Wikipedia talk:Make technical articles understandable

See also: Wikipedia talk:Explain jargon

Making articles more understandable does not necessarily mean that detailed technical content should be removed.

While some articles can be, in places, difficult to understand without a backing in the topic that they discuss, this often has more to do with the subject matter of the article, than it has to do with the word choice of its authors. In order to be factually robust, many articles must talk about things that could come off as complicated. In the past, Wikipedians have been known to insert tone tags into articles which contained language they found overly technical. If you are unsatisfied with the article's readability, a better solution would be to tag it as needing help from an expert-- somebody with a backing in the topic, who can re-write portions of it so that they're easier to read, without compromising their educational value. Generally, the tone tag is reserved for articles which fail to meet a basic standard-- articles that are poorly written, needlessly verbose or flowery, or which are clearly biased. As technical articles are typically created by professionals and tend to be of higher quality, the tone tag is not usually appropriate. I encourage Wikipedians who are interested in helping with this project to remove tone tags from articles which do not need them, so as to avoid confusing copyeditors. Many copyeditors will see the tone tag and look for something completely different. Atomic putty? Rien! (talk) (talk) 20:41, 21 June 2022 (UTC)

Exactly. The idea that people need knowlege pulped and chewed up is a misconception. If one understands everything in a Wikipedia article on a technical subject, that means they know the subject well. Then why bother reading this particular article? It's a waste of time. One of the first books I ever read was an encyclopedia of technology and science. Of course I did not understand, pretty much anything, but I got an overview of how much there is TO learn! Did it bother me? No, of course not. I think there are people who might be bothered by it, and the question is why. Did they get traumatized by someone who did not like answering questions? There are probably plenty such people, but hopefully, they will in time heal. It won't help them heal if we pretend that information is just not there to bother them. I doubt they are visiting technical articles just to feel bad. Morycm (talk) 23:02, 4 February 2023 (UTC)

@Atomic putty? Rien!: I don't think anyone's suggesting dumbing down articles or removing technical content. And an "expert needed" tag won't help, because it is the experts who write these incomprehensible articles. There's a difference between being an expert, and being an expert and a good encyclopedia editor. --Chetvorno^TALK 19:40, 6 February 2023 (UTC)

@Chetvorno Then I have an idea: use team approach. Get an expert, a writer, and a Wikipedia stylistic advocate. They will make sure it is technically correct, easy to understand, and reaches the widest possible audience for that subject. But if you expect to maximize audience, just do what top Youtube channels do: stick to sports, girls, beer, dogs, cats, and comedy. Because for those who look for information, a wikipedia that appeals to an average person from the global crowd would simply be a useless babble. Morycm (talk) 02:17, 13 February 2023 (UTC)

I agree with @Chetvorno 100%. Looking back, my opinion's definitely changed. When I wrote the earlier note, about a year ago, I felt strongly that accuracy shouldn't be compromised for readability-- but honestly, just like they said, a good encyclopedia editor can tone down the heavy detail, improve readability, and conserve accuracy.

Congrats to all parties for participating in the discussion. When in doubt, let's turn to our already-established best practices. I'm not sure why I felt the need to defend the conservation of detail so strongly before. Looking over the article, it does a really good job of keeping to the consensus with regard to detail and readability. ^-^ Atomic putty? Rien! 19:51, 13 February 2023 (UTC)

I also agree with Chetvorno. My particular concern is the lede paragraph of technical, or merely semi-technical articles. All too often Wikipedia writers leap instantly into textbook mode in the opening sentences, as if readers could understand arcane jargon, calculus or otherwise advanced mathematics. Such practice violates multiple policies and guidelines that article ledes should be written for the general reader and should not presume the reader is familiar with a technical subject. The "Bessel function" lede that Chetvorno showed is a very good example. When I do a Google search for something, I want a brief comprehensible summary of an unfamiliar word or concept. But frequently in Google results, I'm confronted with a blurb like Bessel function, and I will do exactly what Chetvorno did--I'll look for the Britannica version, because the Wikipedia introduction, though probably accurate, is nevertheless impenetrable, and therefore useless for my purpose. I also oppose the practice, in the lede, of linking jargon to separate articles. I added text to this Guideline to say that "Terminology in the lead section should be understandable on sight to general readers". Loading up a lede with linked terminology forces readers unfamiliar to stop and start multiple times as they hover or click on the terms, when all they wanted was an accessible summary of the topic which they could read uninterrupted. I don't object when editors include advanced technical material in the body of an article, but doing so in the lede violates policy and is a disservice to readers that should be avoided. DonFB (talk) 11:46, 14 February 2023 (UTC)

@DonFB: Thanks for the addition to the article. I have no objection to a lot of links in the lede, as long as it is not overly dependent on links: it should have brief explanations in ordinary language of the jargon used.

