024 (UTC)
:I haven't heard anything about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:06, 8 December 2024 (UTC)

== Rich's ''Illustrated Companion'' at Wikiversity: Right place? ==

Hello! I am creating a Wiki-version of a classical glossary (''Illustrated Companion to the Latin Dictionary, and Greek Lexicon'' by Anthony Rich, 1849), which explains the meaning of Latin headwords, primarily those &quot;representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans.&quot; The aim is to help understand what a (classical) Latin text is actually about, instead of merely translating it. I already transcribed the entire text and scanned the images (about 1900) from an original 1849-edition. I am currently working on uploading the images to ''Mediawiki Commons'', which probably will take some time. In the meantime I want to prepare the other aspects of the project (more than 3000 articles, already with many internal links). The important thing: this is ''not'' a ''might exist''-project.  {{Color|red|My question: Is ''Wikiversity'' the proper place for it?}} Although I created an exact rendition of the original text, ''Wikisource'' is not applicable, because the project has a broader scope (adding content to the articles, e. g. links to online editions for quotations, adding images, but also adding entirely new articles). Neither is ''Wikibooks'', because this is not a textbook and may otherwise breach its scope. For more about the project see [[w:User:CalRis25/Temp-RICH-Prospectus|my user-page]] at en.wikipedia. {{Color|Red|So, is Wikiversity the right place for it?}} [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:15, 17 August 2024 (UTC)

:Thanks for asking. To be clear, it ''is'' acceptable to make [[:s:en:Category:Wikisource annotations|annotated editions]] of texts at Wikisource and Wikibooks does host at least one [[:b:en:Annotations of The Complete Peanuts|annotated guide to a copyright-protected work]]. So if what you're looking to do is to include inline annotations to a public domain text, you certainly can put that on Wikisource. If you have a textbook or guidebook that is a companion, that would go at Wikibooks. If you have some other kind of learning resources (like maintaining a list of relevant links, organizing a book reading group, etc.), that could go here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:26, 17 August 2024 (UTC)
::Thank you for your quick answer. Actually, ''Wikibooks'' was my first thought. However, this project is not merely an annotated edition. Although at first it ''will'' be a faithful copy of the original text, I want the project to be &quot;open&quot;, i. e. adding articles should be possible. And the project should enable to do a lot more than mere inline annotation. See section [[w:User:CalRis25/Temp-RICH-Prospectus#Improving_RICH|Improving Rich]] in the project description a my user-page (en.Wikipedia). No ''Mediawiki''-project (Wikisource, Wikibooks, Wikipedia, Wiktionary) seemed to be a sufficiently applicable &quot;fit&quot; for the project, so I thought of Wikiversity as a last resort, because it is supposed to be home to all sorts of &quot;learning resources&quot;. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:57, 17 August 2024 (UTC)
:::The scope of Wikiversity ''is'' pretty catch-all and would allow for a pretty flexible place to host most learning resources that don't fit elsewhere.
:::Also, as nitpick, &quot;MediaWiki&quot; is the software that is the basis of these wikis (wikis being collections of interlinked documents that can be edited) and &quot;Wikimedia Foundation&quot; is the non-profit who owns the trademarks and hosts these projects like Wiktionary and Wikivoyage. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 10:06, 17 August 2024 (UTC)
::::Hello Justin, thank you for the reply. '''I think that settles it. I will create this project at ''Wikiversity''.''' Just for additional clarification, why I do so. Let's imagine a full transcription of the original 1849-edition of the ''Illustrated Companion'' by Anthony Rich and call it ''RICH-1849''. We shall call my project, for brevity sake, RICH-2K. And now, let's have a look at the article about the Roman toga (a piece of attire). In ''RICH-1849'' we can can call it ''RICH-1849/Toga'', and it contains ''exactly'' the content of the 1849-book. Now, let's look at the article ''RICH-2K/Toga''. At the beginning its only content would be the article ''RICH-1849/Toga''. Does that make ''RICH-2K/Toga'' and ''RICH-1849/Toga'' the same? Not at all, because in truth ''RICH-2K/Toga'' is a &quot;container&quot; which initially contains only the article ''RICH-1849/Toga'' but later on may include more stuff: images, external links, article text which builds on or extends ''RICH-1849/Toga'' and information from other sources of information (Wikipedia, specialized books). By the way, this added article information would not be a mere copy of the text at en.Wikipedia, because the information needs to looked at through the eyes of someone reading the original text (more citations with direct links to these etc.). [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 11:39, 17 August 2024 (UTC)

== Coming soon: A new sub-referencing feature – try it! ==

&lt;section begin=&quot;Sub-referencing&quot;/&gt;
[[File:Sub-referencing reuse visual.png|{{#ifeq:{{#dir}}|ltr|right|left}}|400px]]
Hello. For many years, community members have requested an easy way to re-use references with different details. Now, a MediaWiki solution is coming: The new sub-referencing feature will work for wikitext and Visual Editor and will enhance the existing reference system. You can continue to use different ways of referencing, but you will probably encounter sub-references in articles written by other users. More information on [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|the project page]].

'''We want your feedback''' to make sure this feature works well for you:

* [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|Please try]] the current state of development on beta wiki and [[m:Talk:WMDE Technical Wishes/Sub-referencing|let us know what you think]]. 
* [[m:WMDE Technical Wishes/Sub-referencing/Sign-up|Sign up here]] to get updates and/or invites to participate in user research activities.

[[m:Special:MyLanguage/Wikimedia Deutschland|Wikimedia Deutschland]]’s [[m:Special:MyLanguage/WMDE Technical Wishes|Technical Wishes]] team is planning to bring this feature to Wikimedia wikis later this year. We will reach out to creators/maintainers of tools and templates related to references beforehand.

Please help us spread the message. --[[m:User:Johannes Richter (WMDE)|Johannes Richter (WMDE)]] ([[m:User talk:Johannes Richter (WMDE)|talk]]) 10:36, 19 August 2024 (UTC)
&lt;section end=&quot;Sub-referencing&quot;/&gt;
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== New [[Template:Form]] ==

Hi! Today I was bold and created [[Template:Form]] (which calls [[Module:WikiForm]] and [[MediaWiki:Gadget-WikiForm.js]]). The template allows to create user-friendly forms that can create pages or add content to existing pages. My motivation and first use case was [[Wikidebate/New|this form]] to create new [[wikidebates]], but I suspect the template can be useful elsewhere on Wikiversity. Let me know if you notice any issues or have any requests or concerns. Kind regards, [[User:Sophivorus|Sophivorus]] ([[User talk:Sophivorus|discuss]] • [[Special:Contributions/Sophivorus|contribs]]) 15:21, 21 August 2024 (UTC)

== Sign up for the language community meeting on August 30th, 15:00 UTC ==

Hi all,

The next language community meeting is scheduled in a few weeks—on August 30th at 15:00 UTC. If you're interested in joining, you can [https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#30_August_2024 sign up on this wiki page].

This participant-driven meeting will focus on sharing language-specific updates related to various projects, discussing technical issues related to language wikis, and working together to find possible solutions. For example, in the last meeting, topics included the Language Converter, the state of language research, updates on the Incubator conversations, and technical challenges around external links not working with special characters on Bengali sites.

Do you have any ideas for topics to share technical updates or discuss challenges? Please add agenda items to the document [https://etherpad.wikimedia.org/p/language-community-meeting-aug-2024 here] and reach out to ssethi(__AT__)wikimedia.org. We look forward to your participation!

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 23:20, 22 August 2024 (UTC)
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== Template consolidation: User talk page block notice ==
Wondering if someone who likes templates could have a go at consolidating or helping decide between use of:
* [[Template:Block]]
* [[Template:Blocked]]

Unless I'm missing something, it seems like we don't need both?

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:16, 23 August 2024 (UTC)
: I tried to figure out a Wikidata item with most links to projects. I found this: [[Wikidata:Q6379131]], which is Template:Uw-block. There is even a corresponding Wikiversity template, [[Template:Uw-block1]] (not used anywhere).
: My impression is that of the three templates, we only need one. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:43, 13 September 2024 (UTC)

== Announcing the Universal Code of Conduct Coordinating Committee ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[https://lists.wikimedia.org/hyperkitty/list/board-elections@lists.wikimedia.org/thread/OKCCN2CANIH2K7DXJOL2GPVDFWL27R7C/ Original message at wikimedia-l]. [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Hello all,

The scrutineers have finished reviewing the vote and the [[m:Special:MyLanguage/Elections Committee|Elections Committee]] have certified the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Results|results]] for the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election|Universal Code of Conduct Coordinating Committee (U4C) special election]].

I am pleased to announce the following individual as regional members of the U4C, who will fulfill a term until 15 June 2026:

* North America (USA and Canada)
** Ajraddatz

The following seats were not filled during this special election:

* Latin America and Caribbean
* Central and East Europe (CEE)
* Sub-Saharan Africa
* South Asia
* The four remaining Community-At-Large seats

Thank you again to everyone who participated in this process and much appreciation to the candidates for your leadership and dedication to the Wikimedia movement and community.

Over the next few weeks, the U4C will begin meeting and planning the 2024-25 year in supporting the implementation and review of the UCoC and Enforcement Guidelines. You can follow their work on [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Meta-Wiki]].

On behalf of the U4C and the Elections Committee,&lt;section end=&quot;announcement-content&quot; /&gt;

[[m:User:RamzyM (WMF)|RamzyM (WMF)]] 14:07, 2 September 2024 (UTC)
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== Re: The Vector 2022 skin as the default in two weeks? ==

[[File:Vector 2022 video-en.webm|thumb|A two minute-long video about Vector 2022]]
Hello everyone, I'm reaching out on behalf of the [[mediawikiwiki:Reading/Web|Wikimedia Foundation Web team]] responsible for the MediaWiki skins. I'd like to revisit the topic of making Vector 2022 the default here on English Wikiversity. I [[Wikiversity:Colloquium/archives/September 2022#The Vector 2022 skin as the default in two weeks?|did post a message about this almost two years ago]] (where you can find all the details about the skin), but we didn't finalize it back then.

What happened in the meantime? We built [[mw:Reading/Web/Accessibility for reading|dark mode and different options for font sizes]], and made Vector 2022 the default on most wikis, including all other Wikiversities. With the not-so-new V22 skin being the default, existing and coming features, like dark mode and [[mw:Trust and Safety Product/Temporary Accounts|temporary accounts]] respectively, will become available for logged-out users here.

So, if no large concerns are raised, we will deploy Vector 2022 here in two weeks, in the week of September 16. Do let me know if you have any questions. Thank you! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 21:48, 2 September 2024 (UTC)

:Sounds good, Szymon - we look forward to the upcoming change of skin {{smile}} Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:35, 13 September 2024 (UTC)
* I for one oppose a switch to Vector 2022. I do not find it preferable. Here is a staggering evidence of user refusal of Vector 2022 once it was deployed: [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]], Junuary 2023. 355 voters supported rollback to Vector 2010 whereas 64 opposed, yielding 84.7% support, as clear a supermajority as one may wish. These people opposing Vector 2022 feel the same way as I do. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:48, 13 September 2024 (UTC)
*:Hey @[[User:Dan Polansky|Dan Polansky]]. Thanks for your comment. I'm open to discussion about problems with our software, and I hope we can maintain a respectful tone.
*:I understand that there are users who prefer Vector legacy or other skins, just as there are people who still stick to Monobook. Such people are active across many wikis. They can keep Vector legacy, although non-default skins don't have the support the default ones do. We are rolling out for technical reasons, as I mentioned above, with benefit to not logged-in users.
*:Regarding the rollback RfC on Wikipedia, two neutral users stated that there was no consensus for rollback, RfC is not a vote, and the numbers were different (355:226:24). I believe this all is pretty easy to verify.
*:So to sum up, Vector 2022 needs to become the default, tons and tons of comments were made about the skin and related stuff, and we have taken many ideas into account, and it's totally OK if you stick to Vector legacy.
*:Thanks! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 19:30, 16 September 2024 (UTC)
*:: Today, I visited Wikiversity and found it switched to Vector 2022. I changed my preference settings to Vector 2010. From what I understand, non-registered visitors are now defaulted to Vector 2022 despite its unpopularity in [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]]. I have not seen any evidence that users prefer Vector 2022, and given the evidence in the linked RfC, I tentatively conclude that the decision to switch has made the site experience worse for the majority of users. The logic of &quot;you can switch&quot; surely applies to Vector 2022 as well: those who prefer it can switch to it. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:08, 17 September 2024 (UTC)

== Have your say: Vote for the 2024 Board of Trustees! ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

The voting period for the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Board of Trustees election]] is now open. There are twelve (12) candidates running for four (4) seats on the Board.

Learn more about the candidates by [[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Candidates|reading their statements]] and their [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Questions_for_candidates|answers to community questions]].

When you are ready, go to the [[Special:SecurePoll/vote/400|SecurePoll]] voting page to vote. '''The vote is open from September 3rd at 00:00 UTC to September 17th at 23:59 UTC'''.

To check your voter eligibility, please visit the [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Voter_eligibility_guidelines|voter eligibility page]].

Best regards,

The Elections Committee and Board Selection Working Group&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:15, 3 September 2024 (UTC)
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== Separate page for hyperbola. ==

Good morning,

I notice that a search for &quot;hyperbola&quot; redirects to &quot;Conic sections&quot;.

At present there is a separate page for &quot;ellipse&quot;. Therefore a separate page for &quot;hyperbola&quot; seems to be justified.

Could this redirection be changed so that search for &quot;hyperbola&quot; goes to a separate page for &quot;hyperbola&quot;?

Many thanks,

[[User:ThaniosAkro|ThaniosAkro]] ([[User talk:ThaniosAkro|discuss]] • [[Special:Contributions/ThaniosAkro|contribs]]) 12:04, 15 September 2024 (UTC)

:It is true that ellipses are covered at [[Conic sections]] (along with hyperbolas, parabolas, etc.) and there is a separate page for [[ellipse]]s that elaborates. We certainly ''could'' have a page about [[hyperbola]]s that is separate, but no one has written sufficient content to spin it off yet. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 12:17, 15 September 2024 (UTC)

== I hereby request for your Unblocking IP address and just reviewed and received a reverted rec ==

Hi there. {{unsigned|Ishmael Raphasha}}
:No one has any clue what you're talking about. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:53, 18 September 2024 (UTC)

== RICH-2K: New project with some initial questions ==

Hello! I'm creating a new learning resource on ''Wikiversity''. The respective project is based on my transcription of a classical dictionary from 1849 by Anthony Rich. For more information about the project see its [[User:CalRis25/RICH: Description|description page]] (see also that page for why not ''Wikisource'' or ''Wikibooks''). The project's scope is fairly big: 3205 article-pages plus 304 REDIRECT-pages. The images (scanned by myself from an original copy) have been uploaded to ''Commons''. I have some initial technical questions (more of these and more detailed ones will follow):

* '''Upload''': Due to the large number of pages it is not realistic to create these manually. Is it possible to bulk-upload these in some way (the Wikitext of the pages is created using a Python-script with one file per article/page)? Is it possible to upload these to a test-environment first where any problems (hopefully none) can be identified and dealt with more easily than on the production-version of ''Wikiversity''?
* '''(Technical) Structure''': I am planning to set up this project at ''&lt;nowiki&gt;https://en.wikiversity.org/wiki/RICH-2K&lt;/nowiki&gt;'' as the main page and anything else as subpages: ''RICH-2K/Subpage_1 ... RICH-2K/Subpage_n''. However, these subpages fall into two categories: 1. Article-pages (content) and 2. Meta/Administrative pages. This project requires search capability restricted to the ''RICH-2K''-namespace. The ''Mediawiki''-software seems to supply a ''Search''-input field with the possibility to restrict the search to some namespace. I would like, however, to restrict the search further to the first group of pages, namely the articles. Is that possible, perhaps by use of (hidden) categories?
* '''External links''': This project will need many external links, and yes, I have read the relevant ''Wikiversity''-pages, but this specific project needs them. The ''Recommended Editions''-page (used for recommended online editions, to which to link when citing texts) alone probably will require several hundred external links. However, only relatively few [[w:Second-level domain|second-level domains]] will be involved, and most of these should be trustworthy (Perseus Digital library, digital collections of universities etc., in some cases, however, also ''Archive.org''). Perhaps there is a list of web-sites, for which external links are generally allowed? And who is allowed to create external links on ''Wikiversity''-pages (I haven't found the relevant policy)?
* '''Categories''': This project requires quite a few of its own categories, which belong to two large groups: 1. Categories (2 levels) of the ''Classed Index'' (about 170 categories), a thematic index of some (but not all) of the articles. 2. Administrative categories. Is there a recommended way to distinguish between different classes of categories within a project (category name or other method)? What about naming conventions for project-specific categories?

I am looking forward to your input. If you think that it's preferable we can move the discussions to the [[User_talk:CalRis25/RICH:_Description|Talk-page]] of the project's description. Thank you in advance. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 05:29, 20 September 2024 (UTC)

:*Admins have access to [[Special:Import]] and can bulk import XML pages. You can create pages in your sandbox if you'd like and make an indefinite amount of them at pages like [[User:CalRis25/sandbox]]. What can and cannot be hosted in user namespace is very loose, but still has to follow in principle Wikiversity's scope.
:*Using subpages is in principle a good way to organize these various resources. Please do not name them after a user name or something obscure. I personally think that &quot;RICH-2K&quot; is a not optimal name. I may recommend something like [[Anthony Rich Dictionary Project]] or [[21st-Century Anthony Rich Dictionary]] or something more obviously intelligible. While we have very few actual policies and guidelines, see [[Wikiversity:Naming conventions]] for a rough consensus of what is probably best practice for naming pages.
:*External linking generally does not use an allowed list (a.k.a. whitelist model), but a disallow (a.k.a. blacklist) model. See [[MediaWiki:Spam-blacklist]] and [[Special:BlockedExternalDomains]] (which is currently empty but is another method of listing blocked domains). It's perfectly fine to aggregate external links in learning resources.
:*I'm not 100% sure what the distinction is that you're drawing, but you can freely arrange categories underneath a main category that has the same name as your larger project. So, following the suggestions I gave, you could have a category like [[:Category:Anthony Rich Dictionary Project]] and then create any number of subcategories that logically help users navigate all these pages. Please make sure the main category you create is itself categorized under some relevant category(ies). If you need help, please ask.
:I think this answers your questions, please let me know if I'm unclear or you have more. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:11, 20 September 2024 (UTC)
::Hello Justin!
::* '''Upload:''' Creating the project in sandbox pages of my User-namespace defeats the purpose, as this is an ''open'' project. Also that would not solve, as such, the problem of having to manually create thousands of pages. I wonder, does ''Wikiversity'' support creation of pages using its API. ''Mediawiki's'' [[mw:API:Main_page|API-description]] seems to imply that it ought to be possible. If that's the case, I should be able to create a Python-script which automatically creates the pages (of course, a few trial pages first).
::* '''(Technical) Structure''': You may be right, here. RICH-2K is, for now, merely a technical name to make a clear but not too verbose distinction between the original text and the current project. I'll give this more thought.
::* '''External links''': I brought this up mainly because when I first edited my ''Wikiversity''-page, I got a message that I was not allowed to create external links. However, I just now tested creating an external link on my user-page and got no error, so this problem seems to be solved.
::* '''Categories''': I think I know what you mean. I'll create a category structure and maybe ask some specific questions once I am ready to do so.
::Thank you for your quick help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 18:51, 20 September 2024 (UTC)
:::re: upload, I'm just suggesting your sandbox(es) as you asked about &quot;a test-environment&quot;. Anyone can edit someone else's sandboxes, but you typically defer to other users to control what's in their own subpages as a collegial thing. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:39, 23 September 2024 (UTC)

Hello! I have two further questions:
# I created a category-structure for the project. Could you (or someone else) have a look at it ([[User:CalRis25/RICH: Categories]]) and answer the questions in the section [[User:CalRis25/RICH:_Categories#Questions|Questions]]? I gave it some thought and believe that this would work fine for the project.
# ''Project boxes'' (see [[Help:Tour of project boxes]]): It is unclear to me, whether these belong only on the main page of the project (that makes the most sense to me), or on every single subpage.
Thanks in advance for your help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 17:51, 24 September 2024 (UTC)

:To answer your questions here:
:*No, you are not contravening any policies we have.
:*A leading &quot;The&quot; is acceptable, but if you want it to sort alphabetically, you will have to use &lt;nowiki&gt;{{DEFAULTSORT:}}&lt;/nowiki&gt;. E.g. to get Category:The Best Stuff to sort under &quot;B&quot;, insert &quot;&lt;nowiki&gt;{{DEFAULTSORT:Best Stuff, The}}&lt;/nowiki&gt;.
:*Trailing &quot;etc.&quot; is acceptable.
:*An accent in a category title is acceptable.
:I'll also note that it looks like you have in mind some tracking categories that are redundant. Pages such as [[Special:LonelyPages]] and [[Special:DeadendPages]] already do automatically what you're proposing to do manually.
:As for project boxes, it's typically the case that the subjects are only placed on the main resource, but as you may imagine, [[Help:Tour of project boxes/1|status completion ones]] may vary from subpage to subpage. As with most things at Wikiversity, there are very few actual rules, so it's pretty much the wild west, even tho this project has been around for almost 20&amp;nbsp;years. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:18, 25 September 2024 (UTC)
::Hello Justin, thanks for the DEFAULTSORT-hint for categories beginning with ''The''. I will restrict the project boxes to the main page. As for the the orphaned/dead-end-categories, I prefer these to be project-specific. Once the project is up and running, putting articles &quot;on the map&quot; (making them accessible from other articles and creating links to other articles) is one of the first tasks to be dealt with. I already know which articles are involved and will add these categories to these articles. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 16:51, 25 September 2024 (UTC)

== Your wiki will be in read-only soon ==

&lt;section begin=&quot;server-switch&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;

[[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-Tech%2FServer+switch&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]

The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster.

All traffic will switch on '''{{#time:j xg|2024-09-25|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2024-09-25T15:00|en}} {{#time:H:i e|2024-09-25T15:00}}]'''.

Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. 

A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. 

'''You will be able to read, but not edit, all wikis for a short period of time.'''

*You will not be able to edit for up to an hour on {{#time:l j xg Y|2024-09-25|en}}.
*If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case.

''Other effects'':

*Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped.
* We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards.
* [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes.

This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. 

'''Please share this information with your community.'''&lt;/div&gt;&lt;section end=&quot;server-switch&quot;/&gt;

[[User:Trizek_(WMF)|Trizek_(WMF)]], 09:37, 20 September 2024 (UTC)
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== 'Wikidata item' link is moving. Find out where... ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;&lt;i&gt;Apologies for cross-posting in English. Please consider translating this message.&lt;/i&gt;{{tracked|T66315}}

Hello everyone, a small change will soon be coming to the user-interface of your Wikimedia project.
The [[d:Q16222597|Wikidata item]] [[w:|sitelink]] currently found under the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''General''&lt;/u&gt;&lt;/span&gt; section of the '''Tools''' sidebar menu will move into the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''In Other Projects''&lt;/u&gt;&lt;/span&gt; section.

We would like the Wiki communities feedback so please let us know or ask questions on the   [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Discussion page]] before we enable the change which can take place October 4 2024, circa 15:00 UTC+2.
More information can be found on [[m:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|the project page]].&lt;br&gt;&lt;br&gt;We welcome your feedback and questions.&lt;br&gt; [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 18:56, 27 September 2024 (UTC)
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==Download as PDF==
[[Phabricator:T376438]]: &quot;Download to PDF&quot; on en.wv is returning error: &quot;{&quot;name&quot;:&quot;HTTPError&quot;,&quot;message&quot;:&quot;500&quot;,&quot;status&quot;:500,&quot;detail&quot;:&quot;Internal Server Error&quot;}&quot;

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 3 October 2024 (UTC)

:I just downloaded this page as a PDF and it worked just fine. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:04, 3 October 2024 (UTC)

== Protected template bug for Pp ==

It seems that templates derivative of {{tlx|Pp}} (compiled in {{tlx|Protection templates}}) are being sorted into protection categories using the name 'Wikipedia' instead of 'Wikiversity' (e.g., [[:Category:Wikipedia pages with incorrect protection templates]]). From what I can tell, it is not in the publicly accessible source code of any of the templates. The only other impacted pages are modules which call {{tlx|pp}}-derivatives (e.g., [[Module:Navbar/styles.css]]).

This does not seem to affect any other pages in [[:Category:Wikiversity protected templates]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 18:59, 4 October 2024 (UTC)

:The problem is that &quot;Wikipedia&quot; is [https://en.wikiversity.org/w/index.php?title=Special%3ASearch&amp;limit=500&amp;offset=0&amp;ns828=1&amp;search=Wikipedia&amp;searchToken=9svkpqlxxoquoq7bnkt55ugts mentioned in several modules that were copied over from en.wp]; many of these are legit and many of them need to be replaced with &quot;Wikiversity&quot; ([https://en.wikiversity.org/w/index.php?title=Module%3APp-move-indef&amp;diff=2662815&amp;oldid=1944984 e.g.]) This particular change ''may'' fix all of these issues...? But 1.) it will take time to propagate across the site and 2.) there are still many more &quot;Wikipedia&quot;s that need to be changed, so I'll go thru a few more, but if you want to give me an assist, if you can just check this one week from now and ping me if the problem persists, that would be nice. Sometimes, I make calendar reminders to follow up on these, but I'm not a perfect person. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:55, 5 October 2024 (UTC)

== Invitation to Participate in Wiki Loves Ramadan Community Engagement Survey ==

Dear all,


We are excited to announce the upcoming [[m:Wiki Loves Ramadan|Wiki Loves Ramadan]] event, a global initiative aimed at celebrating Ramadan by enriching Wikipedia and its sister projects with content related to this significant time of year. As we plan to organize this event globally, your insights and experiences are crucial in shaping the best possible participation experience for the community.

To ensure that Wiki Loves Ramadan is engaging, inclusive, and impactful, we kindly invite you to participate in our community engagement survey. Your feedback will help us understand the needs of the community, set the event's focus, and guide our strategies for organizing this global event.

Survey link: https://forms.gle/f66MuzjcPpwzVymu5

Please take a few minutes to share your thoughts. Your input will make a difference!

Thank you for being a part of our journey to make Wiki Loves Ramadan a success.


Warm regards,

User:ZI Jony 03:19, 6 October 2024 (UTC)

Wiki Loves Ramadan Organizing Team
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== 'Edit to my talk page' notification bug? ==

This may belong at the bug tracker, but does anyone else have an issue disabling ''email'' notifications upon  an 'Edit to my talk page' in [[Special:GlobalPreferences]]? Oddly I ''am'' able to disable the global preference on Wikipedia, MediaWiki, etc, but not here. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:23, 7 October 2024 (UTC)

:I have not experienced this, but to be clear, do you also have the option to get emails when items on your talk page are edited turned on? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:39, 7 October 2024 (UTC)
::The only (non-grayed out) options I have enabled for email are 'Failed login attempts' and 'Login from an unfamiliar device'. 'Edit to my talk page' re-checks after every save. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:54, 7 October 2024 (UTC)
:::That does sound like a [[phab:]] issue, with the caveat that I don't 100% recall how global preferences work and if they override local ones, etc. If you have parsed that and still have this issue, you'll probably need to file a ticket. Maybe someone else has this issue. Wish I could help. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:57, 7 October 2024 (UTC)
::::[[phab:T376601|Off 'n away]] 🫡 [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 10:35, 7 October 2024 (UTC)

== [[Portal:Computer Science]] ➝ [[Portal:Information sciences]] ==

Seeking consensus to complete the merge into the broader portal. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:28, 8 October 2024 (UTC)

:Why should it be merged? Computer Science seems well-enough designed. What is the incentive to collapse it into a broader field of study? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:18, 8 October 2024 (UTC)
::Portals as top level organizations allowing for content to be best centralized. Also note that I did not start the merge, just offering to finish it. Perhaps a {{tlx|prod}} instead? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 07:20, 8 October 2024 (UTC)
:::I have no objections, personally. If it gets done, please use a redirect and should someone want to come along to resurrect it later, it will be easier. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:21, 8 October 2024 (UTC)
: Is computer science really a branch of information sciences? I would not think so, but what do I know. Do we have some external resources/links confirm this idea? [[W:Information science]] currently says: &quot;Information science, documentology[1] or informatology[2][3] is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information.&quot; --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:49, 11 October 2024 (UTC)
::Looking through [https://stackoverflow.com/q/1047014/22673230] [https://businessdegrees.uab.edu/mis-degree-bachelors/resources/computer-information-systems-vs-computer-science/] [https://www.si.umich.edu/student-experience/what-information-science] a few top (not necessarily RS) searches I'm inclined to agree. I am more familiar with the grafted [[:w:Information and computer science|information ''and'' computer science]] which makes an effort to merge the disciplines, but it does not seem like reaching to say that IS is presented as more applications-concerned (certainly with no lack of theoretical abstraction), whereas CS can be more freely associated with any and all 'science related to computers'. It is easy to reason about the connection between the fields, but I think it is clear academia maintains this taxonomy for a good reason.
::With these considerations, I think I will ''stop'' the process of merging in favor of expanding the existing [[School:Library and Information Science]]. 

::Let me know if there is not consensus to redirect [[Portal:Information sciences]] to [[School:Library and Information Science]] (with enough expansion it can generalize away from just library sciences). [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:16, 11 October 2024 (UTC)
::: I do not see that a merge of a ''portal'' to a ''school'' is a good thing. Do you have a clear idea of the concepts of school and portal and how they relate to each other? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:34, 11 October 2024 (UTC)
::::Found [[:Category:Information sciences]]; there are enough existing resources in there to make my other proposed merge excessive. I will simply continue developing the existing [[Portal:Information sciences]] instead. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:05, 11 October 2024 (UTC)
::::: Frankly, I would ideally see [[Portal:Information sciences]] deleted: I don't see what it does that a category would not do well enough. There does not seem to be any material specific to &quot;Information sciences&quot; (whatever that is) in that portal at all. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 17:11, 11 October 2024 (UTC)
::::::Tacked a {{tlx|prod}} for an eventual deletion, but I may still try to develop it as proof of concept at some point. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:33, 11 October 2024 (UTC)

== [[:Category:Occupational Epidemiology]] ==

I propose moving the pages in this category (without leaving redirects) to their equivalent under the parent resource [[Occupational Health Risk Surveillance]]. Also due to the number of subpages, it seems &lt;code&gt;|filing=deep&lt;/code&gt; would be a justified. (Also [[Special:PrefixIndex/Occupational_Epidemiology|there are quite a few]] untagged subpages.) [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 05:11, 9 October 2024 (UTC)
: I above all think that the content should be ''moved out of the mainspace'': I do not see readers learning anything from e.g. [[Occupational Epidemiology/Research tools/Reading of scientific articles for learning epidemiology and biostatstics]] or [[Occupational Epidemiology/Research tools/Ongoing projects/Risk Communication in Seafaring/Writing the article guideline IMRAD]]. Wikiversity can be kind enough to host that material in, say, subspace of [[User:Saltrabook]], but more should not be asked, I think. Let us recall that per [[WV:Deletions]], &quot;Resources may be eligible for proposed deletion when education objectives and learning outcomes are scarce, and objections to deletion are unlikely&quot;; I do not see how learning outcomes can be anything but scarce. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:04, 11 October 2024 (UTC)
::thank you, agree @ [[User:Saltrabook|Saltrabook]] ([[User talk:Saltrabook|discuss]] • [[Special:Contributions/Saltrabook|contribs]]) 21:03, 13 November 2024 (UTC)

== Active editors ==

It is interesting to observe the stats on [https://stats.wikimedia.org/#/en.wikiversity.org/contributing/active-editors/normal|line|all|(page_type)~content*non-content|monthly active editors] through the project's history. October is our month! [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:44, 8 October 2024 (UTC)

:Odd. Maybe related to the school year? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:10, 9 October 2024 (UTC)
::I wonder how many are [[User:Jtneill|Jtneill]]'s crowd... the number is in the hundreds though, so that is one chunky cohort —[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:16, 9 October 2024 (UTC)
:::Yes, [[Motivation and emotion/Book]] involves ~100-150 students editing most intensely during October each year. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:20, 9 October 2024 (UTC)
::::Neat, that still leaves around ~50-100 other students from other avenues each year since 2021. I also wonder which projects were involved in the COVID enrollment spike. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:26, 9 October 2024 (UTC)
:::::Personally I can admit that my editing is much more active during the school season vs. the summer break, so I'm in the same boat as Jtneill's students. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:24, 13 November 2024 (UTC)
:@[[User:Tule-hog|Tule-hog]] This is an interesting topic, but it is not clear to me as an outsider what you and other participants in this discussion find interesting. I  find this graph not very meaningful because it does not tell me if the number of  Active editors has gone up or down during the period covered, which I think was 2000-now. 
:I can see a big jump between 2000 and 2007, but what happened since then? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:45, 16 December 2024 (UTC)

== Intentionally incorrect resource ==

There is a [[Special:Diff/2583464|disclaimer inserted onto a resource]] (by not the original author) that:
&lt;blockquote&gt;I am merely [making this page false] to show you (The viewer) that Wikipedia and this page 'Wikiversity' is bull sh*t and it will not give you the reliability you need when writing an academic piece of writing.&lt;/blockquote&gt;
However, that IP has [[Special:Contributions/86.22.73.151|not made any other edits]], so unless they vandalized via a sock, the intent went un-realized and only that portion need be removed. Bumping here in case there is some obvious jumbo in that essay that someone else can catch. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:58, 9 October 2024 (UTC)

:Removed that portion, which was obviously vandalism. No perspective on the rest of the essay. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:38, 9 October 2024 (UTC)

== [[:Category:Proposed guidelines]] ==

Noting for future editors that WV has collapsed all proposals into [[:Category:Proposed policies|proposed policies]]. Seeking consensus to further collapse [[:Category:Wikiversity proposals]] into the former, or to restore [[:Category:Proposed guidelines]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:19, 9 October 2024 (UTC)

== [[Around Wikiversity in 80 Seconds|Broken 80-second tour]] ==

Bumping a [[Talk:Around_Wikiversity_in_80_Seconds|comment]] on the ''Wikiversity in 80 seconds'' tour. Appears wikisuite is not working with the Vector 2022 appearance. 

Also see [[:w:Wikipedia:Miscellany_for_deletion/Wikiversuite_pages|this thread]] on the Wikiversal package - may not be relevant to Wikiversity, but FYC. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:26, 10 October 2024 (UTC)
: I would just delete the material; I do not see value in it. If others agree, I would try to articulate why I think it should be deleted (or move to author user space). --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:57, 13 October 2024 (UTC)
::Just mark as {{tl|historical}}. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:39, 13 October 2024 (UTC)
::: This thing was created by [[User:Planotse]]. His creations are now being discussed in Wikibooks for deletion: [[B:Wikibooks:Requests for deletion#Wikiversal generated pages]]. It seems he used some kind of tool that is no longer available (the above mentioned &quot;Wikiversal&quot; package) to create this kind of slideshow-like material (believing the Wikibooks discussion). I do not see value of this in the mainspace, not even as historical (I am okay with userspace, but maybe even that is not the best option?). A look at the source code of [[Around Wikiversity in 80 Seconds/Introduction]] confirms the words of Omphalographer, namely that &quot;the HTML-heavy markup generated by Wikiversal makes them [the pages] unreasonably difficult to edit.&quot;
::: I went ahead and marked the page for proposed deletion. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:35, 14 October 2024 (UTC)

== Preliminary results of the 2024 Wikimedia Foundation Board of Trustees elections ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

Thank you to everyone who participated in the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Wikimedia Foundation Board of Trustees election]]. Close to 6000 community members from more than 180 wiki projects have voted.

The following four candidates were the most voted:

# [[User:Kritzolina|Christel Steigenberger]]
# [[User:Nadzik|Maciej Artur Nadzikiewicz]]
# [[User:Victoria|Victoria Doronina]]
# [[User:Laurentius|Lorenzo Losa]]

While these candidates have been ranked through the vote, they still need to be appointed to the Board of Trustees. They need to pass a successful background check and meet the qualifications outlined in the Bylaws. New trustees will be appointed at the next Board meeting in December 2024.

[[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Results|Learn more about the results on Meta-Wiki.]]

Best regards,

The Elections Committee and Board Selection Working Group

&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MPossoupe_(WMF)|MPossoupe_(WMF)]] 08:26, 14 October 2024 (UTC)
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== Seeking volunteers to join several of the movement’s committees ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Each year, typically from October through December, several of the movement’s committees seek new volunteers. 

Read more about the committees on their Meta-wiki pages:
* [[m:Special:MyLanguage/Affiliations_Committee|Affiliations Committee (AffCom)]]
* [[m:Special:MyLanguage/Ombuds_commission|Ombuds commission (OC)]]
* [[m:Special:MyLanguage/Wikimedia Foundation/Legal/Community Resilience and Sustainability/Trust and Safety/Case Review Committee|Case Review Committee (CRC)]]

Applications for the committees open on 16 October 2024. Applications for the Affiliations Committee close on 18 November 2024, and applications for the Ombuds commission and the Case Review Committee close on 2 December 2024. Learn how to apply by [[m:Special:MyLanguage/Wikimedia_Foundation/Legal/Committee_appointments|visiting the appointment page on Meta-wiki]]. Post to the talk page or email [mailto:cst@wikimedia.org cst@wikimedia.org] with any questions you may have.

For the Committee Support team,
&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 23:09, 16 October 2024 (UTC)
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== Interactive elements ==
Can we use interactive elements on Wikiversity? I'd like to add JavaScript to a page. If it's not possible now, where can I suggest this feature? I have a safe integration idea.
[[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 12:10, 17 October 2024 (UTC)
: This is beyond my technical knowledge, but have you checked out:
:* https://www.mediawiki.org/wiki/Manual:Interface/JavaScript?
:* [[Wikipedia:WikiProject JavaScript]]
:* [[MediaWiki:Common.js]]

:What sort of interactive elements are you thinking about?

: Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:39, 18 October 2024 (UTC)
::I was thinking about adding something like a graph with adjustable controls, where users can interact with it and see how different changes affect the outcome. It seems like this could be a useful feature. There might already be discussions about enhancing Wikiversity or similar platforms—perhaps on a relevant talk page or in a Discord group. Do you know where such discussions might be happening? [[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 19:47, 18 October 2024 (UTC)
:::From a quick look, maybe check out:
:::* [[mw:Extension:Graph]]
:::* [[phab:tag/graphs]]
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:40, 18 October 2024 (UTC)
:::: mw:Extension:Graph is currently disabled on Wikipedia etc. wikis, for security reasons, and seems unlikely to be enabled again. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:30, 19 October 2024 (UTC)

== An unexplained spurt of Wikiversity page views ==
The [https://pageviews.wmcloud.org/siteviews/?platform=all-access&amp;source=pageviews&amp;agent=user&amp;start=2024-06-01&amp;end=2024-10-18&amp;sites=en.wikiversity.org|en.wikibooks.org|en.wikiquote.org|en.wikisource.org page view report] shows an unexplained spurt of Wikiversity page views, reaching over 4 times the baseline and then falling back again. Does anyone have any idea what is going on? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:01, 19 October 2024 (UTC)

:Interesting. I wonder why only the English wikiquote and wikiversity and not Wikisource or wikibooks? How reliable do you think those stats are? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:44, 8 December 2024 (UTC)
:I guess the mention in mass media might be a cause. Someone metions it and then thousands go and look. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:02, 17 December 2024 (UTC)

== Center tempate failed on a contributors phone... ==

See the edit comment here - https://en.wikiversity.org/w/index.php?title=Wikiphilosophers&amp;diff=prev&amp;oldid=2673962. I'm puzzled as this is the first failure of this, I've noted recently. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 08:45, 19 October 2024 (UTC)

== Essay-like page in user space that makes little sense and seems incoherent ==
The page [[User:TheoYalur/Illusions]] seems to match the description, at least by my assessment. My understanding is that since the page is only in user space and not in the mainspace, it can stay there even if it has those disqualifying qualities. But if I am wrong and the page belongs deleted, please correct me and let me know. I do not know which policy or guideline, if any, guides the case. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:30, 21 October 2024 (UTC)

== 'Wikidata item' link is moving, finally. ==

Hello everyone, I previously wrote on the 27th September to advise that the ''Wikidata item'' sitelink will change places in the sidebar menu, moving from the '''General''' section into the '''In Other Projects''' section. The scheduled rollout date of 04.10.2024 was delayed due to a necessary request for Mobile/MinervaNeue skin. I am happy to inform that the global rollout can now proceed and will occur later today, 22.10.2024 at 15:00 UTC-2. [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Please let us know]] if you notice any problems or bugs after this change. There should be no need for null-edits or purging cache for the changes to occur. Kind regards, -[[m:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] 11:28, 22 October 2024 (UTC)
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:Hi @[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]]: I Just noticed your post above, and it is timely.
:I have been participating in the English WikiUniversity for a few years, much less often recently. I seems like something in the way the site displays is different, but I cannot put my finger on it. Your posting gave me a clue. Can you please tell me where  the link to wikidata items has moved to? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:23, 11 December 2024 (UTC)
::Hello @[[User:Ottawahitech|Ottawahitech]], sure, I would be happy to. The button/sitelink name didn't change, just its position. You should find it in the sidebar-menu under the section '''In other projects''' (where the links to all other Wikimedia Projects are displayed). If you do not see it, please reach out to us on the [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Move Wikidata item - Discussion page]]. Thank you, -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 09:24, 12 December 2024 (UTC)
:::@[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]], thank you for responding. I intend to followup on the ''Move Wikidata item - Discussion page'' as per your post above by putting it on my ever growing todo list.
:::I don't know about others on this wiki, as I said I have not been visiting here frequently, but for me the constant changes are a big distraction. I have been around wikimedia projects since 2007, so why do I have to spend so much time learning and re-learning how to find what I came here for? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:41, 12 December 2024 (UTC)
::::Hi @[[User:Ottawahitech|Ottawahitech]], thanks for you thoughts. Your input whether positive or critical helps us understand the impacts to editors so we welcome your further thoughts when you reach us in your To Do List :)
::::I can't speak about the other changes you've experienced here but I do hope they are made with a spirit of improvement for the community as a whole. -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 10:43, 16 December 2024 (UTC)

== Final Reminder: Join us in Making Wiki Loves Ramadan Success ==

Dear all,

We’re thrilled to announce the Wiki Loves Ramadan event, a global initiative to celebrate Ramadan by enhancing Wikipedia and its sister projects with valuable content related to this special time of year. As we organize this event globally, we need your valuable input to make it a memorable experience for the community.

Last Call to Participate in Our Survey: To ensure that Wiki Loves Ramadan is inclusive and impactful, we kindly request you to complete our community engagement survey. Your feedback will shape the event’s focus and guide our organizing strategies to better meet community needs.

* Survey Link: [https://docs.google.com/forms/d/e/1FAIpQLSffN4prPtR5DRSq9nH-t1z8hG3jZFBbySrv32YoxV8KbTwxig/viewform?usp=sf_link Complete the Survey]
* Deadline: November 10, 2024
Please take a few minutes to share your thoughts. Your input will truly make a difference!

'''Volunteer Opportunity''': Join the Wiki Loves Ramadan Team! We’re seeking dedicated volunteers for key team roles essential to the success of this initiative. If you’re interested in volunteer roles, we invite you to apply.
* Application Link: [https://docs.google.com/forms/d/e/1FAIpQLSfXiox_eEDH4yJ0gxVBgtL7jPe41TINAWYtpNp1JHSk8zhdgw/viewform?usp=sf_link Apply Here]
* Application Deadline: October 31, 2024
Explore Open Positions: For a detailed list of roles and their responsibilities, please refer to the position descriptions here: [https://docs.google.com/document/d/1oy0_tilC6kow5GGf6cEuFvdFpekcubCqJlaxkxh-jT4/ Position Descriptions]

Thank you for being part of this journey. We look forward to working together to make Wiki Loves Ramadan a success!


Warm regards,&lt;br&gt;
The Wiki Loves Ramadan Organizing Team 05:11, 29 October 2024 (UTC)
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== Android app for Wikiversity ==

Hi, is there an Android app for Wikiversity? How does it work? I have been advised that there is no infrastructure for push notifications for Android apps for sister wikis and I would be interested to know more. Related: [[:phab:T378545]]. Thanks! [[User:Gryllida|Gryllida]] 23:15, 29 October 2024 (UTC)

:Thanks for suggesting this - I agree that it would be useful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:56, 31 October 2024 (UTC)
:@[[User:Gryllida|Gryllida]]: Would you explain your terminology  for those of us not in the know. What does ''push notifications'' mean? I use [https://www.mediawiki.org/wiki/Help:Notifications notifications] when I am communicating on wikimedia projects, but have never heard this term before. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:13, 11 December 2024 (UTC)
:I dont think there is an app.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:01, 17 December 2024 (UTC)
:This would be useful, however we do not have an app for Wikiversity yet. I am thinking of helping out with no-code or low code tools, but I am working on some courses here. I might be able to do some contributions though. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 14:14, 17 December 2024 (UTC)

== Import Resource From Wikibooks? ==

Hello! [[wikibooks:Character_List_for_Baxter&amp;Sagart|Character List for Baxter&amp;Sagart]] and related titles [[wikibooks:Wikibooks:Requests_for_deletion#Character_List_for_Baxter&amp;Sagart|are up for deletion at Wikibooks]] because WB policy does not allow dictionaries like them. However, because they are useful as learning tools, I am wondering if they might have a home here at Wikiversity. Pinging @[[User:Tibetologist|Tibetologist]] here to link them in to this discussion, since they are the affected user. Thank you! —[[User:Kittycataclysm|Kittycataclysm]] ([[User talk:Kittycataclysm|discuss]] • [[Special:Contributions/Kittycataclysm|contribs]]) 18:18, 1 November 2024 (UTC)

:Sure, I can do it. That said, as mentioned there, it does seem like something like this is ideally suited for Wiktionary in the Appendix namespace, but I'm not very familiar with CJK characters and languages. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:23, 3 November 2024 (UTC)
::Oh man, these pages are too big to import and while I've already tried a half-dozen times, it will constantly fail. Strictly speaking, we don't have to use the import feature for licensing purposes. We can just copy and paste the contents and list the usernames or on the talk page. I think that's the solution. {{Ping|Tibetologist}}, are you interested in doing that? If you just copied and pasted these pages and then added [[:Category:Chinese]] and maybe include a couple of links to the pages, that would probably be ideal. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:31, 3 November 2024 (UTC)

== Language translation requests? ==

Is there anywhere on Wikiversity to request translation, for example, requesting Latin or French translation? I would be asking from the context as a student, so I would be interested in translation explanation as well. [[User:Indexcard88|Indexcard88]] ([[User talk:Indexcard88|discuss]] • [[Special:Contributions/Indexcard88|contribs]]) 04:56, 20 November 2024 (UTC)

:I am not too sure about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:44, 17 December 2024 (UTC)

== Sign up for the language community meeting on November 29th, 16:00 UTC ==

Hello everyone,

The next language community meeting is coming up next week, on November 29th, at 16:00 UTC (Zonestamp! For your timezone &lt;https://zonestamp.toolforge.org/1732896000&gt;). If you're interested in joining, you can sign up on this wiki page: &lt;https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#29_November_2024&gt;.

This participant-driven meeting will be organized by the Wikimedia Foundation’s Language Product Localization team and the Language Diversity Hub. There will be presentations on topics like developing language keyboards, the creation of the Moore Wikipedia, and the language support track at Wiki Indaba. We will also have members from the Wayuunaiki community joining us to share their experiences with the Incubator and as a new community within our movement. This meeting will have a Spanish interpretation.

Looking forward to seeing you at the language community meeting! Cheers, [[User:SSethi (WMF)|Srishti]] 19:55, 21 November 2024 (UTC)
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== Events on Wikiversity ==

Since Wikipedia and Wikivoyage are having their &quot;Asian Month&quot; editathon, I was thinking if we could start up a Wikiversity version of that. This would be an &quot;Asian Month&quot; as well, but it would be about creating resources based on Asia and its culture. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:57, 6 December 2024 (UTC)

:Not immediately opposed, but the question is, do we have an active enough community to facilitate this? —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:31, 6 December 2024 (UTC)
::I'm not too sure. As long as we get enough traffic, this could happen. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 08:45, 7 December 2024 (UTC)
:::This is to increase traffic on Wikiversity, which is promoted amongst other communities. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 10:47, 7 December 2024 (UTC)
:Hi @[[User:RockTransport|RockTransport]], This is a good idea, but will it also involve users who are not &quot;professors and scientists&quot;. Just curious. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:30, 9 December 2024 (UTC)
::Yes, considering the fact that Wikiversity is for everyone, and not just for specific users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:09, 10 December 2024 (UTC)
:::because I'm personally not a &quot;professor&quot; or a &quot;scientist&quot; and because '''anyone''' can create resources on Wikiversity. We want to make Wikiversity open for everyone, and not just for certain users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:10, 10 December 2024 (UTC)
::::I am also not a professor or a scientist, but it seems to me that as result I am viewed here as a visitor rather than someone who can contribute. Just my $.02. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:05, 12 December 2024 (UTC)
:I am affraid, that creation of educational resources on certain topic is way harder then wikipedia. Secondly while wikipedia stub does not matter, education resource stub is uselless completly. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:59, 17 December 2024 (UTC)
::How is it useless, you can contribute to other learning resources and maybe improve it as such, if you have some knowledge on a particular topic or something else. This is to increase diversity. Just a kind notice. It's also pretty hard to do it on Wikivoyage, but that's the same for every platform. Stubs may be improved on, and this is the concept. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:19, 17 December 2024 (UTC)
::There are lots of stubs here, on Wikiversity. So the whole purpose of this event is to increase engagement and willingness to edit these pages. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:24, 17 December 2024 (UTC)

== Wikiversity - Newsletters ==

Hello All,

I wanted to create a newsletter on Wikiversity, which would highlight what is going on in certain months and events on Wikiversity; which would bolster engagement by many people. This would be on the website and would have its dedicated 'Newsletter' tab.

I hope you acknowledge this idea. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:05, 8 December 2024 (UTC)

:@[[User:RockTransport|RockTransport]], What sort of things do you plan to include in your newsletter? Will they be different than what is currently in [[Main Page/News]]? Just curious.
:I am also wondering about your motive which I think is: to bolster engagement by many people. I am asking because I wonder if others who are currently active here also think this I is desirable? Have you asked them? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:34, 11 December 2024 (UTC)
::Not yet, which was why I was asking this on the colloquium. I plan to include things that many people have created on Wikiversity over the month, as it is a monthly newsletter. It would be somewhere on the website here. It will be more frequent that the ones seen on [[Main Page/News]]. We will include people's resources to essentially promote them. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 06:50, 12 December 2024 (UTC)
:::@[[User:RockTransport|RockTransport]], I Think what you are saying is that ''Main Page/News'' does not update frequently enough? 
:::If this is the reason, why not start small by simply increasing the frequency of posting news on the main page, instead of trying to start a newsletter?
:::If there is more, can you articulate what else is missing. Thanks in advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:51, 12 December 2024 (UTC)
::::I meant going to detail into topics covered in that month, rather than just giving a few points. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 16:53, 12 December 2024 (UTC)
:::::What sort of details did you have in mind? You can pick one of the links provided in [[Main Page/News]] to illustrate. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:29, 16 December 2024 (UTC)
::::::I'm thinking of the community entering their projects, and discussing those in the newsletter. It depends on what they want, though. There would be a dedicated page for giving the information about their projects [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:24, 16 December 2024 (UTC)
:::::::I might start working on this soon, depending on the projects being created on Wikiversity. @[[User:Ottawahitech|Ottawahitech]] @[[User:Atcovi|Atcovi]] [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:25, 17 December 2024 (UTC)
::::::::I'd recommend you start off with putting this under a userspace page (something like [[User:RockTransport/Wikiversity Newsletter]]), and drafting what you desire. Let us know once it's done, and the community can provide their input. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 18:30, 17 December 2024 (UTC)
:::::::::I will try and make one for this month. This is supposed to be a monthly newsletter, showcasing the different projects mentioned there. Users can put their projects, and we will document them on the newsletter. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:33, 17 December 2024 (UTC)
:::::::::I am hoping for it to be released by January 2025. There's no rush to get it done; it's still in it's planning stage. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:43, 17 December 2024 (UTC)
::::I '''might''' be able to icnrease the frequency there, but it doesn't go into detail about these topics. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:30, 18 December 2024 (UTC)
:Where you are going to get the audience for your website and Wikiversity newsletter? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:38, 18 December 2024 (UTC)
::It's on Wikiversity, not on an outside platform. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:51, 18 December 2024 (UTC)
::The audience will be Wikiversity contributors. There will be a dedicated page for it on Wikiversity. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:55, 18 December 2024 (UTC)

== Describing Wikiversity content on Wikidata ==

Anyone knows how to properly describe Wikiversity pages on Wikidata? Any examples for some content pages like courses, supplement materials etc.? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:36, 18 December 2024 (UTC)

:For general topics that will have other Wikimedia Foundation project links (e.g. [[astronomy]]), there will probably be a sufficient short description already, but for subpages or more obscure topics, you could plausibly use &quot;Wikimedia content page&quot; or some such. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:52, 18 December 2024 (UTC)
::Yeah, general topics are easy to map. While specific projects which does not have Wikipedia counterparts and which are quite specific it would be nice to have few examples - i.e. what are typical properties of a course or research project. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:00, 19 December 2024 (UTC)

== Degrees ==

Why does Wikiversity not provide degrees? I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal. But anyway, why is that? Wikiversity is about opening doors, i.e., removing obstacles. So, what kind of an obstacle was a paper? Was a certain body of knowledge that you learned well?! Because Wikiversity is not accredited for that? Yes, and do we need official US accreditation? We cannot create our system so that the learners who learn here and would like to continue their science career have a recognizable degree they can continue? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:19, 18 December 2024 (UTC)

:&quot;I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal.&quot; Was it? Becoming a degree-granting institution is an extremely high bar in the United States, but what is even the point in becoming a degree-granting institution in... Malawi? Tonga? Somewhere else where the servers aren't located or the WMF aren't incorporated? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:53, 18 December 2024 (UTC)
::I ment certificates. The question is the recognazibility of a certificate. I am not talking here about equal certification, which is provided by governmental institucians to universities, rather on Wikiversity own certification, which might may advocate itself over the time. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:05, 19 December 2024 (UTC)

== Common Corpus and LLM training ==

Greetings. I believe LLM generated content is not currently allowed on this wiki. No problem. I am curious - what if the dataset an [[LLM]] is trained on is all in the public domain; would this or does this change that with regards to LLM generated content being allowed (presuming the LLM output is verified and accurate)? Has there been any discussion on this wiki or other MediaWiki wikis about LLM generated content by LLM's that is trained exclusively on CC-0/public domain data? i.e. Common Corpus https://huggingface.co/blog/Pclanglais/common-corpus
[[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:41, 25 December 2024 (UTC)</text>
      <sha1>c9lcslj8156qtscdqnxgq8t3tli3dqi</sha1>
    </revision>
    <revision>
      <id>2693201</id>
      <parentid>2693200</parentid>
      <timestamp>2024-12-25T18:49:11Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <comment>/* Degrees */</comment>
      <origin>2693201</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="86933" sha1="8asq8xfr5328l9y81ldfai11kzh528o" xml:space="preserve">{{Wikiversity:Colloquium/Header}}
&lt;!-- MESSAGES GO BELOW --&gt;
== Reminder! Vote closing soon to fill vacancies of the first U4C ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Dear all,

The voting period for the Universal Code of Conduct Coordinating Committee (U4C) is closing soon. It is open through 10 August 2024. Read the information on [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Election/2024_Special_Election#Voting|the voting page on Meta-wiki to learn more about voting and voter eligibility]]. If you are eligible to vote and have not voted in this special election, it is important that you vote now.

'''Why should you vote?''' The U4C is a global group dedicated to providing an equitable and consistent implementation of the UCoC. Community input into the committee membership is critical to the success of the UCoC.

Please share this message with members of your community so they can participate as well.

In cooperation with the U4C,&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 15:30, 6 August 2024 (UTC)
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== User group for Wikiversians ==

Was there ever a discussion about the possibility of establishing a user group in the sense of an affiliated organization that would defend the interests of professors and scientists on Wikiversity and possibly actively develop some projects? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:21, 8 August 2024 (UTC)

:Not that I'm aware of. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:20, 8 August 2024 (UTC)
:It's a pleasure to talk to a scientist on Wikiversity. I am a historian of technics and I would like to publish the following biography either on Wikiversity or on Wikipedia: 
:https://en.wikiversity.org/wiki/User:Rbmn/Arthur_Constantin_KREBS_(1850-1935):_Military_engineer,_Automotive_industrialist,_Great_projects_manager
:What would be your advice? [[User:Rbmn|Rbmn]] ([[User talk:Rbmn|discuss]] • [[Special:Contributions/Rbmn|contribs]]) 15:44, 6 October 2024 (UTC)
::The content appears to be largely biographical/encyclopedic, so I think it is likely best suited to Wikipedia. Consider improving/incorporating this content into the existing page: [[w:Arthur Constantin Krebs]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:05, 7 October 2024 (UTC)
::Please do not link to the Wikiversity [[wv:userspace|Userspace]] in Wikipedia articles. You will want to wait until you have a page in the [[wv:mainspace|Wikiversity mainspace]]. You'll also want to use the &lt;code&gt;{{[[:w:Template:Wikiversity|Wikiversity]]}}&lt;/code&gt; template (on Wikipedia) rather than embedding a photo with a link. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:21, 7 October 2024 (UTC)
:I haven't heard anything about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:06, 8 December 2024 (UTC)

== Rich's ''Illustrated Companion'' at Wikiversity: Right place? ==

Hello! I am creating a Wiki-version of a classical glossary (''Illustrated Companion to the Latin Dictionary, and Greek Lexicon'' by Anthony Rich, 1849), which explains the meaning of Latin headwords, primarily those &quot;representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans.&quot; The aim is to help understand what a (classical) Latin text is actually about, instead of merely translating it. I already transcribed the entire text and scanned the images (about 1900) from an original 1849-edition. I am currently working on uploading the images to ''Mediawiki Commons'', which probably will take some time. In the meantime I want to prepare the other aspects of the project (more than 3000 articles, already with many internal links). The important thing: this is ''not'' a ''might exist''-project.  {{Color|red|My question: Is ''Wikiversity'' the proper place for it?}} Although I created an exact rendition of the original text, ''Wikisource'' is not applicable, because the project has a broader scope (adding content to the articles, e. g. links to online editions for quotations, adding images, but also adding entirely new articles). Neither is ''Wikibooks'', because this is not a textbook and may otherwise breach its scope. For more about the project see [[w:User:CalRis25/Temp-RICH-Prospectus|my user-page]] at en.wikipedia. {{Color|Red|So, is Wikiversity the right place for it?}} [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:15, 17 August 2024 (UTC)

:Thanks for asking. To be clear, it ''is'' acceptable to make [[:s:en:Category:Wikisource annotations|annotated editions]] of texts at Wikisource and Wikibooks does host at least one [[:b:en:Annotations of The Complete Peanuts|annotated guide to a copyright-protected work]]. So if what you're looking to do is to include inline annotations to a public domain text, you certainly can put that on Wikisource. If you have a textbook or guidebook that is a companion, that would go at Wikibooks. If you have some other kind of learning resources (like maintaining a list of relevant links, organizing a book reading group, etc.), that could go here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:26, 17 August 2024 (UTC)
::Thank you for your quick answer. Actually, ''Wikibooks'' was my first thought. However, this project is not merely an annotated edition. Although at first it ''will'' be a faithful copy of the original text, I want the project to be &quot;open&quot;, i. e. adding articles should be possible. And the project should enable to do a lot more than mere inline annotation. See section [[w:User:CalRis25/Temp-RICH-Prospectus#Improving_RICH|Improving Rich]] in the project description a my user-page (en.Wikipedia). No ''Mediawiki''-project (Wikisource, Wikibooks, Wikipedia, Wiktionary) seemed to be a sufficiently applicable &quot;fit&quot; for the project, so I thought of Wikiversity as a last resort, because it is supposed to be home to all sorts of &quot;learning resources&quot;. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:57, 17 August 2024 (UTC)
:::The scope of Wikiversity ''is'' pretty catch-all and would allow for a pretty flexible place to host most learning resources that don't fit elsewhere.
:::Also, as nitpick, &quot;MediaWiki&quot; is the software that is the basis of these wikis (wikis being collections of interlinked documents that can be edited) and &quot;Wikimedia Foundation&quot; is the non-profit who owns the trademarks and hosts these projects like Wiktionary and Wikivoyage. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 10:06, 17 August 2024 (UTC)
::::Hello Justin, thank you for the reply. '''I think that settles it. I will create this project at ''Wikiversity''.''' Just for additional clarification, why I do so. Let's imagine a full transcription of the original 1849-edition of the ''Illustrated Companion'' by Anthony Rich and call it ''RICH-1849''. We shall call my project, for brevity sake, RICH-2K. And now, let's have a look at the article about the Roman toga (a piece of attire). In ''RICH-1849'' we can can call it ''RICH-1849/Toga'', and it contains ''exactly'' the content of the 1849-book. Now, let's look at the article ''RICH-2K/Toga''. At the beginning its only content would be the article ''RICH-1849/Toga''. Does that make ''RICH-2K/Toga'' and ''RICH-1849/Toga'' the same? Not at all, because in truth ''RICH-2K/Toga'' is a &quot;container&quot; which initially contains only the article ''RICH-1849/Toga'' but later on may include more stuff: images, external links, article text which builds on or extends ''RICH-1849/Toga'' and information from other sources of information (Wikipedia, specialized books). By the way, this added article information would not be a mere copy of the text at en.Wikipedia, because the information needs to looked at through the eyes of someone reading the original text (more citations with direct links to these etc.). [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 11:39, 17 August 2024 (UTC)

== Coming soon: A new sub-referencing feature – try it! ==

&lt;section begin=&quot;Sub-referencing&quot;/&gt;
[[File:Sub-referencing reuse visual.png|{{#ifeq:{{#dir}}|ltr|right|left}}|400px]]
Hello. For many years, community members have requested an easy way to re-use references with different details. Now, a MediaWiki solution is coming: The new sub-referencing feature will work for wikitext and Visual Editor and will enhance the existing reference system. You can continue to use different ways of referencing, but you will probably encounter sub-references in articles written by other users. More information on [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|the project page]].

'''We want your feedback''' to make sure this feature works well for you:

* [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|Please try]] the current state of development on beta wiki and [[m:Talk:WMDE Technical Wishes/Sub-referencing|let us know what you think]]. 
* [[m:WMDE Technical Wishes/Sub-referencing/Sign-up|Sign up here]] to get updates and/or invites to participate in user research activities.

[[m:Special:MyLanguage/Wikimedia Deutschland|Wikimedia Deutschland]]’s [[m:Special:MyLanguage/WMDE Technical Wishes|Technical Wishes]] team is planning to bring this feature to Wikimedia wikis later this year. We will reach out to creators/maintainers of tools and templates related to references beforehand.

Please help us spread the message. --[[m:User:Johannes Richter (WMDE)|Johannes Richter (WMDE)]] ([[m:User talk:Johannes Richter (WMDE)|talk]]) 10:36, 19 August 2024 (UTC)
&lt;section end=&quot;Sub-referencing&quot;/&gt;
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== New [[Template:Form]] ==

Hi! Today I was bold and created [[Template:Form]] (which calls [[Module:WikiForm]] and [[MediaWiki:Gadget-WikiForm.js]]). The template allows to create user-friendly forms that can create pages or add content to existing pages. My motivation and first use case was [[Wikidebate/New|this form]] to create new [[wikidebates]], but I suspect the template can be useful elsewhere on Wikiversity. Let me know if you notice any issues or have any requests or concerns. Kind regards, [[User:Sophivorus|Sophivorus]] ([[User talk:Sophivorus|discuss]] • [[Special:Contributions/Sophivorus|contribs]]) 15:21, 21 August 2024 (UTC)

== Sign up for the language community meeting on August 30th, 15:00 UTC ==

Hi all,

The next language community meeting is scheduled in a few weeks—on August 30th at 15:00 UTC. If you're interested in joining, you can [https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#30_August_2024 sign up on this wiki page].

This participant-driven meeting will focus on sharing language-specific updates related to various projects, discussing technical issues related to language wikis, and working together to find possible solutions. For example, in the last meeting, topics included the Language Converter, the state of language research, updates on the Incubator conversations, and technical challenges around external links not working with special characters on Bengali sites.

Do you have any ideas for topics to share technical updates or discuss challenges? Please add agenda items to the document [https://etherpad.wikimedia.org/p/language-community-meeting-aug-2024 here] and reach out to ssethi(__AT__)wikimedia.org. We look forward to your participation!

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 23:20, 22 August 2024 (UTC)
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== Template consolidation: User talk page block notice ==
Wondering if someone who likes templates could have a go at consolidating or helping decide between use of:
* [[Template:Block]]
* [[Template:Blocked]]

Unless I'm missing something, it seems like we don't need both?

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:16, 23 August 2024 (UTC)
: I tried to figure out a Wikidata item with most links to projects. I found this: [[Wikidata:Q6379131]], which is Template:Uw-block. There is even a corresponding Wikiversity template, [[Template:Uw-block1]] (not used anywhere).
: My impression is that of the three templates, we only need one. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:43, 13 September 2024 (UTC)

== Announcing the Universal Code of Conduct Coordinating Committee ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[https://lists.wikimedia.org/hyperkitty/list/board-elections@lists.wikimedia.org/thread/OKCCN2CANIH2K7DXJOL2GPVDFWL27R7C/ Original message at wikimedia-l]. [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Hello all,

The scrutineers have finished reviewing the vote and the [[m:Special:MyLanguage/Elections Committee|Elections Committee]] have certified the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Results|results]] for the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election|Universal Code of Conduct Coordinating Committee (U4C) special election]].

I am pleased to announce the following individual as regional members of the U4C, who will fulfill a term until 15 June 2026:

* North America (USA and Canada)
** Ajraddatz

The following seats were not filled during this special election:

* Latin America and Caribbean
* Central and East Europe (CEE)
* Sub-Saharan Africa
* South Asia
* The four remaining Community-At-Large seats

Thank you again to everyone who participated in this process and much appreciation to the candidates for your leadership and dedication to the Wikimedia movement and community.

Over the next few weeks, the U4C will begin meeting and planning the 2024-25 year in supporting the implementation and review of the UCoC and Enforcement Guidelines. You can follow their work on [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Meta-Wiki]].

On behalf of the U4C and the Elections Committee,&lt;section end=&quot;announcement-content&quot; /&gt;

[[m:User:RamzyM (WMF)|RamzyM (WMF)]] 14:07, 2 September 2024 (UTC)
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== Re: The Vector 2022 skin as the default in two weeks? ==

[[File:Vector 2022 video-en.webm|thumb|A two minute-long video about Vector 2022]]
Hello everyone, I'm reaching out on behalf of the [[mediawikiwiki:Reading/Web|Wikimedia Foundation Web team]] responsible for the MediaWiki skins. I'd like to revisit the topic of making Vector 2022 the default here on English Wikiversity. I [[Wikiversity:Colloquium/archives/September 2022#The Vector 2022 skin as the default in two weeks?|did post a message about this almost two years ago]] (where you can find all the details about the skin), but we didn't finalize it back then.

What happened in the meantime? We built [[mw:Reading/Web/Accessibility for reading|dark mode and different options for font sizes]], and made Vector 2022 the default on most wikis, including all other Wikiversities. With the not-so-new V22 skin being the default, existing and coming features, like dark mode and [[mw:Trust and Safety Product/Temporary Accounts|temporary accounts]] respectively, will become available for logged-out users here.

So, if no large concerns are raised, we will deploy Vector 2022 here in two weeks, in the week of September 16. Do let me know if you have any questions. Thank you! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 21:48, 2 September 2024 (UTC)

:Sounds good, Szymon - we look forward to the upcoming change of skin {{smile}} Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:35, 13 September 2024 (UTC)
* I for one oppose a switch to Vector 2022. I do not find it preferable. Here is a staggering evidence of user refusal of Vector 2022 once it was deployed: [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]], Junuary 2023. 355 voters supported rollback to Vector 2010 whereas 64 opposed, yielding 84.7% support, as clear a supermajority as one may wish. These people opposing Vector 2022 feel the same way as I do. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:48, 13 September 2024 (UTC)
*:Hey @[[User:Dan Polansky|Dan Polansky]]. Thanks for your comment. I'm open to discussion about problems with our software, and I hope we can maintain a respectful tone.
*:I understand that there are users who prefer Vector legacy or other skins, just as there are people who still stick to Monobook. Such people are active across many wikis. They can keep Vector legacy, although non-default skins don't have the support the default ones do. We are rolling out for technical reasons, as I mentioned above, with benefit to not logged-in users.
*:Regarding the rollback RfC on Wikipedia, two neutral users stated that there was no consensus for rollback, RfC is not a vote, and the numbers were different (355:226:24). I believe this all is pretty easy to verify.
*:So to sum up, Vector 2022 needs to become the default, tons and tons of comments were made about the skin and related stuff, and we have taken many ideas into account, and it's totally OK if you stick to Vector legacy.
*:Thanks! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 19:30, 16 September 2024 (UTC)
*:: Today, I visited Wikiversity and found it switched to Vector 2022. I changed my preference settings to Vector 2010. From what I understand, non-registered visitors are now defaulted to Vector 2022 despite its unpopularity in [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]]. I have not seen any evidence that users prefer Vector 2022, and given the evidence in the linked RfC, I tentatively conclude that the decision to switch has made the site experience worse for the majority of users. The logic of &quot;you can switch&quot; surely applies to Vector 2022 as well: those who prefer it can switch to it. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:08, 17 September 2024 (UTC)

== Have your say: Vote for the 2024 Board of Trustees! ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

The voting period for the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Board of Trustees election]] is now open. There are twelve (12) candidates running for four (4) seats on the Board.

Learn more about the candidates by [[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Candidates|reading their statements]] and their [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Questions_for_candidates|answers to community questions]].

When you are ready, go to the [[Special:SecurePoll/vote/400|SecurePoll]] voting page to vote. '''The vote is open from September 3rd at 00:00 UTC to September 17th at 23:59 UTC'''.

To check your voter eligibility, please visit the [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Voter_eligibility_guidelines|voter eligibility page]].

Best regards,

The Elections Committee and Board Selection Working Group&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:15, 3 September 2024 (UTC)
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== Separate page for hyperbola. ==

Good morning,

I notice that a search for &quot;hyperbola&quot; redirects to &quot;Conic sections&quot;.

At present there is a separate page for &quot;ellipse&quot;. Therefore a separate page for &quot;hyperbola&quot; seems to be justified.

Could this redirection be changed so that search for &quot;hyperbola&quot; goes to a separate page for &quot;hyperbola&quot;?

Many thanks,

[[User:ThaniosAkro|ThaniosAkro]] ([[User talk:ThaniosAkro|discuss]] • [[Special:Contributions/ThaniosAkro|contribs]]) 12:04, 15 September 2024 (UTC)

:It is true that ellipses are covered at [[Conic sections]] (along with hyperbolas, parabolas, etc.) and there is a separate page for [[ellipse]]s that elaborates. We certainly ''could'' have a page about [[hyperbola]]s that is separate, but no one has written sufficient content to spin it off yet. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 12:17, 15 September 2024 (UTC)

== I hereby request for your Unblocking IP address and just reviewed and received a reverted rec ==

Hi there. {{unsigned|Ishmael Raphasha}}
:No one has any clue what you're talking about. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:53, 18 September 2024 (UTC)

== RICH-2K: New project with some initial questions ==

Hello! I'm creating a new learning resource on ''Wikiversity''. The respective project is based on my transcription of a classical dictionary from 1849 by Anthony Rich. For more information about the project see its [[User:CalRis25/RICH: Description|description page]] (see also that page for why not ''Wikisource'' or ''Wikibooks''). The project's scope is fairly big: 3205 article-pages plus 304 REDIRECT-pages. The images (scanned by myself from an original copy) have been uploaded to ''Commons''. I have some initial technical questions (more of these and more detailed ones will follow):

* '''Upload''': Due to the large number of pages it is not realistic to create these manually. Is it possible to bulk-upload these in some way (the Wikitext of the pages is created using a Python-script with one file per article/page)? Is it possible to upload these to a test-environment first where any problems (hopefully none) can be identified and dealt with more easily than on the production-version of ''Wikiversity''?
* '''(Technical) Structure''': I am planning to set up this project at ''&lt;nowiki&gt;https://en.wikiversity.org/wiki/RICH-2K&lt;/nowiki&gt;'' as the main page and anything else as subpages: ''RICH-2K/Subpage_1 ... RICH-2K/Subpage_n''. However, these subpages fall into two categories: 1. Article-pages (content) and 2. Meta/Administrative pages. This project requires search capability restricted to the ''RICH-2K''-namespace. The ''Mediawiki''-software seems to supply a ''Search''-input field with the possibility to restrict the search to some namespace. I would like, however, to restrict the search further to the first group of pages, namely the articles. Is that possible, perhaps by use of (hidden) categories?
* '''External links''': This project will need many external links, and yes, I have read the relevant ''Wikiversity''-pages, but this specific project needs them. The ''Recommended Editions''-page (used for recommended online editions, to which to link when citing texts) alone probably will require several hundred external links. However, only relatively few [[w:Second-level domain|second-level domains]] will be involved, and most of these should be trustworthy (Perseus Digital library, digital collections of universities etc., in some cases, however, also ''Archive.org''). Perhaps there is a list of web-sites, for which external links are generally allowed? And who is allowed to create external links on ''Wikiversity''-pages (I haven't found the relevant policy)?
* '''Categories''': This project requires quite a few of its own categories, which belong to two large groups: 1. Categories (2 levels) of the ''Classed Index'' (about 170 categories), a thematic index of some (but not all) of the articles. 2. Administrative categories. Is there a recommended way to distinguish between different classes of categories within a project (category name or other method)? What about naming conventions for project-specific categories?

I am looking forward to your input. If you think that it's preferable we can move the discussions to the [[User_talk:CalRis25/RICH:_Description|Talk-page]] of the project's description. Thank you in advance. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 05:29, 20 September 2024 (UTC)

:*Admins have access to [[Special:Import]] and can bulk import XML pages. You can create pages in your sandbox if you'd like and make an indefinite amount of them at pages like [[User:CalRis25/sandbox]]. What can and cannot be hosted in user namespace is very loose, but still has to follow in principle Wikiversity's scope.
:*Using subpages is in principle a good way to organize these various resources. Please do not name them after a user name or something obscure. I personally think that &quot;RICH-2K&quot; is a not optimal name. I may recommend something like [[Anthony Rich Dictionary Project]] or [[21st-Century Anthony Rich Dictionary]] or something more obviously intelligible. While we have very few actual policies and guidelines, see [[Wikiversity:Naming conventions]] for a rough consensus of what is probably best practice for naming pages.
:*External linking generally does not use an allowed list (a.k.a. whitelist model), but a disallow (a.k.a. blacklist) model. See [[MediaWiki:Spam-blacklist]] and [[Special:BlockedExternalDomains]] (which is currently empty but is another method of listing blocked domains). It's perfectly fine to aggregate external links in learning resources.
:*I'm not 100% sure what the distinction is that you're drawing, but you can freely arrange categories underneath a main category that has the same name as your larger project. So, following the suggestions I gave, you could have a category like [[:Category:Anthony Rich Dictionary Project]] and then create any number of subcategories that logically help users navigate all these pages. Please make sure the main category you create is itself categorized under some relevant category(ies). If you need help, please ask.
:I think this answers your questions, please let me know if I'm unclear or you have more. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:11, 20 September 2024 (UTC)
::Hello Justin!
::* '''Upload:''' Creating the project in sandbox pages of my User-namespace defeats the purpose, as this is an ''open'' project. Also that would not solve, as such, the problem of having to manually create thousands of pages. I wonder, does ''Wikiversity'' support creation of pages using its API. ''Mediawiki's'' [[mw:API:Main_page|API-description]] seems to imply that it ought to be possible. If that's the case, I should be able to create a Python-script which automatically creates the pages (of course, a few trial pages first).
::* '''(Technical) Structure''': You may be right, here. RICH-2K is, for now, merely a technical name to make a clear but not too verbose distinction between the original text and the current project. I'll give this more thought.
::* '''External links''': I brought this up mainly because when I first edited my ''Wikiversity''-page, I got a message that I was not allowed to create external links. However, I just now tested creating an external link on my user-page and got no error, so this problem seems to be solved.
::* '''Categories''': I think I know what you mean. I'll create a category structure and maybe ask some specific questions once I am ready to do so.
::Thank you for your quick help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 18:51, 20 September 2024 (UTC)
:::re: upload, I'm just suggesting your sandbox(es) as you asked about &quot;a test-environment&quot;. Anyone can edit someone else's sandboxes, but you typically defer to other users to control what's in their own subpages as a collegial thing. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:39, 23 September 2024 (UTC)

Hello! I have two further questions:
# I created a category-structure for the project. Could you (or someone else) have a look at it ([[User:CalRis25/RICH: Categories]]) and answer the questions in the section [[User:CalRis25/RICH:_Categories#Questions|Questions]]? I gave it some thought and believe that this would work fine for the project.
# ''Project boxes'' (see [[Help:Tour of project boxes]]): It is unclear to me, whether these belong only on the main page of the project (that makes the most sense to me), or on every single subpage.
Thanks in advance for your help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 17:51, 24 September 2024 (UTC)

:To answer your questions here:
:*No, you are not contravening any policies we have.
:*A leading &quot;The&quot; is acceptable, but if you want it to sort alphabetically, you will have to use &lt;nowiki&gt;{{DEFAULTSORT:}}&lt;/nowiki&gt;. E.g. to get Category:The Best Stuff to sort under &quot;B&quot;, insert &quot;&lt;nowiki&gt;{{DEFAULTSORT:Best Stuff, The}}&lt;/nowiki&gt;.
:*Trailing &quot;etc.&quot; is acceptable.
:*An accent in a category title is acceptable.
:I'll also note that it looks like you have in mind some tracking categories that are redundant. Pages such as [[Special:LonelyPages]] and [[Special:DeadendPages]] already do automatically what you're proposing to do manually.
:As for project boxes, it's typically the case that the subjects are only placed on the main resource, but as you may imagine, [[Help:Tour of project boxes/1|status completion ones]] may vary from subpage to subpage. As with most things at Wikiversity, there are very few actual rules, so it's pretty much the wild west, even tho this project has been around for almost 20&amp;nbsp;years. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:18, 25 September 2024 (UTC)
::Hello Justin, thanks for the DEFAULTSORT-hint for categories beginning with ''The''. I will restrict the project boxes to the main page. As for the the orphaned/dead-end-categories, I prefer these to be project-specific. Once the project is up and running, putting articles &quot;on the map&quot; (making them accessible from other articles and creating links to other articles) is one of the first tasks to be dealt with. I already know which articles are involved and will add these categories to these articles. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 16:51, 25 September 2024 (UTC)

== Your wiki will be in read-only soon ==

&lt;section begin=&quot;server-switch&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;

[[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-Tech%2FServer+switch&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]

The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster.

All traffic will switch on '''{{#time:j xg|2024-09-25|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2024-09-25T15:00|en}} {{#time:H:i e|2024-09-25T15:00}}]'''.

Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. 

A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. 

'''You will be able to read, but not edit, all wikis for a short period of time.'''

*You will not be able to edit for up to an hour on {{#time:l j xg Y|2024-09-25|en}}.
*If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case.

''Other effects'':

*Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped.
* We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards.
* [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes.

This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. 

'''Please share this information with your community.'''&lt;/div&gt;&lt;section end=&quot;server-switch&quot;/&gt;

[[User:Trizek_(WMF)|Trizek_(WMF)]], 09:37, 20 September 2024 (UTC)
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== 'Wikidata item' link is moving. Find out where... ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;&lt;i&gt;Apologies for cross-posting in English. Please consider translating this message.&lt;/i&gt;{{tracked|T66315}}

Hello everyone, a small change will soon be coming to the user-interface of your Wikimedia project.
The [[d:Q16222597|Wikidata item]] [[w:|sitelink]] currently found under the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''General''&lt;/u&gt;&lt;/span&gt; section of the '''Tools''' sidebar menu will move into the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''In Other Projects''&lt;/u&gt;&lt;/span&gt; section.

We would like the Wiki communities feedback so please let us know or ask questions on the   [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Discussion page]] before we enable the change which can take place October 4 2024, circa 15:00 UTC+2.
More information can be found on [[m:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|the project page]].&lt;br&gt;&lt;br&gt;We welcome your feedback and questions.&lt;br&gt; [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 18:56, 27 September 2024 (UTC)
&lt;/div&gt;
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==Download as PDF==
[[Phabricator:T376438]]: &quot;Download to PDF&quot; on en.wv is returning error: &quot;{&quot;name&quot;:&quot;HTTPError&quot;,&quot;message&quot;:&quot;500&quot;,&quot;status&quot;:500,&quot;detail&quot;:&quot;Internal Server Error&quot;}&quot;

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 3 October 2024 (UTC)

:I just downloaded this page as a PDF and it worked just fine. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:04, 3 October 2024 (UTC)

== Protected template bug for Pp ==

It seems that templates derivative of {{tlx|Pp}} (compiled in {{tlx|Protection templates}}) are being sorted into protection categories using the name 'Wikipedia' instead of 'Wikiversity' (e.g., [[:Category:Wikipedia pages with incorrect protection templates]]). From what I can tell, it is not in the publicly accessible source code of any of the templates. The only other impacted pages are modules which call {{tlx|pp}}-derivatives (e.g., [[Module:Navbar/styles.css]]).

This does not seem to affect any other pages in [[:Category:Wikiversity protected templates]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 18:59, 4 October 2024 (UTC)

:The problem is that &quot;Wikipedia&quot; is [https://en.wikiversity.org/w/index.php?title=Special%3ASearch&amp;limit=500&amp;offset=0&amp;ns828=1&amp;search=Wikipedia&amp;searchToken=9svkpqlxxoquoq7bnkt55ugts mentioned in several modules that were copied over from en.wp]; many of these are legit and many of them need to be replaced with &quot;Wikiversity&quot; ([https://en.wikiversity.org/w/index.php?title=Module%3APp-move-indef&amp;diff=2662815&amp;oldid=1944984 e.g.]) This particular change ''may'' fix all of these issues...? But 1.) it will take time to propagate across the site and 2.) there are still many more &quot;Wikipedia&quot;s that need to be changed, so I'll go thru a few more, but if you want to give me an assist, if you can just check this one week from now and ping me if the problem persists, that would be nice. Sometimes, I make calendar reminders to follow up on these, but I'm not a perfect person. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:55, 5 October 2024 (UTC)

== Invitation to Participate in Wiki Loves Ramadan Community Engagement Survey ==

Dear all,


We are excited to announce the upcoming [[m:Wiki Loves Ramadan|Wiki Loves Ramadan]] event, a global initiative aimed at celebrating Ramadan by enriching Wikipedia and its sister projects with content related to this significant time of year. As we plan to organize this event globally, your insights and experiences are crucial in shaping the best possible participation experience for the community.

To ensure that Wiki Loves Ramadan is engaging, inclusive, and impactful, we kindly invite you to participate in our community engagement survey. Your feedback will help us understand the needs of the community, set the event's focus, and guide our strategies for organizing this global event.

Survey link: https://forms.gle/f66MuzjcPpwzVymu5

Please take a few minutes to share your thoughts. Your input will make a difference!

Thank you for being a part of our journey to make Wiki Loves Ramadan a success.


Warm regards,

User:ZI Jony 03:19, 6 October 2024 (UTC)

Wiki Loves Ramadan Organizing Team
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== 'Edit to my talk page' notification bug? ==

This may belong at the bug tracker, but does anyone else have an issue disabling ''email'' notifications upon  an 'Edit to my talk page' in [[Special:GlobalPreferences]]? Oddly I ''am'' able to disable the global preference on Wikipedia, MediaWiki, etc, but not here. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:23, 7 October 2024 (UTC)

:I have not experienced this, but to be clear, do you also have the option to get emails when items on your talk page are edited turned on? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:39, 7 October 2024 (UTC)
::The only (non-grayed out) options I have enabled for email are 'Failed login attempts' and 'Login from an unfamiliar device'. 'Edit to my talk page' re-checks after every save. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:54, 7 October 2024 (UTC)
:::That does sound like a [[phab:]] issue, with the caveat that I don't 100% recall how global preferences work and if they override local ones, etc. If you have parsed that and still have this issue, you'll probably need to file a ticket. Maybe someone else has this issue. Wish I could help. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:57, 7 October 2024 (UTC)
::::[[phab:T376601|Off 'n away]] 🫡 [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 10:35, 7 October 2024 (UTC)

== [[Portal:Computer Science]] ➝ [[Portal:Information sciences]] ==

Seeking consensus to complete the merge into the broader portal. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:28, 8 October 2024 (UTC)

:Why should it be merged? Computer Science seems well-enough designed. What is the incentive to collapse it into a broader field of study? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:18, 8 October 2024 (UTC)
::Portals as top level organizations allowing for content to be best centralized. Also note that I did not start the merge, just offering to finish it. Perhaps a {{tlx|prod}} instead? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 07:20, 8 October 2024 (UTC)
:::I have no objections, personally. If it gets done, please use a redirect and should someone want to come along to resurrect it later, it will be easier. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:21, 8 October 2024 (UTC)
: Is computer science really a branch of information sciences? I would not think so, but what do I know. Do we have some external resources/links confirm this idea? [[W:Information science]] currently says: &quot;Information science, documentology[1] or informatology[2][3] is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information.&quot; --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:49, 11 October 2024 (UTC)
::Looking through [https://stackoverflow.com/q/1047014/22673230] [https://businessdegrees.uab.edu/mis-degree-bachelors/resources/computer-information-systems-vs-computer-science/] [https://www.si.umich.edu/student-experience/what-information-science] a few top (not necessarily RS) searches I'm inclined to agree. I am more familiar with the grafted [[:w:Information and computer science|information ''and'' computer science]] which makes an effort to merge the disciplines, but it does not seem like reaching to say that IS is presented as more applications-concerned (certainly with no lack of theoretical abstraction), whereas CS can be more freely associated with any and all 'science related to computers'. It is easy to reason about the connection between the fields, but I think it is clear academia maintains this taxonomy for a good reason.
::With these considerations, I think I will ''stop'' the process of merging in favor of expanding the existing [[School:Library and Information Science]]. 

::Let me know if there is not consensus to redirect [[Portal:Information sciences]] to [[School:Library and Information Science]] (with enough expansion it can generalize away from just library sciences). [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:16, 11 October 2024 (UTC)
::: I do not see that a merge of a ''portal'' to a ''school'' is a good thing. Do you have a clear idea of the concepts of school and portal and how they relate to each other? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:34, 11 October 2024 (UTC)
::::Found [[:Category:Information sciences]]; there are enough existing resources in there to make my other proposed merge excessive. I will simply continue developing the existing [[Portal:Information sciences]] instead. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:05, 11 October 2024 (UTC)
::::: Frankly, I would ideally see [[Portal:Information sciences]] deleted: I don't see what it does that a category would not do well enough. There does not seem to be any material specific to &quot;Information sciences&quot; (whatever that is) in that portal at all. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 17:11, 11 October 2024 (UTC)
::::::Tacked a {{tlx|prod}} for an eventual deletion, but I may still try to develop it as proof of concept at some point. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:33, 11 October 2024 (UTC)

== [[:Category:Occupational Epidemiology]] ==

I propose moving the pages in this category (without leaving redirects) to their equivalent under the parent resource [[Occupational Health Risk Surveillance]]. Also due to the number of subpages, it seems &lt;code&gt;|filing=deep&lt;/code&gt; would be a justified. (Also [[Special:PrefixIndex/Occupational_Epidemiology|there are quite a few]] untagged subpages.) [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 05:11, 9 October 2024 (UTC)
: I above all think that the content should be ''moved out of the mainspace'': I do not see readers learning anything from e.g. [[Occupational Epidemiology/Research tools/Reading of scientific articles for learning epidemiology and biostatstics]] or [[Occupational Epidemiology/Research tools/Ongoing projects/Risk Communication in Seafaring/Writing the article guideline IMRAD]]. Wikiversity can be kind enough to host that material in, say, subspace of [[User:Saltrabook]], but more should not be asked, I think. Let us recall that per [[WV:Deletions]], &quot;Resources may be eligible for proposed deletion when education objectives and learning outcomes are scarce, and objections to deletion are unlikely&quot;; I do not see how learning outcomes can be anything but scarce. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:04, 11 October 2024 (UTC)
::thank you, agree @ [[User:Saltrabook|Saltrabook]] ([[User talk:Saltrabook|discuss]] • [[Special:Contributions/Saltrabook|contribs]]) 21:03, 13 November 2024 (UTC)

== Active editors ==

It is interesting to observe the stats on [https://stats.wikimedia.org/#/en.wikiversity.org/contributing/active-editors/normal|line|all|(page_type)~content*non-content|monthly active editors] through the project's history. October is our month! [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:44, 8 October 2024 (UTC)

:Odd. Maybe related to the school year? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:10, 9 October 2024 (UTC)
::I wonder how many are [[User:Jtneill|Jtneill]]'s crowd... the number is in the hundreds though, so that is one chunky cohort —[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:16, 9 October 2024 (UTC)
:::Yes, [[Motivation and emotion/Book]] involves ~100-150 students editing most intensely during October each year. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:20, 9 October 2024 (UTC)
::::Neat, that still leaves around ~50-100 other students from other avenues each year since 2021. I also wonder which projects were involved in the COVID enrollment spike. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:26, 9 October 2024 (UTC)
:::::Personally I can admit that my editing is much more active during the school season vs. the summer break, so I'm in the same boat as Jtneill's students. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:24, 13 November 2024 (UTC)
:@[[User:Tule-hog|Tule-hog]] This is an interesting topic, but it is not clear to me as an outsider what you and other participants in this discussion find interesting. I  find this graph not very meaningful because it does not tell me if the number of  Active editors has gone up or down during the period covered, which I think was 2000-now. 
:I can see a big jump between 2000 and 2007, but what happened since then? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:45, 16 December 2024 (UTC)

== Intentionally incorrect resource ==

There is a [[Special:Diff/2583464|disclaimer inserted onto a resource]] (by not the original author) that:
&lt;blockquote&gt;I am merely [making this page false] to show you (The viewer) that Wikipedia and this page 'Wikiversity' is bull sh*t and it will not give you the reliability you need when writing an academic piece of writing.&lt;/blockquote&gt;
However, that IP has [[Special:Contributions/86.22.73.151|not made any other edits]], so unless they vandalized via a sock, the intent went un-realized and only that portion need be removed. Bumping here in case there is some obvious jumbo in that essay that someone else can catch. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:58, 9 October 2024 (UTC)

:Removed that portion, which was obviously vandalism. No perspective on the rest of the essay. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:38, 9 October 2024 (UTC)

== [[:Category:Proposed guidelines]] ==

Noting for future editors that WV has collapsed all proposals into [[:Category:Proposed policies|proposed policies]]. Seeking consensus to further collapse [[:Category:Wikiversity proposals]] into the former, or to restore [[:Category:Proposed guidelines]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:19, 9 October 2024 (UTC)

== [[Around Wikiversity in 80 Seconds|Broken 80-second tour]] ==

Bumping a [[Talk:Around_Wikiversity_in_80_Seconds|comment]] on the ''Wikiversity in 80 seconds'' tour. Appears wikisuite is not working with the Vector 2022 appearance. 

Also see [[:w:Wikipedia:Miscellany_for_deletion/Wikiversuite_pages|this thread]] on the Wikiversal package - may not be relevant to Wikiversity, but FYC. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:26, 10 October 2024 (UTC)
: I would just delete the material; I do not see value in it. If others agree, I would try to articulate why I think it should be deleted (or move to author user space). --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:57, 13 October 2024 (UTC)
::Just mark as {{tl|historical}}. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:39, 13 October 2024 (UTC)
::: This thing was created by [[User:Planotse]]. His creations are now being discussed in Wikibooks for deletion: [[B:Wikibooks:Requests for deletion#Wikiversal generated pages]]. It seems he used some kind of tool that is no longer available (the above mentioned &quot;Wikiversal&quot; package) to create this kind of slideshow-like material (believing the Wikibooks discussion). I do not see value of this in the mainspace, not even as historical (I am okay with userspace, but maybe even that is not the best option?). A look at the source code of [[Around Wikiversity in 80 Seconds/Introduction]] confirms the words of Omphalographer, namely that &quot;the HTML-heavy markup generated by Wikiversal makes them [the pages] unreasonably difficult to edit.&quot;
::: I went ahead and marked the page for proposed deletion. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:35, 14 October 2024 (UTC)

== Preliminary results of the 2024 Wikimedia Foundation Board of Trustees elections ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

Thank you to everyone who participated in the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Wikimedia Foundation Board of Trustees election]]. Close to 6000 community members from more than 180 wiki projects have voted.

The following four candidates were the most voted:

# [[User:Kritzolina|Christel Steigenberger]]
# [[User:Nadzik|Maciej Artur Nadzikiewicz]]
# [[User:Victoria|Victoria Doronina]]
# [[User:Laurentius|Lorenzo Losa]]

While these candidates have been ranked through the vote, they still need to be appointed to the Board of Trustees. They need to pass a successful background check and meet the qualifications outlined in the Bylaws. New trustees will be appointed at the next Board meeting in December 2024.

[[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Results|Learn more about the results on Meta-Wiki.]]

Best regards,

The Elections Committee and Board Selection Working Group

&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MPossoupe_(WMF)|MPossoupe_(WMF)]] 08:26, 14 October 2024 (UTC)
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== Seeking volunteers to join several of the movement’s committees ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Each year, typically from October through December, several of the movement’s committees seek new volunteers. 

Read more about the committees on their Meta-wiki pages:
* [[m:Special:MyLanguage/Affiliations_Committee|Affiliations Committee (AffCom)]]
* [[m:Special:MyLanguage/Ombuds_commission|Ombuds commission (OC)]]
* [[m:Special:MyLanguage/Wikimedia Foundation/Legal/Community Resilience and Sustainability/Trust and Safety/Case Review Committee|Case Review Committee (CRC)]]

Applications for the committees open on 16 October 2024. Applications for the Affiliations Committee close on 18 November 2024, and applications for the Ombuds commission and the Case Review Committee close on 2 December 2024. Learn how to apply by [[m:Special:MyLanguage/Wikimedia_Foundation/Legal/Committee_appointments|visiting the appointment page on Meta-wiki]]. Post to the talk page or email [mailto:cst@wikimedia.org cst@wikimedia.org] with any questions you may have.

For the Committee Support team,
&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 23:09, 16 October 2024 (UTC)
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== Interactive elements ==
Can we use interactive elements on Wikiversity? I'd like to add JavaScript to a page. If it's not possible now, where can I suggest this feature? I have a safe integration idea.
[[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 12:10, 17 October 2024 (UTC)
: This is beyond my technical knowledge, but have you checked out:
:* https://www.mediawiki.org/wiki/Manual:Interface/JavaScript?
:* [[Wikipedia:WikiProject JavaScript]]
:* [[MediaWiki:Common.js]]

:What sort of interactive elements are you thinking about?

: Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:39, 18 October 2024 (UTC)
::I was thinking about adding something like a graph with adjustable controls, where users can interact with it and see how different changes affect the outcome. It seems like this could be a useful feature. There might already be discussions about enhancing Wikiversity or similar platforms—perhaps on a relevant talk page or in a Discord group. Do you know where such discussions might be happening? [[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 19:47, 18 October 2024 (UTC)
:::From a quick look, maybe check out:
:::* [[mw:Extension:Graph]]
:::* [[phab:tag/graphs]]
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:40, 18 October 2024 (UTC)
:::: mw:Extension:Graph is currently disabled on Wikipedia etc. wikis, for security reasons, and seems unlikely to be enabled again. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:30, 19 October 2024 (UTC)

== An unexplained spurt of Wikiversity page views ==
The [https://pageviews.wmcloud.org/siteviews/?platform=all-access&amp;source=pageviews&amp;agent=user&amp;start=2024-06-01&amp;end=2024-10-18&amp;sites=en.wikiversity.org|en.wikibooks.org|en.wikiquote.org|en.wikisource.org page view report] shows an unexplained spurt of Wikiversity page views, reaching over 4 times the baseline and then falling back again. Does anyone have any idea what is going on? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:01, 19 October 2024 (UTC)

:Interesting. I wonder why only the English wikiquote and wikiversity and not Wikisource or wikibooks? How reliable do you think those stats are? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:44, 8 December 2024 (UTC)
:I guess the mention in mass media might be a cause. Someone metions it and then thousands go and look. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:02, 17 December 2024 (UTC)

== Center tempate failed on a contributors phone... ==

See the edit comment here - https://en.wikiversity.org/w/index.php?title=Wikiphilosophers&amp;diff=prev&amp;oldid=2673962. I'm puzzled as this is the first failure of this, I've noted recently. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 08:45, 19 October 2024 (UTC)

== Essay-like page in user space that makes little sense and seems incoherent ==
The page [[User:TheoYalur/Illusions]] seems to match the description, at least by my assessment. My understanding is that since the page is only in user space and not in the mainspace, it can stay there even if it has those disqualifying qualities. But if I am wrong and the page belongs deleted, please correct me and let me know. I do not know which policy or guideline, if any, guides the case. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:30, 21 October 2024 (UTC)

== 'Wikidata item' link is moving, finally. ==

Hello everyone, I previously wrote on the 27th September to advise that the ''Wikidata item'' sitelink will change places in the sidebar menu, moving from the '''General''' section into the '''In Other Projects''' section. The scheduled rollout date of 04.10.2024 was delayed due to a necessary request for Mobile/MinervaNeue skin. I am happy to inform that the global rollout can now proceed and will occur later today, 22.10.2024 at 15:00 UTC-2. [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Please let us know]] if you notice any problems or bugs after this change. There should be no need for null-edits or purging cache for the changes to occur. Kind regards, -[[m:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] 11:28, 22 October 2024 (UTC)
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:Hi @[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]]: I Just noticed your post above, and it is timely.
:I have been participating in the English WikiUniversity for a few years, much less often recently. I seems like something in the way the site displays is different, but I cannot put my finger on it. Your posting gave me a clue. Can you please tell me where  the link to wikidata items has moved to? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:23, 11 December 2024 (UTC)
::Hello @[[User:Ottawahitech|Ottawahitech]], sure, I would be happy to. The button/sitelink name didn't change, just its position. You should find it in the sidebar-menu under the section '''In other projects''' (where the links to all other Wikimedia Projects are displayed). If you do not see it, please reach out to us on the [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Move Wikidata item - Discussion page]]. Thank you, -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 09:24, 12 December 2024 (UTC)
:::@[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]], thank you for responding. I intend to followup on the ''Move Wikidata item - Discussion page'' as per your post above by putting it on my ever growing todo list.
:::I don't know about others on this wiki, as I said I have not been visiting here frequently, but for me the constant changes are a big distraction. I have been around wikimedia projects since 2007, so why do I have to spend so much time learning and re-learning how to find what I came here for? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:41, 12 December 2024 (UTC)
::::Hi @[[User:Ottawahitech|Ottawahitech]], thanks for you thoughts. Your input whether positive or critical helps us understand the impacts to editors so we welcome your further thoughts when you reach us in your To Do List :)
::::I can't speak about the other changes you've experienced here but I do hope they are made with a spirit of improvement for the community as a whole. -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 10:43, 16 December 2024 (UTC)

== Final Reminder: Join us in Making Wiki Loves Ramadan Success ==

Dear all,

We’re thrilled to announce the Wiki Loves Ramadan event, a global initiative to celebrate Ramadan by enhancing Wikipedia and its sister projects with valuable content related to this special time of year. As we organize this event globally, we need your valuable input to make it a memorable experience for the community.

Last Call to Participate in Our Survey: To ensure that Wiki Loves Ramadan is inclusive and impactful, we kindly request you to complete our community engagement survey. Your feedback will shape the event’s focus and guide our organizing strategies to better meet community needs.

* Survey Link: [https://docs.google.com/forms/d/e/1FAIpQLSffN4prPtR5DRSq9nH-t1z8hG3jZFBbySrv32YoxV8KbTwxig/viewform?usp=sf_link Complete the Survey]
* Deadline: November 10, 2024
Please take a few minutes to share your thoughts. Your input will truly make a difference!

'''Volunteer Opportunity''': Join the Wiki Loves Ramadan Team! We’re seeking dedicated volunteers for key team roles essential to the success of this initiative. If you’re interested in volunteer roles, we invite you to apply.
* Application Link: [https://docs.google.com/forms/d/e/1FAIpQLSfXiox_eEDH4yJ0gxVBgtL7jPe41TINAWYtpNp1JHSk8zhdgw/viewform?usp=sf_link Apply Here]
* Application Deadline: October 31, 2024
Explore Open Positions: For a detailed list of roles and their responsibilities, please refer to the position descriptions here: [https://docs.google.com/document/d/1oy0_tilC6kow5GGf6cEuFvdFpekcubCqJlaxkxh-jT4/ Position Descriptions]

Thank you for being part of this journey. We look forward to working together to make Wiki Loves Ramadan a success!


Warm regards,&lt;br&gt;
The Wiki Loves Ramadan Organizing Team 05:11, 29 October 2024 (UTC)
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== Android app for Wikiversity ==

Hi, is there an Android app for Wikiversity? How does it work? I have been advised that there is no infrastructure for push notifications for Android apps for sister wikis and I would be interested to know more. Related: [[:phab:T378545]]. Thanks! [[User:Gryllida|Gryllida]] 23:15, 29 October 2024 (UTC)

:Thanks for suggesting this - I agree that it would be useful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:56, 31 October 2024 (UTC)
:@[[User:Gryllida|Gryllida]]: Would you explain your terminology  for those of us not in the know. What does ''push notifications'' mean? I use [https://www.mediawiki.org/wiki/Help:Notifications notifications] when I am communicating on wikimedia projects, but have never heard this term before. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:13, 11 December 2024 (UTC)
:I dont think there is an app.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:01, 17 December 2024 (UTC)
:This would be useful, however we do not have an app for Wikiversity yet. I am thinking of helping out with no-code or low code tools, but I am working on some courses here. I might be able to do some contributions though. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 14:14, 17 December 2024 (UTC)

== Import Resource From Wikibooks? ==

Hello! [[wikibooks:Character_List_for_Baxter&amp;Sagart|Character List for Baxter&amp;Sagart]] and related titles [[wikibooks:Wikibooks:Requests_for_deletion#Character_List_for_Baxter&amp;Sagart|are up for deletion at Wikibooks]] because WB policy does not allow dictionaries like them. However, because they are useful as learning tools, I am wondering if they might have a home here at Wikiversity. Pinging @[[User:Tibetologist|Tibetologist]] here to link them in to this discussion, since they are the affected user. Thank you! —[[User:Kittycataclysm|Kittycataclysm]] ([[User talk:Kittycataclysm|discuss]] • [[Special:Contributions/Kittycataclysm|contribs]]) 18:18, 1 November 2024 (UTC)

:Sure, I can do it. That said, as mentioned there, it does seem like something like this is ideally suited for Wiktionary in the Appendix namespace, but I'm not very familiar with CJK characters and languages. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:23, 3 November 2024 (UTC)
::Oh man, these pages are too big to import and while I've already tried a half-dozen times, it will constantly fail. Strictly speaking, we don't have to use the import feature for licensing purposes. We can just copy and paste the contents and list the usernames or on the talk page. I think that's the solution. {{Ping|Tibetologist}}, are you interested in doing that? If you just copied and pasted these pages and then added [[:Category:Chinese]] and maybe include a couple of links to the pages, that would probably be ideal. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:31, 3 November 2024 (UTC)

== Language translation requests? ==

Is there anywhere on Wikiversity to request translation, for example, requesting Latin or French translation? I would be asking from the context as a student, so I would be interested in translation explanation as well. [[User:Indexcard88|Indexcard88]] ([[User talk:Indexcard88|discuss]] • [[Special:Contributions/Indexcard88|contribs]]) 04:56, 20 November 2024 (UTC)

:I am not too sure about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:44, 17 December 2024 (UTC)

== Sign up for the language community meeting on November 29th, 16:00 UTC ==

Hello everyone,

The next language community meeting is coming up next week, on November 29th, at 16:00 UTC (Zonestamp! For your timezone &lt;https://zonestamp.toolforge.org/1732896000&gt;). If you're interested in joining, you can sign up on this wiki page: &lt;https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#29_November_2024&gt;.

This participant-driven meeting will be organized by the Wikimedia Foundation’s Language Product Localization team and the Language Diversity Hub. There will be presentations on topics like developing language keyboards, the creation of the Moore Wikipedia, and the language support track at Wiki Indaba. We will also have members from the Wayuunaiki community joining us to share their experiences with the Incubator and as a new community within our movement. This meeting will have a Spanish interpretation.

Looking forward to seeing you at the language community meeting! Cheers, [[User:SSethi (WMF)|Srishti]] 19:55, 21 November 2024 (UTC)
&lt;!-- Message sent by User:SSethi (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=27746256 --&gt;

== Events on Wikiversity ==

Since Wikipedia and Wikivoyage are having their &quot;Asian Month&quot; editathon, I was thinking if we could start up a Wikiversity version of that. This would be an &quot;Asian Month&quot; as well, but it would be about creating resources based on Asia and its culture. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:57, 6 December 2024 (UTC)

:Not immediately opposed, but the question is, do we have an active enough community to facilitate this? —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:31, 6 December 2024 (UTC)
::I'm not too sure. As long as we get enough traffic, this could happen. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 08:45, 7 December 2024 (UTC)
:::This is to increase traffic on Wikiversity, which is promoted amongst other communities. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 10:47, 7 December 2024 (UTC)
:Hi @[[User:RockTransport|RockTransport]], This is a good idea, but will it also involve users who are not &quot;professors and scientists&quot;. Just curious. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:30, 9 December 2024 (UTC)
::Yes, considering the fact that Wikiversity is for everyone, and not just for specific users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:09, 10 December 2024 (UTC)
:::because I'm personally not a &quot;professor&quot; or a &quot;scientist&quot; and because '''anyone''' can create resources on Wikiversity. We want to make Wikiversity open for everyone, and not just for certain users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:10, 10 December 2024 (UTC)
::::I am also not a professor or a scientist, but it seems to me that as result I am viewed here as a visitor rather than someone who can contribute. Just my $.02. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:05, 12 December 2024 (UTC)
:I am affraid, that creation of educational resources on certain topic is way harder then wikipedia. Secondly while wikipedia stub does not matter, education resource stub is uselless completly. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:59, 17 December 2024 (UTC)
::How is it useless, you can contribute to other learning resources and maybe improve it as such, if you have some knowledge on a particular topic or something else. This is to increase diversity. Just a kind notice. It's also pretty hard to do it on Wikivoyage, but that's the same for every platform. Stubs may be improved on, and this is the concept. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:19, 17 December 2024 (UTC)
::There are lots of stubs here, on Wikiversity. So the whole purpose of this event is to increase engagement and willingness to edit these pages. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:24, 17 December 2024 (UTC)

== Wikiversity - Newsletters ==

Hello All,

I wanted to create a newsletter on Wikiversity, which would highlight what is going on in certain months and events on Wikiversity; which would bolster engagement by many people. This would be on the website and would have its dedicated 'Newsletter' tab.

I hope you acknowledge this idea. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:05, 8 December 2024 (UTC)

:@[[User:RockTransport|RockTransport]], What sort of things do you plan to include in your newsletter? Will they be different than what is currently in [[Main Page/News]]? Just curious.
:I am also wondering about your motive which I think is: to bolster engagement by many people. I am asking because I wonder if others who are currently active here also think this I is desirable? Have you asked them? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:34, 11 December 2024 (UTC)
::Not yet, which was why I was asking this on the colloquium. I plan to include things that many people have created on Wikiversity over the month, as it is a monthly newsletter. It would be somewhere on the website here. It will be more frequent that the ones seen on [[Main Page/News]]. We will include people's resources to essentially promote them. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 06:50, 12 December 2024 (UTC)
:::@[[User:RockTransport|RockTransport]], I Think what you are saying is that ''Main Page/News'' does not update frequently enough? 
:::If this is the reason, why not start small by simply increasing the frequency of posting news on the main page, instead of trying to start a newsletter?
:::If there is more, can you articulate what else is missing. Thanks in advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:51, 12 December 2024 (UTC)
::::I meant going to detail into topics covered in that month, rather than just giving a few points. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 16:53, 12 December 2024 (UTC)
:::::What sort of details did you have in mind? You can pick one of the links provided in [[Main Page/News]] to illustrate. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:29, 16 December 2024 (UTC)
::::::I'm thinking of the community entering their projects, and discussing those in the newsletter. It depends on what they want, though. There would be a dedicated page for giving the information about their projects [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:24, 16 December 2024 (UTC)
:::::::I might start working on this soon, depending on the projects being created on Wikiversity. @[[User:Ottawahitech|Ottawahitech]] @[[User:Atcovi|Atcovi]] [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:25, 17 December 2024 (UTC)
::::::::I'd recommend you start off with putting this under a userspace page (something like [[User:RockTransport/Wikiversity Newsletter]]), and drafting what you desire. Let us know once it's done, and the community can provide their input. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 18:30, 17 December 2024 (UTC)
:::::::::I will try and make one for this month. This is supposed to be a monthly newsletter, showcasing the different projects mentioned there. Users can put their projects, and we will document them on the newsletter. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:33, 17 December 2024 (UTC)
:::::::::I am hoping for it to be released by January 2025. There's no rush to get it done; it's still in it's planning stage. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:43, 17 December 2024 (UTC)
::::I '''might''' be able to icnrease the frequency there, but it doesn't go into detail about these topics. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:30, 18 December 2024 (UTC)
:Where you are going to get the audience for your website and Wikiversity newsletter? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:38, 18 December 2024 (UTC)
::It's on Wikiversity, not on an outside platform. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:51, 18 December 2024 (UTC)
::The audience will be Wikiversity contributors. There will be a dedicated page for it on Wikiversity. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:55, 18 December 2024 (UTC)

== Describing Wikiversity content on Wikidata ==

Anyone knows how to properly describe Wikiversity pages on Wikidata? Any examples for some content pages like courses, supplement materials etc.? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:36, 18 December 2024 (UTC)

:For general topics that will have other Wikimedia Foundation project links (e.g. [[astronomy]]), there will probably be a sufficient short description already, but for subpages or more obscure topics, you could plausibly use &quot;Wikimedia content page&quot; or some such. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:52, 18 December 2024 (UTC)
::Yeah, general topics are easy to map. While specific projects which does not have Wikipedia counterparts and which are quite specific it would be nice to have few examples - i.e. what are typical properties of a course or research project. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:00, 19 December 2024 (UTC)

== Degrees ==

Why does Wikiversity not provide degrees? I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal. But anyway, why is that? Wikiversity is about opening doors, i.e., removing obstacles. So, what kind of an obstacle was a paper? Was a certain body of knowledge that you learned well?! Because Wikiversity is not accredited for that? Yes, and do we need official US accreditation? We cannot create our system so that the learners who learn here and would like to continue their science career have a recognizable degree they can continue? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:19, 18 December 2024 (UTC)

:&quot;I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal.&quot; Was it? Becoming a degree-granting institution is an extremely high bar in the United States, but what is even the point in becoming a degree-granting institution in... Malawi? Tonga? Somewhere else where the servers aren't located or the WMF aren't incorporated? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:53, 18 December 2024 (UTC)
::I ment certificates. The question is the recognazibility of a certificate. I am not talking here about equal certification, which is provided by governmental institucians to universities, rather on Wikiversity own certification, which might may advocate itself over the time. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:05, 19 December 2024 (UTC)
::: We could issue certificates in some residing in certain jurisdictions probably (?). To my knowledge, there is no legal prohibition federally against doing this in the USA as long as no misrepresentation happens. Although some states might prohibit it (?). Degrees are likely different (at least with respect to accreditation). Please let me know if you believe I am likely incorrect in my understanding. I asked an LLM this prompt, &quot;is there any prohibition legally in USA for a DAO (decentralized autonomous organization or wiki community related to learning, teaching, and research) from issuing certifications or certificates to those who go through learning materials and educational resources that might be on a decentralized or nonprofit wiki that has an active community?&quot; (i won't post the specific result, but I wrote and engineered that prompt myself). The LLM output seemed to indicate my understanding noted here is correct, but LLM's are sometimes wrong. what do you or others think about this? [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:49, 25 December 2024 (UTC)

== Common Corpus and LLM training ==

Greetings. I believe LLM generated content is not currently allowed on this wiki. No problem. I am curious - what if the dataset an [[LLM]] is trained on is all in the public domain; would this or does this change that with regards to LLM generated content being allowed (presuming the LLM output is verified and accurate)? Has there been any discussion on this wiki or other MediaWiki wikis about LLM generated content by LLM's that is trained exclusively on CC-0/public domain data? i.e. Common Corpus https://huggingface.co/blog/Pclanglais/common-corpus
[[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:41, 25 December 2024 (UTC)</text>
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{{Create an account}}
{{TOCright}}   

This page explains why you should create a user account and join the {{NUMBEROFUSERS}} other registered users of the [[Wikiversity|English Wikiversity]].

== Reputation and Privacy ==
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'''You do not need to reveal your offline identity''', but having an account gives you a fixed, Wikiversity identity that other users will recognize. Editing Wikiversity, while logged in, lets you build trust and respect through a history of good edits. It is also easier to communicate and collaborate with an editor if we know who you are (at least, who you are on Wikiversity). It is also easier for veteran users to [[Wikiversity:Assume Good Faith|assume good faith]] from new users who take the effort to create an account (and you may well become a veteran user yourself someday!).

'''If you are not logged in, all your edits are publicly associated''' with your IP address at the time of that edit. If you log in, all your edits are publicly associated with your account name, and are internally associated with your IP address. See [[Wikiversity:Privacy policy|Wikiversity's privacy policy]] for more information on this practice.

You are actually more anonymous (though more [[w:pseudonym|pseudonymous]]) logged in than you are as an &quot;anonymous&quot; editor, owing to the hiding of your IP address. Before selecting your username, you should [[Wikiversity:Username|consider various factors]], including privacy and the possibility of offline harassment. For example, if you include personal information, such as your email address, in your Wikiversity username, you may attract junk and spam mail to your email account.

== Voting ==
{{shortcut|WV:ACCOUNT/V|WV:VOTE}}

If you are logged in, you may see near the top of your window a message similar to: '''Voting has begun in the elections! Voting ends at UTC. Verify your eligibility and vote now.'''

Click on the link, follow the instructions, and, provided that you meet all qualifications, you will be able to vote in that particular election. The first requirement for eligibility to vote in any election is that you must be '''logged in.''' If not logged in, you cannot vote.

For most registered users, eligibility to vote requires a history of good edits, available only to registered users who log in and generate proof of good faith through such a history. If you create an account, login to your account, and do good work on Wikiversity, in time you will become eligible to vote in elections held by Wikiversity and other members of the Wiki Foundation.

== Upload file ==

If you are not logged in, there are limited selections available under &quot;Tools&quot; menu to the left. If you are logged in, an additional selection appears, &quot;Upload file.&quot; When you are logged in, you can upload a file to Wikiversity. If not logged in, you cannot upload. This is how the Wikiversity community assumes good faith on behalf of all registered users who log in. If you create an account and login to your account, you are rewarded with this powerful tool.

== Thank and be thanked ==

If you are not logged and you view the history of any page, it seems that everything is there that should be there.
However, if you are logged in and you review the history of any page, another option appears against the work of another user 
who was logged in and recorded a change, &quot;thank.&quot;
If you are logged in when you contribute to Wikiversity, you can be &quot;thanked&quot; for your work, but only by another user who is logged in.
If you are not logged in, you cannot &quot;thank&quot; or be &quot;thanked.&quot;

== New Pages ==
If you are not logged in, the number of new pages you may create is limited. If you are logged in and your account is [[Wikiversity:Autoconfirmed users|autoconfirmed]], this restriction is lifted.

==Cookies==
{{shortcut|WV:ACCOUNT/C|WV:COOKIE}}

Make sure you set the browser's preferences to accept [[w:HTTP cookie|cookies]] from Wikiversity. [[Special:Log/newusers]] will show when your user account is created. If your browser is not accepting cookies, then you can create an account, but you will '''not''' be able to log in to your account. If you create an account while not accepting cookies, you will see this message after you create your account:
[[Image:Need cookies.png|thumb|center|800px|A Wikiversity alert which appears when trying to log in with cookies not enabled.]]

==See also==
* [[Special:Userlogin/signup|Create a Wikiversity user account]]
* [[Wikiversity:Page protection|Page protection]]
* [[Wikiversity:Username]]

[[Category:Wikiversity FAQ]]
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[[Category:Conferences]]
&lt;div style=&quot;width: 600px; border:1px solid dark-grey; {{box-shadow|0|1px|3px|rgba(0, 0, 0.5, 0)}} {{border-radius|7px}} background-color: light-grey&quot; class=&quot;plainlinks&quot;&gt;
{|
|- 
| '''Date''': || 6–7 December 2012 (Thursday &amp; Friday).  Wednesday evening early registration is optional.
|-
| '''Venue''': || Library, [[:w:University of Indonesia|University of Indonesia]], Depok, Indonesia
|-
| '''Accommodation''': || [http://www.smarthotel.co.id/ Smart Hotel], Jalan Tanjung Karang No. 2, [[w:Jalan MH Thamrin (Jakarta)|Thamrin]], Jakarta ([https://plus.google.com/104667580498334043083/about?gl=au&amp;hl=en Google Maps])&lt;br&gt;
Checkin Wednesday - Leave Saturday unless arranged otherwise.
|-
| '''Sponsors/Partners''': || [[meta:Wikimedia Australia|Wikimedia Australia]], Indonesian International Conference on Communications, University of Indonesia
|-
| '''Contact''': || [[wmau:Committee]]
|-
| '''Social media''': || [https://mobile.twitter.com/search/?q=KemahBahasa&amp;s=typd #KemahBahasa]

[https://mobile.twitter.com/search/?q=indoicc&amp;s=typd indoicc]
|}
&lt;/div&gt;

'''LangCamp 2012''' is a workshop organised by Wikimedia Australia to support the growth and development of wikis in the non-English [[w:languages of Indonesia|languages of Indonesia]] and [[w:languages of Australia|Australia]].  The workshop is being held as part of a second '''Indonesian International Conference on Communications 2012''' (http://indoicc.org/) at University of Indonesia, Jakarta on 6–7 December 2012, with a theme of &quot;Communication, Context and Community&quot;.  IICC aims to provide a multidisciplinary approach towards understanding the role of media in our contemporary regional society.  Our workshop focuses on the role of Wikimedia to provide educational resources that support regional communities.

The workshop proposal can be found at [[wmau:Proposal:2012 Languages conference]].  A languages conference was approved by Wikimedia Australia members in October 2011, but reduced in scope and number of attendees in April 2012, and finally joined the IICC conference in the second half of 2012.

This workshop was planned autonomously from the [[meta:Wikimedia Indigenous Languages]] group which was established in August 2012; however the outcomes will be shared with that group.

== Streams ==
The workshop has two streams: indigenous languages and OER.

=== Indigenous languages ===
The &quot;indigenous languages&quot; stream will explore the challenges facing the language communities establishing wiki projects in indigenous languages, and explore approaches that have been used to seed these established wiki projects using automated content creation.  The [[incubator:|Wikimedia Incubator]] has many Indonesian indigenous language projects that have not been launched, and often the original contributors have lost enthusiasm for their projects and returned to contributing to Indonesian Wikipedia.  Even if these languages leave the incubator, they grow very slowly and fail to lure strategic investment.  It is common for these Indonesian languages to not have any bilingual dictionaries.  The workshop will look at ways that other projects (e.g. [[/Indonesian Wiktionary]], [[/Indonesian Wikibooks]] &amp; [[/Multilingual Wikisource]]) can be used in conjunction with an incubator Wikipedia project to keep the small language group working together.

Two of the languages that will be the subject of attention are the [[w:Minangkabau language|Minangkabau]] and [[w:Balinese language|Balinese]] Wikipedia.
* The [[/Minangkabau language]] Wikipedia is nearing the point where it can be moved from the Incubator to a separate wiki.  The workshop aims to provide the Minangkabau Wikipedia community with ideas on how to increase the impact of their wiki quickly, and foster collaboration between the volunteers and academics to implement these ideas.
* The [[/Balinese language]] Wikipedia is an incubator project with only 15 articles, and the user interface has not been translated into Balinese.  The translation of the user interface into Balinese was approved in November 2012 (see [[translatewiki:Thread:Support/Balinese]]).  Before and during the workshop the user interface translation will commence, and the participants will be planning for Balinese Wikipedia to launch within a year.

=== Open educational resources ===
The &quot;[[w:Open educational resources|Open educational resources]]&quot; (OER; [[w:id:Sumber pembelajaran terbuka|Sumber pembelajaran terbuka]]) stream will be discussing a strategy and program for universities, teachers, educators and volunteers in both Australia and Indonesia to collaborate on developing education resources that use and contribute to Indonesian open-access content-focused projects such as Wikipedia, Wiktionary, Wikibooks, and Wikiversity.  This effort will make use of the existing program design in the  [[outreach:Wikipedia Education Program]], especially the Arabic and Portuguese language programs, but will explore the opportunities available with students learning Indonesian language as a second language.  The participants will be looking at existing Australia–Indonesia collaborations, such as [http://bridge.edu.au/ BRIDGE school partnerships], when designing a feasible pilot program that aims to take advantage of the recent Australian and Indonesian government initiatives.  The Indonesian Government has recently approved universities developing OER [Article 79 para. (4) Law No. 12 Year 2012 regarding Higher Education] and on 28 October 2012 the Australian Prime Minister released the [http://asiancentury.dpmc.gov.au/white-paper Australia in the Asian Century white paper] (commissioned in September 2011) which aims to give all Australian students &quot;continuous access to a priority Asian language – Chinese (Mandarin), Hindi, Indonesian and Japanese.&quot;[http://www.abc.net.au/news/2012-10-29/asian-language-teaching-linked-to-school-funding/4338676].  This workshop will focus on Indonesian, with the intention of being adaptable to similar collaboration between countries.

== Attendees ==
IICC has attendees from Europe, North America and Asia Pacific.  There are (at least) six papers from attendees affiliated with universities in Australia, and an opening and closing keynote from Prof. [http://www.humanities.org.au/Fellowship/FindFellows/tabid/123/articleType/ArticleView/articleId/1472/Sen-Krishna.aspx Krishna Sen] at [[w:University of Western Australia|University of Western Australia]].

Workshop attendees include:
# Syahri Sakidin, Consul/Head of Chancery, [http://www.kri-perth.org.au/ Consul General of Indonesia in Perth]
# [[w:Ivan Lanin|Ivan Lanin]], Creative Commons Indonesia Public Lead, Jakarta
# Ari Juliano Gema, Creative Commons Indonesia Legal Lead, Jakarta
# Alifia Sudharto, Creative Commons Indonesia Admin, Jakarta
# [http://www.linkedin.com/pub/karen-bailey/34/466/352 Karen Bailey], Curriculum consultant at the [[w:Department of Education (Western Australia)|Department of Education Western Australia]] and founder of [http://www.balaibahasaperth.org/ Balai Bahasa Indonesia Perth]
# [http://www.education.murdoch.edu.au/staff/lindy_norris.html Lindy Norris], Senior lecturer at Murdoch University, Perth (and supervisor of Penelope Coutas, below).
# Linden Davis, Indonesian language teacher, Perth
# Penelope Coutas, EdD Candidate at Murdoch University and Indonesian language teacher, Perth
# [[w:user:fcbond|Francis Bond]], Associate Professor at the Division of Linguistics and Multilingual Studies, Nanyang Technological University, Singapore.
# [http://polosseni.com/staff/dag.html Doug Myers], Australian ethnomusicologist - Bali
# [[w:user:Crisco 1492|Chris Woodrich]], Canadian English Wikipedia sysop; Indonesian literature postgraduate student, Gadjah Mada University, Yogyakarta; topic: &quot;The Power of Wiki: Preserving and Promoting Balinese Literature Via the Internet&quot;
# [[w:user:Pratyeka|Walter Stanish]], Australian English Wikipedia sysop; volunteer technical advisor to [http://www.oralliterature.org/ World Oral Literature Project] (Cambridge &amp; Yale Universities), international systems programmer, long term China resident and scholarship recipient, and Asian linguistic hobbyist. Formerly of Macquarie University, Sydney and East China Normal University, Shanghai, China.
# [[w:user:John Vandenberg|John Vandenberg]], President, Wikimedia Australia
# [[w:id:user:Meursault2004|Revi Soekatno]], founder of Indonesian Wikipedia.
# [[meta:User:RamzyM (WMF)|Ramzy Muliawan]], Minangkabau Wikipedia test-administrator, Minangkabau language native speaker - Pekanbaru
# Awettria Susila, University of Indonesia, Masters student
# [[w:id:User:Ezagren|Arief Ezagren]], Wikimedia Incubator contributor
# [[w:id:user:Naval Scene|Ichsan Mochtar]], Minangkabau Wikipedia contributor 
# Hammam Riza, Director of the Agency for the Assessment and Application of Technology (BPPT), UI
# Ruli Manurung, Faculty of Computer Science, UI
# Ari Poespodihardjo, The London School of Public Relations - Jakarta
# Chloe Hart, University of New South Wales, Masters Journalism Student
# [[:w:id:Pengguna:Pras|Pras]], Javanese Wikipedia contributor
# [[:w:id:Pengguna:Siska.Doviana|Siska.Doviana]]
# [[:w:id:Pengguna:Gombang|Gombang]]
# UI Asian languages lecturer Dilah Kencono
# [[:w:id:user:Beeyan|Beeyan]]
# [[:w:id:Pengguna:Ennio morricone|Ennio morricone]]
# [[:w:id:Pengguna:NoiX180|NoiX180]]
# [[:w:id:Pengguna:Riemogerz|Muhammad Rizali Rizqan]]
# [[:w:user:ReveurGAM|Glenn McGrew II]], Erstwhile contributor in various disciplines, long-term resident of Indonesia with fair fluency in Indonesian, 10 years of teaching, workshop and seminar experience in Indonesia, multi-disciplinarian - Baturraden, Central Java

== Workspaces ==
{{special:prefixindex/LangCamp 2012/}}</text>
      <sha1>fljrqktfqsd7rukiph01zr8c0ngzjss</sha1>
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  </page>
  <page>
    <title>Understanding Arithmetic Circuits</title>
    <ns>0</ns>
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      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Adder */</comment>
      <origin>2693271</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3000" sha1="ngbtvw7dsiuewbzga7fp1snh7z6qo98" xml:space="preserve">
== Adder ==

* Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]]  )
 
{| class=&quot;wikitable&quot;
|-
!  Adder type      !! Overview !! Analysis !! VHDL Level Design  !! CMOS Level Design  
|-
| '''1. Ripple Carry Adder'''
|| [[Media:VLSI.Arith.1A.RCA.20211108.pdf|A]]||
|| [[Media:Adder.rca.20140313.pdf|pdf]]
|| [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]]
|-
| '''2. Carry Lookahead Adder'''
|| [[Media:VLSI.Arith.1.A.CLA.20221130.pdf|A]]||
|| [[Media:Adder.cla.20140313.pdf|pdf]]||
|-
| '''3. Carry Save Adder''' 
|| [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]||
|| ||
|-
|| '''4. Carry Select Adder''' 
|| [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]||
|| || 
|-
|| '''5. Carry Skip Adder'''
|| [[Media:VLSI.Arith.5A.CSkip.20241225.pdf|A]]||
|| 
|| [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]]
|- 
|| '''6. Carry Chain Adder'''
|| [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]||
|| [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]],  [[Media:Adder.cca.20140313.pdf|pdf]]
|| [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]]
|- 
|| '''7. Kogge-Stone Adder'''
|| [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]||
|| [[Media:Adder.ksa.20140409.pdf|pdf]]||
|-
|| '''8. Prefix Adder'''
|| [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]||
|| || 
|-
|| '''9.1 Variable Block Adder'''
|| [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]]||
|| || 
|-
|| '''9.2 Multi-Level Variable Block Adder'''
|| [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]||
|| || 
|}
&lt;/br&gt;
 
=== Adder Architectures Suitable for FPGA === 
* FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]])
* FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]])
* FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]])
* FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]])
* Carry-Skip Adder
&lt;/br&gt;

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

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

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

=== Tree Mulltipliers ===
* Lattice Multiplication  ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]])
* Wallace Tree  ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]])
* Dadda Tree  ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]])
&lt;/br&gt;

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

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

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

[[Category:Digital Circuit Design]]
[[Category:FPGA]]</text>
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    <title>User:Michael Ten</title>
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        <username>Michael Ten</username>
        <id>654933</id>
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      <text bytes="4810" sha1="evveksejq0yvnvbrle7zf6v9qkz20yf" xml:space="preserve">Michael Ten is a pen name of mine. 
&lt;!-- If you believe overcoming pro-aging mindsets is important please [http://patreon.com/defeataging support me on Patreon]. --&gt;
Please help me to help people to overcome pro-aging mindsets. 
* [http://michaelten.net Ideas]
__NOTOC__
What if we utilize [[vertical farming]] to convert farmland back into forests? What if we use [[electric cars]] and [[green energy]] to drastically reduce pollution in cities and all over? Some universities study ideas like [[basic income]] that [https://basicincome.stanford.edu/about/what-is-ubi/ may help] to eliminate poverty. [[Automation]] is increasingly changing economic dynamics on Earth. 
* [https://wikipedialibrary.wmflabs.org/users/my_library/ Library]
==Miscellaneous==
{{colbegin|4}}
* [https://en.wikiversity.org/wiki/Special:RecentChanges?hidebots=1&amp;hidecategorization=1&amp;hideWikibase=1&amp;namespace=0&amp;limit=1000&amp;days=15&amp;enhanced=1&amp;urlversion=2 Resources]
* [[Strategies for Engineered Negligible Senescence]]
* [[Overcoming pro-aging mindsets]]
* [[Android programming]]
* [[Renewable energy]]
* [[Ologies]]
* [[Pro se legal representation]]
* [[Business/Employee-owned companies|Employee-owned companies]]
* [[WikiJournal of Business and Economics]]
* [[Technological automation]]
* [[Online social entrepreneurship]]
* [[Large language models]]
* [[Social entrepreneurship]]
* [[Child abuse]]
* [[Business/Earning money]]
* [[Basic income cryptocurrency]]
* [[Open education]]
* [[Affordable housing]]
* [[Careers and Employment/Types of employment|Types of employment|]]
* [[Earthquake-resistant structures]]
* [[Business]]
* [[Basic income]]
* [[Marketing/Marketing educational wikis|Marketing educational wikis]]
* [[Szaszian studies]]
* [[Szaszian]]
* [[Szaszian theory]]
* [[Anti-psychiatry]]
* [[Audacity/Processing vocals|Processing vocals]]
* [[Should suicide be legal?‎‎]]
* [[Social problems]]
* [[Vertical farming]]
* [[Environmental problems]]
* [[Energy storage]]
* [[Eliminating poverty]]
* [[Futurism]]
* [[Nonprofit management]]
* [[Reddit for learning]]
* [[Learning by failing]]
* [[Cryonics]]
* [[Rhyming words for songwriters]]
* [[Product development]]
* [[Music production]]
* [[Online Industrial Community]]
{{colend}}

{{Multicol}}

==Subs==
* [[/Heaven energy/]]
* [[/Later/]]
* [[/More/]]
* [[/Ten/]]
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* [[/Book/]]
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* [[/Areas/]]
* [[/Policy/]]
* [[/Navigating/]]
* [[/Added/]]
* [[/Learning/]]
* [[/Co-learners, co-researchers, co-teachers/]]
* [[/Templates/]]
* [[/Drafts/]]
{{Multicol-break}}

==Miscellaneous==
* [[Special:RandomRootpage/Topic]]
* [[Special:RandomRootpage/School]]
* [[Special:RandomRootpage/Portal]]
* [[Special:RandomRootpage/Draft]]
* [[Special:Random/Draft]]
* [[Special:RandomRootpage/Template]]
* [[Special:RandomRootpage]]
* [https://en.wikiversity.org/w/index.php?title=Special%3APrefixIndex&amp;prefix=&amp;namespace=104 All Topics]
* [https://en.wikiversity.org/w/index.php?title=Special%3APrefixIndex&amp;prefix=&amp;namespace=100 All Schools]
* [https://en.wikiversity.org/w/index.php?title=Special%3APrefixIndex&amp;prefix=&amp;namespace=102 All Portals]
* [[Special:Statistics]]
* [[Wikiversity:Statistics]]
* [[Wiktionary:cosmogony]]
* [[Draft:Index]]
* [https://en.wikiversity.org/wiki/Special:AllPages?from=&amp;to=&amp;namespace=118 Drafts (list)]
{{Multicol-break}}

==Yep==
*[[Controversy]]
* [[Special:Random/Topic]]
* [[Template:Multicol]]
* [http://listen.hatnote.com/ Listen to Wikipedia]
* [https://github.audio/ Listen to GitHub]
* [[Special:UncategorizedPages]]
* [[Draft:Archive/2024]]
* ||||
{{Multicol-break}}

==More==


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hmm

* [[w:Morihei_Ueshiba#Works|The Art of Peace]] by [[q:Morihei Ueshiba|Morihei Ueshiba]]

==== Study and research interests ====
*How might large language models affect learning and research. Will LLM's eventually seen like calculators are in math and sciences now? But for everything (all subjects/topics, including math, physics, ethics, biology, psychology, chemistry, engineering, art)?

==== Ideas to possibly explore ====
* constructive feedback
:: potential search to start &quot;constructive feedback site:.edu&quot; (without quotes)
* Can this Solar System potentially support a prosperous human population of over 500 billion humans who can all live lives of abundance and post-scarcity?
* The integration between large language models and robotics.
* Are there any open source large language models that are able to continually integrate new information as a form of training or fine tuning?</text>
      <sha1>evveksejq0yvnvbrle7zf6v9qkz20yf</sha1>
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      <parentid>2693198</parentid>
      <timestamp>2024-12-25T18:40:53Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
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      <format>text/x-wiki</format>
      <text bytes="4824" sha1="nrk9nbzkjuv7o0vqcy7tfwxf4u03hao" xml:space="preserve">Michael Ten is a pen name of mine. 
&lt;!-- If you believe overcoming pro-aging mindsets is important please [http://patreon.com/defeataging support me on Patreon]. --&gt;
Please help me to help people to overcome pro-aging mindsets. 
* [http://michaelten.net Ideas]
__NOTOC__
What if we utilize [[vertical farming]] to convert farmland back into forests? What if we use [[electric cars]] and [[green energy]] to drastically reduce pollution in cities and all over? Some universities study ideas like [[basic income]] that [https://basicincome.stanford.edu/about/what-is-ubi/ may help] to eliminate poverty. [[Automation]] is increasingly changing economic dynamics on Earth. 
* [https://wikipedialibrary.wmflabs.org/users/my_library/ Library]
==Miscellaneous==
{{colbegin|4}}
* [https://en.wikiversity.org/wiki/Special:RecentChanges?hidebots=1&amp;hidecategorization=1&amp;hideWikibase=1&amp;namespace=0&amp;limit=1000&amp;days=15&amp;enhanced=1&amp;urlversion=2 Resources]
* [[Strategies for Engineered Negligible Senescence]]
* [[Overcoming pro-aging mindsets]]
* [[Android programming]]
* [[Renewable energy]]
* [[Ologies]]
* [[Pro se legal representation]]
* [[Business/Employee-owned companies|Employee-owned companies]]
* [[WikiJournal of Business and Economics]]
* [[Technological automation]]
* [[Online social entrepreneurship]]
* [[Large language models]]
* [[Social entrepreneurship]]
* [[Child abuse]]
* [[Business/Earning money]]
* [[Basic income cryptocurrency]]
* [[Open education]]
* [[Affordable housing]]
* [[Careers and Employment/Types of employment|Types of employment|]]
* [[Earthquake-resistant structures]]
* [[Business]]
* [[Basic income]]
* [[Marketing/Marketing educational wikis|Marketing educational wikis]]
* [[Szaszian studies]]
* [[Szaszian]]
* [[Szaszian theory]]
* [[Anti-psychiatry]]
* [[Audacity/Processing vocals|Processing vocals]]
* [[Should suicide be legal?‎‎]]
* [[Social problems]]
* [[Vertical farming]]
* [[Environmental problems]]
* [[Energy storage]]
* [[Eliminating poverty]]
* [[Futurism]]
* [[Nonprofit management]]
* [[Reddit for learning]]
* [[Learning by failing]]
* [[Cryonics]]
* [[Rhyming words for songwriters]]
* [[Product development]]
* [[Music production]]
* [[Online Industrial Community]]
{{colend}}

{{Multicol}}

==Subs==
* [[/Heaven energy/]]
* [[/Later/]]
* [[/More/]]
* [[/Ten/]]
* [[/Earning money/]]
* [[/Book/]]
* [[/Miscellaneous/]]
* [[/Areas/]]
* [[/Policy/]]
* [[/Navigating/]]
* [[/Added/]]
* [[/Learning/]]
* [[/Co-learners, co-researchers, co-teachers/]]
* [[/Templates/]]
* [[/Notes/]]
* [[/Drafts/]]
{{Multicol-break}}

==Miscellaneous==
* [[Special:RandomRootpage/Topic]]
* [[Special:RandomRootpage/School]]
* [[Special:RandomRootpage/Portal]]
* [[Special:RandomRootpage/Draft]]
* [[Special:Random/Draft]]
* [[Special:RandomRootpage/Template]]
* [[Special:RandomRootpage]]
* [https://en.wikiversity.org/w/index.php?title=Special%3APrefixIndex&amp;prefix=&amp;namespace=104 All Topics]
* [https://en.wikiversity.org/w/index.php?title=Special%3APrefixIndex&amp;prefix=&amp;namespace=100 All Schools]
* [https://en.wikiversity.org/w/index.php?title=Special%3APrefixIndex&amp;prefix=&amp;namespace=102 All Portals]
* [[Special:Statistics]]
* [[Wikiversity:Statistics]]
* [[Wiktionary:cosmogony]]
* [[Draft:Index]]
* [https://en.wikiversity.org/wiki/Special:AllPages?from=&amp;to=&amp;namespace=118 Drafts (list)]
{{Multicol-break}}

==Yep==
*[[Controversy]]
* [[Special:Random/Topic]]
* [[Template:Multicol]]
* [http://listen.hatnote.com/ Listen to Wikipedia]
* [https://github.audio/ Listen to GitHub]
* [[Special:UncategorizedPages]]
* [[Draft:Archive/2024]]
* ||||
{{Multicol-break}}

==More==


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&lt;/syntaxhighlight&gt;

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{{PDate}}
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&lt;/syntaxhighlight&gt;

{{multicol-end}}


hmm

* [[w:Morihei_Ueshiba#Works|The Art of Peace]] by [[q:Morihei Ueshiba|Morihei Ueshiba]]

==== Study and research interests ====
*How might large language models affect learning and research. Will LLM's eventually seen like calculators are in math and sciences now? But for everything (all subjects/topics, including math, physics, ethics, biology, psychology, chemistry, engineering, art)?

==== Ideas to possibly explore ====
* constructive feedback
:: potential search to start &quot;constructive feedback site:.edu&quot; (without quotes)
* Can this Solar System potentially support a prosperous human population of over 500 billion humans who can all live lives of abundance and post-scarcity?
* The integration between large language models and robotics.
* Are there any open source large language models that are able to continually integrate new information as a form of training or fine tuning?</text>
      <sha1>nrk9nbzkjuv7o0vqcy7tfwxf4u03hao</sha1>
    </revision>
  </page>
  <page>
    <title>Haskell programming in plain view</title>
    <ns>0</ns>
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    <revision>
      <id>2693252</id>
      <parentid>2693120</parentid>
      <timestamp>2024-12-26T02:33:54Z</timestamp>
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        <id>21186</id>
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==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]])
&lt;/br&gt;

==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]])

&lt;/br&gt;

==Using GHCi==
* Getting started ([[Media:GHCi.Start.1.A.20170605.pdf |pdf]])
&lt;/br&gt;

==Using Libraries==
* Library ([[Media:Library.1.A.20170605.pdf |pdf]])
&lt;/br&gt;
&lt;/br&gt;


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

==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.20241225.pdf |pdf]])
&lt;/br&gt;
&lt;/br&gt;

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

==Polymorphism==
* Polymorphism Overview ([[Media:Poly.1.A.20180220.pdf |pdf]])
&lt;/br&gt;

==Concurrent Haskell ==
&lt;/br&gt;


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]]</text>
      <sha1>p64rw48b2bbiy50l24bswjfel5pgx5r</sha1>
    </revision>
    <revision>
      <id>2693254</id>
      <parentid>2693252</parentid>
      <timestamp>2024-12-26T02:44:45Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Lambda Calculus */</comment>
      <origin>2693254</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6230" sha1="bz6iuc3j6pk43rjobr06ygbxehcvmv1" xml:space="preserve">
==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]])
&lt;/br&gt;

==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]])

&lt;/br&gt;

==Using GHCi==
* Getting started ([[Media:GHCi.Start.1.A.20170605.pdf |pdf]])
&lt;/br&gt;

==Using Libraries==
* Library ([[Media:Library.1.A.20170605.pdf |pdf]])
&lt;/br&gt;
&lt;/br&gt;


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

==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.20241226.pdf |pdf]])
&lt;/br&gt;
&lt;/br&gt;

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

==Polymorphism==
* Polymorphism Overview ([[Media:Poly.1.A.20180220.pdf |pdf]])
&lt;/br&gt;

==Concurrent Haskell ==
&lt;/br&gt;


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]]</text>
      <sha1>bz6iuc3j6pk43rjobr06ygbxehcvmv1</sha1>
    </revision>
  </page>
  <page>
    <title>The necessities in Microprocessor Based System Design</title>
    <ns>0</ns>
    <id>232469</id>
    <revision>
      <id>2693256</id>
      <parentid>2693123</parentid>
      <timestamp>2024-12-26T03:09:28Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* ARM Assembly Programming (II) */</comment>
      <origin>2693256</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5910" sha1="oxgywt858qhixasx1n8ldki1dmsdg3j" xml:space="preserve">== '''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]]
&lt;/br&gt;

== '''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
&lt;/br&gt;

== '''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 

&lt;/br&gt;

== '''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.20241225.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]]) 


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


&lt;/br&gt;

=== ARM Microcontroller Programming ===
* 1. Input / Output 
* 2. Serial / Parallel Port Interfacing
* 3. Analog I/O Interfacing
* 4. Communication


&lt;/br&gt;


== '''Memory Architecture''' == 
&lt;/br&gt;

=== '''Memory Hierarchy''' === 
&lt;/br&gt;

=== '''System and Peripheral Buses''' === 
&lt;/br&gt;

=== '''Architectural Support''' === 
* High Level Languages
* System Development
* Operating Systems
&lt;/br&gt;


== '''Peripheral Architecture''' == 
&lt;/br&gt;

=== '''Vectored Interrupt Controller ''' === 
&lt;/br&gt;

=== '''Timers ''' === 
* Timer / Counter ([[Media:ARM.4ASM.Timer.20220801.pdf |pdf]]) 
* Real Time Clock
* Watchdog Timer
&lt;/br&gt;

=== '''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
&lt;/br&gt;

=== '''I/Os ''' === 
* General Purpose Input/Output ports (GPIO)
* Pulse Width Modulator
* Analog-to-Digital Converter (ADC)
* Digital-to-Analog Converter (DAC)

&lt;/br&gt;


&lt;!-- == '''Interrupts and Exceptions ''' == --&gt;
&lt;/br&gt;

== '''Synchrnoization'''==
&lt;/br&gt;

=== H/W and S/W Synchronization === 
* busy wait synchronization
* handshake interface
&lt;/br&gt;

=== Interrupt Synchronization === 
* interrupt synchronization
* reentrant programming
* buffered IO
* periodic interrupt
* periodic polling 
&lt;/br&gt;

==''' Interfacing '''==
&lt;/br&gt;

=== Time Interfacing === 
* input capture
* output compare
&lt;/br&gt;


=== Serial Interfacing === 
* Programming UART
* Programming SPI
* Programming I2C
* Programming USB 
&lt;/br&gt;

=== Analog Interfacing === 
* OP Amp
* Filters
* ADC 
* DAC 
&lt;/br&gt;

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


&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]</text>
      <sha1>oxgywt858qhixasx1n8ldki1dmsdg3j</sha1>
    </revision>
    <revision>
      <id>2693258</id>
      <parentid>2693256</parentid>
      <timestamp>2024-12-26T03:10:43Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* ARM Assembly Programming (II) */</comment>
      <origin>2693258</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5910" sha1="4j1sg0r42ooi7g8a1t3x7cfi33l8x6n" xml:space="preserve">== '''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]]
&lt;/br&gt;

== '''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
&lt;/br&gt;

== '''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 

&lt;/br&gt;

== '''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.20241226.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]]) 


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


&lt;/br&gt;

=== ARM Microcontroller Programming ===
* 1. Input / Output 
* 2. Serial / Parallel Port Interfacing
* 3. Analog I/O Interfacing
* 4. Communication


&lt;/br&gt;


== '''Memory Architecture''' == 
&lt;/br&gt;

=== '''Memory Hierarchy''' === 
&lt;/br&gt;

=== '''System and Peripheral Buses''' === 
&lt;/br&gt;

=== '''Architectural Support''' === 
* High Level Languages
* System Development
* Operating Systems
&lt;/br&gt;


== '''Peripheral Architecture''' == 
&lt;/br&gt;

=== '''Vectored Interrupt Controller ''' === 
&lt;/br&gt;

=== '''Timers ''' === 
* Timer / Counter ([[Media:ARM.4ASM.Timer.20220801.pdf |pdf]]) 
* Real Time Clock
* Watchdog Timer
&lt;/br&gt;

=== '''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
&lt;/br&gt;

=== '''I/Os ''' === 
* General Purpose Input/Output ports (GPIO)
* Pulse Width Modulator
* Analog-to-Digital Converter (ADC)
* Digital-to-Analog Converter (DAC)

&lt;/br&gt;


&lt;!-- == '''Interrupts and Exceptions ''' == --&gt;
&lt;/br&gt;

== '''Synchrnoization'''==
&lt;/br&gt;

=== H/W and S/W Synchronization === 
* busy wait synchronization
* handshake interface
&lt;/br&gt;

=== Interrupt Synchronization === 
* interrupt synchronization
* reentrant programming
* buffered IO
* periodic interrupt
* periodic polling 
&lt;/br&gt;

==''' Interfacing '''==
&lt;/br&gt;

=== Time Interfacing === 
* input capture
* output compare
&lt;/br&gt;


=== Serial Interfacing === 
* Programming UART
* Programming SPI
* Programming I2C
* Programming USB 
&lt;/br&gt;

=== Analog Interfacing === 
* OP Amp
* Filters
* ADC 
* DAC 
&lt;/br&gt;

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


&lt;/br&gt; 
go to [ [[Electrical_%26_Computer_Engineering_Studies]] ]</text>
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  <page>
    <title>Talk:What you can change and what you cannot</title>
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      <contributor>
        <username>Lbeaumont</username>
        <id>278565</id>
      </contributor>
      <comment>/* Leverage Points */ new section</comment>
      <origin>2693176</origin>
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      <text bytes="13115" sha1="j0ho1ifhmmffixjsu2sxnhydtbffyfq" xml:space="preserve">Please leave comments, questions, or course feedback here. Thanks! --[[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 15:45, 28 January 2019 (UTC)

== Addictions ==

Consider addressing addictions in the section on what you may be able to change. --[[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 21:06, 28 January 2019 (UTC)

== Reframing ==

Address the ability to reframe a problem or interpretation. Consider the ability to change (choose):
*What you observe,
*what you overlook or ignore,
*how you judge and interpret observations,
*the ideologies you accept, the worldview you accept,
*your beliefs,
* more

Thanks! --[[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 13:50, 13 June 2021 (UTC)

== Some of the examples... ==

The pope did not persecute Galileo because he wanted to change the shape of the earth, but because it was an inconvenient truth that undermined his &quot;authority&quot;. &quot;Reality&quot; did not prevail, Galileo and other critical thinkers did, and only because of their appreciation for the natural world and their need to understand it, or their &quot;philosophy&quot;, in the original sense of the word. Even then, the pope made a much better living by dealing in falsehood than Galileo by dealing in truth. 

Statements like &quot;''Eventually reality prevailed''&quot; encourage a rather complacent perspective, don't you think? The current pope and Trump and countless others, including plenty from both sides of the false political dichotomy, seem to be enjoying quite a comfortable existence compared to Galileo's intellectual progeny, e.g. grad students, honest independent journalists, and so forth. It is folly to presume that liars and frauds will all receive comeuppance by &quot;reality&quot; itself, rather than the painstaking effort of people such as Galileo, for whom it could only be called a pyrrhic victory. Certainly he would have done the same thing whether it meant victory, pyrrhic victory, or defeat, so he deserves a bit more respect than this, don't you agree?. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]])

@[[User:Lbeaumont|Lbeaumont]] I would like to know what you think about my comments above. As is, I feel that the article gives the reader a distorted or complacent perspective. It makes me vaguely uncomfortable. Did Galileo consider whether or not his efforts were futile or that it might cost him too much time and energy to change the beliefs of others? Did he prioritize his own comfort by avoiding frustrations or things that might upset his peace of mind? Was Heliocentrism not believed to be an immutable &quot;law of physics&quot; in his time? He behaved in almost exactly the opposite way that this article suggests one should. I dislike it. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]])

There are more grotesqueries that I could go on about, but I have other commitments so I'll await your response and any other comments that might be forthcoming. 

I'll add a permalink: https://en.wikiversity.org/w/index.php?title=What_you_can_change_and_what_you_cannot&amp;oldid=2254984

:Thanks for this comment. I link to the Galileo affair from the existing article, which explains the role of his courage. Inspired by your comments I added a brief paragraph to the section. --[[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 11:20, 13 September 2023 (UTC)

:: Thank you. Truth and liberty are only sometimes obtained through anger and dissent, but never through resignation and apathy. I feel that people are often far too passive, if anything. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]])

:: @[[User:Lbeaumont|Lbeaumont]] The paragraph you added, ''&quot;Brute facts remain unchanged regardless of your beliefs, wishes, or proclamations. Reality is our common ground.&quot;'', is rather opposite the sort of change I had in mind. I'll leave you with a few more notes so that you might see what I'm getting at. First, the article makes a lot of assertions about the reader, with the words &quot;you&quot; and &quot;your&quot; appearing two hundred and seventy nine times. With a word count of 3,749 words, &quot;you/your&quot; occurs about every 13.5 words. I assume that the subject of this discourse is either people in general, or some smaller population like students. To avoid making statements that may strike some people as presumptuous, I suggest that &quot;you/your&quot; be changed to reflect the proper subject of this discourse accurately and in its entirety. The &quot;you&quot;s and &quot;your&quot;s can be reserved for motivational effect, and I believe they will be more effective when used sparingly and in the right places. Any reader would be made to feel self-conscious reading a complete tabulation of what they can and cannot do, addressed to them directly in the second person. The only spoken conversations with so many &quot;you&quot;s are generally conducted at well over 100 dB and include lots of four letter words, so I don't think it will make the reader very receptive to the message. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]])

:: Not very long ago in America, a man was his own master yet at the same time had stronger social bonds with his community and fellow citizens. Today, our motivation, confidence, self-determination and principles are frequently undermined. I watched a video on youtube about axemanship entitled ''&quot;Ancient wisdom: round splitting wedges = better.&quot;'' in which it was said, '''&quot;A man does not apologize for his nature. Neither does he beg others for acceptance. He remains accountable for, but not guilty of, his choices.&quot;''' I rather like this quote. It shows respect toward the reader, being neither patronizing nor presumptuous. It does not refer to the reader in the second person. When is it ever appropriate to use the second person like this resource does? [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]])

::: Thanks for your comments. The &quot;you&quot; referred to throughout the course is specifically the student studying the course. The reference is intended to be personal and specific and it is an appeal to the agency of the student. The only person who can decide to accept what they cannot change and change what they can is the individual student. Do we agree or disagree on this point? Can you suggest a specific wording change to a specific line of text that will improve the course? Thanks! --[[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 11:50, 15 September 2023 (UTC)

:::: ''&quot;The only person who can decide to accept what they cannot change and change what they can is the individual student.&quot;'' And nobody else? Are they to be addressed as individuals, floating about in the cold vacuum of space? There's a wide dissonance here between the ostensible message and the way in which it's addressed and worded. Compare it to the motivational advice that I quoted from youtube, which conveys a large portion of the same message (or at least the better parts of it), in a single sentence and in a way that does not talk down to the reader. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]])

:::: Also, I can't think of any reason to use the phrase &quot;decide to accept&quot; rather than just the word &quot;accept&quot;. This is what Orwell called a &quot;verbal false limb&quot;. Also, everyone can (decide to) change what they can change, so that part is tautological. If we reword your statement accordingly, it reads ''&quot;The only person who can accept what they cannot change is the student&quot;''. Taken literally this is false, but quite suggestive of &quot;you must accept what you cannot change&quot;. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]])

::::  You ask that I suggest specific wording changes to specific lines of text, but I will pay you (or anyone else) fifty dollars in bitcoin if you can reword this resource line-for-line without any references to the reader in the second person and using only complete sentences (no bullet points), without having it sound silly, tautological or disturbingly Orwellian. 