I absolutely agree with you about the confusing ledes in our technical articles. They are often ridiculously abstract and esoteric, when they are the part of the article that should be most widely understandable. I have rewritten dozens of ledes to be clearer. I think what happens is technically-minded people progressively expand the definition in the lede to be more abstract and cover more special cases, borderline cases and fields, until the definition becomes completely incomprehensible to ordinary readers. The ironic thing is that it is usually possible to incorporate the advanced stuff they want in the lede and still have it be adequately comprehensible to general readers, using ordinary good writing techniques. Most technically-educated Wikipedia editors are used to writing only for others in their specialty. Writing an encyclopedia requires a slightly different style of writing, but one which any educated person can do. Our editors just don't want to. --Chetvorno^TALK 21:01, 15 May 2023 (UTC)

I prefer to see no linked jargon in a lead, although I recognize that it is possible to show jargon with a useful parenthetical definition. However, I want to see such practice held to a bare minimum. It's also reasonable to link from an ordinary word which has special meaning in the context. An example is the link I made in the Tidal Locking lead from the word "variablity". Originally, "libration" appeared in the lead as a link with no parenthetical explanation, an example of exactly what not to do (link only from jargon, with no other help). Recently, I took a somewhat novel approach to making the case for rewriting a jargon-filled lead in the Femur article. The result was a successful revision with no objections and a small followup tweak by another editor. See the Talk topics beginning with Turgid Intro and the next two headings; note the (tl;dr) collapsed Virtual Discussion. DonFB (talk) 04:36, 19 May 2023 (UTC)

Total rewrite attempt

In a sweeping set of changes, CactiStaccingCrane rewrote, in a substantive not copy-editing way, nearly everything in this guideline, and that is of course not how guideline change happens. Each substantive proposed change to the guidance and its meaning should be individually discussed and consensus sought for it, as even seemingly trivial changes to guidelines and policies can affect thousands, even potentially millions, of pages and their content.  — SMcCandlish ☏ ¢ 😼  19:43, 17 October 2023 (UTC)

PS: For the record, I dispute that many of these changes were improvements. Many of them are clumsily, even misleadingly worded, and much of the material is rather emotive and laced with superlatives and over-broad or exaggeratory statements. Perhaps CactiStaccingCrane should consider writing a user essay on this subject to express their heated opinions.  — SMcCandlish ☏ ¢ 😼  19:48, 17 October 2023 (UTC)

I think a good rule of thumb when editing guidelines might be: "If you're thinking about/trying to remedy particular editors' particularized classes of mistakes, you shouldn't be writing a guideline right now". Remsense聊 20:02, 17 October 2023 (UTC)

@Remsense Then what should I do instead then? Isn't a guideline all about trying to do just that? CactiStaccingCrane (talk) 17:59, 21 October 2023 (UTC)

i would disagree with this actually, a guideline written in language as general as possible is preferable, if you're targeting specific editors, that's a tone much more suited to an essay imo Remsense聊 19:01, 21 October 2023 (UTC)

Thanks @SMcCandlish for the revert. I do think it's worth making changes to this guideline though (with discussion), especially to its "lead" section, which doesn't do a great job introducing or summarizing the rest of the page, in my opinion. I'm not sure quite the right tone we should adopt in this kind of guideline, but I somewhat liked Cacti's idea of boldly leading with an emphasis on readability. I really dislike the current sentence, "When adding content and creating new articles, an encyclopedic style with a formal tone is important.", which seems vague, passive, and generally weak. The current mention of "essay-like, argumentative, or opinionated writing" seems somewhat off topic; the problem this guideline is trying to address is overly technical writing, not overly informal or opinionated writing. Etc. –jacobolus (t) 20:05, 17 October 2023 (UTC)

Aye, 'encyclopedic' and 'formal' seem a bit like tautologies. There's some way to phrase that, even in the lead, that's actively helpful. Remsense聊 20:10, 17 October 2023 (UTC)

I agree that CactiStaccingCrane's edit/rewrite was excessive. Also agree with Jacobolus about the off-topic tone in some wording in the opening section. DonFB (talk) 20:21, 17 October 2023 (UTC)

Sure. I actually thought about restoring a copyedited version of some of CactiStaccingCranes lead changes, but I don't want to be acting unilaterally while complaining of someone acting unilaterally.  — SMcCandlish ☏ ¢ 😼  20:29, 17 October 2023 (UTC)

How about this: Wikipedia articles should be written for the widest possible general audience that the subject matter of those articles will allow. Wikipedia serves readers with a diverse range of backgrounds and covers subjects from the everyday to the arcane. Some articles will naturally be targeted to specialists, while others need to be comprehensible by a wider population, and it can happen that a single article should provide value both for novices and for experts. This affects how we organize articles. The introduction of an article should ideally be comprehensible to a broad readership. When organizing the sections that follow the introduction, it is typically a good idea to put the least technical part of an article first. It can be helpful to consider the stage in a student's education when they are introduced to a subject, and to write with an earlier stage in mind. XOR'easter (talk) 02:14, 18 October 2023 (UTC)