:::: Content such as 
:::: &quot;''What you know:''
:::: ''* Facts you have gathered,''
:::: ''* Understanding,''&quot;
:::: Would end up as &quot;''Students know the facts they have gathered. Students know what they understand.''&quot; and so on. 

:::: I think to improve this resource, it has to be made more specific and the important points separated and distilled from the content that is merely obvious, which can be left out. Imprecise language has far-reaching consequences, especially when impressed upon the public. Orwell's essay &quot;Politics and the English Language&quot; is an excellent work and explains why we must be more responsible with our use of language and avoid the idioms and wooden language so often impressed upon us by political media. &quot;''When one watches some tired hack on the platform mechanically repeating the familiar phrases – bestial atrocities, iron heel, blood-stained tyranny, free peoples of the world, stand shoulder to shoulder – one often has a curious feeling that one is not watching a live human being but some kind of dummy: a feeling which suddenly becomes stronger at moments when the light catches the speaker’s spectacles and turns them into blank discs which seem to have no eyes behind them. And this is not altogether fanciful. A speaker who uses that kind of phraseology has gone some distance toward turning himself into a machine. The appropriate noises are coming out of his larynx, but his brain is not involved as it would be if he were choosing his words for himself. If the speech he is making is one that he is accustomed to make over and over again, he may be almost unconscious of what he is saying, as one is when one utters the responses in church. And this reduced state of consciousness, if not indispensable, is at any rate favourable to political conformity.''&quot; -Orwell [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]])

:::: I believe that there's value in this resource though. For example, CBT is quite effective for changing one's habits, and perhaps deserves more attention. ''&quot;Rely on moral reasoning...&quot;'' is also excellent advice, far too many people have confused or half-baked morals. The rest of the sentence, &quot;and exercise agency only for the good&quot;, I would amend or change though, as it is also necessary to exercise agency against cynicism, exploitation, lies, moral bankruptcy, hypocrisy, and so on. These points should be developed further. Conversely, ''&quot;You cannot change another person's beliefs or thoughts (unless they choose to change)&quot;'' is not true. The media distorts and modifies public opinion and the public's behavior as a matter of course. They do it so well that most people can't even discern the extent of this influence or what society might look like without it. This is another instance of something that instills complacence. Objects like &quot;reduce your frustrations, and increase your peace-of-mind&quot; along with the constant use of the second person to address the reader also seems to limit the idea of &quot;change&quot; to just those things one can do alone and without too much frustration or hardship. Aren't there things people can do as a group or perhaps alone but through great hardship that they might not be able to do as a self-serving individual? How might such a group be organized and motivated? How might such an individual endure hardship or despair and yet still persist? It is implied we should change ourselves in response to anger or frustration, but they are natural emotions and do serve a purpose. Sometimes we should be angry and in fact must be angry. Anger is not a pathology any more than joy is. Perhaps someone who's angry has damned good reason to be angry.   [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]])

== Tampering ==

Cite the [https://deming.org/explore/the-funnel-experiment/ Deming funnel experiment] as one example of tampering—taking action intended to help that actually is detrimental.  Find other examples and add them to the article. [[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 23:59, 15 October 2024 (UTC)

== Leverage Points ==

Consider expanding this to include a discussion of leverage points – things we can do to effect change in a larger system. These include the [[w:Twelve_leverage_points|twelve leverage points]] described by Donella Meadows, and approaches to effective institutional, social, and cultural change.  [[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 13:17, 25 December 2024 (UTC)</text>
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  <page>
    <title>Thinking Tools</title>
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      <contributor>
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      <comment>/* Clarify—Strategic Thinking */ Linked to problem finding</comment>
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      <text bytes="87977" sha1="m097r22xnv79qu6ucpb4754erdet69d" xml:space="preserve">—Boosting Imagination
[[File:Julia set spiral.png|thumb| Thinking Tools boost our imagination]]
{{TOC right | limit|limit=2}}
== Introduction ==
Imagine what we could accomplish if we could improve our ability to imagine new solutions and discover more important problems to solve. Fortunately, a variety of thinking tools exist that can help us do exactly that. 

This course presents a collection of tools that are useful in [[w:Creative_problem-solving|creative problem solving]] which generally follows the steps&lt;ref&gt;Creative Thinker’s Toolkit, Gerard Puccio, [[w:The_Great_Courses|The Great Courses]]. &lt;/ref&gt;  of ''clarify'', ''ideate'', ''develop'', and ''implement''. Throughout the process it is important to navigate, integrate and prioritize.

Throughout creative problem solving it is important to determine if [[w:Divergent_thinking|''divergent'' thinking]] is needed to create new alternatives, or if [[w:Convergent_thinking|''convergent'' thinking]] is needed to choose the best option from among existing alternatives. The process alternates between divergent and convergent thinking often as each new phase is entered.

Use the thinking tools presented in this course when you need a better idea. 
== Objectives ==
{{100%done}}{{By|lbeaumont}}
The objectives of this course are to:
*help students boost their creativity;
*introduce students to a variety of thinking tools;
*improve problem solving abilities; and
*assist in transforming good ideas into better ideas.

This course introduces many useful thinking tools, and many others exist. Please browse this inventory of [[/additional thinking tools/]] to continue to improve your ability to solve problems and think creatively.

This is a course in the [[Unleashing_Creativity/possibilities_curriculum|''possibilities'' curriculum]], currently being developed as part of the [[Wisdom/Curriculum|Applied Wisdom Curriculum]].

The course contains many [[w:Hyperlink|hyperlinks]] to further information. Use your judgment and these [[What_Matters/link_following_guidelines|link following guidelines]] to decide when to follow a link, and when to skip over it.

If you wish to contact the instructor, please [[Special:Emailuser/Lbeaumont | click here to send me an email]] or leave a comment or question on the [[Talk:Thinking_Tools|discussion page]].

This [[/Quick Reference/]] on thinking tools may provide a helpful summary and reference.

== Clarify—Strategic Thinking ==
The first phase in solving problems is to clearly identify the problem to be solved. The companion course on [[Problem Finding]] addresses this topic in depth. A brief introduction to identifying problems is provided here.

A problem is a gap between a ''perceived'' state and a ''desired'' state. What may at first appear as a ''problem'' may be recognized as an opportunity—a chance for substantial gain. It is important to recognized that any proposed solution is not a problem statement.

The companion course on [[Problem Finding]] addresses opportunities to attain more important goals by helping discover the ''real'' problem.

During the clarify phase some vague notion of a problem, opportunity, or call to action will be transformed into a precise problem statement. 

The essential task in the clarify phase is to ask, “What is the problem?” and continue to refine answers until a complete and precise problem statement is formed. 

Early in the clarify phase we will work with ''challenge statements'', which are general statements of some problem to be solved.

To form ''challenge statements'':&lt;ref&gt;Creative Thinker’s Toolkit, Gerard Puccio, [[w:The_Great_Courses|The Great Courses]]. Lecture 8&lt;/ref&gt; 
*Begin with an open question starter: (“How might …, What might, … ) 
*Identify an owner (I, you, we, our department, the team, …)
*Include a verb to identify an action, (create, improve, increase, reduce, expand, …)
*Identify the object

For example: “How might I create a course on creative thinking tools?”

Throughout the clarify phase, the team will define goals, gather data, and formulate refined challenge statements. 

The clarify phase is complete when a more [[Thinking_Tools#Stating_a_Problem|complete problem statement]] is formed and adopted by the team.

Begin the clarify phase by asking:
*What do you want to have happen?
*What are the opportunities?

And continue by asking:
*What are the obstacles?
*Are the identified obstacles real?
*What obstacles are we overlooking?

Here are some tools that can help.
=== The Five Ws ===
A tool that is useful at this stage, and at many other stages, is asking [[w:en.wikipedia.org/wiki/Five_Ws|Who, what, where, when, why, and how?]] to get a clearer and deeper understanding of the problem.

Begin with the end in mind.&lt;ref&gt;{{cite book |last=Covey |first=Stephen R. |date=1994 |title=The 7 Habits of Highly Effective People: Powerful Lessons in Personal Change  |publisher=DC Books |pages= |isbn= |author-link=w:Stephen R. Covey}} Chapter 2&lt;/ref&gt;  Describe how it will look, or how it will be, when this problem is solved. If the problem is “I am overweight” then a possible outcome is “Now I can wear the clothes I wore in High School.” If the problem is “I am often late to work” then a possible outcome is “I arrive at work on time every day next month.” If the problem is “global conflict”, then a possible outcome is “Peace on earth, good will toward all.”
=== The Phoenix Checklist ===
Using the [[/Phoenix Checklist/]] can help to clarify a problem statement. The list is designed to help explore challenges from many different viewpoints.

=== SMART Goals ===
Goals statements are most clear, realistic, actionable, and specific when they are stated as [[w:SMART_criteria|SMART goals]].

SMART Goals are:
*''Specific'' – they target a specific area for improvement.
*''Measurable'' – they quantify or at least suggest an indicator of progress.
*''Assignable'' – it is clear who is responsible for achieving the outcome.
*''Realistic'' – state what results can realistically be achieved, given available resources.
*''Time-related'' – specify when the result(s) will be achieved.

The challenge now becomes “How can we attain this SMART Goal?”
==== Assignment ====
#Scan this list of [[/example problem topics/]].
#Choose one of the topics listed, or choose some other problem you are interested in.
#Answer who, what, where, when, why, and how this problem will be addressed.
#Address the [[Thinking_Tools/Phoenix_Checklist|Phoenix Checklist]] questions to further clarify the problem.
#Identify the end state that best represents how it will be when this problem is solved.
#Revise and write down that end state as a SMART goal.
#Ensure the written goal statement is specific, measurable, assigned, realistic, and time-related.

=== Webbing Tool ===
Often the [[w:Presenting_problem|problem as it is initially presented]] is not the real problem that needs to be solved. The ''Webbing tool''&lt;ref&gt;The Creative Thinker’s Toolkit, [[w:The Great Courses|the Great Courses]]. Gerard Puccio, Lecture 9.&lt;/ref&gt; can help you perform divergent thinking, better understand the problem, describe why it is important, explore related and perhaps more relevant problems, and identify the obstacles to achieving your goal. The webbing tool can help move from the problem as initially presented, to the problem as it is better understood.
[[File:Webbing Tool Weight Loss Example.jpg|thumb|The webbing tool used to explore weight loss.]]
Refer to the example diagram on the right. Begin by writing the challenge statement in the middle of the page. In this example “Lose Weight” is the challenge statement. Ask “Why is this important?” and record each reason in an ellipse, connected to the goal by an arrow. Keep asking “[[w:5_Whys|Why?]]” (to move deeper) and “Why else?” (to [[w:Lateral_thinking|move laterally]]) to record all the reasons the goal is important. These are shown in the green ellipses in the figure. Now ask “What is stopping you from achieving the goal?” and “What else?” and record each reason in an ellipse. These are shown in red. Repeatedly asking, “what is stopping you?” can often create a path from an abstract problem to a more concrete action that can be taken. This can provide new insights into the problem. For example, it may be helpful to decide to stop buying snacks, or drink something with less sugar than soda as an intermediate goal toward losing weight.

Add detail to the web as each “why?” question is asked, considered, and answered. The [[w:5_Whys|5 Whys]] technique can be helpful in exploring the cause-and-effect relationships unfolding in the web.

[[w:Mind_map|Mind mapping]] tools may be useful in constructing, improving, and sharing your web. 
==== Assignment ====
#Choose a problem to work on for this assignment. You may choose a problem from this list of [[/example problem topics/]] or choose some other problem you want to work on.
#Begin using the webbing tool as described above using the chosen challenge statement as the focus.
#Ask “Why is this important?” and record each reason in an ellipse. Ask “Why else?” and record more reasons.
#Ask “What is stopping you from achieving the goal?” and “What else?” and record each reason in an ellipse.
#Continue to add detail to the webbing tool diagram.
#Examine the emerging web (network diagram) to identify more suitable problem statements (suggested by the green ellipses) and to identify actions that can help to achieve the goal (suggested by the red ellipses).

=== Storyboarding ===
We use [[w:Storyboard|storyboarding]] to illustrate the steps from the current reality to the desired future state. Because it is a visual tool, it can have a motivational impact as it clarifies what needs to be done, how each step along the way can be completed, and what getting it done can look like.

These are the steps to create a storyboard:
#Sketch at least six blank panels.

#Illustrate the current reality in the first panel
#Illustrate the desired future state in the last panel
#In each intermediate panel, illustrate some step along the way, or achievement of some milestone along the path toward the desired future state. 
#Add additional intermediate panels as needed.

The resulting weight loss storyboard is shown in this example illustration.
==== Assignment ====
#Choose a problem to work on for this assignment. You may choose this from the list of [[/example problem topics/]] or choose some other problem you want to work on.
#Follow the steps described above to create a storyboard illustrating the steps you plan to take to proceed from the present state to the desired future state.

=== Stating a Problem ===
The outcome of the clarify stage is a well-chosen and well-written [[w:Problem_statement|problem statement]]. 

Philosopher [[w:John_Dewey|John Dewey]] noted “It is a familiar and significant saying that a problem well put is half-solved”.&lt;ref&gt;Wikiquote, [[q:John_Dewey|John Dewey]]&lt;/ref&gt; Albert Einstein noted &quot;the formulation of a problem is often more essential than its solution&quot;.&lt;ref&gt;Einstein, A., &amp; Infeld, L. (1938). The evolution of physics. New York: Simon &amp; Schuster.&lt;/ref&gt; Research has shown that ''problem identification'' is the strongest predictor of program effectiveness. 

Problem statements can begin with the vague notion that “we ought to do something” and evolve from a challenge statement to a [[w:Hoshin_Kanri|Hoshin planning]] statement in the form of “objective by means” to a fully-formed problem statement. 

Recall that a challenge statement
*Begins with an open question starter: (“How might …, What might, … ) 
*Identifies an owner (I, you, we, our department, the team, …)
*Includes a verb to identify an action, (create, improve, increase, reduce, expand, …)
*And identifies the object.

For example: “How can I lose weight?”

A Hoshin planning objective statement includes:&lt;ref&gt;Hoshin Planning, Tools, techniques, templates, 1993, Management Systems International, Inc. &lt;/ref&gt;
*An objective describing the end state
*“by” to indicate the means that will be the tactic used to achieve the objective,
*A statement of ''means'', identifying how the end state will be accomplished.

For example: “Lose weight by exercising more”

A fully formed [[w:Problem_statement|problem statement]] includes:&lt;ref&gt;See: [http://www.ceptara.com/blog/how-to-write-problem-statement How To Write A Problem Statement], Ceptuara, March 18, 2009&lt;/ref&gt;
*The ideal outcome, end state, vision, or objective,
*The current reality, a description of the current state
*The consequences, benefits, or reasons to undertake this change, and
*A proposal for how the change can be accomplished. 

For example:
(Ideal) I will lose 30 pounds of weight in the next 6 months and be able to fit comfortably into the suit I wore at our wedding.

(Reality) I currently weigh 215 pounds and have been gaining weight at more than 5 pounds per year for the past 8 years. I get very little exercise, I don’t enjoy exercising, I snack often, eat out often, and I eat unhealthy, high calorie, low nutrition foods. 

(Consequences) This weight loss will improve my appearance and make me healthier. I will feel better and I am likely to live longer. Continuing to gain weight is unhealthy and will soon become dangerous.

(Proposal) I will achieve this weight loss by eliminating soda from my diet, reducing sugar in my diet, eating healthier foods, learning to cook at home, eating out less often, walking outdoors often, finding a physical activity I enjoy doing, taking the stairs instead of the elevator, and walking instead of driving as often as practical.

This problem statement is readily constructed from the materials developed in the webbing tool and storyboard examples. 

==== Assignment: ====
#Choose a problem to work on for this assignment. You may choose from the list of [[/example problem topics/]] or choose some other problem you want to work on.
#Write the problem statement in the form of a ''challenge statement''. 
#Write the problem statement as a ''Hoshin planning objective statement'' in the form of “objective by means”.
#Follow the example above and write a ''fully formed problem statement'' including the ideal, the reality, the consequences, and the proposal.

== Ideate—Blue Sky Thinking, Nonjudgmental ==
[[w:Ideation_(creative_process)|Ideation]] is the creative process of generating, developing, and communicating new ideas. The goal of ideation is to create many ideas that might help us better understand the problem or lead to some solutions. The outcome is a tentative solution, solution concept, or solution approach.

The ideation phase emphasizes divergent thinking Elements of divergent thinking&lt;ref&gt;{{cite book |last1=Kettler |first1=Todd |last2=Lamb |first2=Kristen N. |last3=Mullet |first3=Dianna R. |date=December 1, 2018 |title=Developing Creativity in the Classroom  |publisher=Prufrock Press |pages=240 |isbn=978-1618218049}} Figures 21 and 25.&lt;/ref&gt;  include:
*'''Fluency'''—Quickly producing many ideas in response to an open-ended prompt, challenge, or unstructured problem or opportunity.
*[[w:Cognitive_flexibility|Flexibility]]—Taking a variety of approaches. [[w:Think_different|Thinking different]]. Drawing on backgrounds and experiences from a variety of disciplines, cultures, or professions. 
*[[w:Originality|Originality]]—Unique, unexpected, unusual, and outside typical expectations. 
*[[w:Elaboration|Elaboration]]—Adding detail to an idea, in-depth understanding, embellishment, richness and complexity.
*[[w:Mental_image|Visualization]]—The ability to fantasize, imagine, or see people, places, things, actions, or events in your [[w:Mental_image|mind’s eye]] or as expressive illustrations. The ability to create and manipulate mental images. 
*[[w:Imagination|Imagination]]—The ability to produce and explore ideas, concepts, environments, or events that do not originate though sensory perception. 
*[[w:Intuition|Intuition]]—The ability to acquire knowledge without proof, evidence, or conscious reasoning, or without understanding how the knowledge was acquired. The ability to make connections and see relationships that are not explicit, clear, or apparent. The ability to make mental leaps and close gaps in the available information. 
*'''Extending Boundaries'''—The ability to go beyond what is presented, apparent, or typical. The ability to consider events in a new or different context.
*'''Transformation'''—The ability to see new meanings, applications, uses, forms of some ideal, object, or concept.
*[[w:Point_of_view_(philosophy)|Alternative Perspectives]]—The ability to adopt a variety of viewpoints when examining, understanding, evaluating, extending, or presenting an idea, concept, event, or object.  

Many tools can help us ideate. Several are described in the following sections.
=== Secondary Research ===
[[w:Secondary_research|Secondary research]] can help answer the question “What is already known about this problem?” This is often the first place to start understanding the problem better. 

Because so much information is readily available these days it makes sense to begin solving problems by searching available information. Useful information sources include: general [[w:Web_search_engine|web searches]] such as [[w:Google_Search|Google Search]], specialized web searches such as [[w:Google_Scholar|Google Scholar]], on-line [[w:Encyclopedia|encyclopedias]] such as [[w:Wikipedia|Wikipedia]] and [[w:Scholarpedia|Scholarpedia]]; [[w:Library|libraries]], [[w:Book|books]], [[w:Periodical_literature|periodicals]], [[w:Academic_journal|Academic journals]], [[w:News_media|News media]], [[w:Archive|archives]], [[w:Technical_standard|standards]], [[w:Code_of_law|written law]], [[w:Bibliographic_database|bibliographic databases]], and others.

Depending on the topic being researched, you may be flooded with information, or you may find it difficult to find anything at all. For example, a web search on the term “losing weight” returns more than one billion results.  With so many responses it becomes important to be selective even in the early stages of research. Consider the reliability of the source and the relevance of the information. The Wikipedia tutorial “[[w:Wikipedia:Search_engine_test|Search Engine Test]]” provides useful guidance for interpreting search engine results. The Wikipedia policy on [[w:Wikipedia:Reliable_sources|Reliable Sources]] provides useful guidance in assessing the reliability of various information sources. Include a variety of [[Intellectual honesty|intellectually honest]] viewpoints when selecting information sources. Dismiss intellectually dishonest sources. 
==== Assignment ====
#Choose some topic or problem to research.
#Use any of the information sources listed above to learn more about your topic.
#Identify at least three sources you have determined to be reliable. How do you know?
#Identify any sources that are likely to be unreliable. How do you know?
=== Benchmarking ===
[[w:Benchmarking|Benchmarking]] can help us answer the question “How do they do that?

The simplest approach to benchmarking is to identify some existing solution to your problem, or some related problem, and learn all you can from that solution. We benchmark every day when we ask friends to name their favorite restaurants, smartphone applications, books to read, or college to attend. More formal benchmarking efforts may follow a [[w:Benchmarking#Procedure|comprehensive procedure]]. 

Creative people claim, “Good artists copy; great artists steal.”&lt;ref&gt;https://quoteinvestigator.com/2013/03/06/artists-steal/ &lt;/ref&gt; We certainly don’t advocate theft, plagiarism, or isolation. We also don’t advocate [[w:Reinventing_the_wheel|reinventing the wheel]], or ignorance. Begin with the [[w:Best_practice|best practice]] in mind. 
==== Assignment ====
#Choose some topic or problem to research.
#Identify at least three successful solutions to that problem or a related problem.
#What ''can'' you learn by studying those existing solutions?
#What ''did'' you learn? How have you made use of what was learned?
=== Appreciative Inquiry ===
[[w:Appreciative_inquiry|Appreciative inquiry]] uses ways of asking questions and envisioning the future to foster positive relationships and build on the present potential of a given person, organization or situation. The most common model utilizes a cycle of four processes, which focus on what it calls:
#DISCOVER: The identification of organizational processes that work well.
#DREAM: The envisioning of processes that would work well in the future.
#DESIGN: Planning and prioritizing processes that would work well.
#DESTINY (or DEPLOY): The implementation (execution) of the proposed design.[15]

The aim is to build – or rebuild – organizations around what works, rather than trying to fix what doesn't. Appreciative Inquiry practitioners describe this approach as a complement to problem solving.
==== Assignment ====
#Choose some topic, problem, or success to research.
#[[Practicing Dialogue|Dialogue]] with the participants.
#Identify what is working well now.
#Identify the personal, organizational, procedural, technical, informational, and cultural elements that contribute to this success.
#How can that success be sustained and expanded?
#Sustain and expand the existing successes.
=== Thinking outside the box ===
[[File:Heinz USDA Organic Tomato Ketchup.jpg|thumb|Thinking outside the bottle]]
An early step in ideation is to [[w:Thinking_outside_the_box|''think outside the box'']] which means to think differently, unconventionally, or from a new perspective. This phrase often refers to novel or creative thinking. The goal of thinking outside the box is to go beyond the unspecified but imagined barriers people typically perceive that unhelpfully limits their thinking.

For many years people struggled to get [[w:Ketchup|ketchup]] to flow from its traditional bottle. Shaking, hitting, scooping, waiting, yelling, and shaking again eventually resulted in too much or too little ketchup often landing in the wrong place. Eventually someone thought outside the bottle, turned it upside down, and invented the convenient “upside down” ketchup bottle. 
==== Assignment ====
The “nine dots” problem illustrates obstacles we often face when challenged to think outside the box.
[[File:9dots.svg|thumb|upright=.5|The &quot;nine dots&quot; puzzle.]]
#Look at this image of nine dots. 
#Link all 9 dots using four straight lines or fewer, without lifting the pen and without tracing the same line more than once. Be assured that one straightforward solution exists, and several more-creative solutions also exist. 
#After you have succeeded, or after you have worked at this problem for some time and choose to give up, look at the solution [[w:Thinking_outside_the_box#Nine_dots_puzzle|provided here]]. 
#What insight was key to finding a solution?
#What unspecified boundaries prevent you from imagining solutions to some real-world problem you are facing?
#How can the solution to the nine dots problem serve as a useful metaphor or inspiration in exploring problems and solutions?

=== Metaphor—What is this problem like? ===
A [[w:Metaphor|metaphor]] is a figure of speech that directly refers to one thing by mentioning another. It may provide clarity or identify hidden similarities between two ideas. One of the most commonly cited examples of a metaphor in English literature is the &quot;All the world's a stage&quot; monologue from As You Like It.  

More than a rhetorical tool, a [[w:Conceptual_metaphor|conceptual metaphor]] is a fundamental mechanism of the mind that allows us to use what we know about our physical and social experience to provide understanding of countless other subjects.&lt;ref&gt;{{cite book |last1=Lakoff |first1=George |last2=Johnson |first2=Mark|date=April 15, 2003 |title=Metaphors We Live By |publisher= |pages=242 |isbn=978-0226468013 |author-link=w:George Lakoff }}&lt;/ref&gt;

If we can find a good metaphor for the problem we are facing that metaphor can help us solve problems by creating analogies between the unsolved problem and something similar we are already familiar with. Some metaphors may be useful, and others may be limiting. 

The phrase “[[w:War_on_drugs|war on drugs]]” is a metaphor that frames efforts to reduce illicit drug usage as a battle to be won, with drugs themselves identified as the enemy. This may be helpful in finding various military-based solutions to the problem. However, it may also limit thinking to approaches based on military conflicts.  The phrase “war on drugs” is a solution statement, not a problem statement as discussed in the sections above. Problem statements such as “reduce illicit drug usage” or “reduce the damage caused by drug usage”, or “reduce demand for drugs”  allow thinking to extend beyond a military mindset, and avoid prematurely [[Attributing Blame|identifying a single cause]] of the problem. Alternative metaphors such as “Drugs are deadly candy”, or “Drug users are patients needing treatment”, or “Drugs are irresistible temptations” can focus thinking [[w:War_on_drugs#Alternatives|toward preventing or treating addiction]]. 

Consider these common metaphors:
*Time is money
*Love is a journey
*Love is war
*Love is a rose
*I am a couch potato
*Life is a box of chocolates

A metaphor often has the form X is Y. 

Here are some metaphors related to weight loss:
*Losing weight is a war on calories.
*Losing weight is a marathon.
*Exercise is hell.
*Obesity is an anchor.
*Losing weight is a walk in the park.
*Losing weight is exuberance in action.
*Lost weight is liberty.
==== Assignment ====
#Consider each of the “losing weight” metaphors above. What solutions does each metaphor suggest? What solutions does each metaphor distract us from?
#Choose a problem from this list of [[/example problem topics/]].
#Recast that problem as at least three distinct metaphors.
#What solutions does each metaphor suggest? What solutions does each metaphor distract us from?
#Repeat steps 3-5 for some real problem you are facing. 
=== Brainstorming ===
[[w:Brainstorming|Brainstorming]] is collection of methods that helps people generate new ideas and solutions on some topic. Brainstorming is often used to identify many ideas that may help solve an identified problem. 

Although brainstorming is the best-known technique for ideation, it is only one of many useful tools.

The key principles used in brainstorming are:
#Defer Judgement, and
#Reach for quantity. 

This requires the group to reduce social inhibitions among group members, stimulate idea generation, and increase overall creativity of the group. Participants withhold criticism, welcome wild ideas, and combine and improve ideas throughout brainstorming sessions. 

Following these steps can help a group hold a successful brainstorming session:
#Identify the topic of the brainstorming session. The problem must require generating ideas, such as generating many possible product names, rather than a judgment or decision. 
#Gather a group of participants. Any group can be successful, however a group of about 12 participants including both novices and experts is ideal. 
#Ask participants to contribute their ideas. Simply calling out short statements like “call it ‘New Coke!’” or “How about Elephants?” as participants get ideas is often the most effective approach.
#Encourage participants to contribute any idea that comes to mind. Wild and unexpected answers are particularly valuable because they increase the scope of the participants’ imagination.
#A moderator writes the ideas down immediately on an easel, marker board, chalk board or display screen that is clearly visible to all participants.
#Ensure participants suspend judgement throughout the session. If anyone criticizes, analyzes, discusses, or disparages any of the suggestions made, pause and gently remind the group to defer judgments and reach for quantity. 
#It is helpful for the moderator to notice any participants who are silent or seem to be overwhelmed by the pace of the group. Pause the group and kindly ask each such reticent participant for any ideas they have. Allow adequate time for them to respond.
#The group is likely to pause as if they are stuck or temporarily out of ideas. Wait patiently for this interval to pass because it is likely the best ideas are yet to come.  Remain ready to resume creating and recording ideas.
#When the session finally does end, ensure each of the participants gets a copy of the ideas recorded.
#At some later date hold an evaluation session to choose the ideas that are directly useful, and extract from impractical or bizarre ideas the functional kernel of an idea that can be generalized in some useful way. 

[[w:Edward_de_Bono|Edward de Bono]] argues that the value of a brainstorming session lies in the formality of the setting. He describes brainstorming as a formal setting for the use of [[w:Lateral_thinking|lateral thinking]].&lt;ref&gt;{{cite book |last=de Bono |first=Edward |date=February 24, 2015 |title=Lateral Thinking: Creativity Step by Step  |publisher=Harper Colophon |pages=300 |isbn=978-0060903251 |author-link=w:Edward_de_Bono }}&lt;/ref&gt;

Several [[w:Brainstorming#Variations|variations on this basic brainstorming]] method can also be productive.

In [[w:Nominal_group_technique|''nominal group technique'']], participants are asked to write their ideas anonymously. Then the facilitator collects the ideas and the group votes on each idea. The vote can be as simple as a show of hands in favor of a given idea. This process is called distillation.

[[w:6-3-5_Brainwriting|''Brainwriting'']] includes both individual and group approaches. In brainwriting members write their ideas on a piece of paper and then pass it along to others who add their own ideas.

In ''reverse brainstorming'', the challenge statement is reversed, for example the group may consider how to decrease sales. This can highlight obstacles to increasing sales and encourage other points of view. 
==== Assignment ====
Follow the brainstorming steps described above to generate ideas related to some problem you wish to solve.
=== Forced Relationships ===
Forced relationships can stimulate associative thoughts and expand group members’ thinking.  Asking “How can an elephant help us solve our problem?” is an example of a forced relationship. Introducing the idea of an elephant is likely to be so different from how the group was thinking it often stimulates a series of very new ideas.

Force new relationships by asking the group to connect ideas to some word chosen at random. Several random word generators are available to help with this. It is important to insist the group consider the first random word presented. Waiting for “the word you were looking for” only perpetuates stale thinking. 
==== Assignment ====
#Choose a problem to work on.
#Informally brainstorm a few solution ideas.
#Choose a random word generator to use for this exercise. This might be:
##The wordcounter [https://wordcounter.net/random-word-generator random word generator], or
##The Desiquintans [http://www.desiquintans.com/randomnoun Random Noun Generator], or
##Some other random word generator.
#Use your chosen random word generator to choose some word at random. Stay with the first word chosen regardless of how unsuitable it may seem.
#Generate ideas inspired by that random word that could help solve the problem.
#After several new ideas are stimulated, choose another random word and continue the process.
=== Hieroglyphic Hints ===
Hieroglyphic hints provide an alternative approach to stimulating associative thoughts and expanding group members’ thinking. The [[Thinking Tools/Hieroglyphic Hints|hieroglyphic hints]] page displays several [[w:hieroglyphics|hieroglyphic]] symbols chosen at random. These can invite your imagination to free-associate ideas, stimulate and expand your imagination and discover a new approach to solving problems.&lt;ref&gt;{{cite book |last=Michalko |first=Michael |date=June 8, 2006 |title=Thinkertoys: A Handbook of Creative-Thinking Techniques  |publisher=Ten Speed Press |pages=416 |isbn=978-1580087735 }} Chapter 33.&lt;/ref&gt;  
==== Assignment ====
#Choose a problem to work on for this assignment. Write it down.
#Select a row of hieroglyphic symbols at random from the [[Thinking Tools/Hieroglyphic Hints|hieroglyphic hints]] page.
#As you study each symbol, allow yourself to [[w:Free_association_(psychology)|free associate]] from it. Wonder as you ask: What is it? Why was this symbol chosen? What might this mean? What does this make me think of? How can this symbol help solve my problem? 
#Write down your various interpretations of the symbol.
#Draw some connection from the problem you are working on to your interpretation of each symbol.
#Seek a clue, insight, idea, or connection to some new approach to solving your problem.

=== Lateral Thinking ===
Over the past few decades [[w:Edward_de_Bono|Edward de Bono]] has developed several problem solving concepts, tools, and techniques he calls [[w:Lateral_thinking|''Lateral Thinking'']]. He contrasts lateral thinking with the typical approaches he calls vertical thinking. Where vertical thinking digs deeper, lateral thinking digs in a new place. 

The following table contrasts traditional vertical thinking with salient features of lateral thinking.

{| class=&quot;wikitable&quot;
|-
! Vertical Thinking !! Lateral Thinking
|-
| Historical continuity || Generating new alternatives
|-
| Building upon accepted assumptions || Challenging assumptions
|-
| Leveraging and extending existing patterns || Restructuring familiar patterns
|-
| Sequential Steps || Escape to new patterns, reversal
|-
| Analytical || Generative, Provocative, disruptive
|-
| Construction || Creative destruction
|-
| Correctness || Novelty, random stimulation, different
|-
| Serious, stern, grave, responsible, deep, intense || Playful
|-
| Dig the same hole deeper || Dig a hole in a new place
|}

Some of the tools and techniques developed from lateral thinking are described in this course, including PO, forced relationships using random words, and the six thinking hats. However, there are too many tools and techniques to cover adequately here. I encourage interested students to read and study more about lateral thinking, beginning with the book ''Lateral Thinking: Creativity Step by Step''&lt;ref&gt;{{cite book |last=De Bono |first=Edward |date=February 24, 2015 |title=Lateral Thinking: Creativity Step by Step  |publisher=Harper Colophon |pages=300 |isbn=978-0060903251 |author-link=w:Edward_de_Bono }}&lt;/ref&gt;, and many [[w:Edward_de_Bono#Published_works|others by Edward de Bono]]. 
==== Assignment ====
'''Part 1:'''
#Think of as many uses as you can for a paperclip.
#Write these as a list. List as many uses as you can.
#Keep going, find more uses.
#Compare your list to this list of [https://leoniehallatinnovationiq.wordpress.com/2012/11/21/100-uses-for-paperclips/ 100 uses of a paperclip].

'''Part 2:'''
#Choose several puzzles from these sources:
##See, for example http://lateralpuzzles.com/puzzles/index.php
##Classic Lateral Thinking Exercises See: https://leoniehallatinnovationiq.wordpress.com/2010/08/24/lateral-thinking-brain-teasers/ 
##and the book ''Hall of Fame Lateral thinking puzzles'', Paul Sloane &amp; Des MacHale&lt;ref&gt;{{cite book |last1=Sloane |first1=Paul |last2=MacHale |first2=Des |date=May 3, 2011 |title=Hall of Fame Lateral Thinking Puzzles: Albatross Soup and Dozens of Other Classics  |publisher=Puzzlewright |pages=128 |isbn=978-1402771170 |author-link=w:Paul_Sloane_(author)}}&lt;/ref&gt;
#Solve the puzzles you have chosen
=== PO – Provocative Operation ===
[[w:Edward_de_Bono|Edward de Bono]] created the term “[[w:Po_(lateral_thinking)|Po]]” as part of a [[w:Lateral_thinking|lateral thinking]] technique to indicate movement—a shift, backing off judgment, and invite movement forward in a new direction. Po is as ''provocative operation'' used to signal a deliberate intent to move thinking forward to a new place where new ideas or solutions may be found. Po can be used as an interjection — as a creative alternative to “yes” or “no” — indicating that you reject the [[w:False_dilemma|false dichotomy]], or that you need to know more before responding to an idea or thought. Imagine it as a word that means: &quot;I think I know what you mean, but can you say it in another way so I may more fully understand you&quot;. Its use indicates respect for the other. It is considered a language lubricant — to encourage more conversation, exploration, and explanation. It may mean “supPOse things were different” or simply “let’s pause here and consider other ways to proceed.”

As an example, when you are in a business meeting where a co-worker states &quot;Sales are dropping off because our product is perceived as old fashioned&quot; you, or others at the meeting can respond with:
#po: Change the color of the packaging
#po: Flood the market with even older-looking products to make it seem more appealing
#po: Call it retro
#po: Sell it to old people
#po: Sell it to young people as a gift for old people
#po: Open a museum dedicated to it
#po: Market it as a new product

Some of the above ideas may be impractical, not sensible, not business-minded, not politically correct, or just plain daft. The value of these ideas is that they move thinking from a place where it is entrenched to a place where it can move. The above ideas might develop into more practical ideas such as:

po: Change the color of the packaging → update the product casing to bring it up to date as is often done with electronic goods.

po: Call it retro → instead of ''retro'' say &quot;tried and tested&quot; or &quot;industry standard&quot;

=== Assignment ===
Introduce use of “Po” to your working group or close associates.
#Practice using “Po” in a private setting, perhaps with family or close friends to gain experience and become comfortable with it.
#Describe its benefits and use to a group of coworkers. Invite them to discuss using the technique and to share their concerns.
#Ask them if they are willing to try “Po” when the group works together. Consider “Po – we are using Po effectively to move the team forward” and allow the discussion to unfold.
#Use Po effectively and routinely when this group meets to solve problems.
#Extend your use of Po to other working groups. 
=== Developing Ideas === 
The tools described so far emphasized fluency rather than elaboration.  The following tools help consider ideas further, develop ideas to better understand them, imagine their usefulness, capture the most benefit from a nascent idea and often use one idea as a springboard to generate additional ideas. 
=== Idea Notebooks ===
Keep a journal, diary, or other notebook where you record new ideas and revisit and develop ideas previously recorded. Keep this with you. Write in it often, study it often.
=== Synetics ===
[[w:Synectics|Syntectics]] is a collection of problem-solving tools, collaboration methods, and techniques originated by George M. Prince and William J.J. Gordon originating in the 1950’s. 

They studied recordings of thousands of business meetings to understand what happens. They were particularly interested to learn what behaviors inhibit the discussion, preempt creative thinking, and shut down exploration of new ideas. They then worked to test a variety of approaches that encourage creative thinking and helpful consideration of creative ideas.

Based on their extensive analysis of how meetings unfold, they pioneered concepts of client ownership of idea selection, metaphor, open minded communications, suspending judgement, idea development, climate factors that encourage or discourage ideation, and the prevalence and importance of avoiding the [[Unleashing_Creativity#Cooperation_Cycle|discount and revenge cycle]].&lt;ref&gt;{{cite book |last1=Nolan |first1=Vincent  |last2=Williams |first2=Connie  |date=2010 |title=Imagine That! Celebrating 50 years of Synctics  |url=http://synecticsworld.com/imagine-that/|publisher=Synecticsworld  |isbn=9780615413778 }}&lt;/ref&gt;

Their approach to idea development is presented here, and other Synetics contributions appear in various sections of this course as relevant topics are addressed.

=== Synetics Idea Development ===
The Synetics founders observed that many ideas created in brainstorming sessions or that arose in ideation meetings were lost because they were never understood, or never developed. They introduced the following approach to getting more out of the generated ideas:
#Insist the client own idea selection during brainstorming sessions or other idea generating activities. This overcomes the “[[w:Not_invented_here|not invented here]]” problem that often inhibits many good ideas from being embraced by people or organizations who could benefit from them. The team recognizes that opinions are not relevant unless they are requested by the client.
#The problem owner, typically the client, is expected to check his or her understanding of the idea by discussing it with the idea originator before evaluating the idea.
#The idea must be well understood before identifying important shortcomings.
#Ideas are evaluated in stages:
##Select ideas for newness and appeal
##Build on the nascent idea to create a more fully formed idea.  (Fully bake appealing half-baked ideas.)
##Evaluate the idea with an open mind, first emphasizing the benefits and potential before identifying important shortcomings. (as is done when using [[Thinking_Tools#POINT|POINT]])
##Modify the idea to overcome shortcomings and create more opportunities and greater benefits.  
#Use the idea to support some new course of action.

=== Varying Attributes ===
New products, concepts, or solutions can often be inspired by varying the attributes of some existing product. Consider chairs for example. A typical chair has four legs, a squarish seat, and a back. Removing the back produces a stool. Using three legs provides a three-legged stool. Using a round seat results in a typical three-legged stool with a round seat. Removing the legs creates a cushion. Suspending a net between two trees creates a hammock.

The listed attributes may be: 1) physical attributes, 2) social attributes, 3) process attributes, 4) psychological attributes, or 5) production attributes.&lt;ref&gt;{{cite book |last1=Kettler |first1=Todd |last2=Lamb |first2=Kristen N. |last3=Mullet |first3=Dianna R. |date=December 1, 2018 |title=Developing Creativity in the Classroom  |publisher=Prufrock Press |pages=240 |isbn=978-1618218049  }} Page 139.&lt;/ref&gt; 

Follow these steps to extend your thinking beyond some existing product:
#Begin with an existing product, solution, or process. We will use a chair in our example. 
#Identify the various attributes of that object that can possibly be modified. These form the column headings of the matrix you will create. For example, a chair has legs that can vary in number, or length. A chair can be rigid, retaining its shape, or can have its shape transformed, by folding for example. Various rests support the weight of the user’s torso, arms, head, or feet. Arm rests can be in various positions. The back can have various geometries. A variety of materials can be used. Various “bonus features” can be added to extend the function of the chair. 
#For each column, list several forms or variations that can be imagined for that attribute. Considering chair legs, any number of legs can be used, they can have a variety of lengths or shapes, they can be rocking, swinging, hammock, hang as a [[w:Pendant|pendant]], form a pedestal, swivel, or include wheels.
#Choose one entry from each column to describe one style of chair. For example, four long legs, rigid configuration, seat rest, no arm rests, no back, and wooden materials result in a bar stool.

We use a related tool—often called a ''morphological matrix''—when we order a sandwich or a cup of coffee. We specify the type of bread, toasted or not, the filling, and the toppings when we order a sandwich. We specify the size, coffee variety, sweetener, creamer, caffeine level, brewing method, and topping when we order a coffee. 
==== Assignment ====
#Study the [[/Attribute Matrix Example/]] that describes a variety of attributes for a chair.
#Add any columns that may be missing.
#Add any missing attributes to each column.
#Select one attribute from each column.
#Sketch or describe the chair that is specified by the set of attributes you have chosen.
#Repeat these steps using these examples of [[Thinking_Tools/Attribute_Matrix_Example#Ice-cream_flavors|ice-cream flavors]], or [[Thinking_Tools/Attribute_Matrix_Example#Romance_Novel|romance novels]].
#Create an attribute matrix for a lamp.
#Apply this technique to some real-world problem you wish to solve.

=== SCAMPER ===
[[w:S.C.A.M.P.E.R|SCAMPER]] is an acronym that can guide innovators to think of variations of some product with the intent of discovering a useful innovation. It combines brainstorming and varying attributes in a structured search for new ideas.

Each letter in the SCAMPER acronym suggests some transformation or extension of a base product or topic to be explored to suggest some new product. The letters, and their related operations are:
*''Substitute'' comes up with another topic that is equivalent to the present topic. Remove some part of the original and replace it with something different. Constructing [[w:Pole_vault|vaulting poles]] from fiberglass rather than ash or bamboo provided safer and higher vaults. 
*''Combine'' adds information to the original topic. Join two or more parts together to product something new. Force together two components that are not typically joined. Combining chocolate and peanut butter gave us Reese’s Peanut butter cups. 
*''Adjust or Adapt'' identifies ways to construct the topic in a more flexible and adjusted material. Change a component of the original so that it works in some new way.
*''Modify, magnify, minify'' creatively changes the topic or makes a feature, component, or idea bigger or smaller.
*''Put to other uses'' identifies the possible scenarios and situations where this topic or product can be used.
*''Eliminate'' removes ideas or elements from the topic that are not valuable. Bar codes eliminated the need for individual price stickers in the supermarket. 
*''Reverse or rearrange'' evolves a new concept from the original concept. Change the order or structure of the original. Reverse cause and effect. Reverse input and output. Reverse start and finish. Reverse predator and prey. Reverse top down and bottom up. Use this [[Thinking_Tools/Reversals|list of reversals]] for other ideas.
==== Assignment ====
#Choose something to improve. 
#Identify at least one change that could be made corresponding to each of the SCAMPER transformations described above.

=== Six Thinking Hats ===
Considering each of the distinct points of view described in the book ''Six Thinking Hats''&lt;ref&gt;{{cite book |last=De Bono |first=Edward |date=August 18, 1999 |title=Six Thinking Hats  |publisher= |pages=192 |isbn=978-0316178310 |author-link=w:Edward_de_Bono }}&lt;/ref&gt;  improves group decision making. Each point-of-view is represented by a distinctly colored hat:
*'''White''' — Collect the '''relevant facts''' and information.
*'''Green''' — Create '''new options''', possibilities, alternatives, and new ideas for the group to consider.
*'''Yellow''' — '''Advocate''' the present alternative, highlighting the benefits and opportunities.
*'''Black''' — Use judgment and '''critical thinking''' to examine the present alternative, highlighting the problems, difficulties, and what may go wrong.
*'''Red''' — '''Express feelings''', hunches and intuition and share fears, likes, dislikes, loves, and hates.
*'''Blue''' — '''Facilitate the group''' process by directing attention, discussion, and decision making toward the topics that provide the most insight. 

Each of the six thinking hats is a different way of looking at an issue to be considered and decided. Representing a point of view by a hat has the advantage of allowing people to play with a new perspective to get experience with it. They try on the hat and take on a new role. As an example, people who typically argue by criticism can remain mostly critical. But by putting on the red hat they can voice their emotions, or by putting on the yellow hat they can think about positive effects.

During group discussion, each point of view should be considered before coming to a final decision. This can be done in a variety of ways. Members of a newly formed group, or one beginning to use this method, can wear actual colored hats, while each person strictly plays the role defined by their hat. Ensure that each person is heard from, and rotate hats from time to time throughout the meeting. Groups that are more familiar with the idea can simply announce the color of the point of view they are taking or ask to hear from a specific color point of view before reaching a decision. You will know that it is beginning to work when someone speaks up and says: “As I take off my usual black hat and look at this with a yellow hat on, I can see the benefits of this alternative. I think we are getting close to agreeing on an excellent solution. I would like to see some more green-hat thinking, however, before we finally decide.”

=== Biomimicry === 
[[w:Biomimicry|Biomimicry]] pioneer [[w:Janine_Benyus|Janine Benyus]] encourages designers to ask “How would nature solve this problem?” and then observes “Learning about the natural world is one thing, learning ''from'' the natural world—that’s the switch. That’s the profound switch.” Biomimicry is the examination of nature, its models, systems, processes, and elements to emulate or take inspiration from in order to solve human problems.
==== Assignment ====
#Study the “[[Natural_Inclusion#In_Design|In Design]]” section of the Wikiversity course on [[Natural Inclusion]]. 
#Complete the assignment in that section.

=== TRIZ ===
[[w:TRIZ|TRIZ]] is &quot;a problem-solving, analysis and forecasting tool derived from the study of patterns of invention in the global patent literature&quot;. It was developed by the Soviet inventor and science-fiction author [[w:Genrich_Altshuller|Genrich Altshuller]] and his colleagues, beginning in 1946. In English the name is typically rendered as &quot;the theory of inventive problem solving&quot;

TRIZ includes a practical methodology, tool sets, a knowledge base, and model-based technology for generating innovative solutions for problem solving. It is useful for problem formulation, [[w:System_analysis|system analysis]], [[w:Failure_analysis|failure analysis]], and patterns of system evolution. There is a general similarity of purposes and methods with the field of [[w:Pattern_language|pattern language]], a cross discipline practice for explicitly describing and sharing holistic patterns of design.

The research has produced three primary findings:
#problems and solutions are repeated across industries and sciences
#patterns of technical evolution are also repeated across industries and sciences
#the innovations used scientific effects outside the field in which they were developed.

TRIZ practitioners apply all these findings to create and to improve products, services, and systems

The TRIZ system is more extensive than can be covered here. Interested students are encouraged to study [[w:TRIZ#Books_on_TRIZ|books on TRIZ]], or obtain training elsewhere on the techniques.

=== Assignment ===
Apply your skills in creating possibilities to these [[/example applications/]]. Use divergent thinking skills, tools, and techniques to generate as many possibilities as you can for the chosen example. 
== Develop—Evaluative Thinking, Making Judgments ==
Development is the application of new ideas to solve practical problems. Here we choose from the many ideas that were identified during the ideation phase, use those ideas to propose a solution approach, and enhance those ideas into a detailed solution description.

The goal of the development phase is to describe a solution. The outcome is a proposed solution or a complete and detailed solution description, design specification, or implementation plan.

Many tools exist that can help us develop nascent ideas. Several are described in the following sections.
=== Discard the Unsuitable ===
The ideation phase has provided us with an abundance of tentative solutions, solution concepts, or solution approaches. Begin the development phase by discarding any of these ideas that are definitely unsuitable. An idea may be unsuitable for development if it defies the laws of physics, requires changing something you cannot change, or is not morally acceptable.
==== Assignment ====
'''Part 1:'''
#Complete the Wikiversity course on [[What you can change and what you cannot]].
#Discard any candidate ideas that require changing things you cannot change. 

'''Part 2:'''
#Complete the Wikiversity course on [[Moral Reasoning]].
#Discard any candidate ideas that are not morally acceptable.

=== Evaluate Suitable Ideas ===
With the unsuitable ideas discarded, turn attention to the remaining ideas. These are all judged as suitable but need to be evaluated to select the most promising from among that various candidate ideas. The following tools and techniques can help to evaluate candidate ideas. 
==== POINT ====
POINT discovers the Plusses, Opportunities, Issues, and New Thinking that can further develop, help us better understand, and evaluate a nascent idea.&lt;ref&gt;A new idea protocol, Foursight Online, April 2016 News, https://foursightonline.com/newsletters/2016-april-news-point-and-new-tool-cards/&lt;/ref&gt; 

When encountering a new idea, focus first on the ''plusses'', the possibilities and opportunities it provides. What does the idea offer? What do you like about it? What new ideas might it lead to? What is the spark of brilliance it reveals? 

Now imagine the ''opportunities'' it can unlock. What good things might result if this idea was pursued and came to fruition? How might this idea unlock a better future for someone? 

Only after carefully and conscientiously identifying the plusses and opportunities do you turn attention to the ''issues'' that need to be resolved. Pose each issue as an inquiry into how the problem could be resolved. Rather than “we can’t afford this” ask “How might this be funded?” The [[w:Wright_brothers|Wright Brothers]] solved the many issues that defeated earlier efforts to attain powered flight by identifying each issue, and then finding a solution. Asking “How can we [[w:Wright_brothers#Adding_power|obtain a powerful lightweight engine]] to power our craft?”  led to a solution. Neither overlooking the issue, nor yielding to despair would have resulted in a solution. 

Framing issues as questions can inspire ''New Thinking'' and identify new solutions. After many unsuccessful attempts to find an engine manufacture that could meet their requirements, the Wright Brothers turned to their shop mechanic who built a remarkable engine in only six weeks.

==== Prototyping ====
A [[w:Prototype|prototype]] is an early sample, model, or release of a product built to test a concept or process. Useful prototypes might consist of a sketch, engineering drawing, [[w:3D_rendering|3D rendering]], animation, [[w:Artist's_impression|artist’s rendition]], [[w:Architectural_rendering|architectural rendering]], scale model, [[w:Mathematical_model|mathematical model]], [[w:Simulation|simulation]], [[w:Pilot_plant|pilot plant]], [[w:Breadboard|breadboard]], elementary or illustrative fabrication, or rudimentary implementation of the proposed product. The prototypes are used to gain experience and feedback from users, researchers, engineers, manufacturers, and others. 

Experience gained from exploring each prototype helps to improve the design.  

The Wright Brothers used prototyping extensively throughout their development of powered flight. This included:
*Learning from a simple toy helicopter they played with as children,
*Building and flying toy kites,
*Building and flying winged box kites to experiment with wing warping,
*Building and flying gliders to study flight parameters and flight controls,
*Building a wind tunnel and systematically testing many airfoil designs,
*Improving the mathematical flight formula based on their experiments, and
*Learning from each version of aircraft to help design new and improved versions. 

As another example, it is reported&lt;ref&gt;Steve Jobs dropped the first iPod Prototype into an Aquarium to prove a point, Business Insider, November 18, 2014. See: https://www.businessinsider.com/steve-jobs-threw-ipod-prototype-into-an-aquarium-to-prove-a-point-2014-11&lt;/ref&gt; that Steve Jobs dropped a prototype iPhone into an aquarium. When bubbles rose, he snapped “Those are air bubbles, that means there’s space in there. Make it smaller.”

==== Foresight Scenarios ====
A foresight scenario&lt;ref&gt;Scenario Method, European Foresight Platform. See: http://www.foresight-platform.eu/community/forlearn/how-to-do-foresight/methods/scenario/&lt;/ref&gt; is a type of [[w:Scenario_planning|scenario plan]] used to envision the impact of a new product, policy, or decision. The foresight scenario is a carefully constructed story that describes a future that could unfold if the candidate idea is developed into a final product, service, or policy. 

Effective foresight scenarios are plausible, internally and externally consistent, and must aid in decision making. 

Foresight scenarios can range from science fiction stories, [[w:Storyboard|storyboards]], [[w:Use_case|use cases]], storm damage forecasts, economic forecasts, sales projections, prototype marketing materials, [[w:Wargame|war games]], [[w:System_dynamics|system simulations]], or dystopian or utopian narratives.

The value of a foresight scenario comes from the issues it identifies. Collect these issues from the scenario authors and from those who are asked to review and evaluate it. 

Use what is learned from the foresight scenario to choose among alternative ideas, or to refine a nascent design.

==== Affinity Diagram ====
The [[w:Affinity_diagram|affinity diagram]] is a thinking tool used to organize ideas and data. It is sometimes referred to as the KJ Method. An affinity diagram gathers large amounts of language data originating as ideas, opinions, issues, solutions, etc., and organizes them into groupings based on natural relationships that become apparent and emerge from the data.&lt;ref&gt;''Hoshin Planning, the Developmental Approach'', Bob King, Chapter 4. Page 4-2.&lt;/ref&gt;

The tool is commonly used within project management and allows large numbers of ideas stemming from brainstorming to be sorted into groups, based on their natural relationships, for review and analysis. It is also frequently used in [[w:Contextual_inquiry|contextual inquiry]] as a way to organize notes and insights from field interviews. It can also be used for organizing other freeform comments, such as open-ended survey responses, support call logs, or other qualitative data.

In general, an affinity diagram is created using these steps:
#Assemble the Right Team:
#*Keep the team small, 4 to 6 people.
#*Choose team members who represent varied perspectives.
#*Choose creative, open-minded team members.
#Phrase the Issue to be Considered:
#*Use a broad, neutral statement. It is often best to be vague.
#*State an area of consideration, not a solution.
#*Write down the issue for all to see clearly, be sure it is well understood.
#Generate and Record Ideas:
#*Do not criticize ideas during this brainstorming.
#*It is acceptable to clarify ideas at this point.
#*Avoid one-word cards, include a noun and a verb whenever possible.
#*Use a separate card for each individual idea.
#*Keep ideas visible as recorded on cards.
#Randomly Lay Out Completed Cards:
#*On table, wall or Flip chart.
#Sort Cards into Related Groupings:
#*Quick Process done in silence (to use the creativity of the right side of the brain).
#*Use gut reactions, don't agonize over sorting.
#*Move cards to resolve disagreements.
#*Allow groupings to emerge, don't pigeonhole cards into standard categories.
#Create Header Cards:
#*Look within the group for an appropriate header card (often one will not exist).
#*Use concise multi-word headings, discuss with group while composing.
#*The header card must make sense while standing alone.
#*The header card captures the essential link in all the cards beneath it.
#*Place at the top of the group.
#*Sub-themes can be turned into sub-headers. Very large groups need to be broken into subgroups.
#Draw the Finished Affinity Diagram:
#*Bring together related groupings. The final number of headings should be 5-10 in total.
#*Draw lines associating headers with the cards beneath them.

==== Tree Diagram ====
A [[w:Tree_structure|tree diagram]] visually represents the hierarchical nature of some structure. It is useful to assess completeness and relationships of ideas, tasks, components, or other elements of a complex or composite system. A tree diagram can help to create a [[w:Taxonomy|taxonomy]] of the topic being studied. 

It is often useful to use a tree diagram to further develop and analyze the information that results from creating an affinity diagram. A tree diagram provides an analytical representation that can complement the [[w:Organic_(model)|organic structure]] of an affinity diagram. A completed tree structure includes ''terminal nodes'' or ''leaf nodes'' at the lowest level of the hierarchy. These terminal nodes are clearly defined and cannot be usefully subdivided. 

The [[w:Phylogenetic_tree|biological phylogenetic tree]] is an well-studied example of a tree diagram and will be used here to illustrate concepts. 

In general, a tree diagram is created using these steps:
*Begin with a statement that clearly and simply states the issue, problem or goal to be explored. The top header statement from the affinity diagram is often a good starting point. It may be helpful to add clarity to that statement before continuing to create the tree diagram. This establishes the top level of the hierarchy that is being created. In the example of the biological phylogenetic tree the top-level organizing statement is “Existing Lifeforms”.
*To create the next lower level of the hierarchy, enumerate all the sub-components of the higher level (parent category). Examine this level of the hierarchy to ensure it is complete, each listed component is distinct from the others, and all are at the same [[w:Principle_of_abstraction|level of abstraction]]. The “[[w:Kingdom_(biology)|kingdoms]]” of the phylogenetic tree form the second level of the hierarchy. This level originally included plants and animals and more recently includes bacteria, archaea, and eukaryote. 
*Repeat step 2 until the tree reaches a level of detail that clearly defines each terminal node.  The levels of the phylogenetic tree known are known as kingdom, phylum, class, order, family, genus, and species. In this example the species are the terminal nodes, however, lower level classifications, such as breeds of dogs, are also defined. 

The resulting tree diagram is useful in creating a decision matrix, Quality Function Deployment, action plans, project management, and other thinking tools. 
===== Assignment =====
*Choose a problem or issue to work on for this assignment. Choose from these [[/example problem topics/]], or from some real-world problem you are facing.
*Create an affinity diagram that identifies a large number of topics, ideas, sub-problems, related problems, resources, candidate solutions, or issues related to the chosen problem.
*Using this affinity diagram as the starting point, create a tree diagram that organizes the information concerning this problem.

==== Decision Matrix ====
A [[w:Decision_matrix|decision matrix]] organizes a systematic comparison of decision alternatives, based on identified decision criteria. It can help developers choose among a variety of proposed alternative solutions and narrow a list of options to a best choice.&lt;ref&gt;What is a decision matrix? ASQ Quality Resources. See: https://asq.org/quality-resources/decision-matrix&lt;/ref&gt;  
===== Assignment =====
*Study this [[/new car decision matrix/]] example.
*Choose some real-life choice you must make by evaluating alternative opportunities. 
*Following the new car example, create a decision matrix representing the choice you have decided to study.
*Does the quantitative result from the decision matrix agree with your intuitive decision? Why or why not?

A related tool, called ''targeting'',&lt;ref&gt;The Creative Thinker’s Toolkit, [[w:The Great Courses|the Great Courses]]. Gerard Puccio, Lecture 16.&lt;/ref&gt;  can be used to move alternatives toward a more ideal solution. Begin by drawing a [[w:Shooting_target#World_Archery_Federation|target]], as is used in archery. The [[w:Bullseye_(target)|bullseye]] represents the perfect alternative. This imagined alternative attains a perfect score on each of the decision criteria used in the decision matrix. Now use a [[w:Post-it_Note|Post-it note]] to represent each of the alternatives considered. Place each Post-it note on the target so that its distance from the bullseye reflects the decision matrix score it receives, recognizing only a perfect score would hit the bullseye. Now identify what (low scoring) attributes are keeping an alternative from coming close to that target. Form a challenge statement representing the problem to be solved that could bring that alternative closer. An example challenge statement might be, “how can we improve this alternative so it can move closer to the bullseye?” If the problem represented by the challenge statement can be solved, that alternative can be moved closer to the bullseye.

==== Quality Function Deployment. ====
[[w:Quality_function_deployment|Quality function deployment]] (QFD) is a method developed in Japan beginning in 1966 to help transform the [[w:Voice_of_the_customer|voice of the customer]] into engineering characteristics for a product. Yoji Akao, the original developer, described QFD as a &quot;method to transform qualitative user demands into quantitative parameters, to deploy the functions forming quality, and to deploy methods for achieving the design quality into subsystems and component parts, and ultimately to specific elements of the manufacturing process.”

The core of QFD is a matrix that links [[w:Product_requirements_document|customer needs]] to [[w:Functional_requirement|technical specifications]]. 

The method is too extensive to describe adequately here. Interested students are encouraged to study books on the topic and obtain specialized training in the method.

==== Representation ====
As a design emerges, it can be represented in a variety of forms. These may include a [[w:Sketch_(drawing)|sketch]], narrative description, [[w:Specification_(technical_standard)|technical specifications]],  [[w:Engineering_drawing|engineering drawings]], artistic drawings, physical models, [[w:Breadboard|breadboard]], [[w:Proof_of_concept|proof of concept]], [[w:Computer-aided_design|CAD]] models, [[w:Use_case|use case]] scenarios, [[w:Slide_show|graphic presentations]], video, [[w:Technology_demonstration|technology demonstrations]], or prototypes.

== Implement—Tactical Thinking ==
[[w:Implementation|Implementation]] is ''doing''. It is the realization of an application, or execution of a [[w:Plan|plan]], idea, [[w:Scientific_modelling|model]], [[w:Design|design]], [[w:Specification|specification]], [[w:Standardization|standard]], [[w:Algorithm|algorithm]], or [[w:Policy|policy]]. The goal of implementation is tangible results. Implementation translates a strategy or design into tactics and results. It is adopting a solution and putting a solution into practice. 

For this course, the outcome of the implementation phases is an ''action plan''. In a broader context the outcome may be tangible results in the real world. 
=== Are we doing this? ===
Implementing an idea can be very expensive. It may be worthwhile to critically review the idea, design approach, or design before committing the considerable resources it will take to implement the project. It may be wise to hold a [[/Murder board/]] to examine the project in depth.
 
A murder board, also known as a &quot;scrub-down&quot;, is a committee of questioners set up to critically review a proposal. The aim of the murder board session is to try to destroy the project rather than to defend it.  As a result, at the end of the session the team can be left with all the reasons why this project won’t work. This identifies specific areas where the proposal needs to be improved.

A murder board may be held during or at the completion of the design phase, or at the beginning or anytime during the implementation phase. 
==== Assignment ====
#Hold a [[Thinking_Tools/Murder_board|murder board]] review of the project.
#Adopt the recommendation of the murder board. 

=== Action Planning ===
An [[w:Action_plan|action plan]] is a detailed [[w:Plan|plan]] outlining actions needed to reach one or more [[w:Goal|goals]]. The goal will be clear from completing the earlier phases described in this course. The solution approach chosen, and design details will also be available as outcomes from the earlier phases. 

Begin by identifying all the tasks that need to be completed to progress from the present state (how things are now) to the final state (the goal to be achieved, the problem to be solved.) Use various ideation tools to identify required tasks and events. Group tasks into a [[Thinking_Tools#Tree_Structure|tree structure]] identifying major tasks and related subtasks. Ask “How can this be done?”  or “What are some steps that can help get this done?” or “What else needs to be done?” to add detail to high level or poorly defined tasks.&lt;ref&gt;How-How diagram, Creating Minds. See: http://creatingminds.org/tools/how_how.htm&lt;/ref&gt; Organize these tasks into a time-ordered sequence based on [[w:Dependency_(project_management)|dependencies]] among tasks. Ask “What do we have to do first?”, What do we do next?”, “What has to happen before we can do this?” to identify interdependencies. Use this time-ordered sequence to establish a more specific timeline. Assign responsibilities for accomplishing each task. Plan to iterate and add detail as the plan is carried out.

The action plan may be represented and maintained as a [[w:Work_breakdown_structure|''work breakdown structure'']] that identifies tasks to be completed, subtasks required for each task, resources required, and responsibilities for completing each task. 

The [[w:Gantt_chart|Gannt chart]] is another useful representation of an action plan. It is a type of bar chart that represents the project schedule and may show dependency relationships between activities.

=== Assisters and Resisters ===
Whenever you begin to move forward with some change there will some people who see the benefits of that change, who want to see that change take place, and who may be willing to help make that change happen. There are also others who will oppose the change because they are uncomfortable with change, do not understand the benefits, stand to lose something if the change takes place, or chose to defend the status quo. Those who wish to see the change occur are ''assisters''. Those opposed are the ''resisters''.  

It is important to identify ''assisters'', those who can help the project succeed, along with ''resisters'', those who will oppose this project. It is also helpful to estimate the level of influence each person has.
[[File:Assisters and Resisters.jpg|thumb|An illustration of project Assiters and Resisters]]
#Begin by using divergent thinking to identify the people and other sources of assistance and resistance the project may encounter.
#For each of the people listed, estimate their level of advocacy for the project, estimated as strongly support, moderately support, indifferent, moderately oppose, or strongly oppose. 
#For each of the people listed, estimate the degree of influence they can have on the project, estimated as very powerful, moderately powerful, or slightly powerful. 
#Plot each person on the assisters and resisters chart shown on the right. 
#Estimate or determine the reasons that cause each person to support or oppose the project.
#For each of the identified assisters, ask “How can we engage these assisters to benefit the project?” Record these action steps.
#For those resisters who you may be able to influence, ask “How can we influence these resisters to reduce their opposition, or perhaps win them over as project supporters?” Record these action steps.
#For each person who you may be able to influence, draw an arrow to the location on the chart to show the position you plan to move them to.
#Include this work in the action plan. 
=== Stakeholder Analysis ===
[[w:Stakeholder_analysis|Stakeholder analysis]] is the process of assessing a system and potential changes to it as they relate to the relevant and interested parties, known as ''stakeholders''.

A [[w:Project_stakeholder|project stakeholder]] is, &quot;an individual, group, or organization, who may affect, be affected by, or perceive itself to be affected by a decision, activity, or outcome of a project&quot;. 

Project stakeholders may be inside or outside an organization who:
#[[w:Executive_sponsor|sponsor]] a project, or
#have an interest or a gain upon a successful completion of a project;
#may have a positive or negative influence in the project completion.

Types of stakeholders include: 
*'''Primary stakeholders''': those ultimately most affected, either positively or negatively by an organization's actions
*'''Secondary stakeholders''': the &quot;intermediaries,&quot; that is, persons or organizations who are indirectly affected by an organization's actions
*'''Tertiary stakeholders''': those who will be impacted the least

'''Key stakeholders''' are those with significant influence on or importance within or outside of an organization.
[[File:Stakeholders matrix.svg|thumb|right|250px|A Power-Interest matrix showing strategies to use based on the quadrant the stakeholders is categorized in.]]
To create a stakeholder map:
#Use ideation techniques to identify a list of stakeholders. Be sure to consider project leaders, project sponsors, senior management, project team participants, users, people who will benefit from the project, people who may oppose the project, people who can help, people who may hinder, subcontractors, consultants, and others.
#Estimate the interest each stakeholder has in this project.  Also estimate if they are likely to support, oppose, or be indifferent to the project.&lt;ref&gt;Stakeholder Mapping, Changing Minds. See: http://changingminds.org/disciplines/change_management/stakeholder_change/stakeholder_mapping.htm&lt;/ref&gt;  Those who can support the project are “assisters”. Those who can oppose the project are “resisters”.&lt;ref&gt;Stakeholders – Identify Assistors &amp; Resistors, Stormz See: https://stormz.me/en/templates/identify-who-will-be-an-assistor-or-a-resistor&lt;/ref&gt;  Others who may be uninformed, indifferent, or undecided now may change their positions as the project evolves. 
#Estimate the power each stakeholder has, and their ability to influence the success of the projects.
#Identify the most powerful assisters and resisters.
#To illustrate the [[w:Stakeholder_analysis#Stakeholder_mapping|stakeholder map]], plot the stakeholders on a “Power-Interest” matrix.
#Work closely with the powerful stakeholders who can help or hinder the project. Monitor, inform, satisfy, influence, and persuade the other stakeholders. 
#Include this ongoing work in the action plan. 
=== Project Management ===
[[w:Project_management|Project management]] is the practice of initiating, planning, executing, controlling, and closing the work of a team to achieve specific goals and meet specific success criteria at the specified time. The primary challenge of project management is to achieve all the project goals within the given constraints of time, budget, and performance, including quality, reliability, and customer satisfaction.

The extent of project management activities needed will depend on the [[w:Project_management#Project_Complexity|complexity of the project]] and the size and experience of the project team. Small teams experienced in solving similar problems may be able successfully manage themselves toward a successful project completion. Larger teams, larger challenges, higher risk, more unknowns, and inexperienced team members may require extensive project management efforts.

It is helpful to make progress and problems clearly visible to team members and other stakeholders. Consider maintaining a project [[w:Dashboard_(business)|dashboard]] that displays progress, highlights successes and challenges, and provides information that can encourage the team to collaborate to solve problems as they arise.

== Navigating, Integrating, Prioritizing == 
Throughout creative problem solving it is important to constantly assess and reassess the situation. This requires deciding what is important to do next, navigating through the complexities of creative problem solving, and establishing priorities.

Important questions must be kept in mind to effectively manage the process. These questions include:
#Is creative problem solving the right approach for addressing the problem we are facing?
#Are we now working to define a problem, describe a solution, create a solution, or gain acceptance for an existing solution?
#What phase of problem solving are we presently in?
#How do we establish the priority of the various problems and opportunities we face? 

We can address these questions in order.

Creative problem solving is a useful approach when the problem&lt;ref&gt;Creative Thinker’s Toolkit, Gerard Puccio, [[w:The Great Courses|The Great Courses]]. Lecture 19&lt;/ref&gt;
*Is your problem to solve,
*Can be solved through imagination, and
*It is a priority for you to solve; it is urgent for you.

If the problem does not meet these three tests, creative problem solving may not be the best approach to use.
[[File:Possibility Landscape 2.png|thumb|300px|Explore the problem landscape to create possibilities.]]
The “Creating Possibilities” diagram shown on the right and described in the “[[Creating Possibilities]]” course is a map that can be used to help navigate through problem space. The key decisions are:
#Are we working to find, understand, and better define the problem, or
#Are we working to define and describe a solution to a well-stated problem,  or
#Are we working to implement, launch, or deploy and existing solution.

These questions help us determine if we should be working in the clarify, ideate, develop, or implement phases.

It is also important to determine if ''divergent'' thinking is needed to create new alternatives, or if ''convergent'' thinking is needed to choose the best option from among existing alternatives. As illustrated in the “Creating possibilities” diagram, the process alternates between divergent and convergent thinking often as each new phase is entered.

Strategic thinking occurs in the ''clarify'' phase. This phase focuses on the questions:
*What do you want to have happen?
*What are the opportunities? 

We focus on divergent thinking and generate many candidate alternative solutions in the ideation phase. Creativity is unleased as we pursue fluency, flexibility, originality, and imagination. 

Convergent thinking become prevalent as we enter the develop stage. Evaluation, judgments, clarification, and definition are prominent in the Develop state. Here we are working to describe a solution.

With a solution description on hand we are ready to enter the implementation phase. Here we build the product, launch the product, or gain acceptance or adoption of some policy change. 

[[w:Metacognition|Metacognition]]—thinking about thinking—is essential throughout creative problem-solving processes to choose the most effective approach to tackle the most important problem or make the next decision. 
=== Success Zones ===
A ''success zones'' analysis and map can help the team decide what problems are best to work on based on their importance and likelihood of success. 
[[File:Success Zones.jpg|thumb|Plotting opportunities on this Success Zones chart can help establish priorities.]]
Follow these steps to create a success zones map:
#Begin with a list of candidate problems to solve, projects to undertake, or solutions to implement.
#Assess the ''importance'' of each—the impact they will have if solved—on either a three-point or nine-point scale ranging from ''low'' through ''medium'' to ''high''. 
#Assess the ''likelihood of success''—your estimate of the likelihood of solving this problem—on either a three-point or nine-point scale ranging from ''low'' through ''medium'' to ''high''. 
#Plot each on the Success Zones grid, shown on the right.
#Follow the advice offered by each cell in the Success Zones grid. Drop problems falling in the red zones in favor of those falling in the green zones. Recognize that high importance goals that are unlikely to succeed will require substantial efforts to complete successfully.
#Deploy your efforts as guided by the Success Zones grid.

=== Unleash Creativity ===
Assess and improve the working environment to unleash the team's creativity.

==== Assignment ====
#Complete the Wikiversity course on [[Unleashing Creativity]].
#Work to improve the working environment to unleash the creativity of the team.

== Summary ==
Many tools are available that can boost your imagination and help with [[w:Creative_problem-solving|creative problem solving]]. 

Problem solving often proceeds in four phases:
#[[Thinking_Tools#Clarify—Strategic_Thinking|Clarify]]—Think strategically to arrive at a precise problem statement.
#[[Thinking_Tools#Ideate—Blue_Sky_Thinking,_Nonjudgmental|Ideate]]—generate, develop, and communicate new ideas.
#[[Thinking_Tools#Develop—Evaluative_Thinking,_Making_Judgments|Develop]]—Choose the best ideas and shape them into a specific solution approach, design specification, or implementation plan. 
#[[Thinking_Tools#Implement—Tactical_Thinking|Implement]]—Translate a strategy or design into a detailed action plan or tangible results in the real world.

Throughout creative problem solving it is important to determine if [[w:Divergent_thinking|''divergent'' thinking]] is needed to create new alternatives, or if [[w:Convergent_thinking|''convergent'' thinking]] is needed to choose the best option from among existing alternatives. The process alternates between divergent and convergent thinking often as each new phase is entered.

Use the thinking tools presented in this course when you need a better idea. 

Throughout creative problem solving it is important to constantly assess and reassess the situation. This requires deciding what is important to do next, navigating through the complexities of creative problem solving, and establishing priorities.

== Recommended Reading ==
Students wanting to learn more about creative thinking tools may be interested in reading the following books:
*{{cite book |last=Michalko |first=Michael |date=June 8, 2006 |title=Thinkertoys: A Handbook of Creative-Thinking Techniques  |publisher=Ten Speed Press |pages=416 |isbn= 978-1580087735 }}

*{{cite book |last=von Oech |first=Roger |date=May 5, 2008 |title=A Whack on the Side of the Head: How You Can Be More Creative  |publisher=Grand Central Publishing |pages=256 |isbn=978-0446404662 }}

*{{cite book |last=Gelb |first=Michael J. |date=February 8, 2000 |title=How to Think Like Leonardo da Vinci: Seven Steps to Genius Every Day |publisher=Dell |pages=336 |isbn=978-0440508274 |author-link=w:Michael_J._Gelb}}

*{{cite book |last=Covey |first=Stephen R. |date=1994 |title=The 7 Habits of Highly Effective People: Powerful Lessons in Personal Change  |publisher=DC Books |pages= |isbn= |author-link=w:Stephen R. Covey}}
 
*{{cite book |last=Jones |first=Morgan D. |date=June 30, 1998 |title=The Thinker's Toolkit: 14 Powerful Techniques for Problem Solving  |publisher=Crown Business |pages=384 |isbn=978-0812928082 }}

*{{cite book |last1=Kettler |first1=Todd |last2=Lamb |first2=Kristen N. |last3=Mullet |first3=Dianna R. |date=December 1, 2018 |title=Developing Creativity in the Classroom  |publisher=Prufrock Press |pages=240 |isbn=978-1618218049  }}

*{{cite book |last1=Gause  |first1=Donald C. |last2=Weinberg |first2=Gerald M. |date=March 1, 1990 |title=Are Your Lights On?: How to Figure Out What the Problem Really Is  |publisher=Dorset House Publishing Company |pages=176 |isbn=978-0932633163 |author-link=w:Gerald_Weinberg}}

*{{cite book |title=The Art of Possibility: Transforming Professional and Personal Life |last1=Stone Zander |first1=Rosamund |last2=Zander|first2=Benjamin   |year=224 |publisher=Penguin |isbn=978-0142001103  |pages=224}}

*{{cite book |last=Nierenberg |first=Gerard |date=1996 |title=The Art of Creative Thinking  |publisher=Barnes Noble Books |pages=240 |isbn=978-0760701249  |author-link=w:Gerard_Nierenberg}}

*{{cite book |last=Bransford |first=John D. |date=February 15, 1993 |title=The Ideal Problem Solver: A Guide to Improving Thinking, Learning, and Creativity  |publisher=Worth Publishers |pages= |isbn=978-0716722052 |author-link=w:John_D._Bransford}}

*{{cite book |last=Plucker |first=Jonathan |date=September 1, 2016 |title=Creativity and Innovation: Theory, Research, and Practice  |publisher=Prufrock Press |pages=400 |isbn=978-1618215956  |author-link=w:Jonathan_A._Plucker }}

*{{cite book |last=De Bono |first=Edward |date=February 24, 2015 |title=Lateral Thinking: Creativity Step by Step  |publisher=Harper Colophon |pages=300 |isbn=978-0060903251 |author-link=w:Edward_de_Bono }}

*{{cite book |last1=Sloane |first1=Paul |last2=MacHale |first2=Des |date=May 3, 2011 |title=Hall of Fame Lateral Thinking Puzzles: Albatross Soup and Dozens of Other Classics  |publisher=Puzzlewright |pages=128 |isbn=978-1402771170 |author-link=w:Paul_Sloane_(author)}}

*{{cite book |last=De Bono |first=Edward |date=August 18, 1999 |title=Six Thinking Hats  |publisher= |pages=192 |isbn=978-0316178310 |author-link=w:Edward_de_Bono }}

*{{cite book |last1=Nolan |first1=Vincent  |last2=Williams |first2=Connie  |date=2010 |title=Imagine That! Celebrating 50 years of Synctics  |url=http://synecticsworld.com/imagine-that/|publisher=Synecticsworld  |isbn=9780615413778 }}

*{{cite book |last=Pugh |first=Stuart |date=February 1, 1991 |title=Total Design: Integrated Methods for Successful Product Engineering  |publisher=Addison-Wesley |pages=278 |isbn=978-0201416398 |author-link=w:Stuart_Pugh}}

*{{cite book |last1=Lakoff |first1=George |last2=Johnson |first2=Mark|date=April 15, 2003 |title=Metaphors We Live By |publisher= |pages=242 |isbn=978-0226468013 |author-link=w:George Lakoff }}

I have not yet read the following books, but they seem interesting and relevant. They are listed here to invite further research.
*Little Bets: How Breakthrough Ideas Emerge from Small Discoveries, by Peter Sims
*100 Methods for Total Quality Management, by Kanji and Asher
*Creativity, by Weisberg

== References ==
&lt;references/&gt;

{{CourseCat}} 
[[Category:Life skills]]
[[Category:Applied Wisdom]]
[[Category:Creativity]]
[[Category:Peace studies]]
[[Category:Humanities courses]]
{{Possibilities}}</text>
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      <text bytes="58642" sha1="mj1t4j8gnu7hc6xfkts3sut8o89rszp" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
* Mrs. Guendoline Bourke
* Lady Florence Bourke
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father.

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

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

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

== Acquaintances, Friends and Enemies ==

=== Algernon Bourke ===

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

=== Guendoline Bourke ===

* Lord and Lady Alington, Belvedere House, Scarborough

== Organizations ==

=== Guendoline Bourke ===

* Member, the Ladies Committee for the Prince's Skating Club, which also included [[Social Victorians/People/Princess Louise|Princess Louise]] (Duchess of Argyll), the [[Social Victorians/People/Portland|Duchess of Portland]], [[Social Victorians/People/Londonderry|Lady Londonderry]], [[Social Victorians/People/Campbell|Lady Archibald Campbell]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], and [[Social Victorians/People/Asquith|Mrs. Asquith]]&lt;ref name=&quot;:11&quot;&gt;&quot;What the 'World' Says.&quot; ''Northwich Guardian'' 01 November 1902, Saturday: 6 [of 8], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001975/19021101/134/0006. Print title: The ''Guardian'', p. 6.&lt;/ref&gt; (1902, at least)

=== Algernon Bourke ===
* Eton
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt; ( – 1901 [at least])
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Member, Men's Committee of the Prince's Skating Club, which also included Lord Edward Cecil, Lord Redesdale, Mr. [[Social Victorians/People/Lyttelton|Alfred Lyttelton]], Sir Edgar Vincent, Sir William Hart Dyke, and Mr. [[Social Victorians/People/Grenfell|W. H. Grenfell]]&lt;ref name=&quot;:11&quot; /&gt; (1902, at least)
* [[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)
* Willis's Rooms&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;

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

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

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

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

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

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

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

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

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

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

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

(From the ''World''.)

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

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

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

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

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

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

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

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

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

ALGERNON BOURKE.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

'''1899 July 1, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1899#1 July 1899, Saturday|meeting in London at the Duke of Westminster's Grosvenor House]] about preserving Killarney as part of the National Trust and seems to have been acting for someone who wanted to purchase the Muckross Estate.&lt;p&gt;

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

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

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

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

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

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

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

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

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

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

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

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

'''1902 October 31, Friday''', the [[Social Victorians/Timeline/1900s#31 October 1902, Friday|7th opening of the Prince's Skating Club]]. Guendoline Bourke was on the Women's Committee and Algernon Bourke was on the Men's.

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

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

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

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

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

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

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

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

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

* Salambo in the Oriental procession.&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}
*&quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}

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

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

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

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

== Demographics ==
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;
=== Residences ===
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1890: 33 Cadogan Terrace
*1891: 33 Cadogan Terrace, Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1904: Algernon Bourke was &quot;usually liv[ing] in Venice&quot;&lt;ref name=&quot;:10&quot; /&gt;
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

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

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

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

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

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

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
== Footnotes ==
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      <text bytes="58656" sha1="pnibbirorvob0v9sg7gv4kxwysxri3q" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
* Mrs. Guendoline Bourke
* Lady Florence Bourke
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father.

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

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

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

== Acquaintances, Friends and Enemies ==

=== Algernon Bourke ===

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

=== Guendoline Bourke ===

* Lord and Lady Alington, Belvedere House, Scarborough

== Organizations ==

=== Guendoline Bourke ===

* Member, the Ladies Committee for the Prince's Skating Club, which also included [[Social Victorians/People/Princess Louise|Princess Louise]] (Duchess of Argyll), the [[Social Victorians/People/Portland|Duchess of Portland]], [[Social Victorians/People/Londonderry|Lady Londonderry]], [[Social Victorians/People/Campbell|Lady Archibald Campbell]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], and [[Social Victorians/People/Asquith|Mrs. Asquith]]&lt;ref name=&quot;:11&quot;&gt;&quot;What the 'World' Says.&quot; ''Northwich Guardian'' 01 November 1902, Saturday: 6 [of 8], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001975/19021101/134/0006. Print title: The ''Guardian'', p. 6.&lt;/ref&gt; (1902, at least)

=== Algernon Bourke ===
* Eton
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt; ( – 1901 [at least])
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Member, Men's Committee of the Prince's Skating Club, which also included Lord Edward Cecil, Lord Redesdale, Mr. [[Social Victorians/People/Lyttelton|Alfred Lyttelton]], Sir Edgar Vincent, Sir William Hart Dyke, and Mr. [[Social Victorians/People/Grenfell|W. H. Grenfell]]&lt;ref name=&quot;:11&quot; /&gt; (1902, at least)
* [[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)
* Willis's Rooms&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;

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

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

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

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

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

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

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

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

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

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

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

(From the ''World''.)

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

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

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

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

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

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

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

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

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

ALGERNON BOURKE.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

'''1899 July 1, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1899#1 July 1899, Saturday|meeting in London at the Duke of Westminster's Grosvenor House]] about preserving Killarney as part of the National Trust and seems to have been acting for someone who wanted to purchase the Muckross Estate.&lt;p&gt;

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

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

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

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

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

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

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

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

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

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

The Revising Barrister — lf a lady gave me the name of Mrs. John Smith I should say I had not got the voter’s name. The name Gwendolen must remain.&lt;ref&gt;&quot;Ladies’ Names.&quot; ''Morning Post'' 12 September 1901, Thursday: 7 [of 10], Col. 3a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19010912/130/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1902 September 4, Thursday''', the ''Daily Express'' reported that &quot;Mrs. Algernon Bourke is staying with Lord and Lady Alington at Scarborough.&quot;&lt;ref&gt;&quot;Onlooker.&quot; &quot;My Social Diary.&quot; &quot;Where People Are.&quot; ''Daily Express'' 04 September 1902, Thursday: 5 [of 8], Col. 1b? [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020904/099/0005. Print p. 4, Col. 7b [of 7].&lt;/ref&gt;&lt;p&gt;

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

'''1902 October 31, Friday''', the [[Social Victorians/Timeline/1900s#31 October 1902, Friday|7th opening of the Prince's Skating Club]]. Guendoline Bourke was on the Women's Committee and Algernon Bourke was on the Men's.&lt;p&gt;

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

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

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

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

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

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

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

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

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

* Salambo in the Oriental procession.&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}
*&quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}

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

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

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

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

== Demographics ==
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;
=== Residences ===
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1890: 33 Cadogan Terrace
*1891: 33 Cadogan Terrace, Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1904: Algernon Bourke was &quot;usually liv[ing] in Venice&quot;&lt;ref name=&quot;:10&quot; /&gt;
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

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

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

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

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

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

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
== Footnotes ==
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      <text bytes="58672" sha1="jn8fvhgqjo7e7cvv8m9xoag6o1n0pcz" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
* Mrs. Guendoline Bourke
* Lady Florence Bourke
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father.

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

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

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

== Acquaintances, Friends and Enemies ==

=== Algernon Bourke ===

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

=== Guendoline Bourke ===

* Lord and Lady Alington, Belvedere House, Scarborough

== Organizations ==

=== Guendoline Bourke ===

* Member, the Ladies Committee for the Prince's Skating Club, which also included [[Social Victorians/People/Princess Louise|Princess Louise]] (Duchess of Argyll), the [[Social Victorians/People/Portland|Duchess of Portland]], [[Social Victorians/People/Londonderry|Lady Londonderry]], [[Social Victorians/People/Campbell|Lady Archibald Campbell]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], and [[Social Victorians/People/Asquith|Mrs. Asquith]]&lt;ref name=&quot;:11&quot;&gt;&quot;What the 'World' Says.&quot; ''Northwich Guardian'' 01 November 1902, Saturday: 6 [of 8], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001975/19021101/134/0006. Print title: The ''Guardian'', p. 6.&lt;/ref&gt; (1902, at least)

=== Algernon Bourke ===
* Eton
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt; ( – 1901 [at least])
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Member, Men's Committee of the Prince's Skating Club, which also included Lord Edward Cecil, Lord Redesdale, Mr. [[Social Victorians/People/Lyttelton|Alfred Lyttelton]], Sir Edgar Vincent, Sir William Hart Dyke, and Mr. [[Social Victorians/People/Grenfell|W. H. Grenfell]]&lt;ref name=&quot;:11&quot; /&gt; (1902, at least)
* [[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)
* Willis's Rooms&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;

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

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

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

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

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

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

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

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

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

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

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

(From the ''World''.)

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

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

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

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

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

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

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

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

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

ALGERNON BOURKE.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

'''1899 July 1, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1899#1 July 1899, Saturday|meeting in London at the Duke of Westminster's Grosvenor House]] about preserving Killarney as part of the National Trust and seems to have been acting for someone who wanted to purchase the Muckross Estate.&lt;p&gt;

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

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

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

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

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

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

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

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

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

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

The Revising Barrister — lf a lady gave me the name of Mrs. John Smith I should say I had not got the voter’s name. The name Gwendolen must remain.&lt;ref&gt;&quot;Ladies’ Names.&quot; ''Morning Post'' 12 September 1901, Thursday: 7 [of 10], Col. 3a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19010912/130/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1902 September 4, Thursday''', the ''Daily Express'' reported that &quot;Mrs. Algernon Bourke is staying with Lord and Lady Alington at Scarborough.&quot;&lt;ref&gt;&quot;Onlooker.&quot; &quot;My Social Diary.&quot; &quot;Where People Are.&quot; ''Daily Express'' 04 September 1902, Thursday: 5 [of 8], Col. 1b? [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020904/099/0005. Print p. 4, Col. 7b [of 7].&lt;/ref&gt;&lt;p&gt;

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

'''1902 October 31, Friday''', the [[Social Victorians/Timeline/1900s#31 October 1902, Friday|7th opening of the Prince's Skating Club]]. Guendoline Bourke was on the Women's Committee and Algernon Bourke was on the Men's.&lt;p&gt;

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

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

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

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

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

'''1913 May 7, Wednesday''', Guendoline Bourke presented her daughter Daphne Bourke at court:&lt;blockquote&gt;Mrs. Algernon Bourke presented her daughter, and wore blue and gold broché with a gold lace train.&lt;ref&gt;&quot;Social and Personal.&quot; London ''Daily Chronicle'' 08 May 1913, Thursday: 6 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/19130508/120/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

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

'''1904 September 15, Thursday''', according to what was at the time called the ''Irish Daily Independent and Nation'', Algernon Bourke was living in Venice and not in the UK at this point:&lt;blockquote&gt;Algernon Bourke, who usually lives in Venice, has spent some time in England during the present summer, and has now gone on a fishing expedition to Sweden, accompanied by his brother, Lord Mayo. Lady Mayo has been staying meanwhile in Ireland, and has had a visit from her mother, Lady Maria Ponsonby, who is a sister of Lend Obventry.&lt;ref name=&quot;:10&quot;&gt;&quot;Society Notes.&quot; ''Irish Independent'' 15 September 1904, Thursday: 4 [of 8], Col. 5b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001986/19040915/131/0004. Print title: ''Irish Daily Independent and Nation'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;'''1909 May 22, Saturday''', Algernon Bourke appears to have been living in Pisa. A columnist for the ''Queen'' reported on the Royal School of Art Needlework:&lt;blockquote&gt;Lady Leconfield [?] was there, also her sister-in-law, the Dowager Lady Mayo, only just back from her winter on the Continent, when she spent most of the time at Pisa, where her son Mr Algernon Bourke has also been staying. The latter is a great connoisseur as regards [art?] notably in what is really good in the way of old Italian sculpture and carving. He and his handsome wife have a place near to Putney, and this winter again Mr Bourke, as the result of his Italian travels, has been sending home such relics of the old Italian palace gardens as as stone and marble carved vases, garden seats, and what-not of the kind — not all for himself and his own gardens by any means, I fancy; but his friends, relying on his knowledge in such matters, get him when abroad to choose for [them?] the adornment of their English terraces and gardens.&lt;ref&gt;&quot;My Social Diary.&quot; The ''Queen'' 22 May 1909, Saturday: 31 [of 86], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19090522/203/0031. Print p. 871.&lt;/ref&gt;&lt;/blockquote&gt;

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

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

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

* Salambo in the Oriental procession.&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}
*&quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}

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

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

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

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

== Demographics ==
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;
=== Residences ===
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1890: 33 Cadogan Terrace
*1891: 33 Cadogan Terrace, Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1904: Algernon Bourke was &quot;usually liv[ing] in Venice&quot;&lt;ref name=&quot;:10&quot; /&gt;
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

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

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

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

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

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

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
== Footnotes ==
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      <text bytes="59745" sha1="gq84by2beeanvtfzriypv8pp5y57z4t" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
* Mrs. Guendoline Bourke
* Lady Florence Bourke
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father.

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

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

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

== Acquaintances, Friends and Enemies ==

=== Algernon Bourke ===

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

=== Guendoline Bourke ===

* Lord and Lady Alington, Belvedere House, Scarborough

== Organizations ==

=== Guendoline Bourke ===

* Member, the Ladies Committee for the Prince's Skating Club, which also included [[Social Victorians/People/Princess Louise|Princess Louise]] (Duchess of Argyll), the [[Social Victorians/People/Portland|Duchess of Portland]], [[Social Victorians/People/Londonderry|Lady Londonderry]], [[Social Victorians/People/Campbell|Lady Archibald Campbell]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], and [[Social Victorians/People/Asquith|Mrs. Asquith]]&lt;ref name=&quot;:11&quot;&gt;&quot;What the 'World' Says.&quot; ''Northwich Guardian'' 01 November 1902, Saturday: 6 [of 8], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001975/19021101/134/0006. Print title: The ''Guardian'', p. 6.&lt;/ref&gt; (1902, at least)

=== Algernon Bourke ===
* Eton
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt; ( – 1901 [at least])
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Member, Men's Committee of the Prince's Skating Club, which also included Lord Edward Cecil, Lord Redesdale, Mr. [[Social Victorians/People/Lyttelton|Alfred Lyttelton]], Sir Edgar Vincent, Sir William Hart Dyke, and Mr. [[Social Victorians/People/Grenfell|W. H. Grenfell]]&lt;ref name=&quot;:11&quot; /&gt; (1902, at least)
* [[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)
* Willis's Rooms&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;

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

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

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

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

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

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

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

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

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

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

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

(From the ''World''.)

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

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

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

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

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

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

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

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

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

ALGERNON BOURKE.

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

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

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

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

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

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

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

'''1897 October 30, Saturday''', ''Black and White'' published J.P.B.'s &quot;The Case of Mrs. Elliott,&quot;&lt;ref&gt;J.P.B. &quot;The Case of Mrs. Elliott.&quot; ''Black &amp; White'' 30 October 1897, Saturday: 12 [of 34], Cols. 1a–2b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004617/18971030/036/0012. Print title ''Black and White'', p. 542.&lt;/ref&gt; an odd short short story in which the Honourable Algernon Bourke Herriott is &quot;rude to Mrs. Elliott.&quot; (Col. 2b) J.P.B. echoes the biographical Algernon Bourke's career in the stock market when Mrs. Christine Elliott does not even simulate interest in her husband's bicycling: &quot;a soul is a grievous burthen for a stockbroker's wife.&quot; (Col. 2a) The Hon. Algy&lt;blockquote&gt;was a senior member of several junior clubs. A woman had dubbed him once &quot;a rip with a taste for verses.&quot; The description was severe, but not unwarranted. His was a pretty pagan sensualism, though, singing from a wine palate to Church music. For the rest, he had just imagination enough to despise mediocrity. (Col. 2a)&lt;/blockquote&gt;'''1898 January 5, Wednesday''', the ''Irish Independent'' reported that &quot;Mr Algernon Bourke, the aristocratic stock broker ... was mainly responsible for the living pictures at the Blenheim Palace entertainment.&lt;ref&gt;&quot;Mr Algernon Bourke ....&quot; ''Irish Independent'' 05 January 1898, Wednesday: 6 [of 8], Col. 2c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001985/18980105/115/0006.&lt;/ref&gt;&lt;p&gt;

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

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

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

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

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

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

'''1899 July 1, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1899#1 July 1899, Saturday|meeting in London at the Duke of Westminster's Grosvenor House]] about preserving Killarney as part of the National Trust and seems to have been acting for someone who wanted to purchase the Muckross Estate.&lt;p&gt;

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

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

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

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

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

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

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

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

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

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

The Revising Barrister — lf a lady gave me the name of Mrs. John Smith I should say I had not got the voter’s name. The name Gwendolen must remain.&lt;ref&gt;&quot;Ladies’ Names.&quot; ''Morning Post'' 12 September 1901, Thursday: 7 [of 10], Col. 3a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19010912/130/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1902 September 4, Thursday''', the ''Daily Express'' reported that &quot;Mrs. Algernon Bourke is staying with Lord and Lady Alington at Scarborough.&quot;&lt;ref&gt;&quot;Onlooker.&quot; &quot;My Social Diary.&quot; &quot;Where People Are.&quot; ''Daily Express'' 04 September 1902, Thursday: 5 [of 8], Col. 1b? [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020904/099/0005. Print p. 4, Col. 7b [of 7].&lt;/ref&gt;&lt;p&gt;

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

'''1902 October 31, Friday''', the [[Social Victorians/Timeline/1900s#31 October 1902, Friday|7th opening of the Prince's Skating Club]]. Guendoline Bourke was on the Women's Committee and Algernon Bourke was on the Men's.&lt;p&gt;

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

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

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

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

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

'''1913 May 7, Wednesday''', Guendoline Bourke presented her daughter Daphne Bourke at court:&lt;blockquote&gt;Mrs. Algernon Bourke presented her daughter, and wore blue and gold broché with a gold lace train.&lt;ref&gt;&quot;Social and Personal.&quot; London ''Daily Chronicle'' 08 May 1913, Thursday: 6 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/19130508/120/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

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

'''1904 September 15, Thursday''', according to what was at the time called the ''Irish Daily Independent and Nation'', Algernon Bourke was living in Venice and not in the UK at this point:&lt;blockquote&gt;Algernon Bourke, who usually lives in Venice, has spent some time in England during the present summer, and has now gone on a fishing expedition to Sweden, accompanied by his brother, Lord Mayo. Lady Mayo has been staying meanwhile in Ireland, and has had a visit from her mother, Lady Maria Ponsonby, who is a sister of Lend Obventry.&lt;ref name=&quot;:10&quot;&gt;&quot;Society Notes.&quot; ''Irish Independent'' 15 September 1904, Thursday: 4 [of 8], Col. 5b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001986/19040915/131/0004. Print title: ''Irish Daily Independent and Nation'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;'''1909 May 22, Saturday''', Algernon Bourke appears to have been living in Pisa. A columnist for the ''Queen'' reported on the Royal School of Art Needlework:&lt;blockquote&gt;Lady Leconfield [?] was there, also her sister-in-law, the Dowager Lady Mayo, only just back from her winter on the Continent, when she spent most of the time at Pisa, where her son Mr Algernon Bourke has also been staying. The latter is a great connoisseur as regards [art?] notably in what is really good in the way of old Italian sculpture and carving. He and his handsome wife have a place near to Putney, and this winter again Mr Bourke, as the result of his Italian travels, has been sending home such relics of the old Italian palace gardens as as stone and marble carved vases, garden seats, and what-not of the kind — not all for himself and his own gardens by any means, I fancy; but his friends, relying on his knowledge in such matters, get him when abroad to choose for [them?] the adornment of their English terraces and gardens.&lt;ref&gt;&quot;My Social Diary.&quot; The ''Queen'' 22 May 1909, Saturday: 31 [of 86], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19090522/203/0031. Print p. 871.&lt;/ref&gt;&lt;/blockquote&gt;

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

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

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

* Salambo in the Oriental procession.&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}
*&quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}

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

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

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

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

== Demographics ==
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;
=== Residences ===
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1890: 33 Cadogan Terrace
*1891: 33 Cadogan Terrace, Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1904: Algernon Bourke was &quot;usually liv[ing] in Venice&quot;&lt;ref name=&quot;:10&quot; /&gt;
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

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

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

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

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

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

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
== Footnotes ==
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      <text bytes="59759" sha1="56vo7o4134v0a7htqfcrkt8tw4udrye" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
* Mrs. Guendoline Bourke
* Lady Florence Bourke
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father.

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

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

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

== Acquaintances, Friends and Enemies ==

=== Algernon Bourke ===

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

=== Guendoline Bourke ===

* Lord and Lady Alington, Belvedere House, Scarborough

== Organizations ==

=== Guendoline Bourke ===

* Member, the Ladies Committee for the Prince's Skating Club, which also included [[Social Victorians/People/Princess Louise|Princess Louise]] (Duchess of Argyll), the [[Social Victorians/People/Portland|Duchess of Portland]], [[Social Victorians/People/Londonderry|Lady Londonderry]], [[Social Victorians/People/Campbell|Lady Archibald Campbell]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], and [[Social Victorians/People/Asquith|Mrs. Asquith]]&lt;ref name=&quot;:11&quot;&gt;&quot;What the 'World' Says.&quot; ''Northwich Guardian'' 01 November 1902, Saturday: 6 [of 8], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001975/19021101/134/0006. Print title: The ''Guardian'', p. 6.&lt;/ref&gt; (1902, at least)

=== Algernon Bourke ===
* Eton
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt; ( – 1901 [at least])
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Member, Men's Committee of the Prince's Skating Club, which also included Lord Edward Cecil, Lord Redesdale, Mr. [[Social Victorians/People/Lyttelton|Alfred Lyttelton]], Sir Edgar Vincent, Sir William Hart Dyke, and Mr. [[Social Victorians/People/Grenfell|W. H. Grenfell]]&lt;ref name=&quot;:11&quot; /&gt; (1902, at least)
* [[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)
* Willis's Rooms&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;

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

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

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

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

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

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

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

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

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

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

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

(From the ''World''.)

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

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

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

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

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

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

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

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

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

ALGERNON BOURKE.

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

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

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

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

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

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

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

'''1897 October 30, Saturday''', ''Black and White'' published J.P.B.'s &quot;The Case of Mrs. Elliott,&quot;&lt;ref&gt;J.P.B. &quot;The Case of Mrs. Elliott.&quot; ''Black &amp; White'' 30 October 1897, Saturday: 12 [of 34], Cols. 1a–2b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004617/18971030/036/0012. Print title ''Black and White'', p. 542.&lt;/ref&gt; an odd short short story in which the Honourable Algernon Bourke Herriott is &quot;rude to Mrs. Elliott.&quot;{{rp|Col. 2b}} J.P.B. echoes the biographical Algernon Bourke's career in the stock market when Mrs. Christine Elliott does not even simulate interest in her husband's bicycling: &quot;a soul is a grievous burthen for a stockbroker's wife.&quot;{{rp|Col. 2a}} The Hon. Algy&lt;blockquote&gt;was a senior member of several junior clubs. A woman had dubbed him once &quot;a rip with a taste for verses.&quot; The description was severe, but not unwarranted. His was a pretty pagan sensualism, though, singing from a wine palate to Church music. For the rest, he had just imagination enough to despise mediocrity.{{rp|Col. 2a}}&lt;/blockquote&gt;

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

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

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

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

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

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

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

'''1899 July 1, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1899#1 July 1899, Saturday|meeting in London at the Duke of Westminster's Grosvenor House]] about preserving Killarney as part of the National Trust and seems to have been acting for someone who wanted to purchase the Muckross Estate.&lt;p&gt;

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

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

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

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

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

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

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

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

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

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

The Revising Barrister — lf a lady gave me the name of Mrs. John Smith I should say I had not got the voter’s name. The name Gwendolen must remain.&lt;ref&gt;&quot;Ladies’ Names.&quot; ''Morning Post'' 12 September 1901, Thursday: 7 [of 10], Col. 3a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19010912/130/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1902 September 4, Thursday''', the ''Daily Express'' reported that &quot;Mrs. Algernon Bourke is staying with Lord and Lady Alington at Scarborough.&quot;&lt;ref&gt;&quot;Onlooker.&quot; &quot;My Social Diary.&quot; &quot;Where People Are.&quot; ''Daily Express'' 04 September 1902, Thursday: 5 [of 8], Col. 1b? [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020904/099/0005. Print p. 4, Col. 7b [of 7].&lt;/ref&gt;&lt;p&gt;

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

'''1902 October 31, Friday''', the [[Social Victorians/Timeline/1900s#31 October 1902, Friday|7th opening of the Prince's Skating Club]]. Guendoline Bourke was on the Women's Committee and Algernon Bourke was on the Men's.&lt;p&gt;

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

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

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

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

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

'''1913 May 7, Wednesday''', Guendoline Bourke presented her daughter Daphne Bourke at court:&lt;blockquote&gt;Mrs. Algernon Bourke presented her daughter, and wore blue and gold broché with a gold lace train.&lt;ref&gt;&quot;Social and Personal.&quot; London ''Daily Chronicle'' 08 May 1913, Thursday: 6 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/19130508/120/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

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

'''1904 September 15, Thursday''', according to what was at the time called the ''Irish Daily Independent and Nation'', Algernon Bourke was living in Venice and not in the UK at this point:&lt;blockquote&gt;Algernon Bourke, who usually lives in Venice, has spent some time in England during the present summer, and has now gone on a fishing expedition to Sweden, accompanied by his brother, Lord Mayo. Lady Mayo has been staying meanwhile in Ireland, and has had a visit from her mother, Lady Maria Ponsonby, who is a sister of Lend Obventry.&lt;ref name=&quot;:10&quot;&gt;&quot;Society Notes.&quot; ''Irish Independent'' 15 September 1904, Thursday: 4 [of 8], Col. 5b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001986/19040915/131/0004. Print title: ''Irish Daily Independent and Nation'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;'''1909 May 22, Saturday''', Algernon Bourke appears to have been living in Pisa. A columnist for the ''Queen'' reported on the Royal School of Art Needlework:&lt;blockquote&gt;Lady Leconfield [?] was there, also her sister-in-law, the Dowager Lady Mayo, only just back from her winter on the Continent, when she spent most of the time at Pisa, where her son Mr Algernon Bourke has also been staying. The latter is a great connoisseur as regards [art?] notably in what is really good in the way of old Italian sculpture and carving. He and his handsome wife have a place near to Putney, and this winter again Mr Bourke, as the result of his Italian travels, has been sending home such relics of the old Italian palace gardens as as stone and marble carved vases, garden seats, and what-not of the kind — not all for himself and his own gardens by any means, I fancy; but his friends, relying on his knowledge in such matters, get him when abroad to choose for [them?] the adornment of their English terraces and gardens.&lt;ref&gt;&quot;My Social Diary.&quot; The ''Queen'' 22 May 1909, Saturday: 31 [of 86], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19090522/203/0031. Print p. 871.&lt;/ref&gt;&lt;/blockquote&gt;

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

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

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

* Salambo in the Oriental procession.&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}
*&quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}

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

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

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

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

== Demographics ==
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;
=== Residences ===
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1890: 33 Cadogan Terrace
*1891: 33 Cadogan Terrace, Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1904: Algernon Bourke was &quot;usually liv[ing] in Venice&quot;&lt;ref name=&quot;:10&quot; /&gt;
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

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

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

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

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

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

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
== Footnotes ==
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      <text bytes="60678" sha1="gyn7joq9wjm3zlpqx6o0mmsed19o1en" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
* Mrs. Guendoline Bourke
* Lady Florence Bourke
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father.

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

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

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

== Acquaintances, Friends and Enemies ==

=== Algernon Bourke ===

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

=== Guendoline Bourke ===

* Lord and Lady Alington, Belvedere House, Scarborough

== Organizations ==

=== Guendoline Bourke ===

* Member, the Ladies Committee for the Prince's Skating Club, which also included [[Social Victorians/People/Princess Louise|Princess Louise]] (Duchess of Argyll), the [[Social Victorians/People/Portland|Duchess of Portland]], [[Social Victorians/People/Londonderry|Lady Londonderry]], [[Social Victorians/People/Campbell|Lady Archibald Campbell]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], and [[Social Victorians/People/Asquith|Mrs. Asquith]]&lt;ref name=&quot;:11&quot;&gt;&quot;What the 'World' Says.&quot; ''Northwich Guardian'' 01 November 1902, Saturday: 6 [of 8], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001975/19021101/134/0006. Print title: The ''Guardian'', p. 6.&lt;/ref&gt; (1902, at least)

=== Algernon Bourke ===
* Eton
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt; ( – 1901 [at least])
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Member, Men's Committee of the Prince's Skating Club, which also included Lord Edward Cecil, Lord Redesdale, Mr. [[Social Victorians/People/Lyttelton|Alfred Lyttelton]], Sir Edgar Vincent, Sir William Hart Dyke, and Mr. [[Social Victorians/People/Grenfell|W. H. Grenfell]]&lt;ref name=&quot;:11&quot; /&gt; (1902, at least)
* [[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)
* Willis's Rooms&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;

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

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

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

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

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

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

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

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

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

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

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

(From the ''World''.)

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

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

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

'''1893 February 11, Tuesday''', Algernon Bourke opened Willis's Restaurant:&lt;blockquote&gt;Mr. Algernon Bourke has in his time done many things, and has generally done them well. His recently published history of White's Club is now a standard work. White's Club itself was a few years ago in its agony when Mr. Bourke stepped in and gave it a renewed lease of life. Under Mr. Bourke's auspices &quot;Willis's Restaurant&quot; opened its doors to the public on Tuesday last in a portion of the premises formerly so well known as Willis's Rooms. This new venture is to rival the Amphitryon in the matter of cuisine and wines; but it is not, like the Amphitryon, a club, but open to the public generally. Besides the restaurant proper, there are several ''cabinets particuliers'', and these are decorated with the very best of taste, and contain some fine portraits of the Georges.&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Letter from the Linkman.&quot; ''Truth'' 20 April 1893, Thursday: 25 [of 56], Col. 1a [of 2]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025# https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025]. Print p. 855.&lt;/ref&gt;&lt;/blockquote&gt;'''1893 April 1, Saturday''', Algernon Bourke published a letter to the editor of the ''Times'', reprinted in the ''Kildare Observer'', arguing against Gladstone's Home Rule bill on the grounds that Ireland would not be able to take out a loan on its own behalf because of its obligations to the U.K., including what was called its share of the national debt.&lt;ref&gt;&quot;Irish Unionist Alliance.&quot; ''Kildare Observer and Eastern Counties Advertiser'' 01 April 1893, Saturday: 6 [of 8], Col. 4c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001870/18930401/062/0006. Print: The ''Kildare Observer'', n.p.&lt;/ref&gt;

'''1893 November 30, Thursday''', with Sir Walter Gilbey the Hon. Algernon Bourke &quot;assisted&quot; in &quot;forming [a] collection&quot; of engravings by George Morland that was exhibited at Messrs. J. and W. Vokins’s, Great Portland-street.&lt;ref&gt;&quot;The George Morland Exhibition at Vokins's.&quot; ''Sporting Life'' 30 November 1893, Thursday: 4 [of 4], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000893/18931130/058/0004.&lt;/ref&gt;

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

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

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

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

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

ALGERNON BOURKE.

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

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

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

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

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

'''1896 December 10, Thursday''', Guendoline Bourke was present to help staff a stall at the [[Social Victorians/Timeline/1896#10 December 1896, Thursday|Irish Industries Exhibition and Sale, Brighton]].

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

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

'''1897 October 30, Saturday''', ''Black and White'' published J.P.B.'s &quot;The Case of Mrs. Elliott,&quot;&lt;ref name=&quot;:13&quot;&gt;J.P.B. &quot;The Case of Mrs. Elliott.&quot; ''Black &amp; White'' 30 October 1897, Saturday: 12 [of 34], Cols. 1a–2b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004617/18971030/036/0012. Print title ''Black and White'', p. 542.&lt;/ref&gt; an odd short short story in which the Honourable Algernon Bourke Herriott is &quot;rude to Mrs. Elliott.&quot;&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2b}} J.P.B. echoes the biographical Algernon Bourke's career in the stock market when Mrs. Christine Elliott does not even simulate interest in her husband's bicycling: &quot;a soul is a grievous burthen for a stockbroker's wife.&quot;&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2a}} The Hon. Algy&lt;blockquote&gt;was a senior member of several junior clubs. A woman had dubbed him once &quot;a rip with a taste for verses.&quot; The description was severe, but not unwarranted. His was a pretty pagan sensualism, though, singing from a wine palate to Church music. For the rest, he had just imagination enough to despise mediocrity.&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2a}}&lt;/blockquote&gt;

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

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

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

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

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

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

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

'''1899 July 1, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1899#1 July 1899, Saturday|meeting in London at the Duke of Westminster's Grosvenor House]] about preserving Killarney as part of the National Trust and seems to have been acting for someone who wanted to purchase the Muckross Estate.&lt;p&gt;

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

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

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

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

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

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

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

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

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

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

The Revising Barrister — lf a lady gave me the name of Mrs. John Smith I should say I had not got the voter’s name. The name Gwendolen must remain.&lt;ref&gt;&quot;Ladies’ Names.&quot; ''Morning Post'' 12 September 1901, Thursday: 7 [of 10], Col. 3a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19010912/130/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1902 September 4, Thursday''', the ''Daily Express'' reported that &quot;Mrs. Algernon Bourke is staying with Lord and Lady Alington at Scarborough.&quot;&lt;ref&gt;&quot;Onlooker.&quot; &quot;My Social Diary.&quot; &quot;Where People Are.&quot; ''Daily Express'' 04 September 1902, Thursday: 5 [of 8], Col. 1b? [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020904/099/0005. Print p. 4, Col. 7b [of 7].&lt;/ref&gt;&lt;p&gt;

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

'''1902 October 31, Friday''', the [[Social Victorians/Timeline/1900s#31 October 1902, Friday|7th opening of the Prince's Skating Club]]. Guendoline Bourke was on the Women's Committee and Algernon Bourke was on the Men's.&lt;p&gt;

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

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

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

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

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

'''1913 May 7, Wednesday''', Guendoline Bourke presented her daughter Daphne Bourke at court:&lt;blockquote&gt;Mrs. Algernon Bourke presented her daughter, and wore blue and gold broché with a gold lace train.&lt;ref&gt;&quot;Social and Personal.&quot; London ''Daily Chronicle'' 08 May 1913, Thursday: 6 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/19130508/120/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

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

'''1904 September 15, Thursday''', according to what was at the time called the ''Irish Daily Independent and Nation'', Algernon Bourke was living in Venice and not in the UK at this point:&lt;blockquote&gt;Algernon Bourke, who usually lives in Venice, has spent some time in England during the present summer, and has now gone on a fishing expedition to Sweden, accompanied by his brother, Lord Mayo. Lady Mayo has been staying meanwhile in Ireland, and has had a visit from her mother, Lady Maria Ponsonby, who is a sister of Lend Obventry.&lt;ref name=&quot;:10&quot;&gt;&quot;Society Notes.&quot; ''Irish Independent'' 15 September 1904, Thursday: 4 [of 8], Col. 5b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001986/19040915/131/0004. Print title: ''Irish Daily Independent and Nation'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;'''1909 May 22, Saturday''', Algernon Bourke appears to have been living in Pisa. A columnist for the ''Queen'' reported on the Royal School of Art Needlework:&lt;blockquote&gt;Lady Leconfield [?] was there, also her sister-in-law, the Dowager Lady Mayo, only just back from her winter on the Continent, when she spent most of the time at Pisa, where her son Mr Algernon Bourke has also been staying. The latter is a great connoisseur as regards [art?] notably in what is really good in the way of old Italian sculpture and carving. He and his handsome wife have a place near to Putney, and this winter again Mr Bourke, as the result of his Italian travels, has been sending home such relics of the old Italian palace gardens as as stone and marble carved vases, garden seats, and what-not of the kind — not all for himself and his own gardens by any means, I fancy; but his friends, relying on his knowledge in such matters, get him when abroad to choose for [them?] the adornment of their English terraces and gardens.&lt;ref&gt;&quot;My Social Diary.&quot; The ''Queen'' 22 May 1909, Saturday: 31 [of 86], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19090522/203/0031. Print p. 871.&lt;/ref&gt;&lt;/blockquote&gt;

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

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

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

* Salambo in the Oriental procession.&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}
*&quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}

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

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

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

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

== Demographics ==
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;
=== Residences ===
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1890: 33 Cadogan Terrace
*1891: 33 Cadogan Terrace, Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1904: Algernon Bourke was &quot;usually liv[ing] in Venice&quot;&lt;ref name=&quot;:10&quot; /&gt;
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

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

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

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

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

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

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
== Footnotes ==
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      <text bytes="178270" sha1="iwcxs7q9gguq60my05n6gim9qd2xrwk" xml:space="preserve">[[Social Victorians/Timeline/1850s | 1850s]] [[Social Victorians/Timeline/1860s | 1860s]] [[Social Victorians/Timeline/1870s | 1870s]] [[Social Victorians/Timeline/1880s | 1880s Headlines]] [[Social Victorians/Timeline/1890s | 1890s Headlines]] [[Social Victorians/Timeline/1890 | 1890]] [[Social Victorians/Timeline/1891 | 1891]] [[Social Victorians/Timeline/1892 | 1892]] [[Social Victorians/Timeline/1893 | 1893]] [[Social Victorians/Timeline/1894 | 1894]] [[Social Victorians/Timeline/1895 | 1895]] 1896 [[Social Victorians/Timeline/1897 | 1897]] [[Social Victorians/Timeline/1898 | 1898]] [[Social Victorians/Timeline/1899 | 1899]]  [[Social Victorians/Timeline/1900s|1900s]] [[Social Victorians/Timeline/1910s|1910s]] [[Social Victorians/Timeline/1920s-30s|1920s-30s]]

==Sometime in 1896==
Sometime in the first quarter of 1896 [[Social Victorians/People/William Butler Yeats|William Butler Yeats]] moved to No. 18 Woburn Buildings, London, possibly January, but for sure by March (Harper 80 76, n. 12, 3-4)
==January 1896==
===1 January 1896, Wednesday, New Year's Day===
===13 January 1896, Monday===
On the 24th ''The Literary World'' reports the following: &quot;The Memorial Institute to Mrs. Elizabeth Barrett Browning was opened at Ledbury last week by Mr. Rider Haggard. The institute is a charming building in the half-timbered perpendicular style of architecture, and it occupies one of the most commanding positions in the town. It is bult of Lebury limestone and Etonfield sandstone, with oak timbering, with a clock-tower at the corner. The total cost was £2,330, and it is satisfactory to know that the whole of that sum was obtained from more than 1,000 subscribers, with the exception of about £300. Already several important gifts have been made to the library, including a complete set of the works of Robert and Elizabeth Barrett Browning, presented by Mr. George Malton Barrett, the brother of the poetess; and about one hundred volumes of books, presented by Dr. Furnival, the late president of the Browning Society. Mr. Haggard, who spoke for a considerable time to an appreciative concourse, sketched the life of the poetess in enthusiastic terms, and paid a generous tribute to the memory of 'the greatest poetess the English-speaking people have yet produced.'&quot; &quot;Table Talk,&quot; The Literary World, 24 January 1896, vol. 53, p. 77, col. 1. (Accessed 9 October 2009 in Google Books.)

===18 January 1896, Saturday===
On the 24th ''The Literary World'' reports the following: &quot;A pleasant gathering took place in Edinburgh on Saturday last to do honour to Mr. Andrew Stewart, who for a quarter of a century has been connected with The People's Friend. Mr. Stewart began his career on The Friend as sub-editor, under Mr. David Pae, and among his contributors had such men as the late George Gilfillan and Professor Blackie. Such novelists as Annie S. Swan and Adeline Sergeant have written much of their best work for The Friend, and through its pages their stories were read weekly in a quarter of a million homes. Mr. W. C. Leng, one of the proprietors, took the chair, in the absence of Sir John Leng, who is abroad, and speeches were delivered by Mr. Anderson, Mr. Robert Ford, Mr. J. C. Hadden, Mrs. Lawson, Miss A. S. Falconer, and others.&quot; &quot;Table Talk,&quot; The Literary World, 24 January 1896, vol. 53, p. 77, col. 2. (Accessed 9 October 2009 in Google Books.)

===22 January 1896, Wednesday===
On the 24th ''The Literary World'' reports the following (but really it occurred on the 15th?): &quot;A meeting of the Society of Public Librarians was held at the Whitechapel Public Library on Wednesday evenng last. (Mr. Frowde in the chair), when two excellent papers were delivered -- 'Subject Index to English Literature,' by Mr. Bagguley, and 'Lady Assistants in Public Libraries,&quot; by Mr. Snowsill. The whole of the members present were practically, if ungallantly, strongly opposed to the introduction of females as attendants in public libraries.&quot; &quot;Table Talk,&quot; The Literary World, 24 January 1896, vol. 53, p. 78, col. 1. (Accessed 9 October 2009 in Google Books.)

===24 January 1896, Friday===
The 31 January 1896 ''Literary World'' reports the following: &quot;The recently-formed Publishers' Associaton had a meeting of its members on Friday last, most of the leading publishers attending. No defnite appointments were made, but it is pretty generally understood that the office of President lies between Mr. Charles Longman and Mr. John Murray.&quot; &quot;Table Talk,&quot; The Literary World, 31 January 1896, vol. 53, p. 103, col. 2. (Accessed 9 October 2009 in Google Books.)

===27 January 1896, Monday===
Authors' Society meeting, talk by Mr. Hall Caine on international copyright. &quot;Table Talk,&quot; The Literary World, 31 January 1896, vol. 53, p. 101, col. 3. (Accessed 9 October 2009 in Google Books.)

==February 1896==
Lecture at the Westminster Town Hall reported by ''The Literary World'' on 14 February 1896: &quot;'The transmission of personality is the creed of literature as it is of religion,' said Mr. Birrell in the course of a lecture on Dr. Johnson, at Westminster Town Hall, and the ober dictum is worthy of all acceptation. Mr. Asquith presided, and the audience including 'all the talents,' Lord Roseberry, Mr. Arthur Balfour, Mr. Thomas Hardy, Mr. Henry James, and Mr. Herbert Paul occupying chairs in the front row. / Mr. Asquith uttered the usual orthodoxies concerning the author 'who lived so little by his writings and so much by his personality.' That is a view which we confess we do not share. ...&quot; &quot;Table Talk,&quot; The Literary World, 14 February 1896, vol. 53, p. 149, col. 1. (Accessed 9 October 2009 in Google Books.)

The annual meeting of the Authors' Society, reported on in the 21 February 1896 ''Literary World'': &quot;The annual meeting of the Authors' Society passed off pleasantly, in spite of the minatory motion that stood in the name of Mr. W. H. Wilkins regarding the unfortunate 'Address' to the authors of America, a motion that was gracefully withdrawn in view of the committee's resoluton that the 'Address' had no official character. We congratulate the Society on the access of 14 new members during the year and on the evidence of practical work afforded by the fact that two-thirds of the members had applied for advice and assistance, to say nothing of the MSS. submitted for the same purpose. The printed report, of which a copy has reached us, is full of exceedingly sound advice, of especial value to young or inexperienced authors.&quot; &quot;Table Talk,&quot; The Literary World, 14 February 1896, vol. 53, p. 172, col. 3. (Accessed 9 October 2009 in Google Books.)

===3 February 1896, Monday===
Sometime this week, probably, was a meeting of the Society of Public Librarians, reported on in the 14 February 1896 ''Literary World'': &quot;A meeting of the Society of Public Librarians was held at the Canning Town branch of the West Ham Public Libraries last week, when Mr. Foskett, of the Camberwell Public Libraries, delivered 'A Contribution to Occult Literature,' and Mr. Whitwell, of West Ham, read a paper entitled, 'Some Critical Remarks on the Works of Thomas Love Peacock.' Both papers were very well received, and gave rise to interesting discussions.&quot; &quot;Table Talk,&quot; The Literary World, 14 February 1896, vol. 53, p. 150, col. 1. (Accessed 9 October 2009 in Google Books.)
===5 February 1896, Wednesday===
Dinner: [[Social Victorians/People/George Bernard Shaw|G. B. Shaw]], Richard Burton Haldane, [[Social Victorians/People/Asquith|H. H. Asquith]], [[Social Victorians/People/Balfour|Arthur Balfour]] (Gibbs 124).
===22 February 1896, Saturday===
According to the 28 February 1896 ''Literary World'', &quot;On Saturday last, at Hampstead, the ceremony was witnessed of unveiling the memorial tablet in the house in John-street in which John Keats resided. It was expected that Sir Walter Besant would take part n the ceremony; gout, unhappily, prevented his doing so, but he sent a letter in his place, which was read in due course. Sir Charles Dilke, Mr. S. Colvin, Mr. Edmund Gosse, Dr. Robertson Nicol, and Prof Hall Griffin were among those present. The proceedings were simple in the extreme. Prof. Griffin, in a brief speech, dwelt on the historical nature of the surroundings from a literary point of view and the ceremony terminated, leaving Lawn-Bank, John-street, with the addition of a tablet bearing the following inscription: Erected by the Society of Arts. / JOHN KEATS, / Poet, / Lived in this House. / B. 1795. / D. 1821.&quot; &quot;Table Talk,&quot; The Literary World, 28 February 1896, vol. 53, p. 196, col. 2. (Accessed 9 October 2009 in Google Books.)

==March 1896==
Sometime in March 1896, the Inner Order of the Golden Dawn moved its headquarters to 62 Oakley Square, where it stayed until September 1897 (Howe 126).

Sometime in the first quarter of 1896 W. B. Yeats moved to No. 18 Woburn Buildings, London, possibly January, but for sure by March (Harper 80 76, n. 12, 3-4)
===5 March 1896, Thursday===
&quot;The wedding of Miss Lily Caine, sister of the novelist, with Mr. George Day will take place on March 5 at St. George's, Hanover-square.&quot; &quot;Table Talk,&quot; The Literary World, 28 February 1896, vol. 53, p. 196, col. 2. (Accessed 9 October 2009 in Google Books.)
===7 March 1896, Saturday===
Gilbert and Sullivan's ''The Grand Duke, Or the Statutory Duel'' opens at the Savoy.

=== 11 March 1896, Wednesday ===
Queen's Drawing Room hosted by Alexandra, Princess of Wales, as reported in the London Evening ''Standard'' on Thursday, 12 March 1896. The long list of names is rendered as an ordered or numbered list here to save space and make referring to people easier; the original newspaper story puts each one on a new line as a new paragraph.&lt;blockquote&gt;THE DRAWING ROOM.

The Princess of Wales held the first Drawing Room of the season at Buckingham Palace yesterday afternoon, on behalf of the Queen. Carriages conveying ''débutantes'' commenced to arrive shortly after noon, and by one o'clock the line of vehicles reached right away to Marlborough-yard. The weather was mild though somewhat gloomy, and a large crowd collected in the Mall. Tho number of presentations was about the same as usual; but, from an outsider's point of view, there was an unusual absence of colour. The Princess of Wales was accompanied by the Princesses Victoria and Maud and Prince Charles of Denmark, and the Duke and Duchess of Saxe-Coburg and Gotha and Princess Alexandra, the Duke and Duchess of Connaught, and the Duke and Duchess of York, were present. Escorted by a troop of Life Guards, the State carriage, conveying the Princess of Wales, her two daughters, and Prince Charles of Denmark, arrived at Buckingham Palace from Marlborough House almost precisely at three o'clock. The National Anthem was played as their Royal Highnesses passed into the Palace, and there was general uncovering and cheering among the crowd in front of the Palace gates. The Princess was received by the Officers of State, and conducted to the Throne Room, when the presentations commenced.

The Drawing Room was to a large extent a mourning function as regards dress. All the Royal personages were in black, even the two brides-elect, Princess Maud of Wales and Princess Alexandra of Coburg. The Princesses Victoria and Maud of Wales were dressed alike in black satin, prettily arranged with hart's-tongue fern leaves of lisse outlined in jet on the bodices and skirt foot, and rich black satin ribbon at the waist. The material chosen by the Duchess of Coburg was rich black moiré, and the Princess Alexandra's black satin gown was veiled in gauze brocaded in a small floral design. The Duchess of York was dressed in black silk of English manufacture. The Duchess of Buccleuch, like all the other ladies belonging to the Royal Households, wore black plumes and veil. Her gown was of richest poult de soie, trimmed on the corsage with folds of crape and jet ornaments. The Duchess of Buccleuch presented her niece, Lady Victoria Kerr, daughter of the Marquess of Lothian and goddaughter of the Queen, who wore a charming white satin gown, the bodice veiled in lisse held with bands of silver embroidery. The neck was softened by a drapery of lisse, on which was laid, with very natural effect, a spray of apple-blossom. From the silver waistband fell a scarf of silvered lisse to the bottom of the skirt, fastened there by a bunch of apple-blossoms. The train of striped white brocade was bordered with lisse, knotted at intervals with clusters of apple-blossom. Lady Helen Kerr was also in white satin, with an exceedingly pretty corsage arranged with mousseline de soie, and graceful trails of mauve and white convolvuli. There were folds of mousseline de soie carried down the front of the skirt, widening towards the foot, and enframed by the convolvuli. The pale mauve brocade train had a lace-like pattern in cream silk, and was bordered with the flowers and mousseline de soie. Lady Tweedmouth's black velvet toilet was ornamented with fine jet on the corsage, and had full tulle sleeves. The train was fastened to the shoulder by a large knot and lined with a new material, moiré mouillée. Lady Howard Vincent chose a chène silk gown with design of roses and violets, trimmed on the bodice with a fringe of violets, and shoulder-straps of roses. There was a softening of pink lisse about the neck, and the heliotrope and white train came from under the arms, and was fastened with a coquille bow at the back. Susan, Countess of Malmesbury — presented on her marriage — wore a gown of pearl grey satin, draped with exquisite old needlepoint lace, forming a fichu on the bodice. The train was of black brocade. Lady Eva Cotterell — also presented on her marriage — wore white satin, embroidered in silver, and trimmed on the train with lovely lace and knots of silver ribbon. Lady Emma Crichton was in black satin, embroidered in sapphires and silver swallows, and draped with creamy lace. The black velvet train was lined with white satin. Lady Codrington's heliotrope satin gown was made with pointed Court bodice and stomacher of fine embroidery wrought in gilt thread, and pale rubies and diamonds. The shoulder-pieces, of wine-toned velvet, were ornamented to match, and a large poppy, with diamond heart, was fastened at the side. The train was of velvet. Miss James, niece of Lord James of Hereford, wore a black satin gown, richly worked on overskirt and bodice with jet and brilliants in design of knots and floral sprays. The black velvet train was lined with white satin.

Lady Algernon Gordon Lennox was in black and satin, the train being trimmed with tulle ruches, wide at the hem and narrowing towards the waist. The bodice was softened by folds of tulle caught with diamonds, and a long chain of pearls passed over one shoulder and encircled the figure. Lady Feo Start chose a gown of pinkish mauve satin, embroidered half way down the front seams with bunches of wheat, the leaves and stems being wrought in fine silver and the wheat ears in diamonds. At the foot a larger cluster appeared gracefully tapering to the side. The corsage was embroidered to match, and filled in round the neck by silver tulle, and the embroidered sleeves fell off the arm, held by shoulder-straps of silver. The train was in the same shade of velvet, with bold groups of the wheat at each corner, and diminishing to a point midway up the sides. This train was lined with white satin, and fastened to each shoulder by splendid diamond ornaments. The Countess of Lathom's black satin dress was ornamented with fine jet embroidery, and worn with a black brocade train draped with Chantilly lace. Lady Bertha Wilbraham accompanied her mother, wearing a satin dress in a delicate shade of French grey, very prettily trimmed with chiffon, old lace, and clusters of lilies of the valley. The Countess of Clanwilliam had a rich black broché train with a black satin gown richly pailletted. Lady Elizabeth Meade's white satin gown had a very smart bodice arranged with kilted chiffon forming scollop-shaped frills on the shoulders, and groups of Eucharist lilies were fastened at the bust and waist. Lady Beatrice Meade was in white moiré deftly arranged with lisse, embroidered lace, and white narcissi, which also trimmed the white satin train. Viscountess Cross was attired in a black moiré bengaline satin, bordered with Brussels Point caught with fine jet ornaments, and a black satin gown. The Hon. Mary Cross wore black satin, relieved by a vest and sleeves of silver embroidered white satin and a pearl grey satin train. The ivory satin gown selected by the Hon. Margaret Cross was embroidered in a charming design executed in silver, gold, and steel, and had billowy chiffon sleeves, and a train of striped white satin. Lady Arthur Hill was in black satin, draped with costly old lace, and wore pearl and diamond ornaments. Lady Arthur presented Miss Nina Hill in a sweetly pretty white satin toilet, veiled in Brussels net. The corsage was finished by an ostrich feather ruche in front, and frills of net round the shoulders and back. The train fell from both shoulders, like white wings, showing the figure between. Lady Aline Wentworth Beaumont wore white satin, the corsage softened with chiffon, and the waist encircled by a deep silver band. The handsome train was of gold and cream brocade, with a design of shaded tulips, and was turned back at the corner with bunches of tulips. The Countess of Lytton's black peau de chine dress was trimmed up the side with bows of satin ribbon, and worn with a brocade train. The bodice was arranged with jetted lace. Lady O'Conor wore a black velvet gown, the bodice draped across rich jet embroidery and finished by jet butterflies and roses on the shoulders. The train was of black satin.

The Lady Mayoress of London was beautifully dressed in ivory satin, embroidered in frosted silver, forming a festooned floral design round the skirt foot. There were touches of turquoise blue velvet on the corsage, matching the train, which was lined with primrose satin, and ornamented with bunches of large white ostrich plumes. Lady Wilkin presented her daughter in a charming ''débutante's'' gown of white satin under net. From each side of the waist fell clusters of lilies of the valley and mimosa, stray blossoms of the flowers being scattered in a shower to the skirt foot. The train was trimmed with silver cord and bunches of flowers. Mrs. H. M. Stanley was becomingly attired in grey satin, embroidered in steel paillettes, forming irregular lines about the hips. The bodice was trimmed with grey chiffon and steel embroidered guipure, and the train was of grey and gold brocade. Lady Mary Lygon, in attendance upon the Duchess of York, had a black velvet train, and a black satin gown trimmed with chiffon and jet. Viscountess Chelsea's white satin dress was very beautifully embroidered in diamonds. Lady Playfair was in black satin. The Dowager Lady Westbury wore a black and white brocade [Col. 2/3] gown, trimmed with rare old Spanish lace, and a black velvet train. Viscountess Trafalgar's becoming toilet was carried out in delicate tones of green and pink. Viscountess Dalrymple wore a superb white brocade gown. Lady Rivers Wilson was presented, on her marriage, wearing an oyster-toned satin gown, made in Louis XV. period, with long corsage, trimmed with rare Point de Gaze, caught up with bouquets of white poppies enveloped in tulle. The train of silver tissue formed a Venetian mantle falling under a hood of the lace, and was lined with mauve satin, matching a large straggling branch of orchids which were laid on at the side. Lady Mount-Stephen wore a gown of rich black brocade, with a large design of roses and little trailing blossoms. The bodice was filled in, back and front, with cream satin under filmy lace, and was embroidered in jet. The sleeves were of white chiffon and lace, and the train of rich black velvet. Viscountess Knutsford's black brocade gown was enriched with fine jet embroidery, and her black satin train was trimmed with lace and jet.

By command of the Queen, a Drawing Room was held yesterday afternoon, at Buckingham Palace, by her Royal Highness the Princess of Wales, on behalf of her Majesty.

Presentations to her Royal Highness at this Court are, by the Queen's pleasure, considered as equivalent to presentations to her Majesty.

Their Royal Highnesses the Princess of Wales, Princess Victoria, and Princess Maud of Wales, accompanied by his Royal Highness Prince Charles of Denmark, attended by Lady Suffield (Lady in Waiting), Miss Knollys (Bedchamber Woman in Waiting), Lord Colville of Culross, K.T. (Chamberlain to the Princess of Wales), General Sir D. M. Probyn (Comptroller and Treasurer to the Prince of Wales), Sir Francis Knollys (Private Secretary to the Prince of Wales), and Major General Stanley Clarke (Private Secretary to the Princess of Wales), escorted by a detachment of the Ist Life Guards, arrived at the garden entrance of the Palace from Marlborough House.

Their Royal Highnesses the Duke and Duchess of Saxe-Coburg and Gotha, and Princess Alexandra of Saxe-Coburg and Gotha, arrived from Clarence House, attended by Miss Colville and Captain the Hon. D. Monson.

Their Royal Highnesses the Duke and Duchess of Connaught and Strathearne, attended by Lady Elphinstone and Colonel Alfred Egerton, were present at the Drawing Room.

Their Royal Highnesses the Duke and Duchess of York arrived from York House, attended by Lady Mary Lygon, Major General Sir F. De Winton, and Sir Charles Cust.

His Royal Highness Prince Christian of Schleswig-Holstein and his Highness Prince Christian Victor of Schleswig-Holstein arrived from Cumberland Lodge, attended by the Hon. C. Eliot. His Highness the Duke of Teck was present at the Drawing Room. 

Her Majesty's Body Guard of the Honourable Corps of Gentlemen-at-Arms was on duty in the State Saloons, under the command of Lord Belper (the Captain). The Royal Body Guard of the Yeomen of the Guard were on duty in the interior of the Palace, under the command of Lieut. Colonel H. P. Vance, the Lieutenant (in the unavoidable absence of the Captain, the Eari of Limerick). A Guard of Honour of the 1st Battalion of Grenadier Guards, with the Band of the Regiment, was mounted in the Quadrangle of the Palace, and a Guard of Honour of the Ist Life Guards, with their Band, was stationed in the Courtyard of the Palace; and the Park party was furnished by the Royal Horse Guards. 

The Princess of Wales, accompanied by the other members ol the Royal family, entered the Throne Room at three o'clock, and the Princess of Wales took her station in front of the Throne. 

Her Royai Highness the Princess of Wales wore a gown of black silk embroidered in jet, corsage and train to correspond. Headdress — Tiara of diamonds, black feathers, and veil. Ornaments — Pearls and diamonds. Orders — Victoria and Albert, Crown of India, St. Catherine of Russia, St. John of Jerusalem, the Saxe-Coburg and Gotha, and the Danish Family and Golden Wedding Orders. 

Their Royal Highnesses the Princesses Victoria and Maud of Wales wore gowns of black satin, corsages embroidered with jet applique in the shape of leaves, sleeves of vandyke chiffon with straps of fine jet, the same kind of jet forming the waistbelt; trains of black satin to correspond. Ornaments — Pearls and diamonds. Orders — Victoria and Albert, Crown of India, Danish Golden Wedding, Saxe-Coburg and Gotha, and Jubilee Commemoration Medal. 

Her Royal Highness the Duchess of York wore a dress of rich black English watered silk, embroidered and trimmed with jet and feathers; corsage and train to correspond. Headdress — Tiara, feathers, and veil. Ornaments — Pearls and diamonds. Orders — Victoria aud Albert, Crown of India, St. John of Jerusalem, Saxe-Coburg and Gotha, and Jubilee Commemoration Medal. 

The Foreign Ambassadors and Ministers having been introduced in the order of precedence, the following presentations were made in the Diplomatic Circle: — 

By Countess Deym, Princess Alex Thurn Taxis (''née'' Princess Hohenlohe), Countess Clary Aidringen (''née'' Countess Kinsky), Madame Geoffray, and Mdlle. Demidoff. 

By Mrs. Bayard, Mrs. William Sheffield Cowles. 

By Madame de Bille, Madame de Salis. 

By the Marchioness of Salisbury, Madame Kato and Countess Lewenhaupt. 

The following presentations to the Princess of Wales, on behalf of the Queen, were made, the names having been previously left at the Lord Chamberlain's office, and submitted for her Majesty's approval: — [The long list of names is rendered as an ordered or numbered list here to save space and make referring to people easier; the original newspaper story puts each one on a new line as a new paragraph.] 

# Arnold, Lady, by Lady Suffield. 
# Adair, Mrs. Charles H., by Lady Salmon. 
# Anstruther, Miss Rosamond, by the Hon. Mrs. Anstruther. 
# Ardagh, Lady (Dowager Countess of Malmesbury), by Viscountess Knutsford. 
# Bedford, Lady, by Mrs. Goschen. 
# Bainbridge, Miss Gwendolen, by her mother, Mrs. Hugh Bainbridge. 
# Bell, of Scatwell, Lady, by the Hon. Mrs. Rennel [?] 
# Bannerman, Miss, by the Countess of Ellesmere. 
# Birney, Miss Kerrow, by Lady Hart. 
# Bellew, the Hon. Mrs. Richard, on her marriage, by the Lady Bellew. 
# Bums, Mrs. James C., by the Lady Gertrude Cochrane. 
# Butler, Miss Blanche, by her mother, Hon. Mrs. Robert Butler. 
# Baylis, Mrs. Philip, by Mrs. Wharton Hood. 
# Brown, Miss Hargreaves, by her mother, Mrs. A. Hargreaves Brown. 
# Boodle, Miss Marion Florence, by her mother, Mrs. H. Trelawny Boodle. 
# Baker, Miss Katharine, by her mother, Mrs. George Barrington Baker. 
# Buxton, Mrs. Edward, on her marriage, by her mother, Mrs. Gurney. 
# Brabazon, Lady Mary, by the Countess of Lathom. 
# Buxton, Miss Hilda, by her mother, Hon. Mrs. Francis Buxton. 
# Beilew, The Lady, by the Lady Alexandrina Beaumont. 
# Boulton, Mrs. Oscar, by Mrs. S. B. Boulton. 
# Barclay, Mrs. George, by the Hon. Mrs. Francis Buxton. 
# Bostock, Mrs. Ashton, by Lady Russell Reynolds. 
# Bairstow, Mrs. Walter, by Mrs. Ingilby. 
# Bucknall, Mrs. Sydney, by her mother, Lady Sidgreaves. 
# Bevan, Miss Mary Pauline, by her mother, Mrs. Thomas Bevan. 
# Bruce, The Hon. Mary, by Lady Balfour of Burleigh. 
# Brassey, Lady Violet, by Lady Evelyn Cotterell. 
# Bankes, Mrs. Ralph Vincent, on her marriage, by Mrs. Mount. 
# Beach, Miss Susan Hicks, by her mother, Lady Lucy Hicks Beach. 
# Cotterell. Lady Evelyn, by Hon. Lady Cotterell. 
# Curtis, Miss (of the United States), by Mrs. Bayard. 
# Curtis, Miss Clara (of the United States), by Mrs. Bayard. 
# Campbell, Mrs. Alexander, by the Hon. Mrs. Townley Mitford. 
# Cooper. Mrs. J. R., by the Hon. Lady Ridley. 
# Clay, Miss Sybil, by her mother, Mrs. Walter Holbech. 
# Craven, Miss, by Lady King. 
# Cockerell, Miss Patience, by her mother, Mrs. William Cockerell. 
# Cunningham, the Hon. Lady, by Lady George Hamilton. 
# Cooper, Mrs. Harry, by Lady Comrnerell. 
# Craig, Miss Gibson, by Lady Gibson Craig. 
# Craig, Miss Alice Gibson, by Lady Gibson Craig. 
# Crossley, Miss, by the Hon. Mrs. Montagu Forbes. 
# Cole, Lady Florence, by Countess of Enniskillen. 
# Chaplin, Miss Bertha, by her mother, Mrs. Cecil Chaplin. 
# Colomb, Miss Gwenda, by her mother, Lady Colomb. 
# Clifford, Miss Alice, by Lady Pollock. 
# Callaghan, Mrs. George, by the Hon. Lady Fremantle. 
# Callaghan, Miss Dorothy, by Mrs. George Callaghan. 
# Coddington, Lady, by Viscount Cranborne. 
# Clarkson, Miss, by Mrs. Laurenco Edye. 
# Crossman, Mrs. Douglas, by Lady Grant Duff. 
# Da Costa, Mrs. Oscar, on her marriage, by Mrs. Bertram Ward. 
# De la Rue, Miss Sybil, by Mrs. T. Andros de la Rue. 
# Dale, Mrs., by Lady Dale. 
# Dale, Lady, by the Marchioness of Ripon. 
# Dawnay, Miss Helen, by her mother, Lady Adelaide Dawnay. 
# Digby, Miss Lettice, by her mother, the Hon Mrs. Kenelm Digby. 
# Dalgety, Miss Gladys, by her sister, Viscountess Trafalgar. 
# Dunphie, Mrs. Alfred, on her marriage, by Mrs. Anderson Critchett. 
# Douglass, the Hon. Mrs., on her marriage, by the Hon. Mrs. Paton. 
# Dalison, Miss Joan, by her mother, Mrs. Maximilian Dalison. 
# Dunlop, Mrs. William H., by Mrs. Frank Addison Brace 
# Evans, Miss Gwladys, by Lady Evans. 
# Edge, Miss Kathleen, by Lady Barnes. 
# Egerton, Lady Katharine, by her mother, the Countess of Ellesmere. 
# Earle, Miss Caroline, by Lady Earle. 
# Earle, Miss Evelyn, by Lady Earle. 
# Eustace, Miss Adelaide, by her mother, Lady Katharine Eustace. 
# Eustace, Miss Violet, by her mother, Lady Katharine Eustace. 
# Frere, Mrs. Arthur, on her marriage, by the Countess of Lathom. 
# Fremantle, Honble. Lady, by Mrs. Goschen. 
# Foley, Lady Mary, on her marriage, by Lady Feodorowna Sturt. 
# Fletcher, Mrs. H. Morley, by the Hon. Mrs. Walter R. D. Forbes. 
# Fenwick, Miss Elfreda Gabriel, by her mother, Mrs. Fenwick Fenwick. 
# Forwood, Lady, by the Marchioness of Salisbury. 
# Forwood, Miss Ida, by her mother, Lady Forwood. 
# Fielden, Miss Lorna, by her mother, Mrs. Thomas Fielden. 
# Fowler, Miss, by Mrs. Forrest. 
# Finlay, Lady, by the Marchioness of Salisbury. 
# Fortescue, Hon. Mrs. Lionel, on her marriage, by Lady Lucy Hicks Beach. 
# Floyd, Mrs. Henry, by the Countess of Clanwilliam. 
# Fordham, Mrs. R. Oswald (Lady O'Malley), on her marriage, by Lady Flower. 
# Fowler, Miss Anna, by Mrs. Christie-Miller. 
# Fielden, Miss Gertrude, by her sister-in-law, Mrs. Thos. Fielden.  
# Firebrace, Mrs. Frederick, on her marriage, by the Lady Reay. 
# Finch, Miss Essex, by Mrs. Finch. 
# Gillford, the Lady, by the Countess of Clanwilliam. 
# Greenly, Miss Lucy, by Lady Florence King King. 
# Gambier, Miss Gore, by Mrs. Murdoch. 
# Horsfall. Miss Eva, by Lady Charles Scott. 
# Heygate, Lady, by the Countess Waldegrave. 
# Hill, Miss, by her mother, Lady Arthur Hill. 
# Hutchinson, Mrs. Edward, by Lady Dale. 
# Howard, Miss Gertrude, by her mother, Mrs. John Howard. 
# Hogg, Miss Ethel, by her aunt, Mrs. Horner. 
# Hall, Mrs. Thomas, by Mrs. Chamberlain. 
# Hely-Hutchinson, Lady Evelyn, by Countess of Donoughmore. 
# Hutton, Mrs. Stamford, on her marriage, by her mother, Mrs. Fenwick Fenwick. 
# Hanbury, Mrs. Everard, by her mother, Mrs. Murdoch. 
# Herbert, Miss Gwladys, by Mrs. Edmund M'Clure. 
# Hoskyns, Mrs. [P?]aget, by the Dowager Lady Westbury. 
# Hawke, Hon. Catharine I., by the Lady Hawke. 
# Jowers, Miss Ethel, by Lady George Campbell. 
# Jenkins, Mrs. Lawrence, by Lady George Hamilton. 
# Jervis. Hon. Mrs. Bonald, by Lady Harris. [Col. 3/4] 
# Kennard, Miss Winifred Hegan, by her mother, Mrs. Hegan Kennard.
#Knutsford, the Viscountess, by the Marchioness of Salisbury. 
#King, Miss Alice King, by her mother, Lady Florence King King. 
#Kemble, Miss Dorothea, by her mother, Mrs. Horace Kemble. 
#Kerr, Lady Victoria, by her aunt, the Duchess of Buccleuch. 
#Low, Miss Olive, by Lady Low. 
#Low, Lady, by the Lady Ida Low. 
#Low, Miss Helen, by Lady Low. 
#Loch, Lady, by the Marchioness of Ripon. 
#Leverson, Mrs. George B. C., on her marriage, by the Hon. Mrs. Mostyn. 
#Mount, Miss Evelyn, by her mother, Mrs. Mount. 
#Morris, Miss Lilian, by Mrs. Malcolm Morris. 
#Mackay, Mrs. Alexander Dunlop, by her mother, Hon. Mrs. Townley Mitford. 
#Maunsell, Mrs. Mark, by the Countess of Lauderdale. 
#Mitford, Miss Constance, by her mother, Mrs. Robert Sidney Mitford. 
#MacLeod, Miss Flora, by her aunt, the Hon. Lady Northcote. 
#The Lady Mayoress, by the Marchioness of Salisbury. 
#Maitland, Lady Nora, by the Countess of Lauderdale. 
#Micklethwaite, Mrs., on her marriage, by the Hon. Mrs. Baillie of Dochfour. 
#Mackenzie, Mrs. G. Mackay, on her marriage, by Lady Charley. 
#Maguire, Hon. Mrs., by her aunt, Lady Peel. 
#McDonald, Mrs. Archibald, by Mrs. Edmund McClure. 
#Marshall, Miss, by Mrs. Victor Marshall. 
#Markham, Miss June, by Mrs. Edwin Markham
#Morris, Mrs. Malcolm, by the Countess of Lytton. 
#Noel, Miss Charlotte, by her mother, Mrs. Gerard Noel. 
#[[Social Victorians/People/Oppenheim|Oppenheim]], Miss Linda, by Mrs. Henry [[Social Victorians/People/Oppenheim|Oppenheim]]. 
#Pery, The Lady Florence, by her mother, the Countess of Limerick. 
#Paynter, Mrs. Hugh, by Viscountess Cross. 
#Peckover, Miss Alexandrina, by the Hon. Mrs. Arthur Brand. 
#Pound, Mrs. John, by the Hon. Lady Ridley. 
#Palmer, Mrs. Norman Craig, by the Hon. Mrs. Hanbury Lennox. 
#Phillips, Miss Faudel, by Mrs. Faudel Phillips. 
#Phillips, Miss Norah Faudel, by Mrs. Faudel Phillips. 
#Playfair, Miss, by the Hon. Mrs. Playfair. 
#Parr, Miss Katharine, by Mrs. Charlton Parr. 
#Pakington, the Hon. Mary, by her mother, Lady Hampton. 
#Page, Mrs. Ernest, by Mrs. William Court Gully. 
#Pilcher, Miss Margaret, by Mrs. Henry Drayson Pilcher. 
#Ritchie, Mrs. (of the United States), by Mrs. Bayard. 
#Reid, Lady, by Lady Harcourt. 
#Riddel, Mrs. D. McN., on her marriage, by Lady M'Clintock. 
#Royds, Miss Kathleen, by Mrs. Clement Molyneux Royds. 
#Reynardson, Miss Alice Birch, by her mother, Mrs. Birch Reynardson. 
#Ravenhill, Mrs. Frederick, by Mrs. Richard B. Martin.
#Russell, Miss Edith, by Mrs. Joseph Chamberlain. 
#Stern, Miss Violet, by her mother, Mrs. James Stern. 
#Savile, Miss Beatrice Mary, by the Viscountess Pollington. 
#Scott, the Lady Constance, by the Duchess of Buccleuch. 
#Sterling, Miss Margaret, by her mother, Mrs. Sterling. 
#[[Social Victorians/People/Schreiber|Schrelber]], Miss, by her mother, Mrs. Ernest [[Social Victorians/People/Schreiber|Schrelber]]. 
#[[Social Victorians/People/Schreiber|Schrelber]], Miss Evelyn, by her mother, Mrs. Ernest [[Social Victorians/People/Schreiber|Schrelber]]. 
#Smith, Mrs. Alwyn Dudley, by Mrs. Dudley Smith. 
#Townsend, Mrs. George, by the Lady Rayleigh. 
#Tarbutt, Miss Dorothy Percy, by Mrs. Percy Tarbutt. 
#Thornycroft, Mrs., by Mrs. Gerard Noel. 
#Thornycroft, Miss Ruth, by her mother, Mrs. Thornycroft. 
#Tennant, Mrs. Coombe, on her marriage, by Mrs. Henry Morton Stanley. 
#Tufton, the Hon. Rosamond, by her mother, Lady Hothfield. 
#Tritton, Mrs. Joseph Herbert, by the Viscountess Torrington. 
#Tritton, Miss Elizabeth Mary, by her mother, Mrs. Joseph Herbert Tritton. 
#Tritton, Mrs. Herbert Leslie Melville, by her mother-in-law, Mrs. Joseph Herbert Tritton. 
#Troughton, Miss Lilian Adeline, by Mrs. Gubbins. 
#Vincent, Lady, by the Hon. Lady Ridley. 
#Vandeleur, Miss Evelyn Norah, by her mother, Mrs. Vandeleur. 
#Verney, Hon. Mrs., by Mrs. Oswald. 
#Wright, Miss, by Mrs. George Townsend. 
#Wright, Miss Ettie, by Mrs. George Townsend. 
#Wilkin, Miss, by her mother, the Lady Mayoress. 
#Worcester, the Marchioness of, on her marriage, by the Duchess of Abercorn. 
#Whiteley, Mrs. George, by Mrs. Robert Yerburgh. 
#Warrington, Mrs. Thomas Rolls, by Mrs. Matthew Ingle Joyoe. 
#Walker, Mrs. Frowd, on her marriage, by Mrs. Chamberlain. 
#Wyld, Miss Beatrice, by her mother, Mrs. Wyndham Bewes. 
#Wyld, Miss Violet, by her mother, Mrs. Wyndham Bewes. 
#Wilson, the Hon. Lady Rivers, on her marriage, by the Hon. Mrs. Mostyn. 
#Wood, Mrs. Henry James Theodore, by Lady Powell. 
#Worrall, Miss Katharine, by her mother, Mrs. James Worrall. 
#Walsh, Mrs. William Hussey, on her marriage, by her mother-in-law, Mrs. Hussey Walsh.&lt;ref&gt;&quot;The Drawing Room.&quot; London Evening Standard 12 March 1896, Thursday: 3 [of 10], Col. 2a–4b [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18960312/014/0003.&lt;/ref&gt; 
&lt;/blockquote&gt;

===12 March 1896, Thursday===
[? Date is a guess.] The 20 March 1896 ''Literary World'' reports the following: &quot;Last Thursday week, at Stationers' Hall, the first meeting of the newly-formed Publishers' Union was held, about ninety members, representing nearly fifty of the leading publishing-houses, being present. Mr. C. J. Longman was elected president, Mr. John Murray vice-president, and Mr. Frederick Macmillan treasurer, with ten members of council.&quot; &quot;Table Talk,&quot; The Literary World, 20 March 1896, vol. 53, p. 270, col. 1. (Accessed 10 October 2009 in Google Books.)

=== 25 March 1896, Wednesday ===
On 11 April 1896 the ''Morning Post'' reported on a committee to raise funds for a memorial to George Augustus Sala and for aid to his widow:&lt;blockquote&gt;A Committee, of which the Duke of Abercorn is President and hon. treasurer, was formed at a meeting he[l]d on Wednesday, March 25, at Hampden House, Mayfair, with a view to raise a fund for a memorial to the late George Augustus Sala, in recognition of his long and distinguished journalistic career. It has been decided to devote the proceeds of the fund to the erection of a monument over Mr. Sala's grave and to aiding his widow. The following have consented to act on the Committee:— The Duke of Abercorn, President and hon. treasurer; the Duke of Fife, the Earl of Rosebery, the Marquis of Dufferin and Ava, Lord Glenesk, Lord Ronald Gower, Sir Arthur Otway, Sir Charles Dilke, Sir Henry De Bathe, Sir Douglas Straight, Sir David Salomons, Sir Hugh Gilzean Reid, Sir George Arthur, Sir Walter Besant, Sir George Newnes, Sir Benjamin Ward Richardson, Sir Richard Quain, Sir Harry Bodkin Poland, Sir Eyre Massey Shaw, Sir Augustas Harris, Sir Somers Vine, the Hon. W. F. D. Smith, M.P., the Hon. [[Social Victorians/People/Bourke|Algernon Bourke]], Mr. T. P. O'Connor, M.P., Messrs. Collingridge, Messrs. Lloyd, Messrs. J. S. Wood, A. J. Warden, H. Tiedeman (President Foreign Press Association), W. G. Thistle, M.D., Frederick Gordon, J. L. Toole, George Alexander, George Edwardes, John Hollingshead, E. Routledge, William Black, Wellesley Hammond, Horne Payne, Q.C., Charles Morton, E. A. Goodchild, Tom Bird, M.D., John Leighton, A. P. Watt, Alfred Beyfus, Walter Weblyn, Elwin Drew, John Whitley, Alfred Harmsworth, G. M. Kelson, James R. Parday, Caton Woodville, and M. Hall. The Executive Committee consists of Sir Somers Vine, Sir Thomas Straight, and Messrs. H. Tiedeman, Wellesley Hammond, John Hollingshead (Chairman), and W. G. Thistle (hon. secretary). Subscriptions are invited, and cheques, &amp;c., may be made payable to the Duke of Abercorn, and will be acknowledged by the hon. secretary. Lists of the subscriptions received will be from time to time published in the columns of the Morning Post. The bankers of the fund are Messrs. Coutts and Co.&lt;ref&gt;&quot;The Sala Memorial Fund.&quot; ''Morning Post'' 11 April 1896, Saturday: 5 [of 10], Col. 6c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18960411/074/0005. Print p. 5.&lt;/ref&gt;&lt;/blockquote&gt;

===27 March 1896, Friday===
The 20 March 1896 ''Literary World'' reports the following: &quot;Mr. J. M. Barrie, Mr. Anthony Hope, Sir Douglas Straight, Mr. Henry James, and Mr. James Bryce will be amongst the guests at the quarterly dinner of the Omar-Khayyäm Club next Friday.&quot; &quot;Table Talk,&quot; The Literary World, 20 March 1896, vol. 53, p. 271, col. 2. (Accessed 10 October 2009 in Google Books.)

==April 1896==
===3 April 1896, Friday===
Good Friday
===5 April 1896, Sunday===
Easter Sunday
===6 April 1896, Monday===
The 17 April 1896 ''Literary World'' reports the following: &quot;The Vagabonds flocked to the Holborn Restaurant last week to do honour to Mr. Linley Sambourne — and to be photographed. Mr. à Becket introduced his colleague on Punch in a witty and charming little speech, and Mr. Sambourne replied with a short but eloquent description of the changes in 'black and white' art since he began his career.&quot; &quot;Table Talk,&quot; The Literary World, 17 April 1896, vol. 53, p. 364, col. 2. (Accessed 13 October 2009 in Google Books.) The 17 April 1896 ''Literary World'' also reports the following: &quot;Another function held during the past week was the dinner given by Sir Stuart Knill at the Mansion House to 'The Sette of Odde Vlumes,' of which coteries he has been elected president.&quot; &quot;Table Talk,&quot; The Literary World, 17 April 1896, vol. 53, p. 365, col. 1. (Accessed 13 October 2009 in Google Books.)
===11 April 1896, Saturday===
The 17 April 1896 ''Literary World'' reports the following: &quot;The London Press Society held their annual gathering on Saturday last at Anderton's Hotel, with Mr. L. W. Lason presiding. The chairman, in proposing the chief toast, drew an interesting parallel between the Press of our empire and that of foreign nations. The Continental and American Press were too often coarse and vituperative in their attacks on rivals and political opponents, he remarked; but, taking our Press all round, it could not be denied that it shone to advantage in honest, purity, and quiet courage.&quot; &quot;Table Talk,&quot; The Literary World, 17 April 1896, vol. 53, p. 366, col. 2. (Accessed 13 October 2009 in Google Books.)
===14 April 1896, Tuesday===
The 17 April 1896 ''Literary World'' reports the following: &quot;The twentieth anniversary meeting of the supporters of the Bethnal-green Free Library was held on Tuesday last at Grosvenor House, the Rev. C. J. Ridgeway presiding in the unavoidable absence of the Duke of Westminster.&quot; &quot;Table Talk,&quot; The Literary World, 17 April 1896, vol. 53, p. 365, col. 1. (Accessed 13 October 2009 in Google Books.)
===19 April 1896, Sunday===
&quot;The celebration on Sunday of the anniversary which members of the Primrose League deem suitable for a gentle demonstraiton of Conservative political sentiment, as well as of regard for the interesting personality of the late Lord Beaconsfield, was observed with the customary floral rites and tributes, especially displaed around the pedestal of his statue outside Westminster Abbey. At Hughenden Manor, his country house, and at his tomb in the churchyard there, some pilgrims of this memorial vocation assembled. Other places associated with some incidents of his life — the houses in London where he resided at different periods, and his reputed birthplace, which as been a matter of doubt and discussion — were spoken of, though not formally visited, upon / the same occasion. It now appears to be the most probable opinion that Benjamin Disraeli was born, not in the house at the corner of Bloomsbury Square, or in the house in the Adelphi. where some years of his childhood were passed, but in a house situated in Theobald's Road, overlooking Gray's Inn Gardens, which was certainly occupied by his father, Mr. Isaac Disraeli, at that date.&quot; (&quot;Primrose Day at Westminster.&quot; Illustrated London News (London, England), Saturday, April 25, 1896; pg. 515; Issue 2975, Cols. B-C)
===20 April 1896, Monday===
Not sure of date: the 1 May 1896 ''Literary World'' reports the following: &quot;The new Publishers' Association held their first meeting at Stationer's Hall last week, when the President, Mr. C. J. Longman, delivered a lengthy address, in the course of which he touched on many points of contention in the relations between authors and publishers, and other topics of interest and importance to the book-trade. Amongst those present were Mr. John Murray, Mr. Frederick Macmillan, Mr. R. B. Marston, Mr. Oswald Crawford, Mr. William Heinemann, Mr. T. Fisher Unwin, Mr. Edwin Arnold, Colonel / Routledge, Mr. Richard Bentley, Mr. Edward Bell, and Mr. R. J. Smith.&quot; &quot;Table Talk,&quot; The Literary World, 1 May 1896, vol. 53, p. 412, cols. 1-2. (Accessed 13 October 2009 in Google Books.)
===25 April 1896, Saturday===
The 1 May 1896 ''Literary World'' reports the following: &quot;The fifteenth annual dinner of the Press Club, which took place on Saturday last at the Freemasons' Tavern, was a great and unqualified success. Mr. John Morley, who was enthusiastically received, criticised modern journalism in a speech of some length, reminding his hearers in the course of it that he had been called to his present course from the desk where he was writing his leading article. Sir Frank Lockwood also spoke, as did Mr. Spencer Hughes. Lord Wolseley and Lord Charles Beresford were present, and the chair was taken by Mr. Charles Williams.&quot; &quot;Table Talk,&quot; The Literary World, 1 May 1896, vol. 53, p. 412, col. 2. (Accessed 13 October 2009 in Google Books.)
===27 April 1896, Monday===
The 1 May 1896 ''Literary World'' reports the following: &quot;Sir Walter Besant was prevented, by an attack of incipient influenza, from presiding at last Monday's dinner at the Authors' Club. There was a larger attendance than usual in expectation of seeing him in the chair.&quot; &quot;Table Talk,&quot; The Literary World, 1 May 1896, vol. 53, p. 415, col. 2. (Accessed 13 October 2009 in Google Books.) Column 1 in the same &quot;Table Talk&quot; narrates a story told apparently at this same Authors' Club: &quot;Now that the May Meetings are upon us, a story of Exeter Hall in the old days may be quoted from the recollection of a gentleman who told it at the Authors' Club. The occasion was a meeting for advancing the cause of Foreign Missions, and several speakers had deplored the fact that so many converts had recanted. A young midshipman, who was present, felt moved to get on his feet, and say that he knew of at least one case where a convert had not recanted. Being urged to give details he told how he had once been in a boat at sea with a Kaffir chief. Pushing the chief overboard he had asked him if he would be a Christian. The chief declined as energetically as he could with his mouth half full of water, and the midshipman holding on to his scalp. The latter soused him under again, and in a few seconds pulled him to the surface to ask the same question. The chief still refusing, he was dipped again, and then, on regaining the surface, he loudly declared himself a believer. 'I thereupon,' said the midshipman, 'put him under for ten minutes, and I can assure you that convert never recanted.'&quot; &quot;Table Talk,&quot; The Literary World, 1 May 1896, vol. 53, p. 415, col. 1. (Accessed 13 October 2009 in Google Books.) 

Monday, 1896 April 27, [[Social Victorians/People/Muriel Wilson|Muriel Wilson]] was a bridesmaid the wedding of Lady Angela St. Clair Erskine and James Stewart Forbes (1896-04-28 Aberdeen Journal).

Here is the report of the wedding from the ''Inverness Courier'', with the gift list set as an unordered list to save space and simplify finding people:&lt;blockquote&gt;MARRIAGE OF LADY ANGELA ST. CLAIR ERSKINE.

Yesterday afternoon, at the increasingly fashionable church of St Paul’s, Knightsbridge, S.W., and in the presence of very large and fashionable assembly, the marriage took place of Mr James Stewart Forbes, and Lady Angela Selina Blanche St Clair Erskine. The bridegroom, Mr James Stewart Forbes, of the 9th Lancers, is the only son of the late Mr George Stewart Forbes (who was senior partner in the well-known Indian mercantile firm of Forbes, Forbes, &amp; Co., in the city of London), nephew of Helen Lady Forbes of Newe, Aberdeenshire, and cousin of the present baronet. The bride, Lady Angela Selina Blanche St Clair Erskine, is the charming and accomplished youngest daughter of the late Earl of Rosslyn, and of Blanche, Countess of Rosslyn, of Rosebank, Mid-Lothian, and 20 Charles Street, Berkeley Square, London. She is a sister of the present Peer and also of the Duchess of Sutherland and Countess of Westmoreland, and half-sister of the Countess of Warwick and Lady Algernon Gordon-Lennox.

The service was fully choral, and the Church handsomely decorated with tall palms banked with white flowers, while the altar vases had been specially refilled with white blooms for the ceremony. The Rev. James Fleming, Canon of York and Vicar of St Michael Square. S.W., officiated, assisted by the Rev. Montagu Villiers, M.A., of St Paul’s; the Rev. J. Thompson, domestic Chaplain to the Earl of Rosslyn. The bride arrived with her brother the Earl of Rosslyn, who during the singing of the nuptial hymn, Lead us, heavenly father, lead us,” conducted her to the chancel entrance and gave her away. The bridegroom was supported by his brother officer, Mr F. Allhusen of the 9th Lancers as “best man.” There were eight bridesmaids in attendance upon the bride. These young ladies were — Lady Marjorie Blanche Eva Greville, the daughter of the Earl and Countess of Warwick; Miss Ivy Gordon-Lennox, the daughter of Lord and Lady Algernon Gordon- Lennox, nieces of the bride; Miss Keith Fraser (daughter of General James Keith Fraser, C.M.G., and Mrs Keith Fraser), cousin of the bridegroom; the Hon. Ethel Gerard (daughter of Lord and Lady Gerard), Miss Diana Isabel Sturt (daughter of the Hon. Humphrey and Lady Feadovouno Sturt; Miss Edith Chaplin (daughter of the Right Hon. Henry Chaplin, M.P.); the Hon. Muriel Agnes Stewart Erskine (daughter of Lord and Lady Cardross), and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]] (daughter of Mr and Mrs Arthur Wilson). The bridesmaids were charmingly gowned in white muslin dresses, Louis LVI. style, over satin with frilled fichu, and ruched sleeves to wrist finished with frills and broad white satin ribbon sash. They also wore very handsome white and bright scarlet velvet cloaks, slung from one shoulder, lined with white satin, and large felt white picture hats with white ostrich feathers, and knots of scarlet velvet. The bridegroom’s presents to them were enamel chain bangles with enamel heart in centre, each of different design, and carrying nosegays of lilies of the valley in foliage.

Two smart pages (nephews of the bride), the Marquis of Stafford and Lord Alistair Clair Leveson-Gower (sons of the Duke and Duchess of Sutherland), followed the bride as trainbearer, picturesquely attired in white satin Court costume, with full blouse of gold Indian muslin, and point de Alencon lace chabot and sleeves, ruffles, white shoes and silk stockings, the breeches being fastened at the knee with diamond buckles, and scarlet velvet cloaks from shoulders, “Cavalier&quot; style, to match bridesmaids; white felt “Cavalier&quot; hats, fastened on one side with strap of red velvet, clasped with a diamond ornament, and white ostrich feathers falling over the brim, the bride’s present them being diamond fox-head pins. Lady Angela St Clair Erskine selected a “wedding gown” consisting of white satin Duchesse petticoat “Josephine,” over dress of Brussels lace, with entredeux of fine Indian muslin, the bodice being of satin, with inforcement of Brussels lace and Indian muslin, with bands of Brussels lace, “Mount de cour&quot; of the richest white satin, with very delicate embroidery of sprays of lilies of the valley, wrought in diamonds and silver. Her fine tulle veil covered coronet of real orange blossoms. Her ornaments were pearls, and she carried a bridal bouquet of lilies of the valley, tied with white satin streamers.

The scene inside the church was a most brilliant one. Quite an hour before the time fixed for the ceremony, the large edifice was nearly filled, and at the hour even standing room could not be had. The carriages outside had completely blocked Wilton Place, where the church is situated. The first to arrive was the Dowager-Countess Lovelace, wearing a gown of grey brocaded satin, with black velvet cape. Soon after came Isabella Countess of Wilton, wearing dark purple velvet, Lady Blythswood in black, Lord and Lady Newton Butler, Lord Algernon Gordon Lennox, Viscountess Hood, the Countess of Rosslyn, Lady Esher, Lady Algernon Gordon Lennox, and the Countess of Warwick (the former in pale heliotrope, the latter in white silk, with lovely cape of turquoise blue velvet trimmed with silver). The young Duke and Duchess of Marlborough next arrived. This is the Duchess's first appearance at a society wedding since her marriage. She looked very well in black satin, and wore some magnificent diamonds. The Duke and Duchess of Sutherland followed, the latter in white muslin, arranged with pale yellow silk, and large white hat, ornamented with white plumes and yellow bows. There were also the Duchess of Westminster, Earl and Countess of Westmoreland [sic], Blanch, Countess of Rosslyn, Lord Thorpe, Lady Alwyn Compton, Lady Clementine Walsh, Lady Hothfield, Hon. Rosamond Tufton, Earl of Crewe, Earl of Dunraven, Lady Mabel Kenyon, Lady Slaney, Countess Cairns, Sir Allan and Lady Mackenzie (wearing black and white striped silk), Marchioness of Downshire, Major and Lady Kathleen Pilkington, Mr Wm. Gilett, Marchioness of Tweeddale, Sir Charles and Lady Forbes of Newe, Mrs George Forbes, Miss Forbes, Lady Maud Keppell, Lady Evelyn Dawnay, Lord and Lady William Nevill, Countess of Essex, Sir W. H. Wilkins, Lady St Oswald, Lady Ducane [sic], Lady Lilian Wemyss, Helen Lady Forbes of Newe, Mrs Menzies, Col. Baillie, Mrs Farquharson, Mr Hugh Fraser, Mr Dudley Ward, Mr and Mrs Grenfell, Lady Gerard, Mrs Charles Wilson, Mrs Arthur Wilson of Tranby Croft, Captain Foley, Hon. George and Mrs Curzon, Lady Sarah Wilson, Lady Georgina Curzon, Lord Rowton, Sir George Chetwynd, Mr and Mrs Clayton Glyn, Sir Charles and Lady Hartopp, Countess Deym, Lady Vivian, Lord Vivian, Mr Percy Wyndham, Hon. Mrs Keith Falconer, Mrs Alfred Somerset, Mr Dundas, Miss G. Harvey, Mrs Ernest Chaplin, Colonel and Mrs Gore, Sir Arthur Holkett, Lady Meysey Thompson, Mr and Mrs Alfred Loder, Sir William and Lady Russell, Mr and Lady Mary Jenkins, Hon. Mrs Eliot, Hon. Mrs Percy Mitford, Mrs Balfour, Captain Leigh, and many others.

The procession up the aisle looked very pretty, the unique design of the bridesmaids' gowns and cloaks causing great admiration. Diamonds were the principal ornaments worn, and most of the ladies present wore bright colours, heliotrope and green shades appearing to be the favourites, and it is seldom that London sees such a brilliant gathering. The Prince of Wales would have attended the church, but was unable to do so owing to the levee. He, however, attended the reception, and heartily congratulated the happy pair.

During the service the hymn &quot;O perfect love, all human thoughts transcending,&quot; was sung with great effect, and after the signing of the register, the bridal party adjourned to Stafford House, where Blanche Countess of Rosslyn, gave a large reception. Early in the afternoon Mr James and Lady Angela Forbes left for Easton Lodge, Dunmow, Essex, a seat of the Earl and Countess of Warwick, where the early days of the honeymoon will be spent. The going-away dress was of pale grey canvas, with large white satin collar and revers, and green sash, and large black picture hat, with green feather and shaded yellow roses.

The presents, which numbered over 600, were exhibited in the drawing-room of Stafford House. They included the following:—

* His Royal Highness the Prince of Wales — Sapphire and diamond curb bracelet
*H.S.H. Princess Adolphus of Teck — Ruby and sapphlre safety pin
*The Duke and Duchess of Sutherland and the Earl and Countess of Warwick — A magnificent diamond tiara [Col. 2c / 3a]
*Bridegroom to Bride — Ruby and diamond ring, emerald and diamond bracelet, large diamond bow, enamel and gold muff chain, diamond heart, emerald and diamond necklace, large leather fan with &quot;Angela&quot; in diamonds
* Blanche, Countess of Rosslyn — Old Brussels lace, three rows of pearls, and a long rope of pearls
* Mrs George Forbes — Complete set of silver plate
* The Earl of Crewe — Opal and diamond pendant
* Adelaide, Countess of Westmoreland, and Lady M. Spicer — Umbrella handle
* Lady Sarah Wllson — Shagreen card case
* Mrs Wilfred Marshall — Heart-shaped links
* Mr J. Oswald — Silver-topped toilet bottle
* Mrs Oswald — Silver-mounted memorandum book
* Mrs Scarisbrick — Photo. frame
* Mr Kennard — Silver candles
* Lady Keith Ashley — Silver tea knives
* Rev. Mr and Mrs Pigott — Small silver tray
* Mr and Mrs H. Cherrington — Gold-topped salts-bottle
* Colonel and Lady Mabel Slaney — Picture of Warwick Castle
* Lady Bettine Taylor — Cushion
* Mr and Mrs Alfrel Loder — Card case
* Mr and Mrs de Winton — Fan
* Hon. A. Macdonell — Stationery case
* Lady Edmonstone — Brooch
* Sir John Willoughby — Ruby and diamond bracelet
* The Ladies Cecilie and Mary Willoughby — Photo. frame
* The Earl of Rosslyn — Turquoise bangle and Victoria
* Miss Balfour — Silver box
* The Countess of Ancaster — Fan
* Lord and Lady Burton — Fox and fan
* Mrs Macdonald — Paper knife
* Colonel and Mrs Baillie — Tortoiseshell and silver box
* Mrs Dowdall —Book
* Lady Alwyn Compton — Tortoiseshell and turquoise-handled umbrella
* Hon. John Ward — Small gold and enamel photo. frame
* Lord Herbert Vane Tempest — Turquoise bangle
* Viscountess Hood — Book
* Misses L. and D. de Bremner — Parasol
* Mrs Farquharson — Parasol
* Colonel Poynter — Silver candlesticks
* Count Larisch — Enamel and pearl muff chain
* Mrs Woodhouse — Book
* Mrs Finch — Silver tray
* The Austrian Ambassador — Feather fan
* The Countess of Cork — Diamond and black pearl brooch
* Miss Fleetwood Wilson — Silver-mounted clock
* Comte and Comtesse A Munster — Clock
* The Ladies F. and L. Cecil — Silver tray
* Mrs Baird — Sugar castor
* Mrs L. de Rothschild — Ruby and diamond bangle
* Mrs A. Sassoon — &quot;Duck&quot; brooch
* Mr and Mrs Hufa [sic] Williams — Old gilt candlesticks and shade
* Lord Kenyon — Diamond crescent
* Lord and Lady Raincliffe — Turquolse and diamond bangle
* Mr and Lady Eva Dugdale — Cabinet for miniatures
* [[Social Victorians/People/Holden|Mr Henry Holden]] — Silver-mounted salts bottle
* Countess Cairns — Fan
* Tenants on Lord Rosslyn's Estate — Silver candlesticks
* Mr and Mrs Stuart Menzies — Silver pot
* Lord Cardross — Old tortoiseshell box
* Lady Evelyn Bertie — Smelling bottle
* Lord Hy. Grosvenor — Silver toast racks
* Earl and Countess of Essex — Lamp shade
* Hon. Baillie of Dochfour — Miniature case
* Mrs Gore — Small tray
* Countess Howe — Silver ornaments
* Lady Southampton — Silver box
* Miss Keith Falconer — Photo frame
* Lord and Lady Rothschild — Antique silver tea and coffee service in case
* Mrs Gerard Leigh — Silver-mounted note book
* Mr and Mrs A. Bourke [Rourke?] — Box for miniature
* Major-General Sir Henry Ewart — Two gold candlesticks
* [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]] — Diamond and pearl bangle
* Major Davidson — Links
* Mr and Mrs D. Cooper — Old tortoiseshell tray
* Lady de Trafford — Large green travelling cushion
* Mr Bristow — Tortoiseshell umbrella
* Mr Sykes — Whip
* Mr Dowell — Book
* Mr and Mm F. Hartmann — Old box
* The Countess of Westmorland — Old three-fold gilt screen
* Mrs Forbes — Diamond swallow
* Lady Cotterell — Silver photo. frame
* Lord and Lady Lindsey — Silver paper knife
* Mr and Mrs R. Vigner — Turquoise and diamond ring
* Lady Blanche Conyngham — Silver hand bell
* Mrs Mitford — Silver ornament
* Mrs Asquith — Butterfly brooch
* Lady Dorchester — Silver dish and spoon
* Mr and Mrs Frewer — Louis XVI. candlesticks
* Canon and Mrs Fleming — Silver handled paper knife
* Colonel and Mrs Oldham — Tortoiseshell box
* Mr and Mrs Alwyn Greville — Two old gilt looking-glasses
* Lord Ronald Gower — Old print
* Mr and Mrs J. Lowther — Large gold-topped salts bottle
* Mr and Miss Tufnell — Large box
*Mrs Wall and the Servants at Rosslyn Rest — Silver inkstand
*Hon. Sydney Greville — Silver photo frame
*Mr and Mrs Adrian Hope and Mrs Farnham — Case for writing paper
*Lord Rosebery — Sapphire and diamond bracelet
*Lord Rowton — Silver cup
*Mr R. Charters — Driving whip
*Mrs Lawrence Currie — Amethyst heart brooch
*Captain and Mrs Drummond — Book-case
*The Duchess of Wellington — Enamel clock
*Lady Cardross — Dryfons frame [sic: Dryfus? type seems clear enough...]
*Helen Lady Forbes — Silver teapot, sugar basin, and cream jug
*Mrs R. Brett — Diamond and ruby pin
*Lord W. and Lord R. Nevill — Two gold cups
*Isabella, Countess of Wilton — Silver box
*Duke of Grafton — Coral necklace
*Mr Cough Craven — Turquoise and diamond ring
*The Duke and Duchess of Marlborough — Diamond ring
*Sir Charles and Lady Hartopp — Green travelling bag
*Lord Willoughby de Broke — Fox head safety pin
*Lady Caroline Gordon Lennox — Frame
*Sir William Russell — Book
*Sir George Chetwynd — Saphire [sic] and diamond bangle
*Mrs Bischoffsheim — Parasol
*Mr and Mrs Watson Taylor — Hand-painted fan
*Mr Barclay — Turquoise and diamond ring
*Mr and Madam Von Andre — Gold-mounted travelling bag
*Mr Corbet — Whip
*Viscount Royston — Writing table
*Mrs Marshall — Tortoiseshell salts bottle
*Mrs Somerset — China handled stick
*Countess of Chesterfield — Writing set
*Lord Hy. Bentinck — Photo. frame
*Sir Allan and Lady Mackenzie — Two old silver bowls 
*Mr F. Murray Honey — Menu holders 
*Lady L. Wemyss — Safety pin 
*Mr Tynedale — White candlesticks 
*Mr Cecil Foley — Fox head pin 
*Lord and Lady Curzon — “En tout cas,&quot; with China handle 
*Lord Stafford, Lord Alastair Leveson Gower, Ladv Rose Mary Leveson Gower, Miss K. [R.?] Chaplin, and Miss F. Chaplin — Small watch set with diamonds 
*Mr and Mrs Harry Lawson — Silver mirror 
*Mrs Glyn — Cushions 
*Lord Blythswood — Old Worcester teapot 
*Mrs Hartmann — Louis XVI. settee 
*Mrs George Curzon — Frame 
*Dowager Countess of Warwick—Writing table 
*Lady Wolvarton—Two small silver coffee pots 
*Miss Blanche Forbes — Antique mustard pot 
*Miss Forbes — Silver tea and coffee set in case 
*Mr F. Allhuson — Tortoiseshell and gold box 
*Baron and Baroness de Hirsch de Gererk — Gold coffee set on tray 
*Mr Powell — Gilt basket 
*Viscount Brackley — Six &quot;Initial&quot; menu holders 
*[[Social Victorians/People/Keppel|Mrs George Keppel]] — Box 
*Lord and Lady St Oswald — Three small silver cruets 
*Hon. R. Ward — Luncheon basket 
*Sir Samuel Scott — Luncheon basket 
*Madame de Falbe — Gilt tea set 
*Madame Offenheim — Gilt coffee set 
*Lady Filmer [? Fihaer? Fihner? ] — Ebony and silver paper cutter 
*Lady Du Cane — Silver seal 
*Lady Sandhurst — Gun metal and gold pocket knife 
*Lady M. Jenkins — Two silver boot lifters in case 
*Lady Esher — Silver paper clip 
*Lord and Lady William Nevill — Two silver trays 
*Countess of Romney — Silver cigarette case 
*Mr and Mrs Arthur Sasson [sic] — Silver box 
*Household Servants of Mrs Forbes (Burleigh) — Silver cigarette case 
*Mary Lady Edmonstone — Silver holder 
*Household Servants of Mrs George Forbes — Silver salver 
*Lady C. Walsh — Small silver salver 
*Hon. R. Brett — Silver candlesticks 
*Baron Ferdinand de Rothschild — Silver vase 
*The Marquis of Camden —Two silver candlesticks 
*Lady Evelyn Dawny — Two silver candlesticks &amp;c.&lt;ref&gt;&quot;Marriage of Lady Angela St. Clair Erskine.&quot; ''Inverness Courier'' 28 April 1896 Tuesday: 5 [of 8], Cols. 2a–3c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000446/18960428/037/0005.&lt;/ref&gt; 
&lt;/blockquote&gt;

==May 1896==
===3 May 1896, Monday===
The 8 May 1896 ''Literary World'' reports the following: &quot;Speaking at the Booksellers' dinner in the week, Dr. Welldon remarked that there was a time in history when the dissatisfied author could complain to the Archbishop of Canterbury, who had in certain cases legal authority to redress his grievances. He was sorry this cusom had died out in the profession. It would have been instructive to hear what price the Archbishop would have put on 'Robert Elsmere,' &quot;The Heavenly Twins,' 'The Sorrows of Satan,' or 'Barabbas.'&quot; The next item is also related to the Booksellers' dinner: &quot;Mr. Crockett was also on hand with one or two good stories. One of the best of these concerned himself. Mr. Crockett told how he recently was introduced to a lady, to whom his profession was mentioned. 'Mr. Crockett,' she said during the evening, 'I hear you are an author. Have you published any of your works yet?'&quot; &quot;Table Talk,&quot; The Literary World, 8 May 1896, vol. 53, p. 436, col. 2. (Accessed 13 October 2009 in Google Books.)

===4 May 1896, Tuesday===
&quot;MARLBOROUGH HOUSE, May 6.&quot; &lt;quote&gt;Sir Horace Farquhar, M.P., and Lady Farquhar entertained at dinner last evening at their resident in Grosvenor-square the Duchess of Devonshire, the Duke of Leeds, the Marchioness of Salisbury and Lady Gwendolen Cecil, the Marquis and Marchioness of Londonderry, the Lord Lieutenant of Ireland and Countess Cadogan and Lady Sophie Cadogan, the Countess of Derby, the Earl and Countess of Onslow, the Earl of Dudley, Viscount Royston, Lord James of Hereford, Lord Stanley, M.P., Lady George Hamilton, the Right Hon. George Curzon, M.P., and Mrs. Curzon, the Hon. St. John Brodrick, M.P., and Lady Hilda Brodrick, Sir Samuel Scott, and Mr. Victor Cavendish, M.P. Subsequently Lady Farquhar gave a reception. Those present included the Astro-Hungarian Ambassador and Countess Deym and Countess Isabella Deym, the Brazilian Minister, the Duke of Norfolk, and the Duke of Devonshire.&lt;/quote&gt;&lt;cite&gt;(&quot;Court Circular.&quot; Times [London, England] 7 May 1896: 9. The Times Digital Archive. Web. 2 May 2013.)&lt;/cite&gt;.

===5 May 1896, Wednesday===
&lt;quote&gt;MARLBOROUGH HOUSE, May 6. [/] His Royal Highness the Prince of Wales gave a dinner party this evening, at which the following were present:— His Royal Highness the Duke of Connaught; the German Ambassador, Count Hatzfeldt; the Austro-Hungarian Ambassador, Count Deym; the United States Ambassador, the Hon. T. F. Bayard; the French Ambassador, Baron de Courcel; the Italian Ambassador, Lieutenant-General A. Ferrero; the Spanish Ambassador, Count de Casa Valencia; the Turkish Ambassador, Costaki Anthopoulo Pasha; the Count de Ficalho, Grand Maître de la Cour to the King of Portugal; the Archbishop of Canterbury; the Lord Chancellor, Lord Halsbury; the Lord President of the Council, the Duke of Devonshire; the Marquis of Lansdowne, the Marquis of Salisbury, the Earl of Lathom, the Earl of Rosebery, the Earl of Kimberley, Lord George Hamilton; Field-Marshal Viscount Wolseley, Lord Herschell; the Right Hon G. J. Goschen, the Chancellor of the Exchequer; the Right Hon. J. Chamberlain, the Right Hon. Sir William Vernon Harcourt, the Right Hon. A. J. Balfour, the Right Hon. Sir Henry Fowler, the Right Hon. John Morley, General the Right Hon. Sir Redvers Buller, the Right Hon. Sir Matthew White Ridley, the Right Hon. H. Asquith; the President of the Royal Society, Sir Joseph Lister; General Sir Evelyn Wood, Admiral Sir Frederick Richards; the President of the Society of Antiquaries, Sir Augustus Wollaston Franks; the Director of the Natural History Museum, Sir William Flower; Rear-Admiral Sir John Fisher, Rear-Admiral Sir Frederick Bedford; the Principal Librarian and Secretary of the British Museum, Sir Edward Maunde Thompson; the President of the Royal Geographical Society, Mr. Clements R. Markham; the President of the Royal College of Surgeons, Mr. Christopher Heath; the President of the Royal College of Physicians, Dr. Samuel Wilks; Colonel Alfred Egerton, in attendance on His Royal Highness the Duke of Connaught; and General Sir Dighton Probyn and Major-General A. Ellis, in attendance on His Royal Highness the Prince of Wales. [/] The following were unavoidably prevented from obeying His Royal Highness's command:— The Russian Ambassador, M. de Staal; the Speaker, the Right Hon. W. C. Gully; the President of the Royal Academy, Sir John E. Millais. [/] During dinner the band of the Grenadier Guards, under the direction of Lieutenant Dan Godfrey, played the following selection of music:— [/]&lt;blockquote&gt;March, &quot;Hepp, Hepp, Hurrah!&quot; -- Kràl.&lt;br /&gt;Overture, &quot;Le Singe de Brésil&quot; -- Lindpaintner.&lt;br /&gt;Waltzer, &quot;Gartenlaube&quot; -- Johann Strauss.&lt;br /&gt;Selections of Melodies -- Greig.&lt;br /&gt;March, &quot;Mit Hörnerklang durch Wald und Flur&quot; -- Kohout.&lt;br /&gt;Fantasia, &quot;Hänsel und Gretel&quot; -- Humperdinck.&lt;br /&gt;Polish Dances -- Franz Morgan.&lt;br /&gt;Selection, &quot;Donna Juanita&quot; -- Suppé.&lt;br /&gt;Waltzer, &quot;Mondnacht auf der Alster&quot; -- Fétras.&lt;br /&gt;&lt;/blockquote&gt;

===10 May 1896, Monday===
The 15 May 1896 ''Literary World'' reports the following: &quot;A brilliant gathering took place on Monday last at the Galleries of the Royal Society of British Artists, where, on the invitation of Mr. and Mrs. W. T. Madge, nearly a thousand authors and pressmen, peers and members of Parliament came together to meet the proprietors and editors of the newspapers of the United Kingdom. An excellent musical programme was given under the direction of Mr. William Ganz, and the reception was altogether a thorough success.&quot; &quot;Table Talk,&quot; The Literary World, 15 May 1896, vol. 53, p. 462, col. 3. (Accessed 13 October 2009 in Google Books.)

===13 May 1896, Thursday===
The 22 May 1896 ''Literary World'' reports the following: &quot;Mr. Frankfort Moore, in a racy speech, introduced Mr. Harold Frederic, the London representative of The New York Times, and the author of 'Illumination,' and other well-known novels, to the members of the New Vagabond Club on Thursday, the 14th, and Mr. Frederic responded to the toast of his health in a speech full of point and humour. He touched upon the international question, and quietly hinted that it was only here that the fuss was made, not in America. We daresay he is right as regards the people, but the New York newspapers occasionally give one a different impression. Perhaps what Mr. Frederic meant to convey, but was too courteous to say in an assembly of Englishmen, was that all the American talk about the Venezuela busines from the beginning to end was only a way of pulling the British lion's tail so as to enjoy hearing him roar and to make capital out of the incident for election purposes. Mr. Frederic passed a compliment upon Englishmen as regards their 'splended cosmopolitanism,' as shown in the capacity of Englishmen to live up to everything that is demanded of an Imperial race. He alluded to the number of American authors, from Bret Harte downwards, who had made their homes here — 'not that they loved America less, but that they loved London more.' Among those who attended to do honour to Mr. Harold Frederic were Mr. Grant Allen, Mr. William Le Queux, Mr. C. J. Tibbits, Mr. G. B. Burgin, Mr. Morris / Colles, Mr. Coulson Kernahan, Mr. Bertram Mitford, Mr. Walter Jerrold, and Mr. Douglas Sladen.&quot; &quot;Table Talk,&quot; The Literary World, 22 May 1896, vol. 53, p. 484, cols. 1-2. (Accessed 13 October 2009 in Google Books.)

===14 May 1896, Friday===
The 8 May 1896 ''Literary World'' reports the following: &quot;Mr. Hermann Vezin will assist at the Tenth Annual Public Reading of the Shakespeare Reading Society, to be given at the Steinway Hall on Friday evening, May 15. The play Julius Caesar is arranged and rehearsed under the direction of Mr Wm. Poel; the harp will be plaed by Miss Mary Chatterton. The Reading will be repeated on the following evening to students who are preparing the play for the Oxford and Cambridge local examination.&quot; &quot;Table Talk,&quot; The Literary World, 8 May 1896, vol. 53, p. 436, col. 2. (Accessed 13 October 2009 in Google Books.) The 15 May 1896 Literary World confirms the date: &quot;The Shakespearian Reading Society will meet at the Steinway Hall, Lower Seymour-street, W., to-night at 8.30 p.m., when Julius Caesar will be read by its members, assisted by Mr. Hermann Vezin and Mr. Wm. Poel.&quot; &quot;Table Talk,&quot; The Literary World, 15 May 1896, vol. 53, p. 461, col. 2. (Accessed 13 October 2009 in Google Books.)

===23 May 1896, Sunday===
Whit Sunday

1896 May 23 (or the weekend before, so Saturday May 16?), [[Social Victorians/People/Muriel Wilson|Muriel Wilson]] is at a weekend country-house party at [[Social Victorians/People/Warwick|Warwick Castle]]: &lt;quote&gt;Among the guests entertained by the Earl and Countess of Warwick at Warwick Castle for the weekend were Sir John Willoughby, the Countess of Rosslyn, Lord and Lady Algernon Gordon Lennox, Miss Muriel Wilson, and Miss Tufnell.&lt;/quote&gt; (1896-05-23 Leamington Spa Courier).

===26 May 1896, Wednesday===
The 10 April 1896 ''Literary World'' reports the following: &quot;Mr. George A. Macmillan will preside at the booksellers' Dinner to be held at the Holborn Restaurant on the 27th of next month. He will be assisted by Mr. Joseph W. Darton, and several leading authors and publishers will be there.&quot; &quot;Table Talk,&quot; The Literary World, 10 April 1896, vol. 53, p. 341, col. 2. (Accessed 13 October 2009 in Google Books.)

==June 1896==
The Women Journalist Club's &quot;midsummer party to which all literary, artistic and social London is bidden&quot; (Krout, Mary H., &quot;Women's Clubs,&quot; Chapter 9, A Looker-On in London. Rpt in Victorian London: Publications: Social Investigation/Journalism. Online: www.victorianlondon.org [August 2005].). Here, from victorianlondon.org, is Krout's description of that event:
&lt;blockquote&gt;In June, 1896, this great function was held at Stafford House - the town residence of the Duke and Duchess of Sutherland, and there was such a demand for invitations that the committee was forced to announce through the columns of the morning newspapers that no more cards would be issued, those which had been sent having been inexorably marked &quot;strictly non-transferable.&quot; The invitations included every artist, man or woman, every journalist, author, musician and actor of note in London, with scientists, members of Parliament, cabinet ministers, diplomats and those who lived simply to enliven and adorn the social world. Long before ten o'clock there was a line of carriages stretched down Pall Mall, each awaiting its turn at the entrance in the shadow of the great porte cochère around which was stationed an array of footmen in black and gold livery. The guests were received by the President, Mrs. Craigie, a woman of striking beauty and dignity, who was assisted by Mrs. Johnson, the editor of ''The Gentlewoman'', and other women journalists.

A remarkably varied programme had been arranged, literally suited to all tastes, and the names of the artists who had contributed their services included Mine. [Mme] Albani and Cissy Loftus, Arthur Roberts, the comedian and Johannes Wolff the violinist, Alice Gomez, the contralto of the St. James concerts, and Letty Lind of the Empire Music Hall. Mme. Albani did not appear, but the beautiful and fascinating Cissy Loftus did not disappoint the company, and she gave an extremely clever imitation of a popular actress whose mannerisms were then the delight [-85-] of the Music Hall artists, and a source of pecuniary profit as well. [The page break in the original print copy is marked in the text as &quot;[-85-].&quot;] (A Looker-On in London, by Mary H. Krout, 1899 - Chapter 9 -Women's Clubs)&lt;/blockquote&gt;
===1 June 1896, Monday===
Not sure of date. The 12 June 1896 ''Literary World'' reports the following: &quot;It is authoritatively understood that the offer of one of the most important literary positions in London has been made to Mr. Edward W. Bok, editor of The Ladies' Home Journal, of Philadelphia, who is at present in England. Not alone is the position offered Mr. Bok of the most desirable character, but the honorarium attached to it is reported to be several times larger than the salary received by any editor in England. In addition to this, a ten-year lease of a Grosvenor-quare mansion is included in the offer. The position would require Mr. Bok's permanent residence in London. ... / An offer of the magnitude which the negotiations with Mr. Bok are reported to assume is particularly significant from the fact of the recipient's youth. Mr. Bok, if we err not, has just passed the thirty line in point of age, and is the youngest of all the American magazine editors. He was born in Holland, and comes of excellent Dutch / [col. 2] stock. He came to America at the age of six, and his rise there has been phenomenal. ... / Mr. Bok has been a much-dined and fèted man during his present visit to London. Last week, Lady Morell Mackenzie gave a dinner in his honour, and this week will entertain him with a country house-party at her place at Wargrave.&quot; &quot;Table Talk,&quot; The Literary World, 12 June 1896, vol. 53, p. 556, cols. 1-2. (Accessed 13 October 2009 in Google Books.)

===3 June 1896, Wednesday===
Derby Day at Epsom Downs, so the [[Social Victorians/People/Louisa Montagu Cavendish|Luise Friederike Auguste Montagu]], Duchess of [[Social Victorians/People/Devonshire|Devonshire]], hosted a ball at Devonshire House that night?

Georgiana, Lady Dudley: &lt;quote&gt;After all that umbrella holding she [Georgiana, Lady Dudley] deserved to be the one whom the Prince chose to sup with on the happiest day of his life. This was June 3, 1896, when H.R.H. won the Derby with Persimmon to tumultuous applause. After the usual dinner at the Jockey Club, Albert Edward, so his engagement diary records, went on to 'midnight supper with Lady Dudley'&lt;/quote&gt;&lt;cite&gt;(Leslie 74)&lt;/cite&gt;.

===7 June 1896, Sunday===
Of Mr. Edward W. Bok, &quot;Last Sunday Mr. Bok was the special guest of Madame Adelina Patti at a luncheon of thirty.&quot; &quot;Table Talk,&quot; The Literary World, 12 June 1896, vol. 53, p. 556, col. 2. (Accessed 13 October 2009 in Google Books.)

===8 June 1896, Monday===
Of Mr. Edward W. Bok, Lady Morell Mackenzie &quot;this week will entertain him with a country house-party at her place at Wargrave.&quot; &quot;Table Talk,&quot; The Literary World, 12 June 1896, vol. 53, p. 556, col. 2. (Accessed 13 October 2009 in Google Books.) Also, &quot;Sir Douglas also entertained Mr. Bok at dinner a few evenings ago. Mrs. C. D. Gibson gave him a luncheon; he led the Portland House cotilion with the young Duchess of Marlborough, while Anthony Hope, Jerome K. Jerome, Sir Arthur Sullivan, and Beerbohm Tree have all entertained him.&quot; &quot;Table Talk,&quot; The Literary World, 12 June 1896, vol. 53, p. 556, col. 2. (Accessed 13 October 2009 in Google Books.)

=== 10 June 1896, Wednesday ===
[[Social Victorians/People/Schreiber|Mr. Schreiber]] was present at the fashionable wedding of the Hon. John Tufton and Lady Ierne Hastings, which was reported in the &quot;Court Circular&quot; section of the ''Morning Post'' for 11 June 1896:&lt;blockquote&gt;The marriage of the Hon. John Tufton, eldest son of Lord Hothfield, and Lady Ierne Hastings, third daughter of the late Earl of Huntingdon, was solemnised yesterday at St. Anselm's Church, Davies-street, at half-past two o'clock. The ceremony was performed by the Rev. Herbert Moore, vicar of St. Anselm's, assisted by the Rev. W. F. B. Ward, private Chaplain to the Duke of Newcastle. The bride was given away by her brother, the Earl of Huntingdon. The bridesmaids were Lady Rowena and Lady Noreen Hastings, sisters of the bride; Lady Kathleen Hastings and Miss Pasley, nieces of the bride; Lady Muriel Parsons and Miss Campbell. The bridegroom was attended by the Hon. Charles Wyndham, lst Life Guards. Amongst the immediate relatives and friends in the church and afterwards at Grosvenor-square were the Duke of Newcastle, the Countess of Huntingdon, Mr. and Lady Irene Campbell, Sir Thomas and Lady Constance Pasley, Major and the Hon. Mrs. Candy, Major and the Hon. Mrs. Stirling, Lady Dora Yeoman, Lady Sarah Wilson, Lady Ventry and the Hon. Maud de Moleyns, the Hon. Lady Acland Hood, Lady and the Misses Wilson, General Stracey, Colonel Stracey, Scots Guards; Mr. W. Campbell, Mr. Herbert Wilson, the Countess of Cottenham and Lady M. Pepys, the Countess of Ranfurly, Marchesa Santurce, the Viscountess Galway, Lady Churston, the Countess of Rosse, Viscount and Viscountess Wolseley and the Hon. F. Wolseley, Mrs. Adrian Hope and Miss Hope, Mr. W. Gillett, Mr. Hastings Parker, Sir Hubert Miller, Captain Milner, lst Life Guards; [[Social Victorians/People/Schreiber|Mr. Schreiber, 1st Life Guards]]; Lord Lovat, 1st Life Guards; Captain Boyce, and many others. The Duchess of Newcastle was prevented by illness from being present. Mr. and Lady lerne Tufton left London for the Isle of Wight in the afternoon.&lt;ref&gt;&quot;Court Circular.&quot; ''Morning Post'' 11 June 1896, Thursday: 7 [of 12], Col. 6c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18960611/072/0007.&lt;/ref&gt;&lt;/blockquote&gt;

===12 June 1896, Friday===
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] is at Epsom for the races in Mr, and Mrs.’s D’Arcy’s private stand, which they had lent to Lord and Lady William Nevill, who then “entertained a large party on the Derby and Oak days.” &lt;quote&gt;Mr and Mrs D’Arcy owing to their absence on the Continent, lent their private stand at Epsom to Lord and Lady William Nevill, who entertained a large party on the Derby and Oaks days. The Company comprised the Duke and Duchess of Marlborough, the Duke of Manchester, the Marquess of Abergavenny, the Marchioness of Worcester, Marquis Camdea [?], the Marquis of Waterford, the Marchesa di Serramezzena [?], Donna Flori, Count Palfly, the Earl and Countess of Yarborough, the Earl and Countess Delawarr, Countess Cowley, Lord Sudeley, Lord Suffield, Lady Sandhurst, Lord and Lady Henry Nevill and Miss Nevill, Lord and / Lady George Nevill, Lady Alice Morland, Mr and Lady Violet Brassey, Lady Clementine Walsh, Lady Cicely Gathorne Hardy, and Miss Gathorne Hardy, Hon. Sidney Greville, Hon. F. Stanley, Hon. H. Henniker, Hon. Miriam Thellusson, Hon. R. Molyneux, Hon. Jas. Mansfield, Hon. W. Edwards, Hon. Mrs Oliphant, Sir Edward and Lady Colebrooke, Sir Frederick and Lady Milner, Sir George and Lady Lewis and Miss Lewis, Mr Arnold Morley, Hr and Mrs Henry Labouchere, Mr and Mrs Beerbohm Tree, Mr E. Hatch, [[Social Victorians/People/Arthur Stanley Wilson|Mr and Mrs Wilson]], and Miss Muriel Wilson, Mr Chas. Wyndham, Mr and Mrs Beresford Melville, and Miss Clay, Madame Van André, Mrs Leslie, Mr and Mrs Adrian Hope, Miss Mary Moore, Mr and Mrs George Alexander, Captain Ellison, Captain Peel, Hr H. Spender Clay, Mr George Ellison, Miss Rollit, Mr and Mrs C. Van Raalte, Mr and Mrs Arthur James, Mrs H. V. Higgens, Mr J. B. Leigh, Mr Walter Leslie, Mr and Mrs B. Crawshay, Mr Brinton, Captain Oswald Ames, and many others.&lt;/quote&gt; (1896-06-12 The Courier)

===14 June 1896, Sunday===
Of Mr. Edward W. Bok, &quot;For Sunday next Sir Douglas Straight has invited a party of friends to take the young editor on his private steam-launch for a cruise on the Thames.&quot; &quot;Table Talk,&quot; The Literary World, 12 June 1896, vol. 53, p. 556, col. 2. (Accessed 13 October 2009 in Google Books.)

===15 June 1896, Monday===
The 5 June 1896 ''Literary World'' reports the following: &quot;We understand that Dr. Conan Doyle will preside at the Ladies' dinner of the New Vagabond Club, on the 15th inst., as Mr. Jerome will be absent from London on that date. Eighteen literary ladies have been invited as guests.&quot; (&quot;Table Talk,&quot; The Literary World, 5 June 1896, vol. 53, p. 532, col. 1. [Accessed 13 October 2009 in Google Books].) The 19 June 1896 Literary World goes on at length about the dinner: &quot;The Ladies' Dinner of the New Vagabond Club, held on Monday in the King's Hall, Holborn, was a great success. The most interesting feature was the really able speeches given by the two ladies, Mrs. Burnett Smith (Annie S. Swan) and Mrs. Fenwick Miller, who responded for themselves and their fellow-guests to the toast of their health proposed by Dr. Conan Doyle. If this sort of thing grows, male speakers will soon be at a discount, and no public function will be complete without an oration or two from members of the fair sex. When Mrs. Miller rose to follow Mrs. Burnett Smith in thanking her hosts for their entertainment, the happy thought struck her that it would be as well to observe the strict rule on such occasions; so she desired the other lady guests to stand up while she spoke. This request was complied with, and afforded the audience a better opportunity of distnguishing the special guests of the evening from the larger number who occupied seats at the high table. Their names were, in addition to the two speakers, Mrs. Burton Harrison, Mrs. Flora A. Steel, Mrs. Gertrude Atherton, Mrs. Edith E. Cutbell, Mrs. Andrew Dean, 'George Egerton,' 'Helen Mathers,' Miss Mathilde Blind, and Miss Nora Vynne. / The Vagabonds and their guests could not have been less than 500 in number, and overflowed from the floor of the hall into the galleries. But there was no crowding, and the principal speeches were heard better than is customary at such dinners, probably owing to the eagerness of all to hear, thus preventing the usual under-current of chat. It is impossible to enumerate here all the many literary and otherwise distinguished persons who made up the audience, but it included Sir James Linton, Henniker Heaton, M.P., 'Max O' Rell,' Edward W. Bok, Dr. Moncure D. Conway, Silas K. Hocking, Frankfort Moore, A. W. / [col. 2] a' Beckett, Walter Crane, Oswald Crawford, C.M.G., G. Manville Fenn, Robert Barr, Couldon Kernshan, Dr. Todhunter, Walter Jerrold, W. Morris Colles, D. Havelock Fisher, G. Thompson Hutchinson, and, of course, the vice-chairman, Douglas Sladen and G. B. Burgin, to whom the success of the club is largely due. / ... Dr. Doyle concluded by saying that it would be strange if the New Vagabond Club did not make these ladies welcome, for women had always been noted for being charitable to beggars. / Mrs. Burnett Smth began by remarking that twenty years ago such a meeting as that would have caused a flutter in the breast of Mrs. Grundy. But she was delighted to think that women could thus meet their brothers on equal terms of kindliness and goodwill. Whatever might be said of the 'new woman' movement, it made for good in one direction. A number of old-fashioned ideas about women who write had disappeared. She felt the truth of the quotation: / Woman's cause is man's, / They rise or sink together. / She made an eloquent protest against the old theory that the husband of the literary woman lived in a chronic state of buttonless shirts, undarned socks, and ill-cooked dinners. Her wide experience taught her that wmen writers were conspicuous for their excellent housekeeping. / [Col. 3] Mrs. Fenwick Miller, in her splendidly enunciated little speech, took up the same strain of protest against the prejudiced view of women who write. For herself she was glad to live in this age, as in no previous one had comradeship been so strong. It was possible for a woman to believe that her greatest happiness consisted in the love of one man and the pleasures of one home, and yet to learn to extend her sympathies and so gain more happiness. The world was made for both sexes, and not, as some seemed to imagine, for one.&quot; &quot;Table Talk,&quot; The Literary World, 19 June 1896, vol. 53, p. 581, cols. 1-3. (Accessed 13 October 2009 in Google Books.)

===17 June 1896, Wednesday===
Of Mr. Edward W. Bok: &quot;On Wednesday next he will sail home.&quot; &quot;Table Talk,&quot; The Literary World, 12 June 1896, vol. 53, p. 556, col. 2. (Accessed 13 October 2009 in Google Books.)

===20 June 1896, Saturday===
The 26 June 1896 ''Literary World'' reports the following: &quot;Mr. Clement Shorter, by the way, presided at the gathering of the Omar Khayyám Club at Marlow last Saturday evening. Several prominent writers were present, including 'Maarten Maartens,' Mr. Grant Allen, Mr. J. M. Barrie, Mr. Harold Frederic, Mr. Edmund Gosse, and Mr. George Gissing.&quot; &quot;Table Talk,&quot; The Literary World, 26 June 1896, vol. 53, p. 605, col. 3. (Accessed 14 October 2009 in Google Books.)

===22 June 1896, Monday===
The 26 June 1896 ''Literary World'' reports the following: &quot;Speaking at the Women Writers' Annual Dinner, on Monday last, at the Criterion Restaurant, Mrs. Sydney Webb pleaded for consideration for writers of books which she classed apart from literature, though precisely why dd not transpire. Speaking from her own experience, Mrs. Webb declared that the occupation was a hard one, and that the women who took it up needed all the encouragement presumably that the authors of successful 'Pioneer' and 'Pseudonym' novels could give them. Amongst the speakers were Miss Mary Kingsley, who described the doubtful pleasures of exploring, Miss Clementina Black, and Miss Ella Curtis, who had some serious problems concerning reviewers and reviewing to place before her audience. Others present at the dinner were Mrs. Flora Annie Steel, Mrs. Molesworth, Mrs. Caffyn ('Iota'), Mrs. Sidgwick, 'Helen Mathers,' 'Annie S. Swan,' and Miss Sarah Doudney.&quot; &quot;Table Talk,&quot; The Literary World, 26 June 1896, vol. 53, p. 604, cols. 1-2. (Accessed 14 October 2009 in Google Books.)

===26 June 1896, Friday===
There was apparently a regular celebration of [[Social Victorians/People/Arthur Collins|Arthur Collins]]' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902.

===29 June 1896, Monday===
The 19 June 1896 ''Literary World'' reports the following: &quot;The Authors' Club will entertain Dr. Conan Doyle at dinner at the Club-house on June 29, and Sir Walter Besant will take the chair.&quot; &quot;Table Talk,&quot; The Literary World, 19 June 1896, vol. 53, p. 581, col. 3. (Accessed 13 October 2009 in Google Books.)

[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] was present (among those who “accepted invitations to this function”) at the wedding of Lady Sophie Cadogan and Sir Samuel Scott at Holy Trinity Church, Sloane Street., W., London. The [[Social Victorians/People/Albert Edward, Prince of Wales|Prince]] and [[Social Victorians/People/Alexandra, Princess of Wales|Princess of Wales]] were there, as were “hundreds” from “Society.” The list of notable guests, which includes [[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]] and Muriel Wilson, precedes the groom’s name in the story (1896-06-30 Belfast News-Letter).

Here is the report of the wedding from the ''Morning Post'', with the list of people who attended set as an unordered list to save space and simplify finding people; commas for that list have been silently deleted. The newspaper article made the gift list easy to navigate by using all caps for people's names, so that list is set as it was.&lt;blockquote&gt;MARRIAGE OF SIR SAMUEL SCOTT AND LADY SOPHIE CADOGAN.

Holy Trinity Church, Sloane-street, was filled to its utmost capacity yesterday afternoon, on the occasion of the marriage of Lady Sophie Cadogan, younger daughter of the Lord Lieutenant of Ireland and Countess Cadogan, with Sir Samuel Scott, Bart., Royal Horse Guards. The chancel of the spacious building was beautifully adorned with odontoglossum Alexandrae, white hydrangea, lilium Harrissii, white roses, carnations, azaleas, and ferns, and a variety of palms — Kentias, Seaforthias, and cocos — were arranged on each side and disposed about the choir with excellent taste. The nave was lined by non-commissioned officers and troopers of the bridegroom's regiment in full uniform with cuirasses.

Their Royal Highnesses the Prince and Princess of Wales, accompanied by the Princesses Victoria and Maud, and attended by the Countess of Macclesfield and Major-General Stanley Clarke, arrived shortly before half-past two o'clock, and were shown to seats reserved for them facing the chancel on the bride's side. Their Royal Highnesses the Duke and Duchess of York, who had previously arrived, with Lady Mary Lygon and the Hon. Derek Keppel in waiting, occupied seats on the bridegroom's side, near Sir Horace and Lady Farquhar. His Royal Highness the Duke of Cambridge was also present.

Punctually at half-past two the choir advanced to the west door to receive the bride, while the organist played the Bridal March from &quot;Lohengrin.&quot; Lady Sophie entered the church a few minutes afterwards, accompanied by the Lord Lieutenant. The bridal procession was then formed, and passed up the nave between the ranks of Guardsmen, singing, **0 Jesus, I have promised.&quot; Sir Samuel, who awaited his bride at the chancel steps, was attended by Marquis Camden as best man. The bride wore a trained gown of the richest ivory satin duchesse, handsomely embroidered round the hem in silver and small pearls in a floral design, and finished at the edge with three tiny ruches of chiffon. The bodice had a yoke of narrowly tucked chiffon, bordered with exquisite Brussels lace, from which soft draperies of chiffon inserted with silver and pearl embroidery was drawn into a high satin sash. The transparent sleeves, of drawn chiffon, were finished at the top with bow epaulettes of embroidered satin. Lady Sophie wore a coronet of orange blossoms and a tulle veil. Her lovely bouquet was of rare white orchids intermixed with lilies of the valley. Master Green, nephew of the bridegroom, acted as page, wearing a pale blue satin costume trimmed with lace, the cape lined with white satin. He carried a large white felt hat with blue feathers. Nine bridesmaids followed, Lady Anne Coventry, Lady Helen Craven, and Miss Margaret Van de Weyer, cousins of the bride; Lady Helen Stewart, Lady Isobel Stanley, Lady Kathleen Cole, Miss Bridget Bulkeley, and two little girls, the Hon. Sybil Cadogan, niece of the bride, and the Hon. Victoria Stanley. The elder bridesmaids wore gowns of ivory mousseline-de-soie over kilted glacé silk, the full bodices veiled with deep cream lace lightly embroidered with diamonds, with long lace sleeves and Pompadour sashes fastened on one side with diamond buttons. Their hats were of white fancy straw, draped round the crowns with folds of white tulle, glacé ribbon to match their sashes, and black tulle, with a plume of feathers at the side. The children were in quaint frocks to match the elder ladies, but their picturesque hats were of kilted chiné ribbon, with loops of bébé ribbon and clusters of white feathers. The bridegroom presented each with a gold chain bracelet with turquoise acorn pendant, the cup of which was of diamonds, and a bouquet of pink roses tied with white satin, the children carrying small baskets of pink rosebuds.

The Lord Primate of Ireland performed the nuptial rite, assisted by the Rev. Canon Eyton (late rector of the parish), rector of St. Margaret's, Westminster; the Rev. Henry Bevan, rector of Holy Trinity; the Rev. Gerald Blunt, rector of Chelsea; the Rev. J. J. Roumieu, rector of Culford, Bury St. Edmunds; and the Rev. Edward Symonds, domestic chaplain to Earl Cadogan. The bride was given away by her father. The Service was fully choral, and before the address the hymn, &quot;O perfect life of love,&quot; was sung as an anthem, the solo being taken by a boy soprano. After the Benediction, given by the Archbishop, the choir and congregation sang, &quot;Lead us, Heavenly Father, lead us.&quot; The bride and bridegroom, preceded by the Archbishop of Armagh and clergy, then passed to the vestry to sign the register, Earl Cadogan escorting the Princess of Wales, and the Prince of Wales accompanying Countess Cadogan. Sir Horace Farquhar gave his arm to the Duchess of York, and the Duke of York offered his to Lady Farquhar. A wedding favour of shamrock, white heather, and orange blossom was placed on the seat of each guest. While the registers were being attested a member of the choir sang, &quot;Be thou faithful unto death,&quot; from Mendelssohn's &quot; St. Paul.&quot;

Their Royal Highnesses the Prince and Princess of Wales, the Princesses Victoria and Maud, and the Duke and Duchess of York, with their ladies and gentlemen in waiting, attended the reception afterwards held by Earl and Countess Cadogan at Chelsea House. Those present at the ceremony and reception included

# the Austro-Hungarian Ambassador and Countess Deym and Countess Isabella Deym
# the Brazilian Minister
# Count Koziebrodski
# Princess Pless
# the Duchess of Devonshire
# the Duchess of Manchester
# the Duke and Duchess of Abercorn and Lady Alexandra Hamilton
# the Duke and Duchess of Marlborough
# the Duchess of Buccleuch and the Ladies Scott
# the Duke of Grafton
# the Duke of Manchester
# Sir Horace aud Lady Farquhar
# the Marchioness of Ormonde and Lady Beatrice Butler
# the Marquis and Marchioness of Salisbury
# the Marchioness of Londonderry and Lady Helen Stewart
# the Marchioness of Headfort aud Lady Beatrice Taylour
# the Marchioness of Lansdowne and Lady Beatrice Fitzmaurice
# the Marchioness of Hastings and Miss Olive Chetwynd
# the Archbishop of Armagh and Miss Alexander
# the Earl and Countess of Coventry and Lady Barbara Coventry
# Elizabeth Countess of Wilton and Mr. Pryor
# the Earl of Crewe
# the Earl and Countess of Romney
# the Earl of March
# the Earl and Countess of Kilmorey
# the Earl of Rosse
# Countess Howe and Lady Evelyn Eyre
# the Earl of Clarendon
# the Earl and Countess of Craven
# Evelyn Countess Craven
# the Countess of Lathom and the Ladies Wilbraham
# Countess Grosvenor and Lady Constance Grosvenor
# the Countess of Derby and Lady Isobel Stanley
# Victoria Countess of Yarborough and Mr. Richardson
# the Countess of Ancaster
# Lady Alice Willoughby and Lady Cecelie Goff
# the Countess of Powis
# the Earl of Hardwicke
# the Earl of Listowel and Lady Beatrice Hare
# the Countess of Erne
# the Countess of Enniskillen and Lady Florence Cole
# Georgiana Countess of Dudley
# the Earl of Kimberley
# the Countess of Caledon
# the Countess of Gosford
# the Countess of Huntingdon
# Viscountess Marsham
# Viscount and Viscountess Chelsea
# Viscountess Newport and the Hon. Miss Bridgeman
# Viscountess Helmsley
# Viscount Castlereagh
# Viscountess Coke
# Viscount and Viscountess Deerhurst and Lady Dorothy Coventry
# Viscount and Viscountess Curzon
# Viscount and Viscountess Cross
# the Lord Chancellor of Ireland
# Lord and Lady Lurgan
# Lady Ashbourne and the Hon. Violet Gibson
# Lady Halsbury and the Hon. Evelyn Giffard
# Lord and Lady Glenesk
# Lord and Lady Hastings
# Lord and Lady William Nevill
# Lord and Lady Castletown
# Lady Norreys
# Lady Alice Stanley
# Lady Stratheden
# Lady Arthur Wellesley and Miss Wellesley
# Lady Lucy Hicks-Beach and Miss Hicks-Beach
# Lord and Lady Iveagh
# Lady Barbara Smith
# Lord and Lady Burton and Miss Thorn
# Lord Rowton
# Lord H. Vane-Tempest
# Lady Julia Wombwell and Miss Wombwell
# Lady Aline Beaumont, Lord Charles Montagu
# Lord and Lady Algernon Gordon Lennox
# the Earl of March
# Lady Angela Forbes
# Lord Inchiquin and the Hon. Miss O'Brien
# Lord Berkeley Paget and Miss Paget
# the Hon. Lady and Miss Ridley
# Emily Lady Ampthill
# Lady St. Oswald
# Lady Wolverton
# Lady Musgrave and the Hon. Miss Harbord
# Lady Caroline Gordon Lennox
# Lady De Trafford
# Lady Bulkeley
# Lady Hindlip
# Lady and Miss Forbes
# Lord and Lady Arthur Hill
# Lady Tweedmouth
# Lord and Lady Balfour of Burleigh
# the Dowager Lady Lurgan
# Lady Clementine Walsh
# Lady Jeune and Miss Stanley
# the Hon. Mrs. Maguire
# the Hon. Mrs. Corbett
# the Hon. Mrs. Arthur Cadogan
# the Hon. Mr. and Mrs. Marsham Townshend and Miss Eva Hoare
# the Hon. Mrs. Charles Hay and Miss Hay
# the Hon. Mrs. Charles Cadogan
# the Hon. Mrs. George Campbell
# the Hon. Humphry and Lady Feodore Sturt
# the Hon. Sidney Greville
# Admiral the Hon. John Yorke
# the Hon. Mrs. Algernon Bourke
# the Hon. W. Coventry
# the Hon. C. Brownlow
# the Hon. Otway and Mrs. Cuffe
# the Lord Chief Justice of Ireland and Lady and Miss O'Brien
# the Lord Mayor of Belfast and Mrs. Pirrie
# the Right Hon. G. J. and Mrs. Goschen
# Mr. and Lady Emily Van de Weyer
# Captain and Lady Jane Van Koughnet
# Mr. and Lady Victoria Hamilton
# Captain and Lady Sarah Wilson
# Mr. and Lady Margaret Loder
# Captain the Hon. A. and Mrs. Somerset
# Sir Archibald and Lady Edmonstone
# Sir Albert Rollit, M.P.
# Sir Henry Edwardes
# Mr. Algernon Peel
# Mr. Seymour Corkran
# Sir Charles and Lady Hartopp
# Captain and Mrs. Philip Green
# Baroness and Miss de Brienen
# Mr. and Mrs. Henry White
# Mr. and Mrs. Douglas Gordon
# Colonel and Mrs. Fludyer
# Captain and Mrs. Anstruther Thomson
# Mrs. A. Paget
# Mr. and Mrs. A. Sassoon
# Mr. and Mrs. Arthur Hay
# Mr. and Mrs. W. H. Grenfell
# Mr. Hatch, M.P.
# Mr. and Mrs. Sassoon
# Mr. Horace Cadogan
# Mr. and Mrs. Claud Hay
# Colonel and Miss Crichton
# Mrs. Charrington
# Mrs. James
# Mrs. Cecil Reid and Miss Reid
# Mrs. Arthur Wilson and Miss Wilson
# Mrs. Charles Wilson and Miss Wilson
# Mrs. Molyneux and Miss Dawnay
# Mr. and Mrs. Cornwallis West and Miss West
# Mr. and Mrs. Coles Child
# Mrs. Owen Williams
# Mrs. B. Martin
# Mrs. Prothero
# the Misses Caldwell
# Mrs. Hatford Harter
# Mrs. Henry Villiers
# Mrs. Pease and Miss Pereira
# Mrs. Hwfa Williams
# Mr. and Mrs. F. Sassoon
# Mr. Paley
# Mr. Graham Vivian
# the Misses Montgomery
# Mr. W. Clay
# Mrs. and Miss Ritchie
# Mr. and Mrs. E. Walter Greene and the Misses Greene
# Mr. and Mrs. Helicar and Miss Helicar
# Mrs. Hungerford
# Mrs. Chute. Major and Mrs. de Freville
# Mr. and Mrs. David T. Arnott, Rev. Mr. and the Hon. Mrs. Bevan
# and many others.

The house was beautifully decorated with palms and white flowers, and the Band of the Royal Horse Guards, stationed on the Terrace, played some spirited music during the afternoon. The Royal guests took their departure at four o'clock.

The newly-wedded pair left soon afterwards for Castle Rising Hall, King's Lynn, the seat of Sir Horace Farquhar. [Col. 2c / 3a] Lady Sophie Scott went away in a gown of ivory crêpe de chine, the bodice draped with point d'Alençon, caught with pale malmaisons, the tight-fitting sleeves were of rucked I mousseline-de-soie, and the softly hanging skirt was edged with ruches of mousseline and lace insertion. The bride wore a large white hat covered with white feathers.

The wedding presents were exhibited in the ball-room, and included a large number of costly jewels.

The Prince and Princess of W&lt;small&gt;ALES&lt;/small&gt; presented the bride with a diamond aigrette set with two large turquoises.

The Princesses V&lt;small&gt;ICTORIA&lt;/small&gt; and M&lt;small&gt;AUD&lt;/small&gt; sent her a gold bonnet-pin encrusted with diamonds and a large turquoise.

The Duke and Duchess of Y&lt;small&gt;ORK&lt;/small&gt;'&lt;small&gt;S&lt;/small&gt; gift was a gold parasol handle set round with turquoises and diamonds. 

The Duke and Duchess of F&lt;small&gt;IFE&lt;/small&gt; sent four silver dessert baskets.

The gems given by the B&lt;small&gt;RIDEGROOM&lt;/small&gt; to his bride comprised a superb diamond tiara, a broad diamond collar formed of seven rows of stone, another collar of diamonds and sapphires, a magnificent diamond bracelet, a set of half hoop rings— diamond, ruby, emerald, and sapphire— and a diamond bow brooch.

Sir H&lt;small&gt;ORACE&lt;/small&gt; and Lady F&lt;small&gt;ARQUHAR&lt;/small&gt; gave a valuable parure of sapphires and diamonds, including a coronet, necklace, bracelet, star, &amp;c.

Earl C&lt;small&gt;ADOGAN'S&lt;/small&gt; presents to his daughter were a lovely diamond necklace, formed of five bows, with clustered centres and tassels, terminating with large pear-shaped stones, the bows connected by festoons of smaller diamonds; and a magnificent bracelet of emeralds and diamonds  Countess C&lt;small&gt;ADOGAN&lt;/small&gt; gave her a sapphire and diamond bracelet. Lady L&lt;small&gt;URGAN'S&lt;/small&gt; gifts were a diamond butterfly and gold curb bracelet; Viscount C&lt;small&gt;HELSEA&lt;/small&gt;, gold-mounted dressing case; the Hons. G&lt;small&gt;ERALD&lt;/small&gt;, L&lt;small&gt;EWIN&lt;/small&gt;, W&lt;small&gt;ILLIAM&lt;/small&gt;, E&lt;small&gt;DWARD&lt;/small&gt;, and A&lt;small&gt;LEXANDER&lt;/small&gt; C&lt;small&gt;ADOGAN&lt;/small&gt;, diamond locket with crystal centre; Viscountess C&lt;small&gt;HELSEA&lt;/small&gt;, a chain bracelet with turquoise and diamond drop; Lord L&lt;small&gt;URGAN&lt;/small&gt;, gold-mounted dressing bag.   

The other gifts to the bride included:— From Princess A&lt;small&gt;DOLPHUS&lt;/small&gt; of T&lt;small&gt;ECK&lt;/small&gt;, stick with tortoiseshell and gold handle; Prince and Princess E&lt;small&gt;DWARD&lt;/small&gt; of S&lt;small&gt;AXE&lt;/small&gt;-W&lt;small&gt;EIMAR&lt;/small&gt;, a hand-painted photograph screen; Prince and Princess H&lt;small&gt;ENRY&lt;/small&gt; of P&lt;small&gt;LESS&lt;/small&gt;, large white ostrich feather fan; the Marquis and Marchioness of S&lt;small&gt;ALISBURY&lt;/small&gt;, pink enamel pendant watch, set round with pearls, and attached to an enamel bow; the Duke of M&lt;small&gt;ANCHESTER&lt;/small&gt;, diamond and sapphire combs; the Marquis and Marchioness of L&lt;small&gt;ONDONDERRY&lt;/small&gt;, diamond and turquoise bracelet; the Marquis and Marchioness of Z&lt;small&gt;ETLAND&lt;/small&gt;, turquoise and diamond shamrock brooch; the Earl and Countess of C&lt;small&gt;OVENTRY&lt;/small&gt;, green enamel and pearl bracelet; the Earl and Countess of D&lt;small&gt;ERBY&lt;/small&gt;, bracelet composed of large pearls and diamonds alternately, with pendant heart encrusted with diamonds; the Lord Lieutenant's A&lt;small&gt;IDES&lt;/small&gt;-&lt;small&gt;DE&lt;/small&gt;-C&lt;small&gt;AMP&lt;/small&gt;, inkstand, blotter, and envelope case in tortoiseshell and silver; the Earl of D&lt;small&gt;URHAM&lt;/small&gt;, ruby, diamond, and pearl shamrock brooch; the Earl of R&lt;small&gt;OSEBERY&lt;/small&gt;, massive silver-mounted mirror; the Right Hon. A. J. B&lt;small&gt;ALFOUR&lt;/small&gt;, pair of silver-mounted toilet bottles; G&lt;small&gt;EORGINA&lt;/small&gt; Countess of D&lt;small&gt;UDLEY&lt;/small&gt;, a pearl and diamond bracelet; Lord and Lady R&lt;small&gt;OTHSCHILD&lt;/small&gt;, a lace fan set with monogram in diamonds; the Earl of C&lt;small&gt;HESTERFIELD&lt;/small&gt;, a table; the Earl and Countess B&lt;small&gt;ATHURST&lt;/small&gt;, an enamel watch; the Earl and Countess of L&lt;small&gt;ATHOM&lt;/small&gt;, jewelled hat pin; the Duchess of S&lt;small&gt;UTHERLAND&lt;/small&gt;, a silver hunting flask; the Earl and Countess of C&lt;small&gt;RAVEN&lt;/small&gt;, a silver looking-glass; the Earl of S&lt;small&gt;UFFOLK&lt;/small&gt;, an armchair; the Earl and Countess of A&lt;small&gt;NCASTER&lt;/small&gt;, a silver bowl; the Countess of M&lt;small&gt;ACCLESFIELD&lt;/small&gt;, a Dresden china coffee set; the Duke and Duchess of W&lt;small&gt;ESTMINSTER&lt;/small&gt;, a screen; the Earl of C&lt;small&gt;LARENDON&lt;/small&gt;, a pair of cut glass and silver perfume bottles; the Earl and Countess of C&lt;small&gt;ALEDON&lt;/small&gt;, a silver bowl; the Earl and Countess of E&lt;small&gt;RNE&lt;/small&gt;, a clock; the Earl and Countess of D&lt;small&gt;ALKEITH&lt;/small&gt;, a pair of silver candlesticks; the Dowager Countess of C&lt;small&gt;RAVEN&lt;/small&gt;, a silver tea set; Sir W&lt;small&gt;ILLIAM&lt;/small&gt; and Lady K&lt;small&gt;AYE&lt;/small&gt;, a marble-topped writing table; Mr. A&lt;small&gt;LFORD&lt;/small&gt;, a table; Sir P&lt;small&gt;ETER&lt;/small&gt; and Lady O'B&lt;small&gt;RIEN&lt;/small&gt;, hunting crop; Lord H&lt;small&gt;ERBERT&lt;/small&gt; V&lt;small&gt;ANE&lt;/small&gt;-T&lt;small&gt;EMPEST&lt;/small&gt;, tortoiseshell boxes; Mr. and Mrs. A. S&lt;small&gt;ASSOON&lt;/small&gt;, a diamond bow brooch; Lady M&lt;small&gt;USGRAVE&lt;/small&gt;, a diamond wing brooch; Lord and Lady A&lt;small&gt;RTHUR&lt;/small&gt; H&lt;small&gt;ILL&lt;/small&gt;, a bezique table; the L&lt;small&gt;ORD&lt;/small&gt; C&lt;small&gt;HANCELLOR&lt;/small&gt; of I&lt;small&gt;RELAND&lt;/small&gt; and Lady A&lt;small&gt;SHBOURNE&lt;/small&gt;, a silver cup; Baroness H&lt;small&gt;IRSCH&lt;/small&gt;, jewelled fly; Viscount and Viscountess C&lt;small&gt;ASTLEROSSE&lt;/small&gt;, a jewelled brooch; Lord and Lady L&lt;small&gt;ANGFORD&lt;/small&gt;, a gold curb bracelet set with sapphires and diamonds; the Earl and Countess of A&lt;small&gt;RRAN&lt;/small&gt;, a pair of links; the Countess of G&lt;small&gt;OSFORD&lt;/small&gt;, a muff chain; the Earl and Countess of E&lt;small&gt;SSEX&lt;/small&gt;, a handsome screen; Lord and Lady T&lt;small&gt;WEEDMOUTH&lt;/small&gt;, a gold and diamond heart-shaped smelling-bottle; the Right Hon. G&lt;small&gt;ERALD&lt;/small&gt; and Lady B&lt;small&gt;ETTY&lt;/small&gt; B&lt;small&gt;ALFOUR&lt;/small&gt;, set of enamelled buttons; the Ladies D&lt;small&gt;OROTHY&lt;/small&gt; and A&lt;small&gt;NNE&lt;/small&gt; C&lt;small&gt;OVENTRY&lt;/small&gt;, a diamond buckle; Lady C&lt;small&gt;ONSTANCE&lt;/small&gt; G&lt;small&gt;ROSVENOR&lt;/small&gt;, two jewelled pins; Mr. G&lt;small&gt;EORGE&lt;/small&gt; C&lt;small&gt;ORNWALLIS&lt;/small&gt; W&lt;small&gt;EST&lt;/small&gt;, a jewelled handle for parasol; Mr. P&lt;small&gt;RYOR&lt;/small&gt; and the Countess of W&lt;small&gt;ILTON&lt;/small&gt;, a miniature snuff-box; Mr. and Mrs. B&lt;small&gt;RADLEY&lt;/small&gt; M&lt;small&gt;ARTIN&lt;/small&gt;, a gold chain purse set with sapphires and diamonds; Lady H&lt;small&gt;ELEN&lt;/small&gt; S&lt;small&gt;TEWART&lt;/small&gt; and Lord C&lt;small&gt;ASTLEREAGH&lt;/small&gt;, a gold and glass scent-bottle set with pearls and diamonds; Mr. C&lt;small&gt;YRIL&lt;/small&gt; F&lt;small&gt;OLEY&lt;/small&gt;, a gold, diamond, and turquoise brooch; Miss B&lt;small&gt;LANCHE&lt;/small&gt; F&lt;small&gt;ORBES&lt;/small&gt;, a gold and diamond pin; Captain D&lt;small&gt;UNDAS&lt;/small&gt;, gold case set with diamonds and turquoises; the Duke and Duchess of D&lt;small&gt;EVONSHIRE&lt;/small&gt;, a diamond and ruby safety-pin; Lady W&lt;small&gt;OLVERTON&lt;/small&gt;, a pearl and diamond brooch; Mr. A&lt;small&gt;LFRED&lt;/small&gt; de R&lt;small&gt;OTHSCHILD&lt;/small&gt;, a diamond and ruby double horse-shoe brooch; Lord and Lady A&lt;small&gt;LICE&lt;/small&gt; S&lt;small&gt;TANLEY&lt;/small&gt;, a diamond and enamelled hat-pin; Colonel and Mrs. A&lt;small&gt;RTHUR&lt;/small&gt; P&lt;small&gt;AGET&lt;/small&gt;, a ruby and diamond bracelet; the Earl of C&lt;small&gt;REWE&lt;/small&gt;, a pearl half-hoop bracelet; the Knight of K&lt;small&gt;ERRY&lt;/small&gt; and Lady F&lt;small&gt;ITZGERALD&lt;/small&gt;, a silver scent-bottle; Viscount and Viscountess D&lt;small&gt;EERHURST&lt;/small&gt;, a fan; Lady Victoria H&lt;small&gt;AMILTON&lt;/small&gt;, a pair of silver baskets; the Hon. C&lt;small&gt;HARLES&lt;/small&gt; C&lt;small&gt;OVENTRY&lt;/small&gt;, a torquoise brooch; Viscountess C&lt;small&gt;URZON&lt;/small&gt;, a silver box; Mr. A&lt;small&gt;RTHUR&lt;/small&gt; V&lt;small&gt;ICARS&lt;/small&gt;, a hunting horn and kettle extinguisher; Mrs. C&lt;small&gt;AVENDISH&lt;/small&gt; B&lt;small&gt;ENTINCK&lt;/small&gt;, a watch; Mr. and Lady E&lt;small&gt;MILY&lt;/small&gt; V&lt;small&gt;AN DE&lt;/small&gt; W&lt;small&gt;EYER&lt;/small&gt;, an inlaid writing-desk and table; Lord and Lady B&lt;small&gt;URTON&lt;/small&gt;, a silver bowl; Mr. and Mrs. L&lt;small&gt;EOPOLD DE&lt;/small&gt; R&lt;small&gt;OTHSCHILD&lt;/small&gt;, a diamond comb for the hair: Mr. E&lt;small&gt;DWARD&lt;/small&gt; P&lt;small&gt;ACKE&lt;/small&gt;, a diamond heart-shaped locket on chain: Mr. and Mrs. F. S&lt;small&gt;ASSOON&lt;/small&gt;, six silver shell-shaped salt cellars; Mr. and Lady B&lt;small&gt;ETTY&lt;/small&gt; B&lt;small&gt;ALFOUR&lt;/small&gt;, a pair of links; Mr. C&lt;small&gt;HARLES&lt;/small&gt; B&lt;small&gt;ALFOUR&lt;/small&gt;, set of enamelled pins; the Hon. L&lt;small&gt;EWIN&lt;/small&gt; C&lt;small&gt;ADOGAN&lt;/small&gt;, a scent bottle and Prayer-book; the Hon. A&lt;small&gt;LEXANDER&lt;/small&gt; P&lt;small&gt;ARKER&lt;/small&gt;, a driving whip; Lady H&lt;small&gt;ELEN&lt;/small&gt; C&lt;small&gt;RAVEN&lt;/small&gt;, a silver pepper castor; Viscountess M&lt;small&gt;ARSHAM&lt;/small&gt; and Mrs. P. G&lt;small&gt;REEN&lt;/small&gt;, a fishing rod; Colonel and Mrs. C&lt;small&gt;ORNWALLIS&lt;/small&gt; W&lt;small&gt;EST&lt;/small&gt;, a parasol; Mr. and Mrs. C&lt;small&gt;HARLES&lt;/small&gt; W&lt;small&gt;ILSON&lt;/small&gt;, a gold necklace with diamond and turquoise drops; Mr. A. S&lt;small&gt;PIERS&lt;/small&gt; and Lady A&lt;small&gt;NNE&lt;/small&gt; S&lt;small&gt;PIERS&lt;/small&gt;, a pair of silver lyre candlesticks; Lord A&lt;small&gt;LEXANDER&lt;/small&gt; P&lt;small&gt;AGET&lt;/small&gt;, a gold-topped toilet bottle; Mrs. P&lt;small&gt;ALEY&lt;/small&gt;, a silver inkstand; the Countess of E&lt;small&gt;NNISKILLEN&lt;/small&gt;, a tortoiseshell and gold toilet bottle; Mr. J&lt;small&gt;AMES&lt;/small&gt; M&lt;small&gt;ANSFIELD&lt;/small&gt;, a silver snuff box; Miss K&lt;small&gt;ATHLEEN&lt;/small&gt; S&lt;small&gt;COTT&lt;/small&gt;, silver bonbon tray; Sir F&lt;small&gt;RANCIS&lt;/small&gt; and Lady J&lt;small&gt;EUNE&lt;/small&gt;, a tortoiseshell pen tray with silver figure; Mr. A&lt;small&gt;RTHUR&lt;/small&gt; P&lt;small&gt;ALEY&lt;/small&gt;, a silver powder puff box; Lord R&lt;small&gt;OWTON&lt;/small&gt;, an old silver flask; E&lt;small&gt;MILY&lt;/small&gt; Lady A&lt;small&gt;MPTHILL&lt;/small&gt;, a tortoiseshell and silver-mounted clock; Viscount B&lt;small&gt;RACKLEY&lt;/small&gt;, a glass specimen case; Mr. and Mrs F. S&lt;small&gt;ANDFORD&lt;/small&gt;, an old French ormolu clock; Mr. O&lt;small&gt;SBERT&lt;/small&gt; C&lt;small&gt;RAVEN&lt;/small&gt;, a carriage clock; the R&lt;small&gt;ECORDER&lt;/small&gt; of D&lt;small&gt;UBLIN&lt;/small&gt;, a fine old Irish lace collar; the S&lt;small&gt;OLICITOR&lt;/small&gt;-G&lt;small&gt;ENERAL&lt;/small&gt; of I&lt;small&gt;RELAND&lt;/small&gt; and Mrs. K&lt;small&gt;ENNY&lt;/small&gt;, an antique silver clock; Miss C&lt;small&gt;LARE&lt;/small&gt; O'B&lt;small&gt;RIEN&lt;/small&gt;, a silver stamp-box; Lord H&lt;small&gt;ENRY&lt;/small&gt; V&lt;small&gt;ANE&lt;/small&gt;-T&lt;small&gt;EMPEST&lt;/small&gt;, a silver-mounted writing set, with pair of silver candlesticks; the Rev. G. B&lt;small&gt;LUNT&lt;/small&gt;, two silver muffineers; Mrs. J&lt;small&gt;OHN&lt;/small&gt; W&lt;small&gt;OODFORD&lt;/small&gt;, Venetian glass toilet bottle; Lord and Lady B&lt;small&gt;URTON&lt;/small&gt;, a silver-gilt bowl with cover; Mr. C&lt;small&gt;LAUDE&lt;/small&gt; Y&lt;small&gt;ORKE&lt;/small&gt;, two silver-mounted photo frames; Mr. and Mrs. J. B. D&lt;small&gt;OUGHETY&lt;/small&gt;, a large silver and glass toilet bottle; the L&lt;small&gt;ORD&lt;/small&gt; M&lt;small&gt;AYOR&lt;/small&gt; of B&lt;small&gt;ELFAST&lt;/small&gt; and Mrs. P&lt;small&gt;IRRIE&lt;/small&gt;, a beautiful Irish embroidered handkerchief; Lady H&lt;small&gt;INDLlP&lt;/small&gt;, worktable requisites in crystal casket; M&lt;small&gt;EMBERS&lt;/small&gt; of the I&lt;small&gt;RISH&lt;/small&gt; I&lt;small&gt;NDUSTRIAL&lt;/small&gt; S&lt;small&gt;OCIETY&lt;/small&gt;, beautiful lace handkerchiefs; Mrs. O&lt;small&gt;PPENHEIM&lt;/small&gt;, a silver-gilt mounted blotting book; L&lt;small&gt;ILY&lt;/small&gt; Duchess of M&lt;small&gt;ARLBOROUGH&lt;/small&gt; and Lord W&lt;small&gt;ILLIAM&lt;/small&gt; B&lt;small&gt;ERESFORD&lt;/small&gt;, four tall silver candlesticks; Colonel and Mrs. F&lt;small&gt;LUDYER&lt;/small&gt;, a silver-gilt and glass toilet bottle; Mr. and Lady B&lt;small&gt;ARBARA&lt;/small&gt; S&lt;small&gt;MITH&lt;/small&gt;, an antique covered silver tankard; Mr. B&lt;small&gt;ATES&lt;/small&gt; V&lt;small&gt;AN DE&lt;/small&gt; W&lt;small&gt;EYER&lt;/small&gt;, four silver bonbon baskets; the Marchioness of H&lt;small&gt;ASTINGS&lt;/small&gt;, a silver-mounted photo frame; Miss C&lt;small&gt;HEYWYND&lt;/small&gt;, a silver heart-shaped box; Colonel F&lt;small&gt;ORESTER&lt;/small&gt;, two silver dessert baskets; Mr. and Mrs. A&lt;small&gt;RTHU&lt;/small&gt;R L&lt;small&gt;IDDELL&lt;/small&gt;, an antique silver box; Lord and Lady A&lt;small&gt;MPTHILL&lt;/small&gt;, sealing-wax holder and seal; Lady C&lt;small&gt;AROLINE&lt;/small&gt; G&lt;small&gt;ORDON&lt;/small&gt;-L&lt;small&gt;ENNOX&lt;/small&gt;, a painted glass flower vase; Miss F&lt;small&gt;ARQUHARSON&lt;/small&gt; and Miss E&lt;small&gt;LO&lt;/small&gt; F&lt;small&gt;ARQUHARSON&lt;/small&gt;, a china parrot; Mr. C&lt;small&gt;ECIL&lt;/small&gt; C&lt;small&gt;ADOGAN&lt;/small&gt;, a carriage clock; E&lt;small&gt;VELYN&lt;/small&gt; Countess of C&lt;small&gt;RAVEN&lt;/small&gt;, an old silver box; Mr. A&lt;small&gt;LFRED&lt;/small&gt; O&lt;small&gt;PPENHEIM&lt;/small&gt;, a French gilt clock; [[Social Victorians/People/Muriel Wilson|Miss M&lt;small&gt;URIEL&lt;/small&gt; W&lt;small&gt;ILSON&lt;/small&gt;]], books (7 vols.); Lady B&lt;small&gt;ULKELEY&lt;/small&gt;, a pair of old china ornaments; Lord and Lady I&lt;small&gt;VEAGH&lt;/small&gt;, a Russian table clock mounted in gold and enamel; Lady E&lt;small&gt;DITH&lt;/small&gt; F&lt;small&gt;RANKLIN&lt;/small&gt;, a silver-mounted toilet bottle; Miss A&lt;small&gt;GAR&lt;/small&gt;, a pocket Prayer-book in case; Mr. F&lt;small&gt;RANK&lt;/small&gt; M&lt;small&gt;ILDMAY&lt;/small&gt;, a silver carriage clock; Mr. and Mrs. E&lt;small&gt;WAN&lt;/small&gt; N&lt;small&gt;EPEAN&lt;/small&gt;, a small silver sauce boat; Miss W&lt;small&gt;ILSON&lt;/small&gt;, book-markers; Mr. J. B. L&lt;small&gt;EIGH&lt;/small&gt;, a basket pincushion; Mr. and the Hon. Mrs. B&lt;small&gt;AILLIE&lt;/small&gt; of Dochfour, a pair of china parrots; General and Mrs. O&lt;small&gt;WEN&lt;/small&gt; W&lt;small&gt;ILLIAMS&lt;/small&gt;, a Chinese figure; Mr. T&lt;small&gt;HOMAS&lt;/small&gt; B&lt;small&gt;ARING&lt;/small&gt;, four china figures; Mr. and Lady V&lt;small&gt;IOLET&lt;/small&gt; B&lt;small&gt;RASSEY&lt;/small&gt;, an inlaid tortoiseshell box; the Hon. Mrs. C&lt;small&gt;ORBETT&lt;/small&gt;, a tortoiseshell purse; Lady E&lt;small&gt;VELYN&lt;/small&gt; C&lt;small&gt;OTTERELL&lt;/small&gt;, a hand-painted glass bowl; the Hon. A&lt;small&gt;RTHUR&lt;/small&gt; and Mrs. C&lt;small&gt;ADOGAN&lt;/small&gt;, a pair of silver candlesticks; Miss M&lt;small&gt;ARGARET&lt;/small&gt; V&lt;small&gt;AN DE&lt;/small&gt; W&lt;small&gt;EYER&lt;/small&gt;, a silver pen and pencil in case; Mr. R&lt;small&gt;AYMOND&lt;/small&gt; G&lt;small&gt;REER&lt;/small&gt;, six turquoise and gold buttons; Lady l&lt;small&gt;SOBEL&lt;/small&gt; S&lt;small&gt;TANLEY&lt;/small&gt;, green and gold etui case; the Dowager Lady L&lt;small&gt;URGAN&lt;/small&gt;, a pair of silver fruit dishes; Chevalier &lt;small&gt;DE&lt;/small&gt; S&lt;small&gt;OUZA&lt;/small&gt; C&lt;small&gt;ORREA&lt;/small&gt;, inlaid box; Mr. W&lt;small&gt;ILLIAM&lt;/small&gt; Y&lt;small&gt;OUNG&lt;/small&gt;, four silver salt-cellars; Lord A&lt;small&gt;NNALY&lt;/small&gt;, a round silver clock; Viscountess H&lt;small&gt;OOD&lt;/small&gt;, an antique painting in oval frame; Mr. and Mrs. L&lt;small&gt;AUNCELOT&lt;/small&gt; L&lt;small&gt;OWTHER&lt;/small&gt;, an old two-handled silver cup; Hon. Mrs. G&lt;small&gt;ERVASE&lt;/small&gt; B&lt;small&gt;ECKETT&lt;/small&gt;, writing table clock in silver-mounted case; V&lt;small&gt;ICTORIA&lt;/small&gt; Countess of Y&lt;small&gt;ARBOROUGH&lt;/small&gt;, a silver-mounted mirror; Miss E&lt;small&gt;NID&lt;/small&gt; W&lt;small&gt;ILSON&lt;/small&gt;, green photo frame; Mr. H&lt;small&gt;ORACE&lt;/small&gt; C&lt;small&gt;ADOGAN&lt;/small&gt;, gold and coral mounted scent-bottle; Countess D&lt;small&gt;EYM&lt;/small&gt;, a small silver coffee pot; Mr. and Mrs. M&lt;small&gt;ARSHAM&lt;/small&gt; T&lt;small&gt;OWNSHEND,&lt;/small&gt; a silver-mounted magnifying glass; Colonel O&lt;small&gt;LIPHANT&lt;/small&gt;, an oval enamelled box; Lady H&lt;small&gt;ELEN&lt;/small&gt; C&lt;small&gt;RAVEN&lt;/small&gt;, a silver saucepan; the Earl and Countess of R&lt;small&gt;OSSE&lt;/small&gt;, a large enamelled casket; the M&lt;small&gt;ANAGER&lt;/small&gt; of the R&lt;small&gt;OYAL&lt;/small&gt; I&lt;small&gt;RISH&lt;/small&gt; S&lt;small&gt;CHOOL&lt;/small&gt; of A&lt;small&gt;RT&lt;/small&gt; N&lt;small&gt;EEDLEWORK&lt;/small&gt;, two beautifully worked covers; Lady M. C&lt;small&gt;RICHTON&lt;/small&gt;-M&lt;small&gt;AITLAND&lt;/small&gt; and Miss C&lt;small&gt;RICHTON&lt;/small&gt;-M&lt;small&gt;AITLAND&lt;/small&gt;, a pair of silver and glass bottles; Major and the Hon. Mrs. S&lt;small&gt;TIRLING&lt;/small&gt;, a pair of silver piano candlesticks; Mr. H&lt;small&gt;ENRY&lt;/small&gt; P&lt;small&gt;ARKER&lt;/small&gt;, a chased silver toilet box; Countess H&lt;small&gt;OWE&lt;/small&gt;, a tortoiseshell letter rack; Miss T&lt;small&gt;HORNHILL&lt;/small&gt;, an enamelled box; Mr. R. C&lt;small&gt;RAVE&lt;/small&gt;N, a coin-handled paper knife; Lady S&lt;small&gt;YKES&lt;/small&gt;, an antique brass and marble inkstand; the Marquis and Marchioness of BATH, a silver card tray; Vicount N&lt;small&gt;EWPORT&lt;/small&gt;, a silver heart-shaped stamp box; Mr. A&lt;small&gt;LGERNON&lt;/small&gt; P&lt;small&gt;EEL&lt;/small&gt;, silver and tortoiseshell paper knife in pink shagreen case; Mr. C&lt;small&gt;ORKRAN&lt;/small&gt;, a pair of tortoise-shell and silver-mounted candlesticks; Sir W&lt;small&gt;ILLIAM&lt;/small&gt; E&lt;small&gt;DEN&lt;/small&gt;, an antique enamelled bracelet; [[Social Victorians/People/Holden|Mr. H&lt;small&gt;ENRY&lt;/small&gt; H&lt;small&gt;OLDEN&lt;/small&gt;]], a shamrock photo frame; the G&lt;small&gt;IRLS'&lt;/small&gt; F&lt;small&gt;RIENDLY&lt;/small&gt; S&lt;small&gt;OCIETY'S&lt;/small&gt; C&lt;small&gt;HELSEA&lt;/small&gt; C&lt;small&gt;LUB&lt;/small&gt;, a pair of silver fruit baskets; the Earl of M&lt;small&gt;ARCH&lt;/small&gt;, a silver-mounted leather casket; Lady Margaret L&lt;small&gt;ODER&lt;/small&gt;, a silver cream jug and sugar basin; the Duke and Duchess of A&lt;small&gt;BERCORN&lt;/small&gt;, Japanese box for counters; Mr. O&lt;small&gt;TWA&lt;/small&gt;Y C&lt;small&gt;UFFE&lt;/small&gt;, an antique silver box; the Countess P&lt;small&gt;OWIS&lt;/small&gt;, a silver-gilt photo frame; Lady R&lt;small&gt;IDLEY&lt;/small&gt;, a set of antique paste buttons: Mrs. N&lt;small&gt;ORTON&lt;/small&gt;, a silver stamp case and porte-monnaie; Mr.C. D&lt;small&gt;ALISON&lt;/small&gt;, a silver pin tray; Earl and Countess C&lt;small&gt;ADOGAN'S&lt;/small&gt; H&lt;small&gt;OUSEHOLD&lt;/small&gt;, silver inkstand and candlestick; Mr. W. C&lt;small&gt;OVENTRY&lt;/small&gt;, a card table; the WOMEN on the C&lt;small&gt;ULFORD&lt;/small&gt; E&lt;small&gt;STATE&lt;/small&gt;, a silver wine cooler; the G&lt;small&gt;AMEKEEPERS&lt;/small&gt; on the C&lt;small&gt;ULFORD&lt;/small&gt; E&lt;small&gt;STATE&lt;/small&gt;, a sporting seat; Mr. and Mrs. W&lt;small&gt;HEELER&lt;/small&gt;, a wine bin; the Earl and Countess of W&lt;small&gt;ESTMORLAND,&lt;/small&gt; a silver-mounted stick; Captain F&lt;small&gt;EILDEN&lt;/small&gt;, umbrella, with pencil; Viscount and Viscountess F&lt;small&gt;OLKESTONE&lt;/small&gt;, a parasol; Lord and Lady A&lt;small&gt;LGERNON&lt;/small&gt; G&lt;small&gt;ORDON&lt;/small&gt;-L&lt;small&gt;ENNOX&lt;/small&gt;, an umbrella; Sir C&lt;small&gt;HARLES&lt;/small&gt; and Lady H&lt;small&gt;ARTOPP&lt;/small&gt;, an umbrella; Viscountess H&lt;small&gt;ELMSLEY&lt;/small&gt;, an umbrella; Colonel and Mrs. C&lt;small&gt;ORNWALLIS&lt;/small&gt; W&lt;small&gt;EST&lt;/small&gt;, an umbrella; the Marchioness of H&lt;small&gt;EADFORT,&lt;/small&gt; a gold-handled umbrella; Lord and Lady G&lt;small&gt;ERARD&lt;/small&gt;, a pale blue silk and gold-handled sunshade; Mr. and Mrs P&lt;small&gt;ERCY&lt;/small&gt; W&lt;small&gt;YNDHAM&lt;/small&gt;, old white and gold china tea set; the P&lt;small&gt;EOPLE&lt;/small&gt; of N&lt;small&gt;ORHT&lt;/small&gt; [sic] H&lt;small&gt;ARRIS&lt;/small&gt;, a length of Harris tweed; Sir R and Lady M. B&lt;small&gt;ULKELEY&lt;/small&gt;, a bookstand; Mrs. W. L&lt;small&gt;AWSON&lt;/small&gt;, a hand-painted fan; Viscount and Viscountess D&lt;small&gt;EERHURST&lt;/small&gt;, a fan; Captain and Lady S&lt;small&gt;ARAH&lt;/small&gt; W&lt;small&gt;ILSON&lt;/small&gt;, a natural ostrich feather fan; Lord and Lady G&lt;small&gt;LENESK&lt;/small&gt;, a fan; the Earl of S&lt;small&gt;EFTON&lt;/small&gt;, a marqueterie and ormolu [Col. 3c / 4a] table; Miss N&lt;small&gt;AYLOR&lt;/small&gt;, an old hand-painted fan; Miss &lt;small&gt;DE&lt;/small&gt; B&lt;small&gt;RIENEN&lt;/small&gt; and Miss Daisy &lt;small&gt;DE&lt;/small&gt; B&lt;small&gt;RIENEN&lt;/small&gt;, an old jewelled fan; Mr. H&lt;small&gt;ORACE&lt;/small&gt; P&lt;small&gt;LUNKETT&lt;/small&gt;, a fan; Mr. O&lt;small&gt;LIPHANT&lt;/small&gt;, an oval glass-topped table; Mr. G&lt;small&gt;RIMSTON&lt;/small&gt;, four silver bonbon dishes in case; the Earl and Countess of L&lt;small&gt;ISTOWEL&lt;/small&gt;, a small table; the Earl and Countess of K&lt;small&gt;ILMOREY&lt;/small&gt;, a green leather revolving bookcase; Lord and Lady A&lt;small&gt;RTHUR&lt;/small&gt; H&lt;small&gt;ILL&lt;/small&gt;, a card table; the Earl of H&lt;small&gt;AREWOOD&lt;/small&gt;, a green blotter and letter case; Lord N&lt;small&gt;ORREYS&lt;/small&gt;, two silver ice pails; [[Social Victorians/People/Arthur Stanley Wilson|Mrs. A&lt;small&gt;RTHUR&lt;/small&gt; W&lt;small&gt;ILSON&lt;/small&gt;]], an embroidered footstool; the C&lt;small&gt;HELSEA&lt;/small&gt; G&lt;small&gt;IRLS'&lt;/small&gt; C&lt;small&gt;LUB&lt;/small&gt;, an embroidered afternoon teacloth; Lady A&lt;small&gt;SHBURTON&lt;/small&gt; and Miss B&lt;small&gt;RASSEY&lt;/small&gt;, an ormulu and marble- topped table; Viscountess D&lt;small&gt;OWNE&lt;/small&gt;, an inlaid Indian stool; the Countess of P&lt;small&gt;ORTARLINGTON&lt;/small&gt;, a green leather bag; Mrs. C&lt;small&gt;HAINE&lt;/small&gt;, a set of pale blue enamelled and gold spoons; Mr. and Mrs. D. C&lt;small&gt;OOPER&lt;/small&gt;, four silver bottle stands; the Rev. E. S&lt;small&gt;YMONDS&lt;/small&gt;, books; Lady H&lt;small&gt;ONORIA&lt;/small&gt; C&lt;small&gt;ADOGAN&lt;/small&gt;, a Prayer-book and salts-bottle; Mr. and Mrs. W&lt;small&gt;ALTER&lt;/small&gt; G&lt;small&gt;REEN&lt;/small&gt;, silver basin; Mr. and Mrs. B&lt;small&gt;ONYNGE&lt;/small&gt;, an embroidered blotter; the M&lt;small&gt;OTHERS'&lt;/small&gt; U&lt;small&gt;NION&lt;/small&gt;, a pair of silver-gilt midget photo frames; the Earl and Countess of H&lt;small&gt;UNTINGDON&lt;/small&gt;, china and silver tea set; Miss V&lt;small&gt;AN DE&lt;/small&gt; W&lt;small&gt;EYER&lt;/small&gt;, silver photo screen; Lady M&lt;small&gt;URIEL&lt;/small&gt; P&lt;small&gt;ARSONS&lt;/small&gt;, antique silver ornament; Mrs. C&lt;small&gt;HARLES&lt;/small&gt; C&lt;small&gt;ADOGAN&lt;/small&gt;, a silver box; Miss K. G&lt;small&gt;REENE&lt;/small&gt;, book in worked cover; Sir C&lt;small&gt;HARLES&lt;/small&gt; H&lt;small&gt;ALL&lt;/small&gt;, set of antique silver ornaments; Lady C&lt;small&gt;OLEBROOKE&lt;/small&gt;, six diamond and enamel buttons; Lord and Lady S&lt;small&gt;ETTRINGTON&lt;/small&gt;, silver pincushion; Mr. J&lt;small&gt;AMES&lt;/small&gt; L&lt;small&gt;OWTHER&lt;/small&gt;, silver bell; Miss E&lt;small&gt;VA&lt;/small&gt; H&lt;small&gt;OARE,&lt;/small&gt; silver bird; Captain and Lady J&lt;small&gt;ANE&lt;/small&gt; V&lt;small&gt;AN&lt;/small&gt; K&lt;small&gt;AUGHNET&lt;/small&gt;, two silver baskets; Miss T&lt;small&gt;HORNEWILL&lt;/small&gt; and Miss J&lt;small&gt;ANE&lt;/small&gt; T&lt;small&gt;HORNEWILL&lt;/small&gt;, large silver bowl; Mrs. C&lt;small&gt;ECIL&lt;/small&gt; R&lt;small&gt;EID&lt;/small&gt;, a silver paper knife; Mr. C&lt;small&gt;ARYL&lt;/small&gt; C&lt;small&gt;RAVEN&lt;/small&gt;, a turquoise and gold bangle; the Hon. J. and Mrs. Y&lt;small&gt;ORKE&lt;/small&gt;, pearl and gold bar brooch: Major and Mrs. &lt;small&gt;DE&lt;/small&gt; T&lt;small&gt;RAVILLE&lt;/small&gt;, a gold fox brooch; Sir H&lt;small&gt;ENRY&lt;/small&gt; E&lt;small&gt;DWARDS&lt;/small&gt;, a gold box; Mrs. C&lt;small&gt;HARLES&lt;/small&gt; B&lt;small&gt;ALFOUR&lt;/small&gt;, two jewelled pins; the Hon. Mrs. M&lt;small&gt;AGUIRE&lt;/small&gt;, a diamond and ruby brooch; Captain J. O&lt;small&gt;RR&lt;/small&gt;-E&lt;small&gt;WING&lt;/small&gt;, enamel and pearl chain; Mr. and Mrs. G&lt;small&gt;EORGE&lt;/small&gt; M&lt;small&gt;ORRIS&lt;/small&gt;, an antique gold and pearl brooch; Lord and Lady A&lt;small&gt;LINGTON&lt;/small&gt;, a gold box; Lady Mary C&lt;small&gt;URRIE&lt;/small&gt;, a gold and jewelled chain; Captain H&lt;small&gt;EDWORTH&lt;/small&gt; L&lt;small&gt;AMBTON&lt;/small&gt;, a pair of links. 

The Bridegroom's presents included:— From the B&lt;small&gt;RIDE&lt;/small&gt;, a pearl and diamond pin; Earl C&lt;small&gt;ADOGAN&lt;/small&gt;, a gold snuff box of exquisite workmanship; Countess C&lt;small&gt;ADOGAN&lt;/small&gt;, an ormolu reading lamp; Lady F&lt;small&gt;ARQUHAR&lt;/small&gt;, silver tantalus on table; Viscount C&lt;small&gt;RICHTON&lt;/small&gt;, four silver pierced dessert dishes; the Marquis of L&lt;small&gt;ONDONDERRY&lt;/small&gt;, a silver cigar box; Lady E&lt;small&gt;DMONSTONE&lt;/small&gt;, set of writing-table requisites; Miss P&lt;small&gt;ACKE&lt;/small&gt;, silver inkstand and calendar; Mr. A&lt;small&gt;LFRED&lt;/small&gt; C&lt;small&gt;OOPER&lt;/small&gt;, a cigarette holder in case; Colonel P&lt;small&gt;ERCY&lt;/small&gt;, a walking-stick; Colonel L&lt;small&gt;ARKING&lt;/small&gt;, a bookcase; Mr. and Mrs. C&lt;small&gt;AMPBELL&lt;/small&gt;, a silver inkpot; Sir R&lt;small&gt;OBERT&lt;/small&gt; M&lt;small&gt;ONCREIFFE&lt;/small&gt;, a silver-crest letter-weight; the Marquis C&lt;small&gt;AMDEN&lt;/small&gt;, a pair of links; the Duchess of S&lt;small&gt;UTHERLAND&lt;/small&gt;, a knife on chain; Mr T. B&lt;small&gt;ROWN&lt;/small&gt;, a hunting crop; Mr. W. H. G&lt;small&gt;REEN&lt;/small&gt;, a silver butterfly letter-clip; Mr. and Mrs. L&lt;small&gt;ENNARD&lt;/small&gt;, an antique silver box; Mr. G&lt;small&gt;ODFREY&lt;/small&gt; H&lt;small&gt;ESELTINE&lt;/small&gt;, a silver shaving-pot; Lady &lt;small&gt;DE&lt;/small&gt; T&lt;small&gt;RAFFORD&lt;/small&gt;, a gold and diamond match-box; Mr. K&lt;small&gt;ENNET&lt;/small&gt; [sic] W&lt;small&gt;ILSON&lt;/small&gt;, a gun-metal match-box; Mr. F. B. M&lt;small&gt;ILLER&lt;/small&gt;, four silver-mounted decanters; Miss P&lt;small&gt;EREIRA&lt;/small&gt;, a walking-stick; Mrs. G&lt;small&gt;EORGE&lt;/small&gt; F&lt;small&gt;ORBES&lt;/small&gt;, a snake seal; Mr. A. R. H&lt;small&gt;AY&lt;/small&gt;, a blotter; Mr. and Mrs. W. H&lt;small&gt;OARE&lt;/small&gt;, a writing set and case; Mr. S&lt;small&gt;TEPHEN&lt;/small&gt; W&lt;small&gt;OMBWELL&lt;/small&gt;, a carriage clock; Lieutenant- General H&lt;small&gt;ANKEY&lt;/small&gt;, a gold pencil case; Lord H&lt;small&gt;ERBERT&lt;/small&gt; V&lt;small&gt;ANE&lt;/small&gt;-T&lt;small&gt;EMPEST&lt;/small&gt;, a silver cigar box; Lord D&lt;small&gt;UNSANDLE&lt;/small&gt;, two silver candlesticks; Mr. J. B. L&lt;small&gt;EIGH&lt;/small&gt;, a silver cigar case; Viscountess M&lt;small&gt;ARSHAM&lt;/small&gt; and Mrs. P&lt;small&gt;HILIP&lt;/small&gt; G&lt;small&gt;REEN&lt;/small&gt;, a pair of silver candlesticks; Mr. E. L&lt;small&gt;EVESON&lt;/small&gt;-G&lt;small&gt;OWER&lt;/small&gt;, a marble clock; Mr. P&lt;small&gt;REDDY&lt;/small&gt; M&lt;small&gt;ENZIES&lt;/small&gt;, a silver and enamel cigarette case and match-box; Mr. R&lt;small&gt;EUBEN&lt;/small&gt; S&lt;small&gt;ASSOON&lt;/small&gt;, a gold-topped cane; Mr. and Mrs. W. J&lt;small&gt;AMES&lt;/small&gt;, four gold and enamel spoons; Sir R&lt;small&gt;ALPH&lt;/small&gt; and Lady F&lt;small&gt;LORENCE&lt;/small&gt; H&lt;small&gt;ARE&lt;/small&gt;, four heart- shaped ash trays; Mr. and Lady A&lt;small&gt;LINE&lt;/small&gt; B&lt;small&gt;EAUMONT&lt;/small&gt;, walking-stick with tortoiseshell handle; Mr. J. P. M&lt;small&gt;ILBANKE&lt;/small&gt;, case containing &quot;Bradshaw,&quot; &quot;A. B. C,&quot; &amp;c.; Viscount M&lt;small&gt;ARSHAM&lt;/small&gt;, a gold-mounted cane with pencil in handle; Mr. and Mrs. C&lt;small&gt;LEMENT&lt;/small&gt; S&lt;small&gt;ATTERTHWAITE&lt;/small&gt;, a silver cigarette case; Mr. A. E. B&lt;small&gt;URNABY&lt;/small&gt;, a silver inkstand with clock on lid; Mr. H&lt;small&gt;UNGERFORD&lt;/small&gt;, a silver shaving-pot; Lord and Lady S&lt;small&gt;TRATHEDEN&lt;/small&gt; and C&lt;small&gt;AMPBELL&lt;/small&gt;, a silver cigarette case; Mr. H. S&lt;small&gt;T&lt;/small&gt;. D'A&lt;small&gt;ETH&lt;/small&gt;, a silver cigar case; Mr. and Mrs. A&lt;small&gt;RTHUR&lt;/small&gt; H&lt;small&gt;AY&lt;/small&gt;, a double silver inkstand; Messrs. J&lt;small&gt;ONES&lt;/small&gt;, walking-stick; Captain V&lt;small&gt;ILLERS [sic]&lt;/small&gt;, a silver cigar cutter and lighter; Captain R&lt;small&gt;ICARDO&lt;/small&gt;, a silver box; Captain and Mrs. G&lt;small&gt;ERALD&lt;/small&gt; F&lt;small&gt;ITZ&lt;/small&gt;G&lt;small&gt;ERALD&lt;/small&gt;, a silver match- box; the Countess of R&lt;small&gt;OMNEY&lt;/small&gt;, a silver cigarette case; Captain and Mrs. A&lt;small&gt;LFRED&lt;/small&gt; J&lt;small&gt;OHNES&lt;/small&gt;, a silver inkstand; Captain and Mrs. A&lt;small&gt;RTHUR&lt;/small&gt; S&lt;small&gt;OMERSET&lt;/small&gt;, a set of antique spoons; Mr. H. F. S&lt;small&gt;COTT&lt;/small&gt;, a pair of diamond links; Baron M&lt;small&gt;AX DE&lt;/small&gt; T&lt;small&gt;UYLL&lt;/small&gt;, an antique china box; Mrs. W. H. G&lt;small&gt;REENFELL&lt;/small&gt;, a pencil case: Mr. E&lt;small&gt;RNEST&lt;/small&gt; H&lt;small&gt;ATCH&lt;/small&gt;, a silver tea-caddy; Mr. E. P&lt;small&gt;ACKE&lt;/small&gt;, a double silver inkstand; the Misses C&lt;small&gt;ALDWELL&lt;/small&gt;, a silver-mounted telegram form book; Captain P&lt;small&gt;HILIP&lt;/small&gt; G&lt;small&gt;REEN&lt;/small&gt;, a weather glass; Mr. R&lt;small&gt;ALPH&lt;/small&gt; L&lt;small&gt;AMBTON&lt;/small&gt;, a luncheon case; Mr. L&lt;small&gt;EONARD&lt;/small&gt; B&lt;small&gt;RASSEY&lt;/small&gt;, a gold match-box; Mr. E. S. J&lt;small&gt;OHNES&lt;/small&gt;, two silver ash trays; Mr. A&lt;small&gt;LGERNON&lt;/small&gt; P&lt;small&gt;EEL&lt;/small&gt; and Mr. V&lt;small&gt;ICTOR&lt;/small&gt; C&lt;small&gt;ORKRAN&lt;/small&gt;, a silver sandwich case; Captain the Hon. E. D&lt;small&gt;AWSON&lt;/small&gt;, weather glass; Mrs. C&lt;small&gt;HARRINGTON&lt;/small&gt;, a cigarette case; Mr. J. S. F&lt;small&gt;ORBES&lt;/small&gt;, a gold seal with pencil; Messrs. C&lt;small&gt;OMYNS&lt;/small&gt; and S&lt;small&gt;ONS&lt;/small&gt;, a blotting book; Mr. C. P. B&lt;small&gt;UCKWORTH&lt;/small&gt;, two silver ash trays; the Duke of M&lt;small&gt;ARLBOROUGH&lt;/small&gt;, a silver inkstand; Lord and Lady W&lt;small&gt;ILLIAM&lt;/small&gt; N&lt;small&gt;EVILL&lt;/small&gt;, a silver-mounted blotting-book; Mr. E. B. C&lt;small&gt;HARTERIS&lt;/small&gt;, a knife; Mr. and Mrs. A&lt;small&gt;LISTAIR&lt;/small&gt; H&lt;small&gt;AY&lt;/small&gt;, four silver pepper castors in the shape of dice; Mr. H&lt;small&gt;ATFIELD&lt;/small&gt; H&lt;small&gt;ARTER&lt;/small&gt;, a paper knife; the T&lt;small&gt;ENANTRY&lt;/small&gt; at North Harris, a dressing bag; the Estate and House S&lt;small&gt;ERVANTS&lt;/small&gt;, G&lt;small&gt;AMEKEEPERS&lt;/small&gt;, and G&lt;small&gt;ILLIES&lt;/small&gt; at North Harris, a deer's-foot inkstand, mounted in silver; the Household and Estate S&lt;small&gt;ERVANTS&lt;/small&gt; at Sundridge Park, a silver kettle; Mr. H. M&lt;small&gt;ELLIDEW&lt;/small&gt;, a knife; the C&lt;small&gt;HAPLAIN&lt;/small&gt; to the Royal Horse Guards, a pair of silver candlesticks; Mr. and Mrs. L&lt;small&gt;EOPOLD&lt;/small&gt; R&lt;small&gt;OTHSCHILD&lt;/small&gt;, a pair of silver candlesticks; Captain the Hon. R and Mrs. G&lt;small&gt;REVILLE&lt;/small&gt;, a pair of silver candlesticks; Mr. A. S&lt;small&gt;ASSOON&lt;/small&gt;, a gold-mounted stick; Mr. and Mrs. A. B&lt;small&gt;OURKE&lt;/small&gt;, a print; Mr. C&lt;small&gt;LAUDE&lt;/small&gt; H&lt;small&gt;AY&lt;/small&gt;, a silver box; the T&lt;small&gt;RADESPEOPLE&lt;/small&gt; at Bromley, a silver teapot, &amp;c.; Mr. E&lt;small&gt;GREMONT&lt;/small&gt; M&lt;small&gt;ILLS&lt;/small&gt;, a book; Colonel R&lt;small&gt;OWNEY&lt;/small&gt;, a pencilcase; Captain the Hon. G. F&lt;small&gt;ORESTER&lt;/small&gt;, a silver-mounted glass jug; Dr. B&lt;small&gt;URNEY&lt;/small&gt; Y&lt;small&gt;EO&lt;/small&gt;, a bezique box; Mrs. H&lt;small&gt;AMMOND&lt;/small&gt;, a knife; the Hon. B. B&lt;small&gt;ATHURST&lt;/small&gt;, a silver box; Mr. B&lt;small&gt;ROWN&lt;/small&gt;, a hunting crop; the Hon. G&lt;small&gt;ERALD&lt;/small&gt; C&lt;small&gt;ADOGAN&lt;/small&gt;, a gold-mounted stick; the Hon. A&lt;small&gt;RTHUR&lt;/small&gt; C&lt;small&gt;OVENTRY&lt;/small&gt;, a gold and tortoiseshell-handled stick; Earl C&lt;small&gt;OWLEY&lt;/small&gt;, a gold-mounted stick; Captain and Mrs. A. S&lt;small&gt;OMERSET&lt;/small&gt;, six antique spoons in case; Major B&lt;small&gt;YNG&lt;/small&gt;, a silver shaving-pot; Mr. T. B. M&lt;small&gt;ILLER&lt;/small&gt;, four silver-mounted claret jugs; Mr. and Mrs. C&lt;small&gt;OLES&lt;/small&gt; C&lt;small&gt;HILD&lt;/small&gt;, a glass and silver match-stand; Mr. H&lt;small&gt;UBERT&lt;/small&gt; E&lt;small&gt;ATON&lt;/small&gt;, a silver-mounted blotter; the Hon. D&lt;small&gt;UDLEY&lt;/small&gt; M&lt;small&gt;ARJORIBANKS&lt;/small&gt;, an antique silver casket; Mr. and Mrs. J. P&lt;small&gt;EASE&lt;/small&gt;, six books; Mr. F. P&lt;small&gt;AYNE&lt;/small&gt; and Mr. J. H. L&lt;small&gt;EPPER&lt;/small&gt;, a silver inkstand.&lt;ref&gt;&quot;Marriage of Sir Samuel Scott and Lady Sophie Cadogan.&quot; ''Morning Post'' 30 June 1896 Tuesday: 4 [of 12], Cols. 2a–4b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18960630/029/0004.&lt;/ref&gt; &lt;/blockquote&gt;

==July 1896==
On 4 July 1896 in ''The Queen'', an article begins, &quot;On Monday last Dr Doyle, who is as much beloved by his friends as by his readers, was entertained at a banquet by his fellow-members of the Authors Club&quot; (Orel 135). Doyle gave a speech at that banquet, which the article reprints.
===2 July 1896, Thursday===
The 5 June 1896 ''Literary World'' reports the following: &quot;The date of the promised revival of Marlow's ''Doctor Faustus'' is fixed for Thursday evening, July 2, when the performance will be given before members of the Elizabethan Stage Society and their friends at St. George's Hall. Marlowe's tragedy differs from Goethe's in this, among other things, that Marlowe wrote, as Goethe could not, in the firm belief in the possibility of the situations he created.&quot;&lt;ref&gt;&quot;Table Talk.&quot; The ''Literary World'', 5 June 1896 (Vol. 53): 533, col. 2. ''Google Books''.&lt;/ref&gt;

=== 3 July 1896, Friday ===
Mrs. Goschen's Dance&lt;blockquote&gt;Mrs. Goschen's dance at the Admiralty last night was a great success. Among the guests were the Duchess of Buccleuch and the Ladies Scott, Captain Jedina, Captain Gulich, [[Social Victorians/People/Hadik|Count Hadik]], Count de Pontavice, M. de la Chaussée, the Lord Chancellor and the Hon. Evelyn Giffard, the Earl of Clanwilliam and the ladies Meade, Earl Granville, the Countess of Belmore and Lady Winifred Corry, the Earl of Donoughmore, the Earl of Eldon and Lady Louisa Scott, the Countess of Dunmore and Lady Victoria Murray, Earl Waldegrave and Lady Mary Waldegrave, and a large contingent of &quot;dancing men.&quot;&lt;ref&gt;&quot;Mrs. Goschen's Dance.&quot; ''St James's Gazette'' 04 July 1896 Saturday: 13 [of 16], Col. 1b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/18960704/057/0013.&lt;/ref&gt;&lt;/blockquote&gt;

===4 July 1896, Saturday===
The 26 June 1896 ''Literary World'' reports the following: &quot;We understand that one of the principal features of the performance of Marlowe's Doctor Faustus will be the introduction of the Seven Deadly Sins, the designs for which have been taken from engravings belonging to the sixteenth century, and found in the print rom of the British Museum. The first and last parts of the play will reproduce in colour and costume the university life of Marlowe's day. The middle part of the play, the one most difficult for a stage manager to cope with, will consist of tableaux showing Faustus on his travels, and giving living pictures of the Feast of St. Peter, introducing the picturesque incident of the curse with 'bell, book, and candle'; the banquet at the court of Charles V.; and the Flight of Faustus, in his chariot drawn by yoked dragons, 'to scale Olympus top.' In consequence of the heavy expense attending each representation of the play, there will be only one public performance, that on the afternoon of July 4. Mr. Arnold Dolmetsch will supply the music.&quot;&lt;ref&gt;&quot;Table Talk.&quot; The ''Literary World'', 26 June 1896 (Vol. 53): 604, col. 2. Google Books.&lt;/ref&gt;

===13 July 1896, Monday===
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] attended a Garden Party at Buckingham Palace given by Queen Victoria. Several thousand people were there, it looks like (1896-07-14 Morning Post).

===16 July 1896, Thursday===
The 19 June 1896 ''Literary World'' reports the following: &quot;The idea of Ladies' Dinners seems to have caught on in clubland. A dinner is to be given to Mrs. Hodgson Burnett by the Authors' Club on July 16, and as the accommodation at the Club-house is neither suitable nor adequate, the dinner will be held in the King's Hall of the Holborn Restaurant. Members may take as many guests as they like, either ladies or gentlemen.&quot;&lt;ref&gt;&quot;Table Talk.&quot; The ''Literary World'', 19 June 1896 (Vol. 53): 581, col. 3. ''Google Books''.&lt;/ref&gt;

==August 1896==
Sometime in August 1896 Lady Gregory met William Butler Yeats (I got this from Wade?).

August 1896, the steamer the ''Norse King'' was to take scientists and tourists to the Varanger Fjord to view the solar eclipse. At least in the planning, as reported in January 1896, &quot;The official observers of the joint committee of the Royal Society and the Royal Astronomical Society have arranged to go by the Norse King. Among those on board will be Dr. A. Common, president of the Royal Astronomical Society, and Sir Robert Ball, who has consented to deliver a series of three lecture on the eclipse while the steamer is in the Varanger Fjord.&quot; (From a &quot;special announcement,&quot; quoted in &quot;Table Talk,&quot; The Literary World (3 Januray 1896), vol. 53, p. 13 [accessed 10 October 2009 in Google Books].)

=== 5 August 1896 ===
The ''Gentlewoman'' describes the wedding of the Hon. Terence Bourke and Miss Eveline Haines:&lt;blockquote&gt;The Hon. Terence Bourke to Miss Eveline Haines.

A smart and very pretty ceremony came off in St. Andrew's Church, Westminster, on the 5th inst., on the occasion of the marriage of the Hon. Terence Bourke, son of the late Earl of Mayo, Viceroy of India, with Miss Eveline Haines, daughter of the late Colonel Haines, of Hasketon Manor, Woodbridge. The bride, who was given away by her brother, Captain Haines, York and Lancaster Regiment, was attended by two pages, Master Dicky and Master Valentine Wyndham Quin, in picturesque white and mauve shirts with knee breeches. The five bridesmaids, Miss Mercy Barnes, Miss Robertson, Miss Powell, Miss Constance Mure, and Miss Edith Dods, were prettily gowned in white muslin trimmed with Valenciennes, and wore large white picture hats. Their presents from the bridegroom were gold chains with enamel hearts; the pages' gifts being gold and enamel sleeve links. The rites were solemnised by the Rev. and Hon. George Bourke, Chaplain to the Queen; and Lieut. Cyril Sloane Stanley, 1st Life Guards, supported Mr. Bourke as best man. After the ceremony Mr. and Mrs. Herbert Robertson, uncle and aunt of the bride, held a large reception at Willis's Rooms, amongst those accepting invitations to be present being the Dowager Countess of Mayo, the Earl and Countess of Mayo, Lady Florence Bourke, the Marchioness of Queensberry, Lord Leconfield, Lady Leconfield, Lord and Lady Milton, the Countess of Bective, Major and Lady Eva Wyndham Quin, Lord and Lady Connemara, General the Hon. John Bourke, the Hon. Gerald and Lady Maria Ponsonby, the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], the Hon. Algernon Bourke, the Hon. Percy and Mrs. Wyndham, Mr. Wilfrid and Lady Anne Blunt, Miss Blunt, the Earl and Countess of Roden, Lord and Lady Henry Bentinck, Lord and Lady Douglas, Sir Owen and Lady Agnes Burne, Captain Haines, Master W. Haines, Mrs. and the Misses Dods, Captain and Mrs. Dods, Mr. and Mrs. Powell, Mrs. and Miss Benest, Mr. and Mrs. Ribton, Mr. Erskine and Miss D. Ribton, Captain and Mrs. Inglis, Colonel the Hon. and Mrs. Hubbard, Admiral and Mrs. Saumerez, Mr. and Mrs. B. N. Everard, Mrs. and Miss Drummond, Lady Stawell, &amp;c. In the afternoon the Hon. Terence and Mrs. Bourke took their departure for Paultons, Lieutenant Stanley's place in the New Forest, kindly lent for the honeymoon. The bride left London in a dainty heliotrope canvas costume over white silk, trimmed with white embroidered lisse and [Col. 2c / 3a] chiffon, and a big picture hat arranged with white feathers and purple irises.

The presents, which were very numerous, included: — From bridegroom to bride, diamond tiara, topaz, and diamond necklace, bangle, diamond and ruby ring, ruby ring, fan, stamp album. &amp;c. Mr. Herbert Robertson. M.P., 200 guineas. Mrs. Robertson, silver coffee pot. Miss Robertson and Masters Manning and Nevile Robertson, silver spoons. Captain Haines, silver tea tray, tea pot, sugar basin, and milk jug. The Dowager Countess of Mayo, diamond and turquoise necklace. The Earl and Countess of Mayo, turquoise necklace. Lady Leconfield, pearl, sapphire, and ruby bracelet. Miss E. Dods, pearl bracelet. Lady Eva Wyndham Quin, diamond and sapphire brooch. Lady Florence Bourke, amethyst bangle. The [[Social Victorians/People/Bourke|Hon. and Mrs. Algernon Bourke]], enamel muff chain. Hon. Harry Bourke, cheque. Hon. Edward Bourke, cheque. Hon. J. Bourke, cheque. Lord Connemara, cheque. Mrs. Dods, cheque. Mr. and Mrs. Powell, silver looking-glass. Mrs. Benest, clock. Master Haines, butter dish. Miss M. Haines, cream jug. Mrs. Bischoffsheim, Louis XV. clock. The Hon. Percy and Mrs. Wyndham, pearl and emerald chain and pendant. Marchioness of Queensberry, crown Derby snuff box. Lady Leconfield, silver tea pot. Major and Lady Eva Wyndham Quin, coffee pot and milk pot. Countess of Bective, turquoise and pearl pin. Earl and Countess of Mayo, carriage clock. Lord and Lady Henry Bentinck, gold pencil case. Sir John and Lady Constance Leslie, flower stand. Mr. Wilfrid Blunt, two Arab mares. Sir Raymond and Lady Burrell, Battersea enamel snuff box. Lord Leconfield, cheque £100, &amp;c, &amp;c.&lt;ref&gt;&quot;The Hon. Terence Bourke to Miss Eveline Haines.&quot; ''Gentlewoman'' 15 August 1896, Saturday: 24 [of 54], Col. 2b–3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18960815/128/0024. Print p. 232.&lt;/ref&gt;&lt;/blockquote&gt;

=== 19 August 1896, Wednesday ===
Queen Victoria was at Osborne, accompanied by Princess Henry of Battenberg and the Hon. Frances Drummond, and then also Countess Feodore Gleichen. The dinner party Wednesday night also included people who were at Cowes for the yachting:&lt;blockquote&gt;Her Majesty's dinner party last evening included Captain Acland, her Majesty's ship Australia, guardship at Cowes, and the Hon. Mrs. Acland, Mrs. Lawrence Drummond, [[Social Victorians/People/Young|Sir Allen Young, C.B.]], and Major Strong, 2nd Battalion Scottish Rifles.&lt;ref&gt;&quot;Court Circular.&quot; ''Morning Post'' 20 August 1896 Thursday: 5 [of 8], Col. 4a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18960820/072/0005.&lt;/ref&gt;&lt;/blockquote&gt;

===31 August 1896, Monday===
Summer Bank Holiday

==September 1896==
==October 1896==
===31 October 1896, Saturday===
Halloween.
==November 1896==

=== 2 November 1896, Monday ===
The ''Black and White'' hosted a dinner to welcome Special Artist Charles M. Sheldon back from the Soudan:&lt;blockquote&gt;MR. CHARLES M. SHELDON, ''Black and White''&lt;nowiki/&gt;'s Special Artist, received a welcome back from the Soudan at a dinner presided over by the editor and attended by the directors and other officers of the journal, as well as by a large company, including: Messrs. Angus Evan Abbott, A. H. Beaman, A. S. Boyd, F. Whelan Boyle, J. MacLaren Cobban, Oscar Eckhardt, James Greig, Bernard F. Gribble, Paul Hardy, A. S. Hartrick, Lewis Hind, G. Kenealy, A. L. Lazarus, T. J. Lipton, G. G. Manton, Gilbert Marks, G. E. Matheson, F. Frankfort Moore, J. M. Munro, Henry Norman, Barry Pain, R. B. M. Paxton, Ernest Prater, W. Pett Ridge, Charles Robinson, [[Social Victorians/People/Rook|Clarence Rook]], R. Savage, J. A. Shepherd, Alexander Stuart, E. J. Sullivan, Adolf Thirde [?], Enoch Ward, and Edgar Wilson. Letters of apology were intimated from Messrs. J. H. Bacon, Robert Barr, H. Brown, L. Cope Cornford, J. Finnemore, H. W. Massingham, Arthur Morrison, W. Mudford, H. H. S. Pearse, Eden Phillpotts, G. E. Webster, H. G. Wells, H. Seppings-Wright [?], &amp;c., &amp;c. The Chairman proposed the health of Mr. Sheldon, a toast which was honoured with enthusiasm, and the guest ot the evening, in a characteristically modest speech, urged that campaigning was its own reward, though it was enhanced by such a welcome home as had been accorded him. During the night members of the company furnished songs and stories, Mr. Sheldon contributing two notable items to the programme — ''Drill ye tarriers'', an Irish ditty which has, through his instrumentality, become the chief marching song of the Egyptian Army, and ''Black Lulu'', a genuine negro melody.&lt;ref name=&quot;:0&quot;&gt;&quot;Welcome Back from the Soudan.&quot; ''Black and White'' 07 November 1896, Saturday: 9 [of 35], Cols. 1a, 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004617/18961107/029/0009. Print p. 587.&lt;/ref&gt;{{rp|Col. 1a}}&lt;/blockquote&gt;

The menu for the dinner was printed in the paper because of the puns on North Africa:

* Hors d'oeuvre en Pyramide
* Consomé à la Pacha
* Purée à la Derviche
* Sole à la Noir et Blanc
* Filet de boeuf à la Sirdar Kitchener
* Galatine de Chapon à la Sphinx
* Faisan en Casserole à la Victoria
* Salade Égyptienne
* Souflé à la Khedive
* Bombe à la Dongola
* Petit fours Osman Digna
* Fromage du Nile
* Dessert à la Kartoum&lt;ref name=&quot;:0&quot; /&gt;{{rp|Col. 2b}}

===5 November 1896, Thursday===
Guy Fawkes Day

=== 1896 November 6, Friday ===
The Prince's Club ice-skating rink opened:&lt;blockquote&gt;The building specially constructed at Knightsbridge for the purposes of a skating rink will be formally opened to-morrow. Yesterday the managers invited their friends to a private view of the premises, erected on ground formerly occupied by an oilcloth factory and saw mill. Stoppani's system, which has been in operation for several years at the Palais de Glace and the Pole Nord in Paris, has been adopted, and the sheet of ice, 200ft. long by 50ft. wide, is as perfect as the most fastidious skater could desire. The building is light and airy, and is illuminated at night by arc lamps. M. Olivier Pichat has superintended the decoration of the walls, on which are painted scenes of the Thames, Nile, and Ganges. Among the committee of the club are the [[Social Victorians/People/Lansdowne|Marchioness of Lansdowne]], the [[Social Victorians/People/Londonderry|Marchioness of Londonderry]], the Marchioness of Granby, the [[Social Victorians/People/Minto|Earl and Countess of Minto]], [[Social Victorians/People/Carrington|Countess Carrington]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], Mrs. Cavendish Bentinck, [[Social Victorians/People/Asquith|Mrs. Asquith]], Sir William Hart-Dyke, Bart., M.P., Sir F. Astley Corbett, Bart., Sir [[Social Victorians/People/Arthur Sullivan|Arthur Sullivan]], Admiral Maxse, Messrs. Alfred Lyttelton, M.P., [[Social Victorians/People/Bourke|Algernon Bourke]], W. H. Grenfell, and W. F. Adams. Mr. W. W. Nightingale, who started at Southport in 1878 one of the first artificial ice rinks in the kingdom, is the secretary.&lt;ref&gt;&quot;Prince's Skating Club.&quot; London ''Daily Chronicle'' 06 November 1896, Friday: 9 [of 10], Col. 2c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/18961106/125/0009. Print p. 9.&lt;/ref&gt;&lt;/blockquote&gt;

===23 November 1896, Monday===
&quot;''Little Eyolf'' (in William Archer's translation) opens at the Avenue Theatre, with Janet Achurch, Elizabeth Robins and Mrs Patrick Campbell in the three female roles. [[Social Victorians/People/George Bernard Shaw|[George Bernard] Shaw]]'s review of this production, with a cast including what he described as 'the three best yet undiscovered actresses of their generation', appeared in the ''Saturday Review'' on November 28&quot; (Gibbs 128).

'''1896 November 25, Wednesday''', Lord and Lady Burton hosted a party for Derby Day:&lt;blockquote&gt;Lord and Lady Burton's party at Rangemore for the Derby races included Lady Sarah Wilson, Lord and Lady Hindlip, Lady De Trafford, Sir George Chetwynd, Caytain [sic] Seymour Fortescue, Mr. and Mrs. [[Social Victorians/People/Bourke|Algernon Bourke]], Mr. and Mrs. Baillie, of Dochfour, Mr. and Mrs. Hwfa Williams, Mr. de Murrieta, and Mr. Menzies.&lt;ref&gt;&quot;What the 'World' Says.&quot; ''Sheffield Daily Telegraph'' 25 November 1896, Wednesday: 7 [of 10], Col. 6c [of 8]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0000250/18961125/067/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

==December 1896==
===2 December 1896, Wednesday===
&lt;quote&gt;ACTORS' BENEVOLENT FUND. 

Mr LEOPOLD DE ROTHSCHILD presided over the sixth annual dinner of the Actors' Benevolent Fund, held at the Hotel Métrople on Wednesday evening. Actors have never shown themselves reluctant to assist in the cause of charity, and the profession was strongly represented on this festive occasion. The presence of Sir Henry Irving and other leading actors and managers gave special éclat to the festival, and the dinner proved in all respects to be one of the most successful held since the establishment of the fund. The claims of this admirable charity were pointedly put before the distinguished company by the chairman of the evening, Mr Leopold De Rothschild, who, in the course of his speech, mentioned that at the present time some seventy persons are in receipt of weekly grants from the fund. It is important to bear in mind that the direction of this excellent charity is in the hands of a committee of gentlemen of long and practical experience of the stage, and its modes of assistance are specially devised to meet the contingencies of theatrical life. The dinner took place in the Whitehall Rooms, and the following gentlemen accepted invitations:— [what follows is printed as a 3-column list which in this transcription reads across] Abrahams, Morris / Galer, Elliott / Millwood, W. / Alexander, Geore / Gatti, A. / Morgan, Ernest / Allen, W. E. / Gatti, S. / Mote, Henry / Armytage, H. T. / Gibson, Richard / Mundy, Luther / Asher, S. G. / Gleichen Count /  Nathan, L. / Baker, Col. W. H. / Griffith, Murray / Nathan, H. / Baker, E. / Grossmith, George / Nauheim, Carl / Baker, Ernest H. / Hague, Clarance / Nicholls, E. W. / Barnes, J. H. / Hallard, C. M. / Nicholson, G. J. / Benjamin, David H. / Hamilton, A. / Norman, Fredk. / Bell, H. / Hammond, G. J. / Ochs, James / Betty, H. / Harris, Herbert, A. / Ogilvie, R. A. / Bishop, Alfred / Harrison, Fredk. / Pallant, Walter / Blackley, Frank / Harvey, Edward / Paulton, H. / Blumenthal. M. A. / Heilbut, S. / Phipps, C. I. / Bolton, T. H. Henry, C. S. / Pittar, Parke M. / Bouverie, Hon. K. P. / Herring, George / Power, W. / Brown, G. V. / Herts, H. A. / Pyke, Joseph / Pull, E. H. / Hirsch, Adolph / Renwick, G. / Candy, George / Hollands, A. K. / Ritchie, Clement / Cawston, George / Honey, T. / Robinson, Fredk. / Chamberlain, Rich. / Holdsworth, J. / Roche, L. / Chinnery, H. J. / Howard Hon. K. / Samuel, Sir Saul / Chinnery, Ellis / Howson, Charles / Sarjeant, Arthur / Corgialegno, W. / Hurst, Joseph / Scudamore, F. A. / Cohn, M. / Irving, Sir Henry / Schmidt, H. / Cohen, A. L. / Joels, J. / Shade, A. R. / Cohen, Leonard / Joels, Woolf / Shaw, Sir E. M. / Cohen, J. / Johnson, Sam / Shone, R. V. / Coltson, C. L. / Kelly, C. A. / Silverthorne, E. C. / Cole, C. W. / King, A. P. / Skelly, Francis / Conguest [?], George / Kirchner, T. / Spalding, A. F. M. / Cooper, Frank / Langford, A. E. / Stern, James / Coster, Martin / Latham, T. / Stoker, George / Cruickshanks, C. / Lawrence, E. S. / Tapping, A. B. / Dam, H. J. W. / Lawrence, G. W. / Terry, Edward / Dawes, Richard / Lawrence, W. / Thorne, Thomas / Davidson, Louis / Ledger, Edward / Tidd, J. D. / Davies, Charles / Leign, J. H. / Tite, A. / Dornton, Charles / Lindo, Gabriel / Trevoe, F. M. / Duncannon Visent. [?] / Lockwood, Sir F. / Turner, G. H. / Durham, Frederick / Loewe, S. / Tyars, Frank / Edmonds, W. / Lowenfeld, H. / Villanueva, Dr. H. / Edmonds, W. jun. / Lukach, J. H. / Villiers. R. E. / Edwardes, George / Lumley, Ralph / Vincent, Henry / Ellis, Alfred / Macklin, F. H. / Waley, A. J. / Ellis, Granville / Maddick, E. D. / Waterlow, P. H. / Esmond. H. V. / Marks, H. H. / Wells, / Evill, Henry / Marsden, Peter / Westcott, W. / Fos, Raoul / Martin, Robert J. / Wingatr, H. L. / Forbes [?], Norman / Maskall, T. / Winter, M. / ?rece [?], J. De / Maunder. J. H. / Woolf, Lewis / Gabriel, Chas. S.M. / Mellish, Fuller / Wright, Rev. C. E. / Gabriel, S. / Middlemist, Dr. / Wyndham, Charles&lt;/quote&gt; (1896-12-05 Era)

===3 December 1896, Thursday===
[[Social Victorians/People/Horniman|Annie Horniman]]'s name was removed &quot;from the Roll of the Order&quot; of the Golden Dawn (Howe 136).

=== 9 December 1896, Wednesday ===
Christmas Dinner of the New Vagabonds, Bohemian Club:&lt;blockquote&gt;THE VAGABONDS' DINNER TO LORD ROBERTS, V.C.

S&lt;small&gt;PEECHES&lt;/small&gt; &lt;small&gt;BY&lt;/small&gt; L&lt;small&gt;ORD&lt;/small&gt; R&lt;small&gt;OBERTS&lt;/small&gt;, M&lt;small&gt;R&lt;/small&gt; J. K. J&lt;small&gt;EROME&lt;/small&gt;, D&lt;small&gt;R&lt;/small&gt; C&lt;small&gt;ONAN&lt;/small&gt; D&lt;small&gt;OYLE&lt;/small&gt;, AND S&lt;small&gt;IR&lt;/small&gt; J&lt;small&gt;OHN&lt;/small&gt; R. R&lt;small&gt;OBINSON&lt;/small&gt;.

&lt;big&gt;T&lt;/big&gt;&lt;small&gt;HE CHRISTMAS DINNER&lt;/small&gt; of the New Vagabonds, held on Dec. 9 at the King's Hall of the Holborn Restaurant, is one of the occasions on which this Bohemian club admits ladies. It may fairly be described an unqualified success. In the first place, one of the greatest of living Englishmen — Field Marshal Lord Roberts, V.C.— was courteous enough to come all the way from Ireland expressly to be its guest, and among those who accepted the invitation of the club to meet him were Sir John Robinson, manager of the ''Daily News''; Mr and Mrs Humphry Ward; and Messrs Frank Dicksee, R.A.; Henry Norman, of the ''Daily Chronicle''; Clement Shorter, of the ''Illustrated London News''; Sidney Low, of the ''St. James's Gazette''; J. K. Spender, of the ''Westminster Gazette''; while the editor of the ''Times'', who was kept away by a domestic bereavement, and Sir Edwin Arnold, of the ''Daily Telegraph'', Sir Douglas Straight, of the ''Pail Mall Gazette'', and Mr Alfred Harmsworth, of the ''Daily Mail'', and others, who were kept away by previous engagements, sent letters of regret. The chair was taken by Mr Jerome K. Jerome, and the vice-chairs by Messrs G. B. Burgin, Frankfort Moore, and Douglas Sladen, and amongst others [41, Col. 1a / 1b] present were Miss Helen Mathers, Miss Annie S. Swan, Miss Gertrude Kingston, Mrs Clement Shorter, Miss Marie Connor, Lady Cook, Miss Winifred Graham, Mr and Mrs George Grossmith, Sir James Linton, P.R.I., Mr Conan Doyle, Mr H. G. Wells, Mr Wm. Le Queux, Major Arthur Griffiths, editor of the ''World''; Mr J. G. Clarke, editor of the ''Christian World''; Mr Horace Cox, of the ''Field'' and ''Queen''; Mr F. H. Fisher, editor of the ''Literary World''; Mr Anthony Hope and his father, the rector of St. Bride's; Mr J. Penderel Brodhurst, editor of the ''St. James's Budget''; Mr M. H. Spielmann, editor of the ''Magazine of Art''; Mr John Coleman, author of &quot;The Duchess of Coolgardie;&quot; Mr Kenneth Grahame, author of &quot;The Golden Age;&quot; Mr and Mrs Coulson Kernahan, Mr and Mrs E. W. Hornung, Mr Silas K. Hocking, with Miss Hocking; Major and Mrs Nield, of Sydney, N.S.W.; Mr Neil Turner, Mr Robert Leighton, Mr and Mrs Robert Sauber, Col. Nisbet, Mr Alderman Treloar, Mr Frederick Whyte, Mr Percy White (author of &quot;Corruption&quot; and &quot;Mr Baily-Martin&quot;), Mr F. V. White, Mr and Mrs Will. Sharp, Hon. Mr and Mrs Gilbert Coleridge, Mr and Mrs Adam Black, Mr Reginald Cleaver, Mr I. N. Ford, London correspondent to the ''New York Tribune''; Mr McElway, editor of the ''Brooklyn Eagle''; Mr and Mrs A. S. Boyd, Mr Alfred Parsons, R.I.; Mr A. S. Hartrick, Miss Honner Morton, Mr Richard Le Gallienne, Mr Henry Blackburn, Mr Moncure D. Conway, Mr George Manville Fenn, Mr Zangwill, Mr Solomon, Mr Arthur Reed Ropes (the &quot;Adrian Ross&quot; of [41, Col. 1c / 2a] Gaiety librettos), Mr J. M. Dent, Miss Sarah Doudney, Mr James Greig, Mr G. P. R. Burgess, Mr W. W. Jacob, Dr Yorke Davies, Sir Henry and Lady Bergne, Mr A. C. Calmour, Mr Reginald Geard, Mrs T. P. O'Connor, Mr and Mrs W. B. Dalley, of Sydney; Mr H. W. Lowry, Mr H. Hartley and Mr Hart, of the Indian Exhibition; Mr Lewis Hind, editor of the ''Academy''; [[Social Victorians/People/Rook|Mr and Mrs Clarence Rook]]; Mr and Mrs Wilton Jones (Gertrude Warden), Mr Peter Keary, editor of ''Pearson's''; Mr C. F. Keary, Miss Norma Lorimer (author of &quot;A Sweet Disorder&quot;), Dr S. R. Keightley, author of &quot;The Crimson Sign;&quot; Mr and Mrs Max Pemberton, Mr Pett Ridge, Mr Roger Pocock, Mr Sullivan, [[Social Victorians/People/Todhunter|Dr and Mrs Todhunter]], Mr and Mrs C. N. Williamson, Mr and Mrs Morris Colles, Mr G. Herbert Thring, Mr and Mrs Joseph Hatton, Mr and Mrs Jopling Rowe (Louise Jopling), Mr Arthur Morrison, author of &quot;The Jago&quot; and &quot;Tales of Mean Streets.&quot; The dinner was held in the King's Hall of the Holborn Restaurant, and the company assembled in the Crown Room, the Entrance Hall, and the Lobby. One room could not contain everybody, for between six and seven hundred assembled to do honour to the guest of the evening, and not only was every inch of the floor used for dining tables, but all the galleries and the adjoining lobby. Grace was said by the chaplain, the Rev. St. Barbe S. Sladen; the company, as is usual at Vagabond dinners, having for the most part taken their places before the dinner was announced, and the guests, headed [41, Col. 2a / 2c] by Lord Roberts with Mrs Jerome and Mr Jerome with Mrs Humphry Ward, filed in. This, indeed, is almost the only trace of vagabondage about the club, unless one takes Vagabond and Bohemian in their most up-to-date sense. A Bohemian nowadays does not mean a man who has no bed to sleep on, or a man who wears no collar, but a spotted handkerchief in its place; it does not even imply drunkenness and disorderly conduct. A Bohemian in the London sense, is a person who does what he or she chooses, who conforms with conventionality and lives the ordinary Philistine life when it suits, and is equally prepared to go to a Covent Garden bal ''masqué''.

With one exception, there was not the slightest hitch over seating and arranging the vast assemblage — so skilfully and indefatigably had Messrs Moore and Burgin, who attended to these arrangements, done their work — to the exclusion of all their literary work for the best part of the past month. After the health of the Queen had been drunk with great enthusiasm, the chairman gave the toast of the evening, in a speech characterised by the happiest audacity, which completely captivated the audience, and no one more than its illustrious victim. ...

[43, Col. 1a] Mr Conway Dixon, who is Mr Hayden Coffin's understudy at Daly's, then sang, and his singing was characterised by its finish as well as by the beauty of the voice. Mr Dixon will undoubtedly be heard of in the future, for, in addition to the charm of his singing, he has a face and a figure just suited for a ''jeune premier''. He was vigorously encored, but it was getting on for eleven o'clock, and Mr George Grossmith was yet to come. Mr Grossmith gave his Irving and Beerbohm Tree speeches, and, fired by the brilliant and crowded audience, fairly excelled himself. Those who heard the improvisations which concluded Mr Beerbohm Tree's reply (in Mr Grossmith's imitation) are not likely to forget them. They were Tree to the life, and the great audience roared with laughter till tears ran down its cheeks. It also roared for an encore, but Mr Jerome was firm. There were so many people to be presented to Lord Roberts and Mrs Humphry Ward, that an adjournment had to be made that very moment to the Crown Room and the adjoining lobby, where the ''soirée'' which followed the dinner was to be held. Thus ended what the ''Westminster Gazette'' describes as the most brilliant gathering ever held at the Holborn Restaurant.&lt;ref&gt;&quot;The Vagabonds' Dinner to Lord Robert, V.C.&quot; The ''Queen'' 19 December 1896, Saturday: 41 [of 96], Col. 1a–3c – 43, Col. 1a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18961219/265/0041. Print pp. 1167–1169.&lt;/ref&gt;&lt;/blockquote&gt;

=== 10 December 1896, Thursday ===
Irish Industries Exhibition and Sale, Brighton&lt;blockquote&gt;Irish Industries. Exhibition and Sale at Brighton.

Nothing could have been more thorough than the way in which I did the Irish Industries on the l0th inst. I arrived at the Métropole in the morning and made my way to the Clarence Rooms — a perfectly delightful place for a sale — where, by dint of getting into everybody's way as they were setting out their stalls, I managed to acquire a vast amount of information about Irish work. I knew a good deal to begin with, but what struck me particularly is the resolute way in which the Association refuses to stand still.

At one time this sort of work was associated in the minds of the public with some rather dingy, roughly spun tweeds, certainly durable, but having little in their appearance to recommend them, stockings of somewhat harsh wool, fine pieces of crochet, exquisite specimens of lace at unattainable prices to the many, and quite a fair proportion of well-executed embroideries unhappily bestowed upon articles that nobody particularly wished to use. But in the last few years all this has been changed, and perhaps to a greater degree than much of the outside public are aware of. Some of the most beautiful work that the most up-to-date woman could possibly use, lace of a really lovely description at prices far cheaper than what it is customary to spend on laces made abroad, cloths fine of texture and beautiful in colouring, stockings carefully made and pleasant to touch, all coming under the heading of Irish lndustries; and this has been the work of a devoted band of men and women who, moving in the world and seeing what was required, put their heads together and took designs across the Channel to the village workers and told and taught them what the demand really was and how they might supply it. And it seems highly probable that some of the big firms in London will turn their attention to giving their assistance as well, for during the whole afternoon Mr. Fenwick, of Bond-street, showed gown after gown, made of Irish materials and trimmed with Irish work, on a young lady who kindly acted as model; one teagown of white Irish poplin being particularly admired, angel wing draperies falling on either side from under the arm, revealing both back and front a ''ceinture'' of tine sequin embroidery in shades of amethyst just repeating the tone of the heliotrope linings; the front was of white crêpe de Chine draped over heliotrope sufficiently pink in colour to send a glow of warmth through the otherwlse unrelieved white, while a touch of blue at the throat prevented the gown being a mere contrast of colour.