Well-expressed. I would differ, though, on the matter of "targeted". Certain subjects are highly technical, and the article text will reflect as much. I don't think targeting is needed, per se. The text of any article should be written to be as accessible as possible. My overriding concern is article lead sections, excerpts of which appear in Google search results. As a reader and seeker of information, I am all-too-often disappointed and annoyed when I see jargon-laden or needlessly dense text in those results. DonFB (talk) 02:36, 18 October 2023 (UTC)

How about, "Some articles will naturally be mostly of interest to specialists"? XOR'easter (talk) 03:03, 18 October 2023 (UTC)

Here's my take (anyone rewriting this page should feel free to chop any bits you like):

Wikipedia articles should be written for the widest possible audience.

As a free encyclopedia with the goal of democratizing knowledge, Wikipedia serves readers with a wide range in background, preparation, interests, and goals. Even for articles about the most technically demanding subjects, these readers include not only subject experts but also students and curious laypeople. While upholding the goals of accuracy, neutrality, and full coverage of the most important aspects of a topic, every effort should be made to also render articles accessible and pleasant to read for less-prepared readers.

It is especially important to make the lead section understandable using plain language, but it can be helpful more generally to begin with more common and accessible subtopics, and proceed later to those requiring advanced knowledge or addressing niche specialties.

Articles should be written in encyclopedic style, but this differs from the spare and technically precise style found in scholarly monographs and peer-reviewed papers aimed at specialists. Articles should stay on topic without twisting the truth or telling "lies-to-children", but they should also be self contained when possible, and should not take prerequisite knowledge for granted or gratuitously use unexplained jargon or advanced technical notation: shortcuts which save time and effort for experts can be barriers to the uninitiated.

–jacobolus (t) 03:07, 18 October 2023 (UTC)

I am generally happy with that. XOR'easter (talk) 03:15, 18 October 2023 (UTC)

Generally works for me, but it could use some trimming for concision. E.g. drop "with the goal of democratizing knowledge", "not only subject experts but also", "but it can be helpful more generally to", etc. There's some redundancy here and there; "proceed later to" → "proceed to". However, the fact that WP has "the widest possible general audience", in XOR's original, is valuable, and a point we don't make frequently enough.  — SMcCandlish ☏ ¢ 😼  08:05, 18 October 2023 (UTC)

I don't have any objections to Jacobolus' suggested text. I'm not sure, though, where in the Guideline it would be used, as it seems to reiterate points already present in the current version. My preoccupation with the lead section of an article, to be clear, is not merely due to my own preferences, but is because that's the part of an article that all readers will see, and may be the only part they see. We owe it to them to make the lead readily comprehensible, even for highly technical subjects, to say nothing of subjects that may be merely semi-technical. I'm frankly not overly concerned about highly technical descriptions deep inside some articles. But I want the Introduction (lead) of every article to be clear, free of jargon, and not dependent on links to other articles for meaning. DonFB (talk) 18:45, 18 October 2023 (UTC)

Does the current § Lead section section cover it, or is there more (or something different) we should say? One of CactiStaccingCrane's ideas was to include some examples. Is that something we should try to do here (if so does anyone have recommendations of good examples to look at), or are they a distraction? –jacobolus (t) 19:13, 18 October 2023 (UTC)

Disclosure: the wording that terminology should be recognizable "on sight" is my contribution. I'm not fond of the last sentence in the section, which undercuts the emphasis I favor, but it was retained in a previous discussion. I'm not averse to including an example; elsewhere, I have pointed to revision of the lead of Tidal locking, which I initiated. (Before revisions: https://en.m.wikipedia.org/w/index.php?title=Tidal_locking&oldid=904381140)

DonFB (talk) 19:55, 18 October 2023 (UTC)

I'm happy with the section as is. The last sentence accurately describes how highly technical topics are addressed on Wikipedia, so there is nothing wrong with it. The "on sight" claim may actually be a bit too much; we routinely link potentially unfamiliar keywords in the lead section, and as said elsewhere we do not use a "lies-to-children" approach to dumb down the material. There's a fine line between doing that an avoiding unnecessary jargon. Some jargon is actually necessary, and just has to be made explicable in-context one way or another.  — SMcCandlish ☏ ¢ 😼  20:35, 18 October 2023 (UTC)