Returning in the afternoon, I found I was just in time to hear the address read by Lord Arthur Hill to the Princess Edward of Saxe-Weimar, who had kindly taken the place at the last moment of H.R.H. the Duchess of Connaught, whose sharp attack of bronchitis prevented her fulfilling her promise of opening the sale. After this the crowds flocked from stall to stall, until fresh supplies had to be forthcoming for later arrivals. The stall immediately opposite the platform was especially remarkable for the exquisite ''paillette'' spangle embroideries upon silk and satin, the newest departures being worked upon velvet, a material which was suggested by the Duchess of York.

Lady Duncannon, who has done so much for this work at her Garryhill Cottage Industry, and who was gowned in a charming costume of sapphire velvet, was indefatigable in her labours, in which she was assisted by her daughter, the Hon. Irene Ponsonby, the Hon. Mrs. Charles Eliot, the Misses Borton, and Miss Jeffery.

The stall of the Lucan Tweed Industry was presided over by the Countess of Lucan and H.H. the Princess Edward of Saxe-Weimar, who wore a becoming brown toilette and a black bonnet with heliotrope feathers; the other assistants were the Marchioness of Hamilton, Mrs. Sandford, Mrs. Walter B. Puckle, Miss Wates, and Colonel O'Malley, R.A. The demand for stockings at the Arran Industry Stall kept the Countess of Arran, who wore a yellowy-brown coat and skirt, with yellow silk lapels, exceedingly busy, as well as her assistants, the Mayoress of Brighton, the Countess de la Warr, the Viscountess Gage, the Misses Whitmore, Mrs. Pauncerote, Miss Bell, Miss de Robeck, Miss Watson, and last, but by no means least, her little daughter, Miss Claire Stopford, who, in her green accordion-pleated gown, seemed to be absolutely untirable.

In the centre of the ballroom were five of the Association Stalls. At the first was Lady Fingall, who, in a Foxford green tweed, turned back with lapels lined with old gold velvet, edged with tiny gold buttons, and a white velvet toque twisted round with brown velvet and upstanding sable tails, was especially persuasive with her delicate lace exhibits; so, too, were her assistants, Mrs. Charles Crawley, Miss Treves, Miss Amy Treves, and Miss Baker. Next came Lady Tweedmouth in a black accordion-pleated skirt with sleeves of emerald green velvet, covered with a lattice work of black braiding, her slim ''ceinture'' being fastened with a large paste buckle at the back of her bodice; at the neck was a high Medici collar of Irish lace, and her toque of green velvet with upstanding bunches of violets had sprays of white camelias at one side. Here, too, was Mrs. Adair, in a brown velvet costume, the bodice being cut in an open-work pattern over white silk, and outlined with flame-coloured paillettes. Miss Thesiger in a pretty heliotrope woollen skirt with sleeves to match, the bodice of white satin being tightly covered with guipure; also Mrs. Fletcher, of Dale Park, and Miss Hasler.

Opposite was the Countess of Bective, whose beautiful pearls and diamonds showed well against the grey-green of her blouse, made with a Greek drapery at the back edged with gold braid; with her was Miss Marshall, Mrs. Gore, Mrs. Hoffman, Mrs. Cale, Miss Evelyn Whitmore, the [[Social Victorians/People/Mayo|Dowager Countess of Mayo]] and Mr. and Mrs. Arnott. Much beautiful lace, including fans, fichus, and handkerchiefs were disposed of at the [Col. 1c–2a] end stall, which was presided over by the Marchioness of Londonderry, in black velvet and sable with touches of blue, and a very becoming toque of brown trimmed with sable and two pink roses at the back; assisted by her daughter, Lady Helen Stewart, who looked charming in a black skirt, shot blue-green chiné blouse striped with black and vise lace trimming, wearing a row of pearls and a large black hat; Mrs. J. S. Wood, in a dark blue-green shot and brocaded glacé silk trimmed with Irish lace; Mrs. Engledow, and Mrs. W. Hardy Beaton.

At the next stall the Hon. Mrs. Arthur Henniker presided, wearing a very pretty gold embroidered bolero over a gold satin blouse and black skirt. She was assisted by her cousin, Miss Mary Thornhill, Mrs. Jack Johnson, and Miss Phyllis Johnson.

The sixth of the Association Stalls had a room to itself, which was really required, considering the multitude of beautiful tweeds that were piled up on the long counter. Here Lady Arthur Hill — in a black satin bolero coat and skirt, over heliotrope blouse, and wearing a toque trimmed with violets — was kept unceasingly busy during the afternoon, together with her assistants, Lady Fletcher, Mrs. Dudley Sampson, Mrs. Horace Voules, Mrs. Winans, Miss Hill, and Miss Blanche Hasler. Much demand was being made for the handwoven tweeds front the Cottage Industry of Miss H. H. Reeves, of Tramore; and, by the way, I found that &quot;A Collection of Songs,&quot; written by Mrs. Alexander (late wife of the Primate of Ireland), and music by Lady Arthur Hill, charmingly bound in Irish linen, can be obtained at Novello's.

But there was yet a third room to be traversed, and all sorts of well-executed handicrafts were dispensed by Lade Castlerosse, assisted by the Lady Mary Douglas, Hon. Mrs. Spencer, Hon. Susan Baring in a pretty brown costume, Miss Sullivan, Miss Heatheote, and Mlle. de la Brosse. Some exquisite pieces of embroidery, done on vellum; [sic] were most noticeable on a stall where the [[Social Victorians/People/Mayo|Countess of Mayo]] was assisted by the Lady Dorothy FitzClarence, the Lady Maria Ponsonby, and the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]]; and some very pretty children's [break for photograph]

dresses, pinafores, undergarments, and knick-knacks were on show at the Irish Distressed Ladies' Fund Stall held by Georgina Marchioness of Downshire, who was assisted by the Dowager Lady Westbury, Mrs. W. E. H. Lecky, Lady Duke, Lady Sankey, Lady Agnes Daniell, Mrs. Majolier, and Mrs. Trevor. At the Guild of Impoverished Irish Gentlewomen's Stall were Mrs. Dalison, Miss Dalison, Miss A. Dalison, the Misses Stewart, Mrs. Carey Borrer, Miss Borrer, Miss Colburn, Miss Blaker, Miss H. Blaker, and the Rev. E. W. Dalison. Lady Castletown was assisted by [[Social Victorians/People/Mayo|Lady Florence Bourke]], Miss Wagg, Miss Hennessy, and Sir Egbert Sebright.

Thanks were due to the Brighton and Hove Society of Guitarists and Mandolinists, who, conducted by Mr. Frank Mott Harrison, contributed a continuous programme of music throughout each day, among the vocalists being Miss Maud Bond, who sang the solo part in &quot;God Save the Queen&quot;; Miss Aimée Hine Brown, who, in addition to other songs, sang several composed by Lady Arthur Hill, who played the accompaniments, and at the close congratulated the young singer; Miss Aimée Fowler, whose light soprano was much appreciated; Miss Mary Aukett, Miss Clarice Millar (showed herself to be a brilliant young pianiste); Miss Gertrude Hale played the 'cello with good effect; Miss Harrison performed well on the zither, and Mr. F. Mott Harrison's well-known guitar performances were greatly appreciated; so also was Miss Kate E. Peerless on the mandoline, and Mr. Gamble-Blagrove.

The Brighton and Hove Society of Guitarists and Mandolinists were well to the fore, amongst them being Lady Blount, Mrs. Stickney, Mrs. Tillstone, Miss E. Aylward, Miss Carter, Miss Finnemore, Miss Harrison, Miss Knowles, Miss Lockyer, Miss A. D. Miller, Miss E. Miller, Miss K. E. Peerless, Miss L. E. Peerless, Miss Routledge, Miss Routledge, Miss G. Search, Miss A. Smith, Miss E. M. Watts, Mr. Hansor, Mr. R. Harrison (leader), Mr. R. Mason, the Lady Alice Morland, the Count Ybanez, Mrs. Grinsted, Mrs. Perrott, Mrs. Vigor, Miss B. M. Gibbs, Miss A. L. Lowndes, Mrs. A. C. Miller, Miss Pennifold, Miss Stickney, Master W. F. H. [Col. 2c–3a] 

Grinsted, Mr. A. de Burgh Battersby, Mr. Lifford Hewitt, Mr. F. Harrison, Miss A. E. F. Brewer, Mr. H. Gamble-Blagrove, Miss Mary Aukett, Mr. W. Mason, Mr. Gordon Miller, and Master Grinsted.

It was gratifying to learn in the course of the afternoon that Mr. Gerald and Lady Louise Loder gave a sum of money to Lord Duncannon to make purchases on their behalf.

Miss Thorold and her many friends kindly arranged the admission tickets.

Programmes and tea tickets were untiringly dispensed by Miss Wood, Miss Ethel Wood, Miss Florence Beaton, Miss Adolph, and Miss James.

It is to be hoped that those who were unable to be present or make purchases at this exhibition will not forget that the depot of the Association is at 20, Motcomb-street, Belgrave-square, where, as I can speak from personal experience, even the smallest order receives the utmost attention.&lt;ref&gt;&quot;Irish Industries.&quot; ''Gentlewoman'' 19 December 1896, Saturday: 24 [of 123], Cols. 1a–3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18961219/122/0024. Print p. 882.&lt;/ref&gt;&lt;/blockquote&gt;

===16 December 1896, Wednesday===
Dolmetsch mentioned wanting to go to Florence. &quot;Dolmetsch was always keen to perform in Italy but was unable to afford such a trip on his own account. Horne, as usual, came to the rescue and used his influence to obtain a sponsor, but nowhere is the benefactor named. Although Dolmetsch was scrupulous in limiting his spending to the musical requirements of an undertaking, he was blissfully unconcerned as to the source of the funds so provided. All that occupied his thoughts at the moment was that at last he would be going to Italy — the land where culture pervaded everything and the very speech was music&quot; (Campbell ????).

===25 December 1896, Friday===
Christmas Day
===26 December 1896, Saturday===
Boxing Day
===26 December 1896, Saturday===
December Bank Holiday
==Works Cited==
*[1896-04-28 Aberdeen Journal] &quot;The Forbes-Erskine Marriage.&quot; Aberdeen Journal 28 April 1996, Tuesday: 5 [of 8], Col. 1c [of 8]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000575/18960428/183/0004 (accessed 2019).
*[1896-05-23 Leamington Spa Courier] &quot;Personal Items.&quot; Leamington Spa Courier 23 May 1896, Saturday: 4 [of 8], Col. 6a [of 6]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000319/18960523/025/0004 (accessed July 2019).
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*[1896-06-30 Belfast News-Letter] &quot;Wedding of the Lord Lieutenant’s Daughter. A Brilliant Ceremony. From Our Own Correspondent. By Our Own Private Wire.&quot; Belfast News-Letter 30 June 1896, Tuesday: 5 [of 8], Col. 7a–9c [of 9]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/18960630/023/0005 (accessed July 2019).
*[1896-07-14 Morning Post] &quot;The Queen’s Garden Party.” Morning Post 14 July 1896, Tuesday: 7, Col. 6a – 8, Col. 4a [of 12 pp and 7 cols]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18960714/099/0008 (accessed July 2019).
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*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 14 February 1896, vol. 53, p. 172, col. 3. (Accessed 9 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 28 February 1896, vol. 53, p. 196, col. 2. (Accessed 9 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 20 March 1896, vol. 53, p. 270, col. 1. (Accessed 10 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 20 March 1896, vol. 53, p. 271, col. 2. (Accessed 10 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 10 April 1896, vol. 53, p. 341, col. 2. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 17 April 1896, vol. 53, p. 364, col. 2. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 17 April 1896, vol. 53, p. 365, col. 1. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 17 April 1896, vol. 53, p. 366, col. 2. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 1 May 1896, vol. 53, p. 412, cols. 1-2. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 1 May 1896, vol. 53, p. 412, col. 2. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 1 May 1896, vol. 53, p. 415, col. 2. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 1 May 1896, vol. 53, p. 415, col. 1. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 8 May 1896, vol. 53, p. 436, col. 2. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 15 May 1896, vol. 53, p. 461, col. 2. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 15 May 1896, vol. 53, p. 462, col. 3. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 22 May 1896, vol. 53, p. 484, cols. 1-2. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 5 June 1896, vol. 53, p. 532, col. 1. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 12 June 1896, vol. 53, p. 556, cols. 1-2. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 12 June 1896, vol. 53, p. 556, col. 2. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 19 June 1896, vol. 53, p. 581, cols. 1-3. (Accessed 13 October 2009 in Google Books.)
*&quot;Table Talk,&quot;The Literary World: Choice Readings from the Best New Books, and Critical Reviews, (London: James Clarke), 26 June 1896, vol. 53, p. 604, cols. 1-2. (Accessed 14 October 2009 in Google Books.)

== Footnotes ==
&lt;references /&gt;</text>
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  <page>
    <title>Social Victorians/Timeline/1899</title>
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      <text bytes="37384" sha1="hjtjxaqldgtgum6bt2kzjfbwn6c46ra" xml:space="preserve">[[Social Victorians/Timeline/1850s | 1850s]] [[Social Victorians/Timeline/1860s | 1860s]] [[Social Victorians/Timeline/1870s | 1870s]] [[Social Victorians/Timeline/1880s | 1880s Headlines]] [[Social Victorians/Timeline/1890s | 1890s Headlines]] [[Social Victorians/Timeline/1890 | 1890]] [[Social Victorians/Timeline/1891 | 1891]] [[Social Victorians/Timeline/1892 | 1892]] [[Social Victorians/Timeline/1893 | 1893]] [[Social Victorians/Timeline/1894 | 1894]] [[Social Victorians/Timeline/1895 | 1895]] [[Social Victorians/Timeline/1896 | 1896]] [[Social Victorians/Timeline/1897 | 1897]] [[Social Victorians/Timeline/1898 | 1898]] 1899 [[Social Victorians/Timeline/1900s | 1900s]] [[Social Victorians/Timeline/1910s | 1910s]] [[Social Victorians/Timeline/1920s-30s|1920s-30s]]

==Sometime in 1899==
In 1899 the International Council of Women was held in London.

The year 1899 was the celebration of Victoria's 80th birthday.

==January 1899==
===1 January 1899, Sunday, New Year's Day===

=== 11 January 1899, Wednesday ===
Some social events were organized around Princess Henry of Battenberg's opening of a nurses' home in Romsey:&lt;blockquote&gt;In spite of the bad weather the inhabitants of Romsey gave a hearty welcome on Wednesday to Princess Henry of Battenberg, who came to open a nurses' home which has been built as the borough's Diamond Jubilee memorial. Her Royal Highness, travelling by [a] special train from Southampton, arrived at Romsey Station shortly after 12 o'clock. The station and its precincts had been tastefully decorated, there [the] Princess was met by the Mayor of Romsey (the Right Hon. Evelyn Ashley), and Mr. Basil Montgomery, of Stanfield-hall. Princess Henry, who was accommpanied by Colonel Clerk and Miss Minnie Cochrane, then drove through the gaily-decorated streets, amid the cheers of the crowds, to the Town-hall, where the A and B (Westchester) and D (Romsey) Companies of the Hamps[hire? tead?] Volunteers were drawn up under the command of Major Mortimer. The corps played the National Anthem and the Volunteers gave the Royal salute. Under the awning in front of the Town-hall the Town Clerk (Mr. Harle) read a loyal address from the Mayor aldermen, and burgesses of Romsey. The Princess graciously bowed her thanks for the sentiments contained in the address.

The Royal party then moved, amid the cheers of the people and the ringing of the bells of Romsey Abbey to the Royal Nurses' Home, which is situated in Ch[?]ville-street. At the entrance of a pavilion which had been erected for the purpose the Princess was presented by Miss Montgomery with a basket of flowers, and which Mr. Basil Montgomery presented an address on behalf of the committee of management, elected by [?] subscribers, in which it was stated that funds raised for the home had entirely subscribed by subjects of her Majesty in Romsey and the adjacent parts. Not only had the freehold site been purchased and the home built and furnished, but promises of support had been received which justified the committee in conceiving that the success of the institution was assured. The primary object of the institution was to provide nurses for the sick poor in Romsey and the surrounding parishes. An accident ward was attached to the home, where patients would have the double advantage of receiving not only trained care and attention, from nurses, but also the benefit of the skill of the [medical?] men resident in the district, who had [magnani?]mously offered their support to the institution and had agreed to serve as members of the committee. Her Royal Highness in reply said:— &quot;I declare [the?] Royal Nursing Home, in commemoration of the Queen's Diamond Jubilee, open, and wish it every success. [The?] Princess was then presented with a golden key [that?] opened the home premises, which she inspected. [The?] land on which the home is built was purchased [for?] £l50, and the contractors' price for the [?] £425.

The Royal party afterwards drove to Stanfield-hall, the company at lunch including the Countess of Dudley (sister of Mrs. Montgomery), the [[Social Victorians/People/Bourke|Hon. Mrs Algernon Bourke]], General Oliphant, and the Mayor and Mayoress. At 3 o'clock the party privately viewed the abbey, where they were received by the Rev. J. Cooke-Yarborough (vicar) and the churchwarden, and afterwards Broadlands, the residence of the Mayor was visited. After tea at Broadlands, Princess Henry left at 5 o'clock on her return to Osborne.&lt;ref&gt;&quot;Princess Henry of Battenberg at Romsey.&quot; ''Evening Mail'' 13 January 1899, Friday: 4 [of 8], Col. 6b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003187/18990113/049/0004. Print title: The ''Mail'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

===25 January 1899, Wednesday===
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] at the Holderness Hunt Ball:&lt;blockquote&gt;The Assembly Rooms at Beverley were on Tuesday the scene of much gaiety, the occasion being the ball in connection with the Holderness Hunt. The company numbered over 300, the county families being well represented. The spectacle was a brilliant one. The music was supplied by Wolfe's White Hungarian Band. The arrangements were chiefly in the hands of Mr. Clive Wilson and Mr. Harrison Broadley, whose efforts were certainly most successful. Among the guests were the Countess of Huntingdon, Lady Clementine Walsh, the Hon. Mary Hawke, [[Social Victorians/People/Arthur Stanley Wilson|Mr. and Mrs. Arthur Wilson]], Mrs. Lycett Green, Lady de Ramsey, Lady Beatrice Taylor, the Hon. Alexander Fellowes, Mr. and Mrs. Kenneth Wilson, Miss Muriel Wilson, Colonel and Mrs. Armytage, Colonel Haworth Booth and party, Colonel and Mrs. Grimston, Commander Bethell, M.P., the Hon. Dudley Majoribanks, Mr. Cecil Wellesley, Mr. and Mrs. Calverley-Rudston, Lord and Lady Herries and the Hon. Misses Maxwell, Mr. and Mrs. Gunter, Mr. Marco Wilson, Mr. and Mrs. Hall Watt, Captain Battine, Miss Parsons, Mr. and Mrs. George Duncombe, Mr. J. Hotham, Miss Bethell, Miss B. Walker, Mr. J. J. Harrison, Colonel Burstall, Mr. and Mrs. Harrison Broadley and party, Mr. and Mrs. Roland Heathcote Hacker, [[Social Victorians/People/Keppel|The Hon [sic] George Keppel]], Mr. Arthur Portman, the Hon. Harold Fitzclarence, Miss Daye Baker, Miss Helen Bower, Mr. and Mrs. Ellershaw, Major Macmullen, Sir Spencer Maryon Wilson, Mr. Prince, Sir Charles Hartopp, Mr. and Mrs. Kerr, Mr. Walter Burns, Mr. and Mrs. Wade and party, Mr. Harold Brassey, Miss Joan Wilson, Miss Enid Wilson, Mr. Henry Wilson, Lord Acheson, and many others. Dancing was kept up till the early hours of the morning.&lt;p&gt;

The meet of the hounds next day was at the Beverley Grand Stand. Owing to the frost it was late before the pack arrived from the kennels. Many hundreds of people were present, tempted by the fine, crisp, bracing morning. Leaving Westwood the hounds proceeded to Broadedge Farm, where a fox was found, and he was hunted on to Bentley and Skidky to Cottingham. The company, having seen the throw-off, returned home.&lt;ref&gt;&quot;Holderness Hunt Ball.&quot; ''Yorkshire Herald'' 29 January 1899, Saturday: 10 [of 18], Col. 6c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000500/18990128/086/0010 (accessed July 2019).&lt;/ref&gt;&lt;/blockquote&gt;

==February 1899==

=== 1899 February 7, Tuesday ===
A very high-ranking committee organized a ball at the Hotel Cecil held on 7 February 1899:&lt;blockquote&gt;The ball to be held at the Hotel Cecil on the 7th of this month promises to be a brilliant affair. A very influential list of patrons and patronesses has been obtained, and all the principal lady patronesses have intimated their intention of being present, as well as the majority of the officers of the Household Cavalry. Gottlieb's Orchestra has been engaged, and dancing is to commence at 11.30. Tickets are a guinea each, including supper, and may be obtained at the London libraries or of the Honorary Secretary. The supper is to be one of the great features of the ball, and in order to provide the necessary accommodation — it is expected that between seven and eight hundred will sit down to table at once — the grand drawing-room of the Hotel will for the first time be turned into a supper-room. The tables are to be decorated with ivy and roses and Egyptian lilies. A separate entrance will be provided for the lady patronesses, of whom many intend to bring guests. The Grand Hall, in which the dancing will take place, is one of the finest ball-rooms in London, and includes a large gallery at one end, and a room, with bays, overlooking the dancers. The committee includes Prince Francis of Teck, the [[Social Victorians/People/Crewe-Milnes|Earl of Crewe]], [[Social Victorians/People/Crichton|Viscount Crichton]], and Lord Herbert Vane Tempest; and among the patronesses are the [[Social Victorians/People/Louisa Montagu Cavendish|Duchess of Devonshire]], the Marchioness[es] of [[Social Victorians/People/Londonderry|Londonderry]] and [[Social Victorians/People/Ormonde|Ormonde]], the Countesses of Harrington, Erne, [[Social Victorians/People/Desart|Desart]], and [[Social Victorians/People/Gosford|Gosford]], Lady Clementine Walsh, [[Social Victorians/People/Wolseley|Viscountess Wolseley]], and the Hon. [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]].&lt;ref&gt;&quot;The World of Fashion.&quot; ''Clifton Society'' 02 February 1899, Thursday: 6 [of 16], Col. 1c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002164/18990202/035/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

==March 1899==
===31 March 1899, Friday===
Good Friday

==April 1899==
===2 April 1899, Sunday===
Easter Sunday
==May 1899==
===2 May 1899, Tuesday===
The [[Social Victorians/People/Albert Edward, Prince of Wales|Prince of Wales]] visited Ruthin Castle, in Wales, for the Chester races. Ruthin Castle was the home of Cornwallis-West, and [[Social Victorians/People/Muriel Wilson|Muriel Wilson]] was a part of the house party that made up the reception for the prince (1899-05-03 Daily Telegraph). [[Social Victorians/People/Churchill|Jennie Spencer-Churchill]], Lady Randolph Churchill was there, as was [[Social Victorians/People/Cornwallis-West|George Cornwallis-West]]; their relationship was quite controversial and the Prince, normally quite warm to Jennie Churchill, was cold ().

===8 May 1899, Monday===
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] and [[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]] were at the opening of the Royal Opera, Covent Garden, Wagner’s ''Lohengrin''. The [[Social Victorians/People/Albert Edward, Prince of Wales|Prince of Wales]] was there, as were a number of notable celebrities (1899-05-13 Penny Illustrated Paper)

===15 May 1899, Monday===
&lt;quote&gt;Ipswich High School.— On Monday, May 15, the school was honoured by a visit of H.R.H. the Princess Louise, who came, faithful [386A/B] to a long-standing promise, to give away the prizes and certificates adjudged on the results of the Oxford and Cambridge Joint Board and the Cambridge Local Examinations of last year. Her Royal Highness was accompanied by the Marquis of Lome, K.G., and attended by Mr. E. B. Phipps, Assistant-Secretary to the G.P.D.S. Co., who acted as equerry in the place of Col. Collins. The Princess was received, on her arrival in Ipswich, by Mr. Bousfield, Chairman of the Council of the G P.D.S. Co., and by Lady Digby, Miss Gurney, Mr. Eve, and Mr. Buxton, members of the Council. The visit was of a semi-private character, and hence there was no official reception by the Mayor and Corporation of Ipswich. The High School was reached at two o'clock, and here the Princess was received by members of the Local Committee, with whom were Miss Youngman, the late Headmistress, Miss Kennett, the present Headmistress, and Mr. McDowall, Secretary to the G.P.D.S. Co. The girls, two hundred in number, were drawn up on either side of the Lower Hall, and presented an exceedingly bright appearance in their white dresses and sashes of crimson, the school colour. The Princess graciously consented to walk up the hall between the lines of girls and to receive a bouquet from Janet Stewaid, of Form II , the daughter of Mr. W. Steward, a member of the Local Committee. She then made the tour of the class-rooms, escorted by Mr. Bousfield, Miss Youngman, and Miss Kennett. Luncheon was served in the Upper Hall at 2.15. The number of invited guests included, in addition to those already mentioned, the Mayor of Ipswich, the Marquis of Bristol, Lord Lieutenant of the county, Sir Charles Dalrymple, M.P., Major Bond (in command of the Volunteer guard of honour), and Mr. John Farmer. At four o'clock the party adjourned to the Council Chamber of the Town Hall, where, after several songs by the pupils, under the conductorship of Mr. Farmer, and an exhibition of drill, Mr. Bousfield made a short speech, in which he explained the aims and ideals of the schools of the G.P.D.S. Co., and expressed the gratitude of the Council to Miss Youngman, who for twenty-one years had watched over and guided the development of the Ipswich School with so much energy and judgment. The Princess then distributed the prizes, after which a vote of thanks to her was proposed by Mr. Bousfield, and seconded by the Mayor. Lord Bristol also spoke to the resolution, which was unanimously carried. The Marquis of Lome having briefly responded, the proceedings were closed by the singing of &quot;Auld Lang Syne,&quot; the hymn &quot;O God, our help in ages past,&quot; and &quot;God save the Queen.&quot; The bouquet given to the Princess at the Town Hall was presented by Sybil Casley, of the Kindergarten, and the programme was handed to her Royal Highness by Judith Becher, of the Transition Class. At the conclusion of the afternoon's proceedings the Princess and her party partook of tea in the Mayor's parlour at the Town Hall, and left for London at six o'clock.&lt;/quote&gt; (The Journal of Education. Vol. 21, New Series (January to December 1899). Page 386 [June 1899].Cols. A-B. Google Books: http://books.google.com/books?id=jZFIAAAAYAAJ).

===20 May 1899, Saturday===
Emma Nevada at the Crystal Palace (https://www.msu.edu/~graye/emma/chronolo.html).

===27 May 1899, Saturday===
Emma Nevada at the Crystal Palace (https://www.msu.edu/~graye/emma/chronolo.html).

===31 May 1899, Wednesday===
Derby Day at Epsom Downs, so Luise Friederike Auguste Montagu  Duchess of Devonshire, hosted a ball that night?

==June 1899==
Summer 1899: [[Social Victorians/People/William Butler Yeats|William Butler Yeats]] summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).
===21 June 1899, Wednesday===
The ''Illustrated London News'' reported on a bazaar to raise money for the Charing Cross Hospital. Many celebrities were present. People whose portraits were drawn were Princess Henry of Pless, Marchioness of Granby, Duchess of Marlborough, [[Social Victorians/People/Muriel Wilson|Muriel Wilson]], Countess of Westmorland, Duchess of Sutherland, Mr. Burdett-Coutts, M.P., and mentioned in the story were the following: Princess Louise, Duchesses of Westminster, Portland, Abercorn, Sutherland, and Marlborough; Countesses of Westmorland, Cadogan, Chesterfield, Mrs. Choate (wife of American ambassador; Lord Glenesk (https://www.britishnewspaperarchive.co.uk/viewer/bl/0001578/18990701/054/0017). 

Another report: &lt;quote&gt;The Charing Cross Hospital Bazaar at the Albert Hall was great success. It was a very hot day, but the aristocracy were present in large numbers. There were many exquisite toilettes. [[Social Victorians/People/Arthur Stanley Wilson|Mrs Arthur Wilson]] wore black, with cream embroidery, covered with sequinned net; corn-coloured net toque, with sprays of gold and feathers. Mrs Kenneth Wilson’s costume was palest grey voile, tight fitting, with a lace yoke, and a white tulle hat with osprey in front. Mrs Menzies and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]] were at “Flowerland,&quot; with Ladies Marlborough, Westmoreland. Mar and Kellie, Chelsea, Craven, Juliette Lowther, and Norreys. Miss Muriel Wilson was in white silk and crepe gown, with bands of coarse cream lace and open neck, transparent sleeves of lace and crepe. She wore a large black chip hat of tulle fastened at the chin, and carried a large-handled basket of roses, tied with heliotrope satin ribbon. The three sisters from Warter Priory were at the refreshment stall attired in grey dresses, while fischus, and big white mob caps.&lt;/quote&gt; (1899-06-24 Beverley and East Riding Recorder)

===26 June 1899, Monday===
There was apparently a regular celebration of [[Social Victorians/People/Arthur Collins|Arthur Collins]]' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902.

According to the ''Morning Post'' for 27 June 1899, Mr. Schreiber danced in the Gainesborough Quadrille at the annual Royal Caledonian Ball on Monday, 26 June 1899.&lt;blockquote&gt;THE ROYAL CALEDONIAN BALL.

The annual Ball, held last night at the Whitehall Rooms, Hôtel Métropole, in aid of the funds of the Royal Caledonian Asylum and the Royal Scottish Hospital proved a great success, nearly nine hundred persons being present. The interest ot the evening centred in the eightsome reels and the fancy quadrilles. The former were arranged by the Hon. Mrs. Baillie of Dochfour (who unfortunately through indisposition was prevented attending), and were danced as follows: 

1.

The Marquis of Tullibardine, D.S.O., Royal Horse Guards, and the Countess of Mar and Kellie.

Viscount Fincastle, V.C., 16th Lancers, and Laily Helen Stewart Murray.

The Hon. Alexander Ruthven, V.C., Cameron Highlanders, Miss Katharine Ramsay.

Mr. M'Neil, Seaforth Highlanders, and Miss Sibyl Murray.

2.

The Earl of Mar and Kellie and Lady Helen Graham.

Mr. Alastair Murray, younger, of Lochcarron, and Lady Hilda Keith-Falconer.

The Hon. Alexander Fraser and the Hon. Cecily Drummond.

Mr. M'Lean, Scots Guards, and Miss Baillie.

3.

Lord Lovat and Lady Grizel Cochrane.

Captain Greenhill-Gardyne, Gordon Highlanders, and the Hon. Ethel Fraser.

Mr. Baillie, Seaforth Highlanders, and the Hon. Daisy Fraser.

The Hon. Hugh Fraser, Scots Guards, and Miss Marvel MacGregor.

4.

Mr. Cameron, younger, of Lochiel, Grenadier Guards, and the Countess of Cromartie.

Mr. NIall Campbell and Miss Edith Chaplin.

Mr. Douglas Brodie and Miss Elspeth Campbell.

Mr. Alastair MacGregor of MacGregor and Miss Vere Brodie.

5.

Mr. Ramsay, Black Watch, and Lady Margaret Crichton Stewart.

Mr. M'Ray, Black Watch, and Lady Edith Montgomerie.

Mr. Matheson, Coldstream Guards, and the Hon. Beatrice Dalrymple.

The Hon. Kenneth Campbell and the Hon. Gwendolen Maxwell.

The gentlemen wore Highland dress, while the ladies were in white gowns with sashes formed of their respective tartans, the badges of their clans appearing in their hair and on their dresses.

The Countess of Hopetoun, one of the most energetic of the ladies patronesses, was responsible for the two fancy quadrilles. The undernamed took part in

THE ROMNEY QUADRILLE.

Viscount Crichton, Royal Horse Guards, and Countess Hopetoun.

Mr. C. C. de Crespigny, 2nd Life Guards, and Lady Constance Scott.

Hon. Claud Drummond Willoughby, Coldstream Guards, and Lady Florence Astley.

Hon. Gerald Ward, Ist Life Guards, and Lady Beatrice Herbert.

Mr. Tryon, Grenadier Guards, and Lady Mary Drummond Willoughby.

The Earl of Kerry, Grenadier Guards, and Lady Marjorie Carrington.

Mr. Trotter, Grenadier Guards, and the Hon Alice Grosvenor.

Mr. Hamilton, Grenadier Guards, and Miss Muriel White.

THE GAINSBOROUGH QUADRILLE.

Major Gordon-Gilmour, Grenadier Guards, and Lady Alice Shaw Stewart.

The Hon. Raymond de Montmorency, V.U., 21st Lancers, and Lady Sybil Primrose

Captain Brinton, 2nd Life Guards, and Lady Edith Villiers.

[[Social Victorians/People/Schreiber|Captain Schreiber]], 1st Life Guards, and Hon. Maud de Moleyna.[?]

Captain Heneage, Grenadier Guards, and Miss Long.

Mr. Stirling, Coldstream Guards, and Miss Cotton Jodrell.

Captain Green-Wilkinson, Rifle Brigade, and Miss Sibell Chaplin.

Mr. Vandeleur, D.S.O., Scots Guards, and Miss Muriel Chaplin.

The officers were in uniform, and their partners wera attired in gowns of white mousseline-de-soie over silk slips of different colours, those in the Romney quadrille wearing lace fichus, and those in the Gainsborough quadrille chiffon scarves, and all had their hair threaded with coloured chiffon or ribbon to match their sashes or scarves.

At eleven o'clock a procession was formed, headed by the Pipers, and the Duke of Atholl, Treasurer of the ball, and those taking part in the Reels and Quadrilles entered the ball-room, dancing immediately commencing to Herr Iff's orchestra. The Ladies Patronesses present included the Duchess of Buccleuch, the Duchess of Atholl, the Duchess of Montrose, the Marchioness of Bute, the Countess of Mar and Kellie, Mary Countess of Mar and Kellie, the Counters of Selkirk, the Countess of Dundonald, the Countess of Ancaster, Viscountess Strathallan, Viscountess Dalrymple, Lady Anne Murray, Lady Eleanor Brodie, Lady Herries, Lady Sinclair, Lady Middleton, Lady Ramsay of Bamff, Lady Maxwell of Monreith, Lady Macpherson Grant, Mrs. Munro, and Mrs. Murray of Polmaise. Before dancing became general the boys and girls of the Asylum, headed by their Pipers and band, marched round the ball-room. Much credit is due to the President and Vice-President of the ball, the Duke of Atholl and Marquis of Tullibardine, for their efforts in the cause of charity.&lt;ref&gt;&quot;The Royal Caledonian Ball.&quot; ''Morning Post'' 27 June 1899, Tuesday: 7 [of 12], Col. 7b–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18990627/063/0007.&lt;/ref&gt;&lt;/blockquote&gt;

==July 1899==
July 1899, Emma Nevada sang for Queen Victoria at Osborne House (https://www.msu.edu/~graye/emma/chronolo.html).

=== 1 July 1899, Saturday ===
A meeting was held in London to preserve Kilkenny as a national park:&lt;blockquote&gt;The annual general meeting of the National Trust for for places of historical interest or natural beauty was held at Grosvenor House, under the presidency of his Grace the Duke of Westminster. The meeting was largely attended in view of the proposed formation of a special committee, consisting of members of the Trust and others, to consider what steps can be taken to secure to the nation the enjoyment of the celebrated scenery of the Killarney district. Among those present were — The Earl of Cork, the [[Social Victorians/People/Mayo|Earl of Mayo]], the Lord Mayor of Dublin, the Earl of Rosse, Mr V B Dillon (Dublin), Mr H W Crossley, Right Hon James Bryce, M.P.; Sir M Grant Duff, Mr Seymour Lucas, R.A.; Miss Oc[t]avia Hill, Mr J St Lee Strachey, Editor of the &quot;Spectator&quot;; Sir Joshua Fitch, Sir Benjamin Stone, M.P.; Mr F C Penrose, Hon [[Social Victorians/People/Bourke|Algernon Bourke]], etc.
Letters expressing their inability to attend, but expressing sympathy with the object of the meeting, were received from the Earl of Meath, Mr Lecky[, M.]P., and Lord Carlisle.

The [[Social Victorians/People/Westminster|Duke of Westminster]], in moving the adoption of the annual report, pointed out that an opportunity now existed of acquiring Killarney as a National park, and said a very important question that had arisen lately was the fact that the Lakes of Killarney and the Muckross property was in the market. England had its public parks in the New Forest, and it would be, perhaps, only right that Ireland should have a playground, though it was a good way off, and though it did rain occasionally in that country. (Laughter.) It would be most unfortunate if, by private purchase, any of the parks and private drives in Killarney should be shut up for evermore. They had an unpleasant example in the Giants' Causeway, which, he believed, had been purchased by private individuals and a toll demanded — a state of things that ought not to be. (Hear, hear.) Lord Dufferin, who too ka [sic] great part in the acquisition of Niagara, would move the resolution respecting tho Muckross property.

Sir Robert Hunter, who seconded the resolution, pointed out that under the Irish Local Government Act County Councils were authorised to put in force the provisions of the Ancient Monuments Protection Act, so that in Ireland they had not only a wider scope, but the local authorities were authorised to acquire and preserve those monuments.

The report was adopted.

The Bishop of London remarked that he had never been to Killarney, but he hoped they would preserve it so that he may have an opportunity of visiting tho lakes at some future date.

Mr Shaaw-Lefevre said people were willing to pay £5,000 for a picture of a landscape, then how much more important was it to secure the original from which the picture was taken.

The Marquis of Dufferin moved — &quot;That this meeting desires to record its conviction that it would be deeply to be deplored were the Lakes of Killarney, perhaps more widely celebrated for their natural beauty than any other spot in the British Isles, to be closed against the public or marred by vulgarising and incongruous treatment, and urges that the opportunity offered by the sale of the Muckross Estates should be embraced to secure the lakes permanently to the nation, as the Falls of Niagara have been secured by the joint action of the United States and the Dominion of Canada. That with this object it is desirable that the council of the Trust do organise a special committee of members of the Trust and others, to take such steps as may be practicable to bring about the desired result.&quot; In America there was a vast region which had been entirely devoted as a kind of park or place of recreation for the public at large. In another part of America there was another region equally extensive, he believed, which was devoted to the preservation of all the wild animals which could be found upon the Continent. Again, Canada and the State of New York joined together in the most generous manner to rescue the neighbourhood of the Falls of Niagara from the innumerable quantity of sheds and shanties and every kind of disfiguring buildings which were encroaching upon that beautiful region. (Hear. hear.) One could not but ask oneself whether it was altogether impossible thta [sic] they might induce her Majesty's Government to take the same kind of vview of its obligations. If that appeal were addressed to deaf ears they were not altogether without resources to fall back upon. Ireland was the home of patriotism. Every city in Ireland could point to the various magnificent buildings, public halls, and churches, asylums and hospitals, which were monuments of the munificence of private individuals, and he felt sure that there could be found in Ireland a man or group of men who would combine for this noble and patriotic purpose and if they would do so their names would be regarded with the utmost gratitude by innumerable generations. (Cheers.)

The Right Hon James Bryce., M P, seconded the resolution, which was supported by the Earl of Mayo and Sir Benjamin Stone. M P. Lord Mayo suggested that the name of some Irishmen could be added, and form a committee in Dublin to work with the National Trust. They were as follows:—

The Lord Mayor of Dublin, the Marquis of Dufferin, [[Social Victorians/People/Dunraven|Lord Dunraven]], Lord Ardilaun, [[Social Victorians/People/Iveagh|Lord Iveagh]], Lord Rosse, Mr Lecky, M P; the Mayor of Cork, Mr Thomas Lough, M P; Mr John Redmond, M P; Sir Thomas Esmonde, M P; the Hon Horace Plunkett, M P; Mr John Jameson[,] Mr James Talbot Power, Mr V B Dillon, Mr F W Crossley, Mr Robert Saunders, and Mr D J Wilson. The Lord Mayor's name was also added.

The resolution was adopted.

The Hon [[Social Victorians/People/Bourke|Algernon Bourke]], rising at the end of the room, said he had been authorised by another gentleman to say that he was negotiating for the purchase of the property, and if the negotiations were successful he would be willing to treat with the society to enable them to purchase the right of way over Muckross Estate. The speaker did not mention the name of the purchaser.

A vote of thanks was then passed to the [[Social Victorians/People/Westminster|Duke of Westminster]] for his kindness in allowing the use of his house, and for presiding over the meeting. The proceedings then ended.&lt;ref&gt;&quot;The Muckross Property. Important Meeting in London. Killarney as a National Park.&quot; ''Cork Weekly News'' 01 July 1899, Saturday: 7 [of 8], Col. 2a–b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004163/18990701/122/0007. Print n.p.&lt;/ref&gt;&lt;/blockquote&gt;

===4 July 1899, Tuesday===
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] was at a garden party hosted by Lady Rothschild and Mrs. Leopold Rothschild after the end of the Women’s Congress: &lt;quote&gt;Not the least interesting features of the Women's Congress have been the social entertainments. On Tuesday, after the final sessions had been held, Lady Rothschild and Mrs. Leopold Rothschild invited the delegates to a garden party at Gunnersbury Park. Special trains conveyed the guests to Mill-hill Station. The guests were received by Lady and Mrs. Leopold Rothschild, the former in black lace over pale mauve silk, and the latter in blue and white muslin, and Lady Battersea, in a charming light grey and white frock and a little yellow bonnet that suited her to perfection. By five o'clock the grounds were crowded, and among the well known people to be seen walking about there were Lady Battersea, Lady Harcourt, Mr. and Lady Clementine Walsh, the latter in pale grey and white, Lord and Lady Gosford, and with them Lady Aldra Acheson; Lady Alice Stanley, in rose-pink; Mrs. Rolands [Ronalds?] in white; Mr. and Lady Barbara Smith, and Mrs. Maguire in a becoming frock of pale yellow. Lady Kilmorey, who came quite early in the afternoon wore white muslin, with a large straw hat with roses; Lady Chelsea, in mauve; and Miss Muriel Wilson, in a lovely dress of pale blue, with transparent lace sleeves, and large white hat with roses, looked particularly well. Lady Blandford was in pale grey; Mrs Arthur Sassoon was also in grey. Among some of the late arrivals were Lord and Lady Crewe, with Lady Annabel Milnes, Lady Crewe in a pretty white dress. From the terraces the scene was magnificent. The park stretched over a velvety green lawn, dotted with beds of of [sic] exquisite flowers; bridged over with roses, that gave them the appearance of great baskets. A fountain, with pond lilies nestling in its shadowy spots, lay at the left. At another side of the lawn was an artificial lake, with boats and boatmen at the disposal of visitors. A string band at the bank and a second marquee afforded rest, music, and refreshment to those who preferred to remain in a little world of their own. A three band played lively airs for the American bicycle polo team, who gave an exhibition of their skill on the lawn. And both circus and stage were utilised for the afternoon amusements.&lt;/quote&gt; (1899-07-08 Bridgnorth Journal)

=== 15 July 1899, Saturday ===
&lt;blockquote&gt;Lord Kenyon, Mr. Schomburg McDonnell (Lord Salisbury's private secretary), Colonel Dawson, Mr. H. Ridgway, Lady Gerard, the Hon. Miss Gerard, Mrs. Hartmann, and [[Social Victorians/People/De Jancourt|Mdlle Jancourt]] arrived at Broughton Castle on Saturday night on a weekend visit to Lord and Lady Algernon Gordon Lennox.&lt;ref&gt;&quot;Local Town and Country Notes.&quot; ''Banbury Guardian'' 20 July 1899 Thursday: 8 [of 8], Col. 1b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001523/18990720/116/0008.&lt;/ref&gt;&lt;/blockquote&gt;

==August 1899==
===28 August 1899===
Summer Bank Holiday

==September 1899==
==October 1899==
===31 October 1899, Tuesday===
Halloween.
==November 1899==
===5 November 1899, Sunday===
Guy Fawkes Day

=== 23 November 1899, Thursday ===
Captain C.S. Schreiber attended a Royal and Imperial Dinner Party at Windsor Castle:&lt;blockquote&gt;The Imperial and Royal dinner party included their Imperial Majesties the German Emperor and Empress, their Royal Highnesses the Prince and Princess of Wales, the Duke and Duchess of Connaught, Prince and Princess Christian of Schleswig-Holstein, her Royal Highness Princess Louise Marchioness of Lorne and Marquis of Lorne, their Royal Highnesses Princess Henry of Battenberg, Princess Victoria of Wales, his Serene Highness and her Grand Ducal Highness Prince and Princess Louis of Battenberg, his Highness Prince Albert of Schleswig-Holstein, the Duchess of Buccleuch, Mistress of the Robes; Fraulein von Gersdorff, the Countess Stollberg, the Dowager Lady Ampthill, the Danish Minster, Mons. de Bille; the Belgian Minister, Baron Whettnall; the Portuguese Minister, Mons. de Soveral ; the Greek Chargé d'Affaires, Mons. Metaxas; the Lord Steward, the Lord Chamberlain, his Excellency Count von Bülow, his Excellency Count Eulenburg, his Excellency General von Plessen, Lord Suffield, the Right Hon. Sir Frank Lascelles, Lord Colville of Culross, Sir Francis Knollys, Vice-Admiral Sir John Fullerton, Major-General Swaine, commanding North-Western District, and Signor de Martino.
The band of the Royal Artillery, conducted by Cavaliere L. Zavertal, played the following selection of music in St. George's Hall in the evening:

March from tlie Suite &quot;Sylvia&quot; Delibes.

Vorspiel &quot;Das Heimchen am Herd&quot; Goldmark.

Three Dances from the music to &quot;Henry VIII.&quot; Ed. German.

1, Morris; 2. Shepherd's; 3. Torch.

(a) Adagietto from the Suite &quot;L'Arlésienae&quot; Bizet.

(b) &quot;La Chaise-à-Porteurs&quot; Chaminade.

Ballet Music, &quot;Der Damon&quot; Rubinstein.

&quot;Abendruhe &quot; Loeschhorn.

Angelus from the Suite &quot;Scènes Pittoresques&quot; Massenet.

Overture, &quot;Cleopatra&quot; Mancinelli.

York March.

Her Majesty's guests invited to dine at the Castle, together with the Ladies and Gentlemen of the Royal Household and the suites in attendance on the Queen's Imperial and Royal guests, had the honour of joining the Royal Circle in St. George's Hall.

The following had the honour ot receiving invitations to be present: Lord and Lady Esher, Lady Edwards, Lady and Miss Victoria Bigge, Mr. and Lady Emily Van de Weyer, Miss Loch, Miss Emily Loch, and Miss Catherine Loch, Sir Walter Parratt, the Head Master at Eton and Mrs. Warre, the Provost of Eton and Miss Hornby, Mr. E. C. Austen Leigh, M.A., Mr. A. C. Benson, M.A., Baron and Baroness Campbell von Laurentz, Lieutenant-Colonel C. N. Miles, Captain G. F. Milner, and [[Social Victorians/People/Schreiber|Captain C. S. Schreiber]], 1st Life Guards; Major the Hon. J. St. Aubyn, Captain the Hon. W. Cavendish, and Lieutenant and Adjutant E. Gascoigne, 1st Battalion Grenadier Guards; and Colonel Swinfen, Major Bolton, and Lieutenant-Colonel Tighe, Military Knights of Windsor.

The Queen did not attend the dinner or the concert in St. George's Hall, owing to having so recently received the news of the death of her Grand Ducal Highness the Princess of Leiningen, her Majesty's niece.&lt;ref&gt;&quot;Court Circular.&quot; ''Morning Post'' 24 November 1899, Friday: 5 [of 10], Col. 5a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18991124/045/0005.&lt;/ref&gt;&lt;/blockquote&gt;

==December 1899==
===25 December 1899, Monday===
Christmas Day
===26 December 1899, Tuesday===
Boxing Day
===30 December 1899, Saturday===
[[Social Victorians/People/Arthur Conan Doyle| Arthur Conan Doyle]]'s New Year's Eve party at Hindhead, [[Social Victorians/Haslemere | Haslemere]].

==Works Cited==
*[1899-05-03 Daily Telegraph] &quot;Prince of Wales at Chester Races. Visit to Ruthin Castle. From Our Own Correspondent.&quot; Daily Telegraph &amp; Courier 3 May 1899, Wednesday: 10 [of 16], Col. 3a–c [of 7]. British Newspaper Archive (accessed July 2019).
*[1899-05-13 Penny Illustrated Paper] &quot;At the Opening of the Royal Opera, Covent Garden.&quot; Penny Illustrated Paper 13 May 1899, Saturday: 2 [of 16], Col. 2a, 3a [of 4]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000693/18990513/008/0002 (accessed July 2019).
*[1899-06-24 Beverley and East Riding Recorder] &quot;East Riding Ladies at a London Bazaar.&quot; Beverley and East Riding Recorder 24 June 1899, Saturday: 5 [of 8], Col. 6b [of 6]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001565/18990624/074/0005 (accessed July 2019).
*[1899-07-08 Bridgnorth Journal] &quot;Women’s Congress Ended.&quot; Bridgnorth Journal 8 July 1899, Saturday: 8 [of 8], Col. 3c [of 6]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001961/18990708/138/0008 (accessed July 2019).
*Gray, Eugene F. &quot;Chronology of Events in the Life of Emma Nevada.&quot; Emma Nevada: An American Diva. https://www.msu.edu/~graye/emma/chronolo.html (retrieved 14 April 2010).

== Footnotes ==
&lt;references /&gt;</text>
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    <title>Social Victorians/Timeline/1900s</title>
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        <id>1331941</id>
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      <text bytes="116852" sha1="gy3vknp782tyi4lo71gtk2r7phjgcm3" xml:space="preserve">[[Social Victorians/Timeline/1850s | 1850s]] [[Social Victorians/Timeline/1860s | 1860s]] [[Social Victorians/Timeline/1870s | 1870s]] [[Social Victorians/Timeline/1880s | 1880s]] [[Social Victorians/Timeline/1890s | 1890s]] 1900s

==1900==
1900, early, [[Social Victorians/People/Mathers|MacGregor and Moina Mathers]] were living at 87 Rue Mozart, Paris (Howe 203).
===January 1900===
====1 January 1900, Monday, New Year's Day====
====13 January 1900, Tuesday====
&lt;blockquote&gt;THE HOUSEHOLD TROOPS. ENTERTAINMENT AT HER MAJESTY'S.

The Prince and Princess of Wales, accompanied by Princess Victoria and Prince Charles of Denmark, attended the entertainment to aid the widows and orphans of her Majesty's Household Troops, organised by Mrs. Arthur Paget and presented under the direction of Mr. H. Beerbohm Tree at Her Majesty's Theatre last night.

... [The major part of this story is the program of the entertainment, in which [[Social Victorians/People/Muriel Wilson|Muriel Wilson]], among others, played an important part.]

Among those present at the entertainment were: The Prince and Princess of Wales, Princess Victoria of Wales, and Prince Charles of Denmark, the French Ambassador, the Russian Ambassador, the Portuguese Minister, Count Mensdorff, the Austrian Embassy, Prince and Princess Demidoff, Prince and Princess Hatzfeldt, Prince and Princess Alexis Dolgorouki, Count and Countess Roman Potocki, Count and Countess Alexander Münister, the Duke and Duchess of Devonshire, the Marquis of Downshire, the Earl and Countess of Cork, the Earl and Countess of Westmorland, the Earl and Countess of Gosford, the Earl of Lathom, the Countess of Ancaster, the Countess of Wilton, the Countess of Yarborough, the Countess of Huntingdon, Viscount Curzon, Lord and Lady Farquhar, Lord and Lady Savile, Lord Rowton, Lord Westbury, Baroness d'Erlanger, Count and Countess Seilern, Lord and Lady Ribblesdale, Lord and Lady Hothfield, Lord and Lady Raincliffe, Lord Wandsworth, Lord Charles Montagu, Lady Cunard, Sir Edgar and Lady Helen Vincent, Lady Kathleen and Mr. Pilkington, Lady Violet Brassey, Lady Grey Egerton, the Hon. Humphry and Lady Feodorowna Sturt, Lady Ripley, Lady Katherine Coke, Lady Agneta Montagu, Lady Tatton Sykes, Lady Templemore, Lady Florence Grant, Lady Garrick, Lady Pearson, Lady Constance Haddon, Sir F. Burdett, the Hon. M. Charteris, Sir A. de la Rue, Sir Frederick and Lady Milner, the Hon. E. Stonor, Sir Edward and Lady Sassoon, Mrs. Joseph Chamberlain, the Hon. Mrs. Lawrence, the Hon. Mrs. Napier, Sir Charles Forbes, Mrs. Bradley Martin, Mrs. Cornwallis West, Mr. Arnold Morley, Mr. L. Neumann, Madame Vagliano, Mr. Gillett, Mrs. Godfrey Samuelson, Mrs. Reginald Ward, Mr. and Mrs. Arthur Wilson, Mr. Menzies, Mr. Dreyfous [sic], Mrs. George Coats, Mr. Hartmann, Mrs. Rube, Mrs. Neumann, Mr. Lukach, Mrs. Candy, Mr. Bargrave Deane, Mr. L. V. Harcourt, Mrs. Oppenheim, Mrs. Lionel Phillips, Mr. King. Mr. James Finch, Mrs. Clayton Glyn, Miss Van Wart, Mr. Hall Walker, Mr. Drexell, Mrs. Van Raalte, Mr. Alfred Beit, Mr. Douglas Uzielli, Mrs. Alfred Harmsworth, Mr. Munday, Mrs. William James, Mrs. Newhouse, Mrs. Max Waechter, Mr. G. Prentis, Mrs. M'Calmont, Mr. Blacklock, Mrs. Ausell, Captain Holford (Equerry to the Prince of Wales), Mr. De Nino, Mrs. Keyser, Mrs. Fleming, Mrs. Breitmeyer, Mrs. Wernher, Mrs. Armour, Mr. Van Alan, Mrs. Ewart, Mrs. Carl Meyer, Mrs. Powell, Mr. Hambro, Colonel Charles Allen, Colonel Cunningham, Mrs.Hutchinson, Mrs. Schumacher, Colonel Kennard, Mrs. Fludyer, Mrs. Williamson, Mr. Thellusson, Mr. Sackville West, Captain M'Neil, Mrs. Dalrymple Hamilton, Mrs. Penn Curzon, Mrs. Hamar Bass, Mrs. Kuhliug, General Stracey, Mrs. Jeffcock, Colonel Thynne. (1900-02-14 Morning Post).&lt;/blockquote&gt;

====17 January 1900, Saturday====

1900 February 17, Lady Greville writes about the amateur theatricals Muriel Wilson is involved in: &lt;blockquote&gt;The most notable social event of the week was the amateur performance of tableaux at Her Majesty's Theatre. One is accustomed to the amateurs under every aspect, leaping in where angels fear to tread, essaying the most difficult parts, dabbling in the arts of music and literature, but so full and rich and interesting a performance has rarely been given before. To begin with, there was a masque, modelled on the Elizabethan lines, with song and dance, and special music composed for the occasion by Mr. Hamish McCunn, dresses statuesque and graceful, and a bevy of pretty women to carry out the idea.

One original feature there was, too, which certainly did not present itself before our Virgin Queen, and that was the graceful fencing of Miss Lowther, who looked an ideal young champion in her russet suit and jaunty little cap. A very young debutante appeared in the person of Miss Viola Tree, who, dressed in the nest diaphanous garments, acted with a grace and lightness that promises well for her future career. Mrs. Crutchly, as &quot;Glory,&quot; appeared amid a din of thunder and a rosy glare of limelight, and clashed her cymbals in truly determined fashion. An element of wildness suited to the character, distinguished her agreeable posturing, and her high spiked crown gave distinct individuality to the representation. Mrs. Martineau, Hebe-like in a white robe and a large crown of roses, as if she had just stepped out of a picture by Leighton, then danced and took the palm for poetry and suppleness of movement; Miss [[Social Victorians/People/Muriel Wilson|Muriel Wilson]], meanwhile, having daringly shot up through a trap-door in scarlet robes with a flaming torch, announced herself as &quot;War,&quot; and beckoned to Glory, Victory, and Prosperity, when they finished their performance, to sit beside her on her throne. &quot;Rumour,&quot; alias Mr. Gervase Cary Elwes, sang an excellent topical song, attired in a quaint garb covered with interrogations, and carrying an electric telegraph-post in her hand. Lady Maud Warrender, as &quot;Pity,&quot; advanced from a barge that had just arrived, and sang a doleful ditty which made one wish &quot;Pity&quot; might combine a sense of gaiety. But as Mrs. Willie James, in the part of &quot;Mercy,&quot; dressed as a nurse, recited some bright lines anent Tommy, to the accompaniment of distant fifes and drums, the audience decided to take this as a satisfactory compensation.

All being now harmoniously arranged, &quot;War&quot; performed a sleight-of-hand feat, divested herself of her red dress, her headgear of flaming serpents, and her glistening breastpiece, and appeared in virgin white, crowned with roses, as “Peace,&quot; surrounded by “Music&quot; in a gorgeous gown of gold tissue, by “Painting,&quot; “Science,&quot; and “Literature.&quot; A pleasant finaleof gay music brought the Masque to a close, and left a decidedly agreeable and novel impression behind it.

Tableaux then followed, all more or less well grouped by well-known artists, and represented by beautiful women of Society. Among the familiar faces were Lady St. Oswald, Lady Mary Sackville, Miss Agatha Thynne, Mrs. Fitz Ponsonby, Lady Maitland, Madame von André, &amp;c., but neither Lady Helen Vincent, Lady De Grey, Lady Cynthia Graham, the Duchess of Portland, nor many other well-known and lovely ladies took part in the performance.

Finally, came the Patriotic Tableau, which had evidently engaged all the energies of the organisers of the fête. On a high throne, with a most realistic lion, open-mouthed and fierce-looking, beside her, sat Lady Westmoreland as &quot;Great Britain,&quot; a stately and dignified figure in white satin, draped in a red cloak and crowned with a large wreath of laurel. The stage on each side was lined by genuine stalwart Guardsmen, and to the sound of lively martial music, composed and conducted by Sir Arthur Sullivan, slowly advanced a procession of Great Britain's dependencies, figured by ladies magnificently costumed, their long jewelled trains borne by two little pages in cloth of gold brocade coats, with black silk legs. Very beautiful were the blendings of the colours in this tableau, artistically designed by Mr. Percy Anderson. Lady Claude Hamilton, as &quot;British Columbia,&quot; moved with stately gait in a robe of palest green; Lady Feo Sturt glittered barbarically with jewels; her headdress and her bosom were covered with gems. As the typical representative of &quot;India,&quot; she was dressed in apricot colour and bore branches of hibiscus in her hands. Mrs. Hwfa Williams, in blazing red, carried a parrot and some red flowers. The Hon. Barbara Lister looked lovely and picturesque in her violet robes under a massive wreath of wisteria blossoms; Lady Raincliffe, wearing a curious high head-dress, was dressed in white to represent &quot;Canada.&quot; &quot;Rhodesia&quot; made one of the prettiest figures in her khaki gown and cloak, with the coquettish hat and feathers and the red trimming associated with the Colonial Volunteers. &quot;Natal&quot; appeared appropriately clad all in black, while little &quot;Nigeria,&quot; for the nonce, wore spotless white robes. /

Miss Muriel Wilson spoke an ode, and looked striking in apricot and white, with a high diamond crown and a long standing-up white feather. None of the ladies suffered from shyness; they showed thorough acquaintance with the stage, and moved easily thereon. In fact, costumes, arrangements, music, and the glorious feast of beauty left nothing to be desired.

The final impression in one's mind was that the stage produces strange effects. It idealises some faces, hardens others, and alters many. The large wreaths, almost grotesque in size, proved eminently becoming, and the Grecian draperies carried away the palm for beauty. After them our modern dress seems stiff, angular, and inartistic. The whole performance was one to be commended, and will no doubt be as successful financially as it was from the aesthetic and spectacular point of view.

Mrs. James Stuart Wortley, who died last week, will be regretted by every class of society. This lady, a beauty in her youth, devoted the latter part of her life entirely to works of charity. She founded the East London Nursing Society, to the tender and skilful ministrations of which many a poor woman owes her return to health, and in every philanthropic scheme, emigration, the befriending of young servants, and the education of youth, she took a lively interest. Her clear sense, her logical grasp of subjects and her immense activity were of infinite service in everything she undertook, and her memory will smell sweet in the hearts of the many who loved and depended on her.

I really wonder at the patience of the British taxpayer. During the snow of this week Belgravia, Eaton, and other fashionable squares, remained a morass of slush, ice, and half-melted snow. The pavements as slippery as glass had not been cleansed, and only at the risk of one's life one made one's way from street to street. (Greville 7, Col. 1a-2a)&lt;/blockquote&gt;

'''25 January 1900, Thursday'''

David Lindsay, [[Social Victorians/People/Crawford and Balcarres|Lord Balcarres]] and Constance Lilian Pelly married:
&lt;blockquote&gt;
MARRIAGE OF LORD BALCARRES.

The marriage of Lord Balcarres, M.P. for North Lancashire, eldest son of the Earl of Crawford of Balcarres House, Fife, and Haigh Hall, Wigan, to Miss Pelly, daughter of the late Sir H. Peily, Bart., and granddaughter of the Earl of Wemyss, was solemnised yesterday (Thursday) at St Margaret's Church, Westminster, in the presence of a large gathering of friends.

Among the invited guests were the Earl and Countess of Crawford, the Dowager Countess of Crawford, the Earl of Wemyss, Lord and Lady Elcho, the Hon. E. Lindsay, the Hon. Lionel Lindsay, the Hon. Ronald Lindsay, Lord and Lady Cowper, Mr. A. J. Balfour, the Hon. L. Greville, and many othsrs. The service was fully choral, and was conducted by the Bishop of Stepney, assisted by the the Rev. Canon Gore. Mr Yorke, the stepfather of the bride, gave her away. She wore a dress of white velvet, draped with old Brussels lace, the gift of the Dowager Countess of Crawford: chiffon veil and wreath of natural orange blossoms. Her only ornament was a Maltese cross of diamonds, also the gift of the Dowager Countess of Crawford.

There were nine bridesmaids. Miss Pelly, sister of the bride) [sic], the Hon. Mary Vasey, the Hon. Cynthia Charteris, Miss Brodrick, Miss Sybil Brodrick, Miss Benita Pelly, the Hon. Aline Menjendie, Miss Daisy Benson, and Miss Madeline Bourke. They were attired alike in costumes of white de chine, with lace insertions, with blue chiffon hat, trimmed with plumes of white and blue ostrich feathers. They carried bouquets of violets, and wore red enamel brooches with diamond centres and pearl drops, the gifts of the bridegroom. The Hon E. Lindsay supported his brother as best man.

At the conclusion of the ceremony the guests drove to the town residence of the bride's mother in Queen Anne's Gate, where the wedding reception was held. Later in the day the newly-married couple left town for Wrest Park, Ampthill, kindly lent them for the honeymoon by Earl and Countess Cowper. Princess Louise (the Marchioness of Lorne) sent the bride a handsome silver basket as a wedding present.&lt;ref&gt;&quot;Marriage of Lord Balcarres.&quot; ''Dundee Courier'' 26 January 1900 Friday: 4 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000164/19000126/105/0004.&lt;/ref&gt;
&lt;/blockquote&gt;

===February===
1900, February, a brief account of the Matherses' Isis ceremony appeared in &quot;the New York periodical the ''Humanist'', February 1900&quot; (Howe 201).

==== 15 February 1900, Thursday ====
A number of familiar people took part in [[Social Victorians/People/Arthur Stanley Wilson|Enid Wilson]]'s wedding to the Earl of Chesterfield:&lt;blockquote&gt;This afternoon, at St. Mark's Church, North Audley-street, the [[Social Victorians/People/Chesterfield|Earl of Chesterfield]] is to be married to Miss Enid Wilson, second daughter of Mr. Charles Wilson, M.P., of Marter Priory, Yorkshire, and 41, Grosvenor-square. The bride, who will be given away by her father, will wear a dress of white crêpe de chine wrought with silver and trimmed with fine old lace and ermin. The bridesmaids will be Miss Gladys Wilson, sister of the bride, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], her cousin, Lady Aldra Acheson, daughter of the Earl [[Social Victorians/People/Gosford|and Countess of Gosford]], Lady Mary Willoughby, daughter of the [[Social Victorians/People/Ancaster|Earl and Countess of Ancastor]], Lady Marjorie Carrington, daughter of [[Social Victorians/People/Carrington|Earl and Countess Carrington]], Miss Daphne Bourke, the four-year-old daughter of the [[Social Victorians/People/Bourke|Hon. Algernon and Mrs. Bourke]], [[Social Victorians/People/Balfour|Miss Balfour]], and [[Social Victorians/People/Paget Family|Miss Paget]]. Lace Empire dresses and long bright red cloth Directoire coats trimmed with sable and hats to match. They will carry sable muffs, the gifts to them of the bridegroom. Viscount Ednam, the [[Social Victorians/People/Dudley|Earl and Countess of Dudley]]'s only son, aged six, and Lord Wendover, the only son of Earl and Countess Carrington, aged something over four, will be the youthful trainbearers. After the wedding Mrs. Charles Wilson will hold a reception at 41, Grosvenor-square. The Prince of Wales has given Lord Chesterfield a remarkably handsome embossed silver cigarbox, lined with cedar, monogrammed and coroneted, accompanied by a letter written by his Royal Highness to the bridegroom, cordially wishing him every happiness. The Duke of Fife's gift is a cedar-lined plain silver cigarette-case.&lt;ref&gt;&quot;London Day by Day.&quot; ''Daily Telegraph'' 15 February 1900, Thursday: 8 [of 12], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/19000215/175/0008. Name in British Newspaper Archive: ''Daily Telegraph &amp; Courier'' (London). Print p. 8.&lt;/ref&gt;&lt;/blockquote&gt;Another, more local report: &lt;blockquote&gt;There was very large and fashionable assembly at St. Mark’s Church, North Audley-street, London, on Thursday afternoon, to witness the very pretty wedding of the Right Hon. the Earl of Chesterfield, P.C., of Holme Lacey, Hereford, and Miss Enid Wilson, fourth daughter of Mr. Charles H. Wilson, M.P. for Hull, of Warter Priory, York, and 41, Grosvenor-square, London. The service was fully choral, and the church handsomely decorated.

There were seven bridesmaids in attendance upon the bride. These young ladies were Miss Gladys Wilson (sister). Miss Muriel Wilson (cousin of the bride). Lady Mary Willoughby, Lady Alexandra Acheson, Lady Marjorie Carrington, Miss Dorothy Paget, and Miss Alice Balfour, who were in costumes of quaint, old-fashioned riding coats of red cloth, with white muslin skirts.

The local guests included Sir James and Lady Reckitt, Sir James and Lady Woodhouse, Lord and Lady Herries, Mr. Philip Hodgson, Lord and Lady Raincliffe, Mr. and Mrs. Kenneth Wilson, Mr. and Mrs. Stanley Wilson, Mr. and Mrs. Strickland Constable.

Presents wore also received from Commander Bethell (silver candlestick). Hr. and Mrs. George A. Duncombe, Beverley (Louis XV. sofa). Mr. and Mrs. Frank Lambert, Beverley (inlaid writing table), Colonel and Mrs. Goddard, Cottingham (silver mirror), Mr. Haslewood Taylor, Beverley (pair of prints). (1900-02-21 Beverley Echo)&lt;/blockquote&gt;

==== 27 February, 1900, Tuesday ====
Mardi Gras

===April 1900===

==== 8 April 1900, Sunday ====
Palm Sunday

====14 April 1900, Saturday====
Wynn Westcott assumed W. A. Ayton was on, as he wrote, &quot;the Committee to investigate the G. D. which contains Yeats, Bullock and I suppose Ayton&quot; (Howe 217).

====20 April 1900, Friday====
The R.R. et A.C. was code named Research and Archaeological Association (Howe 226)

====21 April 1900, Saturday====
The Inner Order of the Golden Dawn met at 116 Netherwood Road, West Kensington (Howe 227).

===May 1900===
====26 May 1900, Saturday====
Arthur Sullivan is visited by &quot;Sir George Martin, the organist at St. Paul's Cathedral, and Colonel Arthur Collins, one of the royal equerries&quot; to get him to write a Te Deum thanking God for the end of the Boer War (Ainger, Michael. Gilbert and Sullivan: a Dual Biography. P. 381.).

====30 May 1900, Wednesday====
Derby Day.

According to the Morning Post, &lt;quote&gt;The Derby Day. / The Archbishops of Canterbury and York hold a Reception of Colonial and Missionary Church Workers in the Great Hall of the Church House, 4.30 to 6.30. / ... May Fair and Bazaar, St. George's Drill Hall, Davies-street, Berkeley-square, opened by Lady Edward Spencer Churchill, 2.30.&lt;/quote&gt; (&quot;Arrangements for This Day.&quot; The Morning Post Wednesday, 30 May 1900: p. 7 [of 12], Col. 6C)

===June 1900===
Summer 1900: WBY summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

==== 3 June 1900, Sunday ====
Whit Sunday (Pentecost)

Whitsun party at Sandringham House, described by Lord Knutsford in his letters and summarized by Anita Leslie, whose parent's generation remembered some of these people Knutsford mentions as present:

* The Prince and Princess of Wales
* Princess Victoria
* Other daughters of the Prince and Princess of Wales
* Lord Knutsford
* [[Social Victorians/People/Ripon|Lord and Lady Gladys de Grey]]
* Luís De Soveral
* Tosti
* [[Social Victorians/People/Durham|Hon. George Lambton]]
* [[Social Victorians/People/Churchill|Lady Randolph Churchill]]
* [[Social Victorians/People/Holford|Holford]]
* Lady Musgrave

Leslie's summary of Knutsford's letters:&lt;blockquote&gt;The Whitsun party that year included Lord and Lady de Grey, De Soveral, whose caustic wit always lightened Edward's humour, Tosti, the famous baritone-songwriter (Alexandra and her daughters were so musical — strumming away ''à quatre mains'' while Totti's voice made chandeliers vibrate in after-dinner songs), the Hon. George Lambton (racing trainer), and Lady Randolph Churchill, &quot;just back from her hospital ship which had been a boon in South Africa, but fractiously insisting she is going to marry George Cornwallis-West.&quot;

Lord Knutsford describes the chattering guests travelling in that special train coach from St. Pancras to Wolverton Station where the house party was met by royal carriages with officious flunkeys in red livery who dealt with the luggage — and ''such'' luggage! Big trunks had to be brought for a few days' stay so that the correct attire could be produced for every meal and outing.

How exciting to drive through a forest of rhododendrons and to disembark in front of Sandringham House. The royal host and hostess stood in the hall to welcome their guests. After handshakes Queen Alexandra sat down to pour tea. Dinner was at 9 &lt;small&gt;P&lt;/small&gt;.&lt;small&gt;M&lt;/small&gt;. (at Sandringham all clocks were kept half an hour ahead of time). Footmen informed the gentlemen what waistcoats were to be worn. Ladies' maids scurried to the ironing rooms. At nine, having assembled in the drawing room, each man was told whom he must escort into dinner and where to sit. This saved hesitation and embarrassment. On this occasion Knutsford describes the Prince giving his arm to Lady de Grey, while Alexandra walked beside De Soveral and Lord de Grey escorted the unmarried Princess Victoria. There were, of course, no cocktails, but exquisite wines accompanied each course. The Prince never drank more than a glass or so of claret at dinner and a brandy after the last course.

When the ladies left the dining room cigarettes and cigars were brought by footmen. Heavy drinking was never encouraged, and / after half an hour the gentlemen moved to the drawing room to chat with the ladies, until Alexandra rose and they retired to their bedrooms where the ladies' maids would be waiting to unlace them from their gorgeous satin and velvet gowns. Hard as the existence of a servant might be, they were perhaps consoled by the colossal meals offered in recompense for late hours. A five-course breakfast could be consumed by every scullery maid if she so desired, and many a working-class mother strove to &quot;get her daughter's knees under a good table.&quot;

When the ladies had disappeared upstairs the men went to the billiards room, where the Prince, who idolised his dogs, would roar with laughter when his black bulldog nipped the legs of players. No one could go to bed before Edward, but at twelve-thirty he would certainly retire. There was no thought of any hanky-panky after hours at Sandringham. That would have been considered bad taste and an insult to the royal hostess.

On Sunday morning the breakfast gong sounded at 10 &lt;small&gt;A&lt;/small&gt;.&lt;small&gt;M&lt;/small&gt;. Then came church and a stroll in the garden until lunch at one-thirty. After a fairly heavy meal the ladies went upstairs to change into walking skirts and strong boots. The whole party then underwent a slow three-hour walk to the kennels and stables and farm. Talk was almost entirely about animals — dogs, pedigree cattle and, of course, race horses. Knutsford noticed Alexandra's &quot;touching girl-like love&quot; for every stone and corner of Sandrringham. She reminded him of &quot;a bird escaped from a cage.&quot;

Certainly the royal pair were never so happy as in this big Norfolk house, which they regarded as home, but guests grew weary of trying to do the right thing. Knutsford found dinner very wearing, with the conversation in mingled English and French: &quot;they drop from one to another in the same sentence.&quot;

Then came the local Whitsunday sports. Off drove the house party — Lady de Grey and Holford in the first carriage with Edward. Knutsford found himself in the second carriage with Princess Victoria and Lady Randolph Churchill and Lady Musgrave. The ladies wore coloured blouses and contrasting skirts and jackets over their blouses, white gloves and feather boas. A brisk wind nearly blew off their huge hats. Lady Musgrave in particular had difficulty with her concoction. &quot;Send it to the bazaar!&quot; cried Alexandra, and everyone roared with laughter.

Sandringham parties were called &quot;informal,&quot; but what a relief, nevertheless, when they all got back to the station in those regal carriages followed by the four horse-drawn vans of luggage.

In this spring of 1900 the visitors departed to their homes full to / the brim of food and anecdote. Jennie, who had been argumentative all weekend, would almost immediately marry her young George. Gladys de Grey would get on her newly installed phone to admirer number one, the Hon. Reginald Listen, or if he was not available to admirer number two, Sir John Listen-Kaye. Ladies were now able to ring the men up and guardedly converse instead of sending dangerous notes. Servants might overhear but there would be nothing ''on paper''.&lt;ref&gt;Leslie, Anita. ''The Marlborough House Set''. Doubleday, 1973.&lt;/ref&gt;{{rp|195–197}}&lt;/blockquote&gt;

====26 June 1900, Tuesday====
There was apparently a regular celebration of Arthur Collins' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902.

==== 28 June 1900, Thursday ====
Lady Randolph Churchill and George Cornwallis-West married at St. Paul's, Knightsbridge.&lt;ref&gt;Martin, Ralph G. ''Lady Randolph Churchill : A Biography''. Cardinal, 1974. Internet Archive: https://archive.org/details/ladyrandolphchur0002mart_w8p2/.&lt;/ref&gt;{{rp|220–223}}

===July 1900===
====27 July 1900, Friday====
The [[Social Victorians/People/Albert Edward, Prince of Wales|Prince of Wales]] had dinner at the Arthur Wilsons’:&lt;blockquote&gt;[[Social Victorians/People/Arthur Stanley Wilson|Mr and Mrs Arthur Wilson]] were honoured with the presence of the Prince of Wales at dinner on Friday night. Amongst the guests were the Portuguese Minister, Count Mensdorff, Duke of Roxburghe, Lady Georgina Curzon, Captain and Lady Sarah Wilson (arrived that morning from South Africa), Lord and Lady Tweedmouth, Lord Herbert Vane Tempest, Viscount Villiers, Lady Norreys, Lady Gerard, [[Social Victorians/People/Keppel|Hon Mrs Keppel]], Sir Edward and Lady Colebrook, Mr and Mrs Grenfell, Lady Lister Kaye, Mrs Arthur Paget, Mr and Mrs Arthur Sassoon, Hon. W. Erskine, Mr and Mrs J. Menzies, General Oliphant, Miss Jane Thornewell, Mrs Kenneth Wilson, and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]]. (1900-07-30 Hull Daily Mail)&lt;/blockquote&gt;

===October 1900===
====31 October 1900, Wednesday====
Halloween.
===November 1900===
====5 November 1900, Monday====
Guy Fawkes Day
====9 November 1900, Friday====
A debutante dance for Miss Helyar: &lt;quote&gt;In honour of the coming of age of Miss Helyar, a small dance was given by Lady Savile, at Rufford Abbey, last night. The number of invitations was not so large as it would have been but for the war. The house party included Mrs. and Miss Cavendish Bentinck, Lady Juliet Lowther, Lady Evelyn Ward, Lady Mabel Crichton, Mrs Kenneth Wilson, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Sir Berkeley Sheffield, Miss Sheffield, Lord Hyde, Lord Herbert, the Hon. B. Ward, the Hon. E. FitzGerald, the Hon. W. Erskine, Mr. Laycock, Captain Brinton, the Hon. George Peel, Mr. Harris, Captain Tharp, Captain Heneage, and the Hon. G. Portman.&lt;/quote&gt; (1900-11-10 Yorkshire Post)

====27 November 1900, Tuesday====
Arthur Sullivan's funeral: &lt;quote&gt;At eleven o'clock on Tuesday, November 27th, the [366/367] funeral procession set forth from Victoria Street, Westminster, on its mournful way, first to the Chapel Royal, St. James's, where, by command of the Queen, part of the Burial Service was to take place, and thence to St. Paul's. Throughout the line of route flags drooped at half-mast, whilst beneath them people crowded in their thousands, bare-headed and in silence, waiting to pay their last tribute of respect and gratitude to the lamented master whose genius had done so much to brighten their lives for the past five-and-twenty years. [new paragraph] Into the Royal Chapel, where Arthur Sullivan had begun his career as a chorister, was borne the casket containing his remains. On either side stood men and women famous in society and the wider world of Art in all its branches. The Queen was represented by Sir Walter Parratt, Master of Music, who was the bearer of a wreath with the inscription: &quot;A mark of sincere admiration for his musical talents from Queen Victoria.&quot; Sir Hubert Parry represented the Prince of Wales; the German Emperor was represented by Prince Lynar, Attache of the German Embassy; Prince and Princess Christian by Colonel the Hon. Charles Eliot, and the Duke of Cambridge by General Bateson.

Among the congregation at the Chapel Royal were seen the United States Ambassador; the Earl and Countess of Strafford; Theresa, Countess of Shrewsbury; the Countess of Essex; Lord Glenesk; Lord Rowton; Lord Crofton; Lady Catherine Coke; the Dean of Westminster; Lady Bancroft; Lady [367/368] Barnby; Mr. Arthur Chappell; Mr. and Mrs. F. C. Burnand; Mr. Arthur W. Pinero; Mr. Haddon Chambers; Lieutenant Dan Godfrey; Signor Tosti; Mr. George Grossmith; Mr. Rutland Barrington; Miss Macintyre; Mrs. Ronalds; Canon Duckworth; Lady Lewis; Miss Ella Russell; Mr. Augustus Manns; Mr. Charles Wyndham; Captain Basil Hood; the Chairman and Secretary of Leeds Musical Festival; and Representatives of various British Musical Associations.

The Pall-bearers were Sir Squire Bancroft, Mr. Francois Cellier, Colonel A. Collins (one of the Royal Equerries), Sir Frederick Bridge, Sir George Lewis, Sir Alexander Mackenzie, Sir George Martin, and Sir John Stainer. [new paragraph] he chief mourners were Mr. Herbert Sullivan (nephew), Mr. John Sullivan (uncle), Mrs. Holmes, and Miss Jane Sullivan (nieces), Mr. Wilfred Bendall (Sullivan's secretary), Mr. B. W. Findon, Mr. Edward Dicey, Mr. C. W. Mathews, Mrs. D'Oyly Carte, Dr. Buxton Browne, Mr. Arthur Wagg, Mr. Fred Walker, Mr. Dreseden and Sir Arthur's servants. [new paragraph] Much to their regret, neither Mr. Gilbert nor Mr. Carte was able to attend the funeral. The first was on the Continent for the benefit of his health, the second was laid up by serious illness. The present writer also, having been absent from London at the time, has not the advantage of an eye-witness to give a graphic description of the funeral obsequies of his old friend; and so, rather than attempt to paint the picture from imagination, he gladly avails himself [368/369] again of the courtesy of his brother-author who is so generous as to lend the aid of his experience. [new paragraph] In these sympathetic words, Mr. Findon describes the scenes and incidents in which, as a chief mourner, he took part at the Chapel Royal and St. Paul's Cathedral: &lt;blockquote&gt;&quot;. . . As the casket was borne into the Chapel, it was impossible to avoid thinking of those days when Sullivan himself had worn the gold and scarlet coat of a Chapel Royal Chorister, and his sweet young voice had rung through the sacred edifice. Then the world and its honours lay before him, but we doubt if even in the most sanguine moments of impulsive boyhood he imagined the greatness that one day would be his, or that his bier would pass within those honoured walls amid the silent demonstration of a mourning people. The anthem, 'Yea, though I walk through the valley of the shadow of death,' from his oratorio 'The Light of the World,' was beautifully sung, and the pathos of the music bathed many a face in tears, and touched a tender spot in more than one loving heart. Another of the dead master's exquisite thoughts, ' Wreaths for our graves the Lord has given,' brought the Service at the Chapel Royal to an end, and the procession passed on its way to St. Paul's Cathedral, which was crowded with sympathetic spectators.

&quot;Clerical etiquette and cathedral dignity compelled the beginning of the Burial Service anew, and when the coffin had been lowered into the crypt there came the most poignant moment of the long ceremonial. [new paragraph] &quot;Close to the open vault sat the members of the Savoy Opera Company, including his life-long friend, Mr. Francois Cellier, who had been associated as chef d'orchestre with all his comic operas, and, after [369/370] the Benediction had been given, they sang in voices charged with emotion the touching chorus, 'Brother, thou art gone before us,' from ' The Martyr of Antioch.' The effect was quite remarkable, inasmuch as it was one of those incidents which come but rarely in a life-time.&quot;&lt;/blockquote&gt;It was not in London alone that people mourned for Arthur Sullivan on that November day. Throughout Great Britain and Ireland, on the Continent of Europe, in America and farther across the seas, thousands of fond and grateful hearts ached with grief at the thought that England's dear master of melody had passed away into the silent land. From high-born personages and from people of low estate came floral emblems, wreaths, crosses, and lyres innumerable. Conspicuous among them was a beautiful harp of purple blossoms with strings — one broken — of white violets. To this offering was attached a card bearing the inscription:&lt;blockquote&gt;In Memoriam

ARTHUR SEYMOUR SULLIVAN

Born 13 May, 1842. Died 22 Nov., 1900

FROM MR. D'OYLY CARTE'S &quot;ROSE OF PERSIA&quot; TOURING COMPANY IN TOKEN OF THEIR AFFECTIONATE REGARD
&lt;poem&gt;Dear Master, since thy magic harp is broken,
Where shall we find new melodies^ to sing?
The grief we feel may not in words be spoken;
Our voices with thy songs now heav'nward wing.
Whilst on thy tomb we lay this humble token
Of love which to thy memory shall cling.&lt;/poem&gt;
BELFAST,
24th November, 1900.&lt;/blockquote&gt; [370/371] These simple lines but half expressed the love and esteem in which Sir Arthur Sullivan was held by all whose privilege it was to have been associated with him, and to have served, however humbly, his proud and brilliant life-cause.&lt;/quote&gt; (Cellier, François, and Cunningham Bridgeman. Gilbert and Sullivan and their operas: with recollections and anecdotes of D. Pp. 366-371. Google Books: http://books.google.com/books?id=Au05AAAAIAAJ.)

====30 November 1900, Friday====
The wedding between Lady Randolph Churchill and George Cornwallis West at St. Paul's, Knightsbridge, occurred about this time. [[Social Victorians/People/Muriel Wilson|Muriel Wilson]] attended, as did much of Society (1900-07-30 Times).

===December 1900===
===25 December 1900, Tuesday====
Christmas Day
====26 December 1900, Wednesday====
Boxing Day
===Works Cited===
*[1900-02-14 Morning Post] &quot;The Household Troops. Entertainment at Her Majesty's.&quot; Morning Post 14 February 1900, Wednesday: 3 [of 10], Col. 1a–2b [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19000214/014/0003 (accessed February 2020).
*[1900-07-30 Hull Daily Mail] &quot;Social Record.&quot; Hull Daily Mail 30 July 1900, Monday: 2 [of 6], Col. 5a [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000324/19000730/007/0002 (accessed July 2019).
*[1900-07-30 Times] &quot;Court Circular.&quot; Times, 30 July 1900, p. 6. The Times Digital Archive, http://tinyurl.galegroup.com/tinyurl/AHR8r5. Accessed 20 June 2019.
*[1900-11-10 Yorkshire Post] &quot;Court and Personal.&quot; Yorkshire Post 10 November 1900, Saturday: 6 [of 14], Col. 4c [of 8]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000687/19001110/099/0006 (accessed July 2019).
*Greville, Lady Violet. &quot;Place aux Dames.&quot; The Graphic 17 February 1900, Saturday: 7 [of 40], Col.1a–2a, 2c [of 3]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000057/19000217/008/0007 (accessed July 2019). [Col. 2c only for the last 2 paragraphs, not really relevant to Muriel Wilson]

==1901==
===January===
&quot;There were no winter performances of opera at Covent Garden in those times: there was, in 1901, only a summer season&quot; (Baring-Gould II 704, n. 14, quoting Rolfe Boswell).
====1 January 1901, Tuesday, New Year's Day====
====16 January 1901, Wednesday====
Arnold Dolmetsch sent out notices that he was moving to 85 Charlotte Street, Fitzroy Square (Campbell 137-38).

====22 January 1901, Tuesday====
Queen Victoria died at Osborne House, on the Isle of Wight.

====23 January 1901, Wednesday====
Edward VII formally proclaimed “King of Great Britain and Ireland and Emperor of India, Defender of the Faith” &quot;at Temple Bar, on St. Paul's Cathedral steps and at the Royal Exchange.&quot; &quot;The Privy Council met in St. James' Palace at 2 o'clock in the afternoon for the purpose of signing the accession proclamation of Edward VII. The attendance at the meeting of the Council was more than 200.&quot; (Merrill, Arthur Lawrence, and Henry Davenport Northrop. Life and Times of Queen Victoria: Containing a Full Account of the Most Illustrious Reign of Any Soveriegn in the History of the World, Including the Early Life of Victoria; Her Accession to the Throne and Coronation; Marriage to Prince Albert; Great Events During Her Brilliant Reign; Personal Traits and Characteristics That Endeared Her to Her People; Graphic Descriptions of Her Charming Home Life; Noble Qualities as Wife and Mother; Royal Castles; Public Receptions; Wonderful Growth of the British Empire, Etc. To Which is Added the Life of King Edward VII., and Sketches of the Members of the Royal Family. Philadelphia, PA: World Bible House, 1901. Page 437. Google Books: http://books.google.com/books?id=Kx48AQAAIAAJ)

====26 January 1901, Saturday====
Arnold Dolmetsch gave a performance at his new domicile at 85 Charlotte Street, Fitzroy Square (Campbell 137-38).

===February 1901===
====2 February 1901, Saturday====
Queen Victoria’s funeral at St. George’s Chapel, Windsor Chapel. Consuelo (Vanderbilt), Duchess of Marlborough was there: &lt;blockquote&gt;The service itself was magnificent. The stalls of the Knights of the Garter were occupied by the German Emperor and a dazzling array of kings, queens, ambassadors extraordinary, Indian princes, Colonial dignitaries, generals, admirals and courtiers. Consuelo wore the prescribed deep black mourning and crepe veil, which rather suited her, and it had the effect of extracting what she describes as a 'rare compliment' from her husband who remarked: 'If I die, I see you will not remain a widow long' — a conceit which suggests that he was more of his father's son than he cared to acknowledge.

Consuelo later reflected that the funeral of Queen Victoria was a moment when it truly appeared that no other country in the world had an aristocrac so magnificent, nor a civil service so dedicated, which is precisely what was intended. The great doors were flung open as the royal cortege mounted the steps, a boom of distant guns and clanging swords the only sound other than the funeral march, until Margot Asquith broke the reverential silence with a quip. Consuelo thoroughly enjoyed herself at the reception in the Waterloo Chamber afterwards too. (Stuart, Amanda Mackenzie. Consuelo and Alva Vanderbilt: The Story of a Daughter and a Mother in the Gilded Age. New York and London: HarperCollins, 1005. Page 228. Google Books: http://books.google.com/books?id=44mhoIv12rEC)&lt;/blockquote&gt; Also Henry James saw the funeral procession.

====3 February 1901, Sunday====
1901 February 2–4?: Queen Victoria lay in state for 2 days between her funeral and her interment.

====4 February 1901, Monday====
Queen Victoria’s interment at Frogmore Mausoleum, Windsor Great Park.
====23 February 1901, Saturday====
The wedding of Hugh Richard Arthur, 2nd Duke of Westminster and Constance Edwina Cornwallis-West (1901-02-23 Cheshire Observer).

===March 1901===
Sometime in March 1901 Arthur Conan Doyle and Fletcher Robinson &quot;were on a golfing holiday at the Royal Links Hotel at Cromer in Norfolk,&quot; where Robinson told Doyle a Dartmoor legend of &quot;a spectral hound&quot; (Baring-Gould II 113).

Doyle's &quot;The Hound of the Baskervilles&quot; began publication in the ''Strand'' in January 1902.

===April 1901===
====18-20 April 1901, Thursday-Saturday====
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] and Mrs. Beerbohm Tree took part in 3 performances of &lt;quote&gt;Masks and Faces. The matinées have been organized by [[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]], of Tranby Croft, in aid of the local fund of the Soldiers’ and Sailors’ Families Association. It was originally intended that the matinées should have been given in January last, but, owing to the death of Queen Victoria, they were postponed until Thursday, Friday, and Saturday last week. Additional interest was centered in the event, owing to the cast including no less a name than that of Mrs. Beerbohm Tree, while the fact that Miss Muriel Wilson was to appear as Peg Woffington aroused expectation.&lt;/quote&gt; (1901-04-25 Stage)

===May 1901===

==== '''1901 May 30, Thursday''' ====
The London ''Daily Express'' reported on the opening of the Ladies' Dog Show:&lt;blockquote&gt;There was a very large attendance yesterday at the Botanic Gardens for the summer fête of the Ladies’ Kennel Association, which is under the patronage of the Queen, and the charming grounds had quite the aspect of a garden-party at tea-time, when the band played under the trees.

Among well-known exhibitors to be seen were Sir Claud and Lady Alexander, who was showing a number of cats, Lady Aberdeen, Lady Angela Foster, and the Princess de Moniglyon, who took a first prize. Neither Lady Decies nor Lady Maitland was exhibiting on this occasion. Others to be seen were Lady Algernon Gordon-Lennox in black and white, Mrs., Algernon Bourke all in mauve, the Duchess of Newcastle, Mrs. Baillie of Dochfour, and Mrs. Greville.

The Dogs’ Brigade Parade, which takes place to-day at 4.30, will be in aid of the Princess of Wales' Soldiers and Sailors' Widows and Orphans Fund.&lt;ref&gt;&quot;At the Botanic Gardens.&quot; ''Daily Express'' 31 May 1901, Friday: 4 [of 8], Col. 7a [of 7]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/BL/0004848/19010531/086/0004?browse=true https://www.britishnewspaperarchive.co.uk/viewer/BL/0004848/19010531/086/0004]. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;The ''Birmingham Daily Gazette'' has a different list of names:&lt;blockquote&gt;Yesterday the annual show of the Ladies' Kennel Association was held in the Royal Botanical Gardens, Regent's Park, and attracted a highly fashionable gathering. Among the ladies represented were Princess Victor Dhuleep Singh, Princess Sophie Dhuleep Singh, the Marchioness of Nottingham, the Duchess of Sutherland, the Countess of Aberdeen, Lady Evelyn Ewart, Lady Helen Forbes, the Hon. Mrs. Baillie, Lady Moor, the Hon. Mrs. Alwyne Greville, the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], Lady Alwyne Compton, Lady Chetwode, Lady Cathcart, Lady Angela Forbes, the Hon. Mrs. Fellowes, Lady Gooch, Princess de Montglyon, and Viscountess Southwell, Mrs. Samuelson, Miss Serena, Mrs. Bosanquet, Mrs. Williams, and Mrs. Ingle Bepler. Cats and poultry are also exhibited.&lt;ref&gt;&quot;Ladies' Dog Show.&quot; ''Birmingham Daily Gazette'' 31 May 1901, Friday: 6 [of 8], Col. 5b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000667/19010531/124/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1901===
Summer 1901: William B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).
====17 June 1901, Monday====
&lt;quote&gt;The &quot;Women Writers&quot; held their dinner at the Criterion on Monday, the 17th. Now Mr. Stephen Gwynn, in his paper entitled &quot;A Theory of Talk,&quot; roundly asserts that women are less amusing than men. He says that there is no reason in nature why they should be, but that their inferiority is obvious. He points out that &quot;thirty or forty men will meet at seven o'clock, dine together, and pass the evening very agreeably till midnight. Imagine thirty or forty women called upon to do the same; would they be able to amuse themselves?&quot; It seems almost a pity that the exclusiveness of the women writers would not allow Mr. Gwynn personally to observe whether they were amused or bored on Monday night. In number there were nearly two hundred, and there certainly did not appear to be any lack of enjoyment or of laughter, but then it is also a fundamental belief with men that women are early adepts at hiding their true feelings. / Lucas Malet occupied the chair, and her carefully prepared speech was read out by Miss Sydney Phelps. Standing at the base of the statue of one of the world's greatest authors, and that, we regret to say, not a woman but a &quot;mere man,&quot; Miss Phelps, speaking for Lucas Malet, said there was good cause for women to congratulate themselves that, whereas there had been Thackeray, Dickens, the brothers Kingsley, and Wilkie Collins among authors, authoresses could boast of George Eliot, Mrs. Gaskell, [33 Col B / 34 Col A] Miss Yonge, &amp;c, and she felt that in the future they might equal, she would not say rival, their &quot;brother man.&quot; At this courageous vaunt our glance involuntarily strayed to the statue, anticipating that it would be moved to at least a wink; but overwhelmed, perhaps, by the presence of so many &quot;sisterwomen,&quot; it gave no sign. The speech was long, lasting for over thirty minutes. It touched on the evils of lowering work to what might be a present commercial but fleeting value; it contained much that was excellent, and tendered some good sound advice; perhaps it dwelt a trifle too insistently upon the obvious, and it was serious even to solemnity. But then &quot;women are so serious.&quot; / Mme. Sarah Grand's reply was couched in far lighter vein. It slipped into the anecdotal, and was altogether more in the masculine line of after-dinner speaking. It offered no advice save on the advisability of laughter; it lingered for a moment on the sorrows of misinterpretation and misunderstanding, and included some amusing examples. Mme. Sarah Grand possesses a sympathetic voice, and is very pleasant to listen to. / It is characteristic of the gravity with which even in play hours women regard their &quot;work&quot; that the majority of guests preferred the more serious matter of Lucas Malet to the light personal note of Mme. Grand. The dinner itself was very good, and it was noticeable that whilst at the Authors' dinner on May 1 but few women availed themselves of the permission to smoke, at the women's function scarcely one was without a cigarette. Coffee was served at the table, and afterwards the company broke up into groups. / The committee numbered among its members Miss Beatrice Harraden, Mrs. Steel, Mrs. Craigie, Miss Christabel Coleridge, Miss Violet Hunt, and many other favourite writers. In the company present there were Dr. Jex-Blake, Mrs. Ady, Dr. Margaret Todd, Miss Adeline Sergeant, Mrs. Mona Caird, Mrs. Burnett-Smith, Mme. Albanesi, Miss Nora Maris, Miss Kenealy, and others; and the following presided at the tables : Lucas Malet, Mme. Sarah Grand, Mrs. de la Pasture, Miss Montresor, the Lady Mayoress, Mrs. L. T. Meade, Mrs. Alec Tweedie, Mrs. Walford, Mrs. B. M. Croker, Miss Violet Hunt, Miss Beatrice Harraden, Mrs. Belloc Lowndes, Miss Violet Brooke-Hunt, Miss Thorneycroft Fowler.&lt;/quote&gt; (&quot;The Women Writers' Dinner.&quot; The Author. Vol. XII, No. 2. 1 July 1901. Pp. 33–34.)

====26 June 1901, Wednesday====
There was apparently a regular celebration of Arthur Collins' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902.

====29 June 1901, Saturday====
&quot;To-day sees the public inauguration of the Horniman Musem at Forest Hill. This collection of marvels from many lands, gathered together by a member of the Horniman family, has been generously presented to the public and housed in a handsome new building — set in the midst of fifteen acres, which are now dedicated to use as a public park. The entrance to the museum will be free.&quot; (&quot;The Horniman Museum.&quot; Illustrated London News (London, England), Saturday, June 29, 1901; pg. 928; Issue 3245, Col. B)

===July 1901===
====19 July 1901, Friday====
[[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]] hosted a concert at the Wilson house in Grosvenor-place in London: &lt;quote&gt;Mr. and Mrs. Arthur Wilson lent their house in Grosvenor-place on Friday afternoon for Miss Gwendoline Brogden’s concert. Miss Brogden, who is only eleven years old, is quite a prodigy. She sings quite exquisitely, and great many people, including Lady de Grey and Mrs. Arthur Wilson, are much interested in her future, which promises to be a very brilliant one. Lady Maud Warrender, Miss Rosamond Tufton, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Mr. Bernard Ralt, Signor Ancona, and Signor Tosti, all promised to assist at the concert, and the tickets were a guinea each.&lt;/quote&gt; (1901-07-24 Beverley Echo)

==== 25 July 1901, Thursday, 2:30 p.m. ====
The wedding of William Dixon Mann Thomson — Captain Mann Thomson in the Life Guards — and Violet Hemsley Duncan. Captain Mann Thomson's father had died in 1899. (Guests' names with their gifts set as an unordered list here, to save space; it was typeset as a long list of paragraphs in the newspaper story.)&lt;blockquote&gt;MARRIAGE OF CAPTAIN MANN THOMSON AND MISS DUNCAN.

The marriage of Captain Mann Thomson, Royal Horse Guards, and Miss Violet Duncan, eldest daughter of Mr. A. Lauderdale Duncan, Knossington Grange, Oakham, took place in St. Peter's Chnrch, Eaton-square, London, on Thursday, the inst., 2.30 p.m. The bride, who was given away her father, wore a dress of white satin, draped with white and old Brussels lace, wreath of orange blossoms, and tulle veil. Her ornaments were pearls. She was attended by seven bridesmaids, viz.: — Miss Adèle, Miss Marjory, and Miss Esmè Duncan, sisters; Miss Dorothy and Miss Sybil Thompson, cousins of the bride; Miss Villiers, cousin of the bridegroom; and Miss Joan Dawson. They wore dresses of the palest pink silk, covered with pink gauze, collars of white lace, and pale pink chiffon baby hats. The bride's train was carried by Miss Duncan, her youngest sister. The bridesmaids carried bouquets of pink carnations, and wore diamond brooches in the shape of a violet with sapphire centre, the gifts the bridegroom. A detachment of non-commissioned officers and men of the bridegroom's troop lined the aisle during the ceremony. The bridegroom was supported by the Earl Arran as best man. The officiating clergy were the Rev. Ravenscroft Stewart, Vicar of All Saints', Ennismore-gardens, the Rev. G. Tanner, Rector of St. Peter's, Knossington, Leicestershire, and the Rev. H. Trower. After the ceremony, a reception was held at 8, Rutland-gate, the residence of Mr. and Mrs. Lauderdale Duncan. Among those present were the Duke and Duchess of Westminster, Dowager Countess of Chesterfield, Sir William and Lady Houldsworth, the Hon. C. and Mrs. Stanhope, Miss Hay, Lord and Lady Eglinton, Lord and Lady Castlereagh, Lord Ernest St. Maur, Lord and Lady Pembroke, Mrs. Adair, Mrs. Mann Thomson, Miss Mann Thompson, Earl Arran, Lord Cecil Manners, Mrs. and Miss Wilton Phipps, and many others. Later, the bride and bridegroom left for Dover, ''en route'' for the Continent, where they will spend the honeymoon. The bride's travelling dress was of pale blue crepe-de-chine, and black hat. There were about five hundred gifts from relations and friends. The following is a list:—

* Bridegroom to Bride — Large diamond spray
* Mrs. Mann Thomson (mother of bridegroom) — Diamond ring, diamond and sapphire bangle, and cheque
* Mr. Lauderdale (father of bride) — Diamond and sapphire necklace
* Mrs. Duncan (mother of bride) — Silver-mounted travelling bag
* Dowager Lady Hay (bride's aunt) — Silver tea service
* Miss Mann Thomson (bridegroom's sister) — Brougham
* Mr. and Mrs. Butler Duncan (uncle and aunt) — Gold-mounted claret jug
* The Misses Jackson (bridegroom's aunts) — Silver plate
* Mr. H. Mann Thomson (brother) — Silver-mounted portmanteau
* Mr. Charles Hunt — Diamond and pearl brooch
* Miss Adele Duncan — Gold match-box
* The Earl Arran — Gold cigarette case
* Mr. and Mrs. Lucas — Bracelet
* Earl of Arran — Set of diamond and pearl studs
* Capt. and Lady Riddell — Bracelet
* Mrs. and Miss Wilton Phipps — Gold and ruby buckle
* Hon. H. Stanhope, R.N. — Brilliant buckle
* Mr. and Mrs. Pennington — Ruby necklace
* Mr. A. Butler Duncan — Necklace (old design)
* Mr. and Mrs. Gervase Beckett — Sleeve links
* Duke and Duchess of Westminster—Pair of silver candlesticks
* Duchess of Roxburgh—Dresden china coffee service
* The Countess of Shaftesbury — Walking-stick
* The Earl of Arran — Umbrella
* Lady Napier Magdala — Snuff-box
* Sir Richard Waldie Griffith — Fan
* Officers of the Royal Horse Guards — Massive silver vase
* Lady Houldsworth — Silver inkstand
* Viscount Ingestre — Silver waiter
* Miss Hay — Silver coffee pot
* Lady Hay — Silver tea caddy
* The Countess of Chesterfield — Silver and brilliant-mounted photo frame
* Lord Manners — Set four silver candlesticks
* Lord and Lady Eglinton — Silver cigarette box
* Earl and Countess of Ancaster — Pair of silver peppers
* Lady Augusta Noel — Book-slide
* Mr. and Mrs. Bradley-Martin — Old china coffee service in case
* Mr. and Lady Wilfred Renshaw — Leather-covered book, &quot;Where It?&quot;
* Mrs. Duncan — Silver-mounted stationery case and blotter
* Sir Arthur Fludyer — Hunting crop
* Lady Katherine Cole — Walking-stick
* Lord Hamilton — Oak card table
* Sir John Kelk — Writing case
* Capt. Hon. E. St. Aubyn — Set of silver spoons in case
* Capt. and Mrs. Burns-Hartopp — Set of silver asparagus tongs in case
* Capt. Trotter — Silver sealing-wax stand
* Capt. E. W. Clowes — Silver tobacco box
* Mr. and Mrs. Sands Clayton — Silver scent bottle
* Mr. and Mrs. John Hunt Clayton — Thermometer in silver-mounted case
* Mr. and Mrs. Evan Hanbury — Clock
* Major Atherley — Cigarette box
* Mr. and Mrs. Richard Tryon — Card case
* Mr. and Mrs. Hamilton Stubber — Table mirror in silver frame
* Mr. and Mrs. Gretton — Pair of silver candlesticks
* Miss Adele Duncan — Silver tea service
* Hon. G. Crichton — Silver-mounted paper-knife
* Mrs. Norman Lampson — Parasol
* Capt. Gregson — Photo, &quot;Guards at Pretoria&quot;
* Mr. Alfred Keyser — Leather bag
* Mr. and Mrs. Armytage — lvory paper knife
* Mrs. Boyce — Leather tray with two painted china plaques
* Mr. and Mrs. A. B. Norman — Silver-mounted paper knife
* The Master of Elibank — Pair of silver ash trays
* Mr. Adrian Rose — Pair of silver toast racks
* Mr. Archibald Smith — Hunting crop
* Major Bradford Atkinson — Walking-stick
* Mr. and Mrs. Stanhope — Painted china tea service
* Mr. G. A. Grant — Stationery case
* Mrs. Charles Inge — Copper and brass jardiniere
* Col. and Mrs. Makins — Hunting crop
* Mr. G. F. Trotter — Walking stick
* Mr. and Misses Cardwell — Fan
* Mrs. Dana — Thermometer
* Mrs. Nugent — Card case
* Mr. and Mrs. Ovey — Tortoiseshell box
* Mr. F. Peake — Writing table
* Capt. Boyce — Embroidered table cover
* Mrs. Duncan — Dressing bag case
* Mr. F. C. Fardell and Miss Gilbert Day — Brocaded satin cushion
* Mr. and Mrs. Niel Robson — Visiting book
* Mrs. R. B. Hay — Silver salts in case
* Mr. and Mrs. Harold Broadbent — Pair silver peppers in case
* —— Set silver knives in case
* Mr. and Mrs. Greville Clayton — Six silver vases in case
* Mr. and Mrs. Reginald H. Lewis — Pair silver peppers
* Lord Ernest St. Maur — Set four silver fruit spoons in case
* Rev. Geo. and Mrs. Tanner — Pair of silver salts
* Capt. Thomson's Valet and Groom — Pair of silver peppers
* Mr. Alick Duncan — Silver jug
* Mr. and Mrs. A. Brocklehurst — Silver timepiece in case
* Lieut.-Col. and Mrs. Blackburn — Silver fruit spoon
* Mr. and Lady Georgiana Mure — Silver-mounted ink [sic]
* Mrs. Gerald Fitzgerald — Silver-mounted inkstand
* Mrs. Ruthven — Set of silver knives in case
* Mrs. Blair — Umbrella
* Mrs. Willie Lawson — Hunting crop
* —— Three driving whips
* —— Tea tray
* Mr. and Mrs. Ramsay — Umbrella
* Mr. George Hunt — Silver flower bowl
* Mr. and Mrs. Reginald Cookson — Silver biscuit box
* Mr. Arthur and V. James — Silver two-handled cup and cover
* Mr. Robbio Stubber — Pair of silver scent bottles
* Mr. and Mrs. Geo. Baird — Silver bowl
* Mr. and Mrs. Harrison Broadley — Pair of silver flower vases
* Mrs. Grant—Silver flower-pot stand
* Mrs. Villiers — Silver corkscrew
* Capt. Spender Clay — Antique silver snuffbox
* Mr. and Mrs. Weir — Silver bacon dish
* Mr. Baird — Pair of silver candlesticks
* Mr. Athol Hay — Silver sugar bowl
* Capt. Ewing — Pair of silver fruit dishes
* Mr. and Mrs. C. J. Phillips — Pair of silver baskets
* Miss Esmé Duncan — Silver box
* Mr. and Mrs. Ronald Paton — lvory paper knife
* Dr. Freshfleld — Work case
* Mrs. Arkwright — Silver-mounted blotter
* Mr. and Mrs. Peake — Silver-mounted stationery case
* Miss Goddard — Book
* Mr. D. Baird — Silver inkstand
* J. G. and Jane B. Hay — lnkpot, with silver watch top
* Mr. and Mrs. Wadsworth Ritchie — Pair of silver dishes in case
* Mr. and Mrs. Guy Fenwick — Set of twelve silver knives in case
* Jane and Uncle Willie — Silver sugar basin in case
* Mr. and Miss Millington Knowles — Set of four silver dessert spoons in ease
* Herbert and Lady Beatrix Herbert — Silver flower dish
* Mr. and Mrs. J. B. Thorneycroft — Four silver candlesticks
* Mr. and Mrs. Russell? M [illegible, ink has spread] — Silver bowl [Col. 2c / Col. 3a]
* Mr., Mrs., and the Misses Wm. Cooper — Fan
* Miss Winearls — Silver-mounted scent bottle
* Sir Ernest Cassel — Diamond and enamel brooch
* Mr. John S. Cavendish — Gold pencil case
* —— Diamond and sapphire bracelet
* Miss Lottie Coats — Diamond and pearl brooch
* Hon. T. Robarts — Diamond brooch
* Mr. and Mrs. Chas. E. Hay — Enamel and pearl miniature holder
* Evelyn Ward — Cornomandel [sic] box
* Mr. and Mrs. Slade — China clock
* Lieut.-Col. Jervoise — Fan
* Mr. and Mrs. J. B. Fergusson—Set of four silver menu holders
* Mr. Guy R. F. Dawson — Silver card case
* Rev. E. V. and Mrs. Hodge — Silver dish
* Mr. C. S. and Mrs. Newton — Silver waiter
* Mrs. Metcalfe — Gold, turquoise, and ruby brooch
* Lord and Lady Erne — Set of three gilt decorated liqueur decanters
* Mr. and Mrs. Chas. Grant — Two silver-mounted spirit decanters
* Mr. and Mrs. George Baird — Set of three cut-glass decanters
* Mr. Peter Cookson—Pair of silver-mounted decanters
* Mrs. Featherstonehaugh — China ornament
* Aunt Mary — China coffee service in case
* Mr. H. S. Sykes — Silver-mounted telegram form case
* Capt. Meade — Pair of engraved claret jugs
* Lord and Lady Binning — Silver-mounted claret jug
* Mr. and Mrs. Baldock — Silver-mounted water jug, with inscription
* Mrs. and the Misses Chaplin — Pair of gilt decorated vases
* —— Silver-mounted claret jug
* Kittie, Margie, Hestie, Walter, Phillip, and Millicent Tanner — Pair of silver peppers case
* Mr. J. R. J. Logan — Silver-mounted claret jug
* Miss Ethel Baird — Painted china box
* Mrs. D. A. Neilson — Pair of female figures with Cupids
* M. M. Phillips — Painted china miniature box
* Lady Waldie Griffith — Stationery case
* —— Painted two-fold screen
* Miss Mabel Fitzgerald — Silver-mounted vase
* Major Bouverie — Silver-mounted match holder
* —— Enamelled inkstand and candlesticks to match
* Mrs. Duncan — Stationery case and blotter
* —— Silver-mounted stationery case
* —— Tortoiseshell and silver-mounted paper-knife
* Miss Mills — Dresden china vase, cover, and stand
* —— Six Vols. of Ruskin's &quot;Modern Painters&quot;
* Mrs. W. Baird — Leather bag
* Miss Langridge — Four silver spoons
* Miss Kirk and Miss Hemsley — Silver-mounted photo frame
* Miss Nessie Hemsley — Silver-mounted photo frame
* Captain and Mrs. St. Aubyn Loftus — Silver vase
* Decima Walker Leigh — Pair of silver-mounted menu stands
* Mrs. Charles Thomson — Mirror in silver frame
* Miss Reese — Silver crumb scoop
* —— Silver-mounted seal and case
* Mary Abercorn Alexander and Gladys Hamilton — Silver inkstand
* Mr. and Mrs. Cecil Chaplin — Silver pen, pencil, and knife in case
* Miss Gwendoline Brassey — Silver-mounted ice pail
* Mr. and Mrs. and Misses Clifford Chaplin — Pair of silver candlesticks
* Mr. and Mrs. Magee — lvory paper knife
* Misses Dorothy and Maude Pilcher — Scent bottle
* Miss Ashton — Silver-mounted clock
* Mrs. William Clarence and Miss Watson — Silver crumb scoop
* Major and Mrs. Ed. Baird — Egg-boiler on silver stand
* Mr. A. F. H. Fergusson — Pair of silver coffee pots
* —— Table mirror
* —— Pair of silver vases
* Mrs. R. B. Mnir — Silver fox ornament
* Mr. H. Brassey and Mr. H. R. Molynenx — Silver teapot
* —— Pair of silver sauce boats
* Mr. and Mrs. Heathcote — Silver cream jug
* Misses Thompson — Silver photo frame
* Mr. C. D. Rose — Pair of silver fruit dishes
* Mr. T. Archibald Hope — Silver toast-rack
* Mr. and Mrs. Robert Hunt — Pair of silver sauce boats
* Major and Mrs. Candy — Pair of silver fruit baskets
* Misses Trefusis — Silver-mounted owl mustard-pot
* Mrs. Frank Chaplin — Silver photo frame
* Major Vaughan Lee — Silver waiter
* Major Byng — Pair of silver menu stands
* Lady Wilton — Silver photo stand
* Geoffrey and Sibyll Palmer — Scent bottle
* Dr. Clement Godson — Silver salad cruet
* Mr. Mackenzie — Silver cigar case
* Mr. G. Colvin White — Set of four silver trays
* Mr. Edgar Brassey — Silver pipe lighter
* Miss Emily Dawson — Photo frame
* Mrs. Gerald FitzGerald — Silver match-box holder
* A. Barns — Silver waiter
* Miss Palmer — Letter-clip and dish
* Mr. and Mrs. Aubrey Coventry — Photo frame
* —— Silver bowl three feet
* Mr. and Mrs. Hornsby — Openwork silver basket
* —— Antique silver box
* Mr. and Mrs. H. R. Baird — Silver coffee-pot
* —— Pair of silver salts
* Mr. Hugh Wanemley — Silver-gilt match-box
* Captain Gordon Wilson — Silver snuff-box
* Mrs. Whitelaw — Silver mustard-pot
* Mrs. Palmer — Silver spoon
* Mr. Dudley Majoribanks — Silver bowl and cover
* Mr. Wilfred F. Ricardo — Pair silver candlesticks
* Indoor Servants at Knossington Grange and 8, Rutland Gate — Breakfast warmer and two silver entree dishes and covers
* Outdoor Servants at Knossington Grange — Silver stationery case
* Mr. Waterman (coachman) — Driving-whip
* Mr. Alexander (coachman) and Mrs. Alexander — lnk-stand
* Villagers of Knossington — Silver sugar bowl, sugar tongs, and cream ewer in case
* Silver vase, with inscription — &quot;Capt. Mann Thomson, Royal Horse Guards, from the Estate and Household at Dalkeith, on the occasion of his marriage, 25th July, 1901.&quot;
* Miss Baldock — Pair of scent bottles
* Captain Cook — Paper-knife
* Sir A. Baird — Pair of silver muffineers
* Rev. H. W. Trower — Pair of silver peppers
* Mr. T. Vandeleur — Silver cigarette box
* Lady Miller — Silver milk jug
* Mr. Hedworth Barclay — Silver muffineer
* Miss May A. Jackson — Photo frame
* Mr. Geoffrey Heneage — Silver ash tray
* Mr. and Mrs. R. B. Hay — Pair silver mustard-pots
* Mrs. George Charteris — Silver-mounted calendar
* Royal School of Art Needlework, Exhibition-road — Silvered copper heart-shaped box
* Mr. A. C. Newbigging — Silver fox ornament
* Mr. S. Schreiber — Silver match box
* Mr. and Mrs. J. H. J. Phillips — Silver muffineers
* Mr. and Mrs. Fyfe Jameson — Silver flask
* Mrs. Beaumont Lubbock — Silver bon-bon dish
* Lord Castlereagh — Salad bowl
* Captain Hambro — Silver card case
* Lord Longford — Silver bowl
* Captain —— Silver waiter
* Mrs. Forester — Silver frame
* Mrs. Martin — Tea cloth
* Mr. and Mrs. Cooper — Whip
* Earl Lonsdale — Silver tray
* Lady Augusta Fane — Red box
* Mr. Paul Phipps — Clippers
* Mr. E. Herlick — lnkstand&lt;ref&gt;&quot;Marriage of Captain Mann Thomson and Miss Duncan.&quot; ''Grantham Journal'' 27 July 1901 Saturday: 2 [of 8], Cols. 2a–3b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000400/19010727/003/0002.&lt;/ref&gt;
&lt;/blockquote&gt;

===August 1901===
====30 August 1901, Friday====
[[Social Victorians/People/Horos|The Horoses]] (troublesome members of the Golden Dawn) were thrown out of 99 Gower Street and moved to Gloucester Crescent (King 89 91).
===October 1901===
====31 October 1901, Thursday====
Halloween.
===November 1901===
====5 November 1901, Tuesday====
Guy Fawkes Day
===December 1901===
====25 December 1901, Wednesday====
Christmas Day
====26 December 1901, Thursday====
Boxing Day
===Works Cited===
*[1901-02-23 Cheshire Observer] &quot;Duke of Westminster. Brilliant Function.&quot; Cheshire Observer 23 February 2901, Saturday: 6 [of 8], Col. 1a–6c [of 8]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000157/19010223/114/0006 (accessed July 2019).
*[1901-04-25 Stage] &quot;Provinces.&quot; &quot;Amateurs.&quot; The Stage 25 April 1901, Thursday: 11 [of 24], Col. 3c, 4b–c [of 5]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001179/19010425/028/0011 (accessed July 2019).
*[1901-07-24 Beverley Echo] &quot;Stray Notes.&quot; Beverley Echo 24 July 1901, Wednesday: 2 [of 4], Col. 4b [of 6]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001561/19010724/037/0002 (accessed July 2019).

==1902==
Sometime in 1902, London publisher [[Social Victorians/People/Working in Publishing#George Newnes|George Newnes]] published an edition of [[Social Victorians/People/Arthur Conan Doyle|Arthur Conan Doyle]]'s first (1892) collection of Holmes stories.
===January 1902===
====1 January 1902, Wednesday, New Year's Day====
===February 1902===

==== 13 February 1902, Thursday ====

King Edward VII and Queen Alexandra were present with some of their friends at Niagara, which must have been an ice-skating rink. Mr. and [[Social Victorians/People/Churchill|Mrs. George West]] are Lady Randolph Churchill and George Cornwallis-West.&lt;blockquote&gt;SOCIAL &amp; PERSONAL

Royalty at Niagara.

Quite a record audience was present at Niagara yesterday, when the free skating and waltzing competitions were skated off to the sound of gay music in a brightly lighted, warm atmosphere.

The royal box made a goodly show with its trappings of Oriental hangings and decorations of palms.

The Royal Box.

The King and Queen were accompanied by Princess Victoria and Prince and Princess Charles of Denmark, the Prince and Princess of Wales having previously arrived. Their Majesties were conducted to the spacious box by Mr. Hayes Fisher.

All the royal ladies wore black, the Queen adding a bunch of yellow Lent lilies to her sombre attire. Her two daughters lightened their mourning with touches of white, and the Princess of Wales wore a bunch of violets in her toque, with a twist of white.

In the adjoining box, among members of the suite were the Countess of Gosford, Earl Howe, Mr. Sidney Greville, Mr. H. J. Stonor, Lieut.-Colonel Davidson, Lieut.-Colonel Legge, and Viscount Crichton.

In boxes on the other side of the royal box were Lady Alice Stanley, with the Ladies Acheson, the Countess of Derby, Countess De Grey and Lady Juliet Lowther, [Col. 3c/4b] Mr. and [[Social Victorians/People/Churchill|Mrs. George West]] [Lady Randolph Churchill and George Cornwallis-West], Sir Edgar and Lady Helen Vincent, the Duchess of Bedford and the Marquis of Tavistock, [[Social Victorians/People/de Soveral|M. de Soveral, the Portuguese Minister]], and Viscount and Viscountess Falmouth.

Others to be picked out in the crowd were Consuelo Duchess of Manchester, Viscountess Coke and Mrs. Ellis, Lady Archibald Campbell and her son, Mrs. Grenander, Lord and Lady Lilford, Mr. and Mrs. Edward Stonor, Mrs. [[Social Victorians/People/Bourke|Algernon Bourke]], Mr. Algernon Grosvenor, and Mr. and Mrs. Hwfa Williams.

The royal party took a great interest in the contests, and especially applauded the Swedish couple in their graceful evolutions. Their Majesties remained over an hour, the royal party taking their departure shortly after five.&lt;ref&gt;&quot;Social &amp; Personal.&quot; ''Daily Express'' 14 February 1902, Friday: 4 [of 8], Cols. 3c–4b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020214/088/0004. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

===March 1902===
The last time Bret Harte and Arthur Collins saw each other: &quot;They dined at the Royal Thames Yacht Club, and Collins found his 'poor old friend' 'saldly aged and broken, but genial and kind as ever.' They sat an hour at a music hall and Harte wrote afterwards to thank Collins for having 'forced him out.'&quot; (Nissen, Axel. Bret Harte: Prince and Pauper. Jackson, MS: U P of Mississippi, 2000: 262)
===April 1902===
====9 April 1902, Wednesday====
According to a letter to Lady Gregory, [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] dictated &quot;2000 words in an hour and a half&quot; &quot;to a typewriter; he was working on his novel (Wade 370). At this point, a typewriter was a person who used the machine called typewriter to type.
====10 April 1902, Thursday====
[[Social Victorians/People/William Butler Yeats|W. B. Yeats]] wrote to Lady Gregory from 18 Woburn Buildings about working on his novel &quot;-- dictating to a typewriter&quot; (Wade 370).

===May 1902===
====5 May 1902, Monday====
Bret Harte died. Arthur Collins does not seem to have been there at his death; “his dear friend Madame Van de Velde and her attendants” were, though (Pemberton, T. Edgar. The Life of Bret Harte. Dodd, Meade, 1903. http://books.google.com/books?id=eZMOAAAAMAAJ). Not sure when the funeral occurred, but he is buried “in quiet Frimly churchyard,” (341) and &lt;quote&gt;In accordance with his well-known views on such subjects the funeral was a very simple one. Among the few who followed him to his ivy-lined grave were Mrs. Bret Harte, his son and daughter-in-law, Mr. and Mrs. Francis King Harte, his daughter, Miss Ethel Harte, Madame Van de Velde, Colonel Collins, Mr. A.S. Boyd, and a small cluster of grief-stricken friends.&lt;/quote&gt; (Pemberton, T. Edgar. The Life of Bret Harte. Dodd, Meade, 1903. http://books.google.com/books?id=eZMOAAAAMAAJ (accessed November 2014).

====8 May 1902, Thursday====
&lt;quote&gt;On Thursday, May 8, 1902, in the squat, mid-Victorian church of St. Peter's in the Surrey village of Frimley, a group of about twenty people had come to show their final respects to Francis Bret Harte. Outside it was raining steadily . In the subdued light from the stained-glass windows, one cold discern a small group at the front of the church consisting of Anna Harte, her son Frank, her daughter-in-law Aline, and her daughter Ethel. Another small group was formed around Madame Van de Velde, including one of her unmarried daughters, Miss Norris (the sister of her son-in-law Richard Norris), and Mrs. Clavering Lyne. Of Harte's closest friend, only Arthur Collins and Alexander Stuart Boyd were present. Pemberton had written to Frank the day before that he wished to attend the funeral but that in his &quot;deplorable state of health&quot; it was impossible for him to travel. Beside the small group of family and old friends, the rest of the people who heard the service conducted by the rector of Frimley, Reverend W. Basset, were recent acquaintances from among the local gentry. As one newspaper noted: &quot;The funeral was of the simplest possible character and the phrase 'this our brother' had a peculiar poignancy, for, though a group of villagers stood in the rain under the trees as the hearse arrived, there were few in the church, who had not the right to call Mr. Bret Harte friend.&quot; The simplicity of the service was in keeping with Bret Harte's wishes.&lt;/quote&gt; (Nissen, Axel. Bret Harte: Prince and Pauper. Jackson, MS: U P of Mississippi, 2000: 263)
===June 1902===
Summer 1902: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until Yeats bought the Tower at Ballylee. (I got this from Wade?)
====3 June 1902, Tuesday====
[[Social Victorians/People/William Butler Yeats|W. B. Yeats]] wrote Arnold Dolmetsch, asking him to &quot;chair ... a lecture he [was] soon to give&quot;: &quot;You are the only one, I suppose, in the world now, who knows anything about the old music that was half speech, and I need hardly say that neither [[Social Victorians/People/Florence Farr|Miss Farr]] nor myself, could have done anything in this matter of speaking to notes without your help&quot; (Campbell 142).
====7-9 June 1902, Saturday-Monday====
The [[Social Victorians/People/Warwick|Earl and Countess of Warwick]] hosted a house party: &lt;quote&gt;The Earl and Countess of Warwick entertained a distinguished house party from Saturday to yesterday, including the Grand Duke Michael of Russia and the Countess of Torby, the Earl and Countess of Craven, the Earl and Countess of Kilmorey, Earl Cairns, Lord and Lady Savile, Lord Chesham, Sir Frederick and Lady Milner, Colonel and Lady Gwendoline Colvin. Lady Margaret Orr-Ewing, Lady Eva Dugdale. Mrs. Kenneth Wilson, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Right Hon. H. Chaplin, M.P., Hon. H. Stonor, Mr. J. Pease, M.P., Captain Brinton, and Captain J. Forbes.&lt;/quote&gt; (1902-06-10 Manchester Courier and Lancashire General Advertiser)

====10 June 1902, Tuesday====
[[Social Victorians/People/Florence Farr|Florence Farr]]'s first public performance in which she &quot;recit[ed] to her own accompaniment on the psaltery was at the Hall of Clifford's Inn, Fleet Street, on 10 June 1902 (Campbell 144, n. 18).

==== 12 June 1902, Thursday====
12 June 1902: &lt;quote&gt;Thursday, the 12th inst., being the grand day of Trinity term at Gray's-inn, the Treasurer (Mr. Herbert Reed, K.C.) and the Masters of the Bench entertained at dinner the following guests: The Right Hon. Lord Strathoona and Mount Royal, the Right Hon. Lord Avebury, the Right Hon. H. H. Asquith, K.C, M.P., the Right Hon. Sir Frank Lascelles, G.C.B. (British Minister at Berlin), General Sir Edward Brabant, K.C.B., the Right Hon. Sir Edward Carson (Solicitor-General), Sir Squire Bancroft, Colonel Alfred Egerton, C.B. (Equerry to H.R.H. the Duke of Connaught), Mr. Austen Chamberlain,M.P., Colonel Royds, M.P., and Mr. Frank Dicksee, R.A. The Benchers present in addition to the Treasurer were H.R H. the Duke of Connaught, Lord Ashbourne, Lord Shand, Mr. Henry Griffith, Sir Arthur Collins, K.C, Mr. Hugh Shield, K.C, His Honour Judge Bowen Rowlands, K.C, Mr. James Sheil, Mr. Arthur Beetham, Mr. John Rose, Mr. Paterson, Mr. Mulligan, K.C, Mr. Mattinson, K.C, Mr. Macaskie, K.C., Mr. C. A. Russell, K.C., Mr. Montague Lush, K.C., Mr. Dicey, C B., Mr. Barnard, Mr. H. C. Richards, K.C., M.P., Mr. Duke, K.C., M.P., Sir Julian Salomons, K.C., with the Preacher (the Rev. Canon C. J. Thompson, D.D.).&lt;/quote&gt; (The Solicitor's Journal and Reporter. June 21, 1902. Volume XLVI. 1901-1902 [November 2, 1901, to October 25, 1902]: 588. Google Books: http://books.google.com/books?id=9T84AQAAIAAJ&amp;pg=PA588).

====26 June 1902, Thursday====
Edward VII crowned King of England. 26 June 1902.

There was apparently a regular celebration of Arthur Collins' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in May 1902, so the celebration with Harte present did not take place this year. Did it take place at all?

===July 1902===
====3 July 1902, Thursday====
[[Social Victorians/People/Mathers|MacGregor and Moina Mathers]] were living at 28 Rue Saint Vincent, Buttes Montmartre, Paris (Howe 244).

===September 1902===
''Tristan and Isolde'' at the Covent Garden.
====25 September 1902, Thursday====
&quot;There were no winter performances of opera at Covent Garden in those times .... In 1902 an autumnal series was added, and there were several Wagner nights, the last of which was on Thursday, 25 September, when Philip Brozel and Blanch Marchesi were starred in ''Tristan and Isolda'' with Marie Alexander as Brangane&quot; (Baring-Gould II 704, n. 14, quoting Rolfe Boswell).

===October 1902===

==== 24 October 1902, Friday ====
The ''Daily Express'' reported on the annual opening of the Prince's ice-skating rink, revealing who had an interest in skating:&lt;blockquote&gt;PRINCE’S RINK OPENS.

The first ice of the season was skated upon yesterday. It was the carefully-prepared ice which Mr. H. W. Page and Mr. Nightingale offer to the members of Prince’s Skating Club, in Knightsbridge, and was in grand condition.

The [[Social Victorians/People/Bourke|Hon. Algernon Bourke]] opened the rink for the seventh season, and in the afternoon and evening the West End patronized the popular club to skate or to lounge to the pleasant strains of the Viennese band.

[[Social Victorians/People/Princess Louise|Princess Louise]] is again at the head of the ladies’ committee, with the [[Social Victorians/People/Portland|Duchess of Portland]] and [[Social Victorians/People/Londonderry|Marchioness of Londonderry]] as co-members, and Lord Edward Cecil and many other well-known skaters are identified with the committee work.

The skating hours are from 9.30 to 1 and 3 to 7, and on Sundays 3 to 7 only.&lt;ref&gt;&quot;Prince's Rink Opens.&quot; ''Daily Express'' 25 October 1902, Saturday: 5 [of 8], Col. 6c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19021025/132/0005.&lt;/ref&gt;&lt;/blockquote&gt;

====31 October 1902, Friday====
Halloween.
The 7th seasonal opening of the Prince's Skating Club and its committees:&lt;blockquote&gt;Until some genius, at present undiscovered, can cheapen the process of the manufacture of “real ice” we are not likely to become a nation of figure skaters, but where there are opportunities for practising the fascinating art of edges and turns development has proved to be rapid. This was noticeable on Friday at the opening of the seventh season of Prince’s Skating Club, a large number of really good skaters being present, who all found the fine hard surface to their Iiking, and there was a capital display of ice waltzing, the true poetry of motion, to the music of the Blue Viennese Band. Mr. [[Social Victorians/People/Grosvenor|Algernon Grosvenor]], an enthusiastic member of the committee, who presided at the little ceremony preceding the opening to members, referred to the prospects of continued success for the present season, which lasts until April next, and said that improvement might be expected, as the end of the war had brought many competent skaters home. A well-deserved tribute was paid to the work of Mr. H. W. Page, the secretary, on behalf of the club, which includes on its ladies' committee [[Social Victorians/People/Princess Louise|Princess Louise]] (Duchess of Argyll), the [[Social Victorians/People/Portland|Duchess of Portland]], [[Social Victorians/People/Londonderry|Lady Londonderry]], [[Social Victorians/People/Campbell|Lady Archibald Campbell]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], and [[Social Victorians/People/Asquith|Mrs. Asquith]]; and on the men's committee, Lord Edward Cecil, Lord Redesdale, Mr. [[Social Victorians/People/Bourke|Algernon Bourke]], Mr. [[Social Victorians/People/Lyttelton|Alfred Lyttelton]], Sir Edgar Vincent, Sir William Hart Dyke, and Mr. [[Social Victorians/People/Grenfell|W. H. Grenfell]].&lt;ref&gt;&quot;What the 'World' Says.&quot; ''Northwich Guardian'' 01 November 1902, Saturday: 6 [of 8], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001975/19021101/134/0006. Print title: The ''Guardian'', p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

===November 1902===
====5 November 1902, Wednesday====
Guy Fawkes Day.

==== 8 November 1902, Saturday ====
The Earl and Countess of Warwick hosted a shooting party at Easton Lodge:&lt;blockquote&gt;The [[Social Victorians/People/Warwick|Earl and Countess of Warwick]] are entertaining a large party at Easton Lodge this week-end for [?] shooting, and among their guests are the Grand Duke Michael of Russia and Countess Torby, the Duc d'Alba, the Duke of Sutherland, Earl Howe, Earl Cairns, Lord Dalmeny, Lord Herbert Vane-Tempest, the Hon. John and Lady [Choely?] Scott-Montagu, the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], the Right Hon. Henry Chaplin, M.P., General and Mrs. Arthur Paget, and Miss Leila Paget, Miss Naylor, Miss Deacon, and Mr W. M. Low.&lt;ref&gt;&quot;Guests at Easton Lodge.&quot; ''Birmingham Mail'' 08 November 1902, Saturday: 2 [of 6], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000644/19021108/091/0002. Print title: ''Birmingham Daily Mail''; p. 2.&lt;/ref&gt;&lt;/blockquote&gt;

====29 November 1902, Saturday====
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]]’s cousin, Lady Hartopp, was involved in a divorce case:
&lt;blockquote&gt;Society Women in a Law Court Case.

Mr. Justice Barnes’s Court is now crowded by society people. What is the strange fascination which brings elegantly dressed ladies, accustomed to luxurious surroundings and all the external refinements of life, to sit for hours in stuffy court, where the accommodation is all the plainest, and the surroundings are none too attractive. It would need some assurance to invite a Belgravian Countess, or the wife of Mayfair Millionaire to spend the morning under such conditions unless there were the attraction of a very strong piece of scandal. One could not presume to suggest she should attend Missionary meeting, or social reform movement, under any such conditions. At least I must confess that I never heard of one being packed with a West End crowd as the Court just now. Of course it cannot be mere idle curiosity. Our higher education for girls must have cured Mother Eve’s failing long ago. Cynics suggest that it is the survival in our highly-civilised modern conditions of that instinct of the wild creature which incites attack on the wounded or injured fellow. Wild birds will sometimes peck injured bird to death. Are these fair and soft-voiced ladies animated by the same spirit when they throng witness the ordeal through which a woman of their own class is passing?

The Latest Divorce Case.

Lady Hartopp, the heroine of the story which has been occupying the tongues and thoughts of the upper ten thousand for the last 48 hours, is a member of a well-known and wealthy family, and is herself remarkable for her beauty. Her two sisters are as famous for their charms as herself, and society has given them many flattering titles. The daughters of Mr. C. H. Wilson, the great shipowner, whose sails are on every sea, are as favoured by Fortune as Venus. Miss Muriel Wilson, the society beauty, is a cousin of Lady Hartopp, and Lady Chesterfield is her sister. It was at Tranby Croft, near Hull, the residence of Mr. and Mrs. Arthur Wilson, that the famous baccarat case occurred some years ago. Lady Hartopp is the niece of Mr. Arthur Wilson, and no doubt recollects that incident, and all the consequent stir. It attracted all the more notice at the time, because the then Prince of Wales had taken part in the game; but the Prince, who had nothing to be ashamed of, with characteristic straightforwardness, asked to go into the box and state all he knew. (1902-11-29 Norwich Mercury)&lt;/blockquote&gt;

===December 1902===

==== 9 December 1902, Tuesday ====
&quot;Severe weather&quot; did not prevent Lady Eva Wyndham's &quot;at home&quot; from being a success:&lt;blockquote&gt;Lady Wyndham-Quin's &quot;At Home.&quot;

The severe weather proved to be no detriment to the many visitors who had accepted Lady Eva Wyndham-Quin's invitation to an &quot;at home&quot; at the Welch Industrial depot on Tuesday afternoon, and the admirers and purchasers of the fascinating Christmas gifts were numerous. Lady Eva received her quests wearing a coat of Persian paw and a white feather toque, whilst her two tittle daughters the Misses Olein and Kethlean Wyndham-Quin wore pelisses and hats of pale blue Welsh frieze, trimmed with grebe. Amongst those present were Lady George Hamilton, all in black; Lady Brassey, wearing a lovely sable cape; the [[Social Victorians/People/Bourke|Hon. Mrs Algernon Bourke]], in a fur coat and a black picture hat; and the Hon. Mrs Herbert, of Llanever; Mrs Brynmor Jones was fall of her coming visit to Paris to see her young daughter, and Mrs Richard Helme came with her son, Mr Ernest Helme. Mrs Brenton and her sister, Mrs Ashurst Morris, were also present, as were Lady Eafield, the Dowager Lady Hylton, Lady Dennison Pender [Ponder?], and Lady Blanche Conyngham. Mrs Grinnell Milne brought Miss Murray end Mrs Shelley Bontens, and Mrs James Head came in for a few minutes. Everybody bought largely and the Welsh Christmas cards were an attractive feature, as were some artistic muff chains. Another specimen of Welsh lace sent by Miss Jenkins, of Denbighshire, was much admired and resembles Irish lace both in style and design.&lt;ref&gt;&quot;A Lady Correspondent.&quot; &quot;Society in London.&quot; ''South Wales Daily News'' 11 December 1902, Thursday: 4 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000919/19021211/082/0004. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

====16 December 1902, Tuesday====
A poem satirizing Florence Farr and Arnold Dolmetsch was published in ''Punch''.
====25 December 1902, Thursday====
Christmas Day
====26 December 1902, Friday====
Boxing Day
===Works Cited===
*[1902-06-10 Manchester Courier and Lancashire General Advertiser] &quot;Court and Personal.&quot; Manchester Courier and Lancashire General Advertiser 10 June 1902, Tuesday: 5 [of 10], Col. 3c [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000206/19020610/033/0006 (accessed July 2019).
*[1902-11-29 Norwich Mercury] &quot;Society Women in a Law Court Case.&quot; And &quot;The Latest Divorce Case.&quot; Norwich Mercury 29 November 1902, Saturday: 5 [of 12], Col. 1b [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001669/19021129/072/0005 (accessed July 2019).

==1903==
From sometime in 1891 to sometime in 1903 Eduoard de Reszke was &quot;a leading bass&quot; at the New York Metropolitan Opera (Baring-Gould II 112, n. 114).

&quot;[I]n England in 1903, gramophone distinctly meant the Berliner-Gramophon &amp; Typewriter disc machine, while cyclinder machines were known as phonographs or graphophones &quot; (Baring-Gould II 745, n. 15).

Gerald Balfour was &quot;largely responsible for getting the important Land Acts of 1903 under way&quot; (O'Connor 163).

In a display of &quot;too little, too late,&quot; on March 18, the day after St. Patrick's Day, the ''Daily Mail'' talks about events in London and Dublin in honor of St. Patrick's Day:&lt;blockquote&gt;The bells of St. George’s Chapel, Windsor Castle, were rung yesterday morning in honour of Ireland’s patron Saint. Sprays of shamrock were worn as “button-holes” by some of the residents in Windsor, Eton, and the surrounding districts.&lt;p&gt;

For the first time on record, St. Patrick’s Day was observed as a general holiday in Dublin. A large crowd witnessed the ceremony of the trooping of the colour by the 4th Battalion Royal Warwickshire Regiment, in Upper Yard, Dublin Castle. The Lord Lieutenant, on horseback, attended by his staff, was present.&lt;ref&gt;&quot;A Sale of National Work.&quot; ''Daily News'' (London) 18 March 1903, Wednesday: 12 [of 12], Col. 5c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/19030318/236/0012. Print p. 12.&lt;/ref&gt;&lt;/blockquote&gt;

===January 1903===
====1 January 1903, Thursday, New Year's Day====
====3 January 1903, Saturday====
Madame Troncey was doing a portrait of [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] (Wade 392).

=== March 1903 ===

==== 1903 March 17, Tuesday ====
Aristocratic women supporting Irish-made laces, needlework, and clothing:&lt;blockquote&gt;It was unfortunate weather for the St. Patrick’s Day sale of the Irish Industries Association, yesterday afternoon; but, in spite of this disadvantage, the rooms were crowded, and orders wore being given and taken on all sides. [[Social Victorians/People/Londonderry|Lady Londonderry]] was, as usual, presiding over the laces of the London depôt, though she often left her stall to her assistants and went about receiving her friends. The lace shown on her stall was beautiful. The needlepoint, Limerick, and Carrickmacross flounces, collars, and coatees finding many buyers during the afternoon. The Dowager Lady Downshire presided over the Association’s stall of embroideries, and Lady Gage arrived betimes to arrange them, wearing a dress of black lace over white, trimmed with appliques, also in black and white. Lady Aberdeen, as usual indefatigable, was at the Association’s stall of knitting, carving, and baskets. And Mrs. Marjoribanks was with her, showing in her own white dress how well Irish tweeds can look when made up. Lady Marjorie Gordon was also helping her mother. As for the 21 stalls representing the various cottage industries, these were once again covered with the beautiful work the Irish peasants, or (as in the case of the Gentlewomen’s Guild Handicrafts, the Ulster Ladies’ Work depôt, and the Irish School of Art Needlework) with work done by Irish ladies. The art needlework done by the Irish School needs little recommendation, it known so well for its excellence. And there were beautiful things on its stall this year, including many portières and some very finely-worked pictures. The stall was in charge of [[Social Victorians/People/Mayo|Lady Mayo]], [[Social Victorians/People/Dudley|Georgina Lady Dudley]], [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], and [[Social Victorians/People/Beresford|Miss Beresford]]. [[Social Victorians/People/Lucan|Lady Lucan]], being always on the watch for extending the sale of the tweeds woven by the Castlebar Homespun Industry, this year shows some of a rather heavy description, made for motor coats, and one of these was on show yesterday afternoon. A pretty coat it looked, too, being carried out in cream cloth, with strapped back, and narrow collar of black velvet. Toys and furniture came from the Cushenhall and the Killarney Industries respectively, and were by no means the least patronised yesterday afternoon, whilst there was steady sale of little bunches of shamrock, which came from poor Ulster lady, who grows and gathers the plant for such occasions as these. The sale is continued to-day from 12 until 6.&lt;ref&gt;&quot;A Sale of National Work.&quot; ''Daily News'' (London) 18 March 1903, Wednesday: 12 [of 12], Col. 5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/19030318/236/0012. Print p. 12.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1903===
Summer 1903: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

==== 1903 June 23, Tuesday ====
A children's party at Buckingham Palace:&lt;blockquote&gt;(From the Court Circular.)

Their Majesties gave a children’s party in the garden of the Palace this afternoon in honour of the ninth birthday his Highness Prince Edward of Wales, at which their Royal Highnesses the Prince and Princess of Wales with their children, Princess Louise, Duchess of Fife, and the Duke of Fife, with their children, the Princess Victoria and their Serene Highnesses the Duke and Duchess of Teck, with their children, were present.

The following, with their children, some of whom were unable to obey their Majesties' command, had the honour of receiving invitations: The Duke and Duchess of Beaufort, the Duke and Duchess of Buccleuch and Lady Constance Scott, the Duke and Duchess of Leeds, the Duke and Duchess of Marlborough, the Duke and Duchess of Portland, the Duke and Duchess of Sutherland, Catherine, Duchess of Westminster, the Marquis and Marchioness of Granby, the Marquis and Marchioness of Hamilton, the Countess of Airlie, the Earl and Countess of Albemarle, the Countess of Antrim, the Earl and Countess Carrington, the Earl and Countess of Dalkeith, the Earl and Countess of Denbigh and Desmond, the Earl and Countess of Essex, the Earl and Countess of Mar and Kellie, the Earl and Countess of Normanton, the Earl and Countess of Pembroke and Montgomery, the Earl and Countess of Selborne, the Earl and Countess of Stradbroke, the Countess de Mauny-Talvande, Viscount and Viscountess Chelsea, Viscount and Viscountess Castlereagh, Viscount and Viscountess Churchill, Viscount and Viscountess Coke, Viscount and Viscountess Cranborne, Viscount and Viscountess Falmouth, Lord and Lady Balfour of Burleigh, Lord and Lady De Ramsey, Lady Farquhar, Lady Cynthia Graham, Lord and Lady Hastings, Lord and Lady Hillingdon, Lord and Lady Knollys, Lord and Lady Lurgan, Lord and Lady St. Oswald, Lord and Lady Settringto, Lord and Lady Alice Stanley, Lord and Lady Suffield, Lord and Lady Wolverton, Mr and the Hon. Mrs. Gervase Beckett. Hon. [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], Mr. and the Hon. Mrs. Lionel Cust, Hon. Mrs. Geoffrey Glyn, Lientenant-Colonel Hon. Charles and Mrs. Harbord, Hon. Charles and Mrs. Hardinge, Hon. Sydney and Lady Mary Holland, Hon. Derek and Mrs. Keppel, Hon. George and Mrs. Keppel, Hon. Frederick and Mrs. Lambton, Hon. Lancelot and Mrs. Lowther, Sir Richard and Hon. Lady Musgrave, Hon H. and Lady Feodorowna Sturt, Hon. Dorothy Violet and Hon. Alexandra Vivian, Mr and Lady Aline Beaumont, Mr. and Lady Katherine Brand, Mr. and Lady Violet Brassey, Mr. and Lady Moyra Cavendish, Mr. and Lady Evelyn Cavendish, Sir E. and Lady Colebroke, Captain and Lady Jane Combe, Sir H. and Lady de Trafford, Mr. and Lady Eva Dugdale, Sir E. and Lady Edmonstone, Major-General Sir R. and Lady Beatrice Pole-Carew, Sir G. and Lady Maud Warrender, Mr. and Mrs. Rupert Beckett, Revd. Canon and Mrs. Dalton, Mr. and Mrs. Farquharson of Invercauld, Mr. and Mrs. W. Grenfell, Mr. and Mrs. A. Hay-Drummond, Mr. and Mrs. W. James, Mr. and Mrs. Blundell Leigh, Mr. and Mrs. Sartoris.&lt;ref&gt;&quot;Prince Eddie's Birthday.&quot; ''Daily News'' (London) 24 June 1903, Wednesday: 7 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/19030624/197/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

=== August–September 1903 ===

==== 20 and 25 August and 3 September 1903 ====
The 1903 America's Cup yacht race in New York Harbor with Nathaniel Herreshoff's ''Reliance'' for the US and Sir Thomas Lipton's ''Shamrock III'' for the UK,&lt;ref&gt;{{Cite journal|date=2022-09-11|title=1903 America's Cup|url=https://en.wikipedia.org/w/index.php?title=1903_America%27s_Cup&amp;oldid=1109663279|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/1903_America%27s_Cup.&lt;/ref&gt; the 12th challenge for the cup and &quot;the most expensive Cup challenge in history.&quot;&lt;ref name=&quot;:0&quot;&gt;{{Cite web|url=https://www.americascup.com/history/26_LIPTONS-THIRD-CHALLENGE|title=LIPTON’S THIRD CHALLENGE|last=Cup|first=America's|website=37th America's Cup|language=en|access-date=2024-07-02}} https://www.americascup.com/history/26_LIPTONS-THIRD-CHALLENGE.&lt;/ref&gt; The first race was run on 20 August 1903, the 2nd on 25 August and the 3rd on 3 September.&lt;ref name=&quot;:0&quot; /&gt; Because the ''Reliance'' won the first 3 races, the best 3-out-of-5 race ended after the 3rd one.

===October 1903===
Sometime in October 1903, [[Social Victorians/People/Arthur Conan Doyle|Arthur Conan Doyle]]'s &quot;The Adventure of the Empty House,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 331).
====31 October 1903, Saturday====
Halloween.
===November 1903===
Sometime in November 1903 Arthur Conan Doyle's &quot;The Adventure of the Norwood Builder,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 415).
====5 November 1903, Thursday====
Guy Fawkes Day
===December 1903===
Sometime in December 1903 Arthur Conan Doyle's &quot;The Adventure of the Dancing Men,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 529).
====16 December 1903, Wednesday====
&quot;On 16 December, Punch satirised an activity in which Dolmetsch was concerned. [[Social Victorians/People/Florence Farr|Florence Farr]] was acting as secretary for a newly-formed fellowship known as 'The Dancers', a body whose aim was to 'fight the high and powerful devil, solemnity'. In a poem entitled L'Allegro up to date, the final stanza is devoted to Dolmetsch:
&lt;poem&gt;:The old forgotten dancing-lore,
:The steps we cannot understand,
:DOLMETSCH agrees to take in hand,
:These on the well-trod stage anon,
:When next our learned sock is on,
:We’ll show, while ARNOLD, Fancy’s child,
:Tootles his native wood-wind wild.&lt;/poem&gt;
This verse is curiously prophetic for Dolmetsch had not yet introduced the recorder into his concerts, although he occasionally included a flute. Dolmetsch did know something of the steps of the old dances but it was his wife who later researched the subject most thoroughly and wrote two books on the subject.&quot; (Campbell 151–52)

===25 December 1903, Friday===
Christmas Day
====26 December 1903, Saturday====
Boxing Day
===Works Cited===
*Baring-Gould.
*Campbell.

==1904==
===January 1904===
Sometime in January 1904 [[Social Victorians/People/Arthur Conan Doyle|Arthur Conan Doyle]]'s &quot;The Adventure of the Solitary Cyclist,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 399).
===March 1904===
Sometime in March 1904 Arthur Conan Doyle's &quot;The Adventure of Black Peter,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 384).

===April 1904===
Sometime in April 1904, Arthur Conan Doyle's &quot;The Adventure of Charles Augustus Milverton,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 558, n. 1, and 559).

===June 1904===
Sometime in June 1904 Arthur Conan Doyle's &quot;The Adventure of the Three Students,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 370).

Summer 1904: [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

===July 1904===
Sometime in July 1904, Arthur Conan Doyle's &quot;The Adventure of the Golden Pince-Nez,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 351).
===August 1904===
Sometime in August 1904, Arthur Conan Doyle's &quot;The Adventure of the Missing Three-Quarter,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 476).

===September 1904===
Sometime in September 1904, Arthur Conan Doyle's &quot;The Adventure of the Abbey Grange,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 491).

==1905==
===April 1905===
====3 April 1905, Monday====
[[Social Victorians/People/William Butler Yeats|W. B. Yeats]] wrote to Lady Gregory from Dublin, saying he had &quot;dictated a rough draft of a new Grania second act to Moore's typewriter&quot; (Wade 368).
===June 1905===
Summer 1905: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).
===July 1905===
====10 July 1905, Monday====
1905 July 10, the Austro-Hungarian Ambassador hosted a dinner party:&lt;blockquote&gt;The Austro-Hungarian Ambassador entertained the Duke and Duchess of Connaught and Princess Patricia of Connaught at dinner at the Embassy in Belgrave-square on Monday evening. There were also present the Spanish Ambassador and Mme. Bernabé, the United States Ambassador and Mrs. and Miss Whitelaw Reid, Princess Hohenlohe, Prince Francis of Teck, Princess Teano, the Earl of Essex, the Earl and Countess of Crewe, Viscount Villiers, Viscount Errington, Viscount Newry, Mrs. J. Leslie, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Mr. R. Graham, Mrs. Astor, Lady Maud Warrender, Prince Furstenburg, Count Szenchenyi, Captain A. Meade, and Miss Pelly and Colonel Murray in attendance on the Duke and Duchess.&lt;ref&gt;&quot;Court Circular.&quot; ''Times'', 12 July 1905, p. 7. ''The Times Digital Archive'', http://tinyurl.galegroup.com/tinyurl/AHRNq6. Accessed 20 June 2019.&lt;/ref&gt;&lt;/blockquote&gt;

==== Last week of July, 1905 ====
Lady Cadogan hosted a children's party at Chelsea House:&lt;blockquote&gt;Lady Cadogan’s children’s party last week at Chelsea House was one of the prettiest sights imaginable. Her grandchildren, the little Chelseas, came to help entertain the guests, and nearly all the smart women in London brought their small folk. One of loveliest little girls present was Daphne Bourke, Mrs. [[Social Victorians/People/Bourke|Algernon Bourke]]’s only child; and Lady De Trafford’s young daughter Violet was much admired, and Lady Maud Ramsden’s little people were among daintiest of the small children.&lt;ref&gt;&quot;Court and Social News.&quot; ''Belfast News-Letter'' 01 August 1905, Tuesday: 7 [of 10], Col. 6b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/19050801/157/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

===October 1905===

==== 1905 October 14, Saturday ====
A &quot;send-off dinner&quot; for Jerome K. Jerome before his trip to the U.S. occurred at the Garrick Club &quot;the other evening&quot; before October 14:&lt;blockquote&gt;Jerome K. Jerome has undertaken a six months lecturing tour in the United States. I believe that this tour will be a great success, particularly when the Americans come to realise that Mr. Jerome is not only a humorous writer but a brilliant, serious writer with very genuine pathos. His appeal on this side has not, perhaps, gone home to the English people as much as it should, but the quick-witted Americans will not be slow to recognise his talents of both kinds, nor will they fail to appreciate the significance of the fact that the other evening a send-off dinner was given to Mr. Jerome at the Garrick Club. The hosts of the evening were Mr. Pett Ridge and Mr. W. W. Jacobs, which shows that there is no such thing as literary jealousy among our best humorists.

The presence of quite a galaxy of novelists to the dinner to Mr. Jerome, including Mr. Barrie, Sir Arthur Conan Doyle, Mr. Max Pemberton, Mr. H. G. Wells, Mr. G. B. Burgin, Mr. Arthur Morrison, and Mr. Israel Zangwill, serve to indicate the existence of a pleasant brotherhood among the writers of fiction. The readers of ''Three Men in a Boat'' may be interested to know that there were also present Mr. Jerome's companions in that famous journey — Mr. Carl Hentschel and Mr. C. Wingrove.

When I have named further the presence of three artists in Mr. A. S. Boyd, Mr. John Hassall, and Mr. Will Owen, and two journalists in Dr. Robertson Nicoll and [[Social Victorians/People/Rook|Mr. Clarence Rook]], I have given some record of an exceedingly pleasant dinner party. The essential point, however, of this enumeration of names is that many of them are among the most highly honoured of Englishmen in the United States, and that thus Mr. Jerome cannot fail to reap additional benefit from this dinner so thoughtfully given in his honour by Mr. Jacobs and Mr. Pett Ridge.&lt;ref&gt;S., C. K. &quot;A Literary Letter.&quot; ''The Sphere'' 14 October 1905, Saturday: 16 [of 20], Col. 2a–c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001861/19051014/022/0016. Print p. 56.&lt;/ref&gt;&lt;/blockquote&gt;

===November 1905===
Sometime in November 1905, &quot;Arnold Dolmetsch was again asked to provide music for a Been Greet season in New York — an engagement that brought about his first meeting with two young actors on their first American tour, Sybil Thorndike, and her brother, Russell&quot; (Campbell 169). Dolmetsch's return to the US; was [[Social Victorians/People/Horniman|Annie Horniman]] still with the Thorndikes?

==1906==
===March 1906===
====5 March 1906====
&quot;Mr. Frederick John Horniman, who died on March 5, in his seventy-first year, was the son of that well-known Quaker and tea-merchant, John Horniman, who made a magnificent fortune by retailing tea in air-tight packets, and, like his father, devoted both time and wealth to charitable objects. A great traveller, both for business and pleasure, Mr. Horniman gathered togther an admirable collection of curios, and this is housed at Forest Hill in the museum that bears his name. His private benefactions were also large. Mr. Horniman, who was a Liberal, sat in two Parliaments, representing Penrhyn and Falmouth Boroughs in one. He did not seek re-election in January last.&quot; (&quot;The World's News.&quot; Illustrated London News (London, England), Saturday, March 10, 1906; pg. 338; Issue 3490, Col. C)
===June 1906===
Summer 1906: [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

==1907==
===April 1907===
April 1907, [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] went to Italy with Lady Gregory (Harper 80 28).
===June 1907===
Summer 1907: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

'''1907 June 22, Saturday'''
The annual dinner of the Correctors of the Press was held at De Keyser's Royal Hotel:&lt;blockquote&gt;The London Association of Correctors of the Press held their annual dinner at De Keyser’s Royal Hotel on Saturday. The Chairman was the Lord Mayor, and among his supporters were Sir John Cockburn, Colonel David Bruce, Colonel Earl Church, Lieutenant-Colonel Alsager Pollock, Sheriff Dunn, Mr. J. W. Cleland, M.P., Mr. R. Donald, Mr. T. Seccombe, Mr. Francis H. Skrine, Major H. F. Trippel, Mr. Walter Haddon, Mr. W. Pett Ridge, Mr. W. H. Helm, Mr. R. Warwick Bond, Mr. F. W. Rudler, Major Vane Stow, [[Social Victorians/People/Rook|Mr. Clarence Rook]], Mr. J. Randall (Chairman of the Association), Mr. Foxen, and Mr. Feldwick. Proposing the toast of &quot;Literature,” Mr. W. H. Helm speculated as to what would follow the banning of &quot;Mary Barton&quot; by the Education Committee of the London County Council. In his opinion &quot;The Swiss Family Robinson&quot; was a more immoral book, because beyond any other work it had fostered the Micawber view of life. (Laughter.) The LORD MAYOR [init caps large, rest sm, throughout], submitting the toast of &quot;The Readers' Pension Fund,” apologised for appearing in morning dress. The reason was that he had been to the King’s Garden Party at Windsor, and whlle he was returning to London by motor something burst. (Laughter.) Only that morning he had arrived from Berlin, where he learned some lessons useful to people who give dinners. When the Oberburgomeister of Berlin proposed the health of, say, the Lord Mayor of London, there was an end of the business. He did not push forward the Houses of Parliament, the Navy and Army, or even Literature. (Laughter.) Being a practical people the Germans when they met for a particular purpose applied themselves to no other, and the English would well to copy them. (Hear, hear.) Mr. J. RANDALL said that last year the Association helped five readers and one reader’s widow to pensions, and this year it had done the same for two readers and two widows. One of the men assisted last March had taught himself Greek, Arabic, and Sanscrit, and in leisure moments amused himself by making object glasses for microscopes and telescopes. At this very gathering there was a printer’s reader who was Hebrew scholar. (Hear, hear.) With regard to finance Mr. Randall was happy to say that this dinner would enable the Association to establish a fourth pension. (Cheers.) The Lord Mayor, [[Social Victorians/People/Borthwick|Lord Glenesk]] (President of the Readers' Pensions Committee), the Clothworkers’ Company, and the Cutlers’ Company had contributed ten guineas each, and the total addition to the fund resulting from the dinner was £l90. During the evening excellent entertainment was provided by Miss Helena Foxen, Miss Kathleen Dwyer, Mr. T. C. Bell, Mr. P. E. Syrett, Mr. Prank Rhodes, and Mr. E. Croft-Williams, the last-named being the hon. musical director.&lt;ref&gt;&quot;Correctors of the Press.&quot; ''Morning Post'' 24 June 1907, Monday: 4 [of 14], Col. 3c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19070624/074/0004. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

===November 1907===
====10 November 1907====
&lt;quote&gt;On 10 November, Dolmetsch, 'awfully tired and disquieted with overwork', writes to Horne, 'longing for Florence'.

7, Bayley Street&lt;br /&gt;W.C.&lt;br /&gt;My concert went very well last night. Melodie quite distinguished herself, and a sister of [[Social Victorians/People/George Bernard Shaw|Bernard Shaw]] Lucy Carr Shaw sang delightfully. …&lt;br /&gt;But Symmons [sic] … did not go before 1 o'cl. and yet, by the first post this morning, I got a charming poem on Rameau. … He must have spent all night on it.&lt;/quote&gt; (Campbell 120)

==1908==
In 1908 Sidney Paget died in 1908 in some &quot;untimely&quot; fashion (Baring-Gould II 239).

=== April 1908 ===

==== 1908 April 9, Thursday ====
The Provisional Committee for the Shakespeare Memorial demonstration at the Lyceum Theatre met at the Hôtel Métropole:&lt;blockquote&gt;SHAKESPEARE MEMORIAL.

A meeting of the Provisional Committee for the forthcoming Shakespeare Memorial demonstration at the Lyceum Theatre was held yesterday at the Hôtel Métropole. Mr. T. P. O’Connor, M.P., presided, and there were present : The Earl of Lytton, Mr. Percy Alden, M.P., Mr. Henry Ainley, Mr. Percy Ames, Mr. Robert Barr, Mr. Arthur à Beckett, Mr. Austin Brereton, Mr. Acton Bond (General Director of the British Empire Shakespeare Society), Mr. Dion Boucicault, Mrs. Bateman-Crowe, Professor Boss, Mr. Norreys Connell, Mr. W. M. Crook, Mr. John Cutler, K.C., Mr. J. Comyns Carr, Mr. Ernest Carpenter, the Rev. P. H. Ditchfleld, Mr. Robert Donald, Mr. A. C. Forster Boulton, M.P., Mr. and Mrs. Laurence Gomme, Mr. A. A. Gardiner, Mr. C. T. Hunt (hon. secretary London Shakespeare League), Mr. Laurence Housman, Mr. J. A. Hobson. Mr. Ford Madox Hueffer, Mr. Selwyn Image, Mr. Henry Arthur Jones, Mr. Jerome K. Jerome, Mr. Frederick Kerr, Miss Gertrude Kingston, Professor Knight, Mr. Matheson Lang, the Hon. Mrs. Alfred Lyttelton, Miss Lillah McCarthy, Mr. Justin Huntly McCarthy, Colonel Henry Mapleson, Dr. Gilbert Murray, Mr. T. Fairman Ordish, Mr. A. W. Pinero, Mr. Ernest Rhys, [[Social Victorians/People/Rook|Mr. Clarence Rook]], the Rev. J. Cartmel Robinson, Mr. George Radford, M.P., Mr. Clement Shorter, Mr. Otto Salimann (hon. secretary of the Elizabethan Society), [[Social Victorians/People/George Bernard Shaw|Mr. Bernard Shaw]], Mr. H. W. Smith, Mr. Herbert Trench, [[Social Victorians/People/Todhunter|Dr. Todhunter]], and Mr. James Welch. It was agreed that the Lyceum demonstration should take place in May, and a resolution should be moved in favour of the establishment of a National Theatre as a memorial to Shakespeare.&lt;ref&gt;&quot;Shakespearea Memorial.&quot; ''Morning Post'' 10 April 1908, Friday: 7 [of 12], Col. 3c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19080410/126/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1908===
Summer 1908: [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

==== 1908 June 21, Sunday ====
Very large demonstration for women's suffrage in Hyde Park coming from &quot;seven points in London.&quot;&lt;blockquote&gt;WOMAN'S VOTE.
SUFFRAGISTS' GREAT MARCH TO HYDE PARK TODAY.

WHITE DEMONSTRATION.

AMUSING ADDRESS TO M.P.'s. FROM RIVER LAUNCH.

From seven points in London to-day seven big prossesions will march to Park, and there jointly demand the Parliamentary franchise for women.

The whole town will be alive with demonstrating suffragists. The streets will resound with the cry of &quot;Votes for Women.&quot; In Hyde Park eighty speakers will voice the demand from twenty platforms.

London has been divided into districts for the purposes of the mighty demonstration, and each of theee has an assembling place, from which the processions will move off to Hyde Park, as given in the following official list: —

A. — Euston-road. — Form up at 12 o'clock, east of Euston Station. Start at 1 p.m. March via Euston-road, Portland-place, Upper Regent-street, Oxford-street, to the Marble Arch.

B. — Trafalgar-square. — Form up 12.30. Start 1.30. March via Pall Mall, Regent-street, Piccadilly, Berkeley-street, and Mount-street to the Grosvenor Gate.

C. — Victoria Embankment. [sic] Form up 12.30. Start from Westminster Bridge 1.30. March via Victorla-street, Grosvenor-place, to Hyde Park Corner.

D. — Chelsea Embankment. — Form up 12.30. Start 1.30. March via Oakley-street, King's-road, Sloane-square, Sloane-street to Albert Gate.

E. — Kensington High-street. — Form up 1 o'clock. Start 1.30. March via Kensington into the Alexandra Gate of the Park.

F. — Paddington Station. — Form up 1 p.m. Start 2 p.m. March via Victoria Gate into Hyde Park.

G. — Marylebone-road. — Form up 12.30. Start 1.30. March via Seymour-place, Seymour-street, and Into the Park close to the Marble Arch.

The demonstrators will come from all parts of the country, some seventy special trains being run from the big towns in the provinces. These will be met at the London stations by white-garbed &quot;Captains&quot; and &quot;Stewards,&quot; and their occupants marshalled in proper divisions.

Literature and the drama will be represented in several of the processions. Mr. and Mrs. Bernard Shaw will join in Trafalgar-square, and so will Mr. Pett Ridge. Starting from Euston-road will be a coach carrying Mrs. Parkhurst, Miss Beatrice Harraden, Mrs. Mona Caird, and Miss Elizabeth Robins.

Mrs. Israel Zangwill will chaperon a party on a coach from the Thames Embankment, which will include Professor and Mrs. Ayrton, Madame Sarah Grand, Miss Lillah McCarthy (Mrs. Granville Barker), Miss Marian McCarthy, Mr. Lucien Wolf, Professor Perry, F.R.S. (scientist), Mrs. H. G. Wells, Mrs. Alice Meynell, and Suffragist leaders from Sweden, Finland, and Norway. In Finland women not only have the vote, but they sit in Parliament. Madame Stromberg, from that country, is now in London attending the Horse Show at Olympia, and will be present at to-day's demonstration. Mr. H. Nevinson and Mr. H. N. Brailsford will walk in the Embankment procession.

On the Kensington four-in-hand coach will be:— [[Social Victorians/People/Rook|Mrs. Clarence Rook]], Mrs. Jopling Rowe, Mlle. Stavance (Norwegian editor and authoress), Mrs. French Sheldon, F.R.G.S., and Miss Christine Silver. 

...

In addition to seven four-horse coaches — one for each procession — there will be more than sixty brakes, filled with country suffragists, and elaborately decorated. [Story continues.]&lt;ref&gt;&quot;Women's Vote. Suffragists' Great March to Hyde Park To-day. White Demonstration. Amusing Address to M.P.'s from River Launch.&quot; ''Lloyd's Weekly Newspaper'' 21 June 1908, Sunday: 1 [of 28], Col. 1a–c [of 5], 2, Col. 5. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003216/19080621/002/0001. Print p. 1.&lt;/ref&gt;&lt;/blockquote&gt;

===Works Cited===
*Baring-Gould

==1909==
===January 1909===
====1 January 1909====
Rev. [[Social Victorians/People/Ayton|W. A. Ayton]] died (Howe 85 10-11).
===June 1909===
Summer 1909: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

== Bibliography ==
#&quot;Calendar for the Year 1900.&quot; Jumk.de Webprojects. https://kalender-365.de/public-holidays.php?yy=1900. Accessed November 2023.
#Howe

== Footnotes ==
&lt;references /&gt;</text>
      <sha1>gy3vknp782tyi4lo71gtk2r7phjgcm3</sha1>
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  <page>
    <title>Social Victorians/People/Mayo</title>
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      <text bytes="19748" sha1="in0uh0zimrnxuo3fw4two6wjf5ql2uh" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:6&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* See also the [[Social Victorians/People/Bourke|Bourke page]]
* Earl of Mayo (in the Peerage of Ireland)
** Richard Southwell Bourke, 6th Earl of Mayo (12 August 1867 – 8 February 1872)
** Dermot Robert Wyndham Bourke, 7th Earl of Mayo (8 February 1872 – 31 December 1927)
*Baron Connemara
**Robert Bourke, 1st and last Baron Connemara (12 May 1887 – 3 September 1902)&lt;ref name=&quot;:2&quot;&gt;&quot;Robert Bourke, 1st and last Baron Connemara.&quot; {{Cite web|url=https://www.thepeerage.com/p5752.htm#i57514|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p5752.htm#i57514.&lt;/ref&gt;
* The [[Social Victorians/People/Bourke|Hon. Algernon Bourke]]
* [[Social Victorians/People/Bourke|Lady Florence Bourke]]

==Overview==
Richard Bourke, 6th Earl of Mayo was assassinated while inspecting a convict settlement at Port Blair in the Andaman Islands. Robert Bourke, 1st Baron Connemara and Lady Susan Georgiana Ramsay divorced in a sensational case in which she successfully sued for divorce on the grounds of adultery (with her maid Hannah Moore) and cruelty (infecting her with venereal disease).

[[Social Victorians/People/Bourke|Algernon Bourke]], 3rd son of the 6th Earl, was successful in the stock market and, by and large, in business.

In 1912, when Blanche, Dowager Countess of Mayo was 86 years old, the ''Woodford Times'' summarized her like this:&lt;blockquote&gt;The Dowager Countess of Mayo and Lady Costance Mure the only surviving daughters of the first Lord Leconfield, the inheritor of the famous house and estate of Petworth, and consequently aunts of Mr. George Wyndham. Their mother was one of the Blunts. of Crabbet Park, Sussex, which makes them kinswomen of Mr. Wilfrid Scawen Blunt, poet, Egyptophil and counsel for Arabi Pasha is his trial. The Dowager Lady Mayo is the widow — as she has been for forty years past — of the Governor-General of India, who was assassinated while on a tour of the Andamas Islands. Subsequently the Government voted her a pension, which she still enjoys. She was an extra woman of the Bedchamber for over a quarter of a century, and until the death of Queen Victoria. Beside Lord Mayo, her children are the Hon. [[Social Victorians/People/Bourke|Algernon Bourke]], who was at one time on the Stock Exchange; Lady Eva Wyndham-Quin; Lady Florence Bourke; and the Hon. Terence Bourke, who is British Vice-Consul at Bizerta.&lt;ref&gt;&quot;The Dowager Countess of Mayo ....&quot; ''Woodford Times'' 29 November 1912, Friday: 6 [of 8], Col. 6c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004344/19121129/159/0006. Print n.p.&lt;/ref&gt;&lt;/blockquote&gt;

==Acquaintances, Friends and Enemies==
==Timeline==
'''1863 November 21''', Robert Bourke and Lady Susan Georgiana Ramsay married.&lt;ref name=&quot;:3&quot;&gt;&quot;Lady Susan Georgiana Ramsay.&quot; {{Cite web|url=https://www.thepeerage.com/p23213.htm#i232124|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p23213.htm#i232124.&lt;/ref&gt;

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

'''1872 November 20''', Hon. Edward Roden Bourke and Emma Mary Augusta Hatch married.&lt;ref name=&quot;:5&quot;&gt;&quot;Emma Mary Augusta Hatch.&quot; {{Cite web|url=https://www.thepeerage.com/p5751.htm#i57507|title=Person Page|website=www.thepeerage.com|access-date=2021-08-27}} https://www.thepeerage.com/p5751.htm#i57507.&lt;/ref&gt;

'''1880 February 4, Wednesday''', ball at Palmerstown House hosted by Dermot, 7th Earl of Mayo:&lt;blockquote&gt;A grand ball was given on Wedneeday night at Palmerstown House, the seat of the Earl of Mayo. The ball was given by the noble earl to the friends and admirers of his father, in acknowledgment of their munificence in erecting, by subscription, a new family mansion as a memorial to the late earl. The new house, which is to be called the Memorial House, has just been completed. It is a handsome building, picturesquely situated on an elevated site, a short distance from the old mansion. The large hall, which is to be called the Memorial Hall, was set apart as the ballroom. It was handsomely decorated with evergreens, exotics, &amp;c., and when lit up in the most effective and tasteful style, presented a gay and brilliant appearance. A distinguished company have been staying at Palmerstown House, including the Marchioness of Blandford, Lady Georgina Spencer Churchill, the Hon. Algernon Bourke, Lady Margaret Bourke, Lord Capel, Mr. George Darner, Hon. Charles Lascelles, Hon. Henry and Mrs. Henry Bourke, the Countess of Stradbroke, Lady Sophia Rous [?], the Marchioness of Conyngham and the Ladies Conyngham, Lord Arthur Butler, the Hon. Bernard and Hon. Mrs. FitzPatrick, Mr. lon Trant Hamilton, M.P., and Mrs. Hamilton. Amongst those invited were:— The Duke and Duchess of Leinster, and the Ladies Fitzgerald, the Marquis of Kildare, the Marquis and Marchioness of Drogheda, Mr. and the Hon. Mrs. Skeffington Smyth, Mrs. and Miss Kavanagh, Borris House; Colonel Thackwell, 38th Regiment, and Mrs. Thackwell, the officers 38th Regt., &amp;c.&lt;ref&gt;&quot;Ball at Palmerstown House.&quot; ''Kilkenny Moderator'' 07 February 1880, Saturday: 2 [of 4], Col. 7c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002957/18800207/028/0002. Print title: ''Kilkenny Moderator and Leinster Advertiser'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;'''1886 July 27, Tuesday''', the Bourkes attended a service honoring a memorial at St. Paul's for the Earl of Mayo, who had been assassinated&lt;blockquote&gt;A memorial erected to the late Earl of Mayo was unveiled yesterday in the crypt of St. Paul's Cathedral, by Lord Cranbrook. Among those present were — The Dowager Countess of Mayo, Lord and Lady Drogheda, Lord and Lady Ashbourne, Lord Headfort, Lord John Manners, M.P.; Lord Barrington, Lord Leconfield, Lord and Lady Mayo, Right Hon. Beresford Hope, M.P.; Lord Stalbridge, Sir Peter Lumsden, Sir Owen Burne, Colonel Nigel Kingscote, Hon. Percy Wyndham, Mr. Henry Doyle, Mr. George Batten, Mr. E. Lawson, the Right Hon. Gerard Noel, General Fraser, V.C., M.P.; Canon Liddon, Mr. [[Social Victorians/People/Bourke|Algernon Bourke]], Lady Florence Bourke, and the late Lord Mayo’s six brothers — General Bourke, Right Hon. Robert Bourke, M.P.; Rev. George Bourke, Mr. Charles Bourke, C.B.; Major Bourke, and Mr. Henry Bourke. The following is the inscription at foot of the monument:— &quot;Sacred to the memory of Richard South [sic] well Bourke, Earl of Mayo, and for nearly four years Viceroy of India. He discharged the duties of his high office with conspicuous ability. Wise, kindly, just, and energetic, he won the affection of those about him, and the respect of neighbouring Princes; his work for his God and his Queen thus begun was laid aside when, struck down, alas! by the hand of assassin, he yielded up his soul to Christ on the 8th of February, 1872.&quot;&lt;ref&gt;&quot;Memorial to the Late Earl of Mayo.&quot; ''Northern Whig'' 28 July 1886, Wednesday: 6 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000434/18860728/143/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;'''1887 December 15''', [[Social Victorians/People/Bourke|Hon. Algernon Bourke]] and Guendoline Stanley married.&lt;ref name=&quot;:1&quot;&gt;&quot;Guendoline Irene Emily Stanley.&quot; {{Cite web|url=https://www.thepeerage.com/p51525.htm#i515247|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;

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

'''1890 November 27''', Robert Bourke, 1st Baron Connemara and Lady Susan Georgiana Ramsay divorced in a sensational case in which she successfully sued for divorce on the grounds of adultery (with her maid Hannah Moore) and cruelty (infecting her with venereal disease).&lt;ref&gt;&quot;Another Society Scandal. Connemara Divorce Suit. Shocking Disclosures.&quot; ''South Wales Echo'' 27 November 1890 Thursday: 3 [of 4], Cols. 2a–3a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000902/18901127/031/0003.&lt;/ref&gt; This story is repeated essentially verbatum in a number of newspapers.

'''1892 March 5, Saturday''', two generations of men of the Bourke family are mentioned in this article reporting on &quot;the first reverse&quot; in Capt. the Hon. Maurice Bourke's career. Notable is that the Bourkes were &quot;one of the first aristocratic families of which the members took to the Stock Exchange.&quot;&lt;blockquote&gt;Capt. the Hon. Maurice Bourke, who has just been reprimanded in connection with the stranding of the Victoria, is the brother of the present Lord Mayo, and comes of an enterprising family. The Bourkes have pushed their way with remarkable energy in various professions, but are specially noticeable as one of the first aristocratic families of which the members took to the Stock Exchange. Before the Bourkes took it up the &quot;house&quot; was at a discount in Belgravia; it is now at a premium. Both Mr. Henry Bourke and Major Edward Bourke, uncles of Captain Bourke, and Mr. [[Social Victorians/People/Bourke|Algernon Bourke]], his brother, have reaped considerable incomes as the fruits of their enterprise. Captain Bourke has been singularly lucky In the navy in the matter of promotion, being one of those fortunate mariners who have served on the Queen's yacht. This is the first reverse in his career.&lt;ref&gt;&quot;Captain. the Hon. Maurice Bourke.&quot; ''Carlow Nationalist'' 05 March 1892, Saturday: 9 [of 10], Col. 2b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004580/18920305/082/0009. Print title ''Supplement to the Nationalist and Leinster Times''; n. p.&lt;/ref&gt;&lt;/blockquote&gt;'''1894 January 31, Wednesday''', Dermot, Earl of Mayo and Geraldine, Countess of Mayo hosted [[Social Victorians/Timeline/1894#Also 31 January 1894, Wednesday|the Kildare Hunt Ball]].

'''1894 October 10''', Lady Susan Georgiana Ramsay Bourke and Surgn.-Lt.-Col. William Hamilton Broun married.&lt;ref name=&quot;:3&quot; /&gt;

'''1894 October 22''', Robert Bourke, 1st Baron Connemara and Gertrude Lawrence Knight Walsh married.&lt;ref name=&quot;:4&quot;&gt;&quot;Gertrude Lawrence Knight Walsh.&quot; {{Cite web|url=https://www.thepeerage.com/p23213.htm#i232125|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p23213.htm#i232125.&lt;/ref&gt;

'''1895 April 27, Saturday''', Norah Mary Madeline Bourke and Mr. Henry Lindsay married.&lt;ref&gt;&quot;Mr. Henry E. A. Lindsay to Miss Norah M. M. Bourke.&quot; ''Gentlewoman'' 11 May 1895 Saturday: 97 [of 133], Col. 1c–2a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18950511/437/0097.&lt;/ref&gt;

'''1896 December 10, Thursday''', the Dowager Countess of Mayo, the Countess of Mayo and Florence Bourke were present to help staff a stall at the [[Social Victorians/Timeline/1896#10 December 1896, Thursday|Irish Industries Exhibition and Sale, Brighton]], as was [[Social Victorians/People/Bourke|Guendoline Bourke]].

'''1897 July 2''', [[Social Victorians/People/Bourke|Algernon Bourke]] and Guendoline Sloane-Stanley [[Social Victorians/People/Bourke|Bourke]] attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House.

'''1899 July 1, Saturday''', Dermot, 7th Earl of Mayo was active in a [[Social Victorians/Timeline/1899#1 July 1899, Saturday|meeting in London at the Duke of Westminster's Grosvenor House]] about preserving Killarney as part of the National Trust.

'''1904 September 15, Thursday''', according to what was at the time called the ''Irish Daily Independent and Nation'', [[Social Victorians/People/Bourke|Algernon Bourke]] was living in Venice and not in the UK at this point:&lt;blockquote&gt;Algernon Bourke, who usually lives in Venice, has spent some time in England during the present summer, and has now gone on a fishing expedition to Sweden, accompanied by his brother, Lord Mayo. Lady Mayo has been staying meanwhile in Ireland, and has had a visit from her mother, Lady Maria Ponsonby, who is a sister of Lend Obventry.&lt;ref&gt;&quot;Society Notes.&quot; ''Irish Independent'' 15 September 1904, Thursday: 4 [of 8], Col. 5b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001986/19040915/131/0004. Print title: ''Irish Daily Independent and Nation'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;'''1908 August 5''', Emma Mary Augusta Hatch Bourke and Edward Hyde Villiers, 5th Earl of Clarendon married.&lt;ref name=&quot;:5&quot; /&gt;

'''1909 May 22, Saturday''', [[Social Victorians/People/Bourke|Algernon Bourke]] appears to have been living in Pisa. A columnist for the ''Queen'' reported on the Royal School of Art Needlework:&lt;blockquote&gt;Lady Leconfield [?] was there, also her sister-in-law, the Dowager Lady Mayo, only just back from her winter on the Continent, when she spent most of the time at Pisa, where her son Mr Algernon Bourke has also been staying. The latter is a great connoisseur as regards [art?] notably in what is really good in the way of old Italian sculpture and carving. He and his handsome wife have a place near to Putney, and this winter again Mr Bourke, as the result of his Italian travels, has been sending home such relics of the old Italian palace gardens as as stone and marble carved vases, garden seats, and what-not of the kind — not all for himself and his own gardens by any means, I fancy; but his friends, relying on his knowledge in such matters, get him when abroad to choose for [them?] the adornment of their English terraces and gardens.&lt;ref&gt;&quot;My Social Diary.&quot; The ''Queen'' 22 May 1909, Saturday: 31 [of 86], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19090522/203/0031. Print p. 871.&lt;/ref&gt;&lt;/blockquote&gt;

== Demographics ==
* Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
===Residences===
* London: 20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt;
* Ireland: Palmerstown House (built in 1872 by the 7th Earl in honor of his father after his assassination), Palmerstown, County Galway&lt;ref name=&quot;:6&quot; /&gt;
* Ireland: 1873: Palmerston House, Straffan, Co. Kildare&lt;ref&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
==Family==

* Robert Bourke, 5th Earl of Mayo (12 January 1797 – 12 August 1867)&lt;ref&gt;&quot;Robert Bourke, 5th Earl of Mayo.&quot; {{Cite web|url=https://www.thepeerage.com/p4710.htm#i47094|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p4710.htm#i47094.&lt;/ref&gt;
* Anne Charlotte Jocelyn ( – 26 January 1867)&lt;ref&gt;&quot;Anne Charlotte Jocelyn.&quot; {{Cite web|url=https://www.thepeerage.com/p4710.htm#i47095|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p4710.htm#i47095.&lt;/ref&gt;
*# '''Richard Southwell Bourke, 6th Earl of Mayo''' (21 February 1822 – 8 February 1872)
*# Lt.-Gen. John Jocelyn Bourke (5 October 1823 – 25 September 1904)
*# '''Robert Bourke, 1st and last Baron Connemara''' (11 June 1827 – 3 September 1902)
*# Rev. Hon. George Wingfield Bourke (16 February 1829 – 9 October 1903)
*# Hon. Charles Fowler Bourke (5 September 1832 – 4 April 1899)
*# '''Major Hon. Edward Roden Bourke''' (13 December 1835 – 7 June 1907)
*# Hon. Henry Lorton Bourke (26 September 1840 – 30 January 1911)


* Richard Southwell Bourke, 6th Earl of Mayo (21 February 1822 – 8 February 1872)&lt;ref&gt;&quot;Richard Southwell Bourke, 6th Earl of Mayo.&quot; {{Cite web|url=https://www.thepeerage.com/p2575.htm#i25748|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
* Hon. Blanche Julia Wyndham (21 November 1826 – 31 January 1918)&lt;ref&gt;&quot;Hon. Blanche Julia Wyndham.&quot; {{Cite web|url=https://www.thepeerage.com/p2963.htm#i29627|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
# Lady Eva Constance Aline Bourke ( – 19 January 1940)&lt;ref&gt;&quot;Lady Eva Constance Aline Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p2575.htm#i25747|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
# unknown daughter Bourke
# '''Dermot Robert Wyndham Bourke, 7th Earl of Mayo''' (2 July 1851 – 31 December 1927)
# Captain Hon. Sir Maurice Archibald Bourke (22 December 1853 – 16 September 1900)
# '''Hon. [[Social Victorians/People/Bourke|Algernon Henry Bourke]]''' (31 December 1854 – 7 April 1922)
# Lady Florence Blanche Bourke (16 August 1861 – 1953)
# Hon. Terence Theobald Bourke (2 April 1865 – 13 May 1923)


* Dermot Robert Wyndham Bourke, 7th Earl of Mayo (2 July 1851 – 31 December 1927)&lt;ref&gt;&quot;Dermot Robert Wyndham Bourke, 7th Earl of Mayo.&quot; ''The Peerage: A Genealogical Survey of the Peerage of Britain as well as the Royal Families of Europe''. Person page 14031, Person 140310. https://www.thepeerage.com/p14031.htm#i140310.&lt;/ref&gt;
* Geraldine Sarah Ponsonby ( – 29 November 1944)&lt;ref&gt;&quot;Geraldine Sarah Ponsonby.&quot; ''The Peerage: A Genealogical Survey of the Peerage of Britain as well as the Royal Families of Europe''. Person page, 14031, Person 140309. https://www.thepeerage.com/p14031.htm#i140309.&lt;/ref&gt;


* Robert Bourke, 1st and last Baron Connemara (11 June 1827 – 3 September 1902)&lt;ref name=&quot;:2&quot; /&gt;
* Lady Susan Georgiana Ramsay ( – 22 January 1898)&lt;ref name=&quot;:3&quot; /&gt; [she remarried as well]
* Gertrude Lawrence Knight Walsh (baptised 13 August 1833 – 23 November 1898)&lt;ref name=&quot;:4&quot; /&gt; [he was her 2nd husband as well]


* Emma Mary Augusta Hatch (1855 – 9 March 1935)&lt;ref name=&quot;:5&quot; /&gt;
* Major Hon. Edward Roden Bourke (13 December 1835 – 7 June 1907)&lt;ref&gt;&quot;Major Hon. Edward Roden Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p2096.htm#i20954|title=Person Page|website=www.thepeerage.com|access-date=2021-08-27}} https://www.thepeerage.com/p2096.htm#i20954.&lt;/ref&gt;
*# Norah Mary Madeline Bourke ( – 20 June 1948)
*# Madeline Emmie Louisa Bourke ( – 5 August 1961)
*# Cecil Richard Donoughmore Bourke (29 Sep 1875 – 30 November 1884)
*# Anne Kathleen Julia Bourke (c. 1878 – 16 March 1935)
*# Lt.-Col. Nigel Edward Jocelyn Bourke (21 August 1886 – 27 September 1970)
* Edward Hyde Villiers, [[Social Victorians/People/Villiers|5th Earl of Clarendon]]


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

==Biographical Materials==

==Questions and Notes==
==Footnotes==
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      <text bytes="10328" sha1="fs9mv9rc68fq17lk0qdqlau1xk45j0n" xml:space="preserve">{{title|Episodic memory and planning:&lt;br&gt;What role does episodic memory play in planning?}}
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==Overview==
This chapter examines the term episodic memory and how it affects future planning. We will be going into the details of why it exists, the science behind it and what role memory plays in planning for the future. 

Included in the article is a quiz, some imagery and addition links in order to dive into the topic further.

==What is episodic memory?==
Episodic memory is the ability to remember personally experienced events and situations. These memories include details of the context of the event, emotions associated with it and specific details of the event (Tulving, 1993). 

Examples of episodic memory (Perera, 2021):
* Buying your first car 
* Graduating university 
* Your first kiss 
* What you ate for dinner 
*Your friend's birthday party
* First day at school 

{{tip|The science behind it{{what}} (Wright, 2015).

According to the International Encyclopedia of the Social &amp; Behavioral Sciences, episodic memory refers to a neurocognitive system that renders possible the conscious recollection of events as they were previously experienced}}


==Episodic memory and future planning ==
As episodic memory allows for the recall of specific events, this cognitive function contributes to future planning. With the ability to remember events, past feelings and emotions associated with past experiences, you are able to use this information for future planning purposes (How Episodic Memory Helps You Remember Events, 2020). For example, if you got food poisoning from a Mexican restaurant, you would be very hesitant to go there again as you would remember how you felt previously. This recall of information would lead you to choosing a different restaurant for food next time as you would want to avoid feeling like that again.   

== Why does Episodic Memory exist? ==
The oxford handbook of comparative evolutionary psychology has looked into the theory and reasoning for episodic memory (Vonk &amp; Shackelford, 2012) . They have listed 3 main reasons for this theory.

* to use past information to solve problems in the present and for future issues
*to provide knowledge about oneself in the past and as predicted in the future
*to allow humans to understand and empathize{{Grammar}} while providing information and memories for conversation

==The role of Episodic memory in planning ==


According to the Constructive Episodic Simulation Hypothesis developed in 2007, the ability to remember past events and imagine future events is due to episodic memory (Schacter &amp; Addis, 2007).

When imagining future events, the aspect of the brain that lights up, also becomes active when we remember our past and or past events. The similarity of brain activity indicates that when we draw on memories or imagine future plans, we draw on the same areas of the brain that is required.{{fact}}{{Citation needed}}

A case study from 2019 looked into what is the role of episodic foresight in planning for future needs. Their results indicated that where there were strong feelings or memories against an event which determined future planning, this was confirmed to be influenced by episodic memory (Cheke &amp; Clayton, 2019).{{expand}}

In addition, an article written in 2001 has looked into the concept of ‘episodic future thinking’: a projection of the self into the future to pre-experience an event. This research used the theory of episodic memory combined with future planning to predict one feelings, emotions and thoughts for future events or scenarios (Atance &amp; O’Neill, 2001).{{expand}}  

While these articles are looking at different aspects, all three of these case studies provide an explanation as to the connection of memory and planning. These articles also pose the question of, if we alter someone's memory, can that alter their future? These are the lead on questions that would be fascinating to look into{{vague}}. 

== How memory affects the planning of adults with Depression or Alzheimer  ==
Recent research has uncovered that people who are depressed have impaired memory that makes it difficult to not only remember previous memories and events but makes it difficult to imagine future events as well{{fact}}. Due to the loss of connection{{vague}}, this can make their situation more difficult (L, 2015). 

In addition, another study has looked into the connection of episodic memory and future planning amongst older adults with alzheimer's and amnesia{{fact}}. The results revealed that when episodic memory is compromised there is a corresponding loss of details in future events that they imagined (Madore et al., 2014){{expand}}.

Both of these pieces of research indicate that if there are aspects of the brain that aren't healthy, this can lead to difficulty either viewing the future or creating current memories.     

'''[https://en.wikiversity.org/w/index.php?title=User:Maheenusman&amp;veaction=edit Comment:]''' Adults with depression might struggle to integrate and organize information effectively. This can hinder their ability to generate and execute well-structured plans. Reduced Motivation: Depression can lead to decreased motivation and interest in activities, making it challenging to engage in complex planning tasks. The lack of motivation might result in poor execution of plans.    

===Quiz===
Take a quick quiz to see if you understand the concept!

&lt;quiz display=&quot;simple&quot;&gt;
{Episodic memory and future planning activate the same components in the brain:
|type=&quot;()&quot;}
+ True
- False

{Episodic memory is based off how you were raised:
|type=&quot;()&quot;}
- True
+ False
&lt;/quiz&gt;

==Conclusion==
Episodic memory is the ability to remember personally experienced events, situations and emotions attached (Gillund, 2012).This type of memory allows you to recall your first kiss, first car or even your graduation. While this type of memory allows for the recall of emotions or feelings, it also can affect how someone plans for the future. Since episodic memory and future planning utilize the same area of the brain, studies have found that they not only work together and influence each other, but if one aspect isn't working correctly, the other element is negatively influenced. This type of research has informed us that episodic memory and future planning play a large role in working together to create new memory with the ability to plan ahead for more. 

The future recommendation will be to look at the relationship between fake memories and future planning and future planning based on someone else recollection. This type of future research may assist brain injury victims and those without the ability to create memories{{how}}.

== See also ==
*[[Motivation and emotion/Book/2013/Memory and emotion]] (Book chapter, 2013)
*[[Motivation and emotion/Book/2021/Episodic future thinking and delay discounting|Episodic future thinking and delay discounting]] (Book chapter, 2021)
*[[Human brain]] (Wikiversity)
*[[w:Memory|Memory]] (Wikipedia)
*[[Fundamentals of Neuroscience/Memory]] (Wikiversity)
*[[wikipedia:Depression_(mood)|Depression]] (wikipedia)
*[[wikipedia:Alzheimer's_disease|Alzheimer's disease]] (wikipedia)

==References==

{{Hanging indent|1=

Atance, C. M., &amp; O’Neill, D. K. (2001). Episodic future thinking. ''Trends in Cognitive Sciences'', ''5''(12), 533–539. https://doi.org/10.1016/s1364-6613(00)01804-0

Cheke, L. G., &amp; Clayton, N. S. (2019). What is the role of episodic foresight in planning for future needs? Theory and two experiments. ''Quarterly Journal of Experimental Psychology'', ''72''(8), 1961–1976. https://doi.org/10.1177/1747021818820808

Cherry, K. (2020, March 6). ''What is episodic memory?''. Verywell Mind. https://www.verywellmind.com/what-is-episodic-memory-2795173#:%7E:text=Episodic%20memory%20is%20a%20category,all%20examples%20of%20episodic%20memories

Gillund, G. (2012). Episodic memory. In V. S. Ramachandran (Ed.), ''Encyclopedia of human behavior'' (pp. 68-72). Academic Press. https://doi.org/10.1016/B978-0-12-375000-6.00152-X

Madore, K. P., Gaesser, B., &amp; Schacter, D. L. (2014). Constructive episodic simulation: Dissociable effects of a specificity induction on remembering, imagining, and describing in young and older adults. ''Journal of Experimental Psychology: Learning, Memory, and Cognition'', ''40''(3), 609–622. https://doi.org/10.1037/a0034885

Munoz, L. M. P. (2015, March 16). Linking the past to the future through memory. ''Cognitive Neuroscience Society''. https://www.cogneurosociety.org/memory_addis_yia/

Perera, A. (2021, March 16). Episodic memory: Definitions &amp; Examples. ''Simple Psychology''. https://www.simplypsychology.org/episodic-memory.html

Schacter, D. L., &amp; Addis, D. R. (2007). On the constructive episodic simulation of past and future events. ''Behavioral and Brain Sciences'', ''30''(3), 331–332. https://doi.org/10.1017/s0140525x07002178 

Tulving, E. (1993). What is episodic memory?. ''Current Directions in Psychological Science'', ''2''(3), 67–70. https://doi.org/10.1111/1467-8721.ep10770899 

Vonk, J., &amp; Shackelford, T. K. (Eds.). (2012). ''The Oxford handbook of comparative evolutionary psychology''. Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199738182.001.0001

Wright, J. D. (2015). ''International encyclopedia of the social &amp; behavioral sciences'' (2nd ed.). Elsevier. https://www.sciencedirect.com/referencework/9780080970875/international-encyclopedia-of-the-social-and-behavioral-sciences 

}}

== External sources ==

* [https://human-memory.net/episodic-semantic-memory/ Differences and diagrams of episodic and semantic memory] - (The Human Memory)
* [https://www.sciencedirect.com/topics/neuroscience/episodic-memory Episodic Memory] (sciencedirect.com)
* [https://human-memory.net/episodic-semantic-memory/ Episodic and Semantic Memory] - (human-memory.net)
* [https://memory.ucsf.edu/symptoms/memory Memory is often a large part of a person's identity] - (memory.ucsf.edu)
* [https://www.annualreviews.org/doi/10.1146/annurev.psych.53.100901.135114 Episodic Memory: From Mind to Brain] - (annualreviews.org)

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      <id>2693269</id>
      <parentid>2693160</parentid>
      <timestamp>2024-12-26T08:19:39Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Applications */</comment>
      <origin>2693269</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="9878" sha1="06rg3pdhlg1iacej6r12e9vktpmdd05" xml:space="preserve">=== Introduction ===
* Overview ([[Media:C01.Intro1.Overview.1.A.20170925.pdf |A.pdf]], [[Media:C01.Intro1.Overview.1.B.20170901.pdf |B.pdf]], [[Media:C01.Intro1.Overview.1.C.20170904.pdf |C.pdf]])
* Number System ([[Media:C01.Intro2.Number.1.A.20171023.pdf |A.pdf]], [[Media:C01.Intro2.Number.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro2.Number.1.C.20170914.pdf |C.pdf]])
* Memory System ([[Media:C01.Intro2.Memory.1.A.20170907.pdf |A.pdf]], [[Media:C01.Intro3.Memory.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro3.Memory.1.C.20170914.pdf |C.pdf]])

=== Handling Repetition ===
* Control ([[Media:C02.Repeat1.Control.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat1.Control.1.B.20170918.pdf |B.pdf]], [[Media:C02.Repeat1.Control.1.C.20170926.pdf |C.pdf]])
* Loop ([[Media:C02.Repeat2.Loop.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat2.Loop.1.B.20170918.pdf |B.pdf]])

=== Handling a Big Work ===
* Function Overview ([[Media:C03.Func1.Overview.1.A.20171030.pdf |A.pdf]], [[Media:C03.Func1.Oerview.1.B.20161022.pdf |B.pdf]])
* Functions &amp; Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]])
* Functions &amp; Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]])
* Functions &amp; Recursions ([[Media:C03.Func4.Recursion.1.A.20161214.pdf |A.pdf]], [[Media:C03.Func4.Recursion.1.B.20161214.pdf |B.pdf]])

=== Handling Series of Data ===

==== Background ==== 
* Background ([[Media:C04.Series0.Background.1.A.20180727.pdf |A.pdf]])
 
==== Basics ====
* Pointers ([[Media:C04.S1.Pointer.1A.20240524.pdf |A.pdf]], [[Media:C04.Series2.Pointer.1.B.20161115.pdf |B.pdf]])
* Arrays ([[Media:C04.S2.Array.1A.20240514.pdf |A.pdf]], [[Media:C04.Series1.Array.1.B.20161115.pdf |B.pdf]])
* Array Pointers ([[Media:C04.S3.ArrayPointer.1A.20240208.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]])
* Multi-dimensional Arrays ([[Media:C04.Series4.MultiDim.1.A.20221130.pdf |A.pdf]], [[Media:C04.Series4.MultiDim.1.B.1111.pdf |B.pdf]])
* Array Access Methods ([[Media:C04.Series4.ArrayAccess.1.A.20190511.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]])
* Structures ([[Media:C04.Series3.Structure.1.A.20171204.pdf |A.pdf]], [[Media:C04.Series2.Structure.1.B.20161130.pdf |B.pdf]])

==== Examples ==== 
* Spreadsheet Example Programs
:: Example 1 ([[Media:C04.Series7.Example.1.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.1.C.20171213.pdf |C.pdf]])
:: Example 2 ([[Media:C04.Series7.Example.2.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.2.C.20171213.pdf |C.pdf]])
:: Example 3 ([[Media:C04.Series7.Example.3.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.3.C.20171213.pdf |C.pdf]])
:: Bubble Sort ([[Media:C04.Series7.BubbleSort.1.A.20171211.pdf |A.pdf]])

==== Applications ==== 
* Address-of and de-reference operators ([[Media:C04.SA0.PtrOperator.1A.20241226.pdf |A.pdf]])
* Applications of Pointers ([[Media:C04.SA1.AppPointer.1A.20241121.pdf |A.pdf]])
* Applications of Arrays ([[Media:C04.SA2.AppArray.1A.20240715.pdf |A.pdf]])
* Applications of Array Pointers ([[Media:C04.SA3.AppArrayPointer.1A.20240210.pdf |A.pdf]])
* Applications of Multi-dimensional Arrays ([[Media:C04.Series4App.MultiDim.1.A.20210719.pdf |A.pdf]])
* Applications of Array Access Methods ([[Media:C04.Series9.AppArrAcess.1.A.20190511.pdf |A.pdf]])
* Applications of Structures ([[Media:C04.Series6.AppStruct.1.A.20190423.pdf |A.pdf]])

=== Handling Various Kinds of Data ===
* Types ([[Media:C05.Data1.Type.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data1.Type.1.B.20161212.pdf |B.pdf]])
* Typecasts ([[Media:C05.Data2.TypeCast.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data2.TypeCast.1.B.20161216.pdf |A.pdf]])
* Operators ([[Media:C05.Data3.Operators.1.A.20161219.pdf |A.pdf]], [[Media:C05.Data3.Operators.1.B.20161216.pdf |B.pdf]])
* Files ([[Media:C05.Data4.File.1.A.20161124.pdf |A.pdf]], [[Media:C05.Data4.File.1.B.20161212.pdf |B.pdf]])

=== Handling Low Level Operations ===
* Bitwise Operations ([[Media:BitOp.1.B.20161214.pdf |A.pdf]], [[Media:BitOp.1.B.20161203.pdf |B.pdf]])
* Bit Field ([[Media:BitField.1.A.20161214.pdf |A.pdf]], [[Media:BitField.1.B.20161202.pdf |B.pdf]])
* Union ([[Media:Union.1.A.20161221.pdf |A.pdf]], [[Media:Union.1.B.20161111.pdf |B.pdf]])
* Accessing IO Registers ([[Media:IO.1.A.20141215.pdf |A.pdf]], [[Media:IO.1.B.20161217.pdf |B.pdf]])

=== Declarations ===
* Type Specifiers and Qualifiers ([[Media:C07.Spec1.Type.1.A.20171004.pdf |pdf]])
* Storage Class Specifiers ([[Media:C07.Spec2.Storage.1.A.20171009.pdf |pdf]])
* Scope 


=== Class Notes ===

* TOC ([[Media:TOC.20171007.pdf |TOC.pdf]])
* Day01 ([[Media:Day01.A.20171007.pdf |A.pdf]], [[Media:Day01.B.20171209.pdf |B.pdf]], [[Media:Day01.C.20171211.pdf |C.pdf]]) ...... Introduction (1) Standard Library
* Day02 ([[Media:Day02.A.20171007.pdf |A.pdf]], [[Media:Day02.B.20171209.pdf |B.pdf]], [[Media:Day02.C.20171209.pdf |C.pdf]]) ...... Introduction (2) Basic Elements
* Day03 ([[Media:Day03.A.20171007.pdf |A.pdf]], [[Media:Day03.B.20170908.pdf |B.pdf]], [[Media:Day03.C.20171209.pdf |C.pdf]]) ...... Introduction (3) Numbers
* Day04 ([[Media:Day04.A.20171007.pdf |A.pdf]], [[Media:Day04.B.20170915.pdf |B.pdf]], [[Media:Day04.C.20171209.pdf |C.pdf]]) ...... Structured Programming (1) Flowcharts
* Day05 ([[Media:Day05.A.20171007.pdf |A.pdf]], [[Media:Day05.B.20170915.pdf |B.pdf]], [[Media:Day05.C.20171209.pdf |C.pdf]]) ...... Structured Programming (2) Conditions and Loops
* Day06 ([[Media:Day06.A.20171007.pdf |A.pdf]], [[Media:Day06.B.20170923.pdf |B.pdf]], [[Media:Day06.C.20171209.pdf |C.pdf]]) ...... Program Control
* Day07 ([[Media:Day07.A.20171007.pdf |A.pdf]], [[Media:Day07.B.20170926.pdf |B.pdf]], [[Media:Day07.C.20171209.pdf |C.pdf]]) ...... Function (1) Definitions
* Day08 ([[Media:Day08.A.20171028.pdf |A.pdf]], [[Media:Day08.B.20171016.pdf |B.pdf]], [[Media:Day08.C.20171209.pdf |C.pdf]]) ...... Function (2) Storage Class and Scope
* Day09 ([[Media:Day09.A.20171007.pdf |A.pdf]], [[Media:Day09.B.20171017.pdf |B.pdf]], [[Media:Day09.C.20171209.pdf |C.pdf]]) ...... Function (3) Recursion
* Day10 ([[Media:Day10.A.20171209.pdf |A.pdf]], [[Media:Day10.B.20171017.pdf |B.pdf]], [[Media:Day10.C.20171209.pdf |C.pdf]]) ...... Arrays (1) Definitions
* Day11 ([[Media:Day11.A.20171024.pdf |A.pdf]], [[Media:Day11.B.20171017.pdf |B.pdf]], [[Media:Day11.C.20171212.pdf |C.pdf]]) ...... Arrays (2) Applications
* Day12 ([[Media:Day12.A.20171024.pdf |A.pdf]], [[Media:Day12.B.20171020.pdf |B.pdf]], [[Media:Day12.C.20171209.pdf |C.pdf]]) ...... Pointers (1) Definitions
* Day13 ([[Media:Day13.A.20171025.pdf |A.pdf]], [[Media:Day13.B.20171024.pdf |B.pdf]], [[Media:Day13.C.20171209.pdf |C.pdf]]) ...... Pointers (2) Applications
* Day14 ([[Media:Day14.A.20171226.pdf |A.pdf]], [[Media:Day14.B.20171101.pdf |B.pdf]], [[Media:Day14.C.20171209.pdf |C.pdf]]) ...... C String (1) 
* Day15 ([[Media:Day15.A.20171209.pdf |A.pdf]], [[Media:Day15.B.20171124.pdf |B.pdf]], [[Media:Day15.C.20171209.pdf |C.pdf]]) ...... C String (2)
* Day16 ([[Media:Day16.A.20171208.pdf |A.pdf]], [[Media:Day16.B.20171114.pdf |B.pdf]], [[Media:Day16.C.20171209.pdf |C.pdf]]) ...... C Formatted IO
* Day17 ([[Media:Day17.A.20171031.pdf |A.pdf]], [[Media:Day17.B.20171111.pdf |B.pdf]], [[Media:Day17.C.20171209.pdf |C.pdf]]) ...... Structure (1) Definitions
* Day18 ([[Media:Day18.A.20171206.pdf |A.pdf]], [[Media:Day18.B.20171128.pdf |B.pdf]], [[Media:Day18.C.20171212.pdf |C.pdf]]) ...... Structure (2) Applications
* Day19 ([[Media:Day19.A.20171205.pdf |A.pdf]], [[Media:Day19.B.20171121.pdf |B.pdf]], [[Media:Day19.C.20171209.pdf |C.pdf]]) ...... Union, Bitwise Operators, Enum
* Day20 ([[Media:Day20.A.20171205.pdf |A.pdf]], [[Media:Day20.B.20171201.pdf |B.pdf]], [[Media:Day20.C.20171212.pdf |C.pdf]]) ...... Linked List 
* Day21 ([[Media:Day21.A.20171206.pdf |A.pdf]], [[Media:Day21.B.20171208.pdf |B.pdf]], [[Media:Day21.C.20171212.pdf |C.pdf]]) ...... File Processing
* Day22 ([[Media:Day22.A.20171212.pdf |A.pdf]], [[Media:Day22.B.20171213.pdf |B.pdf]], [[Media:Day22.C.20171212.pdf |C.pdf]]) ...... Preprocessing


&lt;!----------------------------------------------------------------------&gt;
&lt;/br&gt;
See also https://cprogramex.wordpress.com/

== '''Old Materials '''==

until 201201
* Intro.Overview.1.A ([[Media:C.Intro.Overview.1.A.20120107.pdf |pdf]])
* Intro.Memory.1.A ([[Media:C.Intro.Memory.1.A.20120107.pdf |pdf]])
* Intro.Number.1.A ([[Media:C.Intro.Number.1.A.20120107.pdf |pdf]])
* Repeat.Control.1.A ([[Media:C.Repeat.Control.1.A.20120109.pdf |pdf]])
* Repeat.Loop.1.A ([[Media:C.Repeat.Loop.1.A.20120113.pdf |pdf]])
* Work.Function.1.A ([[Media:C.Work.Function.1.A.20120117.pdf |pdf]])
* Work.Scope.1.A ([[Media:C.Work.Scope.1.A.20120117.pdf |pdf]])
* Series.Array.1.A ([[Media:Series.Array.1.A.20110718.pdf |pdf]])
* Series.Pointer.1.A ([[Media:Series.Pointer.1.A.20110719.pdf |pdf]])
* Series.Structure.1.A ([[Media:Series.Structure.1.A.20110805.pdf |pdf]])
* Data.Type.1.A ([[Media:C05.Data2.TypeCast.1.A.20130813.pdf |pdf]])
* Data.TypeCast.1.A ([[Media:Data.TypeCast.1.A.pdf |pdf]])
* Data.Operators.1.A ([[Media:Data.Operators.1.A.20110712.pdf |pdf]])
 
&lt;br&gt;

until 201107
* Intro.1.A ([[Media:Intro.1.A.pdf |pdf]])
* Control.1.A ([[Media:Control.1.A.20110706.pdf |pdf]])
* Iteration.1.A ([[Media:Iteration.1.A.pdf |pdf]])
* Function.1.A ([[Media:Function.1.A.20110705.pdf |pdf]])
* Variable.1.A ([[Media:Variable.1.A.20110708.pdf |pdf]])
* Operators.1.A ([[Media:Operators.1.A.20110712.pdf |pdf]])
* Pointer.1.A ([[Media:Pointer.1.A.pdf |pdf]])
* Pointer.2.A ([[Media:Pointer.2.A.pdf |pdf]])
* Array.1.A ([[Media:Array.1.A.pdf |pdf]])
* Type.1.A ([[Media:Type.1.A.pdf |pdf]])
* Structure.1.A ([[Media:Structure.1.A.pdf |pdf]])


go to [ [[C programming in plain view]] ]

[[Category:C programming language]]

&lt;/br&gt;</text>
      <sha1>06rg3pdhlg1iacej6r12e9vktpmdd05</sha1>
    </revision>
  </page>
  <page>
    <title>Workings of gcc and ld in plain view</title>
    <ns>0</ns>
    <id>285384</id>
    <revision>
      <id>2693203</id>
      <parentid>2693157</parentid>
      <timestamp>2024-12-25T19:19:07Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Dynamic Linking - Directories and Symbolic Links */</comment>
      <origin>2693203</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3547" sha1="rboce261di5ychowlsfy4osuibppgfi" xml:space="preserve">=== Workings of the GNU Compiler for IA-32 ===

==== Overview ====
* Overview ([[Media:Overview.20200211.pdf |pdf]])

==== Data Processing ====
* Access ([[Media:Access.20200409.pdf |pdf]])
* Operators ([[Media:Operator.20200427.pdf |pdf]])

==== Control ====
* Conditions ([[Media:Condition.20230630.pdf |pdf]])
* Control ([[Media:Control.20220616.pdf |pdf]])

==== Function calls ==== 
* Procedure ([[Media:Procedure.20220412.pdf |pdf]])
* Recursion ([[Media:Recursion.20210824-2.pdf |pdf]])

==== Pointer and Aggregate Types ==== 
* Arrays ([[Media:Array.20211018.pdf |pdf]])
* Structures ([[Media:Structure.20220101.pdf |pdf]])
* Alignment ([[Media:Alignment.20201117.pdf |pdf]])
* Pointers ([[Media:Pointer.20201106.pdf |pdf]])

==== Integer Arithmetic ==== 
* Overview ([[Media:gcc.1.Overview.20240813.pdf |pdf]])
* Carry Flag ([[Media:gcc.2.Carry.20241204.pdf |pdf]])
* Overflow Flag ([[Media:gcc.3.Overflow.20241205.pdf |pdf]])
* Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]])
* Borrow ([[Media:Borrow.20241223.pdf |pdf]])

==== Floating point Arithmetic ====
&lt;/br&gt;

=== Workings of the GNU Linker for IA-32 ===

==== Linking Libraries ====

* Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]])
* Shared Libraries ([[Media:LIB.2A.Shared.20241225.pdf |pdf]])

==== Dynamic Linking - Directories and Symbolic Links ====

* Shared Library Names ([[Media:DIR.1A.Names.20241225.pdf |pdf]])
* Managing Shared Libraries ([[Media:DIR.2A.Manage.20241225.pdf |pdf]])

==== Dynamic Loading - API Functions ====

* DL API ([[Media:API.1A.Functions.20241224.pdf |pdf]])

==== Library Search Path ====

* Using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]])

* Using RPATH ([[Media:Link.5A.LibSearch-RPATH.20241101.pdf |A.pdf]], [[Media:Link.5B.LibSearch-RPATH.20240705.pdf |B.pdf]])

==== Linking Process ====

* Object Files ([[Media:Link.3.A.Object.20190121.pdf |A.pdf]], [[Media:Link.3.B.Object.20190405.pdf |B.pdf]])

* Symbols ([[Media:Link.4.A.Symbol.20190312.pdf |A.pdf]], [[Media:Link.4.B.Symbol.20190312.pdf |B.pdf]])

* Relocation ([[Media:Link.5.A.Relocation.20190320.pdf |A.pdf]], [[Media:Link.5.B.Relocation.20190322.pdf |B.pdf]])

* Loading ([[Media:Link.6.A.Loading.20190501.pdf |A.pdf]], [[Media:Link.6.B.Loading.20190126.pdf |B.pdf]])

* Static Linking ([[Media:Link.7.A.StaticLink.20190122.pdf |A.pdf]], [[Media:Link.7.B.StaticLink.20190128.pdf |B.pdf]], [[Media:LNK.5C.StaticLinking.20241128.pdf |C.pdf]])

* Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]], [[Media:LNK.6C.DynamicLinking.20241128.pdf |C.pdf]])

* Position Independent Code ([[Media:Link.9.A.PIC.20190304.pdf |A.pdf]], [[Media:Link.9.B.PIC.20190309.pdf |B.pdf]])

==== Example I ====
* Vector addition ([[Media:Eg1.1A.Vector.20190121.pdf |A.pdf]], [[Media:Eg1.1B.Vector.20190121.pdf |B.pdf]])
* Swapping array elements ([[Media:Eg1.2A.Swap.20190302.pdf |A.pdf]], [[Media:Eg1.2B.Swap.20190121.pdf |B.pdf]])
* Nested functions ([[Media:Eg1.3A.Nest.20190121.pdf |A.pdf]], [[Media:Eg1.3B.Nest.20190121.pdf |B.pdf]])

==== Examples II ====
* analysis of static linking ([[Media:Ex1.A.StaticLinkEx.20190121.pdf |A.pdf]], [[Media:Ex2.B.StaticLinkEx.20190121.pdf |B.pdf]])

* analysis of dynamic linking ([[Media:Ex2.A.DynamicLinkEx.20190121.pdf |A.pdf]])

* analysis of PIC ([[Media:Ex3.A.PICEx.20190121.pdf |A.pdf]])


&lt;/br&gt;
go to [ [[C programming in plain view]] ]

[[Category:C programming language]]</text>
      <sha1>rboce261di5ychowlsfy4osuibppgfi</sha1>
    </revision>
    <revision>
      <id>2693205</id>
      <parentid>2693203</parentid>
      <timestamp>2024-12-25T19:20:11Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Dynamic Linking - Directories and Symbolic Links */</comment>
      <origin>2693205</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3547" sha1="kmkjab590wzkccp0594xl5ur71u6xou" xml:space="preserve">=== Workings of the GNU Compiler for IA-32 ===

==== Overview ====
* Overview ([[Media:Overview.20200211.pdf |pdf]])

==== Data Processing ====
* Access ([[Media:Access.20200409.pdf |pdf]])
* Operators ([[Media:Operator.20200427.pdf |pdf]])

==== Control ====
* Conditions ([[Media:Condition.20230630.pdf |pdf]])
* Control ([[Media:Control.20220616.pdf |pdf]])

==== Function calls ==== 
* Procedure ([[Media:Procedure.20220412.pdf |pdf]])
* Recursion ([[Media:Recursion.20210824-2.pdf |pdf]])

==== Pointer and Aggregate Types ==== 
* Arrays ([[Media:Array.20211018.pdf |pdf]])
* Structures ([[Media:Structure.20220101.pdf |pdf]])
* Alignment ([[Media:Alignment.20201117.pdf |pdf]])
* Pointers ([[Media:Pointer.20201106.pdf |pdf]])

==== Integer Arithmetic ==== 
* Overview ([[Media:gcc.1.Overview.20240813.pdf |pdf]])
* Carry Flag ([[Media:gcc.2.Carry.20241204.pdf |pdf]])
* Overflow Flag ([[Media:gcc.3.Overflow.20241205.pdf |pdf]])
* Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]])
* Borrow ([[Media:Borrow.20241223.pdf |pdf]])

==== Floating point Arithmetic ====
&lt;/br&gt;

=== Workings of the GNU Linker for IA-32 ===

==== Linking Libraries ====

* Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]])
* Shared Libraries ([[Media:LIB.2A.Shared.20241225.pdf |pdf]])

==== Dynamic Linking - Directories and Symbolic Links ====

* Shared Library Names ([[Media:DIR.1A.Names.20241225.pdf |pdf]])
* Managing Shared Libraries ([[Media:DIR.2A.Manage.20241226.pdf |pdf]])

==== Dynamic Loading - API Functions ====

* DL API ([[Media:API.1A.Functions.20241224.pdf |pdf]])

==== Library Search Path ====

* Using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]])

* Using RPATH ([[Media:Link.5A.LibSearch-RPATH.20241101.pdf |A.pdf]], [[Media:Link.5B.LibSearch-RPATH.20240705.pdf |B.pdf]])

==== Linking Process ====

* Object Files ([[Media:Link.3.A.Object.20190121.pdf |A.pdf]], [[Media:Link.3.B.Object.20190405.pdf |B.pdf]])

* Symbols ([[Media:Link.4.A.Symbol.20190312.pdf |A.pdf]], [[Media:Link.4.B.Symbol.20190312.pdf |B.pdf]])

* Relocation ([[Media:Link.5.A.Relocation.20190320.pdf |A.pdf]], [[Media:Link.5.B.Relocation.20190322.pdf |B.pdf]])

* Loading ([[Media:Link.6.A.Loading.20190501.pdf |A.pdf]], [[Media:Link.6.B.Loading.20190126.pdf |B.pdf]])

* Static Linking ([[Media:Link.7.A.StaticLink.20190122.pdf |A.pdf]], [[Media:Link.7.B.StaticLink.20190128.pdf |B.pdf]], [[Media:LNK.5C.StaticLinking.20241128.pdf |C.pdf]])

* Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]], [[Media:LNK.6C.DynamicLinking.20241128.pdf |C.pdf]])

* Position Independent Code ([[Media:Link.9.A.PIC.20190304.pdf |A.pdf]], [[Media:Link.9.B.PIC.20190309.pdf |B.pdf]])

==== Example I ====
* Vector addition ([[Media:Eg1.1A.Vector.20190121.pdf |A.pdf]], [[Media:Eg1.1B.Vector.20190121.pdf |B.pdf]])
* Swapping array elements ([[Media:Eg1.2A.Swap.20190302.pdf |A.pdf]], [[Media:Eg1.2B.Swap.20190121.pdf |B.pdf]])
* Nested functions ([[Media:Eg1.3A.Nest.20190121.pdf |A.pdf]], [[Media:Eg1.3B.Nest.20190121.pdf |B.pdf]])

==== Examples II ====
* analysis of static linking ([[Media:Ex1.A.StaticLinkEx.20190121.pdf |A.pdf]], [[Media:Ex2.B.StaticLinkEx.20190121.pdf |B.pdf]])

* analysis of dynamic linking ([[Media:Ex2.A.DynamicLinkEx.20190121.pdf |A.pdf]])

* analysis of PIC ([[Media:Ex3.A.PICEx.20190121.pdf |A.pdf]])


&lt;/br&gt;
go to [ [[C programming in plain view]] ]

[[Category:C programming language]]</text>
      <sha1>kmkjab590wzkccp0594xl5ur71u6xou</sha1>
    </revision>
    <revision>
      <id>2693224</id>
      <parentid>2693205</parentid>
      <timestamp>2024-12-25T22:31:43Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Dynamic Loading - API Functions */</comment>
      <origin>2693224</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3547" sha1="kg5z9xxxoy1sn1cop0cfxgeuab6r2lz" xml:space="preserve">=== Workings of the GNU Compiler for IA-32 ===

==== Overview ====
* Overview ([[Media:Overview.20200211.pdf |pdf]])

==== Data Processing ====
* Access ([[Media:Access.20200409.pdf |pdf]])
* Operators ([[Media:Operator.20200427.pdf |pdf]])

==== Control ====
* Conditions ([[Media:Condition.20230630.pdf |pdf]])
* Control ([[Media:Control.20220616.pdf |pdf]])

==== Function calls ==== 
* Procedure ([[Media:Procedure.20220412.pdf |pdf]])
* Recursion ([[Media:Recursion.20210824-2.pdf |pdf]])

==== Pointer and Aggregate Types ==== 
* Arrays ([[Media:Array.20211018.pdf |pdf]])
* Structures ([[Media:Structure.20220101.pdf |pdf]])
* Alignment ([[Media:Alignment.20201117.pdf |pdf]])
* Pointers ([[Media:Pointer.20201106.pdf |pdf]])

==== Integer Arithmetic ==== 
* Overview ([[Media:gcc.1.Overview.20240813.pdf |pdf]])
* Carry Flag ([[Media:gcc.2.Carry.20241204.pdf |pdf]])
* Overflow Flag ([[Media:gcc.3.Overflow.20241205.pdf |pdf]])
* Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]])
* Borrow ([[Media:Borrow.20241223.pdf |pdf]])

==== Floating point Arithmetic ====
&lt;/br&gt;

=== Workings of the GNU Linker for IA-32 ===

==== Linking Libraries ====

* Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]])
* Shared Libraries ([[Media:LIB.2A.Shared.20241225.pdf |pdf]])

==== Dynamic Linking - Directories and Symbolic Links ====

* Shared Library Names ([[Media:DIR.1A.Names.20241225.pdf |pdf]])
* Managing Shared Libraries ([[Media:DIR.2A.Manage.20241226.pdf |pdf]])

==== Dynamic Loading - API Functions ====

* DL API ([[Media:API.1A.Functions.20241225.pdf |pdf]])

==== Library Search Path ====

* Using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]])

* Using RPATH ([[Media:Link.5A.LibSearch-RPATH.20241101.pdf |A.pdf]], [[Media:Link.5B.LibSearch-RPATH.20240705.pdf |B.pdf]])

==== Linking Process ====

* Object Files ([[Media:Link.3.A.Object.20190121.pdf |A.pdf]], [[Media:Link.3.B.Object.20190405.pdf |B.pdf]])

* Symbols ([[Media:Link.4.A.Symbol.20190312.pdf |A.pdf]], [[Media:Link.4.B.Symbol.20190312.pdf |B.pdf]])

* Relocation ([[Media:Link.5.A.Relocation.20190320.pdf |A.pdf]], [[Media:Link.5.B.Relocation.20190322.pdf |B.pdf]])

* Loading ([[Media:Link.6.A.Loading.20190501.pdf |A.pdf]], [[Media:Link.6.B.Loading.20190126.pdf |B.pdf]])

* Static Linking ([[Media:Link.7.A.StaticLink.20190122.pdf |A.pdf]], [[Media:Link.7.B.StaticLink.20190128.pdf |B.pdf]], [[Media:LNK.5C.StaticLinking.20241128.pdf |C.pdf]])

* Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]], [[Media:LNK.6C.DynamicLinking.20241128.pdf |C.pdf]])

* Position Independent Code ([[Media:Link.9.A.PIC.20190304.pdf |A.pdf]], [[Media:Link.9.B.PIC.20190309.pdf |B.pdf]])

==== Example I ====
* Vector addition ([[Media:Eg1.1A.Vector.20190121.pdf |A.pdf]], [[Media:Eg1.1B.Vector.20190121.pdf |B.pdf]])
* Swapping array elements ([[Media:Eg1.2A.Swap.20190302.pdf |A.pdf]], [[Media:Eg1.2B.Swap.20190121.pdf |B.pdf]])
* Nested functions ([[Media:Eg1.3A.Nest.20190121.pdf |A.pdf]], [[Media:Eg1.3B.Nest.20190121.pdf |B.pdf]])

==== Examples II ====
* analysis of static linking ([[Media:Ex1.A.StaticLinkEx.20190121.pdf |A.pdf]], [[Media:Ex2.B.StaticLinkEx.20190121.pdf |B.pdf]])

* analysis of dynamic linking ([[Media:Ex2.A.DynamicLinkEx.20190121.pdf |A.pdf]])

* analysis of PIC ([[Media:Ex3.A.PICEx.20190121.pdf |A.pdf]])


&lt;/br&gt;
go to [ [[C programming in plain view]] ]

[[Category:C programming language]]</text>
      <sha1>kg5z9xxxoy1sn1cop0cfxgeuab6r2lz</sha1>
    </revision>
    <revision>
      <id>2693226</id>
      <parentid>2693224</parentid>
      <timestamp>2024-12-25T22:33:17Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Dynamic Loading - API Functions */</comment>
      <origin>2693226</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3547" sha1="tezuakq8nd8nwc6zw034mtogvhpcxgx" xml:space="preserve">=== Workings of the GNU Compiler for IA-32 ===

==== Overview ====
* Overview ([[Media:Overview.20200211.pdf |pdf]])

==== Data Processing ====
* Access ([[Media:Access.20200409.pdf |pdf]])
* Operators ([[Media:Operator.20200427.pdf |pdf]])

==== Control ====
* Conditions ([[Media:Condition.20230630.pdf |pdf]])
* Control ([[Media:Control.20220616.pdf |pdf]])

==== Function calls ==== 
* Procedure ([[Media:Procedure.20220412.pdf |pdf]])
* Recursion ([[Media:Recursion.20210824-2.pdf |pdf]])

==== Pointer and Aggregate Types ==== 
* Arrays ([[Media:Array.20211018.pdf |pdf]])
* Structures ([[Media:Structure.20220101.pdf |pdf]])
* Alignment ([[Media:Alignment.20201117.pdf |pdf]])
* Pointers ([[Media:Pointer.20201106.pdf |pdf]])

==== Integer Arithmetic ==== 
* Overview ([[Media:gcc.1.Overview.20240813.pdf |pdf]])
* Carry Flag ([[Media:gcc.2.Carry.20241204.pdf |pdf]])
* Overflow Flag ([[Media:gcc.3.Overflow.20241205.pdf |pdf]])
* Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]])
* Borrow ([[Media:Borrow.20241223.pdf |pdf]])

==== Floating point Arithmetic ====
&lt;/br&gt;

=== Workings of the GNU Linker for IA-32 ===

==== Linking Libraries ====

* Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]])
* Shared Libraries ([[Media:LIB.2A.Shared.20241225.pdf |pdf]])

==== Dynamic Linking - Directories and Symbolic Links ====

* Shared Library Names ([[Media:DIR.1A.Names.20241225.pdf |pdf]])
* Managing Shared Libraries ([[Media:DIR.2A.Manage.20241226.pdf |pdf]])

==== Dynamic Loading - API Functions ====

* DL API ([[Media:API.1A.Functions.20241226.pdf |pdf]])

==== Library Search Path ====

* Using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]])

* Using RPATH ([[Media:Link.5A.LibSearch-RPATH.20241101.pdf |A.pdf]], [[Media:Link.5B.LibSearch-RPATH.20240705.pdf |B.pdf]])

==== Linking Process ====

* Object Files ([[Media:Link.3.A.Object.20190121.pdf |A.pdf]], [[Media:Link.3.B.Object.20190405.pdf |B.pdf]])

* Symbols ([[Media:Link.4.A.Symbol.20190312.pdf |A.pdf]], [[Media:Link.4.B.Symbol.20190312.pdf |B.pdf]])

* Relocation ([[Media:Link.5.A.Relocation.20190320.pdf |A.pdf]], [[Media:Link.5.B.Relocation.20190322.pdf |B.pdf]])

* Loading ([[Media:Link.6.A.Loading.20190501.pdf |A.pdf]], [[Media:Link.6.B.Loading.20190126.pdf |B.pdf]])

* Static Linking ([[Media:Link.7.A.StaticLink.20190122.pdf |A.pdf]], [[Media:Link.7.B.StaticLink.20190128.pdf |B.pdf]], [[Media:LNK.5C.StaticLinking.20241128.pdf |C.pdf]])

* Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]], [[Media:LNK.6C.DynamicLinking.20241128.pdf |C.pdf]])

* Position Independent Code ([[Media:Link.9.A.PIC.20190304.pdf |A.pdf]], [[Media:Link.9.B.PIC.20190309.pdf |B.pdf]])

==== Example I ====
* Vector addition ([[Media:Eg1.1A.Vector.20190121.pdf |A.pdf]], [[Media:Eg1.1B.Vector.20190121.pdf |B.pdf]])
* Swapping array elements ([[Media:Eg1.2A.Swap.20190302.pdf |A.pdf]], [[Media:Eg1.2B.Swap.20190121.pdf |B.pdf]])
* Nested functions ([[Media:Eg1.3A.Nest.20190121.pdf |A.pdf]], [[Media:Eg1.3B.Nest.20190121.pdf |B.pdf]])

==== Examples II ====
* analysis of static linking ([[Media:Ex1.A.StaticLinkEx.20190121.pdf |A.pdf]], [[Media:Ex2.B.StaticLinkEx.20190121.pdf |B.pdf]])

* analysis of dynamic linking ([[Media:Ex2.A.DynamicLinkEx.20190121.pdf |A.pdf]])

* analysis of PIC ([[Media:Ex3.A.PICEx.20190121.pdf |A.pdf]])


&lt;/br&gt;
go to [ [[C programming in plain view]] ]

[[Category:C programming language]]</text>
      <sha1>tezuakq8nd8nwc6zw034mtogvhpcxgx</sha1>
    </revision>
    <revision>
      <id>2693228</id>
      <parentid>2693226</parentid>
      <timestamp>2024-12-25T23:13:18Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Dynamic Linking - Directories and Symbolic Links */</comment>
      <origin>2693228</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3547" sha1="lsqt8ozdvcfb05vujcaob1xwlxnpff3" xml:space="preserve">=== Workings of the GNU Compiler for IA-32 ===

==== Overview ====
* Overview ([[Media:Overview.20200211.pdf |pdf]])

==== Data Processing ====
* Access ([[Media:Access.20200409.pdf |pdf]])
* Operators ([[Media:Operator.20200427.pdf |pdf]])

==== Control ====
* Conditions ([[Media:Condition.20230630.pdf |pdf]])
* Control ([[Media:Control.20220616.pdf |pdf]])

==== Function calls ==== 
* Procedure ([[Media:Procedure.20220412.pdf |pdf]])
* Recursion ([[Media:Recursion.20210824-2.pdf |pdf]])

==== Pointer and Aggregate Types ==== 
* Arrays ([[Media:Array.20211018.pdf |pdf]])
* Structures ([[Media:Structure.20220101.pdf |pdf]])
* Alignment ([[Media:Alignment.20201117.pdf |pdf]])
* Pointers ([[Media:Pointer.20201106.pdf |pdf]])

==== Integer Arithmetic ==== 
* Overview ([[Media:gcc.1.Overview.20240813.pdf |pdf]])
* Carry Flag ([[Media:gcc.2.Carry.20241204.pdf |pdf]])
* Overflow Flag ([[Media:gcc.3.Overflow.20241205.pdf |pdf]])
* Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]])
* Borrow ([[Media:Borrow.20241223.pdf |pdf]])

==== Floating point Arithmetic ====
&lt;/br&gt;

=== Workings of the GNU Linker for IA-32 ===

==== Linking Libraries ====

* Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]])
* Shared Libraries ([[Media:LIB.2A.Shared.20241225.pdf |pdf]])

==== Dynamic Linking - Directories and Symbolic Links ====

* Shared Library Names ([[Media:DIR.1A.Names.20241226.pdf |pdf]])
* Managing Shared Libraries ([[Media:DIR.2A.Manage.20241226.pdf |pdf]])

==== Dynamic Loading - API Functions ====

* DL API ([[Media:API.1A.Functions.20241226.pdf |pdf]])

==== Library Search Path ====

* Using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]])

* Using RPATH ([[Media:Link.5A.LibSearch-RPATH.20241101.pdf |A.pdf]], [[Media:Link.5B.LibSearch-RPATH.20240705.pdf |B.pdf]])

==== Linking Process ====

* Object Files ([[Media:Link.3.A.Object.20190121.pdf |A.pdf]], [[Media:Link.3.B.Object.20190405.pdf |B.pdf]])

* Symbols ([[Media:Link.4.A.Symbol.20190312.pdf |A.pdf]], [[Media:Link.4.B.Symbol.20190312.pdf |B.pdf]])

* Relocation ([[Media:Link.5.A.Relocation.20190320.pdf |A.pdf]], [[Media:Link.5.B.Relocation.20190322.pdf |B.pdf]])

* Loading ([[Media:Link.6.A.Loading.20190501.pdf |A.pdf]], [[Media:Link.6.B.Loading.20190126.pdf |B.pdf]])

* Static Linking ([[Media:Link.7.A.StaticLink.20190122.pdf |A.pdf]], [[Media:Link.7.B.StaticLink.20190128.pdf |B.pdf]], [[Media:LNK.5C.StaticLinking.20241128.pdf |C.pdf]])

* Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]], [[Media:LNK.6C.DynamicLinking.20241128.pdf |C.pdf]])

* Position Independent Code ([[Media:Link.9.A.PIC.20190304.pdf |A.pdf]], [[Media:Link.9.B.PIC.20190309.pdf |B.pdf]])

==== Example I ====
* Vector addition ([[Media:Eg1.1A.Vector.20190121.pdf |A.pdf]], [[Media:Eg1.1B.Vector.20190121.pdf |B.pdf]])
* Swapping array elements ([[Media:Eg1.2A.Swap.20190302.pdf |A.pdf]], [[Media:Eg1.2B.Swap.20190121.pdf |B.pdf]])
* Nested functions ([[Media:Eg1.3A.Nest.20190121.pdf |A.pdf]], [[Media:Eg1.3B.Nest.20190121.pdf |B.pdf]])

==== Examples II ====
* analysis of static linking ([[Media:Ex1.A.StaticLinkEx.20190121.pdf |A.pdf]], [[Media:Ex2.B.StaticLinkEx.20190121.pdf |B.pdf]])

* analysis of dynamic linking ([[Media:Ex2.A.DynamicLinkEx.20190121.pdf |A.pdf]])

* analysis of PIC ([[Media:Ex3.A.PICEx.20190121.pdf |A.pdf]])


&lt;/br&gt;
go to [ [[C programming in plain view]] ]

[[Category:C programming language]]</text>
      <sha1>lsqt8ozdvcfb05vujcaob1xwlxnpff3</sha1>
    </revision>
    <revision>
      <id>2693250</id>
      <parentid>2693228</parentid>
      <timestamp>2024-12-26T00:38:06Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Linking Libraries */</comment>
      <origin>2693250</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3547" sha1="g3urbzg8ngksf1ewpd44w08l02h0p3f" xml:space="preserve">=== Workings of the GNU Compiler for IA-32 ===

==== Overview ====
* Overview ([[Media:Overview.20200211.pdf |pdf]])

==== Data Processing ====
* Access ([[Media:Access.20200409.pdf |pdf]])
* Operators ([[Media:Operator.20200427.pdf |pdf]])

==== Control ====
* Conditions ([[Media:Condition.20230630.pdf |pdf]])
* Control ([[Media:Control.20220616.pdf |pdf]])

==== Function calls ==== 
* Procedure ([[Media:Procedure.20220412.pdf |pdf]])
* Recursion ([[Media:Recursion.20210824-2.pdf |pdf]])

==== Pointer and Aggregate Types ==== 
* Arrays ([[Media:Array.20211018.pdf |pdf]])
* Structures ([[Media:Structure.20220101.pdf |pdf]])
* Alignment ([[Media:Alignment.20201117.pdf |pdf]])
* Pointers ([[Media:Pointer.20201106.pdf |pdf]])

==== Integer Arithmetic ==== 
* Overview ([[Media:gcc.1.Overview.20240813.pdf |pdf]])
* Carry Flag ([[Media:gcc.2.Carry.20241204.pdf |pdf]])
* Overflow Flag ([[Media:gcc.3.Overflow.20241205.pdf |pdf]])
* Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]])
* Borrow ([[Media:Borrow.20241223.pdf |pdf]])

==== Floating point Arithmetic ====
&lt;/br&gt;

=== Workings of the GNU Linker for IA-32 ===

==== Linking Libraries ====

* Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |pdf]])
* Shared Libraries ([[Media:LIB.2A.Shared.20241226.pdf |pdf]])

==== Dynamic Linking - Directories and Symbolic Links ====

* Shared Library Names ([[Media:DIR.1A.Names.20241226.pdf |pdf]])
* Managing Shared Libraries ([[Media:DIR.2A.Manage.20241226.pdf |pdf]])

==== Dynamic Loading - API Functions ====

* DL API ([[Media:API.1A.Functions.20241226.pdf |pdf]])

==== Library Search Path ====

* Using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]])

* Using RPATH ([[Media:Link.5A.LibSearch-RPATH.20241101.pdf |A.pdf]], [[Media:Link.5B.LibSearch-RPATH.20240705.pdf |B.pdf]])

==== Linking Process ====

* Object Files ([[Media:Link.3.A.Object.20190121.pdf |A.pdf]], [[Media:Link.3.B.Object.20190405.pdf |B.pdf]])

* Symbols ([[Media:Link.4.A.Symbol.20190312.pdf |A.pdf]], [[Media:Link.4.B.Symbol.20190312.pdf |B.pdf]])

* Relocation ([[Media:Link.5.A.Relocation.20190320.pdf |A.pdf]], [[Media:Link.5.B.Relocation.20190322.pdf |B.pdf]])

* Loading ([[Media:Link.6.A.Loading.20190501.pdf |A.pdf]], [[Media:Link.6.B.Loading.20190126.pdf |B.pdf]])

* Static Linking ([[Media:Link.7.A.StaticLink.20190122.pdf |A.pdf]], [[Media:Link.7.B.StaticLink.20190128.pdf |B.pdf]], [[Media:LNK.5C.StaticLinking.20241128.pdf |C.pdf]])

* Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]], [[Media:LNK.6C.DynamicLinking.20241128.pdf |C.pdf]])

* Position Independent Code ([[Media:Link.9.A.PIC.20190304.pdf |A.pdf]], [[Media:Link.9.B.PIC.20190309.pdf |B.pdf]])

==== Example I ====
* Vector addition ([[Media:Eg1.1A.Vector.20190121.pdf |A.pdf]], [[Media:Eg1.1B.Vector.20190121.pdf |B.pdf]])
* Swapping array elements ([[Media:Eg1.2A.Swap.20190302.pdf |A.pdf]], [[Media:Eg1.2B.Swap.20190121.pdf |B.pdf]])
* Nested functions ([[Media:Eg1.3A.Nest.20190121.pdf |A.pdf]], [[Media:Eg1.3B.Nest.20190121.pdf |B.pdf]])

==== Examples II ====
* analysis of static linking ([[Media:Ex1.A.StaticLinkEx.20190121.pdf |A.pdf]], [[Media:Ex2.B.StaticLinkEx.20190121.pdf |B.pdf]])

* analysis of dynamic linking ([[Media:Ex2.A.DynamicLinkEx.20190121.pdf |A.pdf]])

* analysis of PIC ([[Media:Ex3.A.PICEx.20190121.pdf |A.pdf]])


&lt;/br&gt;
go to [ [[C programming in plain view]] ]

[[Category:C programming language]]</text>
      <sha1>g3urbzg8ngksf1ewpd44w08l02h0p3f</sha1>
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  </page>
  <page>
    <title>Wikiversity:GUS2Wiki</title>
    <ns>4</ns>
    <id>285491</id>
    <revision>
      <id>2693207</id>
      <parentid>2692339</parentid>
      <timestamp>2024-12-25T19:28:24Z</timestamp>
      <contributor>
        <username>Alexis Jazz</username>
        <id>791434</id>
      </contributor>
      <comment>Updating gadget usage statistics from [[Special:GadgetUsage]] ([[phab:T121049]])</comment>
      <origin>2693207</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1278" sha1="nz1pjsmltk8sxpzuq5wc7da19etwi50" xml:space="preserve">{{#ifexist:Project:GUS2Wiki/top|{{/top}}|This page provides a historical record of [[Special:GadgetUsage]] through its page history. To get the data in CSV format, see wikitext. To customize this message or add categories, create [[/top]].}}
The following data is cached, and was last updated 2024-12-25T06:40:52Z. A maximum of {{PLURAL:5000|one result is|5000 results are}} available in the cache.
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! Gadget !! data-sort-type=&quot;number&quot; | Number of users !! data-sort-type=&quot;number&quot; | Active users
|-
|CleanDeletions || 75 || 0
|-
|EnhancedTalk || 1372 || 4
|-
|HideFundraisingNotice || 816 || 8
|-
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* [[Special:GadgetUsage]]
* [[m:Meta:GUS2Wiki/Script|GUS2Wiki]]
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  <page>
    <title>User:Dc.samizdat/Rotations</title>
    <ns>2</ns>
    <id>289273</id>
    <revision>
      <id>2693260</id>
      <parentid>2692094</parentid>
      <timestamp>2024-12-26T05:44:14Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <origin>2693260</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="102103" sha1="d4zy1z0k1kctupuim3mpux2jrx4bj1y" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|June 2023 - November 2024}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four or more orthogonal spatial dimensions. Atoms are 4-polytopes, and stars are 4-balls of atomic plasma. A galaxy is a hollow 3-sphere with these objects distributed on its surface; the black hole at its center is the 4-ball of empty space it surrounds. The observable universe of galaxies may be visualized as a 4-sphere expanding radially from an origin point at velocity &lt;math&gt;c&lt;/math&gt;, the propagation speed of light through 3-space, which is also the invariant velocity of all mass-carrying objects through 4-space. The propagation speed of light through 4-space &lt;math&gt;c_4&lt;/math&gt; is &lt;math&gt;c &lt; c_4 &lt; 2c&lt;/math&gt;. This view is compatible with the theories of special and general relativity, and with the quantum mechanical atomic theory. It explains those theories as expressions of intrinsic symmetries.&lt;/blockquote&gt;

== Symmetries ==
It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway|Burgiel|Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s.{{Efn|[[W:Coxeter group|Coxeter theory]] is for geometry what Noether's theorem is for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that obey the principle of relativity and correspond to distinct symmetry groups.}} Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. As I understand [[W:Coxeter group|Coxeter group]] theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic rather than algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional objects, and nature can be understood in terms of their [[W:group action|group actions]], including centrally [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]].

== The geometry of the atomic nucleus ==

In [[W:Euclidean 4-space|Euclidean four dimensional space]], an [[W:atomic nucleus|atomic nucleus]] is a [[24-cell]], the regular 4-polytope with [[W:Coxeter group#Symmetry groups of regular polytopes|𝔽&lt;sub&gt;4&lt;/sub&gt; symmetry]]. Nuclear shells are concentric [[W:3-sphere|3-sphere]]s occupied (fully or partially) by the orbits of this 24-point [[#The 6 regular convex 4-polytopes|regular convex 4-polytope]]. An actual atomic nucleus is a rotating four dimensional object. It is not a ''rigid'' rotating 24-cell, it is a kinematic one, because the nucleus of an actual atom of any [[W:nucleon number|nucleon number]] contains a distinct number of orbiting vertices which may be in different isoclinic rotational orbits. These moving vertices never describe a static 24-cell at any single instant in time, though their orbits do all the time. The physical configuration of the nucleus as a 24-cell can be reduced to the [[W:kinematics|kinematics]] of the orbits of its constituents. The geometry of the atomic nucleus is therefore strictly [[W:Euclidean geometry#19th century|Euclidean]] in four dimensional space.

=== Rotations ===
The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways (like coins flipping) into each other's central planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one or another of the parallel planes of rotation, so all of them move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out.

This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a precise [[24-cell|detailed description]] enabling the reader to visualize it runs to many pages and illustrations, with many accompanying pages of explanatory notes on basic phenomena that arise only in 4-dimensional space: [[24-cell#Squares|completely orthogonal planes]], [[24-cell#Hexagons|Clifford parallelism]] and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Helical hexagrams and their isoclines|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a surprise. [[#The 6 regular convex 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120, and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (generally), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It is much harder for us to visualize, because the only way we can experience it is in our imaginations; we have no body of ''sensory'' experience in 4-dimensional space to draw upon.

For that reason, descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case. [[W:Kinematics|Kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rigid 24-cell. 

To begin with, when we examine the individual parts of the rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertices just once, and no point-object colliding with any other at any time.

That is still an example of a rigid object in a single distinct isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing the characteristic rotation of the 24-cell. But we can also imagine ''combining'' distinct rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible without collisions? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore questions of this kind of [[W:kinematics|kinematics]], and where dynamic stabilites arise, of [[W:kinetics|kinetics]].

=== Isospin ===
A [[W:Nucleon|nucleon]] is a [[W:proton|proton]] or a [[W:neutron|neutron]]. The proton carries a positive net [[W:Electric charge|charge]], and the neutron carries a zero net charge. The proton's [[W:Mass|mass]] is only about 0.13% less than the neutron's, and since they are observed to be identical in other respects, they can be viewed as two states of the same nucleon, together forming an isospin doublet ({{nowrap|''I'' {{=}} {{sfrac|1|2}}}}). In isospin space, neutrons can be transformed into protons and conversely by actions of the [[W:SU(2)|SU(2)]] symmetry group. In nature, protons are very stable (the most stable particle known); a proton and a neutron are a stable nuclide; but free neutrons decay into protons in about 10 or 15 seconds.

According to the [[W:Noether theorem|Noether theorem]], [[W:Isospin|isospin]] is conserved with respect to the [[W:strong interaction|strong interaction]].&lt;ref name=Griffiths2008&gt;{{cite book |author=Griffiths, David J. |title=Introduction to Elementary Particles |edition=2nd revised |publisher=WILEY-VCH |year=2008 |isbn=978-3-527-40601-2}}&lt;/ref&gt;{{rp|129–130}} Nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space.

Isospin was introduced as a concept in 1932 by [[W:Werner Heisenberg|Werner Heisenberg]],&lt;ref&gt;
{{cite journal
 |last=Heisenberg |first=W. |author-link=W:Werner Heisenberg
 |year=1932
 |title=Über den Bau der Atomkerne
 |journal=[[W:Zeitschrift für Physik|Zeitschrift für Physik]]
 |volume=77 |issue=1–2 |pages=1–11
 |doi=10.1007/BF01342433
 |bibcode = 1932ZPhy...77....1H
 |s2cid=186218053
 |language=de}}&lt;/ref&gt; well before the 1960s development of the [[W:quark model|quark model]], to explain the symmetry of the proton and the then newly discovered neutron. Heisenberg introduced the concept of another conserved quantity that would cause the proton to turn into a neutron and vice versa. In 1937, [[W:Eugene Wigner|Eugene Wigner]] introduced the term &quot;isospin&quot; to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.&lt;ref&gt;
{{cite journal
 |last=Wigner |first=E. |author-link=W:Eugene Wigner
 |year=1937
 |title=On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei
 |journal=[[W:Physical Review|Physical Review]]
 |volume=51
 |pages=106–119
 |doi=10.1103/PhysRev.51.106
 |bibcode = 1937PhRv...51..106W
 |issue=2
}}&lt;/ref&gt; Similar to a spin-1/2 particle, which has two states, protons and neutrons were said to be of isospin 1/2. The proton and neutron were then associated with different isospin projections ''I''&lt;sub&gt;3&lt;/sub&gt;&amp;nbsp;=&amp;nbsp;+1/2 and −1/2 respectively.

Isospin is a different kind of rotation entirely than the ordinary spin which objects undergo when they rotate in three-dimensional space. Isospin does not correspond to a [[W:Rotations in 4-dimensional Euclidean space#Simple rotations|simple rotation]] in any space (of any number of dimensions). However, it does seem to correspond exactly to an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]] in a Euclidean space of four dimensions. Isospin space resembles the [[W:3-sphere|3-sphere]], the [[W:Elliptical space#Elliptic space (the 3D case)|curved 3-dimensional space]] that is the surface of a [[W:4-ball (mathematics)#In Euclidean space|4-dimensional ball]].

=== Spinors ===
[[File:Spinor on the circle.png|thumb|upright=1.5|A spinor visualized as a vector pointing along the [[W:Möbius band|Möbius band]], exhibiting a sign inversion when the circle (the &quot;physical system&quot;) is continuously rotated through a full turn of 360°.]][[W:Spinors|Spinors]] are [[W:representation of a Lie group|representations]] of a [[W:spin group|spin group]], which are [[W:Double covering group|double cover]]s of the [[W:special orthogonal group|special orthogonal groups]]. The spin group Spin(4) is the double cover of [[W:SO(4)|SO(4)]], the group of rotations in 4-dimensional Euclidean space. [[600-cell#Fibrations of isocline polygrams|Isoclines]], the helical geodesic paths followed by points under isoclinic rotation, correspond to spinors representing Spin(4).

Spinors can be viewed as the &quot;square roots&quot; of [[W:Section (fiber bundle)|cross sections]] of [[W:vector bundle|vector bundle]]s; in this correspondence, a fiber bundle of isoclines (of a distinct isoclinic rotation) is a cross section (inverse bundle) of a fibration of great circles (in the invariant planes of that rotation).

A spinor can be visualized as a moving vector on a Möbius strip which transforms to its negative when continuously rotated through 360°, just as [[24-cell#Helical hexagrams and their isoclines|an isocline can be visualized as a Möbius strip]] winding twice around the 3-sphere, during which [[24-cell#Isoclinic rotations|720° isoclinic rotation]] the rigid 4-polytope turns itself inside-out twice.{{Sfn|Goucher|2019|loc=Spin Groups}} Under isoclinic rotation, a rigid 4-polytope is an isospin-1/2 object with two states.

=== Isoclinic rotations in the nucleus ===
Isospin is regarded as a symmetry of the strong interaction under the [[W:Group action (mathematics)|action]] of the [[W:Lie group|Lie group]] [[W:SU(2)|SU(2)]], the two [[W:eigenstate|states]] being the [[W:Up quark|up flavour]] and [[W:Down quark|down flavour]]. A 360° isoclinic rotation of a rigid [[W:nuclide|nuclide]] would transform its protons into neutrons and vice versa, exchanging the up and down flavours of their constituent [[W:quarks|quarks]], by turning the nuclide and all its parts inside-out (or perhaps we should say upside-down). Because we never observe this, we know that the nucleus is not a ''rigid'' polytope undergoing isoclinic rotation.

If the nucleus ''were'' a rigid object, nuclides that were isospin-rotated 360° would be isoclinic mirror images of each other, isospin +1/2 and isospin −1/2 states of the whole nucleus. We don't see whole nuclides rotating as a rigid object, but considering what would happen if they ''were'' rigid tells us something about the geometry we must expect inside the nucleons. One way that an isospin-rotated neutron could become a proton would be if the up quark and down quark were a left and right mirror-image pair of the same object; exchanging them in place would turn each down-down-up neutron into an up-up-down proton. But the case cannot be quite that simple, because the up quark and the down quark are not mirror-images of the same object: they have very different mass and other incongruities.

Another way an isospin-rotated neutron could be a proton would be if the up and down quarks were asymmetrical kinematic polytopes (not indirectly congruent mirror-images, and not rigid polytopes), rotating within the nucleus in different ''hybrid'' orbits. By that we mean that they may have vertices orbiting in rotations characteristic of more than one 4-polytope, so they may change shape as they rotate. In that case their composites (protons and neutrons) could have a symmetry not manifest in their components, but emerging from their combination.

....

=== Hybrid isoclinic rotations ===
The 24-cell has [[24-cell#Isoclinic rotations|its own characteristic isoclinic rotations]] in 4 Clifford parallel hexagonal planes (each intersecting 6 vertices), and also inherits the [[16-cell#Rotations|characteristic isoclinic rotations of its 3 Clifford parallel constituent 16-cells]] in 6 Clifford parallel square planes (each intersecting 4 vertices). The twisted circular paths followed by vertices in these two different kinds of rotation have entirely different geometries. Vertices rotating in hexagonal invariant planes follow [[24-cell#Helical hexagrams and their isoclines|helical geodesic curves whose chords form hexagrams]], and vertices rotating in square invariant planes follow [[24-cell#Helical octagrams and their isoclines|helical geodesic curves whose chords form octagrams]].

In a rigid isoclinic rotation, ''all'' the [[24-cell#Geodesics|great circle polygons]] move, in any kind of rotation. What distinguishes the hexagonal and square isoclinic rotations is the invariant planes of rotation the vertices stay in. The rotation described [[#Rotations|above]] (of 8 vertices rotating in 4 Clifford parallel hexagonal planes) is a single hexagonal isoclinic rotation, not a kinematic or hybrid rotation.

A ''kinematic'' isoclinic rotation in the 24-cell is any subset of the 24 vertices rotating through the same angle in the same time, but independently with respect to the choice of a Clifford parallel set of invariant planes of rotation and the chirality (left or right) of the rotation. A ''hybrid'' isoclinic rotation combines moving vertices from different kinds of isoclinic rotations, characteristic of different regular 4-polytopes. For example, if at least one vertex rotates in a square plane and at least one vertex rotates in a hexagonal plane, the kinematic rotation is a hybrid rotation, combining rotations characteristic of the 16-cell and characteristic of the 24-cell.

As an example of the simplest hybrid isoclinic rotation, consider a 24-cell vertex rotating in a square plane, and a second vertex, initially one 24-cell edge-length distant, rotating in a hexagonal plane. Rotating isoclinically at the same rate, the two moving vertices will never collide where their paths intersect, so this is a ''valid'' hybrid rotation.

To understand hybrid rotations in the 24-cell more generally, visualize the relationship between great squares and great hexagons. The [[24-cell#Squares|18 great squares]] occur as three sets of 6 orthogonal great squares,{{Efn|name=six orthogonal planes of the Cartesian basis}} each [[16-cell#Coordinates|forming a 16-cell]]. The three 16-cells are completely disjoint{{Efn|name=completely disjoint}} and [[24-cell#Clifford parallel polytopes|Clifford parallel]]: each has its own 8 vertices (on 4 orthogonal axes) and its own 24 edges (of length {{radic|2}}).{{Efn|name=three isoclinic 16-cells}} The 18 square great circles are crossed by 16 hexagonal great circles; each [[24-cell#Hexagons|hexagon]] has one axis (2 vertices) in each 16-cell.{{Efn|name=non-orthogonal hexagons}} The two [[24-cell#Triangles|great triangles]] inscribed in each great hexagon (occupying its alternate vertices, with edges that are its {{radic|3}} chords) have one vertex in each 16-cell. Thus ''each great triangle is a ring linking three completely disjoint great squares, one from each of the three completely disjoint 16-cells''.{{Efn|There are four different ways (four different ''fibrations'' of the 24-cell) in which the 8 vertices of the 16-cells correspond by being triangles of vertices {{radic|3}} apart: there are 32 distinct linking triangles. Each ''pair'' of 16-cells forms a tesseract (8-cell).{{Efn|name=three 16-cells form three tesseracts}} Each great triangle has one {{radic|3}} edge in each tesseract, so it is also a ring linking the three tesseracts.|name=great linking triangles}} Isoclinic rotations take the elements of the 4-polytope to congruent [[24-cell#Clifford parallel polytopes|Clifford parallel elements]] elsewhere in the 4-polytope. The square rotations do this ''locally'', confined within each 16-cell: for example, they take great squares to other great squares within the same 16-cell. The hexagonal rotations act ''globally'' within the entire 24-cell: for example, they take great squares to other great squares in ''different'' 16-cells. The [[16-cell#Helical construction|chords of the square rotations]] bind the 16-cells together internally, and the [[24-cell#Helical hexagrams and their isoclines|chords of the hexagonal rotations]] bind the three 16-cells together.

....

=== Color ===
When the existence of quarks was suspected in 1964, [[W:Oscar W. Greenberg|Greenberg]] introduced the notion of color charge to explain how quarks could coexist inside some [[W:hadron|hadron]]s in [[W:quark model#The discovery of color|otherwise identical quantum states]] without violating the [[W:Pauli exclusion principle|Pauli exclusion principle]]. The modern concept of [[W:color charge|color charge]] completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [[W:William A. Bardeen|William Bardeen]], [[W:de:Harald Fritzsch|Harald Fritzsch]], and [[W:Murray Gell-Mann|Murray Gell-Mann]].&lt;ref&gt;{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''&lt;sup&gt;0&lt;/sup&gt; decay, and ''e''&lt;sup&gt;+&lt;/sup&gt; ''e''&lt;sup&gt;&amp;minus;&lt;/sup&gt; annihilation |arxiv=hep-ph/0211388 |editor=Gatto, R. |book-title=Scale and conformal symmetry in hadron physics |page=[https://archive.org/details/scaleconformalsy0000unse/page/139 139] |publisher=[[W:John Wiley &amp; Sons|John Wiley &amp; Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}&lt;/ref&gt;&lt;ref&gt;{{cite journal |title=Advantages of the color octet gluon picture |journal=[[W:Physics Letters B|Physics Letters B]] |volume=47 |issue=4 |page=365 |year=1973 |last1=Fritzsch |first1=H. |last2=Gell-Mann |first2=M. |last3=Leutwyler |first3=H. |doi=10.1016/0370-2693(73)90625-4 |bibcode=1973PhLB...47..365F |citeseerx=10.1.1.453.4712}}&lt;/ref&gt;

Color charge is not [[W:electric charge|electric charge]]; the whole point of it is that it is a quantum of something different. But it is related to electric charge, through the way in which the three different-colored quarks combine to contribute fractional quantities of electric charge to a nucleon. As we shall see, color is not really a separate kind of charge at all, but a partitioning of the electric charge into [[24-cell#Clifford parallel polytopes|Clifford parallel subspaces]].

The [[W:Color charge#Red, green, and blue|three different colors]] of quark charge might correspond to three different 16-cells, such as the three disjoint 16-cells inscribed in the 24-cell. Each color might be a disjoint domain in isospin space (the space of points on the 3-sphere).{{Efn|The 8 vertices of each disjoint 16-cell constitute an independent [[16-cell#Coordinates|orthonormal basis for a coordinate reference frame]].}} Alternatively, the three colors might correspond to three different fibrations of the same isospin space: three different ''sequences'' of the same total set of discrete points on the 3-sphere. These alternative possibilities constrain possible representations of the nuclides themselves, for example if we try to represent nuclides as particular rotating 4-polytopes. If the neutron is a (8-point) 16-cell, either of the two color possibilities might somehow make sense as far as the neutron is concerned. But if the proton is a (5-point) 5-cell, only the latter color possibility makes sense, because fibrations (which correspond to distinct isoclinic left-and-right rigid rotations) are the ''only'' thing the 5-cell has three of. Both the 5-cell and the 16-cell have three discrete rotational fibrations. Moreover, in the case of a rigid, isoclinically rotating 4-polytope, those three fibrations always come one-of-a-kind and two-of-a-kind, in at least two different ways. First, one fibration is the set of invariant planes currently being rotated through, and the other two are not. Second, when one considers the three fibrations of each of these 4-polytopes, in each fibration two isoclines carry the left and right rotations respectively, and the third isocline acts simply as a Petrie polygon, the difference between the fibrations being the role assigned to each isocline.

If we associate each quark with one or more isoclinic rotations in which the moving vertices belong to different 16-cells of the 24-cell, and the sign (plus or minus) of the electric charge with the chirality (right or left) of isoclinic rotations generally, we can configure nucleons of three quarks, two performing rotations of one chirality and one performing rotations of the other chirality. The configuration will be a valid kinematic rotation because the completely disjoint 16-cells can rotate independently; their vertices would never collide even if the 16-cells were performing different rigid square isoclinic rotations (all 8 vertices rotating in unison). But we need not associate a quark with a [[16-cell#Rotations|rigidly rotating 16-cell]], or with a single distinct square rotation.

Minimally, we must associate each quark with at least one moving vertex in each of three different 16-cells, following the twisted geodesic isocline of an isoclinic rotation. In the up quark, that could be the isocline of a right rotation; and in the down quark, the isocline of a left rotation. The chirality accounts for the sign of the electric charge (we have said conventionally as +right, −left), but we must also account for the quantity of charge: +{{sfrac|2|3}} in an up quark, and −{{sfrac|1|3}} in a down quark. One way to do that would be to give the three distinct quarks moving vertices of {{sfrac|1|3}} charge in different 16-cells, but provide up quarks with twice as many vertices moving on +right isoclines as down quarks have vertices moving on −left isoclines (assuming the correct chiral pairing is up+right, down−left).

Minimally, an up quark requires two moving vertices (of the up+right chirality).{{Efn|Two moving vertices in one quark could belong to the same 16-cell. A 16-cell may have two vertices moving in the same isoclinic square (octagram) orbit, such as an antipodal pair (a rotating dipole), or two vertices moving in different square orbits of the same up+right chirality.{{Efn|There is only one [[16-cell#Helical construction|octagram orbit]] of each chirality in each fibration of the 16-cell, so two octagram orbits of the same chirality cannot be Clifford parallel (part of the same distinct rotation). Two vertices right-moving on different octagram isoclines in the same 16-cell is a combination of two distinct rotations, whose isoclines will intersect: a kinematic rotation. It can be a valid kinematic rotation if the moving vertices will never pass through a point of intersection at the same time. Octagram isoclines pass through all 8 vertices of the 16-cell, and all eight isoclines (the left and right isoclines of four different fibrations) intersect at ''every'' vertex.}} However, the theory of [[W:Color confinement|color confinement]] may not require that two moving vertices in one quark belong to the same 16-cell; like the moving vertices of different quarks, they could be drawn from the disjoint vertex sets of two different 16-cells.}} Minimally, a down quark requires one moving vertex (of the down−left chirality). In these minimal quark configurations, a proton would have 5 moving vertices and a neutron would have 4.

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=== Nucleons ===
[[File:Symmetrical_5-set_Venn_diagram.svg|thumb|[[W:Branko Grünbaum|Grünbaum's]] rotationally symmetrical 5-set Venn diagram, 1975. It is the [[5-cell]]. Think of it as an [[W:Nuclear magnetic resonance|NMR image]] of the 4-dimensional proton in projection to the plane.]]
The proton is a very stable mass particle. Is there a stable orbit of 5 moving vertices in 4-dimensional Euclidean space? There are few known solutions to the 5-body problem, and fewer still to the [[W:n-body problem|{{mvar|n}}-body problem]], but one is known: the ''central configuration'' of {{mvar|n}} bodies in a space of dimension {{mvar|n}}-1. A [[W:Central configuration|central configuration]] is a system of [[W:Point particle|point masses]] with the property that each mass is pulled by the combined attractive force of the system directly towards the [[W:Center of mass|center of mass]], with acceleration proportional to its distance from the center. Placing three masses in an equilateral triangle, four at the vertices of a regular [[W:Tetrahedron|tetrahedron]], five at the vertices of a regular [[5-cell]], or more generally {{mvar|n}} masses at the vertices of a regular [[W:Simplex|simplex]] produces a central configuration [[W:Central configuration#Examples|even when the masses are not equal]]. In an isoclinic rotation, all the moving vertices orbit at the same radius and the same speed. Therefore if any 5 bodies are orbiting as an isoclinically rotating regular 5-cell (a rigid 4-simplex figure undergoing isoclinic rotation), they maintain a central configuration, describing 5 mutually stable orbits.

Unlike the proton, the neutron is not always a stable particle; a free neutron will decay into a proton. A deficiency of the minimal configurations is that there is no way for this [[W:beta minus decay|beta minus decay]] to occur. The minimal neutron of 4 moving vertices described [[#Color|above]] cannot possibly decay into a proton by losing moving vertices, because it does not possess the four up+right moving vertices required in a proton. This deficiency could be remedied by giving the neutron configuration 8 moving vertices instead of 4: four down−left and four up+right moving vertices. Then by losing 3 down−left moving vertices the neutron could decay into the 5 vertex up-down-up proton configuration.{{Efn|Although protons are very stable, during [[W:stellar nucleosynthesis|stellar nucleosynthesis]] two H&lt;sub&gt;1&lt;/sub&gt; protons are fused into an H&lt;sub&gt;2&lt;/sub&gt; nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus &quot;decay&quot;]] of a proton into a neutron is actually the result of a rare high-energy collision between the two protons, in which a neutron is constructed. With respect to our nucleon configurations of moving vertices, it has to be explained as the conversion of two 5-point 5-cells into a 5-point 5-cell and an 8-point 16-cell, emitting two decay products of at least 1-point each. Thus it must involve the creation of moving vertices, by the conversion of kinetic energy to point-masses.}} A neutron configuration of 8 moving vertices could occur as the 8-point 16-cell, the second-smallest regular 4-polytope after the 5-point 5-cell (the hypothesized proton configuration).

It is possible to double the neutron configuration in this way, without destroying the charge balance that defines the nucleons, by giving down quarks three moving vertices instead of just one: two −left vertices and one +right vertex. The net charge on the down quark remains −{{sfrac|1|3}}, but the down quark becomes heavier (at least in vertex count) than the up quark, as in fact its mass is measured to be.

A nucleon's quark configuration is only a partial specification of its properties. There is much more to a nucleon than what is contained within its three quarks, which contribute only about 1% of the nucleon's energy. The additional 99% of the nucleon mass is said to be associated with the force that binds the three quarks together, rather than being intrinsic to the individual quarks separately. In the case of the proton, 5 moving vertices in the stable orbits of a central configuration (in one of the [[5-cell#Geodesics and rotations|isoclinic rotations characteristic of the regular 5-cell]]) might be sufficient to account for the stability of the proton, but not to account for most of the proton's energy. It is not the point-masses of the moving vertices themselves which constitute most of the mass of the nucleon; if mass is a consequence of geometry, we must look to the larger geometric elements of these polytopes as their major mass contributors. The quark configurations are thus incomplete specifications of the geometry of the nucleons, predictive of only some of the nucleon's properties, such as charge.{{Efn|Notice that by giving the down quark three moving vertices, we seem to have changed the quark model's prediction of the proton's number of moving vertices from 5 to 7, which would be incompatible with our theory that the proton configuration is a rotating regular 5-cell in a central configuration of 5 stable orbits. Fortunately, the actual quark model has nothing at all to say about moving vertices, so we may choose to regard that number as one of the geometric properties the quark model does not specify.}} In particular, they do not account for the forces binding the nucleon together. Moreover, if the rotating regular 5-cell is the proton configuration and the rotating regular 16-cell is the neutron configuration, then a nucleus is a complex of rotating 5-cells and 16-cells, and we must look to the geometric relationship between those two very different regular 4-polytopes for an understanding of the nuclear force binding them together.

The most direct [[120-cell#Relationships among interior polytopes|geometric relationship among stationary regular 4-polytopes]] is the way they occupy a common 3-sphere together. Multiple 16-cells of equal radius can be compounded to form each of the larger regular 4-polytopes, the 8-cell, 24-cell, 600-cell, and 120-cell, but it is noteworthy that multiple regular 5-cells of equal radius cannot be compounded to form any of the other 4-polytopes except the largest, the 120-cell. The 120-cell is the unique intersection of the regular 5-cell and 16-cell: it is a compound of 120 regular 5-cells, and also a compound of 75 16-cells. All regular 4-polytopes except the 5-cell are compounds of 16-cells, but none of them except the largest, the 120-cell, contains any regular 5-cells. So in any compound of equal-radius 16-cells which also contains a regular 5-cell, whether that compound forms some single larger regular 4-polytope or does not, no two of the regular 5-cell's five vertices ever lie in the same 16-cell. So the geometric relationship between the regular 5-cell (our proton candidate) and the regular 16-cell (our neutron candidate) is quite a distant one: they are much more exclusive of each other's elements than they are distantly related, despite their complementary three-quark configurations and other similarities as nucleons. The relationship between a regular 5-cell and a regular 16-cell of equal radius is manifest only in the 120-cell, the most complex regular 4-polytope, which [[120-cell#Geometry|uniquely embodies all the containment relationships]] among all the regular 4-polytopes and their elements.

If the nucleus is a complex of 5-cells (protons) and 16-cells (neutrons) rotating isoclinically around a common center, then its overall motion is a hybrid isoclinic rotation, because the 5-cell and the 16-cell have different characteristic isoclinic rotations, and they have no isoclinic rotation in common.{{Efn|The regular 5-cell does not occur inscribed in any other regular 4-polytope except one, the 600-vertex 120-cell. No two of the 5 vertices of a regular 5-cell can be vertices of the same 16-cell, 8-cell, 24-cell, or 600-cell. The isoclinic rotations characteristic of the regular 5-cell maintain the separation of its 5 moving vertices in 5 disjoint Clifford-parallel subspaces at all times. The [[16-cell#Rotations|isoclinic rotation characteristic of the 16-cell]] maintains the separation of its 8 moving vertices in 2 disjoint Clifford-parallel subspaces (completely orthogonal great square planes) at all times. Therefore, in any hybrid rotation of a concentric 5-cell and 16-cell, at most one 5-cell subspace (containing 1 vertex) might be synchronized with one 16-cell subspace (containing 4 vertices), such that the 1 + 4 vertices they jointly contain occupy the same moving subspace continually, forming a rigid 5-vertex polytope undergoing some kind of rotation. If in fact it existed, this 5-vertex rotating rigid polytope would not be [[5-cell#Geometry|not a 5-cell, since 4 of its vertices are coplanar]]; it is not a 4-polytope but merely a polyhedron, a [[W:square pyramid|square pyramid]].}}

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=== Nuclides ===

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=== Quantum phenomena ===

The Bell-Kochen-Specker (BKS) theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a space of three or more dimensions can be given by exhibiting a finite set of lines through the origin that cannot each be colored black or white in such a way that (i) no two orthogonal lines are both black, and (ii) not all members of a set of ''d'' mutually orthogonal lines are white.{{Efn|&quot;The Bell-Kochen-Specker theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a Hilbert space of dimension d ≥ 3 can be given by exhibiting a finite set of rays [9] that cannot each be assigned the value 0 or 1 in such a way that (i) no two orthogonal rays are both assigned the value 1, and (ii) not all members of a set of d mutually orthogonal rays are assigned the value 0.&quot;{{Sfn|Waegell|Aravind|2009|loc=2. The Bell-Kochen-Specker (BKS) theorem}}|name=BKS theorem}}

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=== Motion ===
What does it mean to say that an object moves through space? Coxeter group theory provides precise answers to questions of this kind. A rigid object (polytope) moves by distinct transformations, changing itself in each discrete step into a congruent object in a different orientation and position.

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== Galilean relativity in a space of four orthogonal dimensions ==

Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions.

General relativity is just Galilean relativity in a general space of four orthogonal dimensions, e.g. Euclidean 4-space &lt;math&gt;R^4&lt;/math&gt;, spherical 4-space &lt;math&gt;S^4&lt;/math&gt;, or any orthogonal 4-manifold.

Light is just reflection. Gravity (and all force) is just rotation. Both motions are just group actions, expressions of intrinsic symmetries. That is all of physics.

Every observer properly sees himself as stationary and the universe as a sphere with himself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and it can be measured by the observer as the speed of light.

=== Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions ===
Perspective effects occur because each observer's ordinary 3-dimensional space is only a curved manifold embedded in 4-dimensional Euclidean space, and its curvature complicates the calculations for him (e.g., he sometimes requires Lorentz transformations). But if  all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) except when you want to calculate a projection, or a shadow, that is, how things will appear from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} The universe really has four spatial dimensions, and space and time behave just as they do in classical 3-vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a spacetime to explain 4-dimensional perspective effects at high velocities, because 4-space is already spatially 4-dimensional, and those perspective effects fall out of the 4-dimensional Pythagorean theorem naturally, just as perspective does in three dimensions. The universe is only strange in the ways the Euclidean fourth dimension is strange; but that does hold many surprises for us. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way that 3-space is much more interesting than 2-space. But all Euclidean spaces are dimensionally analogous. Dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries.

=== General relativity is just Galilean relativity in a general space of four orthogonal dimensions ===
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=== Physics ===
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=== Thoreau's spherical relativity ===
Every observer may properly see himself as stationary and the universe as a 4-sphere with himself at the center observing it, perceptually equidistant from all points on its surface, including his own ''physical'' location which is one of those surface points, distinguished to him but not the center of anything. This statement of the principle of relativity is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in curved, non-Euclidean spacetime, and Coxeter's relativity of orthogonal group actions in Euclidean spaces of any number of dimensions.{{Efn|Let Q denote a rotation, R a reflection, T a translation, and let Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T denote a product of several such transformations, all commutative with one another. Then RT is a glide-reflection (in two or three dimensions), QR is a rotary-reflection, QT is a screw-displacement, and Q&lt;sup&gt;2&lt;/sup&gt; is a double rotation (in four dimensions). Every orthogonal transformation is expressible as
{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt;&lt;br&gt;
where 2''q'' + ''r'' ≤ ''n'', the number of dimensions. Transformations involving a translation are expressible as
{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T&lt;br&gt;
where 2''q'' + ''r'' + 1 ≤ ''n''.&lt;br&gt;
For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q&lt;sup&gt;2&lt;/sup&gt;, or a screw-displacement QT (where the rotation component Q is a simple rotation). [If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either of those, because we can view any QT as a Q&lt;sup&gt;2&lt;/sup&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q&lt;sup&gt;2&lt;/sup&gt;. By the same principle, we can view any QT or Q&lt;sup&gt;2&lt;/sup&gt; as an isoclinic (equi-angled) Q&lt;sup&gt;2&lt;/sup&gt; by appropriate choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} That is to say, Coxeter's relation is a mathematical statement of the principle of relativity, on group-theoretic grounds.{{Efn|Notice that Coxeter's relation correctly captures the limits to relativity, in that we can only exchange the translation (T) for ''one'' of the two rotations (Q). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation up to uncertainty, and can always also distinguish the direction and velocity of his own proper time arrow.}}] Every enantiomorphous transformation in 4-space (reversing chirality) is a QRT.{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}|name=transformations}} It should be known as Thoreau's spherical relativity, since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polytopes in any number of dimensions.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassman and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}}]}}

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== Conclusions==

=== Spherical relativity ===

We began our inquiry by wondering why physical space should be limited to just three dimensions (why ''three''). By visualizing the universe as a Euclidian space of four dimensions, we recognize that relativistic and quantum phenomena are natural consequences of symmetry group operations (including reflections and rotations) in four orthogonal dimensions. We should not then be surprised to see that the universe does not have just four dimensions, either. Physical space must bear as many dimensions as we need to ascribe to it, though the distinct phenomena for which we find a need to do so, in order to explain them, seem to be fewer and fewer as we consider higher and higher dimensions. To laws of physics generally, such as the principle of relativity in particular, we should always append the phrase &quot;in Euclidean spaces of any number of dimensions&quot;. Laws of physics should operate in any flat Euclidean space &lt;math&gt;R^n&lt;/math&gt; and in its corresponding spherical space &lt;math&gt;S^n&lt;/math&gt;.

The first and simplest sense in which we are forced to contemplate a fifth dimension is to accommodate our normal idea of time. Just as Einstein was forced to admit time as a dimension, in his four-dimensional spacetime of three spatial dimensions plus time, for some purposes we require a fifth time dimension to accompany our four spatial dimensions, when our purpose is orthogonal to (in the sense of independent of) the four spatial dimensions. For example, if we theorize that we observe a finite homogeneous universe, and that it is a Euclidean 4-space overall, we may prefer not to have to identify any distinct place within that 4-space as the center where the universe began in a big bang. To avoid having to pick a distinct place as the center of the universe, our model of it must be expanded, at least to be a ''spherical'' 4-dimensional space with the fifth radial dimension as time. Essentially, we require the fifth dimension in order to make our homogeneous 4-space finite, by wrapping it around into a 4-sphere. But perhaps we can still resist admitting the fifth radial dimension as a full-fledged Euclidean spatial dimension, at least so long as we have not observed how any naturally occurring object configurations are best described as 5-polytopes.

One phenomenon which resists explanation in a space of just four dimensions is the propagation of light in a vacuum. The propagation of mass-carrying particles is explained as the consequence of their rotations in closed, curved spaces (3-spheres) of finite size, moving through four-dimensional Euclidean space at a universal constant speed, the speed of light. But an apparent paradox remains that light must seemingly propagate through four-dimensional Euclidean space at more than the speed of light. From a five-dimensional viewpoint, this apparent paradox can be resolved, and in retrospect it is clear how massless particles can translate through four-dimensional space at twice the speed constant, since they are not simultaneously rotating.

Another phenomenon justifying a five-dimensional view of space is the relation between the the 5-cell proton and the 16-cell neutron (the 4-simplex and 4-orthoplex polytopes). Their indirect relationship can be observed in the 4-600-point polytope (the 120-cell), and in its 11-cells,{{Sfn|Christie|2024}} but it is only directly observed (absent a 120-cell) in a five-dimensional reference frame.

=== Nuclear geometry ===
We have seen how isoclinic rotations (Clifford displacements) relate the orbits in the atomic nucleus to each other, just as they relate the regular convex 4-polytopes to each other, in a sequence of nested objects of increasing complexity. We have identified the proton as a  5-point, 5-cell 4-simplex 𝜶&lt;sub&gt;4&lt;/sub&gt;, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽&lt;sub&gt;4&lt;/sub&gt;, and the shell of the atomic nucleus as a 24-point 24-cell. As Coxeter noted, that unique 24-point object stands quite alone in four dimensions, having no analogue above or below.

=== Atomic geometry ===
I'm on a plane flying to Eugene to visit Catalin, we'll talk after I arrive. I've been working on both my unpublished papers, the one going put for pre-publication review soon about 4D geometry, and the big one not going out soon about the 4D sun, 4D atoms, and 4D galaxies and n-D universe. I'vd just added the following paragraph to that big paper:

Atomic geometry

The force binding the protons and neutrons of the nucleus together into a distinct element is specifically an expression of the 11-cell 4-polytope, itself an expression of the pyritohedral symmetry, which binds the distinct 4-polytopes to each other, and relates the n-polytopes to their neighbors of different n by dimensional analogy.


flying over mt shasta out my right-side window at the moment, that last text showing &quot;not delivered&quot; yet because there's no wifi on this plane, gazing at that great peak of the world and feeling as if i've just made the first ascent of it

=== Molecular geometry ===
Molecules are 3-dimensional structures that live in the thin film of 3-membrane only one atom thick in most places that is our ordinary space, but since that is a significantly curved 3-dimensional space at the scale of a molecule, the way the molecule's covalent bonds form is influenced by the local curvature in 4-dimensions at that point.

In the water molecule, there is a reason why the hydrogen atoms are attached to the oxygen atom at an angle of 104.45° in 3-dimensional space, and at root it must be the same symmetry that locates any two of the hydrogen proton's five vertices 104.45° apart on a great circle arc of its tiny 3-sphere.

=== Cosmology ===

==== Solar systems ====

===== Stars =====
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===== The Kepler problem =====
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==== Galaxies ====

The spacetime of general relativity is often illustrated as a projection to a curved 2D surface in which large gravitational objects make gravity wells or dimples in the surface. In the Euclidean 4D view of the universe the 3D surface of a large cosmic object such as a galaxy surrounds an empty 4D space, and large gravitational objects within the galaxy must make dimples in its surface. But should we see them as dimples exactly? Would they dimple inwards or outwards? In the spacetime illustrations they are naturally always shown as dimpling downwards, which is somewhat disingenuous, strongly suggesting to the viewer that the reason for gravity is that it flows downhill - the original tautology we are trying to surmount! In the Euclidean 4D galaxy the dimple, if it is one, must be either inward or outward, and which it is matters since the dimple is flying outward at velocity {{mvar|c}}. The galaxy is not collapsing inward. Is a large gravitational mass (such as a star) ''ahead'' of the smaller masses orbiting around it (such as its planets), or is it ''behind'' them, as they fly through 4-space on their Clifford parallel trajectories? The answer is ''both'' of course, because a star is not a dimple, it is a 4-ball, and it dimples the 3D surface both inwards and outwards. It is a thick place in the 3D surface. We should view it as having its gravitational center precisely at the surface of the expanding 3-sphere. 

What is a black hole? It is the hollow four-dimensional space that a galaxy is the three-dimensional surface of.

When we view another galaxy, such as Andromeda, we are seeing that whole galaxy from a distance, the way the moon astronauts looked back at the whole earth. We see our own milky way galaxy from where we are on its surface, the way we see the earth from its surface, except that the earth is solid, but the galaxy is hollow and transparent. We can look across its empty center and see all the other stars also on its surface, including those opposite ours on the far side of its 3-sphere. The thicker band of stars we see in our night sky and identify as the milky way is not our whole galaxy; the majority of the other visible stars also lie in our galaxy. That dense band is not thicker and brighter than other parts of our galaxy because it lies toward a dense galactic center (our galaxy has an empty center), but for exactly the opposite reason: those apparently more thickly clustered stars lie all around us on the galaxy's surface, in the nearest region of space surrounding us. They appear to be densely packed only because we are looking at them &quot;edge on&quot;. Actually, we are looking into this nearby apparently dense region ''face on'', not edge on, because we are looking at a round sphere of space surrounding us, not a disk. In contrast, stars in our galaxy outside that bright band lie farther off from us, across the empty center of the galaxy, and we see them spread out as they actually are, instead of &quot;edge on&quot; so they appear to be densely clustered. The &quot;dense band&quot; covers only an equatorial band of the night sky instead of all the sky, because when we look out into the four-dimensional space around us, we can see stars above and below our three-dimensional hyperplane in our four-dimensional space. Everything in our solar system lies in our hyperplane, and the nearby stars around us in our galaxy are near our hyperplane (just slightly below it). All the other, more distant stars in our galaxy are also below our hyperplane. We can see objects outside our galaxy, such as other galaxies, both above and below our hyperplane. We can see all around us above our hyperplane (looking up from the galactic surface into the fourth dimension), and all around us below our hyperplane (looking down through our transparent galaxy and out the other side).

== Revolutions ==
The original Copernican revolution displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the stars remaining on a fixed sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

In such fashion the Euclidean four-dimensional viewpoint initially lends itself to a big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the stars need not be equidistant from a single origin in time, any more than they all lie in the same galaxy, equidistant from its center in space. The expanding sphere of matter on the surface of which we find ourselves living might be one of many such spheres, with their big bang origins occurring at distinct times and places in the 4-dimensional universe.

When we look up at the heavens, we have no obvious way of knowing whether the space we are looking into is a curved 3-spherical one or a flat 4-space. In this work we suggest a theory of how light travels that says we can see into all four dimensions, and so when we look up at night we see cosmological objects distributed in 4-dimensional space, and not all located on our own 3-spherical membrane. The view from our solar system suggests that our galaxy is its own hollow 3-sphere, and that galaxies generally are single roughly spherical 3-membranes, with the smaller objects within them all lying on that same 3-spherical surface, equidistant from the galaxy center in 4-space. 

The Euclidean four-dimensional viewpoint requires that all mass-carrying objects are in motion at constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Since their paths away from their origin are not straight lines but various helical isoclines, their 3-sphere will be expanding radially at slightly less than the constant velocity &lt;math&gt;c&lt;/math&gt;. The view from our solar system does ''not'' suggest that each galaxy is its own distinct 3-sphere expanding at this great rate; rather, the standard theory has been that the entire observable universe is expanding from a single big bang origin in time. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also allows theories which require no single origin point in space and time.

These are the voyages of starship Earth, to boldly go where no one has gone before. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't slowed down since.

== Origins of the theory ==
Einstein himself was one of the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean sphere, in what was narrowly the first written articulation of the principle of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below). Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that formulation of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from his perspective; the forthshortenings, clock desynchronizations and other perceptual effects it predicts are exact calculations of actual perspective effects; but space is actually a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four dimensions.''

The Euclidean 4-dimensional theory differs from the standard theory in being a description of the physical universe in terms of a geometry of four or more orthogonal spatial dimensions, rather than in the standard theory's terms of the [[w:Minkowski spacetime|Minkowski spacetime]] geometry (in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions). The invention of geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years. It was first worked out by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] around 1850. Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''polyscheme'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he discovered all the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the six convex regular polyschemes which can be constructed in a space of four dimensions (a set analogous to the five [[w:Platonic solid|Platonic solids]] in three dimensional space). Thus he was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover all its astonishing regular objects. Because most of his work remained almost completely unknown until it was published posthumously in 1901, other researchers had more than fifty years to rediscover the regular polyschemes, and competing terms were coined; today [[W:Alicia Boole Stott|Alicia Boole Stott]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme''.{{Efn|Today Schläfli's original ''polyscheme'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}}

== Boundaries ==
&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schlafli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it, is that there ''is'' a boundary between three and four dimensions. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our world apparently only three dimensional? Why would it have ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schlafli mapped? What is the nature of the boundary which confines us to just three? 

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way by receiving light signals that traveled to us on straight lines through it. The reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creates, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not surprise us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schlafli discovered something else: all the astonishing regular objects that exist in higher dimensions. So this conception now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and not a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation?

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that our universe is properly a Euclidean space of four orthogonal spatial dimensions. Others will have to work out the physics and do the math, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|radius={{radic|2}}|columns=9}}

== Notes ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are 4-dimensionally circular, but not all isoclines on 3-manifolds in 4-space are perfectly circular.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point.{{Sfn|Tyrrell|Semple|1971|loc=§3. Clifford's original definition of parallelism|pp=5-6}} A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the 2-sphere will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect; various sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. Perhaps the simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles.{{Efn|name=six orthogonal planes of the Cartesian basis}} Each completely orthogonal pair is Clifford parallel. The two circles cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 3-sphere.{{Efn|name=only some Clifford parallels are orthogonal}} Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]].|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Notelist|40em}}

== Citations ==
{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

{{Reflist|40em}}

== References ==
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* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1991 | title=Regular Complex Polytopes | place=Cambridge | publisher=Cambridge University Press | edition=2nd }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1995 | title=Kaleidoscopes: Selected Writings of H.S.M. Coxeter | publisher=Wiley-Interscience Publication | edition=2nd | isbn=978-0-471-01003-6 | url=https://archive.org/details/kaleidoscopessel0000coxe | editor1-last=Sherk | editor1-first=F. Arthur | editor2-last=McMullen | editor2-first=Peter | editor3-last=Thompson | editor3-first=Anthony C. | editor4-last=Weiss | editor4-first=Asia Ivic | url-access=registration }}
** (Paper 3) H.S.M. Coxeter, ''Two aspects of the regular 24-cell in four dimensions''
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* {{Cite journal|last1=Perez-Gracia|first1=Alba|last2=Thomas|first2=Federico|date=2017|title=On Cayley's Factorization of 4D Rotations and Applications|url=https://upcommons.upc.edu/bitstream/handle/2117/113067/1749-ON-CAYLEYS-FACTORIZATION-OF-4D-ROTATIONS-AND-APPLICATIONS.pdf|journal=Adv. Appl. Clifford Algebras|volume=27|pages=523–538|doi=10.1007/s00006-016-0683-9|hdl=2117/113067|s2cid=12350382|hdl-access=free}}
* {{Cite arXiv | eprint=1903.06971 | last=Copher | first=Jessica | year=2019 | title=Sums and Products of Regular Polytopes' Squared Chord Lengths | class=math.MG }}
* {{Cite thesis|url= http://resolver.tudelft.nl/uuid:dcffce5a-0b47-404e-8a67-9a3845774d89 |title=Symmetry groups of regular polytopes in three and four dimensions|last=van Ittersum |first=Clara|year=2020|publisher=[[W:Delft University of Technology|Delft University of Technology]]}}
* {{cite arXiv|last1=Kim|first1=Heuna|last2=Rote|first2=G.|date=2016|title=Congruence Testing of Point Sets in 4 Dimensions|class=cs.CG|eprint=1603.07269}}
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* {{Cite book|title=Generalized Clifford parallelism|last1=Tyrrell|first1=J. A.|last2=Semple|first2=J.G.|year=1971|publisher=[[W:Cambridge University Press|Cambridge University Press]]|url=https://archive.org/details/generalizedcliff0000tyrr|isbn=0-521-08042-8}}
* {{Cite journal | last1=Mamone|first1=Salvatore | last2=Pileio|first2=Giuseppe | last3=Levitt|first3=Malcolm H. | year=2010 | title=Orientational Sampling Schemes Based on Four Dimensional Polytopes | journal=Symmetry | volume=2 | pages=1423-1449 | doi=10.3390/sym2031423 }}
* {{Cite journal|last=Dorst|first=Leo|title=Conformal Villarceau Rotors|year=2019|journal=Advances in Applied Clifford Algebras|volume=29|issue=44|url=https://doi.org/10.1007/s00006-019-0960-5}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}}
*{{Citation | last=Goucher | first=A.P. | title=Spin groups | date=19 November 2019 | journal=Complex Projective 4-Space | url=https://cp4space.hatsya.com/2012/11/19/spin-groups/ }}
* {{Citation|last=Christie|first=David Brooks|author-link=User:Dc.samizdat|year=2024|title=A symmetrical arrangement of 120 11-cells|title-link=User:Dc.samizdat/A symmetrical arrangement of 120 11-cells|journal=Wikiversity}}
{{Refend}}</text>
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      <text bytes="102094" sha1="nveg15a2n61x77bcldcclng4d16cnox" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|June 2023 - November 2024}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four or more orthogonal spatial dimensions. Atoms are 4-polytopes, and stars are 4-balls of atomic plasma. A galaxy is a hollow 3-sphere with these objects distributed on its surface; the black hole at its center is the 4-ball of empty space it surrounds. The observable universe of galaxies may be visualized as a 4-sphere expanding radially from an origin point at velocity &lt;math&gt;c&lt;/math&gt;, the propagation speed of light through 3-space, also the invariant velocity of all mass-carrying objects through 4-space. The propagation speed of light through 4-space &lt;math&gt;c_4&lt;/math&gt; is &lt;math&gt;c &lt; c_4 &lt; 2c&lt;/math&gt;. This view is compatible with the theories of special and general relativity, and with the quantum mechanical atomic theory. It explains those theories as expressions of intrinsic symmetries.&lt;/blockquote&gt;

== Symmetries ==
It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway|Burgiel|Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s.{{Efn|[[W:Coxeter group|Coxeter theory]] is for geometry what Noether's theorem is for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that obey the principle of relativity and correspond to distinct symmetry groups.}} Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. As I understand [[W:Coxeter group|Coxeter group]] theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic rather than algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional objects, and nature can be understood in terms of their [[W:group action|group actions]], including centrally [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]].

== The geometry of the atomic nucleus ==

In [[W:Euclidean 4-space|Euclidean four dimensional space]], an [[W:atomic nucleus|atomic nucleus]] is a [[24-cell]], the regular 4-polytope with [[W:Coxeter group#Symmetry groups of regular polytopes|𝔽&lt;sub&gt;4&lt;/sub&gt; symmetry]]. Nuclear shells are concentric [[W:3-sphere|3-sphere]]s occupied (fully or partially) by the orbits of this 24-point [[#The 6 regular convex 4-polytopes|regular convex 4-polytope]]. An actual atomic nucleus is a rotating four dimensional object. It is not a ''rigid'' rotating 24-cell, it is a kinematic one, because the nucleus of an actual atom of any [[W:nucleon number|nucleon number]] contains a distinct number of orbiting vertices which may be in different isoclinic rotational orbits. These moving vertices never describe a static 24-cell at any single instant in time, though their orbits do all the time. The physical configuration of the nucleus as a 24-cell can be reduced to the [[W:kinematics|kinematics]] of the orbits of its constituents. The geometry of the atomic nucleus is therefore strictly [[W:Euclidean geometry#19th century|Euclidean]] in four dimensional space.

=== Rotations ===
The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways (like coins flipping) into each other's central planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one or another of the parallel planes of rotation, so all of them move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out.

This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a precise [[24-cell|detailed description]] enabling the reader to visualize it runs to many pages and illustrations, with many accompanying pages of explanatory notes on basic phenomena that arise only in 4-dimensional space: [[24-cell#Squares|completely orthogonal planes]], [[24-cell#Hexagons|Clifford parallelism]] and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Helical hexagrams and their isoclines|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a surprise. [[#The 6 regular convex 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120, and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (generally), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It is much harder for us to visualize, because the only way we can experience it is in our imaginations; we have no body of ''sensory'' experience in 4-dimensional space to draw upon.

For that reason, descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case. [[W:Kinematics|Kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rigid 24-cell. 

To begin with, when we examine the individual parts of the rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertices just once, and no point-object colliding with any other at any time.

That is still an example of a rigid object in a single distinct isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing the characteristic rotation of the 24-cell. But we can also imagine ''combining'' distinct rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible without collisions? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore questions of this kind of [[W:kinematics|kinematics]], and where dynamic stabilites arise, of [[W:kinetics|kinetics]].

=== Isospin ===
A [[W:Nucleon|nucleon]] is a [[W:proton|proton]] or a [[W:neutron|neutron]]. The proton carries a positive net [[W:Electric charge|charge]], and the neutron carries a zero net charge. The proton's [[W:Mass|mass]] is only about 0.13% less than the neutron's, and since they are observed to be identical in other respects, they can be viewed as two states of the same nucleon, together forming an isospin doublet ({{nowrap|''I'' {{=}} {{sfrac|1|2}}}}). In isospin space, neutrons can be transformed into protons and conversely by actions of the [[W:SU(2)|SU(2)]] symmetry group. In nature, protons are very stable (the most stable particle known); a proton and a neutron are a stable nuclide; but free neutrons decay into protons in about 10 or 15 seconds.

According to the [[W:Noether theorem|Noether theorem]], [[W:Isospin|isospin]] is conserved with respect to the [[W:strong interaction|strong interaction]].&lt;ref name=Griffiths2008&gt;{{cite book |author=Griffiths, David J. |title=Introduction to Elementary Particles |edition=2nd revised |publisher=WILEY-VCH |year=2008 |isbn=978-3-527-40601-2}}&lt;/ref&gt;{{rp|129–130}} Nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space.

Isospin was introduced as a concept in 1932 by [[W:Werner Heisenberg|Werner Heisenberg]],&lt;ref&gt;
{{cite journal
 |last=Heisenberg |first=W. |author-link=W:Werner Heisenberg
 |year=1932
 |title=Über den Bau der Atomkerne
 |journal=[[W:Zeitschrift für Physik|Zeitschrift für Physik]]
 |volume=77 |issue=1–2 |pages=1–11
 |doi=10.1007/BF01342433
 |bibcode = 1932ZPhy...77....1H
 |s2cid=186218053
 |language=de}}&lt;/ref&gt; well before the 1960s development of the [[W:quark model|quark model]], to explain the symmetry of the proton and the then newly discovered neutron. Heisenberg introduced the concept of another conserved quantity that would cause the proton to turn into a neutron and vice versa. In 1937, [[W:Eugene Wigner|Eugene Wigner]] introduced the term &quot;isospin&quot; to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.&lt;ref&gt;
{{cite journal
 |last=Wigner |first=E. |author-link=W:Eugene Wigner
 |year=1937
 |title=On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei
 |journal=[[W:Physical Review|Physical Review]]
 |volume=51
 |pages=106–119
 |doi=10.1103/PhysRev.51.106
 |bibcode = 1937PhRv...51..106W
 |issue=2
}}&lt;/ref&gt; Similar to a spin-1/2 particle, which has two states, protons and neutrons were said to be of isospin 1/2. The proton and neutron were then associated with different isospin projections ''I''&lt;sub&gt;3&lt;/sub&gt;&amp;nbsp;=&amp;nbsp;+1/2 and −1/2 respectively.

Isospin is a different kind of rotation entirely than the ordinary spin which objects undergo when they rotate in three-dimensional space. Isospin does not correspond to a [[W:Rotations in 4-dimensional Euclidean space#Simple rotations|simple rotation]] in any space (of any number of dimensions). However, it does seem to correspond exactly to an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]] in a Euclidean space of four dimensions. Isospin space resembles the [[W:3-sphere|3-sphere]], the [[W:Elliptical space#Elliptic space (the 3D case)|curved 3-dimensional space]] that is the surface of a [[W:4-ball (mathematics)#In Euclidean space|4-dimensional ball]].

=== Spinors ===
[[File:Spinor on the circle.png|thumb|upright=1.5|A spinor visualized as a vector pointing along the [[W:Möbius band|Möbius band]], exhibiting a sign inversion when the circle (the &quot;physical system&quot;) is continuously rotated through a full turn of 360°.]][[W:Spinors|Spinors]] are [[W:representation of a Lie group|representations]] of a [[W:spin group|spin group]], which are [[W:Double covering group|double cover]]s of the [[W:special orthogonal group|special orthogonal groups]]. The spin group Spin(4) is the double cover of [[W:SO(4)|SO(4)]], the group of rotations in 4-dimensional Euclidean space. [[600-cell#Fibrations of isocline polygrams|Isoclines]], the helical geodesic paths followed by points under isoclinic rotation, correspond to spinors representing Spin(4).

Spinors can be viewed as the &quot;square roots&quot; of [[W:Section (fiber bundle)|cross sections]] of [[W:vector bundle|vector bundle]]s; in this correspondence, a fiber bundle of isoclines (of a distinct isoclinic rotation) is a cross section (inverse bundle) of a fibration of great circles (in the invariant planes of that rotation).

A spinor can be visualized as a moving vector on a Möbius strip which transforms to its negative when continuously rotated through 360°, just as [[24-cell#Helical hexagrams and their isoclines|an isocline can be visualized as a Möbius strip]] winding twice around the 3-sphere, during which [[24-cell#Isoclinic rotations|720° isoclinic rotation]] the rigid 4-polytope turns itself inside-out twice.{{Sfn|Goucher|2019|loc=Spin Groups}} Under isoclinic rotation, a rigid 4-polytope is an isospin-1/2 object with two states.

=== Isoclinic rotations in the nucleus ===
Isospin is regarded as a symmetry of the strong interaction under the [[W:Group action (mathematics)|action]] of the [[W:Lie group|Lie group]] [[W:SU(2)|SU(2)]], the two [[W:eigenstate|states]] being the [[W:Up quark|up flavour]] and [[W:Down quark|down flavour]]. A 360° isoclinic rotation of a rigid [[W:nuclide|nuclide]] would transform its protons into neutrons and vice versa, exchanging the up and down flavours of their constituent [[W:quarks|quarks]], by turning the nuclide and all its parts inside-out (or perhaps we should say upside-down). Because we never observe this, we know that the nucleus is not a ''rigid'' polytope undergoing isoclinic rotation.

If the nucleus ''were'' a rigid object, nuclides that were isospin-rotated 360° would be isoclinic mirror images of each other, isospin +1/2 and isospin −1/2 states of the whole nucleus. We don't see whole nuclides rotating as a rigid object, but considering what would happen if they ''were'' rigid tells us something about the geometry we must expect inside the nucleons. One way that an isospin-rotated neutron could become a proton would be if the up quark and down quark were a left and right mirror-image pair of the same object; exchanging them in place would turn each down-down-up neutron into an up-up-down proton. But the case cannot be quite that simple, because the up quark and the down quark are not mirror-images of the same object: they have very different mass and other incongruities.

Another way an isospin-rotated neutron could be a proton would be if the up and down quarks were asymmetrical kinematic polytopes (not indirectly congruent mirror-images, and not rigid polytopes), rotating within the nucleus in different ''hybrid'' orbits. By that we mean that they may have vertices orbiting in rotations characteristic of more than one 4-polytope, so they may change shape as they rotate. In that case their composites (protons and neutrons) could have a symmetry not manifest in their components, but emerging from their combination.

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=== Hybrid isoclinic rotations ===
The 24-cell has [[24-cell#Isoclinic rotations|its own characteristic isoclinic rotations]] in 4 Clifford parallel hexagonal planes (each intersecting 6 vertices), and also inherits the [[16-cell#Rotations|characteristic isoclinic rotations of its 3 Clifford parallel constituent 16-cells]] in 6 Clifford parallel square planes (each intersecting 4 vertices). The twisted circular paths followed by vertices in these two different kinds of rotation have entirely different geometries. Vertices rotating in hexagonal invariant planes follow [[24-cell#Helical hexagrams and their isoclines|helical geodesic curves whose chords form hexagrams]], and vertices rotating in square invariant planes follow [[24-cell#Helical octagrams and their isoclines|helical geodesic curves whose chords form octagrams]].

In a rigid isoclinic rotation, ''all'' the [[24-cell#Geodesics|great circle polygons]] move, in any kind of rotation. What distinguishes the hexagonal and square isoclinic rotations is the invariant planes of rotation the vertices stay in. The rotation described [[#Rotations|above]] (of 8 vertices rotating in 4 Clifford parallel hexagonal planes) is a single hexagonal isoclinic rotation, not a kinematic or hybrid rotation.

A ''kinematic'' isoclinic rotation in the 24-cell is any subset of the 24 vertices rotating through the same angle in the same time, but independently with respect to the choice of a Clifford parallel set of invariant planes of rotation and the chirality (left or right) of the rotation. A ''hybrid'' isoclinic rotation combines moving vertices from different kinds of isoclinic rotations, characteristic of different regular 4-polytopes. For example, if at least one vertex rotates in a square plane and at least one vertex rotates in a hexagonal plane, the kinematic rotation is a hybrid rotation, combining rotations characteristic of the 16-cell and characteristic of the 24-cell.

As an example of the simplest hybrid isoclinic rotation, consider a 24-cell vertex rotating in a square plane, and a second vertex, initially one 24-cell edge-length distant, rotating in a hexagonal plane. Rotating isoclinically at the same rate, the two moving vertices will never collide where their paths intersect, so this is a ''valid'' hybrid rotation.

To understand hybrid rotations in the 24-cell more generally, visualize the relationship between great squares and great hexagons. The [[24-cell#Squares|18 great squares]] occur as three sets of 6 orthogonal great squares,{{Efn|name=six orthogonal planes of the Cartesian basis}} each [[16-cell#Coordinates|forming a 16-cell]]. The three 16-cells are completely disjoint{{Efn|name=completely disjoint}} and [[24-cell#Clifford parallel polytopes|Clifford parallel]]: each has its own 8 vertices (on 4 orthogonal axes) and its own 24 edges (of length {{radic|2}}).{{Efn|name=three isoclinic 16-cells}} The 18 square great circles are crossed by 16 hexagonal great circles; each [[24-cell#Hexagons|hexagon]] has one axis (2 vertices) in each 16-cell.{{Efn|name=non-orthogonal hexagons}} The two [[24-cell#Triangles|great triangles]] inscribed in each great hexagon (occupying its alternate vertices, with edges that are its {{radic|3}} chords) have one vertex in each 16-cell. Thus ''each great triangle is a ring linking three completely disjoint great squares, one from each of the three completely disjoint 16-cells''.{{Efn|There are four different ways (four different ''fibrations'' of the 24-cell) in which the 8 vertices of the 16-cells correspond by being triangles of vertices {{radic|3}} apart: there are 32 distinct linking triangles. Each ''pair'' of 16-cells forms a tesseract (8-cell).{{Efn|name=three 16-cells form three tesseracts}} Each great triangle has one {{radic|3}} edge in each tesseract, so it is also a ring linking the three tesseracts.|name=great linking triangles}} Isoclinic rotations take the elements of the 4-polytope to congruent [[24-cell#Clifford parallel polytopes|Clifford parallel elements]] elsewhere in the 4-polytope. The square rotations do this ''locally'', confined within each 16-cell: for example, they take great squares to other great squares within the same 16-cell. The hexagonal rotations act ''globally'' within the entire 24-cell: for example, they take great squares to other great squares in ''different'' 16-cells. The [[16-cell#Helical construction|chords of the square rotations]] bind the 16-cells together internally, and the [[24-cell#Helical hexagrams and their isoclines|chords of the hexagonal rotations]] bind the three 16-cells together.

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=== Color ===
When the existence of quarks was suspected in 1964, [[W:Oscar W. Greenberg|Greenberg]] introduced the notion of color charge to explain how quarks could coexist inside some [[W:hadron|hadron]]s in [[W:quark model#The discovery of color|otherwise identical quantum states]] without violating the [[W:Pauli exclusion principle|Pauli exclusion principle]]. The modern concept of [[W:color charge|color charge]] completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [[W:William A. Bardeen|William Bardeen]], [[W:de:Harald Fritzsch|Harald Fritzsch]], and [[W:Murray Gell-Mann|Murray Gell-Mann]].&lt;ref&gt;{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''&lt;sup&gt;0&lt;/sup&gt; decay, and ''e''&lt;sup&gt;+&lt;/sup&gt; ''e''&lt;sup&gt;&amp;minus;&lt;/sup&gt; annihilation |arxiv=hep-ph/0211388 |editor=Gatto, R. |book-title=Scale and conformal symmetry in hadron physics |page=[https://archive.org/details/scaleconformalsy0000unse/page/139 139] |publisher=[[W:John Wiley &amp; Sons|John Wiley &amp; Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}&lt;/ref&gt;&lt;ref&gt;{{cite journal |title=Advantages of the color octet gluon picture |journal=[[W:Physics Letters B|Physics Letters B]] |volume=47 |issue=4 |page=365 |year=1973 |last1=Fritzsch |first1=H. |last2=Gell-Mann |first2=M. |last3=Leutwyler |first3=H. |doi=10.1016/0370-2693(73)90625-4 |bibcode=1973PhLB...47..365F |citeseerx=10.1.1.453.4712}}&lt;/ref&gt;

Color charge is not [[W:electric charge|electric charge]]; the whole point of it is that it is a quantum of something different. But it is related to electric charge, through the way in which the three different-colored quarks combine to contribute fractional quantities of electric charge to a nucleon. As we shall see, color is not really a separate kind of charge at all, but a partitioning of the electric charge into [[24-cell#Clifford parallel polytopes|Clifford parallel subspaces]].

The [[W:Color charge#Red, green, and blue|three different colors]] of quark charge might correspond to three different 16-cells, such as the three disjoint 16-cells inscribed in the 24-cell. Each color might be a disjoint domain in isospin space (the space of points on the 3-sphere).{{Efn|The 8 vertices of each disjoint 16-cell constitute an independent [[16-cell#Coordinates|orthonormal basis for a coordinate reference frame]].}} Alternatively, the three colors might correspond to three different fibrations of the same isospin space: three different ''sequences'' of the same total set of discrete points on the 3-sphere. These alternative possibilities constrain possible representations of the nuclides themselves, for example if we try to represent nuclides as particular rotating 4-polytopes. If the neutron is a (8-point) 16-cell, either of the two color possibilities might somehow make sense as far as the neutron is concerned. But if the proton is a (5-point) 5-cell, only the latter color possibility makes sense, because fibrations (which correspond to distinct isoclinic left-and-right rigid rotations) are the ''only'' thing the 5-cell has three of. Both the 5-cell and the 16-cell have three discrete rotational fibrations. Moreover, in the case of a rigid, isoclinically rotating 4-polytope, those three fibrations always come one-of-a-kind and two-of-a-kind, in at least two different ways. First, one fibration is the set of invariant planes currently being rotated through, and the other two are not. Second, when one considers the three fibrations of each of these 4-polytopes, in each fibration two isoclines carry the left and right rotations respectively, and the third isocline acts simply as a Petrie polygon, the difference between the fibrations being the role assigned to each isocline.

If we associate each quark with one or more isoclinic rotations in which the moving vertices belong to different 16-cells of the 24-cell, and the sign (plus or minus) of the electric charge with the chirality (right or left) of isoclinic rotations generally, we can configure nucleons of three quarks, two performing rotations of one chirality and one performing rotations of the other chirality. The configuration will be a valid kinematic rotation because the completely disjoint 16-cells can rotate independently; their vertices would never collide even if the 16-cells were performing different rigid square isoclinic rotations (all 8 vertices rotating in unison). But we need not associate a quark with a [[16-cell#Rotations|rigidly rotating 16-cell]], or with a single distinct square rotation.

Minimally, we must associate each quark with at least one moving vertex in each of three different 16-cells, following the twisted geodesic isocline of an isoclinic rotation. In the up quark, that could be the isocline of a right rotation; and in the down quark, the isocline of a left rotation. The chirality accounts for the sign of the electric charge (we have said conventionally as +right, −left), but we must also account for the quantity of charge: +{{sfrac|2|3}} in an up quark, and −{{sfrac|1|3}} in a down quark. One way to do that would be to give the three distinct quarks moving vertices of {{sfrac|1|3}} charge in different 16-cells, but provide up quarks with twice as many vertices moving on +right isoclines as down quarks have vertices moving on −left isoclines (assuming the correct chiral pairing is up+right, down−left).