"On sight" is, indeed, rather rigorous, but it can be considered aspirational--a reminder that links should be used to supplement info in the lead, not to explain a term that may unfamiliar or incomprehensible, or both. When I read an introduction, I want to stay on the page, not chase after multiple linked terms to figure out what the text means--I believe that's probably the preference of most readers. Such terms appear too often in lead sections, because editors did not endeavor to explain or define the term in plain English, but simply defaulted to language found in textbooks or technical journals with which they're familiar--language that's often not appropriate, in my view, for the introductory section of an encyclopedia article. You said, "we routinely link potentially unfamiliar keywords in the lead section," which is true and is both symptom and cause of problems evident in too many leads. I think the practice should be much less frequent, rather than routine. Yes, we shouldn't dumb down the text, but the Guideline does suggest writing down one level when appropriate. I think a common reason the problem happens is because people want to put in information they know without much regard whether the text helps general readers or befuddles them. One approach, when possible, is to link a plain English term to an article about the technical term or concept,* or put the linked technical term in parentheses (though I am not a fan of parenthetical stage whispers in lead sections).

• An example, from the aforementioned Tidal Locking, was use in the Intro of "variability", linked to the article Libration.

DonFB (talk) 23:48, 18 October 2023 (UTC)

Guidelines and policies generally don't work where they contain aspirational language that can't really be concretized; it simply provides levers for disruptive wikiawyering.  — SMcCandlish ☏ ¢ 😼  00:33, 19 October 2023 (UTC)

That is why we should not encapsulate a complete definition in a sentence. In the case of tidal-locking:

Tidal locking between a pair of co-orbiting astronomical bodies occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where a tidally locked body possesses synchronous rotation, the object takes just as long to rotate around its own axis as it does to revolve around its partner.

Why don't abstractize the idea of "spin–orbit resonance" in the first sentence and explain what is it in the second sentence?

Tidal locking occurs when one astronomical body has a fixed resonance ratio between its rotational and orbital period. The most common resonance ratio is 1:1, meaning that the tidally locked body completes one rotation around its own axis for every revolution around the parent body. This specific phenomenon is also called synchronous rotation.

The first sentence can serve as a formal definition for the topic. It might have a lot of jargon ("resonance ratio", "rotational period", "orbital period") but it is ok when a newcomer to the topic just need to read more to understand what these terms meant. CactiStaccingCrane (talk) 13:37, 21 October 2023 (UTC)

Many highly technical topics on Wikipedia would benefit from putting (significantly) more effort into accessibility for a wider audience. It's not always possible to eliminate jargon, formulas, etc., but especially for basic topics of wide interest, we should try try try.

As a concrete example, I just stopped by Computer programming, and wow what a mess the lead is there. –jacobolus (t) 15:38, 19 October 2023 (UTC)

I tried doing something with the first paragraph, at least. XOR'easter (talk) 23:12, 19 October 2023 (UTC)

Please feel free to write something more concise! (With or without copying bits from my proposed text above.) –jacobolus (t) 19:12, 18 October 2023 (UTC)

Oh, and I did write a user essay of my own that I intended to be a one-stop shop for physics and math people wanting to get started on Wikipedia (and for Wikipedia generalists who have to deal with mathematicians and physicists showing up). XOR'easter (talk) 02:30, 18 October 2023 (UTC)

Your essay is the main motivation I want to rewrite this page. When I asked what makes people hates Wikipedia, almost all said that Wikipedia's article is so so unreadable. It triggers me a lot that we are spending all of our time verifying the facts, copyediting, debating about inane things when we are spending so little time actually making the text understandable to the lay reader. If the lay reader could not even understand what are we talking about and expert readers are just skimming Wiki articles for citations, then we are writing encyclopedic articles for no one really. Too many articles start with false balance filler:

Criticism of Israel is a subject of journalistic and scholarly commentary and research within the scope of international relations theory, expressed in terms of political science)

or punch the reader eyes with jargons for the sake of technical accuracy:

Pharmacology is a branch of medicine, biology, and pharmaceutical sciences concerned with drug or medication action, where a drug may be defined as any artificial, natural, or endogenous (from within the body) molecule which exerts a biochemical or physiological effect on the cell, tissue, organ, or organism (sometimes the word pharmacon is used as a term to encompass these endogenous and exogenous bioactive species).

Yes, I do agree that my rewrite is a bit opinionated. But I want to show in the how-to very clear that readability should be our number 1 priority and why it trumps all other metrics of quality. In my opinion, how-tos needs clear instructions and concrete examples on what to do, and they can be a bit opinionated because it is not an encyclopedic article. CactiStaccingCrane (talk) 13:19, 21 October 2023 (UTC)

Perhaps it would be better to add an additional essay that is more explicitly "how to" / more explicitly opinionated; I agree with @SMcCandlish that a page called a "guideline" is prone to being mined for "levers for disruptive wikilawyering". –jacobolus (t) 15:29, 21 October 2023 (UTC)

[ below comment rethreaded after extracting tangential idea –jacobolus ]