Minimally, an up quark requires two moving vertices (of the up+right chirality).{{Efn|Two moving vertices in one quark could belong to the same 16-cell. A 16-cell may have two vertices moving in the same isoclinic square (octagram) orbit, such as an antipodal pair (a rotating dipole), or two vertices moving in different square orbits of the same up+right chirality.{{Efn|There is only one [[16-cell#Helical construction|octagram orbit]] of each chirality in each fibration of the 16-cell, so two octagram orbits of the same chirality cannot be Clifford parallel (part of the same distinct rotation). Two vertices right-moving on different octagram isoclines in the same 16-cell is a combination of two distinct rotations, whose isoclines will intersect: a kinematic rotation. It can be a valid kinematic rotation if the moving vertices will never pass through a point of intersection at the same time. Octagram isoclines pass through all 8 vertices of the 16-cell, and all eight isoclines (the left and right isoclines of four different fibrations) intersect at ''every'' vertex.}} However, the theory of [[W:Color confinement|color confinement]] may not require that two moving vertices in one quark belong to the same 16-cell; like the moving vertices of different quarks, they could be drawn from the disjoint vertex sets of two different 16-cells.}} Minimally, a down quark requires one moving vertex (of the down−left chirality). In these minimal quark configurations, a proton would have 5 moving vertices and a neutron would have 4.

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=== Nucleons ===
[[File:Symmetrical_5-set_Venn_diagram.svg|thumb|[[W:Branko Grünbaum|Grünbaum's]] rotationally symmetrical 5-set Venn diagram, 1975. It is the [[5-cell]]. Think of it as an [[W:Nuclear magnetic resonance|NMR image]] of the 4-dimensional proton in projection to the plane.]]
The proton is a very stable mass particle. Is there a stable orbit of 5 moving vertices in 4-dimensional Euclidean space? There are few known solutions to the 5-body problem, and fewer still to the [[W:n-body problem|{{mvar|n}}-body problem]], but one is known: the ''central configuration'' of {{mvar|n}} bodies in a space of dimension {{mvar|n}}-1. A [[W:Central configuration|central configuration]] is a system of [[W:Point particle|point masses]] with the property that each mass is pulled by the combined attractive force of the system directly towards the [[W:Center of mass|center of mass]], with acceleration proportional to its distance from the center. Placing three masses in an equilateral triangle, four at the vertices of a regular [[W:Tetrahedron|tetrahedron]], five at the vertices of a regular [[5-cell]], or more generally {{mvar|n}} masses at the vertices of a regular [[W:Simplex|simplex]] produces a central configuration [[W:Central configuration#Examples|even when the masses are not equal]]. In an isoclinic rotation, all the moving vertices orbit at the same radius and the same speed. Therefore if any 5 bodies are orbiting as an isoclinically rotating regular 5-cell (a rigid 4-simplex figure undergoing isoclinic rotation), they maintain a central configuration, describing 5 mutually stable orbits.

Unlike the proton, the neutron is not always a stable particle; a free neutron will decay into a proton. A deficiency of the minimal configurations is that there is no way for this [[W:beta minus decay|beta minus decay]] to occur. The minimal neutron of 4 moving vertices described [[#Color|above]] cannot possibly decay into a proton by losing moving vertices, because it does not possess the four up+right moving vertices required in a proton. This deficiency could be remedied by giving the neutron configuration 8 moving vertices instead of 4: four down−left and four up+right moving vertices. Then by losing 3 down−left moving vertices the neutron could decay into the 5 vertex up-down-up proton configuration.{{Efn|Although protons are very stable, during [[W:stellar nucleosynthesis|stellar nucleosynthesis]] two H&lt;sub&gt;1&lt;/sub&gt; protons are fused into an H&lt;sub&gt;2&lt;/sub&gt; nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus &quot;decay&quot;]] of a proton into a neutron is actually the result of a rare high-energy collision between the two protons, in which a neutron is constructed. With respect to our nucleon configurations of moving vertices, it has to be explained as the conversion of two 5-point 5-cells into a 5-point 5-cell and an 8-point 16-cell, emitting two decay products of at least 1-point each. Thus it must involve the creation of moving vertices, by the conversion of kinetic energy to point-masses.}} A neutron configuration of 8 moving vertices could occur as the 8-point 16-cell, the second-smallest regular 4-polytope after the 5-point 5-cell (the hypothesized proton configuration).

It is possible to double the neutron configuration in this way, without destroying the charge balance that defines the nucleons, by giving down quarks three moving vertices instead of just one: two −left vertices and one +right vertex. The net charge on the down quark remains −{{sfrac|1|3}}, but the down quark becomes heavier (at least in vertex count) than the up quark, as in fact its mass is measured to be.

A nucleon's quark configuration is only a partial specification of its properties. There is much more to a nucleon than what is contained within its three quarks, which contribute only about 1% of the nucleon's energy. The additional 99% of the nucleon mass is said to be associated with the force that binds the three quarks together, rather than being intrinsic to the individual quarks separately. In the case of the proton, 5 moving vertices in the stable orbits of a central configuration (in one of the [[5-cell#Geodesics and rotations|isoclinic rotations characteristic of the regular 5-cell]]) might be sufficient to account for the stability of the proton, but not to account for most of the proton's energy. It is not the point-masses of the moving vertices themselves which constitute most of the mass of the nucleon; if mass is a consequence of geometry, we must look to the larger geometric elements of these polytopes as their major mass contributors. The quark configurations are thus incomplete specifications of the geometry of the nucleons, predictive of only some of the nucleon's properties, such as charge.{{Efn|Notice that by giving the down quark three moving vertices, we seem to have changed the quark model's prediction of the proton's number of moving vertices from 5 to 7, which would be incompatible with our theory that the proton configuration is a rotating regular 5-cell in a central configuration of 5 stable orbits. Fortunately, the actual quark model has nothing at all to say about moving vertices, so we may choose to regard that number as one of the geometric properties the quark model does not specify.}} In particular, they do not account for the forces binding the nucleon together. Moreover, if the rotating regular 5-cell is the proton configuration and the rotating regular 16-cell is the neutron configuration, then a nucleus is a complex of rotating 5-cells and 16-cells, and we must look to the geometric relationship between those two very different regular 4-polytopes for an understanding of the nuclear force binding them together.

The most direct [[120-cell#Relationships among interior polytopes|geometric relationship among stationary regular 4-polytopes]] is the way they occupy a common 3-sphere together. Multiple 16-cells of equal radius can be compounded to form each of the larger regular 4-polytopes, the 8-cell, 24-cell, 600-cell, and 120-cell, but it is noteworthy that multiple regular 5-cells of equal radius cannot be compounded to form any of the other 4-polytopes except the largest, the 120-cell. The 120-cell is the unique intersection of the regular 5-cell and 16-cell: it is a compound of 120 regular 5-cells, and also a compound of 75 16-cells. All regular 4-polytopes except the 5-cell are compounds of 16-cells, but none of them except the largest, the 120-cell, contains any regular 5-cells. So in any compound of equal-radius 16-cells which also contains a regular 5-cell, whether that compound forms some single larger regular 4-polytope or does not, no two of the regular 5-cell's five vertices ever lie in the same 16-cell. So the geometric relationship between the regular 5-cell (our proton candidate) and the regular 16-cell (our neutron candidate) is quite a distant one: they are much more exclusive of each other's elements than they are distantly related, despite their complementary three-quark configurations and other similarities as nucleons. The relationship between a regular 5-cell and a regular 16-cell of equal radius is manifest only in the 120-cell, the most complex regular 4-polytope, which [[120-cell#Geometry|uniquely embodies all the containment relationships]] among all the regular 4-polytopes and their elements.

If the nucleus is a complex of 5-cells (protons) and 16-cells (neutrons) rotating isoclinically around a common center, then its overall motion is a hybrid isoclinic rotation, because the 5-cell and the 16-cell have different characteristic isoclinic rotations, and they have no isoclinic rotation in common.{{Efn|The regular 5-cell does not occur inscribed in any other regular 4-polytope except one, the 600-vertex 120-cell. No two of the 5 vertices of a regular 5-cell can be vertices of the same 16-cell, 8-cell, 24-cell, or 600-cell. The isoclinic rotations characteristic of the regular 5-cell maintain the separation of its 5 moving vertices in 5 disjoint Clifford-parallel subspaces at all times. The [[16-cell#Rotations|isoclinic rotation characteristic of the 16-cell]] maintains the separation of its 8 moving vertices in 2 disjoint Clifford-parallel subspaces (completely orthogonal great square planes) at all times. Therefore, in any hybrid rotation of a concentric 5-cell and 16-cell, at most one 5-cell subspace (containing 1 vertex) might be synchronized with one 16-cell subspace (containing 4 vertices), such that the 1 + 4 vertices they jointly contain occupy the same moving subspace continually, forming a rigid 5-vertex polytope undergoing some kind of rotation. If in fact it existed, this 5-vertex rotating rigid polytope would not be [[5-cell#Geometry|not a 5-cell, since 4 of its vertices are coplanar]]; it is not a 4-polytope but merely a polyhedron, a [[W:square pyramid|square pyramid]].}}

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=== Nuclides ===

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=== Quantum phenomena ===

The Bell-Kochen-Specker (BKS) theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a space of three or more dimensions can be given by exhibiting a finite set of lines through the origin that cannot each be colored black or white in such a way that (i) no two orthogonal lines are both black, and (ii) not all members of a set of ''d'' mutually orthogonal lines are white.{{Efn|&quot;The Bell-Kochen-Specker theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a Hilbert space of dimension d ≥ 3 can be given by exhibiting a finite set of rays [9] that cannot each be assigned the value 0 or 1 in such a way that (i) no two orthogonal rays are both assigned the value 1, and (ii) not all members of a set of d mutually orthogonal rays are assigned the value 0.&quot;{{Sfn|Waegell|Aravind|2009|loc=2. The Bell-Kochen-Specker (BKS) theorem}}|name=BKS theorem}}

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=== Motion ===
What does it mean to say that an object moves through space? Coxeter group theory provides precise answers to questions of this kind. A rigid object (polytope) moves by distinct transformations, changing itself in each discrete step into a congruent object in a different orientation and position.

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== Galilean relativity in a space of four orthogonal dimensions ==

Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions.

General relativity is just Galilean relativity in a general space of four orthogonal dimensions, e.g. Euclidean 4-space &lt;math&gt;R^4&lt;/math&gt;, spherical 4-space &lt;math&gt;S^4&lt;/math&gt;, or any orthogonal 4-manifold.

Light is just reflection. Gravity (and all force) is just rotation. Both motions are just group actions, expressions of intrinsic symmetries. That is all of physics.

Every observer properly sees himself as stationary and the universe as a sphere with himself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and it can be measured by the observer as the speed of light.

=== Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions ===
Perspective effects occur because each observer's ordinary 3-dimensional space is only a curved manifold embedded in 4-dimensional Euclidean space, and its curvature complicates the calculations for him (e.g., he sometimes requires Lorentz transformations). But if  all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) except when you want to calculate a projection, or a shadow, that is, how things will appear from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} The universe really has four spatial dimensions, and space and time behave just as they do in classical 3-vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a spacetime to explain 4-dimensional perspective effects at high velocities, because 4-space is already spatially 4-dimensional, and those perspective effects fall out of the 4-dimensional Pythagorean theorem naturally, just as perspective does in three dimensions. The universe is only strange in the ways the Euclidean fourth dimension is strange; but that does hold many surprises for us. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way that 3-space is much more interesting than 2-space. But all Euclidean spaces are dimensionally analogous. Dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries.

=== General relativity is just Galilean relativity in a general space of four orthogonal dimensions ===
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=== Physics ===
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=== Thoreau's spherical relativity ===
Every observer may properly see himself as stationary and the universe as a 4-sphere with himself at the center observing it, perceptually equidistant from all points on its surface, including his own ''physical'' location which is one of those surface points, distinguished to him but not the center of anything. This statement of the principle of relativity is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in curved, non-Euclidean spacetime, and Coxeter's relativity of orthogonal group actions in Euclidean spaces of any number of dimensions.{{Efn|Let Q denote a rotation, R a reflection, T a translation, and let Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T denote a product of several such transformations, all commutative with one another. Then RT is a glide-reflection (in two or three dimensions), QR is a rotary-reflection, QT is a screw-displacement, and Q&lt;sup&gt;2&lt;/sup&gt; is a double rotation (in four dimensions). Every orthogonal transformation is expressible as
{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt;&lt;br&gt;
where 2''q'' + ''r'' ≤ ''n'', the number of dimensions. Transformations involving a translation are expressible as
{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T&lt;br&gt;
where 2''q'' + ''r'' + 1 ≤ ''n''.&lt;br&gt;
For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q&lt;sup&gt;2&lt;/sup&gt;, or a screw-displacement QT (where the rotation component Q is a simple rotation). [If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either of those, because we can view any QT as a Q&lt;sup&gt;2&lt;/sup&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q&lt;sup&gt;2&lt;/sup&gt;. By the same principle, we can view any QT or Q&lt;sup&gt;2&lt;/sup&gt; as an isoclinic (equi-angled) Q&lt;sup&gt;2&lt;/sup&gt; by appropriate choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} That is to say, Coxeter's relation is a mathematical statement of the principle of relativity, on group-theoretic grounds.{{Efn|Notice that Coxeter's relation correctly captures the limits to relativity, in that we can only exchange the translation (T) for ''one'' of the two rotations (Q). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation up to uncertainty, and can always also distinguish the direction and velocity of his own proper time arrow.}}] Every enantiomorphous transformation in 4-space (reversing chirality) is a QRT.{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}|name=transformations}} It should be known as Thoreau's spherical relativity, since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polytopes in any number of dimensions.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassman and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}}]}}

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== Conclusions==

=== Spherical relativity ===

We began our inquiry by wondering why physical space should be limited to just three dimensions (why ''three''). By visualizing the universe as a Euclidian space of four dimensions, we recognize that relativistic and quantum phenomena are natural consequences of symmetry group operations (including reflections and rotations) in four orthogonal dimensions. We should not then be surprised to see that the universe does not have just four dimensions, either. Physical space must bear as many dimensions as we need to ascribe to it, though the distinct phenomena for which we find a need to do so, in order to explain them, seem to be fewer and fewer as we consider higher and higher dimensions. To laws of physics generally, such as the principle of relativity in particular, we should always append the phrase &quot;in Euclidean spaces of any number of dimensions&quot;. Laws of physics should operate in any flat Euclidean space &lt;math&gt;R^n&lt;/math&gt; and in its corresponding spherical space &lt;math&gt;S^n&lt;/math&gt;.

The first and simplest sense in which we are forced to contemplate a fifth dimension is to accommodate our normal idea of time. Just as Einstein was forced to admit time as a dimension, in his four-dimensional spacetime of three spatial dimensions plus time, for some purposes we require a fifth time dimension to accompany our four spatial dimensions, when our purpose is orthogonal to (in the sense of independent of) the four spatial dimensions. For example, if we theorize that we observe a finite homogeneous universe, and that it is a Euclidean 4-space overall, we may prefer not to have to identify any distinct place within that 4-space as the center where the universe began in a big bang. To avoid having to pick a distinct place as the center of the universe, our model of it must be expanded, at least to be a ''spherical'' 4-dimensional space with the fifth radial dimension as time. Essentially, we require the fifth dimension in order to make our homogeneous 4-space finite, by wrapping it around into a 4-sphere. But perhaps we can still resist admitting the fifth radial dimension as a full-fledged Euclidean spatial dimension, at least so long as we have not observed how any naturally occurring object configurations are best described as 5-polytopes.

One phenomenon which resists explanation in a space of just four dimensions is the propagation of light in a vacuum. The propagation of mass-carrying particles is explained as the consequence of their rotations in closed, curved spaces (3-spheres) of finite size, moving through four-dimensional Euclidean space at a universal constant speed, the speed of light. But an apparent paradox remains that light must seemingly propagate through four-dimensional Euclidean space at more than the speed of light. From a five-dimensional viewpoint, this apparent paradox can be resolved, and in retrospect it is clear how massless particles can translate through four-dimensional space at twice the speed constant, since they are not simultaneously rotating.

Another phenomenon justifying a five-dimensional view of space is the relation between the the 5-cell proton and the 16-cell neutron (the 4-simplex and 4-orthoplex polytopes). Their indirect relationship can be observed in the 4-600-point polytope (the 120-cell), and in its 11-cells,{{Sfn|Christie|2024}} but it is only directly observed (absent a 120-cell) in a five-dimensional reference frame.

=== Nuclear geometry ===
We have seen how isoclinic rotations (Clifford displacements) relate the orbits in the atomic nucleus to each other, just as they relate the regular convex 4-polytopes to each other, in a sequence of nested objects of increasing complexity. We have identified the proton as a  5-point, 5-cell 4-simplex 𝜶&lt;sub&gt;4&lt;/sub&gt;, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽&lt;sub&gt;4&lt;/sub&gt;, and the shell of the atomic nucleus as a 24-point 24-cell. As Coxeter noted, that unique 24-point object stands quite alone in four dimensions, having no analogue above or below.

=== Atomic geometry ===
I'm on a plane flying to Eugene to visit Catalin, we'll talk after I arrive. I've been working on both my unpublished papers, the one going put for pre-publication review soon about 4D geometry, and the big one not going out soon about the 4D sun, 4D atoms, and 4D galaxies and n-D universe. I'vd just added the following paragraph to that big paper:

Atomic geometry

The force binding the protons and neutrons of the nucleus together into a distinct element is specifically an expression of the 11-cell 4-polytope, itself an expression of the pyritohedral symmetry, which binds the distinct 4-polytopes to each other, and relates the n-polytopes to their neighbors of different n by dimensional analogy.


flying over mt shasta out my right-side window at the moment, that last text showing &quot;not delivered&quot; yet because there's no wifi on this plane, gazing at that great peak of the world and feeling as if i've just made the first ascent of it

=== Molecular geometry ===
Molecules are 3-dimensional structures that live in the thin film of 3-membrane only one atom thick in most places that is our ordinary space, but since that is a significantly curved 3-dimensional space at the scale of a molecule, the way the molecule's covalent bonds form is influenced by the local curvature in 4-dimensions at that point.

In the water molecule, there is a reason why the hydrogen atoms are attached to the oxygen atom at an angle of 104.45° in 3-dimensional space, and at root it must be the same symmetry that locates any two of the hydrogen proton's five vertices 104.45° apart on a great circle arc of its tiny 3-sphere.

=== Cosmology ===

==== Solar systems ====

===== Stars =====
...

===== The Kepler problem =====
...

==== Galaxies ====

The spacetime of general relativity is often illustrated as a projection to a curved 2D surface in which large gravitational objects make gravity wells or dimples in the surface. In the Euclidean 4D view of the universe the 3D surface of a large cosmic object such as a galaxy surrounds an empty 4D space, and large gravitational objects within the galaxy must make dimples in its surface. But should we see them as dimples exactly? Would they dimple inwards or outwards? In the spacetime illustrations they are naturally always shown as dimpling downwards, which is somewhat disingenuous, strongly suggesting to the viewer that the reason for gravity is that it flows downhill - the original tautology we are trying to surmount! In the Euclidean 4D galaxy the dimple, if it is one, must be either inward or outward, and which it is matters since the dimple is flying outward at velocity {{mvar|c}}. The galaxy is not collapsing inward. Is a large gravitational mass (such as a star) ''ahead'' of the smaller masses orbiting around it (such as its planets), or is it ''behind'' them, as they fly through 4-space on their Clifford parallel trajectories? The answer is ''both'' of course, because a star is not a dimple, it is a 4-ball, and it dimples the 3D surface both inwards and outwards. It is a thick place in the 3D surface. We should view it as having its gravitational center precisely at the surface of the expanding 3-sphere. 

What is a black hole? It is the hollow four-dimensional space that a galaxy is the three-dimensional surface of.

When we view another galaxy, such as Andromeda, we are seeing that whole galaxy from a distance, the way the moon astronauts looked back at the whole earth. We see our own milky way galaxy from where we are on its surface, the way we see the earth from its surface, except that the earth is solid, but the galaxy is hollow and transparent. We can look across its empty center and see all the other stars also on its surface, including those opposite ours on the far side of its 3-sphere. The thicker band of stars we see in our night sky and identify as the milky way is not our whole galaxy; the majority of the other visible stars also lie in our galaxy. That dense band is not thicker and brighter than other parts of our galaxy because it lies toward a dense galactic center (our galaxy has an empty center), but for exactly the opposite reason: those apparently more thickly clustered stars lie all around us on the galaxy's surface, in the nearest region of space surrounding us. They appear to be densely packed only because we are looking at them &quot;edge on&quot;. Actually, we are looking into this nearby apparently dense region ''face on'', not edge on, because we are looking at a round sphere of space surrounding us, not a disk. In contrast, stars in our galaxy outside that bright band lie farther off from us, across the empty center of the galaxy, and we see them spread out as they actually are, instead of &quot;edge on&quot; so they appear to be densely clustered. The &quot;dense band&quot; covers only an equatorial band of the night sky instead of all the sky, because when we look out into the four-dimensional space around us, we can see stars above and below our three-dimensional hyperplane in our four-dimensional space. Everything in our solar system lies in our hyperplane, and the nearby stars around us in our galaxy are near our hyperplane (just slightly below it). All the other, more distant stars in our galaxy are also below our hyperplane. We can see objects outside our galaxy, such as other galaxies, both above and below our hyperplane. We can see all around us above our hyperplane (looking up from the galactic surface into the fourth dimension), and all around us below our hyperplane (looking down through our transparent galaxy and out the other side).

== Revolutions ==
The original Copernican revolution displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the stars remaining on a fixed sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

In such fashion the Euclidean four-dimensional viewpoint initially lends itself to a big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the stars need not be equidistant from a single origin in time, any more than they all lie in the same galaxy, equidistant from its center in space. The expanding sphere of matter on the surface of which we find ourselves living might be one of many such spheres, with their big bang origins occurring at distinct times and places in the 4-dimensional universe.

When we look up at the heavens, we have no obvious way of knowing whether the space we are looking into is a curved 3-spherical one or a flat 4-space. In this work we suggest a theory of how light travels that says we can see into all four dimensions, and so when we look up at night we see cosmological objects distributed in 4-dimensional space, and not all located on our own 3-spherical membrane. The view from our solar system suggests that our galaxy is its own hollow 3-sphere, and that galaxies generally are single roughly spherical 3-membranes, with the smaller objects within them all lying on that same 3-spherical surface, equidistant from the galaxy center in 4-space. 

The Euclidean four-dimensional viewpoint requires that all mass-carrying objects are in motion at constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Since their paths away from their origin are not straight lines but various helical isoclines, their 3-sphere will be expanding radially at slightly less than the constant velocity &lt;math&gt;c&lt;/math&gt;. The view from our solar system does ''not'' suggest that each galaxy is its own distinct 3-sphere expanding at this great rate; rather, the standard theory has been that the entire observable universe is expanding from a single big bang origin in time. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also allows theories which require no single origin point in space and time.

These are the voyages of starship Earth, to boldly go where no one has gone before. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't slowed down since.

== Origins of the theory ==
Einstein himself was one of the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean sphere, in what was narrowly the first written articulation of the principle of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below). Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that formulation of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from his perspective; the forthshortenings, clock desynchronizations and other perceptual effects it predicts are exact calculations of actual perspective effects; but space is actually a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four dimensions.''

The Euclidean 4-dimensional theory differs from the standard theory in being a description of the physical universe in terms of a geometry of four or more orthogonal spatial dimensions, rather than in the standard theory's terms of the [[w:Minkowski spacetime|Minkowski spacetime]] geometry (in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions). The invention of geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years. It was first worked out by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] around 1850. Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''polyscheme'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he discovered all the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the six convex regular polyschemes which can be constructed in a space of four dimensions (a set analogous to the five [[w:Platonic solid|Platonic solids]] in three dimensional space). Thus he was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover all its astonishing regular objects. Because most of his work remained almost completely unknown until it was published posthumously in 1901, other researchers had more than fifty years to rediscover the regular polyschemes, and competing terms were coined; today [[W:Alicia Boole Stott|Alicia Boole Stott]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme''.{{Efn|Today Schläfli's original ''polyscheme'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}}

== Boundaries ==
&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schlafli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it, is that there ''is'' a boundary between three and four dimensions. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our world apparently only three dimensional? Why would it have ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schlafli mapped? What is the nature of the boundary which confines us to just three? 

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way by receiving light signals that traveled to us on straight lines through it. The reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creates, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not surprise us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schlafli discovered something else: all the astonishing regular objects that exist in higher dimensions. So this conception now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and not a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation?

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that our universe is properly a Euclidean space of four orthogonal spatial dimensions. Others will have to work out the physics and do the math, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|radius={{radic|2}}|columns=9}}

== Notes ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are 4-dimensionally circular, but not all isoclines on 3-manifolds in 4-space are perfectly circular.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point.{{Sfn|Tyrrell|Semple|1971|loc=§3. Clifford's original definition of parallelism|pp=5-6}} A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the 2-sphere will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect; various sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. Perhaps the simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles.{{Efn|name=six orthogonal planes of the Cartesian basis}} Each completely orthogonal pair is Clifford parallel. The two circles cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 3-sphere.{{Efn|name=only some Clifford parallels are orthogonal}} Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]].|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Notelist|40em}}

== Citations ==
{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

{{Reflist|40em}}

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{{Refend}}</text>
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{{align|center|dc@samizdat.org}}
{{align|center|June 2023 - November 2024}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four or more orthogonal spatial dimensions. Atoms are 4-polytopes, and stars are 4-balls of atomic plasma. A galaxy is a hollow 3-sphere with these objects distributed on its surface; the black hole at its center is the 4-ball of empty space it surrounds. The observable universe of galaxies may be visualized as a 4-sphere expanding radially from an origin point at velocity &lt;math&gt;c&lt;/math&gt;, the propagation speed of light through 3-space, also the invariant velocity of mass-carrying objects through 4-space. The propagation speed of light through 4-space &lt;math&gt;c_4&lt;/math&gt; is &lt;math&gt;c &lt; c_4 &lt; 2c&lt;/math&gt;. This view is compatible with the theories of special and general relativity, and with the quantum mechanical atomic theory. It explains those theories as expressions of intrinsic symmetries.&lt;/blockquote&gt;

== Symmetries ==
It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway|Burgiel|Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s.{{Efn|[[W:Coxeter group|Coxeter theory]] is for geometry what Noether's theorem is for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that obey the principle of relativity and correspond to distinct symmetry groups.}} Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. As I understand [[W:Coxeter group|Coxeter group]] theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic rather than algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional objects, and nature can be understood in terms of their [[W:group action|group actions]], including centrally [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]].

== The geometry of the atomic nucleus ==

In [[W:Euclidean 4-space|Euclidean four dimensional space]], an [[W:atomic nucleus|atomic nucleus]] is a [[24-cell]], the regular 4-polytope with [[W:Coxeter group#Symmetry groups of regular polytopes|𝔽&lt;sub&gt;4&lt;/sub&gt; symmetry]]. Nuclear shells are concentric [[W:3-sphere|3-sphere]]s occupied (fully or partially) by the orbits of this 24-point [[#The 6 regular convex 4-polytopes|regular convex 4-polytope]]. An actual atomic nucleus is a rotating four dimensional object. It is not a ''rigid'' rotating 24-cell, it is a kinematic one, because the nucleus of an actual atom of any [[W:nucleon number|nucleon number]] contains a distinct number of orbiting vertices which may be in different isoclinic rotational orbits. These moving vertices never describe a static 24-cell at any single instant in time, though their orbits do all the time. The physical configuration of the nucleus as a 24-cell can be reduced to the [[W:kinematics|kinematics]] of the orbits of its constituents. The geometry of the atomic nucleus is therefore strictly [[W:Euclidean geometry#19th century|Euclidean]] in four dimensional space.

=== Rotations ===
The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways (like coins flipping) into each other's central planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one or another of the parallel planes of rotation, so all of them move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out.

This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a precise [[24-cell|detailed description]] enabling the reader to visualize it runs to many pages and illustrations, with many accompanying pages of explanatory notes on basic phenomena that arise only in 4-dimensional space: [[24-cell#Squares|completely orthogonal planes]], [[24-cell#Hexagons|Clifford parallelism]] and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Helical hexagrams and their isoclines|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a surprise. [[#The 6 regular convex 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120, and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (generally), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It is much harder for us to visualize, because the only way we can experience it is in our imaginations; we have no body of ''sensory'' experience in 4-dimensional space to draw upon.

For that reason, descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case. [[W:Kinematics|Kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rigid 24-cell. 

To begin with, when we examine the individual parts of the rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertices just once, and no point-object colliding with any other at any time.

That is still an example of a rigid object in a single distinct isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing the characteristic rotation of the 24-cell. But we can also imagine ''combining'' distinct rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible without collisions? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore questions of this kind of [[W:kinematics|kinematics]], and where dynamic stabilites arise, of [[W:kinetics|kinetics]].

=== Isospin ===
A [[W:Nucleon|nucleon]] is a [[W:proton|proton]] or a [[W:neutron|neutron]]. The proton carries a positive net [[W:Electric charge|charge]], and the neutron carries a zero net charge. The proton's [[W:Mass|mass]] is only about 0.13% less than the neutron's, and since they are observed to be identical in other respects, they can be viewed as two states of the same nucleon, together forming an isospin doublet ({{nowrap|''I'' {{=}} {{sfrac|1|2}}}}). In isospin space, neutrons can be transformed into protons and conversely by actions of the [[W:SU(2)|SU(2)]] symmetry group. In nature, protons are very stable (the most stable particle known); a proton and a neutron are a stable nuclide; but free neutrons decay into protons in about 10 or 15 seconds.

According to the [[W:Noether theorem|Noether theorem]], [[W:Isospin|isospin]] is conserved with respect to the [[W:strong interaction|strong interaction]].&lt;ref name=Griffiths2008&gt;{{cite book |author=Griffiths, David J. |title=Introduction to Elementary Particles |edition=2nd revised |publisher=WILEY-VCH |year=2008 |isbn=978-3-527-40601-2}}&lt;/ref&gt;{{rp|129–130}} Nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space.

Isospin was introduced as a concept in 1932 by [[W:Werner Heisenberg|Werner Heisenberg]],&lt;ref&gt;
{{cite journal
 |last=Heisenberg |first=W. |author-link=W:Werner Heisenberg
 |year=1932
 |title=Über den Bau der Atomkerne
 |journal=[[W:Zeitschrift für Physik|Zeitschrift für Physik]]
 |volume=77 |issue=1–2 |pages=1–11
 |doi=10.1007/BF01342433
 |bibcode = 1932ZPhy...77....1H
 |s2cid=186218053
 |language=de}}&lt;/ref&gt; well before the 1960s development of the [[W:quark model|quark model]], to explain the symmetry of the proton and the then newly discovered neutron. Heisenberg introduced the concept of another conserved quantity that would cause the proton to turn into a neutron and vice versa. In 1937, [[W:Eugene Wigner|Eugene Wigner]] introduced the term &quot;isospin&quot; to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.&lt;ref&gt;
{{cite journal
 |last=Wigner |first=E. |author-link=W:Eugene Wigner
 |year=1937
 |title=On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei
 |journal=[[W:Physical Review|Physical Review]]
 |volume=51
 |pages=106–119
 |doi=10.1103/PhysRev.51.106
 |bibcode = 1937PhRv...51..106W
 |issue=2
}}&lt;/ref&gt; Similar to a spin-1/2 particle, which has two states, protons and neutrons were said to be of isospin 1/2. The proton and neutron were then associated with different isospin projections ''I''&lt;sub&gt;3&lt;/sub&gt;&amp;nbsp;=&amp;nbsp;+1/2 and −1/2 respectively.

Isospin is a different kind of rotation entirely than the ordinary spin which objects undergo when they rotate in three-dimensional space. Isospin does not correspond to a [[W:Rotations in 4-dimensional Euclidean space#Simple rotations|simple rotation]] in any space (of any number of dimensions). However, it does seem to correspond exactly to an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]] in a Euclidean space of four dimensions. Isospin space resembles the [[W:3-sphere|3-sphere]], the [[W:Elliptical space#Elliptic space (the 3D case)|curved 3-dimensional space]] that is the surface of a [[W:4-ball (mathematics)#In Euclidean space|4-dimensional ball]].

=== Spinors ===
[[File:Spinor on the circle.png|thumb|upright=1.5|A spinor visualized as a vector pointing along the [[W:Möbius band|Möbius band]], exhibiting a sign inversion when the circle (the &quot;physical system&quot;) is continuously rotated through a full turn of 360°.]][[W:Spinors|Spinors]] are [[W:representation of a Lie group|representations]] of a [[W:spin group|spin group]], which are [[W:Double covering group|double cover]]s of the [[W:special orthogonal group|special orthogonal groups]]. The spin group Spin(4) is the double cover of [[W:SO(4)|SO(4)]], the group of rotations in 4-dimensional Euclidean space. [[600-cell#Fibrations of isocline polygrams|Isoclines]], the helical geodesic paths followed by points under isoclinic rotation, correspond to spinors representing Spin(4).

Spinors can be viewed as the &quot;square roots&quot; of [[W:Section (fiber bundle)|cross sections]] of [[W:vector bundle|vector bundle]]s; in this correspondence, a fiber bundle of isoclines (of a distinct isoclinic rotation) is a cross section (inverse bundle) of a fibration of great circles (in the invariant planes of that rotation).

A spinor can be visualized as a moving vector on a Möbius strip which transforms to its negative when continuously rotated through 360°, just as [[24-cell#Helical hexagrams and their isoclines|an isocline can be visualized as a Möbius strip]] winding twice around the 3-sphere, during which [[24-cell#Isoclinic rotations|720° isoclinic rotation]] the rigid 4-polytope turns itself inside-out twice.{{Sfn|Goucher|2019|loc=Spin Groups}} Under isoclinic rotation, a rigid 4-polytope is an isospin-1/2 object with two states.

=== Isoclinic rotations in the nucleus ===
Isospin is regarded as a symmetry of the strong interaction under the [[W:Group action (mathematics)|action]] of the [[W:Lie group|Lie group]] [[W:SU(2)|SU(2)]], the two [[W:eigenstate|states]] being the [[W:Up quark|up flavour]] and [[W:Down quark|down flavour]]. A 360° isoclinic rotation of a rigid [[W:nuclide|nuclide]] would transform its protons into neutrons and vice versa, exchanging the up and down flavours of their constituent [[W:quarks|quarks]], by turning the nuclide and all its parts inside-out (or perhaps we should say upside-down). Because we never observe this, we know that the nucleus is not a ''rigid'' polytope undergoing isoclinic rotation.

If the nucleus ''were'' a rigid object, nuclides that were isospin-rotated 360° would be isoclinic mirror images of each other, isospin +1/2 and isospin −1/2 states of the whole nucleus. We don't see whole nuclides rotating as a rigid object, but considering what would happen if they ''were'' rigid tells us something about the geometry we must expect inside the nucleons. One way that an isospin-rotated neutron could become a proton would be if the up quark and down quark were a left and right mirror-image pair of the same object; exchanging them in place would turn each down-down-up neutron into an up-up-down proton. But the case cannot be quite that simple, because the up quark and the down quark are not mirror-images of the same object: they have very different mass and other incongruities.

Another way an isospin-rotated neutron could be a proton would be if the up and down quarks were asymmetrical kinematic polytopes (not indirectly congruent mirror-images, and not rigid polytopes), rotating within the nucleus in different ''hybrid'' orbits. By that we mean that they may have vertices orbiting in rotations characteristic of more than one 4-polytope, so they may change shape as they rotate. In that case their composites (protons and neutrons) could have a symmetry not manifest in their components, but emerging from their combination.

....

=== Hybrid isoclinic rotations ===
The 24-cell has [[24-cell#Isoclinic rotations|its own characteristic isoclinic rotations]] in 4 Clifford parallel hexagonal planes (each intersecting 6 vertices), and also inherits the [[16-cell#Rotations|characteristic isoclinic rotations of its 3 Clifford parallel constituent 16-cells]] in 6 Clifford parallel square planes (each intersecting 4 vertices). The twisted circular paths followed by vertices in these two different kinds of rotation have entirely different geometries. Vertices rotating in hexagonal invariant planes follow [[24-cell#Helical hexagrams and their isoclines|helical geodesic curves whose chords form hexagrams]], and vertices rotating in square invariant planes follow [[24-cell#Helical octagrams and their isoclines|helical geodesic curves whose chords form octagrams]].

In a rigid isoclinic rotation, ''all'' the [[24-cell#Geodesics|great circle polygons]] move, in any kind of rotation. What distinguishes the hexagonal and square isoclinic rotations is the invariant planes of rotation the vertices stay in. The rotation described [[#Rotations|above]] (of 8 vertices rotating in 4 Clifford parallel hexagonal planes) is a single hexagonal isoclinic rotation, not a kinematic or hybrid rotation.

A ''kinematic'' isoclinic rotation in the 24-cell is any subset of the 24 vertices rotating through the same angle in the same time, but independently with respect to the choice of a Clifford parallel set of invariant planes of rotation and the chirality (left or right) of the rotation. A ''hybrid'' isoclinic rotation combines moving vertices from different kinds of isoclinic rotations, characteristic of different regular 4-polytopes. For example, if at least one vertex rotates in a square plane and at least one vertex rotates in a hexagonal plane, the kinematic rotation is a hybrid rotation, combining rotations characteristic of the 16-cell and characteristic of the 24-cell.

As an example of the simplest hybrid isoclinic rotation, consider a 24-cell vertex rotating in a square plane, and a second vertex, initially one 24-cell edge-length distant, rotating in a hexagonal plane. Rotating isoclinically at the same rate, the two moving vertices will never collide where their paths intersect, so this is a ''valid'' hybrid rotation.

To understand hybrid rotations in the 24-cell more generally, visualize the relationship between great squares and great hexagons. The [[24-cell#Squares|18 great squares]] occur as three sets of 6 orthogonal great squares,{{Efn|name=six orthogonal planes of the Cartesian basis}} each [[16-cell#Coordinates|forming a 16-cell]]. The three 16-cells are completely disjoint{{Efn|name=completely disjoint}} and [[24-cell#Clifford parallel polytopes|Clifford parallel]]: each has its own 8 vertices (on 4 orthogonal axes) and its own 24 edges (of length {{radic|2}}).{{Efn|name=three isoclinic 16-cells}} The 18 square great circles are crossed by 16 hexagonal great circles; each [[24-cell#Hexagons|hexagon]] has one axis (2 vertices) in each 16-cell.{{Efn|name=non-orthogonal hexagons}} The two [[24-cell#Triangles|great triangles]] inscribed in each great hexagon (occupying its alternate vertices, with edges that are its {{radic|3}} chords) have one vertex in each 16-cell. Thus ''each great triangle is a ring linking three completely disjoint great squares, one from each of the three completely disjoint 16-cells''.{{Efn|There are four different ways (four different ''fibrations'' of the 24-cell) in which the 8 vertices of the 16-cells correspond by being triangles of vertices {{radic|3}} apart: there are 32 distinct linking triangles. Each ''pair'' of 16-cells forms a tesseract (8-cell).{{Efn|name=three 16-cells form three tesseracts}} Each great triangle has one {{radic|3}} edge in each tesseract, so it is also a ring linking the three tesseracts.|name=great linking triangles}} Isoclinic rotations take the elements of the 4-polytope to congruent [[24-cell#Clifford parallel polytopes|Clifford parallel elements]] elsewhere in the 4-polytope. The square rotations do this ''locally'', confined within each 16-cell: for example, they take great squares to other great squares within the same 16-cell. The hexagonal rotations act ''globally'' within the entire 24-cell: for example, they take great squares to other great squares in ''different'' 16-cells. The [[16-cell#Helical construction|chords of the square rotations]] bind the 16-cells together internally, and the [[24-cell#Helical hexagrams and their isoclines|chords of the hexagonal rotations]] bind the three 16-cells together.

....

=== Color ===
When the existence of quarks was suspected in 1964, [[W:Oscar W. Greenberg|Greenberg]] introduced the notion of color charge to explain how quarks could coexist inside some [[W:hadron|hadron]]s in [[W:quark model#The discovery of color|otherwise identical quantum states]] without violating the [[W:Pauli exclusion principle|Pauli exclusion principle]]. The modern concept of [[W:color charge|color charge]] completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [[W:William A. Bardeen|William Bardeen]], [[W:de:Harald Fritzsch|Harald Fritzsch]], and [[W:Murray Gell-Mann|Murray Gell-Mann]].&lt;ref&gt;{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''&lt;sup&gt;0&lt;/sup&gt; decay, and ''e''&lt;sup&gt;+&lt;/sup&gt; ''e''&lt;sup&gt;&amp;minus;&lt;/sup&gt; annihilation |arxiv=hep-ph/0211388 |editor=Gatto, R. |book-title=Scale and conformal symmetry in hadron physics |page=[https://archive.org/details/scaleconformalsy0000unse/page/139 139] |publisher=[[W:John Wiley &amp; Sons|John Wiley &amp; Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}&lt;/ref&gt;&lt;ref&gt;{{cite journal |title=Advantages of the color octet gluon picture |journal=[[W:Physics Letters B|Physics Letters B]] |volume=47 |issue=4 |page=365 |year=1973 |last1=Fritzsch |first1=H. |last2=Gell-Mann |first2=M. |last3=Leutwyler |first3=H. |doi=10.1016/0370-2693(73)90625-4 |bibcode=1973PhLB...47..365F |citeseerx=10.1.1.453.4712}}&lt;/ref&gt;

Color charge is not [[W:electric charge|electric charge]]; the whole point of it is that it is a quantum of something different. But it is related to electric charge, through the way in which the three different-colored quarks combine to contribute fractional quantities of electric charge to a nucleon. As we shall see, color is not really a separate kind of charge at all, but a partitioning of the electric charge into [[24-cell#Clifford parallel polytopes|Clifford parallel subspaces]].

The [[W:Color charge#Red, green, and blue|three different colors]] of quark charge might correspond to three different 16-cells, such as the three disjoint 16-cells inscribed in the 24-cell. Each color might be a disjoint domain in isospin space (the space of points on the 3-sphere).{{Efn|The 8 vertices of each disjoint 16-cell constitute an independent [[16-cell#Coordinates|orthonormal basis for a coordinate reference frame]].}} Alternatively, the three colors might correspond to three different fibrations of the same isospin space: three different ''sequences'' of the same total set of discrete points on the 3-sphere. These alternative possibilities constrain possible representations of the nuclides themselves, for example if we try to represent nuclides as particular rotating 4-polytopes. If the neutron is a (8-point) 16-cell, either of the two color possibilities might somehow make sense as far as the neutron is concerned. But if the proton is a (5-point) 5-cell, only the latter color possibility makes sense, because fibrations (which correspond to distinct isoclinic left-and-right rigid rotations) are the ''only'' thing the 5-cell has three of. Both the 5-cell and the 16-cell have three discrete rotational fibrations. Moreover, in the case of a rigid, isoclinically rotating 4-polytope, those three fibrations always come one-of-a-kind and two-of-a-kind, in at least two different ways. First, one fibration is the set of invariant planes currently being rotated through, and the other two are not. Second, when one considers the three fibrations of each of these 4-polytopes, in each fibration two isoclines carry the left and right rotations respectively, and the third isocline acts simply as a Petrie polygon, the difference between the fibrations being the role assigned to each isocline.

If we associate each quark with one or more isoclinic rotations in which the moving vertices belong to different 16-cells of the 24-cell, and the sign (plus or minus) of the electric charge with the chirality (right or left) of isoclinic rotations generally, we can configure nucleons of three quarks, two performing rotations of one chirality and one performing rotations of the other chirality. The configuration will be a valid kinematic rotation because the completely disjoint 16-cells can rotate independently; their vertices would never collide even if the 16-cells were performing different rigid square isoclinic rotations (all 8 vertices rotating in unison). But we need not associate a quark with a [[16-cell#Rotations|rigidly rotating 16-cell]], or with a single distinct square rotation.

Minimally, we must associate each quark with at least one moving vertex in each of three different 16-cells, following the twisted geodesic isocline of an isoclinic rotation. In the up quark, that could be the isocline of a right rotation; and in the down quark, the isocline of a left rotation. The chirality accounts for the sign of the electric charge (we have said conventionally as +right, −left), but we must also account for the quantity of charge: +{{sfrac|2|3}} in an up quark, and −{{sfrac|1|3}} in a down quark. One way to do that would be to give the three distinct quarks moving vertices of {{sfrac|1|3}} charge in different 16-cells, but provide up quarks with twice as many vertices moving on +right isoclines as down quarks have vertices moving on −left isoclines (assuming the correct chiral pairing is up+right, down−left).

Minimally, an up quark requires two moving vertices (of the up+right chirality).{{Efn|Two moving vertices in one quark could belong to the same 16-cell. A 16-cell may have two vertices moving in the same isoclinic square (octagram) orbit, such as an antipodal pair (a rotating dipole), or two vertices moving in different square orbits of the same up+right chirality.{{Efn|There is only one [[16-cell#Helical construction|octagram orbit]] of each chirality in each fibration of the 16-cell, so two octagram orbits of the same chirality cannot be Clifford parallel (part of the same distinct rotation). Two vertices right-moving on different octagram isoclines in the same 16-cell is a combination of two distinct rotations, whose isoclines will intersect: a kinematic rotation. It can be a valid kinematic rotation if the moving vertices will never pass through a point of intersection at the same time. Octagram isoclines pass through all 8 vertices of the 16-cell, and all eight isoclines (the left and right isoclines of four different fibrations) intersect at ''every'' vertex.}} However, the theory of [[W:Color confinement|color confinement]] may not require that two moving vertices in one quark belong to the same 16-cell; like the moving vertices of different quarks, they could be drawn from the disjoint vertex sets of two different 16-cells.}} Minimally, a down quark requires one moving vertex (of the down−left chirality). In these minimal quark configurations, a proton would have 5 moving vertices and a neutron would have 4.

....

=== Nucleons ===
[[File:Symmetrical_5-set_Venn_diagram.svg|thumb|[[W:Branko Grünbaum|Grünbaum's]] rotationally symmetrical 5-set Venn diagram, 1975. It is the [[5-cell]]. Think of it as an [[W:Nuclear magnetic resonance|NMR image]] of the 4-dimensional proton in projection to the plane.]]
The proton is a very stable mass particle. Is there a stable orbit of 5 moving vertices in 4-dimensional Euclidean space? There are few known solutions to the 5-body problem, and fewer still to the [[W:n-body problem|{{mvar|n}}-body problem]], but one is known: the ''central configuration'' of {{mvar|n}} bodies in a space of dimension {{mvar|n}}-1. A [[W:Central configuration|central configuration]] is a system of [[W:Point particle|point masses]] with the property that each mass is pulled by the combined attractive force of the system directly towards the [[W:Center of mass|center of mass]], with acceleration proportional to its distance from the center. Placing three masses in an equilateral triangle, four at the vertices of a regular [[W:Tetrahedron|tetrahedron]], five at the vertices of a regular [[5-cell]], or more generally {{mvar|n}} masses at the vertices of a regular [[W:Simplex|simplex]] produces a central configuration [[W:Central configuration#Examples|even when the masses are not equal]]. In an isoclinic rotation, all the moving vertices orbit at the same radius and the same speed. Therefore if any 5 bodies are orbiting as an isoclinically rotating regular 5-cell (a rigid 4-simplex figure undergoing isoclinic rotation), they maintain a central configuration, describing 5 mutually stable orbits.

Unlike the proton, the neutron is not always a stable particle; a free neutron will decay into a proton. A deficiency of the minimal configurations is that there is no way for this [[W:beta minus decay|beta minus decay]] to occur. The minimal neutron of 4 moving vertices described [[#Color|above]] cannot possibly decay into a proton by losing moving vertices, because it does not possess the four up+right moving vertices required in a proton. This deficiency could be remedied by giving the neutron configuration 8 moving vertices instead of 4: four down−left and four up+right moving vertices. Then by losing 3 down−left moving vertices the neutron could decay into the 5 vertex up-down-up proton configuration.{{Efn|Although protons are very stable, during [[W:stellar nucleosynthesis|stellar nucleosynthesis]] two H&lt;sub&gt;1&lt;/sub&gt; protons are fused into an H&lt;sub&gt;2&lt;/sub&gt; nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus &quot;decay&quot;]] of a proton into a neutron is actually the result of a rare high-energy collision between the two protons, in which a neutron is constructed. With respect to our nucleon configurations of moving vertices, it has to be explained as the conversion of two 5-point 5-cells into a 5-point 5-cell and an 8-point 16-cell, emitting two decay products of at least 1-point each. Thus it must involve the creation of moving vertices, by the conversion of kinetic energy to point-masses.}} A neutron configuration of 8 moving vertices could occur as the 8-point 16-cell, the second-smallest regular 4-polytope after the 5-point 5-cell (the hypothesized proton configuration).

It is possible to double the neutron configuration in this way, without destroying the charge balance that defines the nucleons, by giving down quarks three moving vertices instead of just one: two −left vertices and one +right vertex. The net charge on the down quark remains −{{sfrac|1|3}}, but the down quark becomes heavier (at least in vertex count) than the up quark, as in fact its mass is measured to be.

A nucleon's quark configuration is only a partial specification of its properties. There is much more to a nucleon than what is contained within its three quarks, which contribute only about 1% of the nucleon's energy. The additional 99% of the nucleon mass is said to be associated with the force that binds the three quarks together, rather than being intrinsic to the individual quarks separately. In the case of the proton, 5 moving vertices in the stable orbits of a central configuration (in one of the [[5-cell#Geodesics and rotations|isoclinic rotations characteristic of the regular 5-cell]]) might be sufficient to account for the stability of the proton, but not to account for most of the proton's energy. It is not the point-masses of the moving vertices themselves which constitute most of the mass of the nucleon; if mass is a consequence of geometry, we must look to the larger geometric elements of these polytopes as their major mass contributors. The quark configurations are thus incomplete specifications of the geometry of the nucleons, predictive of only some of the nucleon's properties, such as charge.{{Efn|Notice that by giving the down quark three moving vertices, we seem to have changed the quark model's prediction of the proton's number of moving vertices from 5 to 7, which would be incompatible with our theory that the proton configuration is a rotating regular 5-cell in a central configuration of 5 stable orbits. Fortunately, the actual quark model has nothing at all to say about moving vertices, so we may choose to regard that number as one of the geometric properties the quark model does not specify.}} In particular, they do not account for the forces binding the nucleon together. Moreover, if the rotating regular 5-cell is the proton configuration and the rotating regular 16-cell is the neutron configuration, then a nucleus is a complex of rotating 5-cells and 16-cells, and we must look to the geometric relationship between those two very different regular 4-polytopes for an understanding of the nuclear force binding them together.

The most direct [[120-cell#Relationships among interior polytopes|geometric relationship among stationary regular 4-polytopes]] is the way they occupy a common 3-sphere together. Multiple 16-cells of equal radius can be compounded to form each of the larger regular 4-polytopes, the 8-cell, 24-cell, 600-cell, and 120-cell, but it is noteworthy that multiple regular 5-cells of equal radius cannot be compounded to form any of the other 4-polytopes except the largest, the 120-cell. The 120-cell is the unique intersection of the regular 5-cell and 16-cell: it is a compound of 120 regular 5-cells, and also a compound of 75 16-cells. All regular 4-polytopes except the 5-cell are compounds of 16-cells, but none of them except the largest, the 120-cell, contains any regular 5-cells. So in any compound of equal-radius 16-cells which also contains a regular 5-cell, whether that compound forms some single larger regular 4-polytope or does not, no two of the regular 5-cell's five vertices ever lie in the same 16-cell. So the geometric relationship between the regular 5-cell (our proton candidate) and the regular 16-cell (our neutron candidate) is quite a distant one: they are much more exclusive of each other's elements than they are distantly related, despite their complementary three-quark configurations and other similarities as nucleons. The relationship between a regular 5-cell and a regular 16-cell of equal radius is manifest only in the 120-cell, the most complex regular 4-polytope, which [[120-cell#Geometry|uniquely embodies all the containment relationships]] among all the regular 4-polytopes and their elements.

If the nucleus is a complex of 5-cells (protons) and 16-cells (neutrons) rotating isoclinically around a common center, then its overall motion is a hybrid isoclinic rotation, because the 5-cell and the 16-cell have different characteristic isoclinic rotations, and they have no isoclinic rotation in common.{{Efn|The regular 5-cell does not occur inscribed in any other regular 4-polytope except one, the 600-vertex 120-cell. No two of the 5 vertices of a regular 5-cell can be vertices of the same 16-cell, 8-cell, 24-cell, or 600-cell. The isoclinic rotations characteristic of the regular 5-cell maintain the separation of its 5 moving vertices in 5 disjoint Clifford-parallel subspaces at all times. The [[16-cell#Rotations|isoclinic rotation characteristic of the 16-cell]] maintains the separation of its 8 moving vertices in 2 disjoint Clifford-parallel subspaces (completely orthogonal great square planes) at all times. Therefore, in any hybrid rotation of a concentric 5-cell and 16-cell, at most one 5-cell subspace (containing 1 vertex) might be synchronized with one 16-cell subspace (containing 4 vertices), such that the 1 + 4 vertices they jointly contain occupy the same moving subspace continually, forming a rigid 5-vertex polytope undergoing some kind of rotation. If in fact it existed, this 5-vertex rotating rigid polytope would not be [[5-cell#Geometry|not a 5-cell, since 4 of its vertices are coplanar]]; it is not a 4-polytope but merely a polyhedron, a [[W:square pyramid|square pyramid]].}}

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=== Nuclides ===

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=== Quantum phenomena ===

The Bell-Kochen-Specker (BKS) theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a space of three or more dimensions can be given by exhibiting a finite set of lines through the origin that cannot each be colored black or white in such a way that (i) no two orthogonal lines are both black, and (ii) not all members of a set of ''d'' mutually orthogonal lines are white.{{Efn|&quot;The Bell-Kochen-Specker theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a Hilbert space of dimension d ≥ 3 can be given by exhibiting a finite set of rays [9] that cannot each be assigned the value 0 or 1 in such a way that (i) no two orthogonal rays are both assigned the value 1, and (ii) not all members of a set of d mutually orthogonal rays are assigned the value 0.&quot;{{Sfn|Waegell|Aravind|2009|loc=2. The Bell-Kochen-Specker (BKS) theorem}}|name=BKS theorem}}

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=== Motion ===
What does it mean to say that an object moves through space? Coxeter group theory provides precise answers to questions of this kind. A rigid object (polytope) moves by distinct transformations, changing itself in each discrete step into a congruent object in a different orientation and position.

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== Galilean relativity in a space of four orthogonal dimensions ==

Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions.

General relativity is just Galilean relativity in a general space of four orthogonal dimensions, e.g. Euclidean 4-space &lt;math&gt;R^4&lt;/math&gt;, spherical 4-space &lt;math&gt;S^4&lt;/math&gt;, or any orthogonal 4-manifold.

Light is just reflection. Gravity (and all force) is just rotation. Both motions are just group actions, expressions of intrinsic symmetries. That is all of physics.

Every observer properly sees himself as stationary and the universe as a sphere with himself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and it can be measured by the observer as the speed of light.

=== Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions ===
Perspective effects occur because each observer's ordinary 3-dimensional space is only a curved manifold embedded in 4-dimensional Euclidean space, and its curvature complicates the calculations for him (e.g., he sometimes requires Lorentz transformations). But if  all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) except when you want to calculate a projection, or a shadow, that is, how things will appear from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} The universe really has four spatial dimensions, and space and time behave just as they do in classical 3-vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a spacetime to explain 4-dimensional perspective effects at high velocities, because 4-space is already spatially 4-dimensional, and those perspective effects fall out of the 4-dimensional Pythagorean theorem naturally, just as perspective does in three dimensions. The universe is only strange in the ways the Euclidean fourth dimension is strange; but that does hold many surprises for us. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way that 3-space is much more interesting than 2-space. But all Euclidean spaces are dimensionally analogous. Dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries.

=== General relativity is just Galilean relativity in a general space of four orthogonal dimensions ===
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=== Physics ===
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=== Thoreau's spherical relativity ===
Every observer may properly see himself as stationary and the universe as a 4-sphere with himself at the center observing it, perceptually equidistant from all points on its surface, including his own ''physical'' location which is one of those surface points, distinguished to him but not the center of anything. This statement of the principle of relativity is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in curved, non-Euclidean spacetime, and Coxeter's relativity of orthogonal group actions in Euclidean spaces of any number of dimensions.{{Efn|Let Q denote a rotation, R a reflection, T a translation, and let Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T denote a product of several such transformations, all commutative with one another. Then RT is a glide-reflection (in two or three dimensions), QR is a rotary-reflection, QT is a screw-displacement, and Q&lt;sup&gt;2&lt;/sup&gt; is a double rotation (in four dimensions). Every orthogonal transformation is expressible as
{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt;&lt;br&gt;
where 2''q'' + ''r'' ≤ ''n'', the number of dimensions. Transformations involving a translation are expressible as
{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T&lt;br&gt;
where 2''q'' + ''r'' + 1 ≤ ''n''.&lt;br&gt;
For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q&lt;sup&gt;2&lt;/sup&gt;, or a screw-displacement QT (where the rotation component Q is a simple rotation). [If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either of those, because we can view any QT as a Q&lt;sup&gt;2&lt;/sup&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q&lt;sup&gt;2&lt;/sup&gt;. By the same principle, we can view any QT or Q&lt;sup&gt;2&lt;/sup&gt; as an isoclinic (equi-angled) Q&lt;sup&gt;2&lt;/sup&gt; by appropriate choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} That is to say, Coxeter's relation is a mathematical statement of the principle of relativity, on group-theoretic grounds.{{Efn|Notice that Coxeter's relation correctly captures the limits to relativity, in that we can only exchange the translation (T) for ''one'' of the two rotations (Q). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation up to uncertainty, and can always also distinguish the direction and velocity of his own proper time arrow.}}] Every enantiomorphous transformation in 4-space (reversing chirality) is a QRT.{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}|name=transformations}} It should be known as Thoreau's spherical relativity, since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polytopes in any number of dimensions.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassman and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}}]}}

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== Conclusions==

=== Spherical relativity ===

We began our inquiry by wondering why physical space should be limited to just three dimensions (why ''three''). By visualizing the universe as a Euclidian space of four dimensions, we recognize that relativistic and quantum phenomena are natural consequences of symmetry group operations (including reflections and rotations) in four orthogonal dimensions. We should not then be surprised to see that the universe does not have just four dimensions, either. Physical space must bear as many dimensions as we need to ascribe to it, though the distinct phenomena for which we find a need to do so, in order to explain them, seem to be fewer and fewer as we consider higher and higher dimensions. To laws of physics generally, such as the principle of relativity in particular, we should always append the phrase &quot;in Euclidean spaces of any number of dimensions&quot;. Laws of physics should operate in any flat Euclidean space &lt;math&gt;R^n&lt;/math&gt; and in its corresponding spherical space &lt;math&gt;S^n&lt;/math&gt;.

The first and simplest sense in which we are forced to contemplate a fifth dimension is to accommodate our normal idea of time. Just as Einstein was forced to admit time as a dimension, in his four-dimensional spacetime of three spatial dimensions plus time, for some purposes we require a fifth time dimension to accompany our four spatial dimensions, when our purpose is orthogonal to (in the sense of independent of) the four spatial dimensions. For example, if we theorize that we observe a finite homogeneous universe, and that it is a Euclidean 4-space overall, we may prefer not to have to identify any distinct place within that 4-space as the center where the universe began in a big bang. To avoid having to pick a distinct place as the center of the universe, our model of it must be expanded, at least to be a ''spherical'' 4-dimensional space with the fifth radial dimension as time. Essentially, we require the fifth dimension in order to make our homogeneous 4-space finite, by wrapping it around into a 4-sphere. But perhaps we can still resist admitting the fifth radial dimension as a full-fledged Euclidean spatial dimension, at least so long as we have not observed how any naturally occurring object configurations are best described as 5-polytopes.

One phenomenon which resists explanation in a space of just four dimensions is the propagation of light in a vacuum. The propagation of mass-carrying particles is explained as the consequence of their rotations in closed, curved spaces (3-spheres) of finite size, moving through four-dimensional Euclidean space at a universal constant speed, the speed of light. But an apparent paradox remains that light must seemingly propagate through four-dimensional Euclidean space at more than the speed of light. From a five-dimensional viewpoint, this apparent paradox can be resolved, and in retrospect it is clear how massless particles can translate through four-dimensional space at twice the speed constant, since they are not simultaneously rotating.

Another phenomenon justifying a five-dimensional view of space is the relation between the the 5-cell proton and the 16-cell neutron (the 4-simplex and 4-orthoplex polytopes). Their indirect relationship can be observed in the 4-600-point polytope (the 120-cell), and in its 11-cells,{{Sfn|Christie|2024}} but it is only directly observed (absent a 120-cell) in a five-dimensional reference frame.

=== Nuclear geometry ===
We have seen how isoclinic rotations (Clifford displacements) relate the orbits in the atomic nucleus to each other, just as they relate the regular convex 4-polytopes to each other, in a sequence of nested objects of increasing complexity. We have identified the proton as a  5-point, 5-cell 4-simplex 𝜶&lt;sub&gt;4&lt;/sub&gt;, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽&lt;sub&gt;4&lt;/sub&gt;, and the shell of the atomic nucleus as a 24-point 24-cell. As Coxeter noted, that unique 24-point object stands quite alone in four dimensions, having no analogue above or below.

=== Atomic geometry ===
I'm on a plane flying to Eugene to visit Catalin, we'll talk after I arrive. I've been working on both my unpublished papers, the one going put for pre-publication review soon about 4D geometry, and the big one not going out soon about the 4D sun, 4D atoms, and 4D galaxies and n-D universe. I'vd just added the following paragraph to that big paper:

Atomic geometry

The force binding the protons and neutrons of the nucleus together into a distinct element is specifically an expression of the 11-cell 4-polytope, itself an expression of the pyritohedral symmetry, which binds the distinct 4-polytopes to each other, and relates the n-polytopes to their neighbors of different n by dimensional analogy.


flying over mt shasta out my right-side window at the moment, that last text showing &quot;not delivered&quot; yet because there's no wifi on this plane, gazing at that great peak of the world and feeling as if i've just made the first ascent of it

=== Molecular geometry ===
Molecules are 3-dimensional structures that live in the thin film of 3-membrane only one atom thick in most places that is our ordinary space, but since that is a significantly curved 3-dimensional space at the scale of a molecule, the way the molecule's covalent bonds form is influenced by the local curvature in 4-dimensions at that point.

In the water molecule, there is a reason why the hydrogen atoms are attached to the oxygen atom at an angle of 104.45° in 3-dimensional space, and at root it must be the same symmetry that locates any two of the hydrogen proton's five vertices 104.45° apart on a great circle arc of its tiny 3-sphere.

=== Cosmology ===

==== Solar systems ====

===== Stars =====
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===== The Kepler problem =====
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==== Galaxies ====

The spacetime of general relativity is often illustrated as a projection to a curved 2D surface in which large gravitational objects make gravity wells or dimples in the surface. In the Euclidean 4D view of the universe the 3D surface of a large cosmic object such as a galaxy surrounds an empty 4D space, and large gravitational objects within the galaxy must make dimples in its surface. But should we see them as dimples exactly? Would they dimple inwards or outwards? In the spacetime illustrations they are naturally always shown as dimpling downwards, which is somewhat disingenuous, strongly suggesting to the viewer that the reason for gravity is that it flows downhill - the original tautology we are trying to surmount! In the Euclidean 4D galaxy the dimple, if it is one, must be either inward or outward, and which it is matters since the dimple is flying outward at velocity {{mvar|c}}. The galaxy is not collapsing inward. Is a large gravitational mass (such as a star) ''ahead'' of the smaller masses orbiting around it (such as its planets), or is it ''behind'' them, as they fly through 4-space on their Clifford parallel trajectories? The answer is ''both'' of course, because a star is not a dimple, it is a 4-ball, and it dimples the 3D surface both inwards and outwards. It is a thick place in the 3D surface. We should view it as having its gravitational center precisely at the surface of the expanding 3-sphere. 

What is a black hole? It is the hollow four-dimensional space that a galaxy is the three-dimensional surface of.

When we view another galaxy, such as Andromeda, we are seeing that whole galaxy from a distance, the way the moon astronauts looked back at the whole earth. We see our own milky way galaxy from where we are on its surface, the way we see the earth from its surface, except that the earth is solid, but the galaxy is hollow and transparent. We can look across its empty center and see all the other stars also on its surface, including those opposite ours on the far side of its 3-sphere. The thicker band of stars we see in our night sky and identify as the milky way is not our whole galaxy; the majority of the other visible stars also lie in our galaxy. That dense band is not thicker and brighter than other parts of our galaxy because it lies toward a dense galactic center (our galaxy has an empty center), but for exactly the opposite reason: those apparently more thickly clustered stars lie all around us on the galaxy's surface, in the nearest region of space surrounding us. They appear to be densely packed only because we are looking at them &quot;edge on&quot;. Actually, we are looking into this nearby apparently dense region ''face on'', not edge on, because we are looking at a round sphere of space surrounding us, not a disk. In contrast, stars in our galaxy outside that bright band lie farther off from us, across the empty center of the galaxy, and we see them spread out as they actually are, instead of &quot;edge on&quot; so they appear to be densely clustered. The &quot;dense band&quot; covers only an equatorial band of the night sky instead of all the sky, because when we look out into the four-dimensional space around us, we can see stars above and below our three-dimensional hyperplane in our four-dimensional space. Everything in our solar system lies in our hyperplane, and the nearby stars around us in our galaxy are near our hyperplane (just slightly below it). All the other, more distant stars in our galaxy are also below our hyperplane. We can see objects outside our galaxy, such as other galaxies, both above and below our hyperplane. We can see all around us above our hyperplane (looking up from the galactic surface into the fourth dimension), and all around us below our hyperplane (looking down through our transparent galaxy and out the other side).

== Revolutions ==
The original Copernican revolution displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the stars remaining on a fixed sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

In such fashion the Euclidean four-dimensional viewpoint initially lends itself to a big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the stars need not be equidistant from a single origin in time, any more than they all lie in the same galaxy, equidistant from its center in space. The expanding sphere of matter on the surface of which we find ourselves living might be one of many such spheres, with their big bang origins occurring at distinct times and places in the 4-dimensional universe.

When we look up at the heavens, we have no obvious way of knowing whether the space we are looking into is a curved 3-spherical one or a flat 4-space. In this work we suggest a theory of how light travels that says we can see into all four dimensions, and so when we look up at night we see cosmological objects distributed in 4-dimensional space, and not all located on our own 3-spherical membrane. The view from our solar system suggests that our galaxy is its own hollow 3-sphere, and that galaxies generally are single roughly spherical 3-membranes, with the smaller objects within them all lying on that same 3-spherical surface, equidistant from the galaxy center in 4-space. 

The Euclidean four-dimensional viewpoint requires that all mass-carrying objects are in motion at constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Since their paths away from their origin are not straight lines but various helical isoclines, their 3-sphere will be expanding radially at slightly less than the constant velocity &lt;math&gt;c&lt;/math&gt;. The view from our solar system does ''not'' suggest that each galaxy is its own distinct 3-sphere expanding at this great rate; rather, the standard theory has been that the entire observable universe is expanding from a single big bang origin in time. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also allows theories which require no single origin point in space and time.

These are the voyages of starship Earth, to boldly go where no one has gone before. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't slowed down since.

== Origins of the theory ==
Einstein himself was one of the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean sphere, in what was narrowly the first written articulation of the principle of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below). Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that formulation of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from his perspective; the forthshortenings, clock desynchronizations and other perceptual effects it predicts are exact calculations of actual perspective effects; but space is actually a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four dimensions.''

The Euclidean 4-dimensional theory differs from the standard theory in being a description of the physical universe in terms of a geometry of four or more orthogonal spatial dimensions, rather than in the standard theory's terms of the [[w:Minkowski spacetime|Minkowski spacetime]] geometry (in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions). The invention of geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years. It was first worked out by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] around 1850. Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''polyscheme'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he discovered all the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the six convex regular polyschemes which can be constructed in a space of four dimensions (a set analogous to the five [[w:Platonic solid|Platonic solids]] in three dimensional space). Thus he was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover all its astonishing regular objects. Because most of his work remained almost completely unknown until it was published posthumously in 1901, other researchers had more than fifty years to rediscover the regular polyschemes, and competing terms were coined; today [[W:Alicia Boole Stott|Alicia Boole Stott]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme''.{{Efn|Today Schläfli's original ''polyscheme'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}}

== Boundaries ==
&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schlafli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it, is that there ''is'' a boundary between three and four dimensions. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our world apparently only three dimensional? Why would it have ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schlafli mapped? What is the nature of the boundary which confines us to just three? 

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way by receiving light signals that traveled to us on straight lines through it. The reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creates, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not surprise us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schlafli discovered something else: all the astonishing regular objects that exist in higher dimensions. So this conception now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and not a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation?

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that our universe is properly a Euclidean space of four orthogonal spatial dimensions. Others will have to work out the physics and do the math, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|radius={{radic|2}}|columns=9}}

== Notes ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are 4-dimensionally circular, but not all isoclines on 3-manifolds in 4-space are perfectly circular.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point.{{Sfn|Tyrrell|Semple|1971|loc=§3. Clifford's original definition of parallelism|pp=5-6}} A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the 2-sphere will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect; various sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. Perhaps the simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles.{{Efn|name=six orthogonal planes of the Cartesian basis}} Each completely orthogonal pair is Clifford parallel. The two circles cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 3-sphere.{{Efn|name=only some Clifford parallels are orthogonal}} Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]].|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Notelist|40em}}

== Citations ==
{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

{{Reflist|40em}}

== References ==
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** (Paper 3) H.S.M. Coxeter, ''Two aspects of the regular 24-cell in four dimensions''
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* {{Cite journal|last1=Perez-Gracia|first1=Alba|last2=Thomas|first2=Federico|date=2017|title=On Cayley's Factorization of 4D Rotations and Applications|url=https://upcommons.upc.edu/bitstream/handle/2117/113067/1749-ON-CAYLEYS-FACTORIZATION-OF-4D-ROTATIONS-AND-APPLICATIONS.pdf|journal=Adv. Appl. Clifford Algebras|volume=27|pages=523–538|doi=10.1007/s00006-016-0683-9|hdl=2117/113067|s2cid=12350382|hdl-access=free}}
* {{Cite arXiv | eprint=1903.06971 | last=Copher | first=Jessica | year=2019 | title=Sums and Products of Regular Polytopes' Squared Chord Lengths | class=math.MG }}
* {{Cite thesis|url= http://resolver.tudelft.nl/uuid:dcffce5a-0b47-404e-8a67-9a3845774d89 |title=Symmetry groups of regular polytopes in three and four dimensions|last=van Ittersum |first=Clara|year=2020|publisher=[[W:Delft University of Technology|Delft University of Technology]]}}
* {{cite arXiv|last1=Kim|first1=Heuna|last2=Rote|first2=G.|date=2016|title=Congruence Testing of Point Sets in 4 Dimensions|class=cs.CG|eprint=1603.07269}}
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* {{Cite book|title=Generalized Clifford parallelism|last1=Tyrrell|first1=J. A.|last2=Semple|first2=J.G.|year=1971|publisher=[[W:Cambridge University Press|Cambridge University Press]]|url=https://archive.org/details/generalizedcliff0000tyrr|isbn=0-521-08042-8}}
* {{Cite journal | last1=Mamone|first1=Salvatore | last2=Pileio|first2=Giuseppe | last3=Levitt|first3=Malcolm H. | year=2010 | title=Orientational Sampling Schemes Based on Four Dimensional Polytopes | journal=Symmetry | volume=2 | pages=1423-1449 | doi=10.3390/sym2031423 }}
* {{Cite journal|last=Dorst|first=Leo|title=Conformal Villarceau Rotors|year=2019|journal=Advances in Applied Clifford Algebras|volume=29|issue=44|url=https://doi.org/10.1007/s00006-019-0960-5}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}}
*{{Citation | last=Goucher | first=A.P. | title=Spin groups | date=19 November 2019 | journal=Complex Projective 4-Space | url=https://cp4space.hatsya.com/2012/11/19/spin-groups/ }}
* {{Citation|last=Christie|first=David Brooks|author-link=User:Dc.samizdat|year=2024|title=A symmetrical arrangement of 120 11-cells|title-link=User:Dc.samizdat/A symmetrical arrangement of 120 11-cells|journal=Wikiversity}}
{{Refend}}</text>
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      <text bytes="102082" sha1="9fak7yj4enqxnqzzjqav9snu8h8v9ey" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|June 2023 - November 2024}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Atoms are 4-polytopes, and stars are 4-balls of atomic plasma. A galaxy is a hollow 3-sphere with these objects distributed on its surface. The black hole at its center is the 4-ball of empty space it surrounds. The observable universe of galaxies may be visualized as a 4-sphere expanding radially from an origin point at velocity &lt;math&gt;c&lt;/math&gt;, the propagation speed of light through 3-space, also the invariant velocity of mass-carrying objects through 4-space. The propagation speed of light through 4-space &lt;math&gt;c_4&lt;/math&gt; is &lt;math&gt;c &lt; c_4 &lt; 2c&lt;/math&gt;. This view is compatible with the theories of special and general relativity, and with the quantum mechanical atomic theory. It explains those theories as expressions of intrinsic symmetries.&lt;/blockquote&gt;

== Symmetries ==
It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway|Burgiel|Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s.{{Efn|[[W:Coxeter group|Coxeter theory]] is for geometry what Noether's theorem is for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that obey the principle of relativity and correspond to distinct symmetry groups.}} Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. As I understand [[W:Coxeter group|Coxeter group]] theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic rather than algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional objects, and nature can be understood in terms of their [[W:group action|group actions]], including centrally [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]].

== The geometry of the atomic nucleus ==

In [[W:Euclidean 4-space|Euclidean four dimensional space]], an [[W:atomic nucleus|atomic nucleus]] is a [[24-cell]], the regular 4-polytope with [[W:Coxeter group#Symmetry groups of regular polytopes|𝔽&lt;sub&gt;4&lt;/sub&gt; symmetry]]. Nuclear shells are concentric [[W:3-sphere|3-sphere]]s occupied (fully or partially) by the orbits of this 24-point [[#The 6 regular convex 4-polytopes|regular convex 4-polytope]]. An actual atomic nucleus is a rotating four dimensional object. It is not a ''rigid'' rotating 24-cell, it is a kinematic one, because the nucleus of an actual atom of any [[W:nucleon number|nucleon number]] contains a distinct number of orbiting vertices which may be in different isoclinic rotational orbits. These moving vertices never describe a static 24-cell at any single instant in time, though their orbits do all the time. The physical configuration of the nucleus as a 24-cell can be reduced to the [[W:kinematics|kinematics]] of the orbits of its constituents. The geometry of the atomic nucleus is therefore strictly [[W:Euclidean geometry#19th century|Euclidean]] in four dimensional space.

=== Rotations ===
The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways (like coins flipping) into each other's central planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one or another of the parallel planes of rotation, so all of them move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out.

This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a precise [[24-cell|detailed description]] enabling the reader to visualize it runs to many pages and illustrations, with many accompanying pages of explanatory notes on basic phenomena that arise only in 4-dimensional space: [[24-cell#Squares|completely orthogonal planes]], [[24-cell#Hexagons|Clifford parallelism]] and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Helical hexagrams and their isoclines|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a surprise. [[#The 6 regular convex 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120, and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (generally), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It is much harder for us to visualize, because the only way we can experience it is in our imaginations; we have no body of ''sensory'' experience in 4-dimensional space to draw upon.

For that reason, descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case. [[W:Kinematics|Kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rigid 24-cell. 

To begin with, when we examine the individual parts of the rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertices just once, and no point-object colliding with any other at any time.

That is still an example of a rigid object in a single distinct isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing the characteristic rotation of the 24-cell. But we can also imagine ''combining'' distinct rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible without collisions? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore questions of this kind of [[W:kinematics|kinematics]], and where dynamic stabilites arise, of [[W:kinetics|kinetics]].

=== Isospin ===
A [[W:Nucleon|nucleon]] is a [[W:proton|proton]] or a [[W:neutron|neutron]]. The proton carries a positive net [[W:Electric charge|charge]], and the neutron carries a zero net charge. The proton's [[W:Mass|mass]] is only about 0.13% less than the neutron's, and since they are observed to be identical in other respects, they can be viewed as two states of the same nucleon, together forming an isospin doublet ({{nowrap|''I'' {{=}} {{sfrac|1|2}}}}). In isospin space, neutrons can be transformed into protons and conversely by actions of the [[W:SU(2)|SU(2)]] symmetry group. In nature, protons are very stable (the most stable particle known); a proton and a neutron are a stable nuclide; but free neutrons decay into protons in about 10 or 15 seconds.

According to the [[W:Noether theorem|Noether theorem]], [[W:Isospin|isospin]] is conserved with respect to the [[W:strong interaction|strong interaction]].&lt;ref name=Griffiths2008&gt;{{cite book |author=Griffiths, David J. |title=Introduction to Elementary Particles |edition=2nd revised |publisher=WILEY-VCH |year=2008 |isbn=978-3-527-40601-2}}&lt;/ref&gt;{{rp|129–130}} Nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space.

Isospin was introduced as a concept in 1932 by [[W:Werner Heisenberg|Werner Heisenberg]],&lt;ref&gt;
{{cite journal
 |last=Heisenberg |first=W. |author-link=W:Werner Heisenberg
 |year=1932
 |title=Über den Bau der Atomkerne
 |journal=[[W:Zeitschrift für Physik|Zeitschrift für Physik]]
 |volume=77 |issue=1–2 |pages=1–11
 |doi=10.1007/BF01342433
 |bibcode = 1932ZPhy...77....1H
 |s2cid=186218053
 |language=de}}&lt;/ref&gt; well before the 1960s development of the [[W:quark model|quark model]], to explain the symmetry of the proton and the then newly discovered neutron. Heisenberg introduced the concept of another conserved quantity that would cause the proton to turn into a neutron and vice versa. In 1937, [[W:Eugene Wigner|Eugene Wigner]] introduced the term &quot;isospin&quot; to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.&lt;ref&gt;
{{cite journal
 |last=Wigner |first=E. |author-link=W:Eugene Wigner
 |year=1937
 |title=On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei
 |journal=[[W:Physical Review|Physical Review]]
 |volume=51
 |pages=106–119
 |doi=10.1103/PhysRev.51.106
 |bibcode = 1937PhRv...51..106W
 |issue=2
}}&lt;/ref&gt; Similar to a spin-1/2 particle, which has two states, protons and neutrons were said to be of isospin 1/2. The proton and neutron were then associated with different isospin projections ''I''&lt;sub&gt;3&lt;/sub&gt;&amp;nbsp;=&amp;nbsp;+1/2 and −1/2 respectively.

Isospin is a different kind of rotation entirely than the ordinary spin which objects undergo when they rotate in three-dimensional space. Isospin does not correspond to a [[W:Rotations in 4-dimensional Euclidean space#Simple rotations|simple rotation]] in any space (of any number of dimensions). However, it does seem to correspond exactly to an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]] in a Euclidean space of four dimensions. Isospin space resembles the [[W:3-sphere|3-sphere]], the [[W:Elliptical space#Elliptic space (the 3D case)|curved 3-dimensional space]] that is the surface of a [[W:4-ball (mathematics)#In Euclidean space|4-dimensional ball]].

=== Spinors ===
[[File:Spinor on the circle.png|thumb|upright=1.5|A spinor visualized as a vector pointing along the [[W:Möbius band|Möbius band]], exhibiting a sign inversion when the circle (the &quot;physical system&quot;) is continuously rotated through a full turn of 360°.]][[W:Spinors|Spinors]] are [[W:representation of a Lie group|representations]] of a [[W:spin group|spin group]], which are [[W:Double covering group|double cover]]s of the [[W:special orthogonal group|special orthogonal groups]]. The spin group Spin(4) is the double cover of [[W:SO(4)|SO(4)]], the group of rotations in 4-dimensional Euclidean space. [[600-cell#Fibrations of isocline polygrams|Isoclines]], the helical geodesic paths followed by points under isoclinic rotation, correspond to spinors representing Spin(4).

Spinors can be viewed as the &quot;square roots&quot; of [[W:Section (fiber bundle)|cross sections]] of [[W:vector bundle|vector bundle]]s; in this correspondence, a fiber bundle of isoclines (of a distinct isoclinic rotation) is a cross section (inverse bundle) of a fibration of great circles (in the invariant planes of that rotation).

A spinor can be visualized as a moving vector on a Möbius strip which transforms to its negative when continuously rotated through 360°, just as [[24-cell#Helical hexagrams and their isoclines|an isocline can be visualized as a Möbius strip]] winding twice around the 3-sphere, during which [[24-cell#Isoclinic rotations|720° isoclinic rotation]] the rigid 4-polytope turns itself inside-out twice.{{Sfn|Goucher|2019|loc=Spin Groups}} Under isoclinic rotation, a rigid 4-polytope is an isospin-1/2 object with two states.

=== Isoclinic rotations in the nucleus ===
Isospin is regarded as a symmetry of the strong interaction under the [[W:Group action (mathematics)|action]] of the [[W:Lie group|Lie group]] [[W:SU(2)|SU(2)]], the two [[W:eigenstate|states]] being the [[W:Up quark|up flavour]] and [[W:Down quark|down flavour]]. A 360° isoclinic rotation of a rigid [[W:nuclide|nuclide]] would transform its protons into neutrons and vice versa, exchanging the up and down flavours of their constituent [[W:quarks|quarks]], by turning the nuclide and all its parts inside-out (or perhaps we should say upside-down). Because we never observe this, we know that the nucleus is not a ''rigid'' polytope undergoing isoclinic rotation.

If the nucleus ''were'' a rigid object, nuclides that were isospin-rotated 360° would be isoclinic mirror images of each other, isospin +1/2 and isospin −1/2 states of the whole nucleus. We don't see whole nuclides rotating as a rigid object, but considering what would happen if they ''were'' rigid tells us something about the geometry we must expect inside the nucleons. One way that an isospin-rotated neutron could become a proton would be if the up quark and down quark were a left and right mirror-image pair of the same object; exchanging them in place would turn each down-down-up neutron into an up-up-down proton. But the case cannot be quite that simple, because the up quark and the down quark are not mirror-images of the same object: they have very different mass and other incongruities.

Another way an isospin-rotated neutron could be a proton would be if the up and down quarks were asymmetrical kinematic polytopes (not indirectly congruent mirror-images, and not rigid polytopes), rotating within the nucleus in different ''hybrid'' orbits. By that we mean that they may have vertices orbiting in rotations characteristic of more than one 4-polytope, so they may change shape as they rotate. In that case their composites (protons and neutrons) could have a symmetry not manifest in their components, but emerging from their combination.

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=== Hybrid isoclinic rotations ===
The 24-cell has [[24-cell#Isoclinic rotations|its own characteristic isoclinic rotations]] in 4 Clifford parallel hexagonal planes (each intersecting 6 vertices), and also inherits the [[16-cell#Rotations|characteristic isoclinic rotations of its 3 Clifford parallel constituent 16-cells]] in 6 Clifford parallel square planes (each intersecting 4 vertices). The twisted circular paths followed by vertices in these two different kinds of rotation have entirely different geometries. Vertices rotating in hexagonal invariant planes follow [[24-cell#Helical hexagrams and their isoclines|helical geodesic curves whose chords form hexagrams]], and vertices rotating in square invariant planes follow [[24-cell#Helical octagrams and their isoclines|helical geodesic curves whose chords form octagrams]].

In a rigid isoclinic rotation, ''all'' the [[24-cell#Geodesics|great circle polygons]] move, in any kind of rotation. What distinguishes the hexagonal and square isoclinic rotations is the invariant planes of rotation the vertices stay in. The rotation described [[#Rotations|above]] (of 8 vertices rotating in 4 Clifford parallel hexagonal planes) is a single hexagonal isoclinic rotation, not a kinematic or hybrid rotation.

A ''kinematic'' isoclinic rotation in the 24-cell is any subset of the 24 vertices rotating through the same angle in the same time, but independently with respect to the choice of a Clifford parallel set of invariant planes of rotation and the chirality (left or right) of the rotation. A ''hybrid'' isoclinic rotation combines moving vertices from different kinds of isoclinic rotations, characteristic of different regular 4-polytopes. For example, if at least one vertex rotates in a square plane and at least one vertex rotates in a hexagonal plane, the kinematic rotation is a hybrid rotation, combining rotations characteristic of the 16-cell and characteristic of the 24-cell.

As an example of the simplest hybrid isoclinic rotation, consider a 24-cell vertex rotating in a square plane, and a second vertex, initially one 24-cell edge-length distant, rotating in a hexagonal plane. Rotating isoclinically at the same rate, the two moving vertices will never collide where their paths intersect, so this is a ''valid'' hybrid rotation.

To understand hybrid rotations in the 24-cell more generally, visualize the relationship between great squares and great hexagons. The [[24-cell#Squares|18 great squares]] occur as three sets of 6 orthogonal great squares,{{Efn|name=six orthogonal planes of the Cartesian basis}} each [[16-cell#Coordinates|forming a 16-cell]]. The three 16-cells are completely disjoint{{Efn|name=completely disjoint}} and [[24-cell#Clifford parallel polytopes|Clifford parallel]]: each has its own 8 vertices (on 4 orthogonal axes) and its own 24 edges (of length {{radic|2}}).{{Efn|name=three isoclinic 16-cells}} The 18 square great circles are crossed by 16 hexagonal great circles; each [[24-cell#Hexagons|hexagon]] has one axis (2 vertices) in each 16-cell.{{Efn|name=non-orthogonal hexagons}} The two [[24-cell#Triangles|great triangles]] inscribed in each great hexagon (occupying its alternate vertices, with edges that are its {{radic|3}} chords) have one vertex in each 16-cell. Thus ''each great triangle is a ring linking three completely disjoint great squares, one from each of the three completely disjoint 16-cells''.{{Efn|There are four different ways (four different ''fibrations'' of the 24-cell) in which the 8 vertices of the 16-cells correspond by being triangles of vertices {{radic|3}} apart: there are 32 distinct linking triangles. Each ''pair'' of 16-cells forms a tesseract (8-cell).{{Efn|name=three 16-cells form three tesseracts}} Each great triangle has one {{radic|3}} edge in each tesseract, so it is also a ring linking the three tesseracts.|name=great linking triangles}} Isoclinic rotations take the elements of the 4-polytope to congruent [[24-cell#Clifford parallel polytopes|Clifford parallel elements]] elsewhere in the 4-polytope. The square rotations do this ''locally'', confined within each 16-cell: for example, they take great squares to other great squares within the same 16-cell. The hexagonal rotations act ''globally'' within the entire 24-cell: for example, they take great squares to other great squares in ''different'' 16-cells. The [[16-cell#Helical construction|chords of the square rotations]] bind the 16-cells together internally, and the [[24-cell#Helical hexagrams and their isoclines|chords of the hexagonal rotations]] bind the three 16-cells together.

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=== Color ===
When the existence of quarks was suspected in 1964, [[W:Oscar W. Greenberg|Greenberg]] introduced the notion of color charge to explain how quarks could coexist inside some [[W:hadron|hadron]]s in [[W:quark model#The discovery of color|otherwise identical quantum states]] without violating the [[W:Pauli exclusion principle|Pauli exclusion principle]]. The modern concept of [[W:color charge|color charge]] completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [[W:William A. Bardeen|William Bardeen]], [[W:de:Harald Fritzsch|Harald Fritzsch]], and [[W:Murray Gell-Mann|Murray Gell-Mann]].&lt;ref&gt;{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''&lt;sup&gt;0&lt;/sup&gt; decay, and ''e''&lt;sup&gt;+&lt;/sup&gt; ''e''&lt;sup&gt;&amp;minus;&lt;/sup&gt; annihilation |arxiv=hep-ph/0211388 |editor=Gatto, R. |book-title=Scale and conformal symmetry in hadron physics |page=[https://archive.org/details/scaleconformalsy0000unse/page/139 139] |publisher=[[W:John Wiley &amp; Sons|John Wiley &amp; Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}&lt;/ref&gt;&lt;ref&gt;{{cite journal |title=Advantages of the color octet gluon picture |journal=[[W:Physics Letters B|Physics Letters B]] |volume=47 |issue=4 |page=365 |year=1973 |last1=Fritzsch |first1=H. |last2=Gell-Mann |first2=M. |last3=Leutwyler |first3=H. |doi=10.1016/0370-2693(73)90625-4 |bibcode=1973PhLB...47..365F |citeseerx=10.1.1.453.4712}}&lt;/ref&gt;

Color charge is not [[W:electric charge|electric charge]]; the whole point of it is that it is a quantum of something different. But it is related to electric charge, through the way in which the three different-colored quarks combine to contribute fractional quantities of electric charge to a nucleon. As we shall see, color is not really a separate kind of charge at all, but a partitioning of the electric charge into [[24-cell#Clifford parallel polytopes|Clifford parallel subspaces]].

The [[W:Color charge#Red, green, and blue|three different colors]] of quark charge might correspond to three different 16-cells, such as the three disjoint 16-cells inscribed in the 24-cell. Each color might be a disjoint domain in isospin space (the space of points on the 3-sphere).{{Efn|The 8 vertices of each disjoint 16-cell constitute an independent [[16-cell#Coordinates|orthonormal basis for a coordinate reference frame]].}} Alternatively, the three colors might correspond to three different fibrations of the same isospin space: three different ''sequences'' of the same total set of discrete points on the 3-sphere. These alternative possibilities constrain possible representations of the nuclides themselves, for example if we try to represent nuclides as particular rotating 4-polytopes. If the neutron is a (8-point) 16-cell, either of the two color possibilities might somehow make sense as far as the neutron is concerned. But if the proton is a (5-point) 5-cell, only the latter color possibility makes sense, because fibrations (which correspond to distinct isoclinic left-and-right rigid rotations) are the ''only'' thing the 5-cell has three of. Both the 5-cell and the 16-cell have three discrete rotational fibrations. Moreover, in the case of a rigid, isoclinically rotating 4-polytope, those three fibrations always come one-of-a-kind and two-of-a-kind, in at least two different ways. First, one fibration is the set of invariant planes currently being rotated through, and the other two are not. Second, when one considers the three fibrations of each of these 4-polytopes, in each fibration two isoclines carry the left and right rotations respectively, and the third isocline acts simply as a Petrie polygon, the difference between the fibrations being the role assigned to each isocline.

If we associate each quark with one or more isoclinic rotations in which the moving vertices belong to different 16-cells of the 24-cell, and the sign (plus or minus) of the electric charge with the chirality (right or left) of isoclinic rotations generally, we can configure nucleons of three quarks, two performing rotations of one chirality and one performing rotations of the other chirality. The configuration will be a valid kinematic rotation because the completely disjoint 16-cells can rotate independently; their vertices would never collide even if the 16-cells were performing different rigid square isoclinic rotations (all 8 vertices rotating in unison). But we need not associate a quark with a [[16-cell#Rotations|rigidly rotating 16-cell]], or with a single distinct square rotation.

Minimally, we must associate each quark with at least one moving vertex in each of three different 16-cells, following the twisted geodesic isocline of an isoclinic rotation. In the up quark, that could be the isocline of a right rotation; and in the down quark, the isocline of a left rotation. The chirality accounts for the sign of the electric charge (we have said conventionally as +right, −left), but we must also account for the quantity of charge: +{{sfrac|2|3}} in an up quark, and −{{sfrac|1|3}} in a down quark. One way to do that would be to give the three distinct quarks moving vertices of {{sfrac|1|3}} charge in different 16-cells, but provide up quarks with twice as many vertices moving on +right isoclines as down quarks have vertices moving on −left isoclines (assuming the correct chiral pairing is up+right, down−left).

Minimally, an up quark requires two moving vertices (of the up+right chirality).{{Efn|Two moving vertices in one quark could belong to the same 16-cell. A 16-cell may have two vertices moving in the same isoclinic square (octagram) orbit, such as an antipodal pair (a rotating dipole), or two vertices moving in different square orbits of the same up+right chirality.{{Efn|There is only one [[16-cell#Helical construction|octagram orbit]] of each chirality in each fibration of the 16-cell, so two octagram orbits of the same chirality cannot be Clifford parallel (part of the same distinct rotation). Two vertices right-moving on different octagram isoclines in the same 16-cell is a combination of two distinct rotations, whose isoclines will intersect: a kinematic rotation. It can be a valid kinematic rotation if the moving vertices will never pass through a point of intersection at the same time. Octagram isoclines pass through all 8 vertices of the 16-cell, and all eight isoclines (the left and right isoclines of four different fibrations) intersect at ''every'' vertex.}} However, the theory of [[W:Color confinement|color confinement]] may not require that two moving vertices in one quark belong to the same 16-cell; like the moving vertices of different quarks, they could be drawn from the disjoint vertex sets of two different 16-cells.}} Minimally, a down quark requires one moving vertex (of the down−left chirality). In these minimal quark configurations, a proton would have 5 moving vertices and a neutron would have 4.

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=== Nucleons ===
[[File:Symmetrical_5-set_Venn_diagram.svg|thumb|[[W:Branko Grünbaum|Grünbaum's]] rotationally symmetrical 5-set Venn diagram, 1975. It is the [[5-cell]]. Think of it as an [[W:Nuclear magnetic resonance|NMR image]] of the 4-dimensional proton in projection to the plane.]]
The proton is a very stable mass particle. Is there a stable orbit of 5 moving vertices in 4-dimensional Euclidean space? There are few known solutions to the 5-body problem, and fewer still to the [[W:n-body problem|{{mvar|n}}-body problem]], but one is known: the ''central configuration'' of {{mvar|n}} bodies in a space of dimension {{mvar|n}}-1. A [[W:Central configuration|central configuration]] is a system of [[W:Point particle|point masses]] with the property that each mass is pulled by the combined attractive force of the system directly towards the [[W:Center of mass|center of mass]], with acceleration proportional to its distance from the center. Placing three masses in an equilateral triangle, four at the vertices of a regular [[W:Tetrahedron|tetrahedron]], five at the vertices of a regular [[5-cell]], or more generally {{mvar|n}} masses at the vertices of a regular [[W:Simplex|simplex]] produces a central configuration [[W:Central configuration#Examples|even when the masses are not equal]]. In an isoclinic rotation, all the moving vertices orbit at the same radius and the same speed. Therefore if any 5 bodies are orbiting as an isoclinically rotating regular 5-cell (a rigid 4-simplex figure undergoing isoclinic rotation), they maintain a central configuration, describing 5 mutually stable orbits.

Unlike the proton, the neutron is not always a stable particle; a free neutron will decay into a proton. A deficiency of the minimal configurations is that there is no way for this [[W:beta minus decay|beta minus decay]] to occur. The minimal neutron of 4 moving vertices described [[#Color|above]] cannot possibly decay into a proton by losing moving vertices, because it does not possess the four up+right moving vertices required in a proton. This deficiency could be remedied by giving the neutron configuration 8 moving vertices instead of 4: four down−left and four up+right moving vertices. Then by losing 3 down−left moving vertices the neutron could decay into the 5 vertex up-down-up proton configuration.{{Efn|Although protons are very stable, during [[W:stellar nucleosynthesis|stellar nucleosynthesis]] two H&lt;sub&gt;1&lt;/sub&gt; protons are fused into an H&lt;sub&gt;2&lt;/sub&gt; nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus &quot;decay&quot;]] of a proton into a neutron is actually the result of a rare high-energy collision between the two protons, in which a neutron is constructed. With respect to our nucleon configurations of moving vertices, it has to be explained as the conversion of two 5-point 5-cells into a 5-point 5-cell and an 8-point 16-cell, emitting two decay products of at least 1-point each. Thus it must involve the creation of moving vertices, by the conversion of kinetic energy to point-masses.}} A neutron configuration of 8 moving vertices could occur as the 8-point 16-cell, the second-smallest regular 4-polytope after the 5-point 5-cell (the hypothesized proton configuration).

It is possible to double the neutron configuration in this way, without destroying the charge balance that defines the nucleons, by giving down quarks three moving vertices instead of just one: two −left vertices and one +right vertex. The net charge on the down quark remains −{{sfrac|1|3}}, but the down quark becomes heavier (at least in vertex count) than the up quark, as in fact its mass is measured to be.

A nucleon's quark configuration is only a partial specification of its properties. There is much more to a nucleon than what is contained within its three quarks, which contribute only about 1% of the nucleon's energy. The additional 99% of the nucleon mass is said to be associated with the force that binds the three quarks together, rather than being intrinsic to the individual quarks separately. In the case of the proton, 5 moving vertices in the stable orbits of a central configuration (in one of the [[5-cell#Geodesics and rotations|isoclinic rotations characteristic of the regular 5-cell]]) might be sufficient to account for the stability of the proton, but not to account for most of the proton's energy. It is not the point-masses of the moving vertices themselves which constitute most of the mass of the nucleon; if mass is a consequence of geometry, we must look to the larger geometric elements of these polytopes as their major mass contributors. The quark configurations are thus incomplete specifications of the geometry of the nucleons, predictive of only some of the nucleon's properties, such as charge.{{Efn|Notice that by giving the down quark three moving vertices, we seem to have changed the quark model's prediction of the proton's number of moving vertices from 5 to 7, which would be incompatible with our theory that the proton configuration is a rotating regular 5-cell in a central configuration of 5 stable orbits. Fortunately, the actual quark model has nothing at all to say about moving vertices, so we may choose to regard that number as one of the geometric properties the quark model does not specify.}} In particular, they do not account for the forces binding the nucleon together. Moreover, if the rotating regular 5-cell is the proton configuration and the rotating regular 16-cell is the neutron configuration, then a nucleus is a complex of rotating 5-cells and 16-cells, and we must look to the geometric relationship between those two very different regular 4-polytopes for an understanding of the nuclear force binding them together.

The most direct [[120-cell#Relationships among interior polytopes|geometric relationship among stationary regular 4-polytopes]] is the way they occupy a common 3-sphere together. Multiple 16-cells of equal radius can be compounded to form each of the larger regular 4-polytopes, the 8-cell, 24-cell, 600-cell, and 120-cell, but it is noteworthy that multiple regular 5-cells of equal radius cannot be compounded to form any of the other 4-polytopes except the largest, the 120-cell. The 120-cell is the unique intersection of the regular 5-cell and 16-cell: it is a compound of 120 regular 5-cells, and also a compound of 75 16-cells. All regular 4-polytopes except the 5-cell are compounds of 16-cells, but none of them except the largest, the 120-cell, contains any regular 5-cells. So in any compound of equal-radius 16-cells which also contains a regular 5-cell, whether that compound forms some single larger regular 4-polytope or does not, no two of the regular 5-cell's five vertices ever lie in the same 16-cell. So the geometric relationship between the regular 5-cell (our proton candidate) and the regular 16-cell (our neutron candidate) is quite a distant one: they are much more exclusive of each other's elements than they are distantly related, despite their complementary three-quark configurations and other similarities as nucleons. The relationship between a regular 5-cell and a regular 16-cell of equal radius is manifest only in the 120-cell, the most complex regular 4-polytope, which [[120-cell#Geometry|uniquely embodies all the containment relationships]] among all the regular 4-polytopes and their elements.

If the nucleus is a complex of 5-cells (protons) and 16-cells (neutrons) rotating isoclinically around a common center, then its overall motion is a hybrid isoclinic rotation, because the 5-cell and the 16-cell have different characteristic isoclinic rotations, and they have no isoclinic rotation in common.{{Efn|The regular 5-cell does not occur inscribed in any other regular 4-polytope except one, the 600-vertex 120-cell. No two of the 5 vertices of a regular 5-cell can be vertices of the same 16-cell, 8-cell, 24-cell, or 600-cell. The isoclinic rotations characteristic of the regular 5-cell maintain the separation of its 5 moving vertices in 5 disjoint Clifford-parallel subspaces at all times. The [[16-cell#Rotations|isoclinic rotation characteristic of the 16-cell]] maintains the separation of its 8 moving vertices in 2 disjoint Clifford-parallel subspaces (completely orthogonal great square planes) at all times. Therefore, in any hybrid rotation of a concentric 5-cell and 16-cell, at most one 5-cell subspace (containing 1 vertex) might be synchronized with one 16-cell subspace (containing 4 vertices), such that the 1 + 4 vertices they jointly contain occupy the same moving subspace continually, forming a rigid 5-vertex polytope undergoing some kind of rotation. If in fact it existed, this 5-vertex rotating rigid polytope would not be [[5-cell#Geometry|not a 5-cell, since 4 of its vertices are coplanar]]; it is not a 4-polytope but merely a polyhedron, a [[W:square pyramid|square pyramid]].}}

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=== Nuclides ===

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=== Quantum phenomena ===

The Bell-Kochen-Specker (BKS) theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a space of three or more dimensions can be given by exhibiting a finite set of lines through the origin that cannot each be colored black or white in such a way that (i) no two orthogonal lines are both black, and (ii) not all members of a set of ''d'' mutually orthogonal lines are white.{{Efn|&quot;The Bell-Kochen-Specker theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a Hilbert space of dimension d ≥ 3 can be given by exhibiting a finite set of rays [9] that cannot each be assigned the value 0 or 1 in such a way that (i) no two orthogonal rays are both assigned the value 1, and (ii) not all members of a set of d mutually orthogonal rays are assigned the value 0.&quot;{{Sfn|Waegell|Aravind|2009|loc=2. The Bell-Kochen-Specker (BKS) theorem}}|name=BKS theorem}}

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=== Motion ===
What does it mean to say that an object moves through space? Coxeter group theory provides precise answers to questions of this kind. A rigid object (polytope) moves by distinct transformations, changing itself in each discrete step into a congruent object in a different orientation and position.

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== Galilean relativity in a space of four orthogonal dimensions ==

Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions.

General relativity is just Galilean relativity in a general space of four orthogonal dimensions, e.g. Euclidean 4-space &lt;math&gt;R^4&lt;/math&gt;, spherical 4-space &lt;math&gt;S^4&lt;/math&gt;, or any orthogonal 4-manifold.

Light is just reflection. Gravity (and all force) is just rotation. Both motions are just group actions, expressions of intrinsic symmetries. That is all of physics.

Every observer properly sees himself as stationary and the universe as a sphere with himself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and it can be measured by the observer as the speed of light.

=== Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions ===
Perspective effects occur because each observer's ordinary 3-dimensional space is only a curved manifold embedded in 4-dimensional Euclidean space, and its curvature complicates the calculations for him (e.g., he sometimes requires Lorentz transformations). But if  all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) except when you want to calculate a projection, or a shadow, that is, how things will appear from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} The universe really has four spatial dimensions, and space and time behave just as they do in classical 3-vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a spacetime to explain 4-dimensional perspective effects at high velocities, because 4-space is already spatially 4-dimensional, and those perspective effects fall out of the 4-dimensional Pythagorean theorem naturally, just as perspective does in three dimensions. The universe is only strange in the ways the Euclidean fourth dimension is strange; but that does hold many surprises for us. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way that 3-space is much more interesting than 2-space. But all Euclidean spaces are dimensionally analogous. Dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries.

=== General relativity is just Galilean relativity in a general space of four orthogonal dimensions ===
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=== Physics ===
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=== Thoreau's spherical relativity ===
Every observer may properly see himself as stationary and the universe as a 4-sphere with himself at the center observing it, perceptually equidistant from all points on its surface, including his own ''physical'' location which is one of those surface points, distinguished to him but not the center of anything. This statement of the principle of relativity is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in curved, non-Euclidean spacetime, and Coxeter's relativity of orthogonal group actions in Euclidean spaces of any number of dimensions.{{Efn|Let Q denote a rotation, R a reflection, T a translation, and let Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T denote a product of several such transformations, all commutative with one another. Then RT is a glide-reflection (in two or three dimensions), QR is a rotary-reflection, QT is a screw-displacement, and Q&lt;sup&gt;2&lt;/sup&gt; is a double rotation (in four dimensions). Every orthogonal transformation is expressible as
{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt;&lt;br&gt;
where 2''q'' + ''r'' ≤ ''n'', the number of dimensions. Transformations involving a translation are expressible as
{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T&lt;br&gt;
where 2''q'' + ''r'' + 1 ≤ ''n''.&lt;br&gt;
For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q&lt;sup&gt;2&lt;/sup&gt;, or a screw-displacement QT (where the rotation component Q is a simple rotation). [If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either of those, because we can view any QT as a Q&lt;sup&gt;2&lt;/sup&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q&lt;sup&gt;2&lt;/sup&gt;. By the same principle, we can view any QT or Q&lt;sup&gt;2&lt;/sup&gt; as an isoclinic (equi-angled) Q&lt;sup&gt;2&lt;/sup&gt; by appropriate choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} That is to say, Coxeter's relation is a mathematical statement of the principle of relativity, on group-theoretic grounds.{{Efn|Notice that Coxeter's relation correctly captures the limits to relativity, in that we can only exchange the translation (T) for ''one'' of the two rotations (Q). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation up to uncertainty, and can always also distinguish the direction and velocity of his own proper time arrow.}}] Every enantiomorphous transformation in 4-space (reversing chirality) is a QRT.{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}|name=transformations}} It should be known as Thoreau's spherical relativity, since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polytopes in any number of dimensions.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassman and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}}]}}

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== Conclusions==

=== Spherical relativity ===

We began our inquiry by wondering why physical space should be limited to just three dimensions (why ''three''). By visualizing the universe as a Euclidian space of four dimensions, we recognize that relativistic and quantum phenomena are natural consequences of symmetry group operations (including reflections and rotations) in four orthogonal dimensions. We should not then be surprised to see that the universe does not have just four dimensions, either. Physical space must bear as many dimensions as we need to ascribe to it, though the distinct phenomena for which we find a need to do so, in order to explain them, seem to be fewer and fewer as we consider higher and higher dimensions. To laws of physics generally, such as the principle of relativity in particular, we should always append the phrase &quot;in Euclidean spaces of any number of dimensions&quot;. Laws of physics should operate in any flat Euclidean space &lt;math&gt;R^n&lt;/math&gt; and in its corresponding spherical space &lt;math&gt;S^n&lt;/math&gt;.

The first and simplest sense in which we are forced to contemplate a fifth dimension is to accommodate our normal idea of time. Just as Einstein was forced to admit time as a dimension, in his four-dimensional spacetime of three spatial dimensions plus time, for some purposes we require a fifth time dimension to accompany our four spatial dimensions, when our purpose is orthogonal to (in the sense of independent of) the four spatial dimensions. For example, if we theorize that we observe a finite homogeneous universe, and that it is a Euclidean 4-space overall, we may prefer not to have to identify any distinct place within that 4-space as the center where the universe began in a big bang. To avoid having to pick a distinct place as the center of the universe, our model of it must be expanded, at least to be a ''spherical'' 4-dimensional space with the fifth radial dimension as time. Essentially, we require the fifth dimension in order to make our homogeneous 4-space finite, by wrapping it around into a 4-sphere. But perhaps we can still resist admitting the fifth radial dimension as a full-fledged Euclidean spatial dimension, at least so long as we have not observed how any naturally occurring object configurations are best described as 5-polytopes.

One phenomenon which resists explanation in a space of just four dimensions is the propagation of light in a vacuum. The propagation of mass-carrying particles is explained as the consequence of their rotations in closed, curved spaces (3-spheres) of finite size, moving through four-dimensional Euclidean space at a universal constant speed, the speed of light. But an apparent paradox remains that light must seemingly propagate through four-dimensional Euclidean space at more than the speed of light. From a five-dimensional viewpoint, this apparent paradox can be resolved, and in retrospect it is clear how massless particles can translate through four-dimensional space at twice the speed constant, since they are not simultaneously rotating.

Another phenomenon justifying a five-dimensional view of space is the relation between the the 5-cell proton and the 16-cell neutron (the 4-simplex and 4-orthoplex polytopes). Their indirect relationship can be observed in the 4-600-point polytope (the 120-cell), and in its 11-cells,{{Sfn|Christie|2024}} but it is only directly observed (absent a 120-cell) in a five-dimensional reference frame.

=== Nuclear geometry ===
We have seen how isoclinic rotations (Clifford displacements) relate the orbits in the atomic nucleus to each other, just as they relate the regular convex 4-polytopes to each other, in a sequence of nested objects of increasing complexity. We have identified the proton as a  5-point, 5-cell 4-simplex 𝜶&lt;sub&gt;4&lt;/sub&gt;, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽&lt;sub&gt;4&lt;/sub&gt;, and the shell of the atomic nucleus as a 24-point 24-cell. As Coxeter noted, that unique 24-point object stands quite alone in four dimensions, having no analogue above or below.

=== Atomic geometry ===
I'm on a plane flying to Eugene to visit Catalin, we'll talk after I arrive. I've been working on both my unpublished papers, the one going put for pre-publication review soon about 4D geometry, and the big one not going out soon about the 4D sun, 4D atoms, and 4D galaxies and n-D universe. I'vd just added the following paragraph to that big paper:

Atomic geometry

The force binding the protons and neutrons of the nucleus together into a distinct element is specifically an expression of the 11-cell 4-polytope, itself an expression of the pyritohedral symmetry, which binds the distinct 4-polytopes to each other, and relates the n-polytopes to their neighbors of different n by dimensional analogy.


flying over mt shasta out my right-side window at the moment, that last text showing &quot;not delivered&quot; yet because there's no wifi on this plane, gazing at that great peak of the world and feeling as if i've just made the first ascent of it

=== Molecular geometry ===
Molecules are 3-dimensional structures that live in the thin film of 3-membrane only one atom thick in most places that is our ordinary space, but since that is a significantly curved 3-dimensional space at the scale of a molecule, the way the molecule's covalent bonds form is influenced by the local curvature in 4-dimensions at that point.

In the water molecule, there is a reason why the hydrogen atoms are attached to the oxygen atom at an angle of 104.45° in 3-dimensional space, and at root it must be the same symmetry that locates any two of the hydrogen proton's five vertices 104.45° apart on a great circle arc of its tiny 3-sphere.

=== Cosmology ===

==== Solar systems ====

===== Stars =====
...

===== The Kepler problem =====
...

==== Galaxies ====

The spacetime of general relativity is often illustrated as a projection to a curved 2D surface in which large gravitational objects make gravity wells or dimples in the surface. In the Euclidean 4D view of the universe the 3D surface of a large cosmic object such as a galaxy surrounds an empty 4D space, and large gravitational objects within the galaxy must make dimples in its surface. But should we see them as dimples exactly? Would they dimple inwards or outwards? In the spacetime illustrations they are naturally always shown as dimpling downwards, which is somewhat disingenuous, strongly suggesting to the viewer that the reason for gravity is that it flows downhill - the original tautology we are trying to surmount! In the Euclidean 4D galaxy the dimple, if it is one, must be either inward or outward, and which it is matters since the dimple is flying outward at velocity {{mvar|c}}. The galaxy is not collapsing inward. Is a large gravitational mass (such as a star) ''ahead'' of the smaller masses orbiting around it (such as its planets), or is it ''behind'' them, as they fly through 4-space on their Clifford parallel trajectories? The answer is ''both'' of course, because a star is not a dimple, it is a 4-ball, and it dimples the 3D surface both inwards and outwards. It is a thick place in the 3D surface. We should view it as having its gravitational center precisely at the surface of the expanding 3-sphere. 

What is a black hole? It is the hollow four-dimensional space that a galaxy is the three-dimensional surface of.

When we view another galaxy, such as Andromeda, we are seeing that whole galaxy from a distance, the way the moon astronauts looked back at the whole earth. We see our own milky way galaxy from where we are on its surface, the way we see the earth from its surface, except that the earth is solid, but the galaxy is hollow and transparent. We can look across its empty center and see all the other stars also on its surface, including those opposite ours on the far side of its 3-sphere. The thicker band of stars we see in our night sky and identify as the milky way is not our whole galaxy; the majority of the other visible stars also lie in our galaxy. That dense band is not thicker and brighter than other parts of our galaxy because it lies toward a dense galactic center (our galaxy has an empty center), but for exactly the opposite reason: those apparently more thickly clustered stars lie all around us on the galaxy's surface, in the nearest region of space surrounding us. They appear to be densely packed only because we are looking at them &quot;edge on&quot;. Actually, we are looking into this nearby apparently dense region ''face on'', not edge on, because we are looking at a round sphere of space surrounding us, not a disk. In contrast, stars in our galaxy outside that bright band lie farther off from us, across the empty center of the galaxy, and we see them spread out as they actually are, instead of &quot;edge on&quot; so they appear to be densely clustered. The &quot;dense band&quot; covers only an equatorial band of the night sky instead of all the sky, because when we look out into the four-dimensional space around us, we can see stars above and below our three-dimensional hyperplane in our four-dimensional space. Everything in our solar system lies in our hyperplane, and the nearby stars around us in our galaxy are near our hyperplane (just slightly below it). All the other, more distant stars in our galaxy are also below our hyperplane. We can see objects outside our galaxy, such as other galaxies, both above and below our hyperplane. We can see all around us above our hyperplane (looking up from the galactic surface into the fourth dimension), and all around us below our hyperplane (looking down through our transparent galaxy and out the other side).

== Revolutions ==
The original Copernican revolution displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the stars remaining on a fixed sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

In such fashion the Euclidean four-dimensional viewpoint initially lends itself to a big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the stars need not be equidistant from a single origin in time, any more than they all lie in the same galaxy, equidistant from its center in space. The expanding sphere of matter on the surface of which we find ourselves living might be one of many such spheres, with their big bang origins occurring at distinct times and places in the 4-dimensional universe.

When we look up at the heavens, we have no obvious way of knowing whether the space we are looking into is a curved 3-spherical one or a flat 4-space. In this work we suggest a theory of how light travels that says we can see into all four dimensions, and so when we look up at night we see cosmological objects distributed in 4-dimensional space, and not all located on our own 3-spherical membrane. The view from our solar system suggests that our galaxy is its own hollow 3-sphere, and that galaxies generally are single roughly spherical 3-membranes, with the smaller objects within them all lying on that same 3-spherical surface, equidistant from the galaxy center in 4-space. 

The Euclidean four-dimensional viewpoint requires that all mass-carrying objects are in motion at constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Since their paths away from their origin are not straight lines but various helical isoclines, their 3-sphere will be expanding radially at slightly less than the constant velocity &lt;math&gt;c&lt;/math&gt;. The view from our solar system does ''not'' suggest that each galaxy is its own distinct 3-sphere expanding at this great rate; rather, the standard theory has been that the entire observable universe is expanding from a single big bang origin in time. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also allows theories which require no single origin point in space and time.

These are the voyages of starship Earth, to boldly go where no one has gone before. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't slowed down since.

== Origins of the theory ==
Einstein himself was one of the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean sphere, in what was narrowly the first written articulation of the principle of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below). Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that formulation of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from his perspective; the forthshortenings, clock desynchronizations and other perceptual effects it predicts are exact calculations of actual perspective effects; but space is actually a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four dimensions.''

The Euclidean 4-dimensional theory differs from the standard theory in being a description of the physical universe in terms of a geometry of four or more orthogonal spatial dimensions, rather than in the standard theory's terms of the [[w:Minkowski spacetime|Minkowski spacetime]] geometry (in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions). The invention of geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years. It was first worked out by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] around 1850. Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''polyscheme'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he discovered all the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the six convex regular polyschemes which can be constructed in a space of four dimensions (a set analogous to the five [[w:Platonic solid|Platonic solids]] in three dimensional space). Thus he was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover all its astonishing regular objects. Because most of his work remained almost completely unknown until it was published posthumously in 1901, other researchers had more than fifty years to rediscover the regular polyschemes, and competing terms were coined; today [[W:Alicia Boole Stott|Alicia Boole Stott]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme''.{{Efn|Today Schläfli's original ''polyscheme'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}}

== Boundaries ==
&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schlafli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it, is that there ''is'' a boundary between three and four dimensions. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our world apparently only three dimensional? Why would it have ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schlafli mapped? What is the nature of the boundary which confines us to just three? 

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way by receiving light signals that traveled to us on straight lines through it. The reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creates, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not surprise us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schlafli discovered something else: all the astonishing regular objects that exist in higher dimensions. So this conception now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and not a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation?

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that our universe is properly a Euclidean space of four orthogonal spatial dimensions. Others will have to work out the physics and do the math, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|radius={{radic|2}}|columns=9}}

== Notes ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are 4-dimensionally circular, but not all isoclines on 3-manifolds in 4-space are perfectly circular.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point.{{Sfn|Tyrrell|Semple|1971|loc=§3. Clifford's original definition of parallelism|pp=5-6}} A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the 2-sphere will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect; various sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. Perhaps the simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles.{{Efn|name=six orthogonal planes of the Cartesian basis}} Each completely orthogonal pair is Clifford parallel. The two circles cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 3-sphere.{{Efn|name=only some Clifford parallels are orthogonal}} Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]].|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Notelist|40em}}

== Citations ==
{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

{{Reflist|40em}}

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{{Refend}}</text>
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{{align|center|dc@samizdat.org}}
{{align|center|June 2023 - November 2024}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Atoms are 4-polytopes, and stars are 4-balls of atomic plasma. A galaxy is a hollow 3-sphere with these objects distributed on its surface. The black hole at its center is the 4-ball of empty space it surrounds. The observable universe of galaxies may be visualized as a 4-sphere expanding radially from an origin point at velocity &lt;math&gt;c&lt;/math&gt;, the propagation speed of light through 3-space, also the invariant velocity of mass-carrying objects through 4-space. The propagation speed of light through 4-space &lt;math&gt;c_4&lt;/math&gt; is &lt;math&gt;c &lt; c_4 &lt; 2c&lt;/math&gt;. This model of the universe is compatible with the theories of special and general relativity, and with the quantum mechanical atomic theory. It explains those theories as expressions of intrinsic symmetries.&lt;/blockquote&gt;

== Symmetries ==
It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway|Burgiel|Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s.{{Efn|[[W:Coxeter group|Coxeter theory]] is for geometry what Noether's theorem is for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that obey the principle of relativity and correspond to distinct symmetry groups.}} Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. As I understand [[W:Coxeter group|Coxeter group]] theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic rather than algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional objects, and nature can be understood in terms of their [[W:group action|group actions]], including centrally [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]].

== The geometry of the atomic nucleus ==

In [[W:Euclidean 4-space|Euclidean four dimensional space]], an [[W:atomic nucleus|atomic nucleus]] is a [[24-cell]], the regular 4-polytope with [[W:Coxeter group#Symmetry groups of regular polytopes|𝔽&lt;sub&gt;4&lt;/sub&gt; symmetry]]. Nuclear shells are concentric [[W:3-sphere|3-sphere]]s occupied (fully or partially) by the orbits of this 24-point [[#The 6 regular convex 4-polytopes|regular convex 4-polytope]]. An actual atomic nucleus is a rotating four dimensional object. It is not a ''rigid'' rotating 24-cell, it is a kinematic one, because the nucleus of an actual atom of any [[W:nucleon number|nucleon number]] contains a distinct number of orbiting vertices which may be in different isoclinic rotational orbits. These moving vertices never describe a static 24-cell at any single instant in time, though their orbits do all the time. The physical configuration of the nucleus as a 24-cell can be reduced to the [[W:kinematics|kinematics]] of the orbits of its constituents. The geometry of the atomic nucleus is therefore strictly [[W:Euclidean geometry#19th century|Euclidean]] in four dimensional space.

=== Rotations ===
The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways (like coins flipping) into each other's central planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one or another of the parallel planes of rotation, so all of them move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out.

This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a precise [[24-cell|detailed description]] enabling the reader to visualize it runs to many pages and illustrations, with many accompanying pages of explanatory notes on basic phenomena that arise only in 4-dimensional space: [[24-cell#Squares|completely orthogonal planes]], [[24-cell#Hexagons|Clifford parallelism]] and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Helical hexagrams and their isoclines|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a surprise. [[#The 6 regular convex 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120, and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (generally), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It is much harder for us to visualize, because the only way we can experience it is in our imaginations; we have no body of ''sensory'' experience in 4-dimensional space to draw upon.

For that reason, descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case. [[W:Kinematics|Kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rigid 24-cell. 

To begin with, when we examine the individual parts of the rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertices just once, and no point-object colliding with any other at any time.

That is still an example of a rigid object in a single distinct isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing the characteristic rotation of the 24-cell. But we can also imagine ''combining'' distinct rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible without collisions? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore questions of this kind of [[W:kinematics|kinematics]], and where dynamic stabilites arise, of [[W:kinetics|kinetics]].

=== Isospin ===
A [[W:Nucleon|nucleon]] is a [[W:proton|proton]] or a [[W:neutron|neutron]]. The proton carries a positive net [[W:Electric charge|charge]], and the neutron carries a zero net charge. The proton's [[W:Mass|mass]] is only about 0.13% less than the neutron's, and since they are observed to be identical in other respects, they can be viewed as two states of the same nucleon, together forming an isospin doublet ({{nowrap|''I'' {{=}} {{sfrac|1|2}}}}). In isospin space, neutrons can be transformed into protons and conversely by actions of the [[W:SU(2)|SU(2)]] symmetry group. In nature, protons are very stable (the most stable particle known); a proton and a neutron are a stable nuclide; but free neutrons decay into protons in about 10 or 15 seconds.

According to the [[W:Noether theorem|Noether theorem]], [[W:Isospin|isospin]] is conserved with respect to the [[W:strong interaction|strong interaction]].&lt;ref name=Griffiths2008&gt;{{cite book |author=Griffiths, David J. |title=Introduction to Elementary Particles |edition=2nd revised |publisher=WILEY-VCH |year=2008 |isbn=978-3-527-40601-2}}&lt;/ref&gt;{{rp|129–130}} Nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space.

Isospin was introduced as a concept in 1932 by [[W:Werner Heisenberg|Werner Heisenberg]],&lt;ref&gt;
{{cite journal
 |last=Heisenberg |first=W. |author-link=W:Werner Heisenberg
 |year=1932
 |title=Über den Bau der Atomkerne
 |journal=[[W:Zeitschrift für Physik|Zeitschrift für Physik]]
 |volume=77 |issue=1–2 |pages=1–11
 |doi=10.1007/BF01342433
 |bibcode = 1932ZPhy...77....1H
 |s2cid=186218053
 |language=de}}&lt;/ref&gt; well before the 1960s development of the [[W:quark model|quark model]], to explain the symmetry of the proton and the then newly discovered neutron. Heisenberg introduced the concept of another conserved quantity that would cause the proton to turn into a neutron and vice versa. In 1937, [[W:Eugene Wigner|Eugene Wigner]] introduced the term &quot;isospin&quot; to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.&lt;ref&gt;
{{cite journal
 |last=Wigner |first=E. |author-link=W:Eugene Wigner
 |year=1937
 |title=On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei
 |journal=[[W:Physical Review|Physical Review]]
 |volume=51
 |pages=106–119
 |doi=10.1103/PhysRev.51.106
 |bibcode = 1937PhRv...51..106W
 |issue=2
}}&lt;/ref&gt; Similar to a spin-1/2 particle, which has two states, protons and neutrons were said to be of isospin 1/2. The proton and neutron were then associated with different isospin projections ''I''&lt;sub&gt;3&lt;/sub&gt;&amp;nbsp;=&amp;nbsp;+1/2 and −1/2 respectively.

Isospin is a different kind of rotation entirely than the ordinary spin which objects undergo when they rotate in three-dimensional space. Isospin does not correspond to a [[W:Rotations in 4-dimensional Euclidean space#Simple rotations|simple rotation]] in any space (of any number of dimensions). However, it does seem to correspond exactly to an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]] in a Euclidean space of four dimensions. Isospin space resembles the [[W:3-sphere|3-sphere]], the [[W:Elliptical space#Elliptic space (the 3D case)|curved 3-dimensional space]] that is the surface of a [[W:4-ball (mathematics)#In Euclidean space|4-dimensional ball]].

=== Spinors ===
[[File:Spinor on the circle.png|thumb|upright=1.5|A spinor visualized as a vector pointing along the [[W:Möbius band|Möbius band]], exhibiting a sign inversion when the circle (the &quot;physical system&quot;) is continuously rotated through a full turn of 360°.]][[W:Spinors|Spinors]] are [[W:representation of a Lie group|representations]] of a [[W:spin group|spin group]], which are [[W:Double covering group|double cover]]s of the [[W:special orthogonal group|special orthogonal groups]]. The spin group Spin(4) is the double cover of [[W:SO(4)|SO(4)]], the group of rotations in 4-dimensional Euclidean space. [[600-cell#Fibrations of isocline polygrams|Isoclines]], the helical geodesic paths followed by points under isoclinic rotation, correspond to spinors representing Spin(4).

Spinors can be viewed as the &quot;square roots&quot; of [[W:Section (fiber bundle)|cross sections]] of [[W:vector bundle|vector bundle]]s; in this correspondence, a fiber bundle of isoclines (of a distinct isoclinic rotation) is a cross section (inverse bundle) of a fibration of great circles (in the invariant planes of that rotation).

A spinor can be visualized as a moving vector on a Möbius strip which transforms to its negative when continuously rotated through 360°, just as [[24-cell#Helical hexagrams and their isoclines|an isocline can be visualized as a Möbius strip]] winding twice around the 3-sphere, during which [[24-cell#Isoclinic rotations|720° isoclinic rotation]] the rigid 4-polytope turns itself inside-out twice.{{Sfn|Goucher|2019|loc=Spin Groups}} Under isoclinic rotation, a rigid 4-polytope is an isospin-1/2 object with two states.

=== Isoclinic rotations in the nucleus ===
Isospin is regarded as a symmetry of the strong interaction under the [[W:Group action (mathematics)|action]] of the [[W:Lie group|Lie group]] [[W:SU(2)|SU(2)]], the two [[W:eigenstate|states]] being the [[W:Up quark|up flavour]] and [[W:Down quark|down flavour]]. A 360° isoclinic rotation of a rigid [[W:nuclide|nuclide]] would transform its protons into neutrons and vice versa, exchanging the up and down flavours of their constituent [[W:quarks|quarks]], by turning the nuclide and all its parts inside-out (or perhaps we should say upside-down). Because we never observe this, we know that the nucleus is not a ''rigid'' polytope undergoing isoclinic rotation.

If the nucleus ''were'' a rigid object, nuclides that were isospin-rotated 360° would be isoclinic mirror images of each other, isospin +1/2 and isospin −1/2 states of the whole nucleus. We don't see whole nuclides rotating as a rigid object, but considering what would happen if they ''were'' rigid tells us something about the geometry we must expect inside the nucleons. One way that an isospin-rotated neutron could become a proton would be if the up quark and down quark were a left and right mirror-image pair of the same object; exchanging them in place would turn each down-down-up neutron into an up-up-down proton. But the case cannot be quite that simple, because the up quark and the down quark are not mirror-images of the same object: they have very different mass and other incongruities.

Another way an isospin-rotated neutron could be a proton would be if the up and down quarks were asymmetrical kinematic polytopes (not indirectly congruent mirror-images, and not rigid polytopes), rotating within the nucleus in different ''hybrid'' orbits. By that we mean that they may have vertices orbiting in rotations characteristic of more than one 4-polytope, so they may change shape as they rotate. In that case their composites (protons and neutrons) could have a symmetry not manifest in their components, but emerging from their combination.

....

=== Hybrid isoclinic rotations ===
The 24-cell has [[24-cell#Isoclinic rotations|its own characteristic isoclinic rotations]] in 4 Clifford parallel hexagonal planes (each intersecting 6 vertices), and also inherits the [[16-cell#Rotations|characteristic isoclinic rotations of its 3 Clifford parallel constituent 16-cells]] in 6 Clifford parallel square planes (each intersecting 4 vertices). The twisted circular paths followed by vertices in these two different kinds of rotation have entirely different geometries. Vertices rotating in hexagonal invariant planes follow [[24-cell#Helical hexagrams and their isoclines|helical geodesic curves whose chords form hexagrams]], and vertices rotating in square invariant planes follow [[24-cell#Helical octagrams and their isoclines|helical geodesic curves whose chords form octagrams]].

In a rigid isoclinic rotation, ''all'' the [[24-cell#Geodesics|great circle polygons]] move, in any kind of rotation. What distinguishes the hexagonal and square isoclinic rotations is the invariant planes of rotation the vertices stay in. The rotation described [[#Rotations|above]] (of 8 vertices rotating in 4 Clifford parallel hexagonal planes) is a single hexagonal isoclinic rotation, not a kinematic or hybrid rotation.

A ''kinematic'' isoclinic rotation in the 24-cell is any subset of the 24 vertices rotating through the same angle in the same time, but independently with respect to the choice of a Clifford parallel set of invariant planes of rotation and the chirality (left or right) of the rotation. A ''hybrid'' isoclinic rotation combines moving vertices from different kinds of isoclinic rotations, characteristic of different regular 4-polytopes. For example, if at least one vertex rotates in a square plane and at least one vertex rotates in a hexagonal plane, the kinematic rotation is a hybrid rotation, combining rotations characteristic of the 16-cell and characteristic of the 24-cell.

As an example of the simplest hybrid isoclinic rotation, consider a 24-cell vertex rotating in a square plane, and a second vertex, initially one 24-cell edge-length distant, rotating in a hexagonal plane. Rotating isoclinically at the same rate, the two moving vertices will never collide where their paths intersect, so this is a ''valid'' hybrid rotation.

To understand hybrid rotations in the 24-cell more generally, visualize the relationship between great squares and great hexagons. The [[24-cell#Squares|18 great squares]] occur as three sets of 6 orthogonal great squares,{{Efn|name=six orthogonal planes of the Cartesian basis}} each [[16-cell#Coordinates|forming a 16-cell]]. The three 16-cells are completely disjoint{{Efn|name=completely disjoint}} and [[24-cell#Clifford parallel polytopes|Clifford parallel]]: each has its own 8 vertices (on 4 orthogonal axes) and its own 24 edges (of length {{radic|2}}).{{Efn|name=three isoclinic 16-cells}} The 18 square great circles are crossed by 16 hexagonal great circles; each [[24-cell#Hexagons|hexagon]] has one axis (2 vertices) in each 16-cell.{{Efn|name=non-orthogonal hexagons}} The two [[24-cell#Triangles|great triangles]] inscribed in each great hexagon (occupying its alternate vertices, with edges that are its {{radic|3}} chords) have one vertex in each 16-cell. Thus ''each great triangle is a ring linking three completely disjoint great squares, one from each of the three completely disjoint 16-cells''.{{Efn|There are four different ways (four different ''fibrations'' of the 24-cell) in which the 8 vertices of the 16-cells correspond by being triangles of vertices {{radic|3}} apart: there are 32 distinct linking triangles. Each ''pair'' of 16-cells forms a tesseract (8-cell).{{Efn|name=three 16-cells form three tesseracts}} Each great triangle has one {{radic|3}} edge in each tesseract, so it is also a ring linking the three tesseracts.|name=great linking triangles}} Isoclinic rotations take the elements of the 4-polytope to congruent [[24-cell#Clifford parallel polytopes|Clifford parallel elements]] elsewhere in the 4-polytope. The square rotations do this ''locally'', confined within each 16-cell: for example, they take great squares to other great squares within the same 16-cell. The hexagonal rotations act ''globally'' within the entire 24-cell: for example, they take great squares to other great squares in ''different'' 16-cells. The [[16-cell#Helical construction|chords of the square rotations]] bind the 16-cells together internally, and the [[24-cell#Helical hexagrams and their isoclines|chords of the hexagonal rotations]] bind the three 16-cells together.

....

=== Color ===
When the existence of quarks was suspected in 1964, [[W:Oscar W. Greenberg|Greenberg]] introduced the notion of color charge to explain how quarks could coexist inside some [[W:hadron|hadron]]s in [[W:quark model#The discovery of color|otherwise identical quantum states]] without violating the [[W:Pauli exclusion principle|Pauli exclusion principle]]. The modern concept of [[W:color charge|color charge]] completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [[W:William A. Bardeen|William Bardeen]], [[W:de:Harald Fritzsch|Harald Fritzsch]], and [[W:Murray Gell-Mann|Murray Gell-Mann]].&lt;ref&gt;{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''&lt;sup&gt;0&lt;/sup&gt; decay, and ''e''&lt;sup&gt;+&lt;/sup&gt; ''e''&lt;sup&gt;&amp;minus;&lt;/sup&gt; annihilation |arxiv=hep-ph/0211388 |editor=Gatto, R. |book-title=Scale and conformal symmetry in hadron physics |page=[https://archive.org/details/scaleconformalsy0000unse/page/139 139] |publisher=[[W:John Wiley &amp; Sons|John Wiley &amp; Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}&lt;/ref&gt;&lt;ref&gt;{{cite journal |title=Advantages of the color octet gluon picture |journal=[[W:Physics Letters B|Physics Letters B]] |volume=47 |issue=4 |page=365 |year=1973 |last1=Fritzsch |first1=H. |last2=Gell-Mann |first2=M. |last3=Leutwyler |first3=H. |doi=10.1016/0370-2693(73)90625-4 |bibcode=1973PhLB...47..365F |citeseerx=10.1.1.453.4712}}&lt;/ref&gt;

Color charge is not [[W:electric charge|electric charge]]; the whole point of it is that it is a quantum of something different. But it is related to electric charge, through the way in which the three different-colored quarks combine to contribute fractional quantities of electric charge to a nucleon. As we shall see, color is not really a separate kind of charge at all, but a partitioning of the electric charge into [[24-cell#Clifford parallel polytopes|Clifford parallel subspaces]].

The [[W:Color charge#Red, green, and blue|three different colors]] of quark charge might correspond to three different 16-cells, such as the three disjoint 16-cells inscribed in the 24-cell. Each color might be a disjoint domain in isospin space (the space of points on the 3-sphere).{{Efn|The 8 vertices of each disjoint 16-cell constitute an independent [[16-cell#Coordinates|orthonormal basis for a coordinate reference frame]].}} Alternatively, the three colors might correspond to three different fibrations of the same isospin space: three different ''sequences'' of the same total set of discrete points on the 3-sphere. These alternative possibilities constrain possible representations of the nuclides themselves, for example if we try to represent nuclides as particular rotating 4-polytopes. If the neutron is a (8-point) 16-cell, either of the two color possibilities might somehow make sense as far as the neutron is concerned. But if the proton is a (5-point) 5-cell, only the latter color possibility makes sense, because fibrations (which correspond to distinct isoclinic left-and-right rigid rotations) are the ''only'' thing the 5-cell has three of. Both the 5-cell and the 16-cell have three discrete rotational fibrations. Moreover, in the case of a rigid, isoclinically rotating 4-polytope, those three fibrations always come one-of-a-kind and two-of-a-kind, in at least two different ways. First, one fibration is the set of invariant planes currently being rotated through, and the other two are not. Second, when one considers the three fibrations of each of these 4-polytopes, in each fibration two isoclines carry the left and right rotations respectively, and the third isocline acts simply as a Petrie polygon, the difference between the fibrations being the role assigned to each isocline.

If we associate each quark with one or more isoclinic rotations in which the moving vertices belong to different 16-cells of the 24-cell, and the sign (plus or minus) of the electric charge with the chirality (right or left) of isoclinic rotations generally, we can configure nucleons of three quarks, two performing rotations of one chirality and one performing rotations of the other chirality. The configuration will be a valid kinematic rotation because the completely disjoint 16-cells can rotate independently; their vertices would never collide even if the 16-cells were performing different rigid square isoclinic rotations (all 8 vertices rotating in unison). But we need not associate a quark with a [[16-cell#Rotations|rigidly rotating 16-cell]], or with a single distinct square rotation.

Minimally, we must associate each quark with at least one moving vertex in each of three different 16-cells, following the twisted geodesic isocline of an isoclinic rotation. In the up quark, that could be the isocline of a right rotation; and in the down quark, the isocline of a left rotation. The chirality accounts for the sign of the electric charge (we have said conventionally as +right, −left), but we must also account for the quantity of charge: +{{sfrac|2|3}} in an up quark, and −{{sfrac|1|3}} in a down quark. One way to do that would be to give the three distinct quarks moving vertices of {{sfrac|1|3}} charge in different 16-cells, but provide up quarks with twice as many vertices moving on +right isoclines as down quarks have vertices moving on −left isoclines (assuming the correct chiral pairing is up+right, down−left).

Minimally, an up quark requires two moving vertices (of the up+right chirality).{{Efn|Two moving vertices in one quark could belong to the same 16-cell. A 16-cell may have two vertices moving in the same isoclinic square (octagram) orbit, such as an antipodal pair (a rotating dipole), or two vertices moving in different square orbits of the same up+right chirality.{{Efn|There is only one [[16-cell#Helical construction|octagram orbit]] of each chirality in each fibration of the 16-cell, so two octagram orbits of the same chirality cannot be Clifford parallel (part of the same distinct rotation). Two vertices right-moving on different octagram isoclines in the same 16-cell is a combination of two distinct rotations, whose isoclines will intersect: a kinematic rotation. It can be a valid kinematic rotation if the moving vertices will never pass through a point of intersection at the same time. Octagram isoclines pass through all 8 vertices of the 16-cell, and all eight isoclines (the left and right isoclines of four different fibrations) intersect at ''every'' vertex.}} However, the theory of [[W:Color confinement|color confinement]] may not require that two moving vertices in one quark belong to the same 16-cell; like the moving vertices of different quarks, they could be drawn from the disjoint vertex sets of two different 16-cells.}} Minimally, a down quark requires one moving vertex (of the down−left chirality). In these minimal quark configurations, a proton would have 5 moving vertices and a neutron would have 4.

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=== Nucleons ===
[[File:Symmetrical_5-set_Venn_diagram.svg|thumb|[[W:Branko Grünbaum|Grünbaum's]] rotationally symmetrical 5-set Venn diagram, 1975. It is the [[5-cell]]. Think of it as an [[W:Nuclear magnetic resonance|NMR image]] of the 4-dimensional proton in projection to the plane.]]
The proton is a very stable mass particle. Is there a stable orbit of 5 moving vertices in 4-dimensional Euclidean space? There are few known solutions to the 5-body problem, and fewer still to the [[W:n-body problem|{{mvar|n}}-body problem]], but one is known: the ''central configuration'' of {{mvar|n}} bodies in a space of dimension {{mvar|n}}-1. A [[W:Central configuration|central configuration]] is a system of [[W:Point particle|point masses]] with the property that each mass is pulled by the combined attractive force of the system directly towards the [[W:Center of mass|center of mass]], with acceleration proportional to its distance from the center. Placing three masses in an equilateral triangle, four at the vertices of a regular [[W:Tetrahedron|tetrahedron]], five at the vertices of a regular [[5-cell]], or more generally {{mvar|n}} masses at the vertices of a regular [[W:Simplex|simplex]] produces a central configuration [[W:Central configuration#Examples|even when the masses are not equal]]. In an isoclinic rotation, all the moving vertices orbit at the same radius and the same speed. Therefore if any 5 bodies are orbiting as an isoclinically rotating regular 5-cell (a rigid 4-simplex figure undergoing isoclinic rotation), they maintain a central configuration, describing 5 mutually stable orbits.

Unlike the proton, the neutron is not always a stable particle; a free neutron will decay into a proton. A deficiency of the minimal configurations is that there is no way for this [[W:beta minus decay|beta minus decay]] to occur. The minimal neutron of 4 moving vertices described [[#Color|above]] cannot possibly decay into a proton by losing moving vertices, because it does not possess the four up+right moving vertices required in a proton. This deficiency could be remedied by giving the neutron configuration 8 moving vertices instead of 4: four down−left and four up+right moving vertices. Then by losing 3 down−left moving vertices the neutron could decay into the 5 vertex up-down-up proton configuration.{{Efn|Although protons are very stable, during [[W:stellar nucleosynthesis|stellar nucleosynthesis]] two H&lt;sub&gt;1&lt;/sub&gt; protons are fused into an H&lt;sub&gt;2&lt;/sub&gt; nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus &quot;decay&quot;]] of a proton into a neutron is actually the result of a rare high-energy collision between the two protons, in which a neutron is constructed. With respect to our nucleon configurations of moving vertices, it has to be explained as the conversion of two 5-point 5-cells into a 5-point 5-cell and an 8-point 16-cell, emitting two decay products of at least 1-point each. Thus it must involve the creation of moving vertices, by the conversion of kinetic energy to point-masses.}} A neutron configuration of 8 moving vertices could occur as the 8-point 16-cell, the second-smallest regular 4-polytope after the 5-point 5-cell (the hypothesized proton configuration).

It is possible to double the neutron configuration in this way, without destroying the charge balance that defines the nucleons, by giving down quarks three moving vertices instead of just one: two −left vertices and one +right vertex. The net charge on the down quark remains −{{sfrac|1|3}}, but the down quark becomes heavier (at least in vertex count) than the up quark, as in fact its mass is measured to be.

A nucleon's quark configuration is only a partial specification of its properties. There is much more to a nucleon than what is contained within its three quarks, which contribute only about 1% of the nucleon's energy. The additional 99% of the nucleon mass is said to be associated with the force that binds the three quarks together, rather than being intrinsic to the individual quarks separately. In the case of the proton, 5 moving vertices in the stable orbits of a central configuration (in one of the [[5-cell#Geodesics and rotations|isoclinic rotations characteristic of the regular 5-cell]]) might be sufficient to account for the stability of the proton, but not to account for most of the proton's energy. It is not the point-masses of the moving vertices themselves which constitute most of the mass of the nucleon; if mass is a consequence of geometry, we must look to the larger geometric elements of these polytopes as their major mass contributors. The quark configurations are thus incomplete specifications of the geometry of the nucleons, predictive of only some of the nucleon's properties, such as charge.{{Efn|Notice that by giving the down quark three moving vertices, we seem to have changed the quark model's prediction of the proton's number of moving vertices from 5 to 7, which would be incompatible with our theory that the proton configuration is a rotating regular 5-cell in a central configuration of 5 stable orbits. Fortunately, the actual quark model has nothing at all to say about moving vertices, so we may choose to regard that number as one of the geometric properties the quark model does not specify.}} In particular, they do not account for the forces binding the nucleon together. Moreover, if the rotating regular 5-cell is the proton configuration and the rotating regular 16-cell is the neutron configuration, then a nucleus is a complex of rotating 5-cells and 16-cells, and we must look to the geometric relationship between those two very different regular 4-polytopes for an understanding of the nuclear force binding them together.

The most direct [[120-cell#Relationships among interior polytopes|geometric relationship among stationary regular 4-polytopes]] is the way they occupy a common 3-sphere together. Multiple 16-cells of equal radius can be compounded to form each of the larger regular 4-polytopes, the 8-cell, 24-cell, 600-cell, and 120-cell, but it is noteworthy that multiple regular 5-cells of equal radius cannot be compounded to form any of the other 4-polytopes except the largest, the 120-cell. The 120-cell is the unique intersection of the regular 5-cell and 16-cell: it is a compound of 120 regular 5-cells, and also a compound of 75 16-cells. All regular 4-polytopes except the 5-cell are compounds of 16-cells, but none of them except the largest, the 120-cell, contains any regular 5-cells. So in any compound of equal-radius 16-cells which also contains a regular 5-cell, whether that compound forms some single larger regular 4-polytope or does not, no two of the regular 5-cell's five vertices ever lie in the same 16-cell. So the geometric relationship between the regular 5-cell (our proton candidate) and the regular 16-cell (our neutron candidate) is quite a distant one: they are much more exclusive of each other's elements than they are distantly related, despite their complementary three-quark configurations and other similarities as nucleons. The relationship between a regular 5-cell and a regular 16-cell of equal radius is manifest only in the 120-cell, the most complex regular 4-polytope, which [[120-cell#Geometry|uniquely embodies all the containment relationships]] among all the regular 4-polytopes and their elements.

If the nucleus is a complex of 5-cells (protons) and 16-cells (neutrons) rotating isoclinically around a common center, then its overall motion is a hybrid isoclinic rotation, because the 5-cell and the 16-cell have different characteristic isoclinic rotations, and they have no isoclinic rotation in common.{{Efn|The regular 5-cell does not occur inscribed in any other regular 4-polytope except one, the 600-vertex 120-cell. No two of the 5 vertices of a regular 5-cell can be vertices of the same 16-cell, 8-cell, 24-cell, or 600-cell. The isoclinic rotations characteristic of the regular 5-cell maintain the separation of its 5 moving vertices in 5 disjoint Clifford-parallel subspaces at all times. The [[16-cell#Rotations|isoclinic rotation characteristic of the 16-cell]] maintains the separation of its 8 moving vertices in 2 disjoint Clifford-parallel subspaces (completely orthogonal great square planes) at all times. Therefore, in any hybrid rotation of a concentric 5-cell and 16-cell, at most one 5-cell subspace (containing 1 vertex) might be synchronized with one 16-cell subspace (containing 4 vertices), such that the 1 + 4 vertices they jointly contain occupy the same moving subspace continually, forming a rigid 5-vertex polytope undergoing some kind of rotation. If in fact it existed, this 5-vertex rotating rigid polytope would not be [[5-cell#Geometry|not a 5-cell, since 4 of its vertices are coplanar]]; it is not a 4-polytope but merely a polyhedron, a [[W:square pyramid|square pyramid]].}}

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=== Nuclides ===

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=== Quantum phenomena ===

The Bell-Kochen-Specker (BKS) theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a space of three or more dimensions can be given by exhibiting a finite set of lines through the origin that cannot each be colored black or white in such a way that (i) no two orthogonal lines are both black, and (ii) not all members of a set of ''d'' mutually orthogonal lines are white.{{Efn|&quot;The Bell-Kochen-Specker theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a Hilbert space of dimension d ≥ 3 can be given by exhibiting a finite set of rays [9] that cannot each be assigned the value 0 or 1 in such a way that (i) no two orthogonal rays are both assigned the value 1, and (ii) not all members of a set of d mutually orthogonal rays are assigned the value 0.&quot;{{Sfn|Waegell|Aravind|2009|loc=2. The Bell-Kochen-Specker (BKS) theorem}}|name=BKS theorem}}

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=== Motion ===
What does it mean to say that an object moves through space? Coxeter group theory provides precise answers to questions of this kind. A rigid object (polytope) moves by distinct transformations, changing itself in each discrete step into a congruent object in a different orientation and position.

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== Galilean relativity in a space of four orthogonal dimensions ==

Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions.

General relativity is just Galilean relativity in a general space of four orthogonal dimensions, e.g. Euclidean 4-space &lt;math&gt;R^4&lt;/math&gt;, spherical 4-space &lt;math&gt;S^4&lt;/math&gt;, or any orthogonal 4-manifold.

Light is just reflection. Gravity (and all force) is just rotation. Both motions are just group actions, expressions of intrinsic symmetries. That is all of physics.

Every observer properly sees himself as stationary and the universe as a sphere with himself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and it can be measured by the observer as the speed of light.

=== Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions ===
Perspective effects occur because each observer's ordinary 3-dimensional space is only a curved manifold embedded in 4-dimensional Euclidean space, and its curvature complicates the calculations for him (e.g., he sometimes requires Lorentz transformations). But if  all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) except when you want to calculate a projection, or a shadow, that is, how things will appear from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} The universe really has four spatial dimensions, and space and time behave just as they do in classical 3-vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a spacetime to explain 4-dimensional perspective effects at high velocities, because 4-space is already spatially 4-dimensional, and those perspective effects fall out of the 4-dimensional Pythagorean theorem naturally, just as perspective does in three dimensions. The universe is only strange in the ways the Euclidean fourth dimension is strange; but that does hold many surprises for us. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way that 3-space is much more interesting than 2-space. But all Euclidean spaces are dimensionally analogous. Dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries.

=== General relativity is just Galilean relativity in a general space of four orthogonal dimensions ===
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=== Physics ===
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=== Thoreau's spherical relativity ===
Every observer may properly see himself as stationary and the universe as a 4-sphere with himself at the center observing it, perceptually equidistant from all points on its surface, including his own ''physical'' location which is one of those surface points, distinguished to him but not the center of anything. This statement of the principle of relativity is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in curved, non-Euclidean spacetime, and Coxeter's relativity of orthogonal group actions in Euclidean spaces of any number of dimensions.{{Efn|Let Q denote a rotation, R a reflection, T a translation, and let Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T denote a product of several such transformations, all commutative with one another. Then RT is a glide-reflection (in two or three dimensions), QR is a rotary-reflection, QT is a screw-displacement, and Q&lt;sup&gt;2&lt;/sup&gt; is a double rotation (in four dimensions). Every orthogonal transformation is expressible as
{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt;&lt;br&gt;
where 2''q'' + ''r'' ≤ ''n'', the number of dimensions. Transformations involving a translation are expressible as
{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T&lt;br&gt;
where 2''q'' + ''r'' + 1 ≤ ''n''.&lt;br&gt;
For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q&lt;sup&gt;2&lt;/sup&gt;, or a screw-displacement QT (where the rotation component Q is a simple rotation). [If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either of those, because we can view any QT as a Q&lt;sup&gt;2&lt;/sup&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q&lt;sup&gt;2&lt;/sup&gt;. By the same principle, we can view any QT or Q&lt;sup&gt;2&lt;/sup&gt; as an isoclinic (equi-angled) Q&lt;sup&gt;2&lt;/sup&gt; by appropriate choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} That is to say, Coxeter's relation is a mathematical statement of the principle of relativity, on group-theoretic grounds.{{Efn|Notice that Coxeter's relation correctly captures the limits to relativity, in that we can only exchange the translation (T) for ''one'' of the two rotations (Q). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation up to uncertainty, and can always also distinguish the direction and velocity of his own proper time arrow.}}] Every enantiomorphous transformation in 4-space (reversing chirality) is a QRT.{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}|name=transformations}} It should be known as Thoreau's spherical relativity, since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polytopes in any number of dimensions.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassman and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}}]}}

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== Conclusions==

=== Spherical relativity ===

We began our inquiry by wondering why physical space should be limited to just three dimensions (why ''three''). By visualizing the universe as a Euclidian space of four dimensions, we recognize that relativistic and quantum phenomena are natural consequences of symmetry group operations (including reflections and rotations) in four orthogonal dimensions. We should not then be surprised to see that the universe does not have just four dimensions, either. Physical space must bear as many dimensions as we need to ascribe to it, though the distinct phenomena for which we find a need to do so, in order to explain them, seem to be fewer and fewer as we consider higher and higher dimensions. To laws of physics generally, such as the principle of relativity in particular, we should always append the phrase &quot;in Euclidean spaces of any number of dimensions&quot;. Laws of physics should operate in any flat Euclidean space &lt;math&gt;R^n&lt;/math&gt; and in its corresponding spherical space &lt;math&gt;S^n&lt;/math&gt;.

The first and simplest sense in which we are forced to contemplate a fifth dimension is to accommodate our normal idea of time. Just as Einstein was forced to admit time as a dimension, in his four-dimensional spacetime of three spatial dimensions plus time, for some purposes we require a fifth time dimension to accompany our four spatial dimensions, when our purpose is orthogonal to (in the sense of independent of) the four spatial dimensions. For example, if we theorize that we observe a finite homogeneous universe, and that it is a Euclidean 4-space overall, we may prefer not to have to identify any distinct place within that 4-space as the center where the universe began in a big bang. To avoid having to pick a distinct place as the center of the universe, our model of it must be expanded, at least to be a ''spherical'' 4-dimensional space with the fifth radial dimension as time. Essentially, we require the fifth dimension in order to make our homogeneous 4-space finite, by wrapping it around into a 4-sphere. But perhaps we can still resist admitting the fifth radial dimension as a full-fledged Euclidean spatial dimension, at least so long as we have not observed how any naturally occurring object configurations are best described as 5-polytopes.

One phenomenon which resists explanation in a space of just four dimensions is the propagation of light in a vacuum. The propagation of mass-carrying particles is explained as the consequence of their rotations in closed, curved spaces (3-spheres) of finite size, moving through four-dimensional Euclidean space at a universal constant speed, the speed of light. But an apparent paradox remains that light must seemingly propagate through four-dimensional Euclidean space at more than the speed of light. From a five-dimensional viewpoint, this apparent paradox can be resolved, and in retrospect it is clear how massless particles can translate through four-dimensional space at twice the speed constant, since they are not simultaneously rotating.

Another phenomenon justifying a five-dimensional view of space is the relation between the the 5-cell proton and the 16-cell neutron (the 4-simplex and 4-orthoplex polytopes). Their indirect relationship can be observed in the 4-600-point polytope (the 120-cell), and in its 11-cells,{{Sfn|Christie|2024}} but it is only directly observed (absent a 120-cell) in a five-dimensional reference frame.

=== Nuclear geometry ===
We have seen how isoclinic rotations (Clifford displacements) relate the orbits in the atomic nucleus to each other, just as they relate the regular convex 4-polytopes to each other, in a sequence of nested objects of increasing complexity. We have identified the proton as a  5-point, 5-cell 4-simplex 𝜶&lt;sub&gt;4&lt;/sub&gt;, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽&lt;sub&gt;4&lt;/sub&gt;, and the shell of the atomic nucleus as a 24-point 24-cell. As Coxeter noted, that unique 24-point object stands quite alone in four dimensions, having no analogue above or below.