However, I still do think that this guide should be made more understandable and be more nuanced. The guideline/policy status is pretty arbitrary, we should not follow instructions in pages with template {{guidelines}} and {{policy}} to the letter anyways, because that is against the spirit of the rule. If a person is Wikilawyering then we should get ban of them and not trying to bend our guideline/policy make it needlessly complicated. CactiStaccingCrane (talk) 16:48, 21 October 2023 (UTC)

Sounds nice in theory, but basically never happens. People can wikilawyer the living F out of everyone for literally years in this sphere before ANI, ArbCom, or AE will do anything about it. It is very close to impossible to get anyone topic-banned from doing disruptive things that have anything to do with style or article titles. Anything in a guideline that has to do with writing style has to be very, very carefully crafted to avoid providing wikilawyering leverage. PS: I really don't know why this is categorized as an "editing guideline" instead of part of MoS, since it's entirely about the style of writing technical articles.  — SMcCandlish ☏ ¢ 😼  21:33, 21 October 2023 (UTC)

Social organizing efforts

Alternately, instead of guideline pages, perhaps it would be better to try to start some kind of WikiProject type social group targeted toward lay accessibility of technical content, which could try to encourage / organize collaboration specifically around roaming around locating and improving gratuitously inaccessible pages (especially lead sections), explicitly reviewing technical articles for accessibility, perhaps starting with Vital articles, and/or working with existing WikiProjects related to technical subjects to help them focus on the same. –jacobolus (t) 15:35, 21 October 2023 (UTC)

That's a great idea. CactiStaccingCrane (talk) 16:41, 21 October 2023 (UTC)

The ambitious (but perhaps necessary) thing would be to recruit new editors who are enthusiastic about this kind of improvement. XOR'easter (talk) 17:38, 21 October 2023 (UTC)

I also think this idea has merit. I have mulled creating a Signpost article on the topic, but have not summoned the necessary energy. A Project would certainly be more systematic and seems as though it would gain more attention. A project also has the potential of marshaling forces needed to counter the likely resistance among technically-educated editors who know their stuff, but don't always know how or care to translate their knowledge into comprehensible prose in the Introduction of an article. DonFB (talk) 06:09, 24 October 2023 (UTC)

@Jacobolus, with my Wikipedia:WikiProject Council hat on, I implore you not to start another group (yet). It's far better to join an existing group like Wikipedia:WikiProject Guild of Copy Editors, or, if you can't find a relevant one, to gather up all of your best friends and WP:REVIVE one. The important point is that you really do have to have at least half a dozen editors involved, or the group won't be able to sustain itself. If it's just you and maybe one or two other editors, then the infrastructure (e.g., around tagging articles and describing the group's interest areas) will swamp your actual goal. WhatamIdoing (talk) 01:03, 31 October 2023 (UTC)

I certainly don't want to spend a lot of effort on organizing. Some kind of complicated new bureaucratic system "tagging articles" etc. sounds like a pain. Mostly I just don't know any current page(s) or social structure for people discussing or working on this deliberately. So if such a page doesn't exist, it might be worth making one. But if there are existing relevant pages, leaning on those certainly might be better. My general impression is that the typical WikiProject is over-focused on leaving its tags and ratings around, and not focused enough on discussion and concrete collaboration. YMMV. –jacobolus (t) 01:35, 31 October 2023 (UTC)

New WikiProjects, in particular, tend to fall into that trap.

Dhtwiki could probably tell us whether GOCE would be willing to host such efforts. There are a few thousand pages in Category:Wikipedia articles that are too technical. These 15 articles are tagged for general copyediting (=GOCE's main concern) as well as jargon, so that might be an easy place to start. WhatamIdoing (talk) 01:59, 31 October 2023 (UTC)

I myself would be against suddenly adding potentially thousands of articles to our load, as the GOCE has a year-long backlog already, unless doing so resulted in a flood of new copy editors to our ranks that would more than make up for the increased burden. But I don't speak for the guild, and a talk-page discussion there might yield other opinions. The articles marked as "too technical" are often in need of general copy editing even if not marked as such. So, there's definitely an overlap between our aims.

I can't be sure what constitutes a "gratuitously inaccessible" article, but this quote, at 36 Signal Regiment (Canada), is a likely candidate: The role of 36 Signal Regiment is to force generate combat capable signallers and Communication Information Service (CIS) capabilities to enable command and control in support of Canadian Forces domestic and expeditionary operations. Some articles have the explanatory material but it needs to be made clear. You would expect an article named Ahaetulla prasina to contain recondite terms. However, the attempt to explain "preocular" there ...preocular scale in front of the eye... adds confusion for not having the explanatory text set off. Then there's the attempt to explain by linking to other articles, some of which seem more technical, without being marked as such (compare Transactional memory, linked from Advanced Synchronization Facility), which suggests that either the former article is appropriately technical (I belive in the possibility of that being the case) or that people just haven't gotten around to tagging it yet. Dhtwiki (talk) 07:46, 31 October 2023 (UTC) (edited 05:41, 11 November 2023 (UTC))

More examples (they are legion!) of knowledgeable editors simply making no attempt to convert jargon/bureaucratese/tech manual lingo into ordinary English words and syntax that would be recognizable to non-specialist readers. Their lack of effort is not malign; they simply don't have the concept of writing for a general non-technical readership—especially in the opening sentence or two—and thus don't do it. Jargon terms are linked to other articles, in which the ledes are laden with more jargon, linked to still more jargony articles...a reader can easily click/tap three, four or more levels deep with no guarantee of clarity, but only an excursion into a wilderness of techno-babble. DonFB (talk) 08:17, 31 October 2023 (UTC)

I agree with everything DonFB says here. However I don't think the answer is to prohibit Wikilinks in the lead, as he advocated. Discouraging links in the lead is not going to force jargon-obsessed technical editors to write plain-language explanations for general readers, believe me.

I also don't think another WikiProject is the answer. We should rewrite the Introduction guideline here to strengthen the need for plain language explanation of jargon. I would be willing to bet that 95% of the visitors to most technical articles don't read beyond the introduction. --Chetvorno^TALK 21:13, 8 November 2023 (UTC)

I would be open to strengthening the text in Wikipedia:Make technical articles understandable#The lead section somehow, though to me it seems rather clear already. Do you have thoughts for new phrasing that could augment or replace what currently stands there? XOR'easter (talk) 21:36, 8 November 2023 (UTC)

95% of the visitors to most technical articles don't read beyond the introduction. – My impression is that this is true of all articles, not just technical articles. Which is why ideally the lead section should be a reasonable summary as well as broadly accessible, especially for articles about fundamental concepts. –jacobolus (t) 21:47, 8 November 2023 (UTC)

Quite right, and that's why my focus has consistently been on lede sections; I don't fret about highly technical text/jargon/formulae/etc within the body of articles. It's to be expected that material there can be challenging. But most people don't get that far, and we need to serve them much better in article intros. DonFB (talk) 22:52, 8 November 2023 (UTC)

It may be true that most jargon obsessed editors won't desist, but I think other editors should be encouraged and supported by Policy/Guideline to fix problematic ledes. To me, the biggest problem is unfamiliar or unrecognizable jargon, so discouraging its use would seem to be the approach to take. I don't object to links from things like names of places, events, or people; the basic meaning of the text does not depend on knowing their details; those links are a courtesy to readers who want to know more. DonFB (talk) 23:22, 8 November 2023 (UTC)

The Introduction section already discourages jargon. But I think most editors are going to say it is impossible to write introductions to technical articles without using the appropriate terminology (i.e. jargon). That's my opinion too. So the Introduction section should also strongly suggest that jargon terms that must be used be accompanied by brief plain-language definitions. --Chetvorno^TALK 01:32, 9 November 2023 (UTC)

Maybe what that section of the guideline needs is an example or two. XOR'easter (talk) 05:56, 9 November 2023 (UTC)

Should the section on "Introduction to" articles be deprecated (removed)?

I cannot locate any discussion which resulted in consensus to allow their creation. The section was discussed only once in the past (Wikipedia_talk:Make_technical_articles_understandable/Archive_1#"Introduction"_articles). That section is clearly in disagreement with Wikipedia:REDUNDANTFORK policy. And even our section states "the number of separate introductory articles should be kept to a minimum". Well, 0 is the most miminal number we can get. _{Piotr Konieczny aka Prokonsul Piotrus| reply here} 03:29, 8 November 2023 (UTC)

I don't think there's any harm in having a relatively small number of "Intro To" articles. My thought, however, is that the accessible language in the lede section of such articles could just as easily be used as the lede text in the corresponding regular articles, giving the lie, as it were, to the idea that such subjects are too complex or specialized to be summarized in plain English. DonFB (talk) 06:29, 8 November 2023 (UTC)

You can judge for yourself by examining the examples: Special:AllPages/Introduction to. Most have eventually been merged into the main page about the topic. Others are still separate: general relativity, the mathematics of general relativity, electromagnetism, entropy, evolution, genetics, viruses, quantum mechanics, systolic geometry, M-theory, .... If you think that any of those can be merged into the more technical main article without sacrificing precision or clarity for a technical audience, you are welcome to propose it on the relevant talk pages. –jacobolus (t) 06:52, 8 November 2023 (UTC)

I recently proposed one for deletion as a fork, only to be told that their separate existence is allowed by this policy. Hence I think we need to start at the root of the problem. Note that I am not opposed to mergers - DonFB makes good point that some simpler language would improve the main articles (in fact, I am familiar with many scholarly studies who say that Wikipedia's biggest problem is readability and such). In fact, effort to make main articles readable should go to the main articles, not those mostly forgotten and hard to find by readers 'introduction to' articles. _{Piotr Konieczny aka Prokonsul Piotrus| reply here} 06:55, 8 November 2023 (UTC)