=== Atomic geometry ===
I'm on a plane flying to Eugene to visit Catalin, we'll talk after I arrive. I've been working on both my unpublished papers, the one going put for pre-publication review soon about 4D geometry, and the big one not going out soon about the 4D sun, 4D atoms, and 4D galaxies and n-D universe. I'vd just added the following paragraph to that big paper:

Atomic geometry

The force binding the protons and neutrons of the nucleus together into a distinct element is specifically an expression of the 11-cell 4-polytope, itself an expression of the pyritohedral symmetry, which binds the distinct 4-polytopes to each other, and relates the n-polytopes to their neighbors of different n by dimensional analogy.


flying over mt shasta out my right-side window at the moment, that last text showing &quot;not delivered&quot; yet because there's no wifi on this plane, gazing at that great peak of the world and feeling as if i've just made the first ascent of it

=== Molecular geometry ===
Molecules are 3-dimensional structures that live in the thin film of 3-membrane only one atom thick in most places that is our ordinary space, but since that is a significantly curved 3-dimensional space at the scale of a molecule, the way the molecule's covalent bonds form is influenced by the local curvature in 4-dimensions at that point.

In the water molecule, there is a reason why the hydrogen atoms are attached to the oxygen atom at an angle of 104.45° in 3-dimensional space, and at root it must be the same symmetry that locates any two of the hydrogen proton's five vertices 104.45° apart on a great circle arc of its tiny 3-sphere.

=== Cosmology ===

==== Solar systems ====

===== Stars =====
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===== The Kepler problem =====
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==== Galaxies ====

The spacetime of general relativity is often illustrated as a projection to a curved 2D surface in which large gravitational objects make gravity wells or dimples in the surface. In the Euclidean 4D view of the universe the 3D surface of a large cosmic object such as a galaxy surrounds an empty 4D space, and large gravitational objects within the galaxy must make dimples in its surface. But should we see them as dimples exactly? Would they dimple inwards or outwards? In the spacetime illustrations they are naturally always shown as dimpling downwards, which is somewhat disingenuous, strongly suggesting to the viewer that the reason for gravity is that it flows downhill - the original tautology we are trying to surmount! In the Euclidean 4D galaxy the dimple, if it is one, must be either inward or outward, and which it is matters since the dimple is flying outward at velocity {{mvar|c}}. The galaxy is not collapsing inward. Is a large gravitational mass (such as a star) ''ahead'' of the smaller masses orbiting around it (such as its planets), or is it ''behind'' them, as they fly through 4-space on their Clifford parallel trajectories? The answer is ''both'' of course, because a star is not a dimple, it is a 4-ball, and it dimples the 3D surface both inwards and outwards. It is a thick place in the 3D surface. We should view it as having its gravitational center precisely at the surface of the expanding 3-sphere. 

What is a black hole? It is the hollow four-dimensional space that a galaxy is the three-dimensional surface of.

When we view another galaxy, such as Andromeda, we are seeing that whole galaxy from a distance, the way the moon astronauts looked back at the whole earth. We see our own milky way galaxy from where we are on its surface, the way we see the earth from its surface, except that the earth is solid, but the galaxy is hollow and transparent. We can look across its empty center and see all the other stars also on its surface, including those opposite ours on the far side of its 3-sphere. The thicker band of stars we see in our night sky and identify as the milky way is not our whole galaxy; the majority of the other visible stars also lie in our galaxy. That dense band is not thicker and brighter than other parts of our galaxy because it lies toward a dense galactic center (our galaxy has an empty center), but for exactly the opposite reason: those apparently more thickly clustered stars lie all around us on the galaxy's surface, in the nearest region of space surrounding us. They appear to be densely packed only because we are looking at them &quot;edge on&quot;. Actually, we are looking into this nearby apparently dense region ''face on'', not edge on, because we are looking at a round sphere of space surrounding us, not a disk. In contrast, stars in our galaxy outside that bright band lie farther off from us, across the empty center of the galaxy, and we see them spread out as they actually are, instead of &quot;edge on&quot; so they appear to be densely clustered. The &quot;dense band&quot; covers only an equatorial band of the night sky instead of all the sky, because when we look out into the four-dimensional space around us, we can see stars above and below our three-dimensional hyperplane in our four-dimensional space. Everything in our solar system lies in our hyperplane, and the nearby stars around us in our galaxy are near our hyperplane (just slightly below it). All the other, more distant stars in our galaxy are also below our hyperplane. We can see objects outside our galaxy, such as other galaxies, both above and below our hyperplane. We can see all around us above our hyperplane (looking up from the galactic surface into the fourth dimension), and all around us below our hyperplane (looking down through our transparent galaxy and out the other side).

== Revolutions ==
The original Copernican revolution displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the stars remaining on a fixed sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

In such fashion the Euclidean four-dimensional viewpoint initially lends itself to a big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the stars need not be equidistant from a single origin in time, any more than they all lie in the same galaxy, equidistant from its center in space. The expanding sphere of matter on the surface of which we find ourselves living might be one of many such spheres, with their big bang origins occurring at distinct times and places in the 4-dimensional universe.

When we look up at the heavens, we have no obvious way of knowing whether the space we are looking into is a curved 3-spherical one or a flat 4-space. In this work we suggest a theory of how light travels that says we can see into all four dimensions, and so when we look up at night we see cosmological objects distributed in 4-dimensional space, and not all located on our own 3-spherical membrane. The view from our solar system suggests that our galaxy is its own hollow 3-sphere, and that galaxies generally are single roughly spherical 3-membranes, with the smaller objects within them all lying on that same 3-spherical surface, equidistant from the galaxy center in 4-space. 

The Euclidean four-dimensional viewpoint requires that all mass-carrying objects are in motion at constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Since their paths away from their origin are not straight lines but various helical isoclines, their 3-sphere will be expanding radially at slightly less than the constant velocity &lt;math&gt;c&lt;/math&gt;. The view from our solar system does ''not'' suggest that each galaxy is its own distinct 3-sphere expanding at this great rate; rather, the standard theory has been that the entire observable universe is expanding from a single big bang origin in time. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also allows theories which require no single origin point in space and time.

These are the voyages of starship Earth, to boldly go where no one has gone before. It made the jump to lightspeed long ago, in whatever big bang its atoms emerged from, and hasn't slowed down since.

== Origins of the theory ==
Einstein himself was one of the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean sphere, in what was narrowly the first written articulation of the principle of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below). Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that formulation of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from his perspective; the forthshortenings, clock desynchronizations and other perceptual effects it predicts are exact calculations of actual perspective effects; but space is actually a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four dimensions.''

The Euclidean 4-dimensional theory differs from the standard theory in being a description of the physical universe in terms of a geometry of four or more orthogonal spatial dimensions, rather than in the standard theory's terms of the [[w:Minkowski spacetime|Minkowski spacetime]] geometry (in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions). The invention of geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years. It was first worked out by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] around 1850. Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''polyscheme'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he discovered all the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the six convex regular polyschemes which can be constructed in a space of four dimensions (a set analogous to the five [[w:Platonic solid|Platonic solids]] in three dimensional space). Thus he was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover all its astonishing regular objects. Because most of his work remained almost completely unknown until it was published posthumously in 1901, other researchers had more than fifty years to rediscover the regular polyschemes, and competing terms were coined; today [[W:Alicia Boole Stott|Alicia Boole Stott]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme''.{{Efn|Today Schläfli's original ''polyscheme'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}}

== Boundaries ==
&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schlafli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it, is that there ''is'' a boundary between three and four dimensions. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our world apparently only three dimensional? Why would it have ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schlafli mapped? What is the nature of the boundary which confines us to just three? 

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way by receiving light signals that traveled to us on straight lines through it. The reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creates, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not surprise us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schlafli discovered something else: all the astonishing regular objects that exist in higher dimensions. So this conception now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and not a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation?

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that our universe is properly a Euclidean space of four orthogonal spatial dimensions. Others will have to work out the physics and do the math, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|radius={{radic|2}}|columns=9}}

== Notes ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are 4-dimensionally circular, but not all isoclines on 3-manifolds in 4-space are perfectly circular.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point.{{Sfn|Tyrrell|Semple|1971|loc=§3. Clifford's original definition of parallelism|pp=5-6}} A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the 2-sphere will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect; various sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. Perhaps the simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles.{{Efn|name=six orthogonal planes of the Cartesian basis}} Each completely orthogonal pair is Clifford parallel. The two circles cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 3-sphere.{{Efn|name=only some Clifford parallels are orthogonal}} Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]].|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Notelist|40em}}

== Citations ==
{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

{{Reflist|40em}}

== References ==
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* {{Cite book | last1=Conway | first1=John H. | author-link1=W:John Horton Conway | last2=Burgiel | first2=Heidi | last3=Goodman-Strauss | first3=Chaim | author-link3=W:Chaim Goodman-Strauss | year=2008 | title=The Symmetries of Things | publisher=A K Peters | place=Wellesley, MA | title-link=W:The Symmetries of Things }}
* {{Cite journal|last1=Perez-Gracia|first1=Alba|last2=Thomas|first2=Federico|date=2017|title=On Cayley's Factorization of 4D Rotations and Applications|url=https://upcommons.upc.edu/bitstream/handle/2117/113067/1749-ON-CAYLEYS-FACTORIZATION-OF-4D-ROTATIONS-AND-APPLICATIONS.pdf|journal=Adv. Appl. Clifford Algebras|volume=27|pages=523–538|doi=10.1007/s00006-016-0683-9|hdl=2117/113067|s2cid=12350382|hdl-access=free}}
* {{Cite arXiv | eprint=1903.06971 | last=Copher | first=Jessica | year=2019 | title=Sums and Products of Regular Polytopes' Squared Chord Lengths | class=math.MG }}
* {{Cite thesis|url= http://resolver.tudelft.nl/uuid:dcffce5a-0b47-404e-8a67-9a3845774d89 |title=Symmetry groups of regular polytopes in three and four dimensions|last=van Ittersum |first=Clara|year=2020|publisher=[[W:Delft University of Technology|Delft University of Technology]]}}
* {{cite arXiv|last1=Kim|first1=Heuna|last2=Rote|first2=G.|date=2016|title=Congruence Testing of Point Sets in 4 Dimensions|class=cs.CG|eprint=1603.07269}}
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* {{Cite journal | last1=Mamone|first1=Salvatore | last2=Pileio|first2=Giuseppe | last3=Levitt|first3=Malcolm H. | year=2010 | title=Orientational Sampling Schemes Based on Four Dimensional Polytopes | journal=Symmetry | volume=2 | pages=1423-1449 | doi=10.3390/sym2031423 }}
* {{Cite journal|last=Dorst|first=Leo|title=Conformal Villarceau Rotors|year=2019|journal=Advances in Applied Clifford Algebras|volume=29|issue=44|url=https://doi.org/10.1007/s00006-019-0960-5}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}}
*{{Citation | last=Goucher | first=A.P. | title=Spin groups | date=19 November 2019 | journal=Complex Projective 4-Space | url=https://cp4space.hatsya.com/2012/11/19/spin-groups/ }}
* {{Citation|last=Christie|first=David Brooks|author-link=User:Dc.samizdat|year=2024|title=A symmetrical arrangement of 120 11-cells|title-link=User:Dc.samizdat/A symmetrical arrangement of 120 11-cells|journal=Wikiversity}}
{{Refend}}</text>
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      <text bytes="28240" sha1="f5fo0tr380vqznxa1ai1g8un1azo2bk" xml:space="preserve">{{title|Overchoice and motivation:&lt;br&gt;What is the overchoice effect, why does it occur, and who are most susceptible to it? }}
{{MECR3|1=https://www.youtube.com/watch?v=U5qpYaWAABY}}
__TOC__

==Overview==
{{RoundBoxTop|theme=3}}
[[File:Far, far too much choice, Ballyvaughan-Baile ui Bheachain - geograph.org.uk - 1268283.jpg|thumb|187px|'''Figure 1'''. Excess choice can be overwhelming]]

; Have you ever...

Have you ever been in a situation where you needed to make a choice but there were so many options you just couldn’t decide? Maybe you were picking a topic for a school assignment, or what movie to watch, or which career path to take? Choices are everywhere, and when you have too many options, it can become overwhelming and produce unwanted consequences. This is known as the overchoice effect (Scheibehenne et al., 2010; see Figure 1). 
{{RoundBoxBottom}}

The overchoice effect is an important area of research in motivational psychology, as excessive options can disrupt people’s ability to make decisions – costing them time, energy, and ultimately reducing their satisfaction with their choices (Chernev et al., 2015). Since decision-making is a fundamental part of human behaviour, research on the effects of assortment size on motivation has extensive practical applicability, especially in marketing and educational contexts (Iyengar &amp; Lepper, 2000). This chapter uses psychological science to explore key aspects of the overchoice effect – including the defining features of the overchoice effect, the mechanisms behind this phenomenon, and how personal characteristics can increase people’s susceptibility to its effects.

{{RoundBoxTop|theme=3}}
;Focus questions:
* What is the overchoice effect?
* Why does the overchoice effect occur? 
* Who is most susceptible to the overchoice effect?
{{RoundBoxBottom}}

==What is the overchoice effect? ==
The term, ''overchoice'' was first coined by Alvin Toffler in the 1970s; it was used to predict a future in which an abundance of choice would prevent people from making optimal decisions (Gourville &amp; Soman, 2005).The overchoice effect (also known as choice overload), describes a phenomenon in which people experience various negative consequences, such as demotivation and decreased choice satisfaction, when they are required to choose from many options (Scheibehenne et al., 2010). Whilst the presence of a large choice set is a necessary precondition of the overchoice effect, more choices does not necessarily mean negative effects are inevitable (Scheibehenne et al., 2010). In fact, perceived choice deprivation is a more reliable predictor of decreased choice satisfaction than perceived choice excess (Reutskaja et al., 2022). Based on previous research, Chernev et al. (2015) developed a conceptual model of choice overload, which explains that the effect of assortment size on the overchoice effect is moderated by characteristics of both decisions (extrinsic factors) and decision makers (intrinsic factors). That is, certain factors related to a choice can increase or decrease the extent to which overchoice produces negative emotional and behavioural consequences{{gr}}. These factors are presented in Table 1.

'''Table 1''' 

''Antecedent Factors of Choice Overload''
{| class=&quot;wikitable&quot; style=&quot;margin: auto;&quot;
|-
! Antecedent factor !! Description 
|-
| Decision task difficulty || Factors which make choices more effortful and taxing (e.g., time constraints, decision accountability, presentation format).
|-
| Choice set complexity || How the features of the options within a choice set are related to each other (e.g., a lack of differentiation between options).
|-
|Preference uncertainty
|Extent to which decision makers have preferences and feel knowledgeable about the choice being made.
|-
|Decision goal
|The level of cognitive effort involved in the decision-making process (e.g., intention to make a decision, rather than just browse options).
|}
''Note''. Adapted from Chernev et al. (2015) 

=== Intrinsic motivation ===
Many dominant perspectives in psychology subscribe to the idea that providing choice is essential for promoting [[Motivation and emotion/Book/2013/Intrinsic motivation|''intrinsic motivation'']], a person’s motivation to engage in behaviours solely because they find it enjoyable (Patall et al., 2008). According to [[Motivation and emotion/Book/2011/Self-determination theory|self-determination theory]], the basic human needs for competence, relatedness, and autonomy lay the foundations for intrinsic motivation (Ryan &amp; Deci, 2000). Since choice allows for greater autonomy, it may be considered that more choices would increase intrinsic motivation. However, the overchoice effect contradicts this assumption. 

In a famous study of overchoice by Iyengar and Lepper (2000), students were presented with a list of either six or 30 essay topics for an extra credit assessment. It was found that students in the limited-choice condition were more likely to successfully choose a topic and complete the essay. These students also received, on average, higher essay marks than those who selected their topic from an extensive list. Since all students were informed that their essay would not be graded, the higher quality of essays produced by the limited-choice group was suggested to reflect higher intrinsic motivation. These findings demonstrate that excessive choice may have demotivating effects. Although, since the study did not include a medium-size choice condition, it is not clear whether overchoice decreased intrinsic motivation or if limited choice increased intrinsic motivation.

=== Decision paralysis ===
Overchoice may also result in [[wikipedia:Analysis_paralysis|''decision paralysis'']], a phenomenon in which decision makers experience impaired or inhibited decision-making (Manolică et al., 2021). This concept is similar to what Chernev et al. (2015) describes as ''choice deferral'', which is when people postpone making a decision. Decision makers may struggle to commit to a choice when choosing among many options, due to factors such as overthinking (Manolică et al., 2021). This can cause people to become stuck or &quot;paralysed&quot; in the decision-making process. In one of Iyengar and Lepper’s (2000) experiments, it was found that whilst shoppers were more likely to approach a tasting table with an extensive array of jams, only 3% of those shoppers actually purchased a jam, whereas 30% of shoppers who had viewed a limited selection proceeded to purchase a jam. This shows that whilst a large assortment of options may initially entice decision makers and motivate them to approach a choice, it ultimately hinders their motivation to make a final decision, resulting in no decision being made. 

=== Overchoice in online dating ===

Most research on overchoice has focused on decision-making in typical consumer contexts, with items such as jams, chocolates, birthday cards, and cleaning supplies (Dar-Nimrod et al., 2009; Diehl &amp; Poyner, 2010; Iyengar &amp; Lepper, 2000). Whilst these studies have advanced our knowledge of the choice overload phenomenon, it should be noted that decision-making affects people in various aspects of their lives, not just how they behave as consumers. As such, the overchoice effect is applicable to many different settings, including overchoice in online dating (see Figure 2).     

In a recent study, Thomas et al. (2022) tested the effects of overchoice on dating apps by asking participants to evaluate fake dating profiles. Participants first completed partner-matching questions, then were informed of the number of matches they received. This was manipulated experimentally between groups, including a low, moderate, and high number of matches. Results showed that as dating app users’ perceptions of a high number of potential partners increased, so did their fears of being single. The researchers suggested that when people are overwhelmed by excessive choice, it becomes harder to evaluate options and increases the expectation of being able to find a suitable partner – which, when unmet, may induce fears of being single.

{{RoundBoxTop|theme=1}}
;Mini case study
Francis adopted a pet dog six months ago and is still struggling to decide what to name it. Whenever Francis thinks they are ready to commit to a name, they start to worry that there might be better alternative options, and ends up not being able to decide at all.

{{RoundBoxBottom}}&lt;quiz display=&quot;simple&quot;&gt;
{Which of these concepts best captures what Francis is experiencing? 
|type=&quot;()&quot;}
- Expectation disconfirmation
+ Decision paralysis
- Intrinsic motivation
&lt;/quiz&gt;

==Why does the overchoice effect occur?==
So far, this chapter has touched on the antecedent factors of the overchoice effect and briefly discussed how researchers have studied this phenomenon. Considering people encounter many types of decisions that occur in vastly different domains of life, how can psychological science construct an all-encompassing explanation of why the overchoice effect occurs? Rather than offering a single explanation, researchers have proposed several potential mechanisms for the overchoice effect. Understanding why the overchoice effect occurs is valuable, as it may provide useful insight into ways of mitigating its effects.  

=== Expectation disconfirmation ===
One indication of choice overload is experiencing dissatisfaction with the choice (Chernev et al., 2015). The experience of perceiving an unwanted discrepancy between expectations and reality is known as negative expectation disconfirmation (Diehl &amp; Poyner, 2010). Experimental studies of overchoice have shown that extensive choice sets can lead to more negative expectation disconfirmation, such that decision makers who believe a product has been selected from a large rather than small assortment, set high initial expectations and end up dissatisfied (Diehl &amp; Poyner, 2010). When options are extensive, people may set unrealistically high expectations about being able to achieve a desired outcome, which ultimately increases their chances of experiencing disappointment (Grant &amp; Schwartz, 2011). These findings suggest that decision makers in overchoice situations may benefit from setting realistic or even low expectations which are likely to be met or exceeded.  

=== Increased cognitive costs ===
[[File:Man considering which of three labeled cups to choose while an opponent looks on.webp|left|thumb|213x213px|'''Figure 3'''. Overchoice is costly to mental energy]]

Another mechanism which may explain the overchoice effect is increased cognitive costs. Having too many options to select from means more cognitive resources and mental energy is required to compare the different options (see Figure 3). This is a type of [[wikipedia:Information_overload|information overload]], which can make the decision-making process more onerous and demotivate people from making a choice (Scheibehenne et al., 2010). Cognitive costs may therefore explain why overchoice can result in outcomes such as decision paralysis and choice deferral.  

Referring back to self-determination theory (Ryan &amp; Deci, 2000), whilst choices may increase autonomy, the cognitive resources required to make decisions in overchoice settings could undermine people's psychological need for competence. For example, excessive choices may make people feel like they do not have the mental energy or the expertise to make an informed decision, thus hindering their intrinsic motivation. In terms of addressing this problem, decision makers could try to reduce cognitive resource costs in overchoice situations by setting boundaries on how much time and effort they spend comparing different options.         

=== Anticipated regret ===
Researchers have hypothesised that people experience the overchoice effect due to a fear of future regret (Iyengar &amp; Lepper, 2000). As options increase, so does the potential for decision makers to engage in counterfactual thinking and dwell on “what ifs” after making their choice (Grant &amp; Schwartz, 2011). Indeed, studies show that decision makers who select from extensive assortments tend to experience more regret about their choices compared to those who select from limited assortments (Iyengar &amp; Lepper, 2000). Regret can also impact the decision-making process. For example, Gourville and Soman (2005) found that consumers were more likely to make a choice from a larger assortment if they were informed that their purchase was refundable. This demonstrates that reversibility of choice may mitigate the overchoice effect, as it reduces the potential for later regret. Based on these findings, decision makers may be able to better navigate overchoice by making room for potential future regret. For example, consumers could select products with a flexible return policy or a trial period.

=== The inverted U and brain activity ===
A study by Shah and Wolford (2007) suggested that the overchoice effect follows an inverted U shape. Their study found that whilst purchasing-behaviour increased with the number of options, this peaked at a moderate assortment size and began to decline again once the optimal selection size was surpassed. The mechanism behind this pattern of behaviour has been explored from a physiological perspective. For example, activity in the left striatum and right anterior cingulate cortex – structures involved in motivating decision-making behaviour, appears highest when participants select from a moderate-size choice set and lower when participants select from limited or extensive choice sets (Reutskaja et al., 2018) . This suggests an optimal level of choice facilitates behaviour by activating brain areas which motivate decision-making. It also illustrates that brain activity in extensive-choice conditions are similar to those observed in conditions of limited choice. Taken together, these findings show that whilst too many options can negatively impact decision-making motivation, it is ill-advised to offer too few options.

{{RoundBoxTop|theme=1}}
;Mini case study
Ollie goes to a large book store to find the perfect book to read. After choosing what he believed to be the &quot;best&quot; option, he discovers the book is not interesting, and feels disappointed as a result. {{RoundBoxBottom}}&lt;quiz display=&quot;simple&quot;&gt;
{Which of these concepts best captures what Ollie is experiencing? 
|type=&quot;()&quot;}
- Decision paralysis
- Cognitive resource costs
+ Negative expectation disconfirmation
&lt;/quiz&gt;

== Who is most susceptible to the overchoice effect? ==
The intensity of choice overload is influenced by individual differences and factors related to the decision maker (Chernev et al., 2015). A perceived excess of choice also appears to have varying effects on choice satisfaction across different countries, such that in some countries (e.g., Japan), excess choice actually has a positive effect on choice satisfaction (Reutskaja et al., 2022). In other words, overchoice does not affect everyone in the same way.  

=== Lack of familiarity ===
[[File:HK 中環 Central 皇后大道中 Queen's Road Central the L-Place shop U-Select Supermarket bottled wines October 2020 SS2 01.jpg|thumb|266x266px|'''Figure 4.''' Those who are unfamiliar with a choice domain are more likely to be overwhelmed by large assortment sizes]]

One personal factor which may make someone more susceptible to the overchoice effect is ''preference uncertainty'', which is a lack of prior preferences and expertise (Chernev et al., 2015). When a person is unfamiliar with a decision area, more cognitive resources are required to evaluate different options. Anticipating these time and energy costs may impair or demotivate decision-making all together (Scheibehenne et al., 2010). In a study by Beneke (2015), a sample of participants from South Africa were asked to select a wine from an online store. This was manipulated between groups, so that participants selected from either a large or reduced assortment. The results showed that assortment satisfaction did not differ between the two choice sets for consumers who felt highly familiar with wine. However, those with less familiarity experienced lower assortment satisfaction and higher perceived assortment costs (e.g., processing time, overwhelm, confusion) when the choice set was large (see Figure 4). Based on these findings, decision makers who are unfamiliar with the decision domain may be able to better navigate overchoice by consulting someone with more expertise.  

=== Decision-making orientation ===
Overchoice may also affect people differently based on their decision-making orientation. For example, according to [[Motivation and emotion/Book/2019/Regulatory focus theory and goal pursuit|regulatory focus theory]], people’s decisions are driven by either a ''promotion orientation'' – characterised by a sensitivity to positive outcomes, or a ''prevention orientation'' – characterised by a sensitivity to negative outcomes (Polman, 2012). Theoretically, those who are prevention-oriented would be more vulnerable to the overchoice effect, because a larger choice set is likely to contain more unsatisfactory options; whereas promotion-oriented people would benefit from having more choices, as that would increase their chances of finding a suitable option (Polman, 2012). 

A study by Polman (2012) revealed that when participants were making a decision for themselves, they tended to report a prevention focus and were more likely to experience choice overload. However, this effect was reversed when participants were asked to make a decision for someone else, such that they tended to report a promotion focus and were more likely to be satisfied with a larger choice set. Interestingly, the study found that this reversed effect in proxy decision makers was absent when the decision makers were induced to feel accountable for their choices, presumably because it activated a prevention-focused orientation. Overall, this study demonstrates that large choice sets are more likely to negatively affect decision makers who feel a sense of accountability for their choices – whether they are making a decision for themselves or someone else, due to a heightened sensitivity to potential negative outcomes.

=== Maximisers vs satisficers ===
Similar to decision-making orientation, the effects of overchoice can also differ based on whether people adopt a maximising or satisficing decision-making strategy. [[wikipedia:Maximization_(psychology)|''Maximisers'']] are motivated to get the most out of their choice, often spending considerable effort comparing options in search of the best one (Schwartz et al., 2002). ''Satisficers'', however, make decisions based on what is “good enough”, without expending additional effort to go beyond an acceptable standard (Schwartz et al., 2002). The ‘maximisation paradox’ explains that those with maximising tendencies are more likely to sacrifice resources such as time and energy to increase their choice set, which ultimately results in higher choice dissatisfaction (Dar-Nimrod et al., 2009). 

This concept was illustrated in a study by Dar-Nimrod et al. (2009), which found that maximisers were more willing to give up their time (by completing an additional survey) to obtain a larger array of choices, compared to satisficers. The study also found that maximisers who selected from the larger array were less satisfied with their choice, compared to maximisers who selected from a smaller selection. Furthermore, choice satisfaction did not differ between selection sizes for satisficers. This may be because satisficers tend to minimise search costs by spending less effort searching different options within an extensive choice set  (Reed et al., 2011). In terms of practical application, those who struggle with maximising tendencies could try to adopt a satisficing approach when evaluating options and avoid seeking out large selection sizes.

{{RoundBoxTop|theme=1}};Mini case study
Jen has recently started online dating. She spends a considerable amount of time swiping through profiles to try to find the perfect partner. She wants to make sure she has carefully evaluated all her options before deciding who to go on a date with.

&lt;quiz display=&quot;simple&quot;&gt;

{What decision-making strategy does Jen seem to be using? 
|type=&quot;()&quot;}
+ Maximising
- Satisficing 
- Proxy decision making

{Based on research on the overchoice effect, what is one way Jen might be able to reduce the negative effects of overchoice? 
|type=&quot;()&quot;}
- Spend more time swiping through profiles 
- Sign up to other dating apps to increase her options 
+ Try to limit the number of profiles she swipes through 

&lt;/quiz&gt;
{{RoundBoxBottom}}

==Conclusion==
The overchoice effect is a widely occurring psychological phenomenon in which excessive choice undermines intrinsic motivation (Iyengar &amp; Lepper, 2000) and inhibits decision-making (Manolică et al., 2021). Overchoice can be observed in various contexts – including in consumer behaviour, education, and online dating. However, it is important to remember that increased choice does not guarantee negative outcomes, and choice deprivation also has undesirable consequences (Reutsakaja et al., 2022). Mechanisms underlying the overchoice effect include expectation disconfirmation (Diehl &amp; Poyner, 2010), increased cognitive costs (Scheibehenne et al., 2010), anticipated regret (Iyengar &amp; Lepper, 2000), and reduced activation in brain areas that motivate decision-making (Reutskaja et al., 2018). People who are most susceptible to the overchoice effect include those who lack familiarity with the choice (Beneke, 2015), feel accountable for their decisions (Polman, 2012), and seek to find the “best” option (Dar-Nimrod et al., 2009). 

A key message to take from the overchoice effect is that &quot;more&quot; is not always better. When people seek out more choices, they may unintentionally be making it harder for themselves to come to a satisfactory decision. However, decision makers can take comfort in knowing the overchoice effect is not inevitable. By understanding why this phenomenon occurs and who are most affected, it may be possible to mitigate its effects. Presented below is a summary of the practical recommendations that psychological science has to offer regarding the overchoice effect. 

{{RoundBoxTop|theme=3}}
;Recommendations for decision makers 
* Set realistic expectations (Diehl &amp; Poyner, 2010) 
* Minimise cognitive costs by reducing the time and energy spent making decisions (Scheibehenne et al., 2010)
* Select choices that are reversible (Lepper &amp; Iyengar, 2000)
* Adopt a satisficing approach by settling for a “good enough” option (Dar-Nimrod et al., 2009)
* Increase familiarity with the choice domain (Beneke, 2015)
{{RoundBoxBottom}}

==See also==

* [[Motivation and emotion/Book/2023/Overchoice, motivation, and emotion|Overchoice, motivation, and emotion]] (Book chapter, 2023)
* [[Motivation and emotion/Book/2023/Choice and emotion|Choice and emotion]] (Book chapter, 2023)
* [[Motivation and emotion/Book/2022/Choice overload|Choice overload]] (Book chapter, 2022)
* [[wikipedia:Information_overload|Information overload]] (Wikipedia)
* [[wikipedia:Maximization_(psychology)|Maximisation (psychology)]] (Wikipedia)
* [[wikipedia:Analysis_paralysis|Analysis paralysis]] (Wikipedia)
==References==
{{Hanging indent|1=

Beneke, J. (2015). Are consumers really bewildered by overchoice? An experimental approach to the tyranny of “too much”. ''Journal of Food Products Marketing'', ''21''(1), 90–101. https://doi.org/10.1080/10454446.2013.843490

Chernev, A., Böckenholt, U., &amp; Goodman, J. (2015). Choice overload: A conceptual review and meta-analysis. ''Journal of Consumer Psychology'', ''25''(2), 333–358. https://doi.org/10.1016/j.jcps.2014.08.002

Dar-Nimrod, I., Rawn, C. D., Lehman, D. R., &amp; Schwartz, B. (2009). The maximization paradox: The costs of seeking alternatives. ''Personality and Individual Differences'', ''46''(5), 631–635. https://doi.org/10.1016/j.paid.2009.01.007

Diehl, K, &amp; Poyner, C. (2010). Great expectations?! Assortment size, expectations, and satisfaction. ''Journal of Marketing Research'', ''47''(2), 313–322. https://doi.org/10.1509/jmkr.47.2.312

Grant, A. M., &amp; Schwartz, B. (2011). Too much of a good thing: The challenge and opportunity of the inverted U. ''Perspectives on Psychological Science'', ''6''(1), 61–76. https://doi.org/10.1177/1745691610393523

Gourville, J. T., &amp; Soman, D. (2005). Overchoice and assortment type: When and why variety backfires. ''Marketing Science (Providence, R.I.)'', ''24''(3), 382–395. https://doi.org/10.1287/mksc.1040.0109

Iyengar, S. S., &amp; Lepper, M. R. (2000). When choice is demotivating: Can one desire too much of a good thing? ''Journal of Personality and Social Psychology'', ''79''(6), 995–1006. https://doi.org/10.1037/0022-3514.79.6.995

Manolică, A., Guță, A-S., Roman, T., &amp; Dragăn, L. M. (2021). Is consumer overchoice a reason for decision paralysis? ''Sustainability (Basel, Switzerland)'', ''13''(11), 5920. https://doi.org/10.3390/su13115920

Patall, E. A., Cooper, H., &amp; Robinson, J. C. (2008). The effects of choice on intrinsic motivation and related outcomes: A meta-analysis or research findings. ''Psychological Bulletin'', ''13''(2), 270–300. https://doi.org/10.1037/0033-2909.134.2.270

Polman, E. (2012). Effects of self-other decision making on regulatory focus and choice overload. ''Journal of Personality and Social Psychology'', ''102''(5), 980–993. https://doi.org/10.1037/a0026966

Reed, D. D., Reed, F. D. D., Chok, J., &amp; Brozyna, G. A. (2011). The “tyranny of choice”: Choice overload as a possible instance of effort discounting. ''The Psychological Record'', ''61''(4), 547–560. https://doi.org/10.1007/BF03395776

Reutskaja, E., Cheek, N. N., Iyengar, S., &amp; Schwartz, B. (2022). Choice deprivation, choice overload, and satisfaction with choices across six nations. ''Journal of International Marketing (East Lansing, Mich.)'', ''30''(3), 18–34. https://doi.org/10.1177/1069031X211073821

Reutskaja, E., Lindner, Nagel, R., Andersen, R. A., &amp; Camerer, C.F. (2018). Choice overload reduces neural signatures of choice set value in dorsal striatum and anterior cingulate cortex. ''Nature Human Behaviour'', ''2''(12), 925–935. https://doi.org/10.1038/s41562-018-0440-2

Ryan, R. M., &amp; 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

Scheibehenne, B., Greifeneder, R., &amp; Todd, P. M. (2010). Can there ever be too many options? A meta-analytic review of choice overload. ''Journal of Consumer Research'', ''37''(3), 409–425. https://doi.org/10.1086/651235

Schwartz, B., Ward, A., Monterosso, J., Lyubomirsky, S., White, K., Lehman, D. R., &amp; Diener, E. (2002). Maximizing versus satisficing: Happiness is a matter of choice. ''Journal of Personality and Social Psychology'', ''83''(5), 1178–1197. https://doi.org/10.1037/0022-3514.83.5.1178

Shah, A. M., &amp; Wolford, G. (2007). Buying behavior as a function of parametric variation of number of choices. ''Psychological Science'', ''18''(5), 369–370. https://doi.org/10.1111/j.1467-9280.2007.01906.x

Thomas, M. F., Binder, A., &amp; Matthes, J. (2022). The agony of partner choice: The effect of excessive partner availability on fear of being single, self-esteem, and partner choice overload. ''Computers in Human Behaviour'', ''126'', 106977. https://doi.org/10.1016/j.chb.2021.106977
}}

==External links==
* [https://www.youtube.com/watch?v=1pq5jnM1C-A Sheena Iyengar: How to make choosing easier] (Youtube, 2012)
* [https://youtu.be/VO6XEQIsCoM The paradox of choice ''| Barry Schwartz'']  (Youtube, 2007)
* [https://thedecisionlab.com/biases/choice-overload-bias Why do we have a harder time choosing when we have more options?] (The Decision Lab, n.d)

[[Category:{{#titleparts:{{PAGENAME}}|3}}]]
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{{Shortcut|Boolf-term}}

* {{anchor|BF}} '''Boolean function''', '''BF''' {{spaces|4}} usually meant as BF with infinite arity and periodic truth table {{spaces|4}} &lt;small&gt;similar to {{w|Boolean expression}}&lt;/small&gt;

* {{anchor|TT}} '''truth table''', '''TT''' {{spaces|4}} usually meant as a truth table of finite length, determined by an {{sect|arity}}

* {{anchor|weight}} '''weight''' {{spaces|4}} The weight of a BF is a fraction between 0 and 1. The weight of a TT is a non-negative integer.

* {{anchor|valency|adicity|arity}} '''valency &amp;le; adicity &amp;le; arity'''
** Valency is the number of arguments actually used. It is the number of circles in the Euler diagram.
** Adicity follows from the biggest atom. 2&lt;sup&gt;''adicity''&lt;/sup&gt; is the required TT length&lt;span style=&quot;opacity: .5;&quot;&gt;, or the period length of the infinite truth table.&lt;/span&gt;
** The term ''arity'' is used in two slightly different ways:
*** arity ''n'' as an argument &lt;small&gt;(e.g. of a class method)&lt;/small&gt; to get a finite truth table of length &lt;math&gt;2^n&lt;/math&gt; &amp;nbsp; &lt;small&gt;E.g. &lt;math&gt;B \land C&lt;/math&gt; can be shown as 3-ary &lt;code&gt;0000 0011&lt;/code&gt; or as 4-ary &lt;code&gt;0000 0011 0000 0011&lt;/code&gt;.&lt;/small&gt;
*** arity ''n'' as a shorthand for &lt;math&gt;adicity \le n&lt;/math&gt; &amp;nbsp; &lt;small&gt;(as in: ''the 16 2-ary Boolean functions'')&lt;/small&gt;
***&lt;small style=&quot;opacity: .5;&quot;&gt;(For a while there may also be a third way, namely the erroneous use instead of valency or adicity.)&lt;/small&gt;

* {{anchor|atom}} '''atom''' {{spaces|4}} Atoms are also called sets or arguments of a BF. {{spaces|4}} &lt;small&gt;what is usually shown by a circle and labeled A, B, C...&lt;/small&gt;

* {{anchor|atomvals}} '''atomvals''' {{spaces|4}} the vector of atoms of a BF

* {{anchor|dense}} '''dense''' {{spaces|4}} A dense BF has no gaps before or between the {{sect|atom|atoms}}. Its {{sect|valency|valency and adicity}} are equal. {{spaces|4}} &lt;small&gt;often called non-degenerate&lt;/small&gt; {{spaces|4}}

* {{anchor|spread}} '''spread''' {{spaces|4}} not dense

* {{anchor|root}} '''root''' {{spaces|4}} The root of a BF is its dense equivalent. &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;The term is also used for the TT of the root BF. It is a binary vector of length 2&lt;sup&gt;''valency''&lt;/sup&gt; without repeating patterns.&lt;/small&gt;

* {{anchor|segment}} '''segment''' {{spaces|4}} geometric element of an Euler diagram, e.g. its cells and the walls between them {{spaces|4}} &lt;small&gt;The number of segments in a Venn diagram is 3&lt;sup&gt;''valency''&lt;/sup&gt;.&lt;/small&gt;

{{Collapsible START|dimension of a segment|collapsed wide}}
A segment has a '''dimension''', namely the number of zeros in its ternary label.&lt;br&gt;
&lt;small&gt;(From the perspective of Euler diagrams the term is counter-intuitive, because it corresponds to the {{w|hypercube}}, rather than to the {{w|cross polytope}}. For the {{sect|hypersplit|hypersplits}} it is used in the same way.)&lt;/small&gt;

&lt;div style=&quot;font-size: 80%;&quot;&gt;
The relationships between segments that differ in only one digit are important:
* Another segment with a 0 in the differing place is a '''superior'''. &lt;small&gt;(Points are superior to lines, lines to areas, etc.)&lt;/small&gt;
* Another segment with + or − in the differing place is an '''inferior'''.
* Another segment with the opposite sign in the differing place is a '''neighbor'''.
&lt;/div&gt;

{| class=&quot;collapsible-with-classes collapsible collapsed light followed wide center gap-above&quot;
!colspan=&quot;2&quot;| 2D example {{boolflink|kinide}}
|-
| [[File:EuDi; 2x3 kinide.svg|300px]]&lt;br&gt;Cell 4 is a gapspot.
| [[File:EuDi; 2x3 ternary.svg|600px]]
|}

{| class=&quot;collapsible-with-classes collapsible collapsed light wide center&quot;
!colspan=&quot;2&quot;| 3D example {{boolflink|medusa}}
|-
| [[File:EuDi; medusa.png|400px]]
| [[File:EuDi; medusa ternary.svg|800px]]
|}
{{Collapsible END}}

* {{anchor|spot}} '''spot''' {{spaces|4}} cell of an Euler diagram {{spaces|4}} &lt;small&gt;defined as {{sect|segment}} with dimension 0&lt;/small&gt; {{spaces|4}} &lt;small&gt;The number of spots in a Venn diagram is 2&lt;sup&gt;''valency''&lt;/sup&gt;.&lt;/small&gt;

* {{anchor|fullspot}} '''fullspot''' {{spaces|4}} corresponds to true place in TT

* {{anchor|gapspot}} '''gapspot''' {{spaces|4}} corresponds to false place in TT, but necessary for geometrically sound Euler diagram

* {{anchor|link}} '''link''' {{spaces|4}} connection between neighboring spots, i.e. wall between cells {{spaces|4}} &lt;small&gt;defined as {{sect|segment}} with dimension 1&lt;/small&gt;

* {{anchor|border}} '''border''' {{spaces|4}} set of links that belong to the same {{sect|atom}}, i.e. all walls of the same color

* {{anchor|splits}} [[Studies of Euler diagrams/splits|'''split''']] {{spaces|4}} set without the notion of inside and outside {{spaces|4}} &lt;small&gt;usually the same as a partition into two blocks&lt;/small&gt;

* {{anchor|hypersplit}} [[Studies of Euler diagrams/splits#hypersplits|'''hypersplit''']] {{spaces|4}} generalization of a split {{spaces|4}} partitions space into 2&lt;sup&gt;''n''&lt;/sup&gt; orthants

* {{anchor|filtrate}} [[Studies of Euler diagrams/filtrates|'''filtrate''']] {{spaces|4}} reduction of a BF to a subset of its {{sect|atom|atoms}}, i.e. what remains when some circles are removed from the Euler diagram

* {{anchor|bundle}} '''bundle''' {{spaces|4}} part of an Euler diagram that is connected by crossing borders {{spaces|4}}&lt;small&gt;see e.g. [[Studies of Euler diagrams/decompose|decompose]], [[Studies of Euler diagrams/gap variants/multi-bundle 3-2-2-1|multi-bundle 3-2-2-1]], [[Studies of Euler diagrams/blightless/4-ary/bundles|4-ary bundles]]&lt;/small&gt;

* {{anchor|blighted}} [[Studies of Euler diagrams/blighted|'''blighted''']] {{spaces|4}} arity can be reduced {{spaces|4}} &lt;small&gt;bloated or blotted&lt;/small&gt; {{spaces|4}} &lt;small style=&quot;opacity: .5;&quot;&gt;(blight, blightless)&lt;/small&gt;

* {{anchor|bloated}} [[Studies of Euler diagrams/bloated|'''bloated''']] {{spaces|4}} some arguments are equal or complementary to each other {{spaces|4}} &lt;small style=&quot;opacity: .5;&quot;&gt;(bloat, bloatless)&lt;/small&gt;

* {{anchor|blotted}} [[Studies of Euler diagrams/blotted|'''blotted''']] {{spaces|4}} some arguments are equal or complementary to niverse or empty set {{spaces|4}} &lt;small style=&quot;opacity: .5;&quot;&gt;(blot, blotless)&lt;/small&gt;

* {{anchor|transformation}} [[Studies of Euler diagrams/transformations|'''transformation''']] {{spaces|4}} signed permutation that turns elements of the same {{sect|clan}} into each other

* {{anchor|Zhegalkin_twin|twin}} [[Zhegalkin twins|'''(Zhegalkin) twin''']] {{spaces|4}} Zhegalkin index interpreted as TT of the same length {{spaces|4}} &lt;small style=&quot;opacity: .5;&quot;&gt;(E.g. ''all bits true'' and ''only left bit true'' are always twins, because the Zhegalkin index of the tautology is 1.)&lt;/small&gt;

* {{anchor|zhe}} [[Zhegalkin matrix|'''Zhegalkin index''']], '''Ж''' {{spaces|4}} non-negative integer identifying a Boolean function {{spaces|4}} &lt;small&gt;related to [[algebraic normal form]]&lt;/small&gt;

* {{anchor|representative}} '''representative''' {{spaces|4}} some Boolean function that represents its whole [[Equivalence classes of Boolean functions|equivalence class]] {{spaces|4}} &lt;small&gt;typically the [[smallest Zhegalkin index]] of a {{sect|clan}}&lt;/small&gt;

* {{anchor|junior|senior}} '''junior &lt;small&gt;(senior)&lt;/small&gt;''' {{spaces|4}} Boolean functions of {{sect|arity}} ''n''&amp;minus;1 are junior to those of arity ''n'' &lt;small&gt;(and those of arity ''n''+1 are senior)&lt;/small&gt; {{spaces|4}} 

* {{anchor|quadrant}} '''quadrant''' {{spaces|2}} = {{spaces|2}} {{sect|odd|parity}} + 2 &amp;middot; {{sect|odious|depravity}} {{spaces|2}} &lt;small&gt;&amp;in; {0, 1, 2, 3}&lt;/small&gt;

* {{anchor|reverse}} '''reverse''' {{spaces|2}} BF with reversed TT

* {{anchor|junarity|senarity}} '''junarity &lt;small&gt;(senarity)&lt;/small&gt;''' {{spaces|4}} arity &amp;minus; 1 &lt;small&gt;(arity + 1)&lt;/small&gt;

* {{anchor|noble}} '''[[Noble Boolean functions|noble]]''' {{spaces|4}} TT is noble, iff identical to its {{sect|twin}}

* {{anchor|patron}} '''[[Noble Boolean functions#patrons|patron]]''' {{spaces|4}} XOR of twins, a noble TT

* {{anchor|gentle}} '''[[Gentle sets of Boolean functions|gentle]]''' {{spaces|4}} set of TTs is gentle, iff identical to set of twins


==properties==

&lt;small&gt;see [[Properties of Boolean functions]] and [[Properties of truth tables|of truth tables]]&lt;/small&gt;

* {{anchor|clan}} '''{{BF-prop|clan}}''' {{spaces|4}} negation and permutation equivalence class {{spaces|4}} &lt;small&gt;partitioned into families and factions&lt;/small&gt;

* {{anchor|family}} '''{{BF-prop|family}}''' {{spaces|4}} negation EC

* {{anchor|faction}} '''{{BF-prop|faction}}''' {{spaces|4}} permutation EC

* {{anchor|splinter}} '''splinter''' {{spaces|4}} intersection of family and faction

* {{anchor|tribe}} '''{{TT-prop|tribe}}''' {{spaces|4}} {{sect|sharp|Blunt}} TT form tribes, denoted by their {{sect|consul}} weight.

* {{anchor|super}} '''{{BF-prop|super}}''' {{spaces|4}} Prefix used for EC of BF extended by complement.

* {{anchor|ultra}} '''{{TT-prop|ultra}}''' {{spaces|4}} Prefix used for EC of TT extended by half-complement.

[[File:Foibles of Boolean functions.svg|thumb|160px|foibles]]
* {{anchor|foible}} '''foible''' {{spaces|4}} The foibles are seven properties, that correspond to the vertices of a Fano plane. &amp;nbsp; &lt;small style=&quot;opacity: .5;&quot;&gt;(see [[commons:Category:Quadrant colors in hypercube matrices (image set)|here]] for an overview)&lt;/small&gt;

** {{anchor|even|odd|parity}} '''&lt;span style=&quot;opacity: .5;&quot;&gt;even/&lt;/span&gt;odd''' {{spaces|4}} &lt;span style=&quot;opacity: .5;&quot;&gt;foible of a BF,&lt;/span&gt; equal to first digit of TT {{spaces|4}} &lt;small&gt;'''oddness''' also called '''parity'''&lt;/small&gt;

** {{anchor|evil|odious|depravity}} '''&lt;span style=&quot;opacity: .5;&quot;&gt;evil/&lt;/span&gt;odious''' {{spaces|4}} &lt;span style=&quot;opacity: .5;&quot;&gt;foible of a BF,&lt;/span&gt; equal to last digit of TT {{spaces|4}} &lt;small&gt;'''odiousness''' also called '''depravity'''&lt;/small&gt; {{spaces|4}} &lt;small&gt;BF is odious, iff {{sect|zhe|Ж}} has odd weight&lt;/small&gt;

** {{anchor|ugly}} '''&lt;span style=&quot;opacity: .5;&quot;&gt;pretty/&lt;/span&gt;ugly''' {{spaces|4}} &lt;span style=&quot;opacity: .5;&quot;&gt;foible of a BF,&lt;/span&gt; XOR of odd and odious {{spaces|4}} &lt;small&gt;'''uglyness'''&lt;/small&gt;

** {{anchor|sharp|blunt|dull}} '''&lt;span style=&quot;opacity: .5;&quot;&gt;blunt/&lt;/span&gt;sharp''' {{spaces|4}} &lt;span style=&quot;opacity: .5;&quot;&gt;foible of a TT,&lt;/span&gt; equal to parity of TT weight {{spaces|4}} &lt;small&gt;'''sharpness'''&lt;/small&gt;

** {{anchor|obtuse|acute}} '''&lt;span style=&quot;opacity: .5;&quot;&gt;obtuse/&lt;/span&gt;acute''' {{spaces|4}} &lt;span style=&quot;opacity: .5;&quot;&gt;foible of a TT,&lt;/span&gt; similar to sharpness {{spaces|4}} &lt;small&gt;'''acuteness'''&lt;/small&gt;

** {{anchor|rude|rough}} '''&lt;span style=&quot;opacity: .5;&quot;&gt;polite/&lt;/span&gt;rude''' and '''&lt;span style=&quot;opacity: .5;&quot;&gt;smooth/&lt;/span&gt;rough''' {{spaces|4}} &lt;span style=&quot;opacity: .5;&quot;&gt;foibles of a TT,&lt;/span&gt; similar to sharpness and acuteness  {{spaces|4}} &lt;small&gt;'''rudeness''' and '''roughness'''&lt;/small&gt;

* {{anchor|male|female|gender}} '''&lt;span style=&quot;opacity: .5;&quot;&gt;female/&lt;/span&gt;male''' {{spaces|4}} BF is male, iff its {{sect|root}} is {{sect|sharp}}. {{spaces|4}} &lt;small&gt;'''[[Gender of Boolean functions|gender]]'''&lt;/small&gt;

* {{anchor|prefect}} '''{{BF-prop|prefect}}''' {{spaces|4}}  BF ↦ linear BF

* {{anchor|subprefect|sub-prefect}} '''sub-prefect''' {{spaces|4}}  BF ↦ senior linear BF &amp;nbsp; &lt;small&gt;([[commons:Category:3-ary Boolean functions in octeract matrix; great subprefects|category]])&lt;/small&gt;

* {{anchor|consul}} '''{{TT-prop|consul}}''' {{spaces|4}} TT ↦ linear TT &amp;nbsp; &lt;small style=&quot;opacity: .5;&quot;&gt;(basically twin prefect)&lt;/small&gt;

* {{anchor|praetor}} '''{{TT-prop|praetor}}''' {{spaces|4}} XOR of left and right half of TT

* {{anchor|quaestor}} '''{{TT-prop|quaestor}}''' {{spaces|4}} XOR of left and reversed right half of TT

* {{anchor|principality|dominion}} {{TT-prop|principalities and dominions|'''principality''' and '''dominion'''}} {{spaces|4}} &amp;nbsp; {{sect|junior|juniors}} corresponding to {{sect|noble}} {{sect|faction|factions}} 

&lt;div style=&quot;opacity: .5;&quot;&gt;
===provisional===

* {{anchor|partner|friend}} '''partner/friend''' {{spaces|4}} BF whose TT differ only in least/most significant bit. Applies also to factions.

* {{anchor|squad}} '''squad''' {{spaces|4}} Union of a faction with its complement, its partner and its complement partner. Always four factions.

* {{anchor|platoon}} '''platoon''' {{spaces|4}} Union of a squad and its twin. May consist of one of two squads, i.e. four or eight factions.

* {{anchor|company}} '''company''' {{spaces|4}} The name would make sense for the union of a platoon and its friend. May consist of one or two platoons.

* {{anchor|cluster}} '''cluster''' {{spaces|4}} That name is still used for platoon.

* {{anchor|federation}} '''federation''' {{spaces|4}} related to clusters and great dominions

&lt;/div&gt;

==general terms==

These words are sometimes used in variable names.

* {{anchor|recto|verso}} '''{{w|recto and verso}}''' {{spaces|2}} inside and outside of a set &amp;nbsp; &lt;small&gt;(see also {{sect|split}})&lt;/small&gt;

* {{anchor|paltry|plenty|plethora|galore}} powers of two and factorial

{| class=&quot;wikitable&quot; style=&quot;text-align: center;&quot;
| &lt;math&gt;n&lt;/math&gt; || &lt;math&gt;2^n&lt;/math&gt; || &lt;math&gt;2^{2^n}&lt;/math&gt; || &lt;math&gt;n!&lt;/math&gt;
|- style=&quot;font-weight: bold;&quot;
| paltry || plenty || plethora || galore
|}


&lt;span style=&quot;height: 1000px; display: inline-block;&quot;&gt;
&lt;!-- empty space to make the links jump to line --&gt;
&lt;/span&gt;


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    <title>Studies of Boolean functions</title>
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    <id>304964</id>
    <revision>
      <id>2693210</id>
      <parentid>2692932</parentid>
      <timestamp>2024-12-25T19:34:07Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693210</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4211" sha1="h2qsxt2hpaccek0jaqv61zsjdqtnv3f" xml:space="preserve">These articles about Boolean functions use a similar style and terminology. &amp;nbsp;
&lt;small style=&quot;opacity: .7;&quot;&gt;They are created by [[User:Watchduck|Watchduck]] a.k.a. Tilman Piesk.&lt;/small&gt;

* '''[[Studies of Boolean functions/terminology]]'''
* '''[[Studies of Boolean functions/examples]]'''
* '''[[Discrete helpers/boolf]]'''

* [[hard properties of Boolean functions|hard]] and [[soft properties of Boolean functions|soft]] [[properties of Boolean functions]]
* [[Integer sequences related to Boolean functions]]
* [[Linear Boolean functions]]
* [[Gender of Boolean functions]]
* [[Mentors of Boolean functions]]
* [[Principalities and dominions of Boolean functions]]
* [[Families of Boolean functions]]
* [[Nonlinearity of Boolean functions]]
* &lt;small&gt;[[Tesseract and 16-cell faces]]&lt;/small&gt;

==[[Studies of Euler diagrams]]==
&lt;gallery&gt;
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
&lt;/gallery&gt;


==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=&quot;text-align: center; background-color: #f8f9fa; border: 1px solid #a2a9b1&quot;
|style=&quot;padding-right: 20px;&quot;| [[commons:Category:3-ary Zhegalkin indices in octeract matrix; great principalities; with entries on diagonal|3-ary]] &lt;span style=&quot;font-size: 70%; opacity: .6;&quot;&gt;(4)&lt;/span&gt;
|style=&quot;padding-right: 20px;&quot;| [[commons:Category:4-ary Zhegalkin indices in 16-cube matrix; great principalities; with entries on diagonal|4-ary]] &lt;span style=&quot;font-size: 70%; opacity: .6;&quot;&gt;(20)&lt;/span&gt;
|rowspan=&quot;2&quot; style=&quot;text-align: right; padding-right: 10px;&quot;| great principalities &lt;small&gt;with entries&lt;/small&gt;
|style=&quot;text-align: left; padding-right: 0 20px;&quot;| on diagonal &amp;nbsp; &lt;span style=&quot;font-size: 70%; opacity: .6;&quot;&gt;(related to patron dominions)&lt;/span&gt;
|-
|style=&quot;padding-right: 20px;&quot;| [[commons:Category:3-ary Zhegalkin indices in octeract matrix; great principalities; with entries in top row|3-ary]] &lt;span style=&quot;font-size: 70%; opacity: .6;&quot;&gt;(4)&lt;/span&gt;
|style=&quot;padding-right: 20px;&quot;| [[commons:Category:4-ary Zhegalkin indices in 16-cube matrix; great principalities; with entries in top row|4-ary]] &lt;span style=&quot;font-size: 70%; opacity: .6;&quot;&gt;(22)&lt;/span&gt;
|style=&quot;text-align: left; padding-right: 0 20px;&quot;| in top row &amp;nbsp; &lt;span style=&quot;font-size: 70%; opacity: .6;&quot;&gt;(related to patron principalities)&lt;/span&gt;
|}


{| class=&quot;wikitable&quot; style=&quot;width: 800px; text-align: center;&quot;
|
[[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=&quot;wikitable&quot; style=&quot;width: 800px; text-align: center;&quot;
|
[[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]]</text>
      <sha1>h2qsxt2hpaccek0jaqv61zsjdqtnv3f</sha1>
    </revision>
  </page>
  <page>
    <title>Gender of Boolean functions</title>
    <ns>0</ns>
    <id>305297</id>
    <revision>
      <id>2693171</id>
      <parentid>2668986</parentid>
      <timestamp>2024-12-25T12:20:02Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693171</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3322" sha1="8mzd3fxh2uzigaavtazupjzda57y1ur" xml:space="preserve">{{Boolf header}}

[[File:Gender ratio of Boolean functions.svg|thumb|300px|gender ratio for arities 0...5]]

A Boolean function shall be called ''male'', iff its [[Boolf-term#root|root]] is [[Boolf-term#sharp|sharp]] &lt;small&gt;(i. e. iff its compressed truth table has odd weight)&lt;/small&gt;.&lt;br&gt;
&lt;small&gt;(Equivalently, it is ''female'', iff after removing all repetitions, the weight of the truth table is still even.)&lt;/small&gt;

For positive arities, there are more males than females. The imbalance peaks for arity 2. For higher arities, the ratio is almost balanced.&lt;br&gt;
&lt;small&gt;The ratio is balanced for the infinite set of all Boolean functions. Both sets are countable, so there is a trivial bijection. But is there a meaningful bijection?&lt;/small&gt;

{{Gender of Boolean functions/triangles}}


----


{{Collapsible START|truth tables &amp;nbsp; &lt;small&gt;(Zhegalkin matrix)&lt;/small&gt;|collapsed wide followed}}
These matrices show the 97 females and 159 males among the first 256 Boolean functions.&lt;br&gt;
The matrix above shows the Zhegalkin indices. The [[Zhegalkin matrix]] below shows the truth tables.&lt;br&gt;
&lt;small&gt;The male truth tables on the left side of the matrix contain repetitions, i.e. their pattern can be described by a shorter truth table.&lt;/small&gt;

[[File:Gender of 3-ary Boolean functions.svg|left|1400px]]
{{Collapsible END}}

{{Collapsible START|atomvals &amp;nbsp; &lt;small&gt;(bitwise OR)&lt;/small&gt;|collapsed wide}}
The upper matrix shows the Zhegalkin indices. The one below shows [[Boolf-term#atomvals|atomvals]] of the corresponding Boolean functions.&lt;br&gt;
This is sequence {{oeis|A327041}}, the bitwise ORs of the binary exponents seen above.
[[File:Gender of 3-ary Boolean functions with bitwise OR of Zhegalkin exponents.svg|left|1400px]]
{{Collapsible END}}


----


{{Gender of Boolean functions/Zhegalkin indices}}


==gender and honesty==

The XOR of all members of a [[Families of Boolean functions|family]] is either the tautology or the contradiction. Where it is the tautology, the BF shall be called ''honest''.

{{Collapsible START|female &lt;small&gt;(97)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 1017990932654081869095106387729709156216293000755592970863399350444565463617.svg|800px]]
{{Collapsible END}}
{{Collapsible START|dishonest &lt;small&gt;(57)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 7494979546278868352838388259605652777030681542822747306921801562456065.svg|800px]]
{{Collapsible END}}
{{Collapsible START|balanced &lt;small&gt;(70)&lt;/small&gt;|collapsed center wide}}
These are the BF whose truth table has weight 4. Almost all dishonest BF are balanced. The contradiction is the only exception.&lt;br&gt;
[[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|800px]]
{{Collapsible END}}

{{Collapsible START|male &lt;small&gt;(159)&lt;/small&gt;|collapsed center wide followed light gap-above}}
[[File:Set of 3-ary Boolean functions 114774098304662113554475878620958198697053691664884971068594184657468564176318.svg|800px]]
{{Collapsible END}}
{{Collapsible START|honest &lt;small&gt;(199)&lt;/small&gt;|collapsed center wide light}}
[[File:Set of 3-ary Boolean functions 115792081742336649144702632170299648247617207634959021216710277086111567183870.svg|800px]]
{{Collapsible END}}


[[Category:Gender of Boolean functions]]</text>
      <sha1>8mzd3fxh2uzigaavtazupjzda57y1ur</sha1>
    </revision>
    <revision>
      <id>2693178</id>
      <parentid>2693171</parentid>
      <timestamp>2024-12-25T13:33:28Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693178</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4089" sha1="cjluxafj3z4g755ondgltbzcd5l5zcg" xml:space="preserve">{{Boolf header}}

[[File:Gender ratio of Boolean functions.svg|thumb|300px|gender ratio for arities 0...5]]

A Boolean function shall be called ''male'', iff its [[Boolf-term#root|root]] is [[Boolf-term#sharp|sharp]] &lt;small&gt;(i. e. iff its compressed truth table has odd weight)&lt;/small&gt;.&lt;br&gt;
&lt;small&gt;(Equivalently, it is ''female'', iff after removing all repetitions, the weight of the truth table is still even.)&lt;/small&gt;

For positive arities, there are more males than females. The imbalance peaks for arity 2. For higher arities, the ratio is almost balanced.&lt;br&gt;
&lt;small&gt;The ratio is balanced for the infinite set of all Boolean functions. Both sets are countable, so there is a trivial bijection. But is there a meaningful bijection?&lt;/small&gt;

{{Gender of Boolean functions/triangles}}


----


{{Collapsible START|truth tables &amp;nbsp; &lt;small&gt;(Zhegalkin matrix)&lt;/small&gt;|collapsed wide followed}}
These matrices show the 97 females and 159 males among the first 256 Boolean functions.&lt;br&gt;
The matrix above shows the Zhegalkin indices. The [[Zhegalkin matrix]] below shows the truth tables.&lt;br&gt;
&lt;small&gt;The male truth tables on the left side of the matrix contain repetitions, i.e. their pattern can be described by a shorter truth table.&lt;/small&gt;

[[File:Gender of 3-ary Boolean functions.svg|left|1400px]]
{{Collapsible END}}

{{Collapsible START|atomvals &amp;nbsp; &lt;small&gt;(bitwise OR)&lt;/small&gt;|collapsed wide}}
The upper matrix shows the Zhegalkin indices. The one below shows [[Boolf-term#atomvals|atomvals]] of the corresponding Boolean functions.&lt;br&gt;
This is sequence {{oeis|A327041}}, the bitwise ORs of the binary exponents seen above.
[[File:Gender of 3-ary Boolean functions with bitwise OR of Zhegalkin exponents.svg|left|1400px]]
{{Collapsible END}}


----


{{Gender of Boolean functions/Zhegalkin indices}}


==gender and honesty==

The XOR of all members of a [[Families of Boolean functions|family]] is either the tautology or the contradiction. Where it is the tautology, the BF shall be called ''honest''.&lt;br&gt;
Apparently there are no dishonest males. &lt;small&gt;So every dishonest is female, and every male is honest.&lt;/small&gt;
&lt;small style=&quot;font-size: 60%; opacity: .5;&quot;&gt;(It should be kept in mind, that these are statements about Boolean functions. Generally, it is discouraged to assume, that all males are honest.)&lt;/small&gt;

{{Collapsible START|blunt &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed}}
[[File:Set of 3-ary Boolean functions 68033174967769840440887906939858451149105560803546820641877549596291376780905.svg|800px]]
{{Collapsible END}}
{{Collapsible START|female &lt;small&gt;(97)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 1017990932654081869095106387729709156216293000755592970863399350444565463617.svg|800px]]
{{Collapsible END}}
{{Collapsible START|dishonest &lt;small&gt;(57)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 7494979546278868352838388259605652777030681542822747306921801562456065.svg|800px]]
{{Collapsible END}}
{{Collapsible START|balanced &lt;small&gt;(70)&lt;/small&gt;|collapsed center wide}}
These are the BF whose truth table has weight 4. Almost all dishonest BF are balanced. Only the contradiction is not.&lt;br&gt;
[[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|800px]]
{{Collapsible END}}

{{Collapsible START|sharp &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed light gap-above}}
[[File:Set of 3-ary Boolean functions 47758914269546354982683078068829456704164423862093743397580034411621752859030.svg|800px]]
{{Collapsible END}}
{{Collapsible START|male &lt;small&gt;(159)&lt;/small&gt;|collapsed center wide followed light}}
[[File:Set of 3-ary Boolean functions 114774098304662113554475878620958198697053691664884971068594184657468564176318.svg|800px]]
{{Collapsible END}}
{{Collapsible START|honest &lt;small&gt;(199)&lt;/small&gt;|collapsed center wide light}}
[[File:Set of 3-ary Boolean functions 115792081742336649144702632170299648247617207634959021216710277086111567183870.svg|800px]]
{{Collapsible END}}


[[Category:Gender of Boolean functions]]</text>
      <sha1>cjluxafj3z4g755ondgltbzcd5l5zcg</sha1>
    </revision>
    <revision>
      <id>2693181</id>
      <parentid>2693178</parentid>
      <timestamp>2024-12-25T14:05:17Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>/* gender and honesty */</comment>
      <origin>2693181</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4343" sha1="o34nsgxcp8wrd515wn8nm952ctpmg2j" xml:space="preserve">{{Boolf header}}

[[File:Gender ratio of Boolean functions.svg|thumb|300px|gender ratio for arities 0...5]]

A Boolean function shall be called ''male'', iff its [[Boolf-term#root|root]] is [[Boolf-term#sharp|sharp]] &lt;small&gt;(i. e. iff its compressed truth table has odd weight)&lt;/small&gt;.&lt;br&gt;
&lt;small&gt;(Equivalently, it is ''female'', iff after removing all repetitions, the weight of the truth table is still even.)&lt;/small&gt;

For positive arities, there are more males than females. The imbalance peaks for arity 2. For higher arities, the ratio is almost balanced.&lt;br&gt;
&lt;small&gt;The ratio is balanced for the infinite set of all Boolean functions. Both sets are countable, so there is a trivial bijection. But is there a meaningful bijection?&lt;/small&gt;

{{Gender of Boolean functions/triangles}}


----


{{Collapsible START|truth tables &amp;nbsp; &lt;small&gt;(Zhegalkin matrix)&lt;/small&gt;|collapsed wide followed}}
These matrices show the 97 females and 159 males among the first 256 Boolean functions.&lt;br&gt;
The matrix above shows the Zhegalkin indices. The [[Zhegalkin matrix]] below shows the truth tables.&lt;br&gt;
&lt;small&gt;The male truth tables on the left side of the matrix contain repetitions, i.e. their pattern can be described by a shorter truth table.&lt;/small&gt;

[[File:Gender of 3-ary Boolean functions.svg|left|1400px]]
{{Collapsible END}}

{{Collapsible START|atomvals &amp;nbsp; &lt;small&gt;(bitwise OR)&lt;/small&gt;|collapsed wide}}
The upper matrix shows the Zhegalkin indices. The one below shows [[Boolf-term#atomvals|atomvals]] of the corresponding Boolean functions.&lt;br&gt;
This is sequence {{oeis|A327041}}, the bitwise ORs of the binary exponents seen above.
[[File:Gender of 3-ary Boolean functions with bitwise OR of Zhegalkin exponents.svg|left|1400px]]
{{Collapsible END}}


----


{{Gender of Boolean functions/Zhegalkin indices}}


==gender and honesty==

The XOR of all members of a [[Families of Boolean functions|family]] is either the tautology or the contradiction. Where it is the tautology, the BF shall be called ''honest''.&lt;br&gt;
Apparently there are no dishonest males. &lt;small&gt;So every dishonest BF is female, and every male BF is honest.&lt;/small&gt;
&lt;small style=&quot;font-size: 60%; opacity: .5;&quot;&gt;(It should be kept in mind, that these are statements about Boolean functions. Generally, it is discouraged to assume, that all males are honest.)&lt;/small&gt;

{{Collapsible START|blunt &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed}}
[[File:Set of 3-ary Boolean functions 68033174967769840440887906939858451149105560803546820641877549596291376780905.svg|800px]]
{{Collapsible END}}
{{Collapsible START|female &lt;small&gt;(97)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 1017990932654081869095106387729709156216293000755592970863399350444565463617.svg|800px]]
{{Collapsible END}}
{{Collapsible START|dishonest &lt;small&gt;(57)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 7494979546278868352838388259605652777030681542822747306921801562456065.svg|800px]]
{{Collapsible END}}
{{Collapsible START|balanced &lt;small&gt;(70)&lt;/small&gt;|collapsed center wide}}
These are the BF whose truth table has weight 4. Almost all dishonest BF are balanced. Only the contradiction is not.&lt;br&gt;
[[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|800px]]
{{Collapsible END}}

{{Collapsible START|honest female &lt;small&gt;(40)&lt;/small&gt;|collapsed center wide gap-above color-beige}}
[[File:Set of 3-ary Boolean functions 1017983437674535590226753549341449550563515970074050148116092428643003007552.svg|800px]]
{{Collapsible END}}

{{Collapsible START|sharp &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed gap-above light}}
[[File:Set of 3-ary Boolean functions 47758914269546354982683078068829456704164423862093743397580034411621752859030.svg|800px]]
{{Collapsible END}}
{{Collapsible START|male &lt;small&gt;(159)&lt;/small&gt;|collapsed center wide followed light}}
[[File:Set of 3-ary Boolean functions 114774098304662113554475878620958198697053691664884971068594184657468564176318.svg|800px]]
{{Collapsible END}}
{{Collapsible START|honest &lt;small&gt;(199)&lt;/small&gt;|collapsed center wide light}}
[[File:Set of 3-ary Boolean functions 115792081742336649144702632170299648247617207634959021216710277086111567183870.svg|800px]]
{{Collapsible END}}


[[Category:Gender of Boolean functions]]</text>
      <sha1>o34nsgxcp8wrd515wn8nm952ctpmg2j</sha1>
    </revision>
    <revision>
      <id>2693183</id>
      <parentid>2693181</parentid>
      <timestamp>2024-12-25T14:19:15Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693183</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4709" sha1="tqeq2yqmp9kvc6gs2mgrvuaw8nnzepr" xml:space="preserve">{{Boolf header}}

[[File:Gender ratio of Boolean functions.svg|thumb|300px|gender ratio for arities 0...5]]

A Boolean function shall be called ''male'', iff its [[Boolf-term#root|root]] is [[Boolf-term#sharp|sharp]] &lt;small&gt;(i. e. iff its compressed truth table has odd weight)&lt;/small&gt;.&lt;br&gt;
&lt;small&gt;(Equivalently, it is ''female'', iff after removing all repetitions, the weight of the truth table is still even.)&lt;/small&gt;

For positive arities, there are more males than females. The imbalance peaks for arity 2. For higher arities, the ratio is almost balanced.&lt;br&gt;
&lt;small&gt;The ratio is balanced for the infinite set of all Boolean functions. Both sets are countable, so there is a trivial bijection. But is there a meaningful bijection?&lt;/small&gt;

{{Gender of Boolean functions/triangles}}


----


{{Collapsible START|truth tables &amp;nbsp; &lt;small&gt;(Zhegalkin matrix)&lt;/small&gt;|collapsed wide followed}}
These matrices show the 97 females and 159 males among the first 256 Boolean functions.&lt;br&gt;
The matrix above shows the Zhegalkin indices. The [[Zhegalkin matrix]] below shows the truth tables.&lt;br&gt;
&lt;small&gt;The male truth tables on the left side of the matrix contain repetitions, i.e. their pattern can be described by a shorter truth table.&lt;/small&gt;

[[File:Gender of 3-ary Boolean functions.svg|left|1400px]]
{{Collapsible END}}

{{Collapsible START|atomvals &amp;nbsp; &lt;small&gt;(bitwise OR)&lt;/small&gt;|collapsed wide}}
The upper matrix shows the Zhegalkin indices. The one below shows [[Boolf-term#atomvals|atomvals]] of the corresponding Boolean functions.&lt;br&gt;
This is sequence {{oeis|A327041}}, the bitwise ORs of the binary exponents seen above.
[[File:Gender of 3-ary Boolean functions with bitwise OR of Zhegalkin exponents.svg|left|1400px]]
{{Collapsible END}}


----


{{Gender of Boolean functions/Zhegalkin indices}}


==gender and honesty==

The XOR of all members of a [[Families of Boolean functions|family]] is either the tautology or the contradiction. Where it is the tautology, the BF shall be called ''honest''.&lt;br&gt;
Apparently there are no dishonest males. &lt;small&gt;So every dishonest BF is female, and every male BF is honest.&lt;/small&gt;
&lt;small style=&quot;font-size: 60%; opacity: .5;&quot;&gt;(It should be kept in mind, that these are statements about Boolean functions. Generally, it is discouraged to assume, that all males are honest.)&lt;/small&gt;

The following images show 3-ary Boolean functions.&lt;br&gt;
&lt;small&gt;The pattern of Zhegalkin indices for dishonest BF is similar to a [[c:File:Binary Walsh matrix of order 8 with row numbers (gray).svg|Walsh matrix]] &lt;small&gt;(with columns 3 and 7 exchanged)&lt;/small&gt;. But that is specific to arity 3. So is the fact, that all non-trivial dishonest BF are balanced.&lt;/small&gt;

{{Collapsible START|blunt &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed}}
[[File:Set of 3-ary Boolean functions 68033174967769840440887906939858451149105560803546820641877549596291376780905.svg|800px]]
{{Collapsible END}}
{{Collapsible START|female &lt;small&gt;(97)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 1017990932654081869095106387729709156216293000755592970863399350444565463617.svg|800px]]
{{Collapsible END}}
{{Collapsible START|dishonest &lt;small&gt;(57)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 7494979546278868352838388259605652777030681542822747306921801562456065.svg|800px]]
{{Collapsible END}}
{{Collapsible START|balanced &lt;small&gt;(70)&lt;/small&gt;|collapsed center wide}}
These are the BF whose truth table has weight 4. Almost all dishonest BF are balanced. Only the contradiction is not.&lt;br&gt;
[[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|800px]]
{{Collapsible END}}

{{Collapsible START|honest female &lt;small&gt;(40)&lt;/small&gt;|collapsed center wide gap-above color-beige}}
[[File:Set of 3-ary Boolean functions 1017983437674535590226753549341449550563515970074050148116092428643003007552.svg|800px]]
{{Collapsible END}}

{{Collapsible START|sharp &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed gap-above light}}
[[File:Set of 3-ary Boolean functions 47758914269546354982683078068829456704164423862093743397580034411621752859030.svg|800px]]
{{Collapsible END}}
{{Collapsible START|male &lt;small&gt;(159)&lt;/small&gt;|collapsed center wide followed light}}
[[File:Set of 3-ary Boolean functions 114774098304662113554475878620958198697053691664884971068594184657468564176318.svg|800px]]
{{Collapsible END}}
{{Collapsible START|honest &lt;small&gt;(199)&lt;/small&gt;|collapsed center wide light}}
[[File:Set of 3-ary Boolean functions 115792081742336649144702632170299648247617207634959021216710277086111567183870.svg|800px]]
{{Collapsible END}}


[[Category:Gender of Boolean functions]]</text>
      <sha1>tqeq2yqmp9kvc6gs2mgrvuaw8nnzepr</sha1>
    </revision>
    <revision>
      <id>2693184</id>
      <parentid>2693183</parentid>
      <timestamp>2024-12-25T14:19:54Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>/* gender and honesty */</comment>
      <origin>2693184</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4759" sha1="smmx1npraybdnazzk2fnafq0ne113u8" xml:space="preserve">{{Boolf header}}

[[File:Gender ratio of Boolean functions.svg|thumb|300px|gender ratio for arities 0...5]]

A Boolean function shall be called ''male'', iff its [[Boolf-term#root|root]] is [[Boolf-term#sharp|sharp]] &lt;small&gt;(i. e. iff its compressed truth table has odd weight)&lt;/small&gt;.&lt;br&gt;
&lt;small&gt;(Equivalently, it is ''female'', iff after removing all repetitions, the weight of the truth table is still even.)&lt;/small&gt;

For positive arities, there are more males than females. The imbalance peaks for arity 2. For higher arities, the ratio is almost balanced.&lt;br&gt;
&lt;small&gt;The ratio is balanced for the infinite set of all Boolean functions. Both sets are countable, so there is a trivial bijection. But is there a meaningful bijection?&lt;/small&gt;

{{Gender of Boolean functions/triangles}}


----


{{Collapsible START|truth tables &amp;nbsp; &lt;small&gt;(Zhegalkin matrix)&lt;/small&gt;|collapsed wide followed}}
These matrices show the 97 females and 159 males among the first 256 Boolean functions.&lt;br&gt;
The matrix above shows the Zhegalkin indices. The [[Zhegalkin matrix]] below shows the truth tables.&lt;br&gt;
&lt;small&gt;The male truth tables on the left side of the matrix contain repetitions, i.e. their pattern can be described by a shorter truth table.&lt;/small&gt;

[[File:Gender of 3-ary Boolean functions.svg|left|1400px]]
{{Collapsible END}}

{{Collapsible START|atomvals &amp;nbsp; &lt;small&gt;(bitwise OR)&lt;/small&gt;|collapsed wide}}
The upper matrix shows the Zhegalkin indices. The one below shows [[Boolf-term#atomvals|atomvals]] of the corresponding Boolean functions.&lt;br&gt;
This is sequence {{oeis|A327041}}, the bitwise ORs of the binary exponents seen above.
[[File:Gender of 3-ary Boolean functions with bitwise OR of Zhegalkin exponents.svg|left|1400px]]
{{Collapsible END}}


----


{{Gender of Boolean functions/Zhegalkin indices}}


==honesty and gender==

The XOR of all members of a [[Families of Boolean functions|family]] is either the tautology or the contradiction. Where it is the tautology, the BF shall be called ''honest''.&lt;br&gt;
Apparently there are no dishonest males. &lt;small&gt;So every dishonest BF is female, and every male BF is honest.&lt;/small&gt;
&lt;small style=&quot;font-size: 60%; opacity: .5;&quot;&gt;(It should be kept in mind, that these are statements about Boolean functions. Generally, it is discouraged to assume, that all males are honest.)&lt;/small&gt;

The following images show 3-ary Boolean functions. See also: [[Boolf prop/3-ary/honesty and gender]]&lt;br&gt;
&lt;small&gt;The pattern of Zhegalkin indices for dishonest BF is similar to a [[c:File:Binary Walsh matrix of order 8 with row numbers (gray).svg|Walsh matrix]] &lt;small&gt;(with columns 3 and 7 exchanged)&lt;/small&gt;. But that is specific to arity 3. So is the fact, that all non-trivial dishonest BF are balanced.&lt;/small&gt;

{{Collapsible START|blunt &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed}}
[[File:Set of 3-ary Boolean functions 68033174967769840440887906939858451149105560803546820641877549596291376780905.svg|800px]]
{{Collapsible END}}
{{Collapsible START|female &lt;small&gt;(97)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 1017990932654081869095106387729709156216293000755592970863399350444565463617.svg|800px]]
{{Collapsible END}}
{{Collapsible START|dishonest &lt;small&gt;(57)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 7494979546278868352838388259605652777030681542822747306921801562456065.svg|800px]]
{{Collapsible END}}
{{Collapsible START|balanced &lt;small&gt;(70)&lt;/small&gt;|collapsed center wide}}
These are the BF whose truth table has weight 4. Almost all dishonest BF are balanced. Only the contradiction is not.&lt;br&gt;
[[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|800px]]
{{Collapsible END}}

{{Collapsible START|honest female &lt;small&gt;(40)&lt;/small&gt;|collapsed center wide gap-above color-beige}}
[[File:Set of 3-ary Boolean functions 1017983437674535590226753549341449550563515970074050148116092428643003007552.svg|800px]]
{{Collapsible END}}

{{Collapsible START|sharp &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed gap-above light}}
[[File:Set of 3-ary Boolean functions 47758914269546354982683078068829456704164423862093743397580034411621752859030.svg|800px]]
{{Collapsible END}}
{{Collapsible START|male &lt;small&gt;(159)&lt;/small&gt;|collapsed center wide followed light}}
[[File:Set of 3-ary Boolean functions 114774098304662113554475878620958198697053691664884971068594184657468564176318.svg|800px]]
{{Collapsible END}}
{{Collapsible START|honest &lt;small&gt;(199)&lt;/small&gt;|collapsed center wide light}}
[[File:Set of 3-ary Boolean functions 115792081742336649144702632170299648247617207634959021216710277086111567183870.svg|800px]]
{{Collapsible END}}


[[Category:Gender of Boolean functions]]</text>
      <sha1>smmx1npraybdnazzk2fnafq0ne113u8</sha1>
    </revision>
    <revision>
      <id>2693185</id>
      <parentid>2693184</parentid>
      <timestamp>2024-12-25T14:20:43Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>/* honesty and gender */</comment>
      <origin>2693185</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4781" sha1="0rufz40zry4cot3pv0xm0n4er0hz1v8" xml:space="preserve">{{Boolf header}}

[[File:Gender ratio of Boolean functions.svg|thumb|300px|gender ratio for arities 0...5]]

A Boolean function shall be called ''male'', iff its [[Boolf-term#root|root]] is [[Boolf-term#sharp|sharp]] &lt;small&gt;(i. e. iff its compressed truth table has odd weight)&lt;/small&gt;.&lt;br&gt;
&lt;small&gt;(Equivalently, it is ''female'', iff after removing all repetitions, the weight of the truth table is still even.)&lt;/small&gt;

For positive arities, there are more males than females. The imbalance peaks for arity 2. For higher arities, the ratio is almost balanced.&lt;br&gt;
&lt;small&gt;The ratio is balanced for the infinite set of all Boolean functions. Both sets are countable, so there is a trivial bijection. But is there a meaningful bijection?&lt;/small&gt;

{{Gender of Boolean functions/triangles}}


----


{{Collapsible START|truth tables &amp;nbsp; &lt;small&gt;(Zhegalkin matrix)&lt;/small&gt;|collapsed wide followed}}
These matrices show the 97 females and 159 males among the first 256 Boolean functions.&lt;br&gt;
The matrix above shows the Zhegalkin indices. The [[Zhegalkin matrix]] below shows the truth tables.&lt;br&gt;
&lt;small&gt;The male truth tables on the left side of the matrix contain repetitions, i.e. their pattern can be described by a shorter truth table.&lt;/small&gt;

[[File:Gender of 3-ary Boolean functions.svg|left|1400px]]
{{Collapsible END}}

{{Collapsible START|atomvals &amp;nbsp; &lt;small&gt;(bitwise OR)&lt;/small&gt;|collapsed wide}}
The upper matrix shows the Zhegalkin indices. The one below shows [[Boolf-term#atomvals|atomvals]] of the corresponding Boolean functions.&lt;br&gt;
This is sequence {{oeis|A327041}}, the bitwise ORs of the binary exponents seen above.
[[File:Gender of 3-ary Boolean functions with bitwise OR of Zhegalkin exponents.svg|left|1400px]]
{{Collapsible END}}


----


{{Gender of Boolean functions/Zhegalkin indices}}


==honesty and gender==

The XOR of all members of a [[Families of Boolean functions|family]] is either the tautology or the contradiction. Where it is the tautology, the BF shall be called ''honest''.&lt;br&gt;
Apparently there are no dishonest males. &lt;small&gt;So every dishonest BF is female, and every male BF is honest.&lt;/small&gt;
&lt;small style=&quot;font-size: 60%; opacity: .5;&quot;&gt;(It should be kept in mind, that these are statements about Boolean functions. Generally, it is discouraged to assume, that all males are honest.)&lt;/small&gt;

The following images show 3-ary Boolean functions. &amp;nbsp; &lt;small&gt;See also: [[Boolf prop/3-ary/honesty and gender]]&lt;/small&gt;&lt;br&gt;
&lt;small&gt;The pattern of Zhegalkin indices for dishonest BF is similar to a [[c:File:Binary Walsh matrix of order 8 with row numbers (gray).svg|Walsh matrix]] &lt;small&gt;(with columns 3 and 7 exchanged)&lt;/small&gt;. But that is specific to arity 3. So is the fact, that all non-trivial dishonest BF are balanced.&lt;/small&gt;

{{Collapsible START|blunt &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed}}
[[File:Set of 3-ary Boolean functions 68033174967769840440887906939858451149105560803546820641877549596291376780905.svg|800px]]
{{Collapsible END}}
{{Collapsible START|female &lt;small&gt;(97)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 1017990932654081869095106387729709156216293000755592970863399350444565463617.svg|800px]]
{{Collapsible END}}
{{Collapsible START|dishonest &lt;small&gt;(57)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 7494979546278868352838388259605652777030681542822747306921801562456065.svg|800px]]
{{Collapsible END}}
{{Collapsible START|balanced &lt;small&gt;(70)&lt;/small&gt;|collapsed center wide}}
These are the BF whose truth table has weight 4. Almost all dishonest BF are balanced. Only the contradiction is not.&lt;br&gt;
[[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|800px]]
{{Collapsible END}}

{{Collapsible START|honest female &lt;small&gt;(40)&lt;/small&gt;|collapsed center wide gap-above color-beige}}
[[File:Set of 3-ary Boolean functions 1017983437674535590226753549341449550563515970074050148116092428643003007552.svg|800px]]
{{Collapsible END}}

{{Collapsible START|sharp &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed gap-above light}}
[[File:Set of 3-ary Boolean functions 47758914269546354982683078068829456704164423862093743397580034411621752859030.svg|800px]]
{{Collapsible END}}
{{Collapsible START|male &lt;small&gt;(159)&lt;/small&gt;|collapsed center wide followed light}}
[[File:Set of 3-ary Boolean functions 114774098304662113554475878620958198697053691664884971068594184657468564176318.svg|800px]]
{{Collapsible END}}
{{Collapsible START|honest &lt;small&gt;(199)&lt;/small&gt;|collapsed center wide light}}
[[File:Set of 3-ary Boolean functions 115792081742336649144702632170299648247617207634959021216710277086111567183870.svg|800px]]
{{Collapsible END}}


[[Category:Gender of Boolean functions]]</text>
      <sha1>0rufz40zry4cot3pv0xm0n4er0hz1v8</sha1>
    </revision>
    <revision>
      <id>2693192</id>
      <parentid>2693185</parentid>
      <timestamp>2024-12-25T17:02:24Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>/* honesty and gender */</comment>
      <origin>2693192</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5506" sha1="azqzk2xdwg5zmve48zsnuragzvvc559" xml:space="preserve">{{Boolf header}}

[[File:Gender ratio of Boolean functions.svg|thumb|300px|gender ratio for arities 0...5]]

A Boolean function shall be called ''male'', iff its [[Boolf-term#root|root]] is [[Boolf-term#sharp|sharp]] &lt;small&gt;(i. e. iff its compressed truth table has odd weight)&lt;/small&gt;.&lt;br&gt;
&lt;small&gt;(Equivalently, it is ''female'', iff after removing all repetitions, the weight of the truth table is still even.)&lt;/small&gt;

For positive arities, there are more males than females. The imbalance peaks for arity 2. For higher arities, the ratio is almost balanced.&lt;br&gt;
&lt;small&gt;The ratio is balanced for the infinite set of all Boolean functions. Both sets are countable, so there is a trivial bijection. But is there a meaningful bijection?&lt;/small&gt;

{{Gender of Boolean functions/triangles}}


----


{{Collapsible START|truth tables &amp;nbsp; &lt;small&gt;(Zhegalkin matrix)&lt;/small&gt;|collapsed wide followed}}
These matrices show the 97 females and 159 males among the first 256 Boolean functions.&lt;br&gt;
The matrix above shows the Zhegalkin indices. The [[Zhegalkin matrix]] below shows the truth tables.&lt;br&gt;
&lt;small&gt;The male truth tables on the left side of the matrix contain repetitions, i.e. their pattern can be described by a shorter truth table.&lt;/small&gt;

[[File:Gender of 3-ary Boolean functions.svg|left|1400px]]
{{Collapsible END}}

{{Collapsible START|atomvals &amp;nbsp; &lt;small&gt;(bitwise OR)&lt;/small&gt;|collapsed wide}}
The upper matrix shows the Zhegalkin indices. The one below shows [[Boolf-term#atomvals|atomvals]] of the corresponding Boolean functions.&lt;br&gt;
This is sequence {{oeis|A327041}}, the bitwise ORs of the binary exponents seen above.
[[File:Gender of 3-ary Boolean functions with bitwise OR of Zhegalkin exponents.svg|left|1400px]]
{{Collapsible END}}


----


{{Gender of Boolean functions/Zhegalkin indices}}


==honesty and gender==

The XOR of all members of a [[Families of Boolean functions|family]] is either the tautology or the contradiction. Where it is the tautology, the BF shall be called ''honest''.&lt;br&gt;
Apparently there are no dishonest males. &lt;small&gt;So every dishonest BF is female, and every male BF is honest.&lt;/small&gt;
&lt;small style=&quot;font-size: 60%; opacity: .5;&quot;&gt;(It should be kept in mind, that these are statements about Boolean functions. Generally, it is discouraged to assume, that all males are honest.)&lt;/small&gt;

{| class=&quot;wikitable collapsible collapsed&quot; style=&quot;text-align: center;&quot;\
!colspan=&quot;6&quot;| sequences
|-
! !! 0 !! 1 !! 2 !! 3 !! 4
|- style=&quot;background-color: #f5aed3; border-top: 3px solid black;&quot;
! female
| 1 || 1 || 3 || 97 || 32199
|- style=&quot;border-top: 3px solid gray;&quot;
! dishonest &lt;span style=&quot;opacity: .5;&quot;&gt;female&lt;/span&gt;
| 1 || 1 || 1 || 57 || 30537
|-
! honest female
| 0 || 0 || 2 || 40 || 1662
|- style=&quot;background-color: #a6c5f7; &quot;
! &lt;span style=&quot;opacity: .5;&quot;&gt;honest&lt;/span&gt; male
| 1 || 3 || 13 || 159 || 33337
|- style=&quot;border-top: 3px solid gray;&quot;
! honest
| 1 || 3 || 15 || 199 || 34999
|- style=&quot;border-top: 3px solid gray; font-weight: bold; border-top: 3px solid black;&quot;
! all
| 2 || 4 || 16 || 256 || 65536
|}


The following images show 3-ary Boolean functions. &amp;nbsp; &lt;small&gt;See also: [[Boolf prop/3-ary/honesty and gender]]&lt;/small&gt;&lt;br&gt;
&lt;small&gt;The pattern of Zhegalkin indices for dishonest BF is similar to a [[c:File:Binary Walsh matrix of order 8 with row numbers (gray).svg|Walsh matrix]] &lt;small&gt;(with columns 3 and 7 exchanged)&lt;/small&gt;. But that is specific to arity 3. So is the fact, that all non-trivial dishonest BF are balanced.&lt;/small&gt;

{{Collapsible START|blunt &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed}}
[[File:Set of 3-ary Boolean functions 68033174967769840440887906939858451149105560803546820641877549596291376780905.svg|800px]]
{{Collapsible END}}
{{Collapsible START|female &lt;small&gt;(97)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 1017990932654081869095106387729709156216293000755592970863399350444565463617.svg|800px]]
{{Collapsible END}}
{{Collapsible START|dishonest &lt;small&gt;(57)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 7494979546278868352838388259605652777030681542822747306921801562456065.svg|800px]]
{{Collapsible END}}
{{Collapsible START|balanced &lt;small&gt;(70)&lt;/small&gt;|collapsed center wide}}
These are the BF whose truth table has weight 4. Almost all dishonest BF are balanced. Only the contradiction is not.&lt;br&gt;
[[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|800px]]
{{Collapsible END}}

{{Collapsible START|honest female &lt;small&gt;(40)&lt;/small&gt;|collapsed center wide gap-above color-beige}}
[[File:Set of 3-ary Boolean functions 1017983437674535590226753549341449550563515970074050148116092428643003007552.svg|800px]]
{{Collapsible END}}

{{Collapsible START|sharp &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed gap-above light}}
[[File:Set of 3-ary Boolean functions 47758914269546354982683078068829456704164423862093743397580034411621752859030.svg|800px]]
{{Collapsible END}}
{{Collapsible START|male &lt;small&gt;(159)&lt;/small&gt;|collapsed center wide followed light}}
[[File:Set of 3-ary Boolean functions 114774098304662113554475878620958198697053691664884971068594184657468564176318.svg|800px]]
{{Collapsible END}}
{{Collapsible START|honest &lt;small&gt;(199)&lt;/small&gt;|collapsed center wide light}}
[[File:Set of 3-ary Boolean functions 115792081742336649144702632170299648247617207634959021216710277086111567183870.svg|800px]]
{{Collapsible END}}


[[Category:Gender of Boolean functions]]</text>
      <sha1>azqzk2xdwg5zmve48zsnuragzvvc559</sha1>
    </revision>
    <revision>
      <id>2693194</id>
      <parentid>2693192</parentid>
      <timestamp>2024-12-25T17:06:44Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693194</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4832" sha1="db2r4snbedx2wp2xa57gcduxsr6nl6e" xml:space="preserve">{{Boolf header}}

[[File:Gender ratio of Boolean functions.svg|thumb|300px|gender ratio for arities 0...5]]

A Boolean function shall be called ''male'', iff its [[Boolf-term#root|root]] is [[Boolf-term#sharp|sharp]] &lt;small&gt;(i. e. iff its compressed truth table has odd weight)&lt;/small&gt;.&lt;br&gt;
&lt;small&gt;(Equivalently, it is ''female'', iff after removing all repetitions, the weight of the truth table is still even.)&lt;/small&gt;

For positive arities, there are more males than females. The imbalance peaks for arity 2. For higher arities, the ratio is almost balanced.&lt;br&gt;
&lt;small&gt;The ratio is balanced for the infinite set of all Boolean functions. Both sets are countable, so there is a trivial bijection. But is there a meaningful bijection?&lt;/small&gt;

{{Gender of Boolean functions/triangles}}


----


{{Collapsible START|truth tables &amp;nbsp; &lt;small&gt;(Zhegalkin matrix)&lt;/small&gt;|collapsed wide followed}}
These matrices show the 97 females and 159 males among the first 256 Boolean functions.&lt;br&gt;
The matrix above shows the Zhegalkin indices. The [[Zhegalkin matrix]] below shows the truth tables.&lt;br&gt;
&lt;small&gt;The male truth tables on the left side of the matrix contain repetitions, i.e. their pattern can be described by a shorter truth table.&lt;/small&gt;

[[File:Gender of 3-ary Boolean functions.svg|left|1400px]]
{{Collapsible END}}

{{Collapsible START|atomvals &amp;nbsp; &lt;small&gt;(bitwise OR)&lt;/small&gt;|collapsed wide}}
The upper matrix shows the Zhegalkin indices. The one below shows [[Boolf-term#atomvals|atomvals]] of the corresponding Boolean functions.&lt;br&gt;
This is sequence {{oeis|A327041}}, the bitwise ORs of the binary exponents seen above.
[[File:Gender of 3-ary Boolean functions with bitwise OR of Zhegalkin exponents.svg|left|1400px]]
{{Collapsible END}}


----


{{Gender of Boolean functions/Zhegalkin indices}}


==honesty and gender==

The XOR of all members of a [[Families of Boolean functions|family]] is either the tautology or the contradiction. Where it is the tautology, the BF shall be called ''honest''.&lt;br&gt;
Apparently there are no dishonest males. &lt;small&gt;So every dishonest BF is female, and every male BF is honest.&lt;/small&gt;
&lt;small style=&quot;font-size: 60%; opacity: .5;&quot;&gt;(It should be kept in mind, that these are statements about Boolean functions. Generally, it is discouraged to assume, that all males are honest.)&lt;/small&gt;

{{Gender of Boolean functions/sequences honesty}}

The following images show 3-ary Boolean functions. &amp;nbsp; &lt;small&gt;See also: [[Boolf prop/3-ary/honesty and gender]]&lt;/small&gt;&lt;br&gt;
&lt;small&gt;The pattern of Zhegalkin indices for dishonest BF is similar to a [[c:File:Binary Walsh matrix of order 8 with row numbers (gray).svg|Walsh matrix]] &lt;small&gt;(with columns 3 and 7 exchanged)&lt;/small&gt;. But that is specific to arity 3. So is the fact, that all non-trivial dishonest BF are balanced.&lt;/small&gt;

{{Collapsible START|blunt &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed}}
[[File:Set of 3-ary Boolean functions 68033174967769840440887906939858451149105560803546820641877549596291376780905.svg|800px]]
{{Collapsible END}}
{{Collapsible START|female &lt;small&gt;(97)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 1017990932654081869095106387729709156216293000755592970863399350444565463617.svg|800px]]
{{Collapsible END}}
{{Collapsible START|dishonest &lt;small&gt;(57)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 7494979546278868352838388259605652777030681542822747306921801562456065.svg|800px]]
{{Collapsible END}}
{{Collapsible START|balanced &lt;small&gt;(70)&lt;/small&gt;|collapsed center wide}}
These are the BF whose truth table has weight 4. Almost all dishonest BF are balanced. Only the contradiction is not.&lt;br&gt;
[[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|800px]]
{{Collapsible END}}

{{Collapsible START|honest female &lt;small&gt;(40)&lt;/small&gt;|collapsed center wide gap-above color-beige}}
[[File:Set of 3-ary Boolean functions 1017983437674535590226753549341449550563515970074050148116092428643003007552.svg|800px]]
{{Collapsible END}}

{{Collapsible START|sharp &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed gap-above light}}
[[File:Set of 3-ary Boolean functions 47758914269546354982683078068829456704164423862093743397580034411621752859030.svg|800px]]
{{Collapsible END}}
{{Collapsible START|male &lt;small&gt;(159)&lt;/small&gt;|collapsed center wide followed light}}
[[File:Set of 3-ary Boolean functions 114774098304662113554475878620958198697053691664884971068594184657468564176318.svg|800px]]
{{Collapsible END}}
{{Collapsible START|honest &lt;small&gt;(199)&lt;/small&gt;|collapsed center wide light}}
[[File:Set of 3-ary Boolean functions 115792081742336649144702632170299648247617207634959021216710277086111567183870.svg|800px]]
{{Collapsible END}}


[[Category:Gender of Boolean functions]]</text>
      <sha1>db2r4snbedx2wp2xa57gcduxsr6nl6e</sha1>
    </revision>
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    <title>Motivation and emotion/Book/2024/Fear of judgement and social media</title>
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      <text bytes="32085" sha1="5qzismk1t41zpu0gtajehzkojpg7c9k" xml:space="preserve">{{title|Fear of judgment and social media: &lt;br&gt; How does the fear of being judged undermine posting on social media and how can this be overcome?}}
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==Overview==
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[[File:Social media addiction.jpg|thumb|Figure 1. Social media can become extremely overwhelming]]
'''Have you ever...'''

Ever paused before clicking the &quot;post&quot; button on social media? Perhaps you spent hours creating the perfect caption for the perfect photo. But wait! Aunt [[w:Karen (slang)|Karen]] might think the lighting isn't good enough! We've all been there: staring at our phones, wondering if others will like it or, worse, judge us (see Figure 2). Welcome to the world of social media, where a simple post can be a nerve-racking decision. 

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Imagine a world where our self-worth is determined by a double tap or a comment, where the number of likes can bolster or deflate our confidence, and where follows and shares assess our social connections. Sound familiar? With six billion global users, [[Social media]] is a complicated digital ecosystem in which people must navigate platform alternatives, reaction expectations, anticipated audiences, and posting standards (See figure 1; Kelly et al., 2020; Piko et al., 2024). Likes and views can serve as a status and popularity symbol, leading to low self-esteem (Winstone et al., 2023). Furthermore, people utilise filters and [[wikipedia:Photograph_manipulation|Photoshop]] to satisfy unattainable expectations. Fear of judgment and social media is an important field of emotional study as it focuses on the psychological consequences of online interactions. It is also known as fear of negative evaluation (FNE) in which individuals are apprehensive towards others' opinions of them (Watson and Friend, 1969). High FNE is associated with high levels of anxiety, particularly that of social. This anxiety can inhibit people from expressing themselves, resulting in higher emotional suffering and decreased [https://www.healthdirect.gov.au/mental-health-and-wellbeing mental well-being] (Kumar et al., 2015). Furthermore, resolving this issue is critical for creating healthy online environments in which people feel comfortable and empowered to communicate their authentic self without fear of being judged. This chapter employs psychological research to investigate crucial aspects of social media fear of judgement, such as its psychological consequences, the function of social comparison, and how reframing negative beliefs may lead to healthier thinking patterns and emotional well-being.      
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;Focus questions:
* Why do people fear being judged?
* How is social media associated with fear of judgement? 
* Who is most susceptible to the fear of judgment?
* What strategies can be used to approach fear of judgment?
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==What is the fear of judgement?==
[[File:Information bias.png|left|thumb|Figure 3. Individuals can form biases which can lead to FNE and social disengagement ]]

Judgement involves evaluating oneself or others in light of social norms (Carleton et al., 2007). Fear of judgement is the anxiety of being assessed adversely, which can lead to social withdrawal, particularly in people with a high FNE (Leary, 1983). These people may exhibit attentional biases, making them more susceptible to evaluative risks (Asmundson &amp; Murray, 1994). This influences their self-perception and behaviour, particularly in social media contexts. Low self-esteem might exacerbate these biases by enhancing the fear of judgement and increasing sensitivity to rejection or criticism (Dandeneau &amp; Baldwin, 2004). Understanding these processes is essential for studying behaviour in social settings.


'''Table 1.'''

''Factors Influencing Fear of Judgment''
{| class=&quot;wikitable&quot;
|+
!Factor
!Example
|-
|Fear of Negative Evaluation
|Sandra is afraid to share her idea in a team meeting because she is afraid of being judged, so she remains quiet. 
|-
|Cognitive Biases
|Leon could not come to dinner on the weekend with Max. Max avoided him as a result because he believed Leon did not like him anymore. 
|-
|Social Evaluation 
|Michael is worried that his new colleagues won't invite him to team activities because of the clothes he wears to work.   
|-
|Social Comparison
|Mary loves the photo she took of the ocean but will not post it on her Instagram because she does not believe it is to the standard that everyone posts. 
|}
''Note.'' Adapted from Festinger (1954); Watson and Friend (1969); Dandeneau and Baldwin (2004) and Dempsey et al. (2019)

=== Social evaluation ===

Numerous studies in psychology has shown social evaluation as a major contributor to fear of judgement, impacting self-esteem and interactions (Dempsey et al., 2019). [[Motivation and emotion/Book/2021/Imposter syndrome|The Imposter Phenomenon]] (IP), is a psychological pattern in which people disdain their accomplishments and attribute them to outside circumstances, limiting their potential (Clance &amp; Imes, 1978). In a study conducted by Clance and Imes (1978), 150 successful women from various professions acknowledged a lack of internal achievement, feeling intimidated by high achievers and labelling themselves as &quot;imposters.&quot; These women expressed imagining that others would regard them as weak or worthless, thus they frequently attributed their achievement to happenstance rather than ability. This demonstrates how fear of unfavourable judgement has a tremendous impact on self-perception and can lead to chronic emotions of worry and self doubt. However, the study's focus on a small demographic raises important questions about the findings' generalizability across different socioeconomic backgrounds and genders, emphasising the need for additional research that includes a broader range of experiences and perspectives in understanding intellectual property.  
[[File:Xaviera Lopez - Self portrait (GIPHY).gif|thumb|Figure 4. People may misrepresent their self-image in response to perceived judgements from others.]]  

=== Cognitive biases ===

Cognitive biases are systematic deviations from logical cognition that frequently lead to inaccurate conclusions (Korteling and Toet, 2020). Individuals with poor self-esteem process information in ways that emphasise their lack of control over events, which has a substantial impact on how they view and portray themselves socially (see Figure 4) (Dandeneau and Baldwin, 2004). According to ''[[wikipedia:Sociometer|Sociometer Theory]]'', self-esteem indicates social acceptance or rejection (Leary, 1995). Those who have experienced genuine or perceived rejection often have reduced self-esteem, making them more prone to see others as judgmental (Dandeneau and Baldwin, 2004). 

Reitz et al. (2022) investigated the self-esteem and peer-perceived popularity of 1,057 13-year-olds from both immigrant and host countries. Their findings revealed that in-group popularity predicted self-esteem substantially, as mediated by self-perceived popularity, but out-group popularity had no influence. This lends credence to Sociometer Theory, which emphasises the role of social acceptance from one's community in creating self-esteem. The study also discovered that self-esteem affected self-perceived popularity but not peer-perceived popularity, indicating people with poor self-esteem may exaggerate emotions of rejection and perceived judgement, in line with Dandeneau and Baldwin's (2004) findings. These findings provide light on the complicated link between self-esteem, social acceptability, and fear of judgement, demonstrating how people's perceptions of social settings affect their emotional well-being and relationships.  

=== Social comparison theory ===

Schachter (1959) built on Festinger's (1954) [[Motivation and emotion/Book/2021/Social comparison and emotion|social comparison theory]] emphasising its emotional component, notably fear. He contended that upward comparisons to people viewed as better off can lead to feelings of inadequacy and fear of adverse judgement, whilst downward comparisons may provide short relief or superiority but can lead to complacency. Buunk et al. (1990) evaluated 55 cancer patients and discovered that upward comparisons increased stress, confirming Schachter's theory. Downward comparisons increased self-esteem temporarily but had no long-term benefit. A more recent study on adolescent females using [[wikipedia:Facebook|Facebook]] found that upward comparisons with classmates and celebrities resulted in [[wikipedia:Body_image|body dissatisfaction]] and fear of negative evaluation (FNE), which mirrored Buunk et al.'s findings (Scully et al. 2023). Downward comparisons improved self-esteem temporarily but provided no long-term impact. These findings emphasise the harmful mental health implications of social comparison, particularly in social media environments where idealised lifestyles are viewed on a regular basis. 

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&lt;quiz display=&quot;simple&quot;&gt;
&lt;big&gt;''' Now that we've learned about the fear of judgment, let's hypothesize how social media comes into play!'''&lt;/big&gt;

What do you believe is an influencing factor in the undermining of posting on social media? 
|type=&quot;()&quot;}
- Fear of FNE
- Desire for social approval and validaiton
- Low self-esteem and cognitive bias
+ All of the above
&lt;/quiz&gt;
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== Why do people fear posting on social media? ==
[[File:Human-brain-mri-gif-brain-mri-gif.gif|thumb|Figure 5. fMRI machines can be used to examine the brain regions associated with regulating our ideal selves to our actual selves.]]
So far, this chapter has examined the fundamental notions of fear of judgement and how these psychological mechanisms influence individual behaviour. Given that fear of judgement presents itself in a variety of social circumstances, how can psychological science obtain a thorough grasp of its consequences on posting behaviour? Rather than offering a single explanation, researchers have found several elements underlying the widespread fear. 

=== Social media and brain activity ===

The neurological impacts of social media use are critical for understanding its rising relation to negative mental health outcomes. Individuals actively create their online identities to appear socially desirable, which increases their fear of judgement, according to [[Motivation and emotion/Book/2023/Toxic positivity|Impression Management Theory]] (Goffman, 2004). Tailoring posts to accommodate social norms increases self-consciousness and fear of negative feedback, leading users to avoid sharing anything that may provoke criticism. This self-monitoring corresponds to brain activity in areas associated with social awareness. Farrow et al. (2015) discovered that efforts to regulate impressions stimulate the[[wikipedia:Prefrontal_cortex|medial prefrontal cortex]] and [[wikipedia:Ventrolateral_prefrontal_cortex|left ventrolateral prefrontal cortex]], which are involved in self-monitoring and social appraisal. Similarly, Shi et al. (2016) demonstrated that differences between one's real and ideal selves activate brain areas related to emotional regulation and self-awareness; aligning with the concept of emotional discomfort in the [[Motivation and emotion/Book/2023/Self-discrepancy theory and emotion|Self-Discrepancy Theory]] (Higgins, 1987). These findings imply that maintaining an idealised online image requires substantial cognitive effort, heightening concern over social judgement. The overlap in brain networks that manage self-discrepancy and social impressions might explain why the difference between online and offline personalities frequently causes anxiety, emphasising the emotional cost of presenting a faultless image online. Understanding this link is critical for treating the mental health issues connected with social media use.  

=== Anticipated regret ===

[[Motivation and emotion/Book/2021/Anticipatory regret and motivation|Anticipated regret]] the concern over future negative outcomes, is a key factor in social media use (Brewer et al., 2017). The growth of [[Digital Media Concepts/Cancel Culture|cancel culture]] has heightened this worry, as users are concerned about the consequences of straying from social norms (Wang et al., 2011). People who anticipate regret may avoid posting or communicating on social media for fear of being publicly shamed (NeuroLaunch, 2024). Wang et al. (2011) investigated post-regret (fear of posting) among 569 American Facebook users and discovered that variables such as the desire to be viewed positively, failure to evaluate the implications, and misunderstanding social norms all contributed to regret after posting. Velasco (2020) investigated how cancel culture exacerbates these worries by creating a &quot;virtual collective consciousness,&quot; in which similar beliefs across online groups heighten the fear of judgement. People with poor self-esteem are more likely to interpret social media negatively, as explained by cognitive biases (Korteling and Toet, 2020). To minimise potential regret, many users utilise self-regulation tactics such as restricting their audience or avoiding sensitive content. This demonstrates how the fear of judgement and social repercussions encourages cautious online behaviour, perpetuating a cycle of worry and self-doubt. 

=== Social online self-regulation theory ===

[[wikipedia:Self-regulation_theory|The Social Online Self-Regulation Theory]] (SOS-T) posits how people use social media to pursue personal objectives while moderating their online behaviour to avoid negative consequences (Ozimek &amp; Forester, 2021). This hypothesis is consistent with Self-Discrepancy theory, which states that users engage in self-regulation activities like self-presentation and social comparisons to align their online behaviour with their desired self-image and social acceptance. Our understanding of comparison theory implies that they elicit complicated emotional responses, particularly when individuals evaluate themselves against perceived social standards.  

Individuals prone to social comparison, particularly those with poor self-esteem, may be more vulnerable to these unpleasant emotions, forcing them to carefully cultivate their online profiles. Someone with poor self-esteem, for example, may meticulously edit their posts to project a socially acceptable image out of fear of being judged. The above research can argue that these people experience enhanced prefrontal brain activity, indicating a higher sensitivity to social assessments. The SOS-T model highlights how emotional regulation strategies, such as limiting exposure to triggering information, are employed to ease anxiety caused by social comparisons and fear of judgement, emphasising the cognitive effort required to manage online identities (Farrow et al., 2015; Shi et al., 2016). 

=== Fear of missing out ===
[[File:Hair pulling stress.jpg|thumb|Figure 7. FOMO can impact the decisions people make on social media due to concerns others are experiencing better opportunities]]
[[Motivation and emotion/Book/2015/Fear of missing out|Fear of Missing Out (FoMO)]] is the anxiety caused by feeling that others are having better experiences, prompting people to seek social connection through digital platforms. This concept has a considerable influence on social media behaviour, notably the inhibition to post due to fear of judgement. According to Roberts and David (2019), despite improved connection, social isolation has increased, with many individuals lacking close confidants. FoMO increases social media participation since people want affirmation and connection, according to the [[wikipedia:Belongingness|Belongingness Hypothesis]] (Maslow, 2015). However, the desire to connect might cause concern over social approval. When consumers see idealised images of other people's life, they may feel inadequate, fearing that their own experiences may not measure up. Individuals second-guess their posts because they are afraid of receiving bad feedback or being ridiculed (see figure 7). As a result, people with high FoMO may choose to lurk rather than participate, reducing their online participation. Furthermore, the Information Foraging Theory proposes that users filter through social media for signs that affirm their identity, similar to cognitive biases (Pirolli and Card, 1999). The abundance of possibilities to interact can worsen FoMO, making users hyper-aware of how their information will be interpreted. As a result, while FoMO can motivate social media use, it also promotes a fear of judgement, causing unwillingness to share and eventually contributing to feelings of social isolation. 
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;Mini case study:
Jimmy scrolls through Instagram and finds his friends enjoying a concert he was not invited to. He feels envious and anxious, concerned that he is missing out on fun experiences. This continual comparison to others makes him unwilling to share about his own activities, worried they will fall short.
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&lt;quiz display=&quot;simple&quot;&gt;
&lt;big&gt;''' What psychological phenomena does Jimmy experience as a result of his social media use?'''&lt;/big&gt;
|type=&quot;()&quot;}
+ FOMO
- Impression management
- Anticipated regret
- Cognitive dissonance
&lt;/quiz&gt;
{{RoundBoxBottom}}

== Who is most susceptible to fear of judgment on social media? ==
Individual variations and many psychological aspects impact fear of judgement on social media (Qahri-Saremi &amp; Turel, 2020). Notably, the interplay between social validation and personal expectations influences online behaviour, demonstrating that not everyone interprets social feedback in the same way (Steers et al., 2014).

=== Social validation ===

One factor affecting social media behaviour is [https://www.monterey.ai/knowledge-base/feedback-loop-psychology the feedback loop theory] which states that individuals' behaviours are impacted by the reactions they receive from their surroundings (Kampmann, 2012). This dynamic tandem is especially visible in the field of social validation, where others' approval has a considerable influence on online behaviour. The demand for social acceptability can set up a feedback loop in which positive responses drive further involvement and negative feedback discourages future participation. Qahri-Saremi and Turel (2020) conducted five studies to investigate how social validation influences user behaviour on social media. They altered the display of &quot;like&quot; numbers to determine their influence on participants' behaviour. Interestingly, even when &quot;like&quot; counts were suppressed to prevent social comparison, individuals still felt negative impacts from internal comparisons. Users frequently compared their actual social validation to their expectations; getting less likes resulted in technology-mediated hazardous behaviours, such as unsafe self-disclosure (Qahri-Saremi and Turel (2020). These findings show that the feedback loop uses both external and internal validation, implying that interventions to reduce harmful social media behaviours should address both external cues and internal expectations.
[[File:The grass is always greener, on the other side^ - geograph.org.uk - 1988469.jpg|thumb|Figure 8. Although they may have great opportunities in front of them, some individuals still have a comparative mindset.]]
=== Grass is always greener ===

[https://www.promly.org/post/what-exactly-is-the-highlight-reel-effect The highlight reel effect theory] argues that people frequently portray an idealised image of themselves online, leading to social idealisation and unfavourable comparisons (Stanisci, 2022). This behaviour is especially visible on platforms where users constantly participate in social comparisons, which have an impact on their psychological health. Steers et al. (2014) executed two studies to investigate how Facebook interactions affect users' mental health. Results from Study 1, which included 180 participants, revealed that social comparisons acted as a mediator relationship between Facebook use and depression symptoms, especially in men. Study 2 found that social comparisons, both upward and downward, moderated the association between Facebook use and depressed symptoms in 152 individuals using a 14-day diary design (Steers et al., 2014). These findings highlight the detrimental psychological effects of this comparative mindset, which perpetuates the notion that everything is better somewhere else, even when the reality is frequently more complicated and less perfect (see figure 8).

=== Optimism vs. pessimism ===

The consequences of pessimism and optimism on social media use can alter sensitivity to fear of judgement. According to Wu (2022), pessimistic people are more prone to participate in harmful network behaviour, which is influenced by both negative affect and risk perception. Pessimists may be motivated by heightened risk perception, anticipating negative feedback and judgement online, which is consistent with cognitive theories indicating that those with negative biases expect unfavourable outcomes (Beck, 1976). This inclination makes individuals more subject to fear of judgement, since they see ambiguous social media interactions as possible threats.  

In contrast, Urun et al. (2022) discovered that optimism in teenagers is connected with better social media usage, with optimists being less prone to addiction and negative emotional reactions. Optimistic people, aided by a positive cognitive bias, are less likely to focus on prospective judgement and more likely to interpret social encounters favourably, minimising fear of judgement. This is consistent with Fredrickson's [[wikipedia:Broaden-and-build|broaden-and-build hypothesis]] (2001), which holds that positive emotions help individuals develop resilience and resources, making them less vulnerable to perceived threats.

== Strategies for overcoming fear of judgment ==
=== Cognitive restructuring ===

[[wikipedia:Cognitive_restructuring|Cognitive restructuring]] is a psychological strategy used to change dysfunctional cognitive processes which is particularly useful for people who have negative cognitive biases, self evaluations, and social comparisons (Shi et al., 2016). Individuals can improve their cognitive habits and lower their anxiety by moving from negative, experiential thinking to more analytical processing. Wong and Moulds (2012) found that socially anxious people who use an analytical processing (critically assessing situations) mode during anticipatory processing create less negative beliefs than those who use an experiential mode (subjective interpretations). This research lends credence to cognitive restructuring's efficacy, demonstrating its ability to assist individuals in confronting and reframing their concerns, hence fostering more adaptive behaviours in social contexts.

=== Mindfulness and acceptance ===
[[File:Starman 07.jpg|thumb|figure 9. Mindfulness techniques can be useful for fear of judgment and social media.]]
[[Motivation and emotion/Book/2013/Acceptance and Commitment Therapy and emotion|Mindfulness and Acceptance Commitment Therapy]] (ACT) is useful for overcoming the anxiety of being judged when posting on social media. ACT emphasises accepting ideas and feelings rather than striving to control or avoid them, hence fostering [[Motivation and emotion/Book/2019/Psychological flexibility and emotional health|psychological flexibility]]. Uğur and Koç (2021) discovered that participants in an ACT-based psychoeducation program demonstrated a substantial reduction in FNE over time. This suggests that mindfulness techniques, such as meditation and breath work, can help individuals address and defuse unpleasant thoughts connected with social interactions (see figure 9). Individuals who practice mindfulness can learn to embrace their concerns, which reduces the effect of judgement and allows them to communicate more freely and truthfully online.

=== Building supportive networks ===

Building supportive networks can help overcome FNE when posting on social media. Cho et al. (2023) found that [https://www.sciencedirect.com/topics/social-sciences/perceived-social-support perceived social support] from social media usage improves coping mechanisms, resulting in less negative emotional reactions such as anxiety and loneliness. Individuals who participate in supportive communities might receive encouragement and affirmation, reducing the fear of being judged for expressing personal thoughts and experiences. However, the study emphasises the necessity of avoiding social liability, implying that developing real connections based on empathy is critical for providing effective help while managing FNE online.

== Conclusion ==
Fear of judgment considerably reduces individuals' willingness to connect with social media. Users are continually comparing themselves to curated online identities, which is rooted in social anxiety. This continual comparison causes avoidance behaviours, less self-expression, and reluctance to join in digital groups, all of which have an influence on mental health and personal growth (Leary &amp; Kowalski, 1995). A key takeaway is that judgement frequently distorts our view of self-worth. Individuals can overcome their fear by understanding the psychological factors that drive it, such as anticipated regret, cognitive biases and FOMO (Vogel et al., 2014). Cultivating self-compassion helps to reframe thinking, allowing for healthier responses to criticism. Engaging with supportive groups promotes belonging and honest self-expression, hence lessening the impact of external judgement (Weeks et al., 2005). Embracing a growth attitude changes how people see their online presence. Individuals may overcome comparison and enjoy their distinctive voices by recognising that mistakes and negative comments are learning opportunities rather than reflections of worth. This transformation strengthens personal resilience and leads to a more diverse online environment in which authenticity thrives.

Furthermore, overcoming the fear of judgement on social media is about enabling people to recover their agency in the digital world. The process of overcoming these fears provides access to authentic connections, creativity, and personal fulfilment. Individuals who actively seek to alleviate this anxiety contribute to a healthier online environment that values authenticity over conformity, which benefits both themselves and the larger community.

==See also==
* [[Motivation and emotion/Book/2019/Body image and emotional well-being|Body image and emotional well-being]] (Book chapter, 2019)
* [[wikipedia:Digital_media_use_and_mental_health|Digital use and mental health]] (Wikipedia) 
* [[wikipedia:Fear_of_missing_out|Fear of missing out]] (Wikipedia)
* [[wikipedia:Fear_of_negative_evaluation|Fear of negative evaluation]] (Wikipedia)
* [[Motivation and emotion/Book/2021/Fitspiration and body image|Fitspiration and body image]]
* [[Motivation and emotion/Book/2021/Social comparison and emotion|Social comparison and emotion]]  (Book chapter, 2021) 
* [[Motivation and emotion/Book/2019/Social comparison, social media, and emotion|Social comparison, social media, and emotion]] (Book chapter, 2019)

==References ==
{{Hanging indent|1= Asmundson, G. J. G., &amp; Stein, M. B. (1994). Selective processing of social threat in patients with generalized social phobia: Evaluation using a dot-probe paradigm. ''Journal of Anxiety Disorders'', ''8''(2), 107–117. https://doi.org/10.1016/0887-6185(94)90009-4

Brewer, N. T., DeFrank, J. T., &amp; Gilkey, M. B. (2016). Anticipated regret and health behavior: A meta-analysis. ''Health Psychology'', ''35''(11), 1264–1275. https://doi.org/10.1037/hea0000294

Buunk, B. P., Collins, R. L., Taylor, S. E., VanYperen, N. W., &amp; Dakof, G. A. (1990). The affective consequences of social comparison: Either direction has its ups and downs. ''Journal of Personality and Social Psychology'', ''59''(6), 1238–1249. https://doi.org/10.1037/0022-3514.59.6.1238

Cho, H., Li, P., Ngien, A., Tan, M. G., Chen, A., &amp; Nekmat, E. (2023). The bright and dark sides of social media use during COVID-19 lockdown: Contrasting social media effects through social liability vs. social support. ''Computers in Human Behavior'', ''146'', 107795. https://doi.org/10.1016/j.chb.2023.107795

Clance, P. R., &amp; Imes, S. A. (1978). The imposter phenomenon in high achieving women: Dynamics and therapeutic intervention. Psychotherapy: Theory, ''Research &amp; Practice'', ''15''(3), 241–247. https://doi.org/10.1037/h0086006

Dempsey, A. E., O’Brien, K. D., Tiamiyu, M. F., &amp; Elhai, J. D. (2019). Fear of missing out (FoMO) and rumination mediate relations between social anxiety and problematic Facebook use. ''Addictive Behaviors Reports'', ''9'', 100150. https://doi.org/10.1016/j.abrep.2018.100150

Farrow, T. F. D., Burgess, J., Wilkinson, I. D., &amp; Hunter, M. D. (2015). Neural correlates of self-deception and impression-management. ''Neuropsychologia'', ''67'', 159–174. https://doi.org/10.1016/j.neuropsychologia.2014.12.016

Goffman, E. (2021). ''Organizational identity''. Google Books. https://books.google.com.au/books?hl=en&amp;lr=&amp;id=l2R7DwAAQBAJ&amp;oi=fnd&amp;pg=PA35&amp;dq=goffman+impression+management&amp;ots=AB-y5ThYKK&amp;sig=mGjV3Lbc8xOVQrC4be2-Zr00Q5M

Higgins, E. T. (1987). Self-discrepancy: A theory relating self and affect. ''Psychological Review'', ''94''(3), 319–340. https://doi.org/10.1037/0033-295X.94.3.319

Kelly, L., Keaten, J. A., &amp; Millette, D. (2020). Seeking safer spaces: The mitigating impact of young adults’ Facebook and Instagram audience expectations and posting type on fear of negative evaluation. ''Computers in Human Behavior'', ''106'', 106333. https://doi.org/10.1016/j.chb.2020.106333

Korteling, J. E., &amp; Toet, A. (2020). Cognitive biases. ''Reference Module in Neuroscience and Biobehavioral Psychology'', ''3''. https://doi.org/10.1016/b978-0-12-809324-5.24105-9

Piko, B. F., Krajczár, S. K., &amp; Kiss, H. (2024). Social media addiction, personality factors and fear of negative evaluation in a sample of young adults. ''Youth'', ''4''(1), 357–368. https://doi.org/10.3390/youth4010025

Scully, M., Swords, L., &amp; Nixon, E. (2020). Social comparisons on social media: Online appearance-related activity and body dissatisfaction in adolescent girls. ''Irish Journal of Psychological Medicine'', ''40''(1), 1–12. https://doi.org/10.1017/ipm.2020.93

Shi, Z., Ma, Y., Wu, B., Wu, X., Wang, Y., &amp; Han, S. (2016). Neural correlates of reflection on actual versus ideal self-discrepancy. ''NeuroImage'', ''124'', 573–580. https://doi.org/10.1016/j.neuroimage.2015.08.077

Watson, D., &amp; Friend, R. (1969). Measurement of social-evaluative anxiety. ''Journal of Consulting and Clinical Psychology'', ''33''(4), 448–457. https://doi.org/10.1037/h0027806

Winstone, L., Mars, B., Haworth, C. M. A., &amp; Kidger, J. (2023). Types of social media use and digital stress in early adolescence. ''The Journal of Early Adolescence'', ''43''(3), 027243162211055. https://doi.org/10.1177/02724316221105560

Wong, Q. J. J., &amp; Moulds, M. L. (2012). Processing mode during repetitive thinking in socially anxious individuals: Evidence for a maladaptive experiential mode. ''Journal of Behavior Therapy and Experimental Psychiatry'', ''43''(4), 1064–1073. https://doi.org/10.1016/j.jbtep.2012.05.002 }}

==External links==
* [https://www.youtube.com/watch?v=wBTEJsDP-nU&amp;t=6s Judgment. Don't let it frighten you] (TED Talk, 2015)
* [https://www.youtube.com/watch?v=HJQGHiBqBcA Social media isn't real (even if it looks like it is)] (TED Talk, 2019)
* [https://www.addrc.org/confronting-the-fear-of-being-judged-a-step-by-step-approach/ Confronting the fear of being judged: a step by step approach] (ADD Resource Center, 2024) 
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[[Category:Motivation and emotion/Book/Fear]]
[[Category:Motivation and emotion/Book/Judgement]]
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    <title>Soft properties of Boolean functions</title>
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__NOTOC__
{{Boolf header}}
{| style=&quot;float: right;&quot;
| {{Properties of Boolean functions}}
|-
| {{Shortcut|Boolf-soft}}
|}
The number of [[w:Boolean function|Boolean functions]] with arity &lt;math&gt;n&lt;/math&gt; (short for [[Boolf-term|adicity]] &lt;math&gt;\le n&lt;/math&gt;)  is &lt;math&gt;2^{2^n}&lt;/math&gt; ({{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 &amp;nbsp;&amp;nbsp; '''sharp''': odd weight &amp;nbsp;&amp;nbsp; '''blunt:''' 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==

&lt;small&gt;see also: [[Extended families and clans of Boolean functions]]&lt;/small&gt;

===ultra &lt;small class=&quot;heading-details&quot;&gt;(extension with half-complement)&lt;/small&gt;===

{| class=&quot;wikitable&quot; style=&quot;float:right; text-align: center;&quot;
|colspan=&quot;3&quot;|
The two families on the left form a super-family.&lt;br&gt;
The family on the right is a super-family on its own.&lt;br&gt;
Together these two super-families form an ultra-family.
|-
|colspan=&quot;2&quot;| [[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. &lt;small&gt;(The truth table is complemented on the left or on the right side.)&lt;/small&gt;&lt;br&gt;
A super-family has a unique half-complement. Merging them gives an ultra-family.&lt;br&gt;
As super-clans consist of super-families, they can be extended in the same way.&lt;br&gt;
&lt;small style=&quot;opacity: .5;&quot;&gt;(Factions do not have a unique half-complement, so it does not seem useful to define ultra-factions.)&lt;/small&gt;

===={{anchor|ultra-family}} '''ultra-family''' &lt;small class=&quot;heading-details&quot;&gt;(negation, complement, half-complement)&lt;/small&gt;====

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]].&lt;br&gt;
&lt;small&gt;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]])&lt;/small&gt;

===={{anchor|ultra-clan}} '''ultra-clan''' &lt;small class=&quot;heading-details&quot;&gt;(negation, permutation, complement, half-complement)&lt;/small&gt;====

An ultra-clan is the merge of a super-clan and its half-complement.&lt;br&gt;
It can also be seen as a merge of ultra-families, that are permutations of each other.&lt;br&gt;
&lt;small&gt;See [[4-ary Boolean functions#ggbec|here]] for a table of the 39 ultra-families of 4-ary Boolean functions.&lt;/small&gt;


==partitions into blocks of equal size==

==={{anchor|consul|consuls}} consul &lt;small&gt;(binary Walsh spectrum)&lt;/small&gt;===
&lt;span style=&quot;opacity: .5;&quot;&gt;The [[w:Hadamard transform|Walsh spectrum]] of a TT is its product with a [[w:Walsh matrix|Walsh matrix]].&lt;/span&gt;&lt;br&gt;
The ''binary'' Walsh spectrum of a TT is its product with a ''binary'' Walsh matrix, using [[w:Finite field|'''F'''&lt;sub&gt;2&lt;/sub&gt;]] operations ([[w:Modular arithmetic|mod]] 2).&lt;br&gt;
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]]. &lt;small style=&quot;opacity: .7;&quot;&gt;The consul is essentially the prefect of the twin, but without the negation.&lt;/small&gt;&lt;br&gt;
&lt;small style=&quot;opacity: .5;&quot;&gt;(One could also define a sign for the consul, by using a ''negated'' binary Walsh matrix. But the sign would just be the sharpness.)&lt;/small&gt;

{| style=&quot;border: 1px solid lightgray; width: 700px;&quot;
|- style=&quot;vertical-align: top;&quot;
| [[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|blunt family with consul 2&lt;br&gt;&lt;small&gt;(compare [[c:File:Walsh spectra of family patina.svg|4-ary family with consul 6]])&lt;/small&gt;]]
|-
|colspan=&quot;2&quot;| 3-ary [[Boolf-EC#family|families]] with Walsh spectra &lt;small&gt;(integers)&lt;/small&gt; and consuls &lt;small&gt;(red backgrounds on the right)&lt;/small&gt;
|}

{{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.)&lt;br&gt;
Blunt TT belong to ultra-clans with a unique consul weight, which belong to a blunt tribe denoted by that consul weight.&lt;br&gt;
Sharp TT form a tribe on their own.

{{Properties of truth tables/tribes}}
{{Collapsible END}}

&lt;small style=&quot;opacity: .5;&quot;&gt;[[3-ary_Boolean_functions#Walsh spectrum]], [[4-ary_Boolean_functions#wec]]&lt;/small&gt;

===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. &amp;nbsp;&amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;[[c:Category:3-ary Boolean functions in octeract matrix; great patrons|(3-ary images)]]&lt;/small&gt;

===praetor===

XOR of left and right half of the TT. &amp;nbsp;&amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;[[c:Category:3-ary Boolean functions in octeract matrix; great praetors|(3-ary images)]]&lt;/small&gt;

===quaestor===

XOR of left and reversed right half of the truth table &lt;small&gt;(i.e. of the coordinates in the Hasse matrix)&lt;/small&gt; &amp;nbsp;&amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;[[c:Category:3-ary Boolean functions in octeract matrix; great quaestors|(3-ary images)]]&lt;/small&gt;

[[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.</text>
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{| class=&quot;collapsible-with-classes collapsible collapsed light&quot;
! 3-ary
|-
| [[File:3-ary Boolean functions; tribes.svg|thumb|left|500px|Blunt tribes are gray or red: &amp;nbsp; {{colorbox|#e60000}} 0 &amp;nbsp; {{colorbox|#bbb}} 1 &amp;nbsp; {{colorbox|#666}} 2 &amp;nbsp; {{colorbox|#ffb4b4}} 3&lt;br&gt;Sharp tribes are white.]]
|}&lt;noinclude&gt;
[[Category:Studies of Boolean functions]]
&lt;/noinclude&gt;</text>
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    <title>Basic Scratch Coding</title>
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      <text bytes="1576" sha1="abfid6xqz83hn6m8x7kiosl8ggs1eig" xml:space="preserve">Coding is very important in many aspects of computer science, so this Wikiversity course is designed to bring the key concepts of Scratch coding, which includes discussing key principles and creating Scratch programs, to light. These projects can then be optionally published on the Scratch website or on the internet. This course is designed for people of all ages, so anyone is welcome to join with this course. This course will currently go through four programs, with more programs/ courses coming in the future:

=== Scratch Account: ===
You will not require a Scratch account to complete this course, but if you do have a Scratch account, you can also complete this course with no problems, with the offline editor.[[File:Scratch Logo.svg|thumb|This course involves Scratch, which is a free programming language.]]

=== Topics: ===
[[/Hello World/]]

[[/Two-Player Pong/]]

[[/Maths Quiz/]]

[[/Clicker Game/]]

These projects will be rigorously explained and easy to follow, so the basics will be explained clearly and will allow you, by the end of this course, to apply basic skills whenever creating projects with Scratch and further projects, which is vital when using '''any''' programming language.

=== Links and Applications Required ===
For accessing Scratch, visit: https://scratch.mit.edu and press the &quot;Create&quot; button which will create a fresh, new project for you to work on.

Alternatively, you may also download the offline editor from: https://scratch.mit.edu/download, which will not require an internet connection. 


[[Category:Basic Scratch Coding]]</text>
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{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater twin mentor|greater twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
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    </revision>
    <revision>
      <id>2693239</id>
      <parentid>2693182</parentid>
      <timestamp>2024-12-25T23:40:29Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
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      <text bytes="36449" sha1="ilsgg2dcleolhz27xwvip2o489beqqa" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 112, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/nonlinearity|nonlinearity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation weight|zhegalkin deviation weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater twin mentor|greater twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin linear|zhegalkin linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation|zhegalkin deviation]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
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    </revision>
    <revision>
      <id>2693243</id>
      <parentid>2693239</parentid>
      <timestamp>2024-12-26T00:08:38Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693243</origin>
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      <text bytes="36998" sha1="m3rw91j8gq69pxlwarxqp1yt0trfvrl" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 112, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/nonlinearity|nonlinearity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation weight|zhegalkin deviation weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater twin mentor|greater twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin weight|zhegalkin weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin linear|zhegalkin linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation|zhegalkin deviation]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
      <sha1>m3rw91j8gq69pxlwarxqp1yt0trfvrl</sha1>
    </revision>
    <revision>
      <id>2693244</id>
      <parentid>2693243</parentid>
      <timestamp>2024-12-26T00:17:12Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693244</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="37304" sha1="nupiflczeuv82kr0afqse5m1d0v8ngp" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_patron|zhegalkin deviation patron]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 112, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/nonlinearity|nonlinearity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation weight|zhegalkin deviation weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater twin mentor|greater twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin weight|zhegalkin weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin linear|zhegalkin linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation|zhegalkin deviation]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
      <sha1>nupiflczeuv82kr0afqse5m1d0v8ngp</sha1>
    </revision>
    <revision>
      <id>2693246</id>
      <parentid>2693244</parentid>
      <timestamp>2024-12-26T00:22:57Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693246</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="37616" sha1="5dls4ds8nofiqiu48d3ucxh1iop2s1l" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_patron|zhegalkin deviation patron]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_is_odious|zhegalkin deviation is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 112, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/nonlinearity|nonlinearity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation weight|zhegalkin deviation weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater twin mentor|greater twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin weight|zhegalkin weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin linear|zhegalkin linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation|zhegalkin deviation]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
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    </revision>
    <revision>
      <id>2693248</id>
      <parentid>2693246</parentid>
      <timestamp>2024-12-26T00:27:34Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693248</origin>
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      <text bytes="37884" sha1="ql5fnhsyhbs7h7dexnonlxvixb71y4m" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_patron|zhegalkin deviation patron]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_is_odious|zhegalkin deviation is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rude|is rude]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 112, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/nonlinearity|nonlinearity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation weight|zhegalkin deviation weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater twin mentor|greater twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin weight|zhegalkin weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin linear|zhegalkin linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation|zhegalkin deviation]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
      <sha1>ql5fnhsyhbs7h7dexnonlxvixb71y4m</sha1>
    </revision>
    <revision>
      <id>2693277</id>
      <parentid>2693248</parentid>
      <timestamp>2024-12-26T11:02:46Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693277</origin>
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      <text bytes="38493" sha1="kury0v1wtsyt3901v8p6ms1uftrdn4x" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_patron|zhegalkin deviation patron]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_is_odious|zhegalkin deviation is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rude|is rude]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 112, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/nonlinearity|nonlinearity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation weight|zhegalkin deviation weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater twin mentor|greater twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin weight|zhegalkin weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin linear|zhegalkin linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation|zhegalkin deviation]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 38
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 14, 9, 8, 12, 4, 20, 2, 23, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;9&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;23&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight pair|weight pair]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
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    </revision>
    <revision>
      <id>2693282</id>
      <parentid>2693277</parentid>
      <timestamp>2024-12-26T11:33:52Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
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      <text bytes="39025" sha1="hf8jgqip5lyt6headvyzqivunfsh0xi" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_patron|zhegalkin deviation patron]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_is_odious|zhegalkin deviation is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rude|is rude]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 112, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/nonlinearity|nonlinearity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation weight|zhegalkin deviation weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater twin mentor|greater twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin weight|zhegalkin weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 13
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 1, 12, 2, 24, 7, 48, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/platoon|platoon]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin linear|zhegalkin linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation|zhegalkin deviation]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 38
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 14, 9, 8, 12, 4, 20, 2, 23, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;9&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;23&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight pair|weight pair]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
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    </revision>
    <revision>
      <id>2693285</id>
      <parentid>2693282</parentid>
      <timestamp>2024-12-26T11:52:54Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
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      <text bytes="40110" sha1="75rzw2f7hagl8nadvkejeh3k0durkuf" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_patron|zhegalkin deviation patron]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_is_odious|zhegalkin deviation is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rude|is rude]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 112, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/nonlinearity|nonlinearity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater guild|greater guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation weight|zhegalkin deviation weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 1, 24, 3, 48, 1, 56, 1, 72, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;72&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/battalion|battalion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/greater twin mentor|greater twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin weight|zhegalkin weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 13
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 1, 12, 2, 24, 7, 48, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/platoon|platoon]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 13
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 6, 24, 2, 36, 2, 56, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;36&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/half battalion|half battalion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin linear|zhegalkin linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation|zhegalkin deviation]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 38
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 14, 9, 8, 12, 4, 20, 2, 23, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;9&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;23&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight pair|weight pair]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
      <sha1>75rzw2f7hagl8nadvkejeh3k0durkuf</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/prefect</title>
    <ns>0</ns>
    <id>317262</id>
    <revision>
      <id>2693218</id>
      <parentid>2693165</parentid>
      <timestamp>2024-12-25T21:40:39Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693218</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5239" sha1="2scsg70aeu1j0gvgz0gtf4hvi4g3dst" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 6928706295070929573599405754551337583186506210420311235022011754348801.svg|thumb|500px|The truth tables are reverse [[Boolf prop/3-ary/zhegalkin linear|Zhegalkin linears]].]]

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| prefect
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;/span&gt;0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_16711935.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 1&lt;/span&gt;¬4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_4278255360.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 1&lt;/span&gt;¬2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[32, 33, 34, 35, 36, 37, 38, 39, 48, 49, 50, 51, 52, 53, 54, 55]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_71777214277877760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 0&lt;/span&gt;6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[40, 41, 42, 43, 44, 45, 46, 47, 56, 57, 58, 59, 60, 61, 62, 63]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_18374966855136706560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 1&lt;/span&gt;¬1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[64, 65, 66, 67, 68, 69, 70, 71, 80, 81, 82, 83, 84, 85, 86, 87]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_308280787921469235485736960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 0&lt;/span&gt;5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[72, 73, 74, 75, 76, 77, 78, 79, 88, 89, 90, 91, 92, 93, 94, 95]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_78919881707896124284348661760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 0&lt;/span&gt;3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[96, 97, 98, 99, 100, 101, 102, 103, 112, 113, 114, 115, 116, 117, 118, 119]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1324055902107822182681362917658460160.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 1&lt;/span&gt;¬7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[104, 105, 106, 107, 108, 109, 110, 111, 120, 121, 122, 123, 124, 125, 126, 127]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_338958310939602478766428906920565800960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 0&lt;/span&gt;7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5686776797628873740399791320050227284918927360.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 1&lt;/span&gt;¬3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[136, 137, 138, 139, 140, 141, 142, 143, 152, 153, 154, 155, 156, 157, 158, 159]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1455814860192991677542346577932858184939245404160.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 1&lt;/span&gt;¬5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[160, 161, 162, 163, 164, 165, 166, 167, 176, 177, 178, 179, 180, 181, 182, 183]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_24424520365467623060330297684840395266093667022599618560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 0&lt;/span&gt;1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[168, 169, 170, 171, 172, 173, 174, 175, 184, 185, 186, 187, 188, 189, 190, 191]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_6252677213559711503444556207319141188119978757785502351360.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 1&lt;/span&gt;¬6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[192, 193, 194, 195, 196, 197, 198, 199, 208, 209, 210, 211, 212, 213, 214, 215]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_104902516190169408790974063514334012647585517534779054617274613760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 0&lt;/span&gt;2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[200, 201, 202, 203, 204, 205, 206, 207, 216, 217, 218, 219, 220, 221, 222, 223]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_26855044144683368650489360259669507237781892488903437982022301122560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 0&lt;/span&gt;4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[224, 225, 226, 227, 228, 229, 230, 231, 240, 241, 242, 243, 244, 245, 246, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_450552876304888127456888502778291411541830171175110582166992262750231592960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 1&lt;/span&gt;¬0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[232, 233, 234, 235, 236, 237, 238, 239, 248, 249, 250, 251, 252, 253, 254, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_115341536334051360628963456711242601354708523820828309034750019264059287797760.svg|420px]]
|}

[[Category:Boolf prop/3-ary|prefect]]</text>
      <sha1>2scsg70aeu1j0gvgz0gtf4hvi4g3dst</sha1>
    </revision>
    <revision>
      <id>2693219</id>
      <parentid>2693218</parentid>
      <timestamp>2024-12-25T21:42:41Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693219</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5218" sha1="rodxju61re1t9lsp3p3s8khaliwab36" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 6928706295070929573599405754551337583186506210420311235022011754348801.svg|thumb|500px|reversed [[Boolf prop/3-ary/zhegalkin linear|Zhegalkin linears]]]]

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| prefect
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;/span&gt;0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_16711935.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 1&lt;/span&gt;¬4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_4278255360.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 1&lt;/span&gt;¬2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[32, 33, 34, 35, 36, 37, 38, 39, 48, 49, 50, 51, 52, 53, 54, 55]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_71777214277877760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 0&lt;/span&gt;6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[40, 41, 42, 43, 44, 45, 46, 47, 56, 57, 58, 59, 60, 61, 62, 63]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_18374966855136706560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 1&lt;/span&gt;¬1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[64, 65, 66, 67, 68, 69, 70, 71, 80, 81, 82, 83, 84, 85, 86, 87]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_308280787921469235485736960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 0&lt;/span&gt;5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[72, 73, 74, 75, 76, 77, 78, 79, 88, 89, 90, 91, 92, 93, 94, 95]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_78919881707896124284348661760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 0&lt;/span&gt;3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[96, 97, 98, 99, 100, 101, 102, 103, 112, 113, 114, 115, 116, 117, 118, 119]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1324055902107822182681362917658460160.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 1&lt;/span&gt;¬7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[104, 105, 106, 107, 108, 109, 110, 111, 120, 121, 122, 123, 124, 125, 126, 127]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_338958310939602478766428906920565800960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 0&lt;/span&gt;7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5686776797628873740399791320050227284918927360.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 1&lt;/span&gt;¬3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[136, 137, 138, 139, 140, 141, 142, 143, 152, 153, 154, 155, 156, 157, 158, 159]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1455814860192991677542346577932858184939245404160.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 1&lt;/span&gt;¬5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[160, 161, 162, 163, 164, 165, 166, 167, 176, 177, 178, 179, 180, 181, 182, 183]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_24424520365467623060330297684840395266093667022599618560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 0&lt;/span&gt;1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[168, 169, 170, 171, 172, 173, 174, 175, 184, 185, 186, 187, 188, 189, 190, 191]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_6252677213559711503444556207319141188119978757785502351360.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 1&lt;/span&gt;¬6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[192, 193, 194, 195, 196, 197, 198, 199, 208, 209, 210, 211, 212, 213, 214, 215]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_104902516190169408790974063514334012647585517534779054617274613760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 0&lt;/span&gt;2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[200, 201, 202, 203, 204, 205, 206, 207, 216, 217, 218, 219, 220, 221, 222, 223]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_26855044144683368650489360259669507237781892488903437982022301122560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 0&lt;/span&gt;4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[224, 225, 226, 227, 228, 229, 230, 231, 240, 241, 242, 243, 244, 245, 246, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_450552876304888127456888502778291411541830171175110582166992262750231592960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 1&lt;/span&gt;¬0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[232, 233, 234, 235, 236, 237, 238, 239, 248, 249, 250, 251, 252, 253, 254, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_115341536334051360628963456711242601354708523820828309034750019264059287797760.svg|420px]]
|}

[[Category:Boolf prop/3-ary|prefect]]</text>
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      <id>2693245</id>
      <parentid>2692673</parentid>
      <timestamp>2024-12-26T00:17:44Z</timestamp>
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__NOTOC__

==16 / 240==

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==24 / 232==

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==57 / 199==

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==62 / 194==

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==64 / 192==

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!colspan=&quot;2&quot;| {{anchor|great_quaestor_dominion}} great quaestor dominion
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{| class=&quot;collapsible-with-classes collapsible wide center&quot;
!colspan=&quot;2&quot;| {{anchor|great_quaestor_sword_dominion}} great quaestor sword dominion
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==66 / 190==

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==96 / 160==

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==97 / 159==

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==128 / 128==

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!colspan=&quot;2&quot;| {{anchor|zhegalkin_deviation_patron}} zhegalkin deviation patron
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[[Category:Boolf prop/3-ary| ]]</text>
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__NOTOC__

==16 / 240==

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==24 / 232==

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==57 / 199==

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==62 / 194==

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!colspan=&quot;2&quot;| {{anchor|is_blotless}} is blotless
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==64 / 192==

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!colspan=&quot;2&quot;| {{anchor|great_quaestor_dominion}} great quaestor dominion
|-
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!colspan=&quot;2&quot;| {{anchor|great_quaestor_sword_dominion}} great quaestor sword dominion
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|}

==66 / 190==

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!colspan=&quot;2&quot;| {{anchor|is_bloatless}} is bloatless
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==96 / 160==

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|}

==97 / 159==

{| class=&quot;collapsible-with-classes collapsible wide center&quot;
!colspan=&quot;2&quot;| {{anchor|is_male}} is male
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==128 / 128==

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|class=&quot;val&quot;| 0
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{| class=&quot;collapsible-with-classes collapsible wide center followed&quot;
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|class=&quot;val&quot;| 0
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{| class=&quot;collapsible-with-classes collapsible wide center followed&quot;
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{| class=&quot;collapsible-with-classes collapsible wide center followed&quot;
!colspan=&quot;2&quot;| {{anchor|zhegalkin_deviation_patron}} zhegalkin deviation patron
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|class=&quot;val&quot;| 0
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{| class=&quot;collapsible-with-classes collapsible wide center&quot;
!colspan=&quot;2&quot;| {{anchor|zhegalkin_deviation_is_odious}} zhegalkin deviation is odious
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[[Category:Boolf prop/3-ary| ]]</text>
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__NOTOC__

==16 / 240==

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!colspan=&quot;2&quot;| {{anchor|is_noble}} is noble
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{| class=&quot;collapsible-with-classes collapsible wide center&quot;
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==24 / 232==

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==57 / 199==

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==62 / 194==

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==64 / 192==

{| class=&quot;collapsible-with-classes collapsible wide center followed&quot;
!colspan=&quot;2&quot;| {{anchor|great_quaestor_dominion}} great quaestor dominion
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{| class=&quot;collapsible-with-classes collapsible wide center&quot;
!colspan=&quot;2&quot;| {{anchor|great_quaestor_sword_dominion}} great quaestor sword dominion
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==66 / 190==

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!colspan=&quot;2&quot;| {{anchor|is_bloatless}} is bloatless
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==96 / 160==

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==97 / 159==

{| class=&quot;collapsible-with-classes collapsible wide center&quot;
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==128 / 128==

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{| class=&quot;collapsible-with-classes collapsible wide center followed&quot;
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{| class=&quot;collapsible-with-classes collapsible wide center followed&quot;
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|class=&quot;val&quot;| 0
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|class=&quot;val&quot;| 128
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[[Category:Boolf prop/3-ary| ]]</text>
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      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693177</origin>
      <model>wikitext</model>
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      <text bytes="3652" sha1="4mc1p6gvfnanmzj25zy1kx70c10pz2z" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;9&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| weight
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|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| 0
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|-
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|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 2, 4, 8, 16, 32, 64, 128]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_340282366920938463481821351509772796182.svg|420px]]
|-
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|-
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|-
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|-
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|-
|class=&quot;size&quot;| 28
|class=&quot;prop&quot;| 6
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[63, 95, 111, 119, 123, 125, 126, 159, 175, 183, 187, 189, 190, 207, 215, 219, 221, 222, 231, 235, 237, 238, 243, 245, 246, 249, 250, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_10135356007067392298401852992480860869043946928093127336450413029551874506752.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| 7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[127, 191, 223, 239, 247, 251, 253, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_47267576113963700113891037153651775520272614183047870828201421166580517044224.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| 8
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57896044618658097711785492504343953926634992332820282019728792003956564819968.svg|420px]]
|}

[[Category:Boolf prop/3-ary|weight]]</text>
      <sha1>4mc1p6gvfnanmzj25zy1kx70c10pz2z</sha1>
    </revision>
  </page>
  <page>
    <title>Template:Families of Boolean functions/table of super-clans</title>
    <ns>10</ns>
    <id>317412</id>
    <revision>
      <id>2693175</id>
      <parentid>2692912</parentid>
      <timestamp>2024-12-25T13:14:40Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693175</origin>
      <model>wikitext</model>
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      <text bytes="6451" sha1="sa0ge4nr007ltl0pa8sp21u3j7tlxhf" xml:space="preserve">&lt;templatestyles src=&quot;Families of Boolean functions/table of super-clans/style.css&quot; /&gt;

{| class=&quot;wikitable sortable&quot; id=&quot;super-clans&quot;
!class=&quot;super-clan-size&quot;| &lt;abbr title=&quot;super-clan&quot;&gt;s.-c.&lt;/abbr&gt;&lt;br&gt;size
!class=&quot;family-size&quot;| family&lt;br&gt;size
!class=&quot;weight&quot;| weight
!class=&quot;tribe&quot;| tribe
!class=&quot;quaestor-weight&quot;| quaestor&lt;br&gt;weight
!class=&quot;rep&quot;| &lt;abbr title=&quot;representative&quot;&gt;rep.&lt;/abbr&gt;
!class=&quot;matrix&quot;| truth&lt;br&gt;tables
!class=&quot;matrix&quot;| Zhegalkin&lt;br&gt;indices
!class=&quot;matrix&quot;| reverse
|-
|class=&quot;super-clan-size&quot;| 2
|class=&quot;family-size&quot;| 1
|class=&quot;weight&quot;| 0, 8
|class=&quot;tribe&quot;| blunt '''0'''
| 0
| 0&lt;br&gt;[[File:Venn 0000 0000.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 0&lt;br&gt;[[File:Venn 0000 0000.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 0.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 0 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 0.svg|200px]]
|-
|class=&quot;super-clan-size&quot;| 2
|class=&quot;family-size&quot;| 2
|class=&quot;weight&quot;| 4
|class=&quot;tribe&quot;| blunt '''0'''
| 4
| 150&lt;br&gt;[[File:Venn 0110 1001.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 22&lt;br&gt;[[File:Venn 0110 1000.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 22.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 22 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 22.svg|200px]]
|-
|class=&quot;super-clan-size&quot;| 6
|class=&quot;family-size&quot;| 2
|class=&quot;weight&quot;| 4
|class=&quot;tribe&quot;| blunt '''0'''
| 4
| 170&lt;br&gt;[[File:Venn 0101 0101.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 2&lt;br&gt;[[File:Venn 0100 0000.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 2.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 2 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 2.svg|200px]]
|-
|class=&quot;super-clan-size&quot;| 6
|class=&quot;family-size&quot;| 2
|class=&quot;weight&quot;| 4
|class=&quot;tribe&quot;| blunt '''0'''
| 0
| 102&lt;br&gt;[[File:Venn 0110 0110.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 6&lt;br&gt;[[File:Venn 0110 0000.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 6.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 6 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 6.svg|200px]]
|-
|class=&quot;super-clan-size&quot;| 8
|class=&quot;family-size&quot;| 4
|class=&quot;weight&quot;| 2, 6
|class=&quot;tribe&quot;| blunt '''3'''
| 0
| 66&lt;br&gt;[[File:Venn 0100 0010.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 106&lt;br&gt;[[File:Venn 0101 0110.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 106.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 106 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 106.svg|200px]]
|-
|class=&quot;super-clan-size&quot;| 8
|class=&quot;family-size&quot;| 8
|class=&quot;weight&quot;| 4
|class=&quot;tribe&quot;| blunt '''3'''
| 4
| 232&lt;br&gt;[[File:Venn 0001 0111.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 104&lt;br&gt;[[File:Venn 0001 0110.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 104.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 104 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 104.svg|200px]]
|-
|class=&quot;super-clan-size&quot;| 16
|class=&quot;family-size&quot;| 8
|class=&quot;weight&quot;| 1, 7
|class=&quot;tribe&quot;| sharp
| 1
| 128&lt;br&gt;[[File:Venn 0000 0001.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 128&lt;br&gt;[[File:Venn 0000 0001.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 128.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 128 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 128.svg|200px]]
|-
|class=&quot;super-clan-size&quot;| 16
|class=&quot;family-size&quot;| 8
|class=&quot;weight&quot;| 3, 5
|class=&quot;tribe&quot;| sharp
| 3
| 22&lt;br&gt;[[File:Venn 0110 1000.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 150&lt;br&gt;[[File:Venn 0110 1001.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 150.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 150 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 150.svg|200px]]
|-
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|class=&quot;family-size&quot;| 4
|class=&quot;weight&quot;| 2, 6
|class=&quot;tribe&quot;| blunt '''2'''
| 2
| 40&lt;br&gt;[[File:Venn 0001 0100.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 40&lt;br&gt;[[File:Venn 0001 0100.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 40.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 40 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 40.svg|200px]]
|-
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|class=&quot;family-size&quot;| 4
|class=&quot;weight&quot;| 2, 6
|class=&quot;tribe&quot;| blunt '''1'''
| 2
| 136&lt;br&gt;[[File:Venn 0001 0001.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 8&lt;br&gt;[[File:Venn 0001 0000.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 8.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 8 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 8.svg|200px]]
|-
|class=&quot;super-clan-size&quot;| 24
|class=&quot;family-size&quot;| 8
|class=&quot;weight&quot;| 4
|class=&quot;tribe&quot;| blunt '''1'''
| 2
| 120&lt;br&gt;[[File:Venn 0001 1110.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 24&lt;br&gt;[[File:Venn 0001 1000.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 24.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 24 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 24.svg|200px]]
|-
|class=&quot;super-clan-size&quot;| 24
|class=&quot;family-size&quot;| 8
|class=&quot;weight&quot;| 4
|class=&quot;tribe&quot;| blunt '''2'''
| 2
| 228&lt;br&gt;[[File:Venn 0010 0111.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 44&lt;br&gt;[[File:Venn 0011 0100.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 44.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 44 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 44.svg|200px]]
|-
|class=&quot;super-clan-size&quot;| 48
|class=&quot;family-size&quot;| 8
|class=&quot;weight&quot;| 3, 5
|class=&quot;tribe&quot;| sharp
| 3
| 42&lt;br&gt;[[File:Venn 0101 0100.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 130&lt;br&gt;[[File:Venn 0100 0001.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 130.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 130 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 130.svg|200px]]
|-
|class=&quot;super-clan-size&quot;| 48
|class=&quot;family-size&quot;| 8
|class=&quot;weight&quot;| 3, 5
|class=&quot;tribe&quot;| sharp
| 1
| 230&lt;br&gt;[[File:Venn 0110 0111.svg|30px]]&lt;br&gt;&lt;br&gt;Ж 134&lt;br&gt;[[File:Venn 0110 0001.svg|30px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 134.svg|200px]]
| [[File:3-ary Boolean functions; super-clan of Zhe 134 (indices).svg|200px]]
| [[File:3-ary Boolean functions; transposed super-clan of Zhe 134.svg|200px]]
|}&lt;noinclude&gt;

[[Category:Families of Boolean functions]]
&lt;/noinclude&gt;</text>
      <sha1>sa0ge4nr007ltl0pa8sp21u3j7tlxhf</sha1>
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  </page>
  <page>
    <title>Complex Analysis/Example Computation with Laurent Series</title>
    <ns>0</ns>
    <id>317466</id>
    <revision>
      <id>2693276</id>
      <parentid>2693116</parentid>
      <timestamp>2024-12-26T10:35:35Z</timestamp>
      <contributor>
        <username>Eshaa2024</username>
        <id>2993595</id>
      </contributor>
      <comment>/* Tasks */</comment>
      <origin>2693276</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="8540" sha1="2s651zz0mxrm5egu9khf3vc9r6w9fvh" xml:space="preserve">In this learning resource, rational functions are developed into Laurent series to extract the residue.
== From a Rational Function to a Laurent Series ==
Initially, a simple rational function of the following form is given:
* &lt;math&gt;f: G \to \mathbb{C}&lt;/math&gt; with 
* &lt;math&gt;G:=\mathbb{C}\setminus \{-a\}, a\in \mathbb{C}&lt;/math&gt; 
* &lt;math&gt;f(z):=\frac{1}{a+z}&lt;/math&gt;
The goal is to develop it into a Laurent series with the expansion point &lt;math&gt;z_o \in \mathbb{C}&lt;/math&gt;..
=== Definition of Constants ===
The following constants are defined to better illustrate the operations:
* &lt;math&gt;b:=-a&lt;/math&gt;
* &lt;math&gt;c:=b-z_o=-a-z_o&lt;/math&gt;  
* &lt;math&gt;c_n:=\frac{1}{(b-z_o)^{n+1}}=\frac{1}{(-z_o-a)^{n+1}}&lt;/math&gt;
* &lt;math&gt;q:=\frac{z-z_0}{c}&lt;/math&gt;
=== Transformation into a Laurent Series ===
Let &lt;math&gt;z_o \not = -a &lt;/math&gt;, then:
:&lt;math&gt;\begin{array}{rl}   \displaystyle f(z) &amp;= \frac{1}{a+z} = \displaystyle -\frac{1}{b-z} \ \ (b:=-a)\\          
&amp;= \displaystyle -\frac{1}{b\underbrace{-z_o+z_o}_{=0}-z} = -\frac{1}{(b-z_o)-(z-z_o)} \\        
&amp;= \displaystyle -\frac{1}{(\underbrace{b-z_o}_{=c})-(z-z_o)} = -\frac{1}{c-(z-z_o)}\\        
&amp;= \displaystyle -\frac{1}{c} \cdot \frac{1}{1-\frac{z-z_o}{c}} = - \frac{1}{c} \cdot \frac{1}{1-\underbrace{\frac{z-z_o}{c}}_{:=q}}\\   
&amp;= \displaystyle - \frac{1}{c} \cdot \frac{1}{1-q} = -  \frac{1}{c} \cdot\sum_{n=0}^{+\infty} q^n = -  \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{c^{(n+1)}} \\
&amp;= \displaystyle - \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{(z_o-a)^{n+1}} = - \sum_{n=0}^{+\infty}  \underbrace{\frac{1}{(-z_o-a)^{n+1}}}_{c_n:=} \cdot (z-z_o)^n \\
&amp;= \displaystyle -  \sum_{n=0}^{+\infty}  c_n \cdot (z-z_o)^n
\end{array} &lt;/math&gt; :
The residue &lt;math&gt;res_{z_0}(f)= 0 &lt;/math&gt; ,since in the Laurent expansion, the principal part coefficients are all zero (i.e., the principal part vanishes).