Proposing for deletion seems like a drastic and somewhat hostile first step. I think you should start by making a discussion on the talk page of the relevant "introduction to" page and the relevant main article for the same subject, and maybe directly ping the top few authors of the introduction page so they hopefully notice the conversation. If you want to get rid of these articles altogether, perhaps try opening a discussion somewhere like Wikipedia talk:WikiProject Physics, which I would expect to get more readers than this page. –jacobolus (t) 07:03, 8 November 2023 (UTC)

Yes, it would be drastic/hostile to some, but more to our point here it would be actually destructive in costing us good summary material we can use. I would suggest following WP:PM process, and tagging them all for merger into their respective main articles, and opening a discussion (on the merge-to article's talk page, not the merge-from article's talk page) for each, mentioning in particular that the more accessible introductory wording at the merge-from page should be used to improve the readability of the main article's lead (otherwise people will just say that the intro article covers the same material as the main one and thus there is nothing to merge). I agree with the OP point that there is no consensus to have this guideline suggesting the creation of such articles in the first place.  — SMcCandlish ☏ ¢ 😼  14:30, 8 November 2023 (UTC)

Please don't "tag them all for merger". Go start a conversation instead of trying to browbeat people with bureaucratic processes and eyesore banners. Edit: and please do one at a time instead of trying to do this in mass. Note that at least Introduction to viruses is a featured article, so people are likely to be resistant to breaking it based on one person's personal preference. –jacobolus (t) 14:48, 8 November 2023 (UTC)

Why do you have to turn everything into a WP:BATTLEGROUND even when people are mostly agreeing with you? Your attitude on page after page is out-of-the-blue blowhard hostility like this, directed at anyone who diverges even slightly from your own ideas or preferences, and it's completely corrosive to consensus formation, in every discussion in which I encounter you.

We have a process for doing mergers. That process ensures that they are handled consistently and that notices of them appear in a centralized listing for community review. If you don't like merger process (which, guess what, ensures that the conversations you want to see are in fact opened instead of someone proposing a merge a with a tag, doing no discussion, and then making the merge as if they have consensus), then don't participate in it and go find something else to do.  — SMcCandlish ☏ ¢ 😼  15:42, 8 November 2023 (UTC)

Dude, WTF is your problem? We were all having a polite conversation here. Please keep your gratuitous insults to yourself. –jacobolus (t) 15:52, 8 November 2023 (UTC)

Yes, we were having a polite conversation until you turned it on its ear with a rant about browbeating and bureaucracy and eyesores after someone simply recommended actual standard practice.

Back to the substance of the matter: There are multiple ways to approach this, but the most practical appears to me to be to identify the intro articles that are least useful as stand-alone articles and propose those mergers first. One article with a title like this being an FA is an unusual outlier, and might need to be approached differently. It might even turn out in the long run that there will emerge a consensus to keep some articles like this separate, but we'll never know until we start going through merge discussions and seeing how they turn out and why.  — SMcCandlish ☏ ¢ 😼  16:07, 8 November 2023 (UTC)

If you start by threatening to smash people's articles apart without even bothering to figure out why they exist in the first place or what people like about them, you'll get a lot of resistance, probably even more than the resistance you'll get by diving into other people's conversations and slinging off-topic insults. –jacobolus (t) 16:33, 8 November 2023 (UTC)

Just more battlegroundy ranting. Did you have something constructive to input with regard to this set of articles and how to go about opening the discussions we both clearly want to happen (again, it is not constructive to go off on people who don't actually disagree with you), since you don't find my idea to your liking?  — SMcCandlish ☏ ¢ 😼  17:25, 8 November 2023 (UTC)

Please desist now. Your insults are increasingly tiresome.

both clearly want to happen – No, I think starting aggressive conversations about this is a waste of time, and I personally don't care one way or the other about these "introduction" articles. I was merely advising the user:Piotrus to take a measured, open-minded, and consensus-seeking approach to whatever conversations they try to start, rather than trying to pick fights. –jacobolus (t) 17:41, 8 November 2023 (UTC)

And I've advised engaging in the actually prescribed process (which is not "aggressive" in any way, but designed to prevent problems like doing unilateral merges) for opening such consensus-seeking discussions about this sort of case in the first place, about which you've picked an aggressive fight right from the start. I trust Piotrus will figure out what to do. I won't respond to you further on this because I can't see anything constructive coming from it.  — SMcCandlish ☏ ¢ 😼  17:53, 8 November 2023 (UTC)

Tacking a "I threaten to slash your article up and delete its current page in X days unless you mount an immediate defense" banner across the top of pages is a hostile and incredibly obnoxious first step in dealing with work that other people put a lot of time and effort into. It's not an appropriate use of the merge banners, which are intended for cases where e.g. a few short and mediocre articles duplicate the same content. It would cause much less drama to start a gentle conversation on the talk page (probably of the main article rather than the "introduction to" article, but with a link from both) in a single one of these cases, and explicitly ping whichever editors put the bulk of the work int "introduction to..." article and maybe also some of the top contributors to the main article, providing whatever arguments or evidence for why you think readers would benefit from having a more accessible "main" page and why the content from the "introduction" article would fit well there, and then sit back and see what people have to say when they aren't under threat. For the most convincing proposal, do the content merge yourself and put it in user space somewhere, so that other contributors have something concrete to compare.

Nobody is trying to fight you buddy. Please cut the crap. –jacobolus (t) 18:11, 8 November 2023 (UTC)

I'm trying to follow your discussion here, but I'm not sure what the conflict is. Is it to delete the "Introduction to..." section on this page? or actually propose merging all "Introduction to..." articles? Maybe we could ask for outside comment? --Chetvorno^TALK 18:29, 8 November 2023 (UTC)

@Chetvorno: Looking into this a bit more, Piotrus made a proposed deletion of Introduction to M-theory with a somewhat unfriendly proposal at Wikipedia:Articles for deletion/Introduction to M-theory (2nd nomination). Most of the folks at that discussion were opposed to the deletion, but folks on both sides of the discussion pointed to this Wikipedia:Make technical articles understandable guideline as a justification. I think Piotrus's idea here is that if they can change the text here, then that will give them an argument to leverage in future similar deletion discussions. It would have been nice if this discussion started with that context though. –jacobolus (t) 18:46, 8 November 2023 (UTC)

More or less. Note that it is perfectly fine to have a deletion discuussion end in a merge verdict, and it takes usually less time and attracts more (and less partisan) comments than many merge discussions do. _{Piotr Konieczny aka Prokonsul Piotrus| reply here} 02:30, 9 November 2023 (UTC)

"Taking less time" doesn't seem like a very important criterion to me. The goal should be to get to a result which leaves people satisfied (including whoever put the work into the articles you want to delete/merge) and best helps readers of the encyclopedia to find the information they are looking for and best helps the Wikipedia project as a whole and the specific articles in question to flourish. Not just to most efficiently enforce your own personal preferences. –jacobolus (t) 05:59, 9 November 2023 (UTC)

WP:BEFORE says to consider merging or redirecting to an existing article before starting a deletion discussion, and WP:AFDHOWTO says to Use Wikipedia:Proposed mergers for discussion of mergers. I think starting an AfD when the nominator clearly has merging in mind to begin with is somewhat frowned upon. It can come across as using the wrong venue, and it can seem more confrontational than necessary.

In the present case, we're not talking about paid promotions, attack pages about living people, or any of the other kinds of material that we really should remove as quickly as possible. At worst, the pages in question here are cruft. The time pressure for dealing with such things is comparatively low. XOR'easter (talk) 06:29, 9 November 2023 (UTC)

There's nothing wrong with the advice currently given in the section in question. Really. It's fine. It doesn't conflict with any policies. WP:REDUNDANTFORK is a guideline, not a policy; but it doesn't conflict with that, either. A less technical introduction to a topic is not redundant with a fully technical treatment of it. They are not about the exact same thing: one is about the heavy-duty math, and the other is about the analogies invented to convey something about the heavy-duty math. Having an "Introduction to..." article is morally no different from taking an overlong "History" section in an article and spinning it off into its own "History of..." page. Whether an "Introduction to..." article ought to exist for any given topic is a thing we can decide on a case-by-case basis. For example, when it comes to pop science about the frontiers of physics, there is a vast amount of technical literature and a big pile of popularized writing. That makes the existence of a separate "Introduction to..." arguably warranted. Moreover, the 0 is the most miminal number we can get remark is an argument that presumes its own conclusion. If "Introduction to..." articles are helpful in any circumstance, then having zero of them would not be the minimal number, but an insufficient number. XOR'easter (talk) 21:09, 8 November 2023 (UTC)

I largely agree with XOR'easter on taking these case by case.
One way to look at it is this: Most articles of sufficiently length have a lead that is a summary of the longer article. However, if the lead can't capture the "introduction to" aspect due to the level of understanding required to introduce the topic, and the article would benefit from a "middle level" of summary between lead and full article, one way to solve that problem is with an "Introduction to" style article.
Another way to look at this is as the general/specialized idea from the first pillar. In some cases the article that would be in a specialist encyclopedia differs vastly from the one that would exist in a general encyclopedia, and that too might sometimes be solved by an "Introduction to" style article. —siroχo 05:50, 9 November 2023 (UTC)

How are "Introduction to" articles different from articles over at the Simple English Wikipedia about the root subject?    — The Transhumanist   00:38, 13 November 2023 (UTC)

The most obvious difference is that they are not written in "Simple English", and