=== Tasks ===

*Why is the condition  required for the above calculation [[Laurent Series|Laurent Series]] (or [[w:en:Power series|power series]])&lt;math&gt; z_o \not= - a &lt;/math&gt;?
*Compute the Laurent series for &lt;math&gt;z_o = -a &lt;/math&gt; and determine the [[Complex Analysis/Residue|Residue]] of the Laurent expansion for &lt;math&gt;f(z):=\frac{1}{a+z}&lt;/math&gt; in &lt;math&gt;z_o = -a &lt;/math&gt; at!***

== Factored Powers with Expansion Point in the Denominator ==
=== Definition of the Function  ===
First,we are given a simple rational function of the form:
* &lt;math&gt;g: G \to \mathbb{C}&lt;/math&gt; mit 
* &lt;math&gt;G:=\mathbb{C}\setminus \{-a\}, a\in \mathbb{C}&lt;/math&gt; 
* &lt;math&gt;g(z):=\frac{1}{ (z-z_o)^m \cdot (a+z)}&lt;/math&gt; 
The goal is to develop it into a Laurent series with the expansion point &lt;math&gt;z_o \in \mathbb{C}\setminus \{-a\}&lt;/math&gt;.
=== Definition of Constants ===
The following constants are defined to better illustrate the operations:
* &lt;math&gt;c:=z_o-a&lt;/math&gt;  
* &lt;math&gt;c_n:=\frac{1}{(b+z_o)^{n+1}}=\frac{1}{(z_o-a)^{n+1}}&lt;/math&gt;
* &lt;math&gt;q:=\frac{z-z_o}{c}= \frac{z-z_o}{z_o-a}&lt;/math&gt;
=== Transformation into a Laurent Series ===
:&lt;math&gt;\begin{array}{rl}   \displaystyle g(z) &amp;= \displaystyle  \frac{1}{(z-z_o)^m\cdot (a+z)} =  \frac{1}{(z-z_o)^m} \cdot \frac{1}{a+z}\ \ (c:=z_o-a)\\          
&amp;= \displaystyle - \frac{1}{(z-z_o)^m} \cdot \frac{1}{z_o-a} \cdot \frac{1}{1-\frac{z-z_o}{z_o-a}} = - \frac{1}{(z-z_o)^m} \cdot \frac{1}{c} \cdot \frac{1}{1-q} \\
&amp;= \displaystyle -  \frac{1}{(z-z_o)^m} \cdot  \frac{1}{c} \cdot\sum_{n=0}^{+\infty} q^n = -  \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{c^{n+1}} \\
&amp;= \displaystyle - \frac{1}{(z-z_o)^m} \cdot \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{(z_o-a)^{n+1}} \\
&amp;= \displaystyle - \frac{1}{(z-z_o)^m} \cdot \sum_{n=0}^{+\infty}  \underbrace{\frac{1}{(z_o-a)^{n+1}}}_{c_n:=} \cdot (z-z_o)^n \\
&amp;= \displaystyle -  \frac{1}{(z-z_o)^m} \cdot  \sum_{n=0}^{+\infty}  c_n \cdot (z-z_o)^n \\
&amp;= \displaystyle -  \sum_{n=-m}^{+\infty}  c_{n+m} \cdot (z-z_o)^n \\
\end{array} &lt;/math&gt;
the residue &lt;math&gt;res_{z_0}(g)= c_{-1+m}= \frac{1}{(b-z_o)^{-1+m+1}}= \frac{1}{(b-z_o)^{m}}=\frac{1}{(-z_o-a)^{m}}&lt;/math&gt;.
== Laurent Series with Infinite Principal Part Terms ==
A simple rational function of the following form is given:
* &lt;math&gt;h: G \to \mathbb{C}&lt;/math&gt; with 
* &lt;math&gt;G:=\mathbb{C}\setminus \{-a\}, a\in \mathbb{C}\setminus \{-a\}&lt;/math&gt; 
* &lt;math&gt;h(z):=\frac{(z-z_0)^m}{z+a}&lt;/math&gt; 
The goal is to develop it into a Laurent series with the expansion point &lt;math&gt;z_o \in \mathbb{C}\setminus \{-a\}&lt;/math&gt;.
=== Definition of Constants ===
The following constants are defined for better clarity:
* &lt;math&gt;b:=-z_0-a&lt;/math&gt;
* &lt;math&gt;c_n:=b^n&lt;/math&gt;
* &lt;math&gt;q:=\frac{b}{z-z_o} = -\frac{z_0+a}{z-z_o}&lt;/math&gt;
=== Transformation into a Laurent Series with  ===
:&lt;math&gt;\begin{array}{rl}   \displaystyle h(z) &amp;= \displaystyle \frac{z-z_0}{z+a} = \frac{z-z_0}{z\underbrace{-z_o+z_o}_{=0}+a} \\
&amp;= \displaystyle \frac{z-z_0}{(z-z_o)-\underbrace{(-z_o-a)}_{=b}} = \frac{z-z_0}{(z-z_o)-b}\\        
&amp;= \displaystyle \frac{1}{1-\frac{b}{z-z_0}} = \frac{1}{1-\underbrace{\frac{b}{z-z_o}}_{:=q}}\\   
&amp;= \displaystyle \sum_{n=0}^{+\infty} q^n =  \sum_{n=0}^{+\infty} \frac{b^n}{(z-z_o)^{n}} \\
&amp;= \displaystyle \sum_{n=0}^{+\infty} b^n \cdot (z-z_o)^{-n} =   \sum_{n=-\infty}^{0}  c_{-n} \cdot (z-z_o)^n
\end{array} &lt;/math&gt;
The residue&lt;math&gt;res_{z_0}(h)= c_{1} = b^1 = -z_o-a&lt;/math&gt;
=== Transformation into a Laurent Series with  ===
:&lt;math&gt;\begin{array}{rl}   \displaystyle h(z) &amp;= \displaystyle \frac{(z-z_0)^m}{z+a} = \frac{(z-z_0)^m}{z\underbrace{-z_o+z_o}_{=0}+a} \\
&amp;= \displaystyle \frac{(z-z_0)^m}{(z-z_o)-\underbrace{(-z_o-a)}_{=b}} = \frac{(z-z_0)^m}{(z-z_o)-b}\\        
&amp;= \displaystyle \frac{(z-z_0)^{m-1}}{1-\frac{b}{z-z_0}} = \frac{(z-z_0)^{m-1}}{1-\underbrace{\frac{b}{z-z_o}}_{:=q}}\\   
&amp;= (z-z_0)^{m-1} \cdot \displaystyle \sum_{n=0}^{+\infty} q^n =  (z-z_0)^{m-1} \cdot \sum_{n=0}^{+\infty} \frac{b^n}{(z-z_o)^{n}} \\
&amp;= (z-z_0)^{m-1} \cdot \displaystyle \sum_{n=0}^{+\infty} b^n \cdot (z-z_o)^{-n} =  (z-z_0)^{m-1} \cdot  \sum_{n=-\infty}^{0}  c_{-n} \cdot (z-z_o)^n\\
&amp;= \displaystyle \sum_{n=-\infty}^{0}  c_{-n} \cdot (z-z_o)^{n+m-1} = \displaystyle \sum_{n=-\infty}^{m-1}  c_{m-1-n} \cdot (z-z_o)^{n}
\end{array} &lt;/math&gt;
The residue for  is &lt;math&gt;n=-1&lt;/math&gt; erhält man &lt;math&gt;res_{z_0}(h)= c_{m-1-(-1)}= c_{m} = b^{m} = (-z_o-a)^{m}&lt;/math&gt;
== See Also ==
*[[w:en:Laurent_series|Theorem on Laurent Series Expansion]]


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=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen|Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen]] - URL:https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Integrationsweg
* Date: 11/20/2024

&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen&quot; srclang=&quot;de&quot; date=&quot;12/17/2024&quot; time=&quot;11:42&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;[[de:Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen]]&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
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      <id>2693279</id>
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      <timestamp>2024-12-26T11:18:03Z</timestamp>
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        <id>2993595</id>
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      <text bytes="7116" sha1="gihgjdgt10lauz6zduefkjaurw9uuku" xml:space="preserve">In this learning resource, rational functions are developed into Laurent series to extract the residue.
== From a Rational Function to a Laurent Series ==
Initially, a simple rational function of the following form is given:
* &lt;math&gt;f: G \to \mathbb{C}&lt;/math&gt; with 
* &lt;math&gt;G:=\mathbb{C}\setminus \{-a\}, a\in \mathbb{C}&lt;/math&gt; 
* &lt;math&gt;f(z):=\frac{1}{a+z}&lt;/math&gt;
The goal is to develop it into a Laurent series with the expansion point &lt;math&gt;z_o \in \mathbb{C}&lt;/math&gt;..
=== Definition of Constants ===
The following constants are defined to better illustrate the operations:
* &lt;math&gt;b:=-a&lt;/math&gt;
* &lt;math&gt;c:=b-z_o=-a-z_o&lt;/math&gt;  
* &lt;math&gt;c_n:=\frac{1}{(b-z_o)^{n+1}}=\frac{1}{(-z_o-a)^{n+1}}&lt;/math&gt;
* &lt;math&gt;q:=\frac{z-z_0}{c}&lt;/math&gt;
=== Transformation into a Laurent Series ===
Let &lt;math&gt;z_o \not = -a &lt;/math&gt;, then:
:&lt;math&gt;\begin{array}{rl}   \displaystyle f(z) &amp;= \frac{1}{a+z} = \displaystyle -\frac{1}{b-z} \ \ (b:=-a)\\          
&amp;= \displaystyle -\frac{1}{b\underbrace{-z_o+z_o}_{=0}-z} = -\frac{1}{(b-z_o)-(z-z_o)} \\        
&amp;= \displaystyle -\frac{1}{(\underbrace{b-z_o}_{=c})-(z-z_o)} = -\frac{1}{c-(z-z_o)}\\        
&amp;= \displaystyle -\frac{1}{c} \cdot \frac{1}{1-\frac{z-z_o}{c}} = - \frac{1}{c} \cdot \frac{1}{1-\underbrace{\frac{z-z_o}{c}}_{:=q}}\\   
&amp;= \displaystyle - \frac{1}{c} \cdot \frac{1}{1-q} = -  \frac{1}{c} \cdot\sum_{n=0}^{+\infty} q^n = -  \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{c^{(n+1)}} \\
&amp;= \displaystyle - \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{(z_o-a)^{n+1}} = - \sum_{n=0}^{+\infty}  \underbrace{\frac{1}{(-z_o-a)^{n+1}}}_{c_n:=} \cdot (z-z_o)^n \\
&amp;= \displaystyle -  \sum_{n=0}^{+\infty}  c_n \cdot (z-z_o)^n
\end{array} &lt;/math&gt; :
The residue &lt;math&gt;res_{z_0}(f)= 0 &lt;/math&gt; ,since in the Laurent expansion, the principal part coefficients are all zero (i.e., the principal part vanishes).

=== Tasks ===

*Why is the condition  required for the above calculation [[Laurent Series|Laurent Series]] (or [[w:en:Power series|power series]])&lt;math&gt; z_o \not= - a &lt;/math&gt;?
*Compute the Laurent series for &lt;math&gt;z_o = -a &lt;/math&gt; and determine the [[Complex Analysis/Residue|Residue]] of the Laurent expansion for &lt;math&gt;f(z):=\frac{1}{a+z}&lt;/math&gt; in &lt;math&gt;z_o = -a &lt;/math&gt; at!***

== Factored Powers with Expansion Point in the Denominator ==
=== Definition of the Function  ===
First,we are given a simple rational function of the form:
* &lt;math&gt;g: G \to \mathbb{C}&lt;/math&gt; mit 
* &lt;math&gt;G:=\mathbb{C}\setminus \{-a\}, a\in \mathbb{C}&lt;/math&gt; 
* &lt;math&gt;g(z):=\frac{1}{ (z-z_o)^m \cdot (a+z)}&lt;/math&gt; 
The goal is to develop it into a Laurent series with the expansion point &lt;math&gt;z_o \in \mathbb{C}\setminus \{-a\}&lt;/math&gt;.
=== Definition of Constants ===
The following constants are defined to better illustrate the operations:
* &lt;math&gt;c:=z_o-a&lt;/math&gt;  
* &lt;math&gt;c_n:=\frac{1}{(b+z_o)^{n+1}}=\frac{1}{(z_o-a)^{n+1}}&lt;/math&gt;
* &lt;math&gt;q:=\frac{z-z_o}{c}= \frac{z-z_o}{z_o-a}&lt;/math&gt;
=== Transformation into a Laurent Series ===
:&lt;math&gt;\begin{array}{rl}   \displaystyle g(z) &amp;= \displaystyle  \frac{1}{(z-z_o)^m\cdot (a+z)} =  \frac{1}{(z-z_o)^m} \cdot \frac{1}{a+z}\ \ (c:=z_o-a)\\          
&amp;= \displaystyle - \frac{1}{(z-z_o)^m} \cdot \frac{1}{z_o-a} \cdot \frac{1}{1-\frac{z-z_o}{z_o-a}} = - \frac{1}{(z-z_o)^m} \cdot \frac{1}{c} \cdot \frac{1}{1-q} \\
&amp;= \displaystyle -  \frac{1}{(z-z_o)^m} \cdot  \frac{1}{c} \cdot\sum_{n=0}^{+\infty} q^n = -  \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{c^{n+1}} \\
&amp;= \displaystyle - \frac{1}{(z-z_o)^m} \cdot \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{(z_o-a)^{n+1}} \\
&amp;= \displaystyle - \frac{1}{(z-z_o)^m} \cdot \sum_{n=0}^{+\infty}  \underbrace{\frac{1}{(z_o-a)^{n+1}}}_{c_n:=} \cdot (z-z_o)^n \\
&amp;= \displaystyle -  \frac{1}{(z-z_o)^m} \cdot  \sum_{n=0}^{+\infty}  c_n \cdot (z-z_o)^n \\
&amp;= \displaystyle -  \sum_{n=-m}^{+\infty}  c_{n+m} \cdot (z-z_o)^n \\
\end{array} &lt;/math&gt;
the residue &lt;math&gt;res_{z_0}(g)= c_{-1+m}= \frac{1}{(b-z_o)^{-1+m+1}}= \frac{1}{(b-z_o)^{m}}=\frac{1}{(-z_o-a)^{m}}&lt;/math&gt;.
== Laurent Series with Infinite Principal Part Terms ==
A simple rational function of the following form is given:
* &lt;math&gt;h: G \to \mathbb{C}&lt;/math&gt; with 
* &lt;math&gt;G:=\mathbb{C}\setminus \{-a\}, a\in \mathbb{C}\setminus \{-a\}&lt;/math&gt; 
* &lt;math&gt;h(z):=\frac{(z-z_0)^m}{z+a}&lt;/math&gt; 
The goal is to develop it into a Laurent series with the expansion point &lt;math&gt;z_o \in \mathbb{C}\setminus \{-a\}&lt;/math&gt;.
=== Definition of Constants ===
The following constants are defined for better clarity:
* &lt;math&gt;b:=-z_0-a&lt;/math&gt;
* &lt;math&gt;c_n:=b^n&lt;/math&gt;
* &lt;math&gt;q:=\frac{b}{z-z_o} = -\frac{z_0+a}{z-z_o}&lt;/math&gt;
=== Transformation into a Laurent Series with  ===
:&lt;math&gt;\begin{array}{rl}   \displaystyle h(z) &amp;= \displaystyle \frac{z-z_0}{z+a} = \frac{z-z_0}{z\underbrace{-z_o+z_o}_{=0}+a} \\
&amp;= \displaystyle \frac{z-z_0}{(z-z_o)-\underbrace{(-z_o-a)}_{=b}} = \frac{z-z_0}{(z-z_o)-b}\\        
&amp;= \displaystyle \frac{1}{1-\frac{b}{z-z_0}} = \frac{1}{1-\underbrace{\frac{b}{z-z_o}}_{:=q}}\\   
&amp;= \displaystyle \sum_{n=0}^{+\infty} q^n =  \sum_{n=0}^{+\infty} \frac{b^n}{(z-z_o)^{n}} \\
&amp;= \displaystyle \sum_{n=0}^{+\infty} b^n \cdot (z-z_o)^{-n} =   \sum_{n=-\infty}^{0}  c_{-n} \cdot (z-z_o)^n
\end{array} &lt;/math&gt;
The residue&lt;math&gt;res_{z_0}(h)= c_{1} = b^1 = -z_o-a&lt;/math&gt;
=== Transformation into a Laurent Series with  ===
:&lt;math&gt;\begin{array}{rl}   \displaystyle h(z) &amp;= \displaystyle \frac{(z-z_0)^m}{z+a} = \frac{(z-z_0)^m}{z\underbrace{-z_o+z_o}_{=0}+a} \\
&amp;= \displaystyle \frac{(z-z_0)^m}{(z-z_o)-\underbrace{(-z_o-a)}_{=b}} = \frac{(z-z_0)^m}{(z-z_o)-b}\\        
&amp;= \displaystyle \frac{(z-z_0)^{m-1}}{1-\frac{b}{z-z_0}} = \frac{(z-z_0)^{m-1}}{1-\underbrace{\frac{b}{z-z_o}}_{:=q}}\\   
&amp;= (z-z_0)^{m-1} \cdot \displaystyle \sum_{n=0}^{+\infty} q^n =  (z-z_0)^{m-1} \cdot \sum_{n=0}^{+\infty} \frac{b^n}{(z-z_o)^{n}} \\
&amp;= (z-z_0)^{m-1} \cdot \displaystyle \sum_{n=0}^{+\infty} b^n \cdot (z-z_o)^{-n} =  (z-z_0)^{m-1} \cdot  \sum_{n=-\infty}^{0}  c_{-n} \cdot (z-z_o)^n\\
&amp;= \displaystyle \sum_{n=-\infty}^{0}  c_{-n} \cdot (z-z_o)^{n+m-1} = \displaystyle \sum_{n=-\infty}^{m-1}  c_{m-1-n} \cdot (z-z_o)^{n}
\end{array} &lt;/math&gt;
The residue for  is &lt;math&gt;n=-1&lt;/math&gt; erhält man &lt;math&gt;res_{z_0}(h)= c_{m-1-(-1)}= c_{m} = b^{m} = (-z_o-a)^{m}&lt;/math&gt;
== See Also ==
*[[w:en:Laurent_series|Theorem on Laurent Series Expansion]]


== Page information ==
=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen|Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen]] - URL:https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Integrationsweg
* Date: 11/20/2024

&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen&quot; srclang=&quot;de&quot; date=&quot;12/17/2024&quot; time=&quot;11:42&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;[[de:Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen]]&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
      <sha1>gihgjdgt10lauz6zduefkjaurw9uuku</sha1>
    </revision>
    <revision>
      <id>2693280</id>
      <parentid>2693279</parentid>
      <timestamp>2024-12-26T11:19:52Z</timestamp>
      <contributor>
        <username>Eshaa2024</username>
        <id>2993595</id>
      </contributor>
      <comment>/* Tasks */</comment>
      <origin>2693280</origin>
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      <format>text/x-wiki</format>
      <text bytes="7099" sha1="hfzr8diym6i72cxzo4s2uqqf5le3wtc" xml:space="preserve">In this learning resource, rational functions are developed into Laurent series to extract the residue.
== From a Rational Function to a Laurent Series ==
Initially, a simple rational function of the following form is given:
* &lt;math&gt;f: G \to \mathbb{C}&lt;/math&gt; with 
* &lt;math&gt;G:=\mathbb{C}\setminus \{-a\}, a\in \mathbb{C}&lt;/math&gt; 
* &lt;math&gt;f(z):=\frac{1}{a+z}&lt;/math&gt;
The goal is to develop it into a Laurent series with the expansion point &lt;math&gt;z_o \in \mathbb{C}&lt;/math&gt;..
=== Definition of Constants ===
The following constants are defined to better illustrate the operations:
* &lt;math&gt;b:=-a&lt;/math&gt;
* &lt;math&gt;c:=b-z_o=-a-z_o&lt;/math&gt;  
* &lt;math&gt;c_n:=\frac{1}{(b-z_o)^{n+1}}=\frac{1}{(-z_o-a)^{n+1}}&lt;/math&gt;
* &lt;math&gt;q:=\frac{z-z_0}{c}&lt;/math&gt;
=== Transformation into a Laurent Series ===
Let &lt;math&gt;z_o \not = -a &lt;/math&gt;, then:
:&lt;math&gt;\begin{array}{rl}   \displaystyle f(z) &amp;= \frac{1}{a+z} = \displaystyle -\frac{1}{b-z} \ \ (b:=-a)\\          
&amp;= \displaystyle -\frac{1}{b\underbrace{-z_o+z_o}_{=0}-z} = -\frac{1}{(b-z_o)-(z-z_o)} \\        
&amp;= \displaystyle -\frac{1}{(\underbrace{b-z_o}_{=c})-(z-z_o)} = -\frac{1}{c-(z-z_o)}\\        
&amp;= \displaystyle -\frac{1}{c} \cdot \frac{1}{1-\frac{z-z_o}{c}} = - \frac{1}{c} \cdot \frac{1}{1-\underbrace{\frac{z-z_o}{c}}_{:=q}}\\   
&amp;= \displaystyle - \frac{1}{c} \cdot \frac{1}{1-q} = -  \frac{1}{c} \cdot\sum_{n=0}^{+\infty} q^n = -  \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{c^{(n+1)}} \\
&amp;= \displaystyle - \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{(z_o-a)^{n+1}} = - \sum_{n=0}^{+\infty}  \underbrace{\frac{1}{(-z_o-a)^{n+1}}}_{c_n:=} \cdot (z-z_o)^n \\
&amp;= \displaystyle -  \sum_{n=0}^{+\infty}  c_n \cdot (z-z_o)^n
\end{array} &lt;/math&gt; :
The residue &lt;math&gt;res_{z_0}(f)= 0 &lt;/math&gt; ,since in the Laurent expansion, the principal part coefficients are all zero (i.e., the principal part vanishes).

=== Tasks ===

*Why is the condition  required for the above calculation [[Laurent Series|Laurent Series]] (or [[w:en:Power series|power series]])&lt;math&gt; z_o \not= - a &lt;/math&gt;?
*Compute the Laurent series for &lt;math&gt;z_o = -a &lt;/math&gt; and determine the [[Residue|Residue]] of the Laurent expansion for &lt;math&gt;f(z):=\frac{1}{a+z}&lt;/math&gt; in &lt;math&gt;z_o = -a &lt;/math&gt; at!***

== Factored Powers with Expansion Point in the Denominator ==
=== Definition of the Function  ===
First,we are given a simple rational function of the form:
* &lt;math&gt;g: G \to \mathbb{C}&lt;/math&gt; mit 
* &lt;math&gt;G:=\mathbb{C}\setminus \{-a\}, a\in \mathbb{C}&lt;/math&gt; 
* &lt;math&gt;g(z):=\frac{1}{ (z-z_o)^m \cdot (a+z)}&lt;/math&gt; 
The goal is to develop it into a Laurent series with the expansion point &lt;math&gt;z_o \in \mathbb{C}\setminus \{-a\}&lt;/math&gt;.
=== Definition of Constants ===
The following constants are defined to better illustrate the operations:
* &lt;math&gt;c:=z_o-a&lt;/math&gt;  
* &lt;math&gt;c_n:=\frac{1}{(b+z_o)^{n+1}}=\frac{1}{(z_o-a)^{n+1}}&lt;/math&gt;
* &lt;math&gt;q:=\frac{z-z_o}{c}= \frac{z-z_o}{z_o-a}&lt;/math&gt;
=== Transformation into a Laurent Series ===
:&lt;math&gt;\begin{array}{rl}   \displaystyle g(z) &amp;= \displaystyle  \frac{1}{(z-z_o)^m\cdot (a+z)} =  \frac{1}{(z-z_o)^m} \cdot \frac{1}{a+z}\ \ (c:=z_o-a)\\          
&amp;= \displaystyle - \frac{1}{(z-z_o)^m} \cdot \frac{1}{z_o-a} \cdot \frac{1}{1-\frac{z-z_o}{z_o-a}} = - \frac{1}{(z-z_o)^m} \cdot \frac{1}{c} \cdot \frac{1}{1-q} \\
&amp;= \displaystyle -  \frac{1}{(z-z_o)^m} \cdot  \frac{1}{c} \cdot\sum_{n=0}^{+\infty} q^n = -  \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{c^{n+1}} \\
&amp;= \displaystyle - \frac{1}{(z-z_o)^m} \cdot \sum_{n=0}^{+\infty} \frac{(z-z_o)^n}{(z_o-a)^{n+1}} \\
&amp;= \displaystyle - \frac{1}{(z-z_o)^m} \cdot \sum_{n=0}^{+\infty}  \underbrace{\frac{1}{(z_o-a)^{n+1}}}_{c_n:=} \cdot (z-z_o)^n \\
&amp;= \displaystyle -  \frac{1}{(z-z_o)^m} \cdot  \sum_{n=0}^{+\infty}  c_n \cdot (z-z_o)^n \\
&amp;= \displaystyle -  \sum_{n=-m}^{+\infty}  c_{n+m} \cdot (z-z_o)^n \\
\end{array} &lt;/math&gt;
the residue &lt;math&gt;res_{z_0}(g)= c_{-1+m}= \frac{1}{(b-z_o)^{-1+m+1}}= \frac{1}{(b-z_o)^{m}}=\frac{1}{(-z_o-a)^{m}}&lt;/math&gt;.
== Laurent Series with Infinite Principal Part Terms ==
A simple rational function of the following form is given:
* &lt;math&gt;h: G \to \mathbb{C}&lt;/math&gt; with 
* &lt;math&gt;G:=\mathbb{C}\setminus \{-a\}, a\in \mathbb{C}\setminus \{-a\}&lt;/math&gt; 
* &lt;math&gt;h(z):=\frac{(z-z_0)^m}{z+a}&lt;/math&gt; 
The goal is to develop it into a Laurent series with the expansion point &lt;math&gt;z_o \in \mathbb{C}\setminus \{-a\}&lt;/math&gt;.
=== Definition of Constants ===
The following constants are defined for better clarity:
* &lt;math&gt;b:=-z_0-a&lt;/math&gt;
* &lt;math&gt;c_n:=b^n&lt;/math&gt;
* &lt;math&gt;q:=\frac{b}{z-z_o} = -\frac{z_0+a}{z-z_o}&lt;/math&gt;
=== Transformation into a Laurent Series with  ===
:&lt;math&gt;\begin{array}{rl}   \displaystyle h(z) &amp;= \displaystyle \frac{z-z_0}{z+a} = \frac{z-z_0}{z\underbrace{-z_o+z_o}_{=0}+a} \\
&amp;= \displaystyle \frac{z-z_0}{(z-z_o)-\underbrace{(-z_o-a)}_{=b}} = \frac{z-z_0}{(z-z_o)-b}\\        
&amp;= \displaystyle \frac{1}{1-\frac{b}{z-z_0}} = \frac{1}{1-\underbrace{\frac{b}{z-z_o}}_{:=q}}\\   
&amp;= \displaystyle \sum_{n=0}^{+\infty} q^n =  \sum_{n=0}^{+\infty} \frac{b^n}{(z-z_o)^{n}} \\
&amp;= \displaystyle \sum_{n=0}^{+\infty} b^n \cdot (z-z_o)^{-n} =   \sum_{n=-\infty}^{0}  c_{-n} \cdot (z-z_o)^n
\end{array} &lt;/math&gt;
The residue&lt;math&gt;res_{z_0}(h)= c_{1} = b^1 = -z_o-a&lt;/math&gt;
=== Transformation into a Laurent Series with  ===
:&lt;math&gt;\begin{array}{rl}   \displaystyle h(z) &amp;= \displaystyle \frac{(z-z_0)^m}{z+a} = \frac{(z-z_0)^m}{z\underbrace{-z_o+z_o}_{=0}+a} \\
&amp;= \displaystyle \frac{(z-z_0)^m}{(z-z_o)-\underbrace{(-z_o-a)}_{=b}} = \frac{(z-z_0)^m}{(z-z_o)-b}\\        
&amp;= \displaystyle \frac{(z-z_0)^{m-1}}{1-\frac{b}{z-z_0}} = \frac{(z-z_0)^{m-1}}{1-\underbrace{\frac{b}{z-z_o}}_{:=q}}\\   
&amp;= (z-z_0)^{m-1} \cdot \displaystyle \sum_{n=0}^{+\infty} q^n =  (z-z_0)^{m-1} \cdot \sum_{n=0}^{+\infty} \frac{b^n}{(z-z_o)^{n}} \\
&amp;= (z-z_0)^{m-1} \cdot \displaystyle \sum_{n=0}^{+\infty} b^n \cdot (z-z_o)^{-n} =  (z-z_0)^{m-1} \cdot  \sum_{n=-\infty}^{0}  c_{-n} \cdot (z-z_o)^n\\
&amp;= \displaystyle \sum_{n=-\infty}^{0}  c_{-n} \cdot (z-z_o)^{n+m-1} = \displaystyle \sum_{n=-\infty}^{m-1}  c_{m-1-n} \cdot (z-z_o)^{n}
\end{array} &lt;/math&gt;
The residue for  is &lt;math&gt;n=-1&lt;/math&gt; erhält man &lt;math&gt;res_{z_0}(h)= c_{m-1-(-1)}= c_{m} = b^{m} = (-z_o-a)^{m}&lt;/math&gt;
== See Also ==
*[[w:en:Laurent_series|Theorem on Laurent Series Expansion]]


== Page information ==
=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen|Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen]] - URL:https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Integrationsweg
* Date: 11/20/2024

&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen&quot; srclang=&quot;de&quot; date=&quot;12/17/2024&quot; time=&quot;11:42&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;[[de:Kurs:Funktionentheorie/Beispielrechnung mit Laurentreihen]]&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
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  <page>
    <title>PLC/Training Labs</title>
    <ns>0</ns>
    <id>317471</id>
    <revision>
      <id>2693211</id>
      <parentid>2693156</parentid>
      <timestamp>2024-12-25T19:46:24Z</timestamp>
      <contributor>
        <username>Ekbreckenridge</username>
        <id>2994477</id>
      </contributor>
      <comment>Added two basic labs</comment>
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      <text bytes="7540" sha1="dc3pwhtzmntmacnuqsw6j9kq8jzysdr" xml:space="preserve">This will have a comprehensive set of labs to learn how to write ladder logic programs using the Free Automation Direct Do-More PLC software ([https://www.automationdirect.com/support/software-downloads?itemcode=Do-more%20Designer Link to software]), which has a built in PLC simulator.  

=== Warning ===
'''SEE [[Wikipedia: Electric shock]] AND UNDERSTAND THE RISKS. This warning is from the Electrical Circuit Analysis page and is especially applicable here, while building a PLC.'''

If you decide to put together a trainer board, please read this warning. As little as 10 mA AC current can cause temporary paralysis and an inability to let go or withdraw from the current source. If the current bypasses the skin, as little as 10 uA may cause heart failure. Direct current is much less dangerous, unless voltages are high or there is direct connection bypassing the skin. Wet skin has lower resistance, never approach AC-mains-connected electrical equipment or wiring with wet skin or bare feet. Pay special attention to proper grounding of AC power plugs and of anything which may be, deliberately or accidentally, connected to a hot (energized) wire. With good grounding, an accidental short circuit is likely to blow a fuse or circuit breaker, instead of maintaining a shock hazard. Low-voltage circuits, up to 12 VAC or DC may be handled quite safely, as long as the skin is not bypassed (such as with wide contact -- such as grasping non-insulated pliers -- or wet skin, or a metal ring). Working with higher voltages requires serious caution.


==== If using the Direct Do-More PLC and simulator see below, if using a different software, please see user manual: ====
Download the software from the link above, and open a new project. Under hardware class, select the simulator. It will put you in Editor mode, and you will be able to start programming. 

Discreet inputs start at X0 and go to X15. Discreet Inputs will be things like push buttons, selector switches. Things that are either on or off. 

Discreet outputs start at Y0 and go to Y15. They will be things like relays, lights, motor starters. 

Analog Inputs start at WX0, and go to WX7. They will be things like pressure sensors, temperatures sensors. 

Analog output starts at WY0 and go to WY7. They can be used for things like Variable Frequency Drive (VFD) to control motor speed of Alternating Current Drives, or how open or closed a flow gate can be.

Counters are incremental counting devices that keep track of the count. CT0 through CT3 are the designations in the simulator.

Timers are used to counting second. T0 through T2 are the designations in the simulator, 

Internal bits that can be used for logic are C0-C2047

== Labs ==
Assume all switches are discreet switches and lights, unless specifically mentioned.

=== Lab 1: ===
Input 1 is a momentary normally open (NO) switch that when pressed will momentarily turn on output 1, which is a signal light.
[[File:Lab 1 Solution.png|thumb|Lab 1 Solution]]

=== Lab 2: ===
Lab 2 builds on Lab 1. 

Input 1 is a momentary normally closed (NC) button. Input 2 is a momentary NO button. Output 1 is a signal light. When input 2 is pressed, the light should turn on and stay on, until input is pressed. 


There are two potential solutions. Both have similar looking logic, where something 'holds' the ladder logic on. Both are common uses of an 'or' solution in ladder logic. If the normally closed button is still closed, and If the push button or the bit holding the logic is on, the bit will be on. If the normally closed button is pushed, it will stop the power to either the NO push button, or the item holding power to the rung. 
[[File:Lab2-s1.png|thumb|Lab 2 Solution 1]]
[[File:Lab2-S2.png|alt=Lab 2, Solution 2|thumb|Lab 2, Solution 2]]
The reason this typically works is due to a quick 'scan time' or 'cycle time'. Cycle time is related to how fast the PLC checks the inputs, checks the logic based on those inputs, and turns on or off the outputs. The typical scan or cycle time is between 10ms and 50ms, depending on system complexity and external I/O. 

The button being pushed for a second or two will be long enough for the PLC to recognize the button is pushed, turn on the light, and use the light as a second input to ensure the light stays on, until the NC button is pressed. The NC button will remove power to the light, and then turn off the light being used as an input, and will need the NO push button to turn the light back on. 


=== Trainer Board Purchasing List: ===


For those that want to build a small trainer board that they can physically interact with attached is a list of parts that can be used with the labs written below. This is not a comprehensive list, and some mounting hardware may be required. There is no sponsorship with automation direct. Automation Direct is a common industrial supplier in North America. Please consult with local suppliers if not in North America, or see here: [https://www.automationdirect.com/adc/international/international Automation Direct International Suppliers] 
{| class=&quot;wikitable&quot;
|+
!Product name
!Product Description
!Product Code
|-
|
|
|If not specifically indicated, the product is from https://www.automationdirect.com/
|-
|Productivity1000 AC/DC power supply
|Power supply for the modules
|P1-01AC
|-
|Productivity1000 CPU
|The 'core' of the PLC trainer. Handles all the logic instructions
|P1-540
|-
|Productivity1000 discrete input module
|The input module handles all push buttons, selector switches and other input items
|P1-08NA
|-
|Productivity1000 discrete output module
|The output module handles outputting signals to whatever outputs the PLC needs to interact with
|P1-08TA
|-
|ZIPLink feedthrough module (2x needed)
|The ZIPLink feedthrough module makes it easier to connect I/O items to the PLC. (If this is not used, terminal blocks will need to sourced for the I/O modules
|ZL-RTB20
|-
|ZIPLink PLC I/O cable (2x needed)
|This connects an I/O module to a Ziplink module
|ZL-P1-CBL10 
|-
|USB A to microB-USB Programming Cable
|This is used to connect from your computer to the PLC
|USB-CBL-AMICB15
|-
|AutomationDirect standard memory card
|This SD card is not needed, but is useful if you want to mess around with logging
|MICSD-16G
|-
|DINnector DIN rail, slotted
|The PLC modules will be mounted onto the DIN rail
|DN-R35S1
|-
|Red Push Button
|This is a normally closed switch (used as a stand-in for an E-stop or a stop button)
|GCX1211-120L
|-
|Green Push Button (2x)
|This a normally open switch (Used as a standard input push button for various different items)
|GCX1202-120L
|-
|Red Selector Switch
|A normally open selector switch with a red LED indicator light
|GCX3251-120L
|-
|Green Selector Switch
|A normally open selector switch with a green LED indicator light
|GCX1252-120L
|-
|Push Button Enclosure
|A 5 hole push button enclosure to hold the selector switches and push bittons
|SA111
|-
|Industrial Signal Light 120v
|The Industrial Signal Light is a standard sort of light used in the auto industry. It can be used to indicate various states, or used as a stand-in for other outputs during testing
|Look on Amazon or other industrial sites for industrial signal light 120v.
|-
|White wire
|This will be used for the line side (Or Negative side) for returning voltage back to the power sorce
|AWM26WH10
|-
|Black Wire
|This will be used for the load side (Or positive side) for supplying the power to the Input or output items
|AWM26BK10                                            
|}</text>
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      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt; &lt;/div&gt;  {| class=&quot;wikitable sortable boolf-blocks&quot; !class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt; !c...&quot;</comment>
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&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| honesty and gender
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 57
|class=&quot;prop&quot;| dishonest &lt;span class=&quot;light&quot;&gt;female&lt;/span&gt;
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[0, 23, 27, 29, 30, 39, 43, 45, 46, 53, 54, 57, 58, 71, 75, 77, 78, 83, 86, 89, 92, 99, 101, 106, 108, 113, 114, 116, 120, 135, 139, 141, 142, 147, 149, 154, 156, 163, 166, 169, 172, 177, 178, 180, 184, 197, 198, 201, 202, 209, 210, 212, 216, 225, 226, 228, 232]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7494979546278868352838388259605652777030681542822747306921801562456065.svg|420px]]
|-
|class=&quot;size&quot;| 159
|class=&quot;prop&quot;| &lt;span class=&quot;light&quot;&gt;honest&lt;/span&gt; male
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_114774098304662113554475878620958198697053691664884971068594184657468564176318.svg|420px]]
|-
|class=&quot;size&quot;| 40
|class=&quot;prop&quot;| honest female
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[6, 9, 18, 20, 24, 33, 36, 40, 60, 65, 66, 72, 90, 96, 102, 105, 111, 123, 125, 126, 129, 130, 132, 144, 150, 153, 159, 165, 183, 189, 190, 195, 215, 219, 222, 231, 235, 237, 246, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1017983437674535590226753549341449550563515970074050148116092428643003007552.svg|420px]]
|}

[[Category:Boolf prop/3-ary|honesty and gender]]</text>
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        <id>137431</id>
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      <comment>New resource with &quot;{| class=&quot;wikitable collapsible collapsed&quot; style=&quot;text-align: center;&quot;\ !colspan=&quot;6&quot;| sequences |- ! !! 0 !! 1 !! 2 !! 3 !! 4 |- style=&quot;background-color: #f5aed3; border-top: 3px solid black;&quot; ! female | 1 || 1 || 3 || 97 || 32199 |- style=&quot;border-top: 3px solid gray;&quot; ! dishonest &lt;span style=&quot;opacity: .5;&quot;&gt;female&lt;/span&gt; | 1 || 1 || 1 || 57 || 30537 |- ! honest female | 0 || 0 || 2 || 40 || 1662 |- style=&quot;background-color: #a6c5f7; &quot; ! &lt;span style=&quot;opacity: .5;&quot;&gt;honest&lt;/...&quot;</comment>
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!colspan=&quot;6&quot;| sequences
|-
! !! 0 !! 1 !! 2 !! 3 !! 4
|- style=&quot;background-color: #f5aed3; border-top: 3px solid black;&quot;
! female
| 1 || 1 || 3 || 97 || 32199
|- style=&quot;border-top: 3px solid gray;&quot;
! dishonest &lt;span style=&quot;opacity: .5;&quot;&gt;female&lt;/span&gt;
| 1 || 1 || 1 || 57 || 30537
|-
! honest female
| 0 || 0 || 2 || 40 || 1662
|- style=&quot;background-color: #a6c5f7; &quot;
! &lt;span style=&quot;opacity: .5;&quot;&gt;honest&lt;/span&gt; male
| 1 || 3 || 13 || 159 || 33337
|- style=&quot;border-top: 3px solid gray;&quot;
! honest
| 1 || 3 || 15 || 199 || 34999
|- style=&quot;border-top: 3px solid gray; font-weight: bold; border-top: 3px solid black;&quot;
! all
| 2 || 4 || 16 || 256 || 65536
|}&lt;noinclude&gt;
[[Category:Gender of Boolean functions]]
&lt;/noinclude&gt;</text>
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  <page>
    <title>User:Michael Ten/Notes</title>
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      <timestamp>2024-12-25T18:50:11Z</timestamp>
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        <username>Michael Ten</username>
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      <comment>New resource with &quot;===Notes about learning, research, education, and learning to learn===  Some of this is added here for self reference in case some of this is archived elsewhere on this wiki.   === LLM training===  ====Common Corpus and LLM training==== Greetings. I believe LLM generated content is not currently allowed on this wiki. No problem. I am curious - what if the dataset an [[LLM]] is trained on is all in the public domain; would this or does this change that with regards to LLM...&quot;</comment>
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      <text bytes="1966" sha1="bgjr5y2a7b53n5ri6uwq9evkc1fafyy" xml:space="preserve">===Notes about learning, research, education, and learning to learn===

Some of this is added here for self reference in case some of this is archived elsewhere on this wiki. 

=== LLM training===

====Common Corpus and LLM training====
Greetings. I believe LLM generated content is not currently allowed on this wiki. No problem. I am curious - what if the dataset an [[LLM]] is trained on is all in the public domain; would this or does this change that with regards to LLM generated content being allowed (presuming the LLM output is verified and accurate)? Has there been any discussion on this wiki or other MediaWiki wikis about LLM generated content by LLM's that is trained exclusively on CC-0/public domain data? i.e. Common Corpus https://huggingface.co/blog/Pclanglais/common-corpus
[[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:50, 25 December 2024 (UTC)

=== Certs===

We could issue certificates in some residing in certain jurisdictions probably (?). To my knowledge, there is no legal prohibition federally against doing this in the USA as long as no misrepresentation happens. Although some states might prohibit it (?). Degrees are likely different (at least with respect to accreditation). Please let me know if you believe I am likely incorrect in my understanding. I asked an LLM this prompt, &quot;is there any prohibition legally in USA for a DAO (decentralized autonomous organization or wiki community related to learning, teaching, and research) from issuing certifications or certificates to those who go through learning materials and educational resources that might be on a decentralized or nonprofit wiki that has an active community?&quot; (i won't post the specific result, but I wrote and engineered that prompt myself). The LLM output seemed to indicate my understanding noted here is correct, but LLM's are sometimes wrong. what do you or others think about this?</text>
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    <title>File:DIR.2A.Manage.20241225.pdf</title>
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      <comment>{{Information
|Description=DIR.2A: Managing Shared Libraries (20241225 - 20241224)
|Source={{own|Young1lim}}
|Date=2024-12-26
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
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      <text bytes="277" sha1="tpmhifuxbms5emhwhtzyol9nafdb9j1" xml:space="preserve">== Summary ==
{{Information
|Description=DIR.2A: Managing Shared Libraries (20241225 - 20241224)
|Source={{own|Young1lim}}
|Date=2024-12-26
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}
== Licensing ==
{{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}</text>
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    <title>File:DIR.2A.Manage.20241226.pdf</title>
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      <comment>{{Information
|Description=DIR.2A: Managing Shared Libraries (20241226 - 20241225)
|Source={{own|Young1lim}}
|Date=2024-12-26
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
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      <text bytes="277" sha1="cvxvkwm86630saxdle5cjf8vaekld2y" xml:space="preserve">== Summary ==
{{Information
|Description=DIR.2A: Managing Shared Libraries (20241226 - 20241225)
|Source={{own|Young1lim}}
|Date=2024-12-26
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}
== Licensing ==
{{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}</text>
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    <title>Linear Boolean function</title>
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    <redirect title="Linear Boolean functions" />
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      <contributor>
        <username>Watchduck</username>
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      <comment>Redirected page to [[Linear Boolean functions]]</comment>
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      <text bytes="38" sha1="76g6e46v3yu6o71inf3al3d917vhm18" xml:space="preserve">#REDIRECT [[Linear Boolean functions]]</text>
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  <page>
    <title>Nonlinearity of Boolean functions</title>
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      <comment>New resource with &quot;{{Boolf header}}  The {{w|Nonlinearity (disambiguation)|nonlinearity}} of a Boolean functions measures how far it is from being a [[linear Boolean function]].&lt;br&gt; It is usually defined as a [[Soft properties of Boolean functions|soft property]], i.e. dependent on arity.&lt;br&gt; &lt;small&gt;A Boolean function with the highest possible nonlinearity is a {{w|bent function}}.&lt;/small&gt;     [[Category:Studies of Euler diagrams]]&quot;</comment>
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      <text bytes="416" sha1="eqdptlm6izavqc6ywdoly9vx9kqu46l" xml:space="preserve">{{Boolf header}}

The {{w|Nonlinearity (disambiguation)|nonlinearity}} of a Boolean functions measures how far it is from being a [[linear Boolean function]].&lt;br&gt;
It is usually defined as a [[Soft properties of Boolean functions|soft property]], i.e. dependent on arity.&lt;br&gt;
&lt;small&gt;A Boolean function with the highest possible nonlinearity is a {{w|bent function}}.&lt;/small&gt;


[[Category:Studies of Euler diagrams]]</text>
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    <revision>
      <id>2693212</id>
      <parentid>2693209</parentid>
      <timestamp>2024-12-25T19:50:08Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693212</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1005" sha1="cl064exdwcy87rpw53cdcz07t6krzrq" xml:space="preserve">{{Boolf header}}

The {{w|Nonlinearity (disambiguation)|nonlinearity}} of a Boolean functions measures how far it is from being a [[linear Boolean function]].&lt;br&gt;
It is usually defined as a [[Soft properties of Boolean functions|soft property]], i.e. dependent on arity.&lt;br&gt;
&lt;small&gt;A Boolean function with the highest possible nonlinearity is a {{w|bent function}}.&lt;/small&gt;


{| class=&quot;wikitable&quot; style=&quot;text-align: center;&quot;
! {{Diagonal split header|a|nl}} !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !!style=&quot;border-left: 3px solid gray;&quot;| total || sequence
|-
! 1
| 4 || || || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''4''' ||
|-
! 2
| 8 || 8 || || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''16''' ||
|-
! 3
| 16 || 128 || 112 || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''256''' || {{oeislink|A207676}}

|-
! 4
| 32 || 512 || 3840 || 17920 || 28000 || 14336 || 896 ||style=&quot;border-left: 3px solid gray;&quot;| '''65536''' || {{oeislink|A207328}}


[[Category:Studies of Euler diagrams]]</text>
      <sha1>cl064exdwcy87rpw53cdcz07t6krzrq</sha1>
    </revision>
    <revision>
      <id>2693213</id>
      <parentid>2693212</parentid>
      <timestamp>2024-12-25T20:13:43Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693213</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1197" sha1="7q0gz5sbgxdp248w5gdww434wnikyum" xml:space="preserve">{{Boolf header}}

The {{w|Nonlinearity (disambiguation)|nonlinearity}} of a Boolean functions measures how far it is from being a [[linear Boolean function]].&lt;br&gt;
It is usually defined as a [[Soft properties of Boolean functions|soft property]], i.e. dependent on arity

Let &lt;math&gt;b = 2^{n-1} - 2^{\frac{n}{2} - 1}&lt;/math&gt;. The highest nonlinearity for arity &lt;math&gt;n&lt;/math&gt; is &lt;math&gt;\lfloor b \rfloor&lt;/math&gt;.&lt;br&gt;
A Boolean function with nonlinearity &lt;math&gt;b&lt;/math&gt; is a {{w|bent function}}. This happens when &lt;math&gt;b&lt;/math&gt; is an integer, i.e. for even &lt;math&gt;n&lt;/math&gt;.

{| class=&quot;wikitable&quot; style=&quot;text-align: center;&quot;
! {{Diagonal split header|a|nl}} !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !!style=&quot;border-left: 3px solid gray;&quot;| total || sequence
|-
! 1
| 4 || || || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''4''' ||
|-
! 2
| 8 || 8 || || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''16''' ||
|-
! 3
| 16 || 128 || 112 || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''256''' || {{oeislink|A207676}}

|-
! 4
| 32 || 512 || 3840 || 17920 || 28000 || 14336 || 896 ||style=&quot;border-left: 3px solid gray;&quot;| '''65536''' || {{oeislink|A207328}}


[[Category:Studies of Euler diagrams]]</text>
      <sha1>7q0gz5sbgxdp248w5gdww434wnikyum</sha1>
    </revision>
    <revision>
      <id>2693238</id>
      <parentid>2693213</parentid>
      <timestamp>2024-12-25T23:36:37Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693238</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1557" sha1="bl36aznhv53wgr5p9o21wy586ri5wlr" xml:space="preserve">{{Boolf header}}

The {{w|Nonlinearity (disambiguation)|nonlinearity}} of a Boolean function measures how far it is from being a [[linear Boolean function]].&lt;br&gt;
It is the smallest {{w|Hamming distance}} of its truth table to that of a linear.&lt;br&gt;
As an integer it is a [[Soft properties of Boolean functions|soft property]] &lt;small&gt;(i.e. dependent on arity)&lt;/small&gt;.
But it can be easily defined as a fraction, which is a [[Hard properties of Boolean functions|hard property]].&lt;br&gt;
: arity &lt;math&gt;a&lt;/math&gt;, {{spaces|3}} soft nonlinearity &lt;math&gt;n&lt;/math&gt;, {{spaces|3}} hard nonlinearity &lt;math&gt;\frac{n}{2^a}&lt;/math&gt;

Let &lt;math&gt;b = 2^{a-1} - 2^{\frac{a}{2} - 1}&lt;/math&gt;. The highest nonlinearity for arity &lt;math&gt;a&lt;/math&gt; is &lt;math&gt;\lfloor b \rfloor&lt;/math&gt;.&lt;br&gt;
A Boolean function with nonlinearity &lt;math&gt;b&lt;/math&gt; is a {{w|bent function}}. They exist when &lt;math&gt;b&lt;/math&gt; is an integer, i.e. for even &lt;math&gt;a&lt;/math&gt;.

{{Nonlinearity of Boolean functions/table overview/integers}}

{{Nonlinearity of Boolean functions/table overview/fractions}}


==Zhegalkin deviation==

&lt;small style=&quot;opacity: .5;&quot;&gt;The terminology used is likely to be changed again.&lt;/small&gt;

Boolean functions can also be assigned unique integers, that are not dependent on the used arity. They are the [[Zhegalkin matrix|Zhegalkin indices]].&lt;br&gt;
Their binary exponents shall be called Zhegalkin exponents. The Zhegalkin exponents of Walsh functions are only powers of two. For negated Walsh functions also 0.&lt;br&gt;
So a different notion of Hamming distance 


[[Category:Studies of Euler diagrams]]</text>
      <sha1>bl36aznhv53wgr5p9o21wy586ri5wlr</sha1>
    </revision>
    <revision>
      <id>2693241</id>
      <parentid>2693238</parentid>
      <timestamp>2024-12-26T00:04:23Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693241</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2209" sha1="do1qgat3xioanslsacnpoioffkjs5gu" xml:space="preserve">{{Boolf header}}

The {{w|Nonlinearity (disambiguation)|nonlinearity}} of a Boolean function measures how far it is from being a [[linear Boolean function]].&lt;br&gt;
It is the smallest {{w|Hamming distance}} of its truth table to that of a linear.&lt;br&gt;
As an integer it is a [[Soft properties of Boolean functions|soft property]] &lt;small&gt;(i.e. dependent on arity)&lt;/small&gt;.
But it can be easily defined as a fraction, which is a [[Hard properties of Boolean functions|hard property]].&lt;br&gt;
: arity &lt;math&gt;a&lt;/math&gt;, {{spaces|3}} soft nonlinearity &lt;math&gt;n&lt;/math&gt;, {{spaces|3}} hard nonlinearity &lt;math&gt;\frac{n}{2^a}&lt;/math&gt;

Let &lt;math&gt;b = 2^{a-1} - 2^{\frac{a}{2} - 1}&lt;/math&gt;. The highest nonlinearity for arity &lt;math&gt;a&lt;/math&gt; is &lt;math&gt;\lfloor b \rfloor&lt;/math&gt;.&lt;br&gt;
A Boolean function with nonlinearity &lt;math&gt;b&lt;/math&gt; is a {{w|bent function}}. They exist when &lt;math&gt;b&lt;/math&gt; is an integer, i.e. for even &lt;math&gt;a&lt;/math&gt;.

{{Nonlinearity of Boolean functions/table overview/integers}}

{{Nonlinearity of Boolean functions/table overview/fractions}}

'''{{Boolf prop 3-ary|nonlinearity}}'''

==Zhegalkin deviation==

&lt;small style=&quot;opacity: .5;&quot;&gt;The terminology used here is likely to be changed again.&lt;/small&gt;

Boolean functions can also be assigned unique integers, that are not dependent on the arity used. They are the [[Zhegalkin matrix|Zhegalkin indices]].&lt;br&gt;
Their binary exponents shall be called Zhegalkin exponents. The Zhegalkin exponents of Walsh functions are only powers of two &lt;small style=&quot;opacity: .7;&quot;&gt;([[c:File:Variadic logical connectives with up to 5 arguments; XOR twin.svg|see here]])&lt;/small&gt;. For negated Walsh functions also 0.&lt;br&gt;
The Zhegalkin exponents of the BF are split into those that are 0 or powers of two, and those that are not.&lt;br&gt;
So the BF is split in two, which shall be called Zhegalkin linear and deviation.&lt;br&gt;
The Zhegalkin weight of the deviation &lt;small&gt;(the number of Zhegalkin exponents that are not 0 or powers of two)&lt;/small&gt; is a different notion of Hamming distance from linears.&lt;br&gt;
'''{{Boolf prop 3-ary|zhegalkin linear}}''', '''{{Boolf prop 3-ary|zhegalkin deviation}}''', '''{{Boolf prop 3-ary|zhegalkin deviation weight}}'''


[[Category:Studies of Euler diagrams]]</text>
      <sha1>do1qgat3xioanslsacnpoioffkjs5gu</sha1>
    </revision>
  </page>
  <page>
    <title>Talk:Workings of gcc and ld in plain view</title>
    <ns>1</ns>
    <id>317485</id>
    <revision>
      <id>2693214</id>
      <timestamp>2024-12-25T20:18:58Z</timestamp>
      <contributor>
        <username>Michael Ten</username>
        <id>654933</id>
      </contributor>
      <comment>/* PDF's */ new section</comment>
      <origin>2693214</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="250" sha1="qfmqb40i43iaq0if0rs2srava0ye80a" xml:space="preserve">== PDF's ==

are PDF&quot;s really ideal for the content of this? mediawiki markup is available, on wiki. [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 20:18, 25 December 2024 (UTC)</text>
      <sha1>qfmqb40i43iaq0if0rs2srava0ye80a</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/zhegalkin linear</title>
    <ns>0</ns>
    <id>317486</id>
    <revision>
      <id>2693217</id>
      <timestamp>2024-12-25T21:38:19Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; &lt;/div&gt;  {| class=&quot;wikitable sortable boolf-blocks&quot; !class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt; !class=&quot;prop&quot;| zhegalkin linear !class=&quot;block&quot;| block |- |class=&quot;size&quot;| 16 |class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;/span&gt;0...&quot;</comment>
      <origin>2693217</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5540" sha1="7nz8eqgpui9p1f9bxwycdv6e17wwzo3" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| zhegalkin linear
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;/span&gt;0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 8, 32, 40, 64, 72, 96, 104, 128, 136, 160, 168, 192, 200, 224, 232]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_6928706295070929573599405754551337583186506210420311235022011754348801.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 1&lt;/span&gt;¬7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 9, 33, 41, 65, 73, 97, 105, 129, 137, 161, 169, 193, 201, 225, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_13857412590141859147198811509102675166373012420840622470044023508697602.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 0&lt;/span&gt;1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 10, 34, 42, 66, 74, 98, 106, 130, 138, 162, 170, 194, 202, 226, 234]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_27714825180283718294397623018205350332746024841681244940088047017395204.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 1&lt;/span&gt;¬6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 11, 35, 43, 67, 75, 99, 107, 131, 139, 163, 171, 195, 203, 227, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_55429650360567436588795246036410700665492049683362489880176094034790408.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 0&lt;/span&gt;2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 12, 36, 44, 68, 76, 100, 108, 132, 140, 164, 172, 196, 204, 228, 236]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_110859300721134873177590492072821401330984099366724979760352188069580816.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 1&lt;/span&gt;¬5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 13, 37, 45, 69, 77, 101, 109, 133, 141, 165, 173, 197, 205, 229, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_221718601442269746355180984145642802661968198733449959520704376139161632.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 0&lt;/span&gt;3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 14, 38, 46, 70, 78, 102, 110, 134, 142, 166, 174, 198, 206, 230, 238]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_443437202884539492710361968291285605323936397466899919041408752278323264.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 1&lt;/span&gt;¬4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 15, 39, 47, 71, 79, 103, 111, 135, 143, 167, 175, 199, 207, 231, 239]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_886874405769078985420723936582571210647872794933799838082817504556646528.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 0&lt;/span&gt;4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[16, 24, 48, 56, 80, 88, 112, 120, 144, 152, 176, 184, 208, 216, 240, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_454079695753768440535410655530276459851710871006105517098402562333003022336.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 1&lt;/span&gt;¬3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[17, 25, 49, 57, 81, 89, 113, 121, 145, 153, 177, 185, 209, 217, 241, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_908159391507536881070821311060552919703421742012211034196805124666006044672.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 0&lt;/span&gt;5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 26, 50, 58, 82, 90, 114, 122, 146, 154, 178, 186, 210, 218, 242, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1816318783015073762141642622121105839406843484024422068393610249332012089344.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 1&lt;/span&gt;¬2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[19, 27, 51, 59, 83, 91, 115, 123, 147, 155, 179, 187, 211, 219, 243, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3632637566030147524283285244242211678813686968048844136787220498664024178688.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 0&lt;/span&gt;6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 28, 52, 60, 84, 92, 116, 124, 148, 156, 180, 188, 212, 220, 244, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7265275132060295048566570488484423357627373936097688273574440997328048357376.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 1&lt;/span&gt;¬1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[21, 29, 53, 61, 85, 93, 117, 125, 149, 157, 181, 189, 213, 221, 245, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14530550264120590097133140976968846715254747872195376547148881994656096714752.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 0&lt;/span&gt;7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[22, 30, 54, 62, 86, 94, 118, 126, 150, 158, 182, 190, 214, 222, 246, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_29061100528241180194266281953937693430509495744390753094297763989312193429504.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 1&lt;/span&gt;¬0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[23, 31, 55, 63, 87, 95, 119, 127, 151, 159, 183, 191, 215, 223, 247, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_58122201056482360388532563907875386861018991488781506188595527978624386859008.svg|420px]]
|}

[[Category:Boolf prop/3-ary|zhegalkin linear]]</text>
      <sha1>7nz8eqgpui9p1f9bxwycdv6e17wwzo3</sha1>
    </revision>
    <revision>
      <id>2693220</id>
      <parentid>2693217</parentid>
      <timestamp>2024-12-25T21:42:43Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693220</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5653" sha1="jwmxjuhg3e3a18btj2rpwxienyuv6jk" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 16711935.svg|thumb|500px|reversed [[Boolf prop/3-ary/prefect|prefects]]]]

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| zhegalkin linear
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;/span&gt;0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 8, 32, 40, 64, 72, 96, 104, 128, 136, 160, 168, 192, 200, 224, 232]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_6928706295070929573599405754551337583186506210420311235022011754348801.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 1&lt;/span&gt;¬7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 9, 33, 41, 65, 73, 97, 105, 129, 137, 161, 169, 193, 201, 225, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_13857412590141859147198811509102675166373012420840622470044023508697602.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 0&lt;/span&gt;1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 10, 34, 42, 66, 74, 98, 106, 130, 138, 162, 170, 194, 202, 226, 234]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_27714825180283718294397623018205350332746024841681244940088047017395204.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 1&lt;/span&gt;¬6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 11, 35, 43, 67, 75, 99, 107, 131, 139, 163, 171, 195, 203, 227, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_55429650360567436588795246036410700665492049683362489880176094034790408.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 0&lt;/span&gt;2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 12, 36, 44, 68, 76, 100, 108, 132, 140, 164, 172, 196, 204, 228, 236]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_110859300721134873177590492072821401330984099366724979760352188069580816.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 1&lt;/span&gt;¬5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 13, 37, 45, 69, 77, 101, 109, 133, 141, 165, 173, 197, 205, 229, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_221718601442269746355180984145642802661968198733449959520704376139161632.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 0&lt;/span&gt;3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 14, 38, 46, 70, 78, 102, 110, 134, 142, 166, 174, 198, 206, 230, 238]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_443437202884539492710361968291285605323936397466899919041408752278323264.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 1&lt;/span&gt;¬4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 15, 39, 47, 71, 79, 103, 111, 135, 143, 167, 175, 199, 207, 231, 239]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_886874405769078985420723936582571210647872794933799838082817504556646528.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 0&lt;/span&gt;4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[16, 24, 48, 56, 80, 88, 112, 120, 144, 152, 176, 184, 208, 216, 240, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_454079695753768440535410655530276459851710871006105517098402562333003022336.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 1&lt;/span&gt;¬3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[17, 25, 49, 57, 81, 89, 113, 121, 145, 153, 177, 185, 209, 217, 241, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_908159391507536881070821311060552919703421742012211034196805124666006044672.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 0&lt;/span&gt;5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 26, 50, 58, 82, 90, 114, 122, 146, 154, 178, 186, 210, 218, 242, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1816318783015073762141642622121105839406843484024422068393610249332012089344.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 1&lt;/span&gt;¬2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[19, 27, 51, 59, 83, 91, 115, 123, 147, 155, 179, 187, 211, 219, 243, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3632637566030147524283285244242211678813686968048844136787220498664024178688.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 0&lt;/span&gt;6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 28, 52, 60, 84, 92, 116, 124, 148, 156, 180, 188, 212, 220, 244, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7265275132060295048566570488484423357627373936097688273574440997328048357376.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 1&lt;/span&gt;¬1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[21, 29, 53, 61, 85, 93, 117, 125, 149, 157, 181, 189, 213, 221, 245, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14530550264120590097133140976968846715254747872195376547148881994656096714752.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 0&lt;/span&gt;7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[22, 30, 54, 62, 86, 94, 118, 126, 150, 158, 182, 190, 214, 222, 246, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_29061100528241180194266281953937693430509495744390753094297763989312193429504.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 1&lt;/span&gt;¬0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[23, 31, 55, 63, 87, 95, 119, 127, 151, 159, 183, 191, 215, 223, 247, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_58122201056482360388532563907875386861018991488781506188595527978624386859008.svg|420px]]
|}

[[Category:Boolf prop/3-ary|zhegalkin linear]]</text>
      <sha1>jwmxjuhg3e3a18btj2rpwxienyuv6jk</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/zhegalkin deviation</title>
    <ns>0</ns>
    <id>317487</id>
    <revision>
      <id>2693221</id>
      <timestamp>2024-12-25T21:54:00Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  [[File:Set of 3-ary Boolean functions 6928706295070929573599405754551337583186506210420311235022011754348801.svg|thumb|500px|The values are Zhegalkin indices. The corresponding BF are those whose [[Boolf prop/3-ary/zhegalkin linear|Zhegalkin linear]] is the contradiction.]]  [[File:Set of 3-ary Boolean functions 16711935.svg|thumb|500px|twins of [[Boolf prop/3-ary/prefect|prefects]]]]  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;num...&quot;</comment>
      <origin>2693221</origin>
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      <text bytes="5416" sha1="qzv01f4yku67fb1esonpnyig39dp1dq" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 6928706295070929573599405754551337583186506210420311235022011754348801.svg|thumb|500px|The values are Zhegalkin indices. The corresponding BF are those whose [[Boolf prop/3-ary/zhegalkin linear|Zhegalkin linear]] is the contradiction.]]

[[File:Set of 3-ary Boolean functions 16711935.svg|thumb|500px|twins of [[Boolf prop/3-ary/prefect|prefects]]]]

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| zhegalkin deviation
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 15, 51, 60, 85, 90, 102, 105, 150, 153, 165, 170, 195, 204, 240, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57897811465722901857340599372141125877898447968637535478756498579041934147585.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 232
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 14, 50, 61, 84, 91, 103, 104, 151, 152, 164, 171, 194, 205, 241, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28951556003458657071677739092956946135619122706355792693282208781717391556610.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 168
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 13, 49, 62, 87, 88, 100, 107, 148, 155, 167, 168, 193, 206, 242, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14481078542923740821853742923502613842124034659520964376489360239136461561860.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 64
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 12, 48, 63, 86, 89, 101, 106, 149, 154, 166, 169, 192, 207, 243, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7251140353850694982956620671039380413469332311823890781636029662318198525960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 200
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 11, 55, 56, 81, 94, 98, 109, 146, 157, 161, 174, 199, 200, 244, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3646772341702587666667016378367403341433440597116706374234496243404894111760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 32
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 10, 54, 57, 80, 95, 99, 108, 147, 156, 160, 175, 198, 201, 245, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1865790500405977467650609635551317876781027381829649411126327537639834518560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 96
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 9, 53, 58, 83, 92, 96, 111, 144, 159, 163, 172, 197, 202, 246, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1017703909312356002459417927496300401146490525776248205159395630651732394560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 136
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 8, 52, 59, 82, 93, 97, 110, 145, 158, 162, 173, 196, 203, 247, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_678469272874912538497980057227216842050565003464393052205157579602710757760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 224
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[16, 31, 35, 44, 69, 74, 118, 121, 134, 137, 181, 186, 211, 220, 224, 239]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_883452180623535228133548365533788238671046940860671376092212114147573760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 8
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[17, 30, 34, 45, 68, 75, 119, 120, 135, 136, 180, 187, 210, 221, 225, 238]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_441769057726768532518518856447552126878909094570805009982618249082306560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 72
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 29, 33, 46, 71, 72, 116, 123, 132, 139, 183, 184, 209, 222, 226, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_220970463693385746857535524266504193310027882076516220891252605023682560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 160
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[19, 28, 32, 47, 70, 73, 117, 122, 133, 138, 182, 185, 208, 223, 227, 236]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_110657101506695995537351745135772614302308256569338281070072402356469760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 40
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 27, 39, 40, 65, 78, 114, 125, 130, 141, 177, 190, 215, 216, 228, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_55645487889437992838968555297866106293533788939454846032720379966914560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 192
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[21, 26, 38, 41, 64, 79, 115, 124, 131, 140, 176, 191, 214, 217, 229, 234]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28469940633170468523487102893351529934971673935860629164049935902965760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 128
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[22, 25, 37, 42, 67, 76, 112, 127, 128, 143, 179, 188, 213, 218, 230, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_15529363693482294405229561713630554352568764521031082485233307887861760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 104
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[23, 24, 36, 43, 66, 77, 113, 126, 129, 142, 178, 189, 212, 219, 231, 232]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_10353468600538208444310694314657383780144713909989122391595405604290560.svg|420px]]
|}

[[Category:Boolf prop/3-ary|zhegalkin deviation]]</text>
      <sha1>qzv01f4yku67fb1esonpnyig39dp1dq</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/zhegalkin deviation weight</title>
    <ns>0</ns>
    <id>317488</id>
    <revision>
      <id>2693222</id>
      <timestamp>2024-12-25T21:59:51Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; &lt;/div&gt;  {| class=&quot;wikitable sortable boolf-blocks&quot; !class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt; !cl...&quot;</comment>
      <origin>2693222</origin>
      <model>wikitext</model>
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      <text bytes="2376" sha1="iqq5x64zpcjc2bm8084cmncn0dsjgb2" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| zhegalkin deviation weight
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 15, 51, 60, 85, 90, 102, 105, 150, 153, 165, 170, 195, 204, 240, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57897811465722901857340599372141125877898447968637535478756498579041934147585.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 14, 50, 61, 84, 91, 103, 104, 151, 152, 164, 171, 194, 205, 241, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28951556003458657071677739092956946135619122706355792693282208781717391556610.svg|420px]]
|-
|class=&quot;size&quot;| 64
|class=&quot;prop&quot;| 3
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[2, 4, 11, 13, 16, 23, 24, 31, 35, 36, 43, 44, 49, 55, 56, 62, 66, 69, 74, 77, 81, 87, 88, 94, 98, 100, 107, 109, 113, 118, 121, 126, 129, 134, 137, 142, 146, 148, 155, 157, 161, 167, 168, 174, 178, 181, 186, 189, 193, 199, 200, 206, 211, 212, 219, 220, 224, 231, 232, 239, 242, 244, 251, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_18128744690275552561957337160929865629179926448292441411222340290061107537940.svg|420px]]
|-
|class=&quot;size&quot;| 64
|class=&quot;prop&quot;| 1
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[3, 5, 10, 12, 17, 22, 25, 30, 34, 37, 42, 45, 48, 54, 57, 63, 67, 68, 75, 76, 80, 86, 89, 95, 99, 101, 106, 108, 112, 119, 120, 127, 128, 135, 136, 143, 147, 149, 154, 156, 160, 166, 169, 175, 179, 180, 187, 188, 192, 198, 201, 207, 210, 213, 218, 221, 225, 230, 233, 238, 243, 245, 250, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_9117388152678092701434154055008859472931591171512632028854825051515003212840.svg|420px]]
|-
|class=&quot;size&quot;| 96
|class=&quot;prop&quot;| 2
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_1696588925180991231161155327651110737640896370842162427341711305577693184960.svg|420px]]
|}

[[Category:Boolf prop/3-ary|zhegalkin deviation weight]]</text>
      <sha1>iqq5x64zpcjc2bm8084cmncn0dsjgb2</sha1>
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  <page>
    <title>File:API.1A.Functions.20241225.pdf</title>
    <ns>6</ns>
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    <revision>
      <id>2693225</id>
      <timestamp>2024-12-25T22:32:56Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=API.2A: Functions (20241225 - 20241224)
|Source={{own|Young1lim}}
|Date=2024-12-26
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}</comment>
      <origin>2693225</origin>
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      <format>text/x-wiki</format>
      <text bytes="262" sha1="nqr6pfs2g9t9qygtqst1h8vdfpf0agb" xml:space="preserve">== Summary ==
{{Information
|Description=API.2A: Functions (20241225 - 20241224)
|Source={{own|Young1lim}}
|Date=2024-12-26
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}

== Licensing ==
{{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}</text>
      <sha1>nqr6pfs2g9t9qygtqst1h8vdfpf0agb</sha1>
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  <page>
    <title>File:API.1A.Functions.20241226.pdf</title>
    <ns>6</ns>
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    <revision>
      <id>2693227</id>
      <timestamp>2024-12-25T22:33:49Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=API.2A: Functions (20241226 - 20241225)
|Source={{own|Young1lim}}
|Date=2024-12-26
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}</comment>
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      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="262" sha1="10au4vaa58qgilr1mjrsg37m7stzi8b" xml:space="preserve">== Summary ==
{{Information
|Description=API.2A: Functions (20241226 - 20241225)
|Source={{own|Young1lim}}
|Date=2024-12-26
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}

== Licensing ==
{{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}</text>
      <sha1>10au4vaa58qgilr1mjrsg37m7stzi8b</sha1>
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  </page>
  <page>
    <title>File:DIR.1A.Names.20241226.pdf</title>
    <ns>6</ns>
    <id>317491</id>
    <revision>
      <id>2693229</id>
      <timestamp>2024-12-25T23:13:54Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=DIR.1A: Shared Library Names (20241226 - 20241225)
|Source={{own|Young1lim}}
|Date=2024-12-26
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}</comment>
      <origin>2693229</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="273" sha1="ooafqka80mhzdj7bcknypwd56bte9nb" xml:space="preserve">== Summary ==
{{Information
|Description=DIR.1A: Shared Library Names (20241226 - 20241225)
|Source={{own|Young1lim}}
|Date=2024-12-26
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}

== Licensing ==
{{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}</text>
      <sha1>ooafqka80mhzdj7bcknypwd56bte9nb</sha1>
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  </page>
  <page>
    <title>Category:Nonlinearity of Boolean functions</title>
    <ns>14</ns>
    <id>317492</id>
    <revision>
      <id>2693230</id>
      <timestamp>2024-12-25T23:17:39Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;[[Category:Studies of Euler diagrams]]&quot;</comment>
      <origin>2693230</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="38" sha1="5mx45zegd9yniznd6jrn4mv5vpy3u0o" xml:space="preserve">[[Category:Studies of Euler diagrams]]</text>
      <sha1>5mx45zegd9yniznd6jrn4mv5vpy3u0o</sha1>
    </revision>
    <revision>
      <id>2693231</id>
      <parentid>2693230</parentid>
      <timestamp>2024-12-25T23:17:57Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693231</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="41" sha1="8d5h2ie6o1p539musn2sgcl9fe7uy0v" xml:space="preserve">[[Category:Studies of Boolean functions]]</text>
      <sha1>8d5h2ie6o1p539musn2sgcl9fe7uy0v</sha1>
    </revision>
  </page>
  <page>
    <title>Template:Nonlinearity of Boolean functions/table overview/integers</title>
    <ns>10</ns>
    <id>317493</id>
    <revision>
      <id>2693232</id>
      <timestamp>2024-12-25T23:18:08Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;{| class=&quot;wikitable&quot; style=&quot;text-align: center;&quot; !rowspan=&quot;2&quot;| arity !colspan=&quot;7&quot;| nonlinearity !rowspan=&quot;2&quot; style=&quot;border-left: 3px solid gray;&quot;| total !rowspan=&quot;2&quot;| sequence |- ! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 |- ! 1 | 4 || || || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''4''' || |- ! 2 | 8 || 8 || || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''16''' || |- ! 3 | 16 || 128 || 112 || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''256''' || {{oeisli...&quot;</comment>
      <origin>2693232</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="698" sha1="epnflfmk9pydtvsqrmq15c4a0e2y5td" xml:space="preserve">{| class=&quot;wikitable&quot; style=&quot;text-align: center;&quot;
!rowspan=&quot;2&quot;| arity
!colspan=&quot;7&quot;| nonlinearity
!rowspan=&quot;2&quot; style=&quot;border-left: 3px solid gray;&quot;| total
!rowspan=&quot;2&quot;| sequence
|-
! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6
|-
! 1
| 4 || || || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''4''' ||
|-
! 2
| 8 || 8 || || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''16''' ||
|-
! 3
| 16 || 128 || 112 || || || || ||style=&quot;border-left: 3px solid gray;&quot;| '''256''' || {{oeislink|A207676}}
|-
! 4
| 32 || 512 || 3840 || 17920 || 28000 || 14336 || 896 ||style=&quot;border-left: 3px solid gray;&quot;| '''65536''' || {{oeislink|A207328}}
|}&lt;noinclude&gt;
[[Category:Nonlinearity of Boolean functions]]
&lt;/noinclude&gt;</text>
      <sha1>epnflfmk9pydtvsqrmq15c4a0e2y5td</sha1>
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  </page>
  <page>
    <title>Template:Nonlinearity of Boolean functions/table overview/fractions</title>
    <ns>10</ns>
    <id>317494</id>
    <revision>
      <id>2693236</id>
      <timestamp>2024-12-25T23:34:30Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;{| class=&quot;wikitable collapsible open&quot; style=&quot;text-align: center;&quot; !colspan=&quot;10&quot;| fractions instead of integers |- !rowspan=&quot;2&quot;| arity !rowspan=&quot;2&quot; style=&quot;color: gray;&quot;| period&lt;br&gt;length !colspan=&quot;7&quot;| nonlinearity !rowspan=&quot;2&quot; style=&quot;border-left: 3px solid gray;&quot;| total |- ! &lt;math&gt;0&lt;/math&gt; ! &lt;math&gt;\frac{1}{16}&lt;/math&gt; ! &lt;math&gt;\frac{1}{8}&lt;/math&gt; ! &lt;math&gt;\frac{3}{16}&lt;/math&gt; ! &lt;math&gt;\frac{1}{4}&lt;/math&gt; ! &lt;math&gt;\frac{5}{16}&lt;/math&gt; ! &lt;math&gt;\frac{3}{8}&lt;/math&gt; |- ! 1 !style=&quot;color...&quot;</comment>
      <origin>2693236</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1418" sha1="9poa7qmvxl5udc4nb9b6vafylsgsnsn" xml:space="preserve">{| class=&quot;wikitable collapsible open&quot; style=&quot;text-align: center;&quot;
!colspan=&quot;10&quot;| fractions instead of integers
|-
!rowspan=&quot;2&quot;| arity
!rowspan=&quot;2&quot; style=&quot;color: gray;&quot;| period&lt;br&gt;length
!colspan=&quot;7&quot;| nonlinearity
!rowspan=&quot;2&quot; style=&quot;border-left: 3px solid gray;&quot;| total
|-
! &lt;math&gt;0&lt;/math&gt;
! &lt;math&gt;\frac{1}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{8}&lt;/math&gt;
! &lt;math&gt;\frac{3}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{4}&lt;/math&gt;
! &lt;math&gt;\frac{5}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{8}&lt;/math&gt;
|-
! 1
!style=&quot;color: gray;&quot;| 2
| 4  &lt;!-- 0 --&gt;
|   &lt;!-- 1 / 16 --&gt;
|   &lt;!-- 1 / 8 --&gt;
|   &lt;!-- 3 / 16 --&gt;
|   &lt;!-- 1 / 4 --&gt;
|   &lt;!-- 5 / 16 --&gt;
|   &lt;!-- 3 / 8 --&gt;
|style=&quot;border-left: 3px solid gray;&quot;| '''4'''
|-
! 2
!style=&quot;color: gray;&quot;| 4
| 8  &lt;!-- 0 --&gt;
|   &lt;!-- 1 / 16 --&gt;
|   &lt;!-- 1 / 8 --&gt;
|   &lt;!-- 3 / 16 --&gt;
| 8  &lt;!-- 1 / 4 --&gt;
|   &lt;!-- 5 / 16 --&gt;
|   &lt;!-- 3 / 8 --&gt;
|style=&quot;border-left: 3px solid gray;&quot;| '''16'''
|-
! 3
!style=&quot;color: gray;&quot;| 8
| 16  &lt;!-- 0 --&gt;
|   &lt;!-- 1 / 16 --&gt;
| 128  &lt;!-- 1 / 8 --&gt;
|   &lt;!-- 3 / 16 --&gt;
| 112  &lt;!-- 1 / 4 --&gt;
|   &lt;!-- 5 / 16 --&gt;
|   &lt;!-- 3 / 8 --&gt;
|style=&quot;border-left: 3px solid gray;&quot;| '''256'''
|-
! 4
!style=&quot;color: gray;&quot;| 16
| 32  &lt;!-- 0 --&gt;
| 512  &lt;!-- 1 / 16 --&gt;
| 3840  &lt;!-- 1 / 8 --&gt;
| 17920  &lt;!-- 3 / 16 --&gt;
| 28000  &lt;!-- 1 / 4 --&gt;
| 14336  &lt;!-- 5 / 16 --&gt;
| 896  &lt;!-- 3 / 8 --&gt;
|style=&quot;border-left: 3px solid gray;&quot;| '''65536'''
|}&lt;noinclude&gt;
[[Category:Nonlinearity of Boolean functions]]
&lt;/noinclude&gt;</text>
      <sha1>9poa7qmvxl5udc4nb9b6vafylsgsnsn</sha1>
    </revision>
    <revision>
      <id>2693237</id>
      <parentid>2693236</parentid>
      <timestamp>2024-12-25T23:34:42Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2693237</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1423" sha1="9foceavz6sliyzmfar8vxtds51x30gd" xml:space="preserve">{| class=&quot;wikitable collapsible collapsed&quot; style=&quot;text-align: center;&quot;
!colspan=&quot;10&quot;| fractions instead of integers
|-
!rowspan=&quot;2&quot;| arity
!rowspan=&quot;2&quot; style=&quot;color: gray;&quot;| period&lt;br&gt;length
!colspan=&quot;7&quot;| nonlinearity
!rowspan=&quot;2&quot; style=&quot;border-left: 3px solid gray;&quot;| total
|-
! &lt;math&gt;0&lt;/math&gt;
! &lt;math&gt;\frac{1}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{8}&lt;/math&gt;
! &lt;math&gt;\frac{3}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{4}&lt;/math&gt;
! &lt;math&gt;\frac{5}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{8}&lt;/math&gt;
|-
! 1
!style=&quot;color: gray;&quot;| 2
| 4  &lt;!-- 0 --&gt;
|   &lt;!-- 1 / 16 --&gt;
|   &lt;!-- 1 / 8 --&gt;
|   &lt;!-- 3 / 16 --&gt;
|   &lt;!-- 1 / 4 --&gt;
|   &lt;!-- 5 / 16 --&gt;
|   &lt;!-- 3 / 8 --&gt;
|style=&quot;border-left: 3px solid gray;&quot;| '''4'''
|-
! 2
!style=&quot;color: gray;&quot;| 4
| 8  &lt;!-- 0 --&gt;
|   &lt;!-- 1 / 16 --&gt;
|   &lt;!-- 1 / 8 --&gt;
|   &lt;!-- 3 / 16 --&gt;
| 8  &lt;!-- 1 / 4 --&gt;
|   &lt;!-- 5 / 16 --&gt;
|   &lt;!-- 3 / 8 --&gt;
|style=&quot;border-left: 3px solid gray;&quot;| '''16'''
|-
! 3
!style=&quot;color: gray;&quot;| 8
| 16  &lt;!-- 0 --&gt;
|   &lt;!-- 1 / 16 --&gt;
| 128  &lt;!-- 1 / 8 --&gt;
|   &lt;!-- 3 / 16 --&gt;
| 112  &lt;!-- 1 / 4 --&gt;
|   &lt;!-- 5 / 16 --&gt;
|   &lt;!-- 3 / 8 --&gt;
|style=&quot;border-left: 3px solid gray;&quot;| '''256'''
|-
! 4
!style=&quot;color: gray;&quot;| 16
| 32  &lt;!-- 0 --&gt;
| 512  &lt;!-- 1 / 16 --&gt;
| 3840  &lt;!-- 1 / 8 --&gt;
| 17920  &lt;!-- 3 / 16 --&gt;
| 28000  &lt;!-- 1 / 4 --&gt;
| 14336  &lt;!-- 5 / 16 --&gt;
| 896  &lt;!-- 3 / 8 --&gt;
|style=&quot;border-left: 3px solid gray;&quot;| '''65536'''
|}&lt;noinclude&gt;
[[Category:Nonlinearity of Boolean functions]]
&lt;/noinclude&gt;</text>
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    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/nonlinearity</title>
    <ns>0</ns>
    <id>317495</id>
    <revision>
      <id>2693240</id>
      <timestamp>2024-12-25T23:40:32Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt; &lt;/div&gt;  {| class=&quot;wikitable sortable boolf-blocks&quot; !class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt; !...&quot;</comment>
      <origin>2693240</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1223" sha1="ez8w55vcexpq0i1bqdixlkj9oseddkq" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| nonlinearity
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 15, 51, 60, 85, 90, 102, 105, 150, 153, 165, 170, 195, 204, 240, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57897811465722901857340599372141125877898447968637535478756498579041934147585.svg|420px]]
|-
|class=&quot;size&quot;| 128
|class=&quot;prop&quot;| 1
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_47758914269546354982683078068829456704164423862093743397580034411621752859030.svg|420px]]
|-
|class=&quot;size&quot;| 112
|class=&quot;prop&quot;| 2
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_10135363502046938583547307567717325271207112834909285163121051017249442633320.svg|420px]]
|}

[[Category:Boolf prop/3-ary|nonlinearity]]</text>
      <sha1>ez8w55vcexpq0i1bqdixlkj9oseddkq</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/zhegalkin weight</title>
    <ns>0</ns>
    <id>317496</id>
    <revision>
      <id>2693242</id>
      <timestamp>2024-12-26T00:08:24Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;9&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span clas...&quot;</comment>
      <origin>2693242</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3225" sha1="9inb4v8kcw0ufpliml43qlfm9wkkaht" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;9&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| zhegalkin weight
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| 0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| 8
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_2.svg|420px]]
|-
|class=&quot;size&quot;| 70
|class=&quot;prop&quot;| 4
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_80069177398200828458670140847044886780.svg|420px]]
|-
|class=&quot;size&quot;| 28
|class=&quot;prop&quot;| 2
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[8, 10, 12, 15, 32, 34, 40, 42, 48, 51, 60, 63, 64, 68, 72, 76, 80, 85, 90, 95, 96, 102, 106, 108, 112, 119, 120, 127]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_172140628589919773281930489534768780544.svg|420px]]
|-
|class=&quot;size&quot;| 28
|class=&quot;prop&quot;| 6
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[9, 11, 13, 14, 33, 35, 41, 43, 49, 50, 61, 62, 65, 69, 73, 77, 81, 84, 91, 94, 97, 103, 107, 109, 113, 118, 121, 126]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_88072560932817861722773977049954544128.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| 1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[128, 136, 160, 170, 192, 204, 240, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57897811465722901813400887179114964632008146155984603054314538836602543669248.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| 7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[129, 137, 161, 171, 193, 205, 241, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28951556003458657059123535601713998374063803812738783079035889667270240108544.svg|420px]]
|-
|class=&quot;size&quot;| 56
|class=&quot;prop&quot;| 3
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[130, 132, 135, 138, 140, 143, 144, 147, 149, 150, 153, 154, 156, 159, 162, 165, 166, 168, 172, 175, 176, 179, 180, 183, 184, 187, 188, 191, 195, 196, 198, 200, 202, 207, 208, 210, 213, 215, 216, 218, 221, 223, 224, 226, 228, 230, 232, 234, 236, 238, 243, 245, 247, 248, 250, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_9795989084610926096148648529792108121198929591488135106311387831232807043072.svg|420px]]
|-
|class=&quot;size&quot;| 56
|class=&quot;prop&quot;| 5
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[131, 133, 134, 139, 141, 142, 145, 146, 148, 151, 152, 155, 157, 158, 163, 164, 167, 169, 173, 174, 177, 178, 181, 182, 185, 186, 189, 190, 194, 197, 199, 201, 203, 206, 209, 211, 212, 214, 217, 219, 220, 222, 225, 227, 229, 231, 233, 235, 237, 239, 242, 244, 246, 249, 251, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_19146732683523710454897913698066836725658822738508104336332393065375770607616.svg|420px]]
|}

[[Category:Boolf prop/3-ary|zhegalkin weight]]</text>
      <sha1>9inb4v8kcw0ufpliml43qlfm9wkkaht</sha1>
    </revision>
  </page>
  <page>
    <title>File:LIB.2A.Shared.20241226.pdf</title>
    <ns>6</ns>
    <id>317497</id>
    <revision>
      <id>2693251</id>
      <timestamp>2024-12-26T00:38:51Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=LIB.2A: Shared Libraries (20241226 - 20241225)
|Source={{own|Young1lim}}
|Date=2024-12-26
|Author=Young W. Lim
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== Licensing ==
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  <page>
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      <comment>New resource with &quot;==Definition== Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a domain, &lt;math&gt;z_0 \in G&lt;/math&gt;, and let &lt;math&gt;f&lt;/math&gt; be holomorphic except for isolated singularities &lt;math&gt;S \subset G&lt;/math&gt;, i.e., &lt;math&gt;f\colon G \setminus S \to \mathbb{C}&lt;/math&gt; is holomorphic. If &lt;math&gt;z_0 \in S \subset G&lt;/math&gt; is an [[Complex_analysis/Isolated_singularity|isolated singularity]] of &lt;math&gt;f&lt;/math&gt; with &lt;math&gt;D_r(z_0) \cap S = {z_0}&lt;/math&gt;, the residue is defined as:  :&lt;math&gt;\mathrm{res}...&quot;</comment>
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      <text bytes="6902" sha1="15veoqah0mxbz0t7bz8n54iiatmaxtx" xml:space="preserve">==Definition==
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a domain, &lt;math&gt;z_0 \in G&lt;/math&gt;, and let &lt;math&gt;f&lt;/math&gt; be holomorphic except for isolated singularities &lt;math&gt;S \subset G&lt;/math&gt;, i.e., &lt;math&gt;f\colon G \setminus S \to \mathbb{C}&lt;/math&gt; is holomorphic. If &lt;math&gt;z_0 \in S \subset G&lt;/math&gt; is an [[Complex_analysis/Isolated_singularity|isolated singularity]] of &lt;math&gt;f&lt;/math&gt; with &lt;math&gt;D_r(z_0) \cap S = {z_0}&lt;/math&gt;, the residue is defined as:

:&lt;math&gt;\mathrm{res}{z_0}(f) := \frac{1}{2\pi i} \int{\partial D_r(z_0)} f(\xi), d\xi = \frac{1}{2\pi i} \int_{|\xi-z_0|=r} f(\xi), d\xi&lt;/math&gt;.

== Relation Between Residue and Laurent Series ==
If &lt;math&gt;f&lt;/math&gt; is represented around an isolated singularity &lt;math&gt;z_0 \in S \subset G&lt;/math&gt; as a Laurent series, the residue can be computed as follows.
With &lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt; as the [[Laurent Series|Laurent Series]] expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt;, it holds that:
:&lt;math&gt;\mathrm{res}{z_0}(f) = \frac{1}{2\pi i} \int{\partial D_r(z_0)} f(\xi), d\xi = \frac{1}{2\pi i} \int_{\partial D_r(z_0)} a_{-1}\cdot (\xi-z_0)^{-1}, d\xi = \frac{1}{2\pi i}  a_{-1} \cdot \underbrace{\int_{\partial D_r(z_0)} (\xi-z_0)^{-1} , d\xi}{=2\pi i} = a{-1}&lt;/math&gt;.
It must be taken into account that the closed disk &lt;math&gt;\overline{D_r(z_0)}&lt;/math&gt; contains only the singularity &lt;math&gt;z_0 \in S &lt;/math&gt;, i.e&lt;math&gt;\overline{D_r(z_0)} \cap s = \{z_0\}&lt;/math&gt;.

Thus, one can read off the 'residue' &lt;math&gt;\mathrm{res}_{z_0}(f) = a_{-1}&lt;/math&gt; from the Laurent expansion of  around  at the  &lt;math&gt;f&lt;/math&gt; um &lt;math&gt;z_0&lt;/math&gt; an -1-ten coefficient of .
==Considerations==
The closed disk &lt;math&gt;\overline{D_r(z_0)}&lt;/math&gt; must contain only the singularity &lt;math&gt;z_0 \in S&lt;/math&gt;, meaning&lt;math&gt;\overline{D_r(z_0)} \cap S = {z_0}&lt;/math&gt;.
Thus, the residue &lt;math&gt;\mathrm{res}{z_0}(f) = a{-1}&lt;/math&gt; can be read off directly as the coefficient of &lt;math&gt;(z-z_0)^{-1}&lt;/math&gt; in the Laurent series expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt;.
==Etymology==
The term &quot;residue&quot; (from Latin residuere – to remain) is used because in integration along the path &lt;math&gt;\gamma(t) := z_0 + r\cdot e^{it}&lt;/math&gt; with &lt;math&gt;t \in [0, 2\pi]&lt;/math&gt; around the circle centered at &lt;math&gt;z_0&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;
\begin{array}{rl}
   \displaystyle \int_{|w-z_0|=r} f(w)\, dw &amp;= \displaystyle \sum_{n=-\infty}^{+\infty} a_n \int_{|w-z_0|=r} (w-z_0)^n \, dw\\
                             &amp;= 2\pi i \cdot a_{-1}.
\end{array}
&lt;/math&gt;&lt;/center&gt;  
Thus, the residue is what remains after integrating.  
==Computation for Poles==
If &lt;math&gt;z_0 \in U&lt;/math&gt; is a pole of order &lt;math&gt;m&lt;/math&gt; of &lt;math&gt;f&lt;/math&gt;, the [[Laurent Series|Laurent Series]] expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt; has the form:
:&lt;math&gt;f(z) = \sum_{k=-m}^\infty a_k (z-z_0)^k&lt;/math&gt;
with &lt;math&gt;a_{-m} \neq 0&lt;/math&gt;.

===Proof 1: Removing Principal Part by Multiplication===
By multiplying with &lt;math&gt;(z-z_0)^m&lt;/math&gt;, we get:
:&lt;math&gt;g_m(z) := (z-z_0)^m \cdot f(z) = \sum_{k=0}^\infty a_{k-m} (z-z_0)^k.&lt;/math&gt;
The residue &lt;math&gt;a_{-1}&lt;/math&gt; is then the coefficient of &lt;math&gt;(z-z_0)^{m-1}&lt;/math&gt; in the power series of &lt;math&gt;g_m(z)&lt;/math&gt;.

===Proof 2: Using (m-1)-fold Differentiation===
By differentiating &lt;math&gt;m-1&lt;/math&gt; times, the first &lt;math&gt;m-1&lt;/math&gt; terms from &lt;math&gt;n=0&lt;/math&gt; to &lt;math&gt;n=m-2&lt;/math&gt; vanish. The residue is then found as the coefficient of &lt;math&gt;(z-z_0)^0&lt;/math&gt; in:
:&lt;math&gt;g_m^{(m-1)}(z) = \sum_{k=m-1}^\infty \frac{k!}{(k-m+1)!} a_{k-m}(z-z_0)^{k-m+1}.&lt;/math&gt;

===Proof 3: Limit Process to Compute Coefficient of &lt;math&gt;(z-z_0)^0&lt;/math&gt;===
By shifting the index:
:&lt;math&gt;g_m^{(m-1)}(z) = \sum_{k=-1}^\infty \frac{(m+k)!}{(k+1)!} a_k (z-z_0)^{k+1}.&lt;/math&gt;
Taking the limit &lt;math&gt;z \to z_0&lt;/math&gt;, all terms with &lt;math&gt;k \geq 0&lt;/math&gt; vanish, leaving:
:&lt;math&gt;\lim_{z \to z_0} g_m^{(m-1)}(z) = \frac{(m-1)!}{0!} \cdot a_{-1} \cdot (z-z_0)^0 = (m-1)! \cdot a_{-1}.&lt;/math&gt;
Thus, the residue can be computed &lt;math&gt;z \to z_0&lt;/math&gt; using:
:&lt;math&gt;\mathrm{res}{z_0}(f) = a{-1} = \frac{1}{(m-1)!} \cdot \lim_{z \to z_0} g_m^{(m-1)}(z).&lt;/math&gt;

==Exercises for Students==

*Explain why, in the Laurent series expansion, all terms from the principal and outer parts, i.e., &lt;math&gt;n \in \mathbb{Z}&lt;/math&gt; with &lt;math&gt;n \neq -1&lt;/math&gt;, yield integrals that evaluate to zero:
:&lt;math&gt;\int_{\partial D_r(z_0)} a_n \cdot (\xi - z_0)^n, d\xi = 0.&lt;/math&gt;

*Why can the order of integration and series expansion be interchanged?
::&lt;math&gt;\sum_{n=-\infty}^{+\infty} \int_{\partial D_r(z_0)} a_n (\xi-z_0)^n d\xi = \int_{\partial D_r(z_0)} \sum_{n=-\infty}^{+\infty} a_n (\xi-z_0)^n d\xi =
\frac{1}{2\pi i} \int_{\partial D_r(z_0)} f(\xi), d\xi = \mathrm{res}_{z_0}(f).&lt;/math&gt;

*Given the function &lt;math&gt;f:\mathbb{C}\setminus {i} \to \mathbb{C}&lt;/math&gt; with &lt;math&gt;z \mapsto f(z) = \frac{e^{z-i}}{(z-i)^5}&lt;/math&gt;, calculate the residue &lt;math&gt;\mathrm{res}_{z_0}(f)&lt;/math&gt; at &lt;math&gt;z_0 := i&lt;/math&gt;.

==See Also==

*[[Residue|Residue]]
*[[Complex_analysis/Examples_of_Laurent_series|Examples of Laurent Series]]
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      <text bytes="5797" sha1="dka9bqwu6fehjngd5jt9gr5n44yohsu" xml:space="preserve">==Definition==
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a domain, &lt;math&gt;z_0 \in G&lt;/math&gt;, and let &lt;math&gt;f&lt;/math&gt; be holomorphic except for isolated singularities &lt;math&gt;S \subset G&lt;/math&gt;, i.e., &lt;math&gt;f\colon G \setminus S \to \mathbb{C}&lt;/math&gt; is holomorphic. If &lt;math&gt;z_0 \in S \subset G&lt;/math&gt; is an [[Complex_analysis/Isolated_singularity|isolated singularity]] of &lt;math&gt;f&lt;/math&gt; with &lt;math&gt;D_r(z_0) \cap S = {z_0}&lt;/math&gt;, the residue is defined as:

:&lt;math&gt;\mathrm{res}{z_0}(f) := \frac{1}{2\pi i} \int{\partial D_r(z_0)} f(\xi), d\xi = \frac{1}{2\pi i} \int_{|\xi-z_0|=r} f(\xi), d\xi&lt;/math&gt;.

== Relation Between Residue and Laurent Series ==
If &lt;math&gt;f&lt;/math&gt; is represented around an isolated singularity &lt;math&gt;z_0 \in S \subset G&lt;/math&gt; as a Laurent series, the residue can be computed as follows.
With &lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt; as the [[Laurent Series|Laurent Series]] expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt;, it holds that:
:&lt;math&gt;\mathrm{res}{z_0}(f) = \frac{1}{2\pi i} \int{\partial D_r(z_0)} f(\xi), d\xi = \frac{1}{2\pi i} \int_{\partial D_r(z_0)} a_{-1}\cdot (\xi-z_0)^{-1}, d\xi = \frac{1}{2\pi i}  a_{-1} \cdot \underbrace{\int_{\partial D_r(z_0)} (\xi-z_0)^{-1} , d\xi}{=2\pi i} = a{-1}&lt;/math&gt;.
It must be taken into account that the closed disk &lt;math&gt;\overline{D_r(z_0)}&lt;/math&gt; contains only the singularity &lt;math&gt;z_0 \in S &lt;/math&gt;, i.e&lt;math&gt;\overline{D_r(z_0)} \cap s = \{z_0\}&lt;/math&gt;.

Thus, one can read off the 'residue' &lt;math&gt;\mathrm{res}_{z_0}(f) = a_{-1}&lt;/math&gt; from the Laurent expansion of  around  at the  &lt;math&gt;f&lt;/math&gt; um &lt;math&gt;z_0&lt;/math&gt; an -1-ten coefficient of .
==Considerations==
The closed disk &lt;math&gt;\overline{D_r(z_0)}&lt;/math&gt; must contain only the singularity &lt;math&gt;z_0 \in S&lt;/math&gt;, meaning&lt;math&gt;\overline{D_r(z_0)} \cap S = {z_0}&lt;/math&gt;.
Thus, the residue &lt;math&gt;\mathrm{res}{z_0}(f) = a{-1}&lt;/math&gt; can be read off directly as the coefficient of &lt;math&gt;(z-z_0)^{-1}&lt;/math&gt; in the Laurent series expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt;.
==Etymology==
The term &quot;residue&quot; (from Latin residuere – to remain) is used because in integration along the path &lt;math&gt;\gamma(t) := z_0 + r\cdot e^{it}&lt;/math&gt; with &lt;math&gt;t \in [0, 2\pi]&lt;/math&gt; around the circle centered at &lt;math&gt;z_0&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;
\begin{array}{rl}
   \displaystyle \int_{|w-z_0|=r} f(w)\, dw &amp;= \displaystyle \sum_{n=-\infty}^{+\infty} a_n \int_{|w-z_0|=r} (w-z_0)^n \, dw\\
                             &amp;= 2\pi i \cdot a_{-1}.
\end{array}
&lt;/math&gt;&lt;/center&gt;  
Thus, the residue is what remains after integrating.  
==Computation for Poles==
If &lt;math&gt;z_0 \in U&lt;/math&gt; is a pole of order &lt;math&gt;m&lt;/math&gt; of &lt;math&gt;f&lt;/math&gt;, the [[Laurent Series|Laurent Series]] expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt; has the form:
:&lt;math&gt;f(z) = \sum_{k=-m}^\infty a_k (z-z_0)^k&lt;/math&gt;
with &lt;math&gt;a_{-m} \neq 0&lt;/math&gt;.

===Proof 1: Removing Principal Part by Multiplication===
By multiplying with &lt;math&gt;(z-z_0)^m&lt;/math&gt;, we get:
:&lt;math&gt;g_m(z) := (z-z_0)^m \cdot f(z) = \sum_{k=0}^\infty a_{k-m} (z-z_0)^k.&lt;/math&gt;
The residue &lt;math&gt;a_{-1}&lt;/math&gt; is then the coefficient of &lt;math&gt;(z-z_0)^{m-1}&lt;/math&gt; in the power series of &lt;math&gt;g_m(z)&lt;/math&gt;.

===Proof 2: Using (m-1)-fold Differentiation===
By differentiating &lt;math&gt;m-1&lt;/math&gt; times, the first &lt;math&gt;m-1&lt;/math&gt; terms from &lt;math&gt;n=0&lt;/math&gt; to &lt;math&gt;n=m-2&lt;/math&gt; vanish. The residue is then found as the coefficient of &lt;math&gt;(z-z_0)^0&lt;/math&gt; in:
:&lt;math&gt;g_m^{(m-1)}(z) = \sum_{k=m-1}^\infty \frac{k!}{(k-m+1)!} a_{k-m}(z-z_0)^{k-m+1}.&lt;/math&gt;

===Proof 3: Limit Process to Compute Coefficient of &lt;math&gt;(z-z_0)^0&lt;/math&gt;===
By shifting the index:
:&lt;math&gt;g_m^{(m-1)}(z) = \sum_{k=-1}^\infty \frac{(m+k)!}{(k+1)!} a_k (z-z_0)^{k+1}.&lt;/math&gt;
Taking the limit &lt;math&gt;z \to z_0&lt;/math&gt;, all terms with &lt;math&gt;k \geq 0&lt;/math&gt; vanish, leaving:
:&lt;math&gt;\lim_{z \to z_0} g_m^{(m-1)}(z) = \frac{(m-1)!}{0!} \cdot a_{-1} \cdot (z-z_0)^0 = (m-1)! \cdot a_{-1}.&lt;/math&gt;
Thus, the residue can be computed &lt;math&gt;z \to z_0&lt;/math&gt; using:
:&lt;math&gt;\mathrm{res}{z_0}(f) = a{-1} = \frac{1}{(m-1)!} \cdot \lim_{z \to z_0} g_m^{(m-1)}(z).&lt;/math&gt;

==Exercises for Students==

*Explain why, in the Laurent series expansion, all terms from the principal and outer parts, i.e., &lt;math&gt;n \in \mathbb{Z}&lt;/math&gt; with &lt;math&gt;n \neq -1&lt;/math&gt;, yield integrals that evaluate to zero:
:&lt;math&gt;\int_{\partial D_r(z_0)} a_n \cdot (\xi - z_0)^n, d\xi = 0.&lt;/math&gt;

*Why can the order of integration and series expansion be interchanged?
::&lt;math&gt;\sum_{n=-\infty}^{+\infty} \int_{\partial D_r(z_0)} a_n (\xi-z_0)^n d\xi = \int_{\partial D_r(z_0)} \sum_{n=-\infty}^{+\infty} a_n (\xi-z_0)^n d\xi =
\frac{1}{2\pi i} \int_{\partial D_r(z_0)} f(\xi), d\xi = \mathrm{res}_{z_0}(f).&lt;/math&gt;

*Given the function &lt;math&gt;f:\mathbb{C}\setminus {i} \to \mathbb{C}&lt;/math&gt; with &lt;math&gt;z \mapsto f(z) = \frac{e^{z-i}}{(z-i)^5}&lt;/math&gt;, calculate the residue &lt;math&gt;\mathrm{res}_{z_0}(f)&lt;/math&gt; at &lt;math&gt;z_0 := i&lt;/math&gt;.

==See Also==

*[[Residue|Residue]]
*[[Complex_analysis/Examples_of_Laurent_series|Examples of Laurent Series]]
== Page Information ==
=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Residuum 
Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/Residuum|Kurs:Funktionentheorie/Residuum ]] - URL:
https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Residuum 
* Date: 12/26/2024&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Residuum &quot; srclang=&quot;de&quot; date=&quot;12/26/2024&quot; time=&quot;11:28&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Kurs:Funktionentheorie/Residuum ]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
      <sha1>dka9bqwu6fehjngd5jt9gr5n44yohsu</sha1>
    </revision>
    <revision>
      <id>2693288</id>
      <parentid>2693281</parentid>
      <timestamp>2024-12-26T11:57:32Z</timestamp>
      <contributor>
        <username>Eshaa2024</username>
        <id>2993595</id>
      </contributor>
      <comment>/* Definition */</comment>
      <origin>2693288</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5797" sha1="3214c4axdx87e93or3xoe3y6n7lacjp" xml:space="preserve">==Definition==
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a domain, &lt;math&gt;z_0 \in G&lt;/math&gt;, and let &lt;math&gt;f&lt;/math&gt; be holomorphic except for isolated singularities &lt;math&gt;S \subset G&lt;/math&gt;, i.e., &lt;math&gt;f\colon G \setminus S \to \mathbb{C}&lt;/math&gt; is holomorphic. If &lt;math&gt;z_0 \in S \subset G&lt;/math&gt; is an [[Complex_analysis/isolated_singularity|isolated singularity]] of &lt;math&gt;f&lt;/math&gt; with &lt;math&gt;D_r(z_0) \cap S = {z_0}&lt;/math&gt;, the residue is defined as:

:&lt;math&gt;\mathrm{res}{z_0}(f) := \frac{1}{2\pi i} \int{\partial D_r(z_0)} f(\xi), d\xi = \frac{1}{2\pi i} \int_{|\xi-z_0|=r} f(\xi), d\xi&lt;/math&gt;.

== Relation Between Residue and Laurent Series ==
If &lt;math&gt;f&lt;/math&gt; is represented around an isolated singularity &lt;math&gt;z_0 \in S \subset G&lt;/math&gt; as a Laurent series, the residue can be computed as follows.
With &lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt; as the [[Laurent Series|Laurent Series]] expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt;, it holds that:
:&lt;math&gt;\mathrm{res}{z_0}(f) = \frac{1}{2\pi i} \int{\partial D_r(z_0)} f(\xi), d\xi = \frac{1}{2\pi i} \int_{\partial D_r(z_0)} a_{-1}\cdot (\xi-z_0)^{-1}, d\xi = \frac{1}{2\pi i}  a_{-1} \cdot \underbrace{\int_{\partial D_r(z_0)} (\xi-z_0)^{-1} , d\xi}{=2\pi i} = a{-1}&lt;/math&gt;.
It must be taken into account that the closed disk &lt;math&gt;\overline{D_r(z_0)}&lt;/math&gt; contains only the singularity &lt;math&gt;z_0 \in S &lt;/math&gt;, i.e&lt;math&gt;\overline{D_r(z_0)} \cap s = \{z_0\}&lt;/math&gt;.

Thus, one can read off the 'residue' &lt;math&gt;\mathrm{res}_{z_0}(f) = a_{-1}&lt;/math&gt; from the Laurent expansion of  around  at the  &lt;math&gt;f&lt;/math&gt; um &lt;math&gt;z_0&lt;/math&gt; an -1-ten coefficient of .
==Considerations==
The closed disk &lt;math&gt;\overline{D_r(z_0)}&lt;/math&gt; must contain only the singularity &lt;math&gt;z_0 \in S&lt;/math&gt;, meaning&lt;math&gt;\overline{D_r(z_0)} \cap S = {z_0}&lt;/math&gt;.
Thus, the residue &lt;math&gt;\mathrm{res}{z_0}(f) = a{-1}&lt;/math&gt; can be read off directly as the coefficient of &lt;math&gt;(z-z_0)^{-1}&lt;/math&gt; in the Laurent series expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt;.
==Etymology==
The term &quot;residue&quot; (from Latin residuere – to remain) is used because in integration along the path &lt;math&gt;\gamma(t) := z_0 + r\cdot e^{it}&lt;/math&gt; with &lt;math&gt;t \in [0, 2\pi]&lt;/math&gt; around the circle centered at &lt;math&gt;z_0&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;
\begin{array}{rl}
   \displaystyle \int_{|w-z_0|=r} f(w)\, dw &amp;= \displaystyle \sum_{n=-\infty}^{+\infty} a_n \int_{|w-z_0|=r} (w-z_0)^n \, dw\\
                             &amp;= 2\pi i \cdot a_{-1}.
\end{array}
&lt;/math&gt;&lt;/center&gt;  
Thus, the residue is what remains after integrating.  
==Computation for Poles==
If &lt;math&gt;z_0 \in U&lt;/math&gt; is a pole of order &lt;math&gt;m&lt;/math&gt; of &lt;math&gt;f&lt;/math&gt;, the [[Laurent Series|Laurent Series]] expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt; has the form:
:&lt;math&gt;f(z) = \sum_{k=-m}^\infty a_k (z-z_0)^k&lt;/math&gt;
with &lt;math&gt;a_{-m} \neq 0&lt;/math&gt;.

===Proof 1: Removing Principal Part by Multiplication===
By multiplying with &lt;math&gt;(z-z_0)^m&lt;/math&gt;, we get:
:&lt;math&gt;g_m(z) := (z-z_0)^m \cdot f(z) = \sum_{k=0}^\infty a_{k-m} (z-z_0)^k.&lt;/math&gt;
The residue &lt;math&gt;a_{-1}&lt;/math&gt; is then the coefficient of &lt;math&gt;(z-z_0)^{m-1}&lt;/math&gt; in the power series of &lt;math&gt;g_m(z)&lt;/math&gt;.

===Proof 2: Using (m-1)-fold Differentiation===
By differentiating &lt;math&gt;m-1&lt;/math&gt; times, the first &lt;math&gt;m-1&lt;/math&gt; terms from &lt;math&gt;n=0&lt;/math&gt; to &lt;math&gt;n=m-2&lt;/math&gt; vanish. The residue is then found as the coefficient of &lt;math&gt;(z-z_0)^0&lt;/math&gt; in:
:&lt;math&gt;g_m^{(m-1)}(z) = \sum_{k=m-1}^\infty \frac{k!}{(k-m+1)!} a_{k-m}(z-z_0)^{k-m+1}.&lt;/math&gt;

===Proof 3: Limit Process to Compute Coefficient of &lt;math&gt;(z-z_0)^0&lt;/math&gt;===
By shifting the index:
:&lt;math&gt;g_m^{(m-1)}(z) = \sum_{k=-1}^\infty \frac{(m+k)!}{(k+1)!} a_k (z-z_0)^{k+1}.&lt;/math&gt;
Taking the limit &lt;math&gt;z \to z_0&lt;/math&gt;, all terms with &lt;math&gt;k \geq 0&lt;/math&gt; vanish, leaving:
:&lt;math&gt;\lim_{z \to z_0} g_m^{(m-1)}(z) = \frac{(m-1)!}{0!} \cdot a_{-1} \cdot (z-z_0)^0 = (m-1)! \cdot a_{-1}.&lt;/math&gt;
Thus, the residue can be computed &lt;math&gt;z \to z_0&lt;/math&gt; using:
:&lt;math&gt;\mathrm{res}{z_0}(f) = a{-1} = \frac{1}{(m-1)!} \cdot \lim_{z \to z_0} g_m^{(m-1)}(z).&lt;/math&gt;

==Exercises for Students==

*Explain why, in the Laurent series expansion, all terms from the principal and outer parts, i.e., &lt;math&gt;n \in \mathbb{Z}&lt;/math&gt; with &lt;math&gt;n \neq -1&lt;/math&gt;, yield integrals that evaluate to zero:
:&lt;math&gt;\int_{\partial D_r(z_0)} a_n \cdot (\xi - z_0)^n, d\xi = 0.&lt;/math&gt;

*Why can the order of integration and series expansion be interchanged?
::&lt;math&gt;\sum_{n=-\infty}^{+\infty} \int_{\partial D_r(z_0)} a_n (\xi-z_0)^n d\xi = \int_{\partial D_r(z_0)} \sum_{n=-\infty}^{+\infty} a_n (\xi-z_0)^n d\xi =
\frac{1}{2\pi i} \int_{\partial D_r(z_0)} f(\xi), d\xi = \mathrm{res}_{z_0}(f).&lt;/math&gt;

*Given the function &lt;math&gt;f:\mathbb{C}\setminus {i} \to \mathbb{C}&lt;/math&gt; with &lt;math&gt;z \mapsto f(z) = \frac{e^{z-i}}{(z-i)^5}&lt;/math&gt;, calculate the residue &lt;math&gt;\mathrm{res}_{z_0}(f)&lt;/math&gt; at &lt;math&gt;z_0 := i&lt;/math&gt;.

==See Also==

*[[Residue|Residue]]
*[[Complex_analysis/Examples_of_Laurent_series|Examples of Laurent Series]]
== Page Information ==
=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Residuum 
Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/Residuum|Kurs:Funktionentheorie/Residuum ]] - URL:
https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Residuum 
* Date: 12/26/2024&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Residuum &quot; srclang=&quot;de&quot; date=&quot;12/26/2024&quot; time=&quot;11:28&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Kurs:Funktionentheorie/Residuum ]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
      <sha1>3214c4axdx87e93or3xoe3y6n7lacjp</sha1>
    </revision>
    <revision>
      <id>2693289</id>
      <parentid>2693288</parentid>
      <timestamp>2024-12-26T11:58:28Z</timestamp>
      <contributor>
        <username>Eshaa2024</username>
        <id>2993595</id>
      </contributor>
      <comment>/* Definition */</comment>
      <origin>2693289</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5797" sha1="2hjkdbq9rw6lcgt8d9zorjlcq5ua6yg" xml:space="preserve">==Definition==
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a domain, &lt;math&gt;z_0 \in G&lt;/math&gt;, and let &lt;math&gt;f&lt;/math&gt; be holomorphic except for isolated singularities &lt;math&gt;S \subset G&lt;/math&gt;, i.e., &lt;math&gt;f\colon G \setminus S \to \mathbb{C}&lt;/math&gt; is holomorphic. If &lt;math&gt;z_0 \in S \subset G&lt;/math&gt; is an [[Complex_analysis/Isolated Singularity|Isolated Singularity]] of &lt;math&gt;f&lt;/math&gt; with &lt;math&gt;D_r(z_0) \cap S = {z_0}&lt;/math&gt;, the residue is defined as:

:&lt;math&gt;\mathrm{res}{z_0}(f) := \frac{1}{2\pi i} \int{\partial D_r(z_0)} f(\xi), d\xi = \frac{1}{2\pi i} \int_{|\xi-z_0|=r} f(\xi), d\xi&lt;/math&gt;.

== Relation Between Residue and Laurent Series ==
If &lt;math&gt;f&lt;/math&gt; is represented around an isolated singularity &lt;math&gt;z_0 \in S \subset G&lt;/math&gt; as a Laurent series, the residue can be computed as follows.
With &lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt; as the [[Laurent Series|Laurent Series]] expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt;, it holds that:
:&lt;math&gt;\mathrm{res}{z_0}(f) = \frac{1}{2\pi i} \int{\partial D_r(z_0)} f(\xi), d\xi = \frac{1}{2\pi i} \int_{\partial D_r(z_0)} a_{-1}\cdot (\xi-z_0)^{-1}, d\xi = \frac{1}{2\pi i}  a_{-1} \cdot \underbrace{\int_{\partial D_r(z_0)} (\xi-z_0)^{-1} , d\xi}{=2\pi i} = a{-1}&lt;/math&gt;.
It must be taken into account that the closed disk &lt;math&gt;\overline{D_r(z_0)}&lt;/math&gt; contains only the singularity &lt;math&gt;z_0 \in S &lt;/math&gt;, i.e&lt;math&gt;\overline{D_r(z_0)} \cap s = \{z_0\}&lt;/math&gt;.

Thus, one can read off the 'residue' &lt;math&gt;\mathrm{res}_{z_0}(f) = a_{-1}&lt;/math&gt; from the Laurent expansion of  around  at the  &lt;math&gt;f&lt;/math&gt; um &lt;math&gt;z_0&lt;/math&gt; an -1-ten coefficient of .
==Considerations==
The closed disk &lt;math&gt;\overline{D_r(z_0)}&lt;/math&gt; must contain only the singularity &lt;math&gt;z_0 \in S&lt;/math&gt;, meaning&lt;math&gt;\overline{D_r(z_0)} \cap S = {z_0}&lt;/math&gt;.
Thus, the residue &lt;math&gt;\mathrm{res}{z_0}(f) = a{-1}&lt;/math&gt; can be read off directly as the coefficient of &lt;math&gt;(z-z_0)^{-1}&lt;/math&gt; in the Laurent series expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt;.
==Etymology==
The term &quot;residue&quot; (from Latin residuere – to remain) is used because in integration along the path &lt;math&gt;\gamma(t) := z_0 + r\cdot e^{it}&lt;/math&gt; with &lt;math&gt;t \in [0, 2\pi]&lt;/math&gt; around the circle centered at &lt;math&gt;z_0&lt;/math&gt;, the following holds:

&lt;center&gt;&lt;math&gt;
\begin{array}{rl}
   \displaystyle \int_{|w-z_0|=r} f(w)\, dw &amp;= \displaystyle \sum_{n=-\infty}^{+\infty} a_n \int_{|w-z_0|=r} (w-z_0)^n \, dw\\
                             &amp;= 2\pi i \cdot a_{-1}.
\end{array}
&lt;/math&gt;&lt;/center&gt;  
Thus, the residue is what remains after integrating.  
==Computation for Poles==
If &lt;math&gt;z_0 \in U&lt;/math&gt; is a pole of order &lt;math&gt;m&lt;/math&gt; of &lt;math&gt;f&lt;/math&gt;, the [[Laurent Series|Laurent Series]] expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt; has the form:
:&lt;math&gt;f(z) = \sum_{k=-m}^\infty a_k (z-z_0)^k&lt;/math&gt;
with &lt;math&gt;a_{-m} \neq 0&lt;/math&gt;.

===Proof 1: Removing Principal Part by Multiplication===
By multiplying with &lt;math&gt;(z-z_0)^m&lt;/math&gt;, we get:
:&lt;math&gt;g_m(z) := (z-z_0)^m \cdot f(z) = \sum_{k=0}^\infty a_{k-m} (z-z_0)^k.&lt;/math&gt;
The residue &lt;math&gt;a_{-1}&lt;/math&gt; is then the coefficient of &lt;math&gt;(z-z_0)^{m-1}&lt;/math&gt; in the power series of &lt;math&gt;g_m(z)&lt;/math&gt;.

===Proof 2: Using (m-1)-fold Differentiation===
By differentiating &lt;math&gt;m-1&lt;/math&gt; times, the first &lt;math&gt;m-1&lt;/math&gt; terms from &lt;math&gt;n=0&lt;/math&gt; to &lt;math&gt;n=m-2&lt;/math&gt; vanish. The residue is then found as the coefficient of &lt;math&gt;(z-z_0)^0&lt;/math&gt; in:
:&lt;math&gt;g_m^{(m-1)}(z) = \sum_{k=m-1}^\infty \frac{k!}{(k-m+1)!} a_{k-m}(z-z_0)^{k-m+1}.&lt;/math&gt;

===Proof 3: Limit Process to Compute Coefficient of &lt;math&gt;(z-z_0)^0&lt;/math&gt;===
By shifting the index:
:&lt;math&gt;g_m^{(m-1)}(z) = \sum_{k=-1}^\infty \frac{(m+k)!}{(k+1)!} a_k (z-z_0)^{k+1}.&lt;/math&gt;
Taking the limit &lt;math&gt;z \to z_0&lt;/math&gt;, all terms with &lt;math&gt;k \geq 0&lt;/math&gt; vanish, leaving:
:&lt;math&gt;\lim_{z \to z_0} g_m^{(m-1)}(z) = \frac{(m-1)!}{0!} \cdot a_{-1} \cdot (z-z_0)^0 = (m-1)! \cdot a_{-1}.&lt;/math&gt;
Thus, the residue can be computed &lt;math&gt;z \to z_0&lt;/math&gt; using:
:&lt;math&gt;\mathrm{res}{z_0}(f) = a{-1} = \frac{1}{(m-1)!} \cdot \lim_{z \to z_0} g_m^{(m-1)}(z).&lt;/math&gt;

==Exercises for Students==

*Explain why, in the Laurent series expansion, all terms from the principal and outer parts, i.e., &lt;math&gt;n \in \mathbb{Z}&lt;/math&gt; with &lt;math&gt;n \neq -1&lt;/math&gt;, yield integrals that evaluate to zero:
:&lt;math&gt;\int_{\partial D_r(z_0)} a_n \cdot (\xi - z_0)^n, d\xi = 0.&lt;/math&gt;

*Why can the order of integration and series expansion be interchanged?
::&lt;math&gt;\sum_{n=-\infty}^{+\infty} \int_{\partial D_r(z_0)} a_n (\xi-z_0)^n d\xi = \int_{\partial D_r(z_0)} \sum_{n=-\infty}^{+\infty} a_n (\xi-z_0)^n d\xi =
\frac{1}{2\pi i} \int_{\partial D_r(z_0)} f(\xi), d\xi = \mathrm{res}_{z_0}(f).&lt;/math&gt;

*Given the function &lt;math&gt;f:\mathbb{C}\setminus {i} \to \mathbb{C}&lt;/math&gt; with &lt;math&gt;z \mapsto f(z) = \frac{e^{z-i}}{(z-i)^5}&lt;/math&gt;, calculate the residue &lt;math&gt;\mathrm{res}_{z_0}(f)&lt;/math&gt; at &lt;math&gt;z_0 := i&lt;/math&gt;.

==See Also==

*[[Residue|Residue]]
*[[Complex_analysis/Examples_of_Laurent_series|Examples of Laurent Series]]
== Page Information ==
=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Residuum 
Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/Residuum|Kurs:Funktionentheorie/Residuum ]] - URL:
https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Residuum 
* Date: 12/26/2024&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Residuum &quot; srclang=&quot;de&quot; date=&quot;12/26/2024&quot; time=&quot;11:28&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Kurs:Funktionentheorie/Residuum ]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
      <sha1>2hjkdbq9rw6lcgt8d9zorjlcq5ua6yg</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/burden</title>
    <ns>0</ns>
    <id>317507</id>
    <revision>
      <id>2693278</id>
      <timestamp>2024-12-26T11:05:20Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  [[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|thumb|500px|(truth table) [[Boolf prop/3-ary/weight|weight]] 4]] [[File:Set of 3-ary Boolean functions 80069177398200828458670140847044886780.svg|thumb|500px|[[Boolf prop/3-ary/zhegalkin weight|Zhegalkin weight]] 4]]  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;co...&quot;</comment>
      <origin>2693278</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="9428" sha1="rgsdjfp9h8sonebwo3d3i5pydf3p8ot" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|thumb|500px|(truth table) [[Boolf prop/3-ary/weight|weight]] 4]]
[[File:Set of 3-ary Boolean functions 80069177398200828458670140847044886780.svg|thumb|500px|[[Boolf prop/3-ary/zhegalkin weight|Zhegalkin weight]] 4]]

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;38&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;9&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;23&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| weight pair
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| (0, 0)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| (1, 8)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_2.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (1, 4)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 4, 16]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_65556.svg|420px]]
|-
|class=&quot;size&quot;| 9
|class=&quot;prop&quot;| (2, 4)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 5, 6, 17, 18, 20, 24, 36, 66]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_73786976363575902312.svg|420px]]
|-
|class=&quot;size&quot;| 20
|class=&quot;prop&quot;| (3, 4)
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[7, 19, 21, 22, 25, 26, 28, 37, 38, 44, 52, 56, 67, 70, 74, 82, 88, 98, 100, 104]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_21867287194867765063387766587520.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (1, 2)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[8, 32, 64]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_18446744078004519168.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (2, 6)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[9, 33, 65]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_36893488156009038336.svg|420px]]
|-
|class=&quot;size&quot;| 9
|class=&quot;prop&quot;| (2, 2)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[10, 12, 34, 40, 48, 68, 72, 80, 96]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_79229376457598622863384908800.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| (3, 6)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[11, 13, 14, 35, 41, 49, 50, 69, 73, 81, 84, 97]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_158478095728312205693471975424.svg|420px]]
|-
|class=&quot;size&quot;| 9
|class=&quot;prop&quot;| (4, 2)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[15, 51, 60, 85, 90, 102, 106, 108, 120]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1329638715856015485898113705029173248.svg|420px]]
|-
|class=&quot;size&quot;| 23
|class=&quot;prop&quot;| (4, 4)
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[23, 27, 29, 30, 39, 45, 46, 53, 54, 57, 58, 71, 75, 78, 83, 86, 89, 92, 99, 101, 105, 114, 116]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_103889676774519634310907416364974080.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| (5, 4)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[31, 47, 55, 59, 79, 87, 93, 110, 115, 117, 122, 124]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_26793549874313211552840646019958964224.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (3, 2)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[42, 76, 112]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5192296858610385492260808699150336.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (4, 6)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[43, 77, 113]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_10384593717220770984521617398300672.svg|420px]]
|-
|class=&quot;size&quot;| 9
|class=&quot;prop&quot;| (5, 6)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[61, 62, 91, 94, 103, 107, 109, 118, 121]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_2991584450387929320740109725133176832.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (6, 2)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[63, 95, 119]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_664614037506539202807444363766923264.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (6, 4)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[111, 123, 125]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_53171715979825902329966547659378393088.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| (6, 6)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[126]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_85070591730234615865843651857942052864.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| (7, 2)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[127]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_170141183460469231731687303715884105728.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| (1, 1)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[128]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_340282366920938463463374607431768211456.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| (2, 7)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[129]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_680564733841876926926749214863536422912.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (2, 3)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[130, 132, 144]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_22307550845869041910804985764796996870209536.svg|420px]]
|-
|class=&quot;size&quot;| 9
|class=&quot;prop&quot;| (3, 5)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[131, 133, 134, 145, 146, 148, 152, 164, 194]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_25108406964936948895192162057100570117740705509753615286272.svg|420px]]
|-
|class=&quot;size&quot;| 20
|class=&quot;prop&quot;| (4, 3)
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[135, 147, 149, 150, 153, 154, 156, 165, 166, 172, 180, 184, 195, 198, 202, 210, 216, 226, 228, 232]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7441052244809532022255575855098061541171806476706749552323906890629120.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (2, 1)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[136, 160, 192]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_6277101736848182488278978273171597895442537966652629188608.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (3, 7)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[137, 161, 193]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_12554203473696364976557956546343195790885075933305258377216.svg|420px]]
|-
|class=&quot;size&quot;| 9
|class=&quot;prop&quot;| (3, 3)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[138, 140, 162, 168, 176, 196, 200, 208, 224]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_26960359750661738282316453158984117888600841619383213102677675212800.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| (4, 5)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[139, 141, 142, 163, 169, 177, 178, 197, 201, 209, 212, 225]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_53927301519553144512686748242099354398634187143454433371679667257344.svg|420px]]
|-
|class=&quot;size&quot;| 9
|class=&quot;prop&quot;| (5, 3)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[143, 179, 188, 213, 218, 230, 234, 236, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_452452609381202100815903215357421756553903823647912245591481221591322329088.svg|420px]]
|-
|class=&quot;size&quot;| 23
|class=&quot;prop&quot;| (5, 5)
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[151, 155, 157, 158, 167, 173, 174, 181, 182, 185, 186, 199, 203, 206, 211, 214, 217, 220, 227, 229, 233, 242, 244]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_35351825111484788975203103024835962725810281641519939081497323445399060480.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| (6, 3)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[159, 175, 183, 187, 207, 215, 221, 238, 243, 245, 250, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_9117372569445512904238451931420414304594892851168509083640346829510770950144.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (4, 1)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[170, 204, 240]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1766847064804095338292937922828216753893183071784675679834258561581449216.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (5, 7)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[171, 205, 241]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3533694129608190676585875845656433507786366143569351359668517123162898432.svg|420px]]
|-
|class=&quot;size&quot;| 9
|class=&quot;prop&quot;| (6, 5)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[189, 190, 219, 222, 231, 235, 237, 246, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1017983437621879394163401061060446564310147155177051195411448556160016187392.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (7, 3)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[191, 223, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_226156437771606530900532845121941495453627987222484645961029556549277712384.svg|420px]]
|-
|class=&quot;size&quot;| 3
|class=&quot;prop&quot;| (7, 5)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[239, 251, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_18093397366863044727097758056357857061331348845954775940644308304337072816128.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| (7, 7)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28948022309329048855892746252171976963317496166410141009864396001978282409984.svg|420px]]
|-
|class=&quot;size&quot;| 1
|class=&quot;prop&quot;| (8, 1)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57896044618658097711785492504343953926634992332820282019728792003956564819968.svg|420px]]
|}

[[Category:Boolf prop/3-ary|weight pair]]</text>
      <sha1>rgsdjfp9h8sonebwo3d3i5pydf3p8ot</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/platoon</title>
    <ns>0</ns>
    <id>317508</id>
    <revision>
      <id>2693283</id>
      <timestamp>2024-12-26T11:34:33Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;13&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span cla...&quot;</comment>
      <origin>2693283</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4589" sha1="9kqngboly5osagnid0i7ib878vyiw1m" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;13&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| platoon
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| 0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 1, 254, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_86844066927987146567678238756515930889952488499230423029593188005934847229955.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| 170
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[2, 3, 4, 5, 14, 15, 16, 17, 50, 51, 84, 85, 170, 171, 204, 205, 238, 239, 240, 241, 250, 251, 252, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_27145396591488979376661515898305270242258702818147575966445310112090460241980.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| 153
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[6, 7, 18, 19, 20, 21, 60, 61, 90, 91, 102, 103, 152, 153, 164, 165, 194, 195, 234, 235, 236, 237, 248, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1357352650530606674272439460731672771907939385395895001134015256034889433280.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| 136
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[8, 9, 32, 33, 62, 63, 64, 65, 94, 95, 118, 119, 136, 137, 160, 161, 190, 191, 192, 193, 222, 223, 246, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_339234656657409815182104478227459708018373721404780464128709633561468076800.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| 10
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[10, 11, 12, 13, 34, 35, 48, 49, 68, 69, 80, 81, 174, 175, 186, 187, 206, 207, 220, 221, 242, 243, 244, 245]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_106010828942001592264551517252273245832597465068946641349143452266518297600.svg|420px]]
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| 150
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[22, 23, 104, 105, 150, 151, 232, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_20705239040371691362304271868574154475293817320180023025244823586078720.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| 135
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[24, 25, 36, 37, 66, 67, 106, 107, 108, 109, 120, 121, 134, 135, 146, 147, 148, 149, 188, 189, 218, 219, 230, 231]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5177573507594122483391828253793242460230150515820620278668478403051520.svg|420px]]
|-
|class=&quot;size&quot;| 48
|class=&quot;prop&quot;| 45
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[26, 27, 28, 29, 38, 39, 44, 45, 52, 53, 56, 57, 70, 71, 74, 75, 82, 83, 88, 89, 98, 99, 100, 101, 154, 155, 156, 157, 166, 167, 172, 173, 180, 181, 184, 185, 198, 199, 202, 203, 210, 211, 216, 217, 226, 227, 228, 229]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1617917693906254262672834271039487326373103480477771149564319681740800.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| 30
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[30, 31, 54, 55, 86, 87, 168, 169, 200, 201, 224, 225]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_80879844822266053283405129357078610224829424474093477939445822914560.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| 40
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[40, 41, 72, 73, 96, 97, 158, 159, 182, 183, 214, 215]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_78984218769807837609955415061230177455423158000941432336988241920.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| 130
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[42, 43, 76, 77, 110, 111, 112, 113, 122, 123, 124, 125, 130, 131, 132, 133, 142, 143, 144, 145, 178, 179, 212, 213]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_19746054689003844161592695125666622283558813672742493878726164480.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| 46
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[46, 47, 58, 59, 78, 79, 92, 93, 114, 115, 116, 117, 138, 139, 140, 141, 162, 163, 176, 177, 196, 197, 208, 209]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1234429719161563544230119874054978799700774637947426872607375360.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| 126
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[126, 127, 128, 129]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1276058875953519237987654777869130792960.svg|420px]]
|}

[[Category:Boolf prop/3-ary|platoon]]</text>
      <sha1>9kqngboly5osagnid0i7ib878vyiw1m</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/super chunky burden</title>
    <ns>0</ns>
    <id>317509</id>
    <revision>
      <id>2693284</id>
      <timestamp>2024-12-26T11:51:42Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span cla...&quot;</comment>
      <origin>2693284</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3112" sha1="9uwwmaruv2z20ozrrk07zpiirmwv9ah" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;72&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| battalion
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 8
|class=&quot;prop&quot;| ((0, 0), (6, 6))
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 1, 126, 127, 128, 129, 254, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_86844066927987146567678238756515930891228547375183942267580842783803978022915.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| ((1, 4), (5, 4))
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[2, 3, 4, 5, 16, 17, 110, 111, 122, 123, 124, 125, 130, 131, 132, 133, 144, 145, 238, 239, 250, 251, 252, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_27140096050294567090646637084536852514729318450027635179418706668985287639100.svg|420px]]
|-
|class=&quot;size&quot;| 48
|class=&quot;prop&quot;| ((2, 4), (4, 2))
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[6, 7, 18, 19, 20, 21, 24, 25, 36, 37, 60, 61, 66, 67, 90, 91, 102, 103, 106, 107, 108, 109, 120, 121, 134, 135, 146, 147, 148, 149, 152, 153, 164, 165, 188, 189, 194, 195, 218, 219, 230, 231, 234, 235, 236, 237, 248, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1357357828104114268394922852559926565150399615546410821754293924513292484800.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| ((1, 2), (5, 6))
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[8, 9, 32, 33, 62, 63, 64, 65, 94, 95, 118, 119, 136, 137, 160, 161, 190, 191, 192, 193, 222, 223, 246, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_339234656657409815182104478227459708018373721404780464128709633561468076800.svg|420px]]
|-
|class=&quot;size&quot;| 72
|class=&quot;prop&quot;| ((2, 2), (4, 4))
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_106010909902065063019574201811588137846492846153495048081510250921936829440.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| ((3, 2), (3, 6))
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[14, 15, 42, 43, 50, 51, 76, 77, 84, 85, 112, 113, 142, 143, 170, 171, 178, 179, 204, 205, 212, 213, 240, 241]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5300541214158340703882657930010422655050990403499600699345936983898767360.svg|420px]]
|-
|class=&quot;size&quot;| 56
|class=&quot;prop&quot;| ((3, 4), (3, 4))
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[22, 23, 26, 27, 28, 29, 38, 39, 44, 45, 52, 53, 56, 57, 70, 71, 74, 75, 82, 83, 88, 89, 98, 99, 100, 101, 104, 105, 150, 151, 154, 155, 156, 157, 166, 167, 172, 173, 180, 181, 184, 185, 198, 199, 202, 203, 210, 211, 216, 217, 226, 227, 228, 229, 232, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_22323156734277945624977106139613641801666920800657794174809143267819520.svg|420px]]
|}

[[Category:Boolf prop/3-ary|battalion]]</text>
      <sha1>9uwwmaruv2z20ozrrk07zpiirmwv9ah</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/chunky burden</title>
    <ns>0</ns>
    <id>317510</id>
    <revision>
      <id>2693286</id>
      <timestamp>2024-12-26T11:53:34Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>New resource with &quot;&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;  &lt;div class=&quot;intpart&quot;&gt; &lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;13&lt;/span&gt;&lt;/span&gt; Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;36&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span cl...&quot;</comment>
      <origin>2693286</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4599" sha1="lw9k1eql8p7jv130d7kb1b8ezrc1cgd" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;13&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;36&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| half battalion
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| (0, 0)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 1, 128, 129]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1020847100762815390390123822295304634371.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| (1, 4)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 3, 4, 5, 16, 17, 130, 131, 132, 133, 144, 145]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_66922652537607125732414957294390990610825276.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| (2, 4)
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[6, 7, 18, 19, 20, 21, 24, 25, 36, 37, 66, 67, 134, 135, 146, 147, 148, 149, 152, 153, 164, 165, 194, 195]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_75325220894810712840271410957050245523528888676370351915200.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| (1, 2)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[8, 9, 32, 33, 64, 65, 136, 137, 160, 161, 192, 193]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_18831305210544547464836934819514793686382954132191901123328.svg|420px]]
|-
|class=&quot;size&quot;| 36
|class=&quot;prop&quot;| (2, 2)
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[10, 11, 12, 13, 34, 35, 40, 41, 48, 49, 68, 69, 72, 73, 80, 81, 96, 97, 138, 139, 140, 141, 162, 163, 168, 169, 176, 177, 196, 197, 200, 201, 208, 209, 224, 225]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_80881079251985214846949359476952353666040212987522435176623180364800.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| (3, 6)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[14, 15, 50, 51, 84, 85, 142, 143, 178, 179, 212, 213]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_19746054689003844161525772393355864297569742503366378873056968704.svg|420px]]
|-
|class=&quot;size&quot;| 56
|class=&quot;prop&quot;| (3, 4)
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[22, 23, 26, 27, 28, 29, 38, 39, 44, 45, 52, 53, 56, 57, 70, 71, 74, 75, 82, 83, 88, 89, 98, 99, 100, 101, 104, 105, 150, 151, 154, 155, 156, 157, 166, 167, 172, 173, 180, 181, 184, 185, 198, 199, 202, 203, 210, 211, 216, 217, 226, 227, 228, 229, 232, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_22323156734277945624977106139613641801666920800657794174809143267819520.svg|420px]]
|-
|class=&quot;size&quot;| 36
|class=&quot;prop&quot;| (4, 4)
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[30, 31, 46, 47, 54, 55, 58, 59, 78, 79, 86, 87, 92, 93, 114, 115, 116, 117, 158, 159, 174, 175, 182, 183, 186, 187, 206, 207, 214, 215, 220, 221, 242, 243, 244, 245]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_106010829020985811034359354862228660894139180113282060559075074298756464640.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| (3, 2)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[42, 43, 76, 77, 112, 113, 170, 171, 204, 205, 240, 241]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5300541194412286014878813768484650261695126105929858195979558110841798656.svg|420px]]
|-
|class=&quot;size&quot;| 24
|class=&quot;prop&quot;| (4, 2)
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[60, 61, 90, 91, 102, 103, 106, 107, 108, 109, 120, 121, 188, 189, 218, 219, 230, 231, 234, 235, 236, 237, 248, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1357357828104114193069701957749213724878988658496165298225405248142940569600.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| (5, 6)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[62, 63, 94, 95, 118, 119, 190, 191, 222, 223, 246, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_339234656657409796350799267682912243181438901889986777745755501369566953472.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| (5, 4)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[110, 111, 122, 123, 124, 125, 238, 239, 250, 251, 252, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_27140096050294567090646637084536785592076780842901902764461412277994676813824.svg|420px]]
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| (6, 6)
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[126, 127, 254, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_86844066927987146567678238756515930890207700274421126877190718961508673388544.svg|420px]]
|}

[[Category:Boolf prop/3-ary|half battalion]]</text>
      <sha1>lw9k1eql8p7jv130d7kb1b8ezrc1cgd</sha1>
    </revision>
  </page>
  <page>
    <title>Complex analysis/Isolated singularity</title>
    <ns>0</ns>
    <id>317511</id>
    <revision>
      <id>2693287</id>
      <timestamp>2024-12-26T11:54:49Z</timestamp>
      <contributor>
        <username>Eshaa2024</username>
        <id>2993595</id>
      </contributor>
      <comment>New resource with &quot;== Definition == Let &lt;math&gt;G \subseteq \mathbb C&lt;/math&gt; be a domain and &lt;math&gt;z_0 \in G&lt;/math&gt;. If &lt;math&gt;f \colon G\setminus {z_0} \to \mathbb C&lt;/math&gt; is a [[w:en:Holomorphic function|holomorphic]] function, then &lt;math&gt;z_0&lt;/math&gt; is called an ''isolated singularity'' of &lt;math&gt;f&lt;/math&gt;. == Classification ==  Depending on the behavior of &lt;math&gt;f&lt;/math&gt; in the neighborhood of &lt;math&gt;z_0&lt;/math&gt;, one distinguishes three different types of isolated singularities of &lt;math&gt;f&lt;/ma...&quot;</comment>
      <origin>2693287</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4703" sha1="htfdpfg2vky4yvcjcx8hpdmh9itiyw7" xml:space="preserve">== Definition ==
Let &lt;math&gt;G \subseteq \mathbb C&lt;/math&gt; be a domain and &lt;math&gt;z_0 \in G&lt;/math&gt;. If &lt;math&gt;f \colon G\setminus {z_0} \to \mathbb C&lt;/math&gt; is a [[w:en:Holomorphic function|holomorphic]] function, then &lt;math&gt;z_0&lt;/math&gt; is called an ''isolated singularity'' of &lt;math&gt;f&lt;/math&gt;.
== Classification == 
Depending on the behavior of &lt;math&gt;f&lt;/math&gt; in the neighborhood of &lt;math&gt;z_0&lt;/math&gt;, one distinguishes three different types of isolated singularities of &lt;math&gt;f&lt;/math&gt;.

=== Removable Singularities === 
If &lt;math&gt;f&lt;/math&gt; can be holomorphically extended to the entire domain &lt;math&gt;G&lt;/math&gt;, then we say that &lt;math&gt;z_0&lt;/math&gt; is a ''removable singularity''. According to the [[Riemann Removability Theorem|Riemann Removability Theorem]], this is the case if &lt;math&gt;f&lt;/math&gt; is bounded in a neighborhood of &lt;math&gt;z_0&lt;/math&gt;.
=== Poles ===
If &lt;math&gt;z_0&lt;/math&gt; is not a removable singularity, but there exists an &lt;math&gt;n \ge 1&lt;/math&gt; such that &lt;math&gt;(\cdot - z_0)^n \cdot f&lt;/math&gt; has a removable singularity at &lt;math&gt;z_0&lt;/math&gt;, then we say that &lt;math&gt;f&lt;/math&gt; has a ''pole'' at &lt;math&gt;z_0&lt;/math&gt;. The smallest such &lt;math&gt;n&lt;/math&gt; is called the ''order'' of the pole.
=== Essential Singularities === 
If &lt;math&gt;z_0&lt;/math&gt; is neither removable nor a pole, then &lt;math&gt;z_0&lt;/math&gt; is called an ''essential singularity'' of &lt;math&gt;f&lt;/math&gt;.
== Examples ==
*Since &lt;math&gt;\lim_{z\to 0} \frac{\sin z}z = 1&lt;/math&gt;, the function &lt;math&gt;f_1(z) = \frac{\sin z}z&lt;/math&gt; has a removable singularity at &lt;math&gt;z_0 = 0&lt;/math&gt;.
*The function &lt;math&gt;f_2(z) = \frac 1{\sin z}&lt;/math&gt; does not have &lt;math&gt;z_0 = 0&lt;/math&gt; a removable singularity at, since&lt;math&gt;f_2&lt;/math&gt; is unbounded at &lt;math&gt;0&lt;/math&gt;, but &lt;math&gt;f_2&lt;/math&gt; has a first-order pole at &lt;math&gt;0&lt;/math&gt;, because &lt;math&gt;f_2(z) \cdot (z - 0)^1 = f_2(z)z = \frac{z}{\sin z}&lt;/math&gt; and &lt;math&gt;\lim_{z \to 0} \frac{z}{\sin z} = 1&lt;/math&gt;, which has a removable singularity at 0 .

*The function &lt;math&gt;f_3(z) = \sin \frac 1z&lt;/math&gt; has an essential singularity at &lt;math&gt;z_0 = 0&lt;/math&gt;, since for every &lt;math&gt;n \ge 1&lt;/math&gt;, the function &lt;math&gt;f_3(z)z^n = z^n \sin \frac 1z&lt;/math&gt; is unbounded in any neighborhood of &lt;math&gt;0&lt;/math&gt;. To see this, consider&lt;math&gt;\sin z^{-1} = \frac{e^{iz^{-1}} - e^{-iz^{-1}}}{2i}&lt;/math&gt;.For &lt;math&gt;z = it&lt;/math&gt; with &lt;math&gt;t \in \mathbb R&lt;/math&gt; is also &lt;math&gt;f_3(it)(it)^n = (it)^n \frac{e^{t^{-1}} - e^{-t^{-1}}}{2i}&lt;/math&gt;,which diverges as &lt;math&gt;t \to 0^+&lt;/math&gt; . 
== Laurent Expansions ==
The type of isolated singularity can also be inferred from the [[Complex Analysis/Laurent Expansion|Laurent Expansion]] of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt;. Let&lt;center&gt;&lt;math&gt; f(z) = \sum_{n = -\infty}^\infty a_n (z-z_0)^n &lt;/math&gt;&lt;/center&gt; 
be the [[Laurent Series]] of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt;. We define 
&lt;center&gt;&lt;math&gt; o_z(f) = \sup\{n \in \mathbb Z | \forall k &lt; n : a_k = 0\}&lt;/math&gt;.&lt;/center&gt;
Then, &lt;math&gt;f&lt;/math&gt; has the following singularities:If &lt;math&gt;o_z(f) \ge 0&lt;/math&gt;, i.e., all negative coefficients vanish, the [[Laurent Series#Main part and remainder|main part]] of the series is zero, and the singularity is removable.

If &lt;math&gt;-\infty &lt; o_z(f) &lt; 0&lt;/math&gt;, i.e., only finitely many negative coefficients are nonzero, there is a pole of order &lt;math&gt;-o_z(f)&lt;/math&gt;.
If &lt;math&gt;o_z(f) = -\infty&lt;/math&gt;, i.e., infinitely many negative coefficients are nonzero, the singularity is essential.
=== Examples ===
Let us consider our three examples again:

It is &lt;math&gt;f_1(z) = \frac{\sin z}z = \sum_{k=0}^\infty (-1)^n\frac{z^{2n}}{(2n+1)!}&lt;/math&gt;, so &lt;math&gt;o_0(f_1) = 0&lt;/math&gt;, a removable singularity.

It is &lt;center&gt;&lt;math&gt;f_2(z) = \frac 1{\sin z} = \frac 1z + \frac z6 + \frac 7{360}z^3 + \ldots &lt;/math&gt;&lt;/center&gt; so &lt;math&gt;o_0(f_2) = -1&lt;/math&gt;, a pole of first order.

It is &lt;math&gt;f_3(z) = \sin z^{-1} = \sum_{n=-\infty}^0 \frac{(-1)^n}{(-2n+1)!}z^{2n-1}&lt;/math&gt;, so &lt;math&gt;o_0(f_3) = -\infty&lt;/math&gt;, an essential singularity.
== Page information ==
=== Translation and Version Control ===
This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/isolierte Singularität Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/isolierte Singularität
|Kurs:Funktionentheorie/isolierte Singularität]] - URL:https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/isolierte Singularität
* Date: 11/20/2024

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&lt;noinclude&gt;[[de:Kurs:Funktionentheorie/isolierte Singularität]]&lt;/noinclude&gt;

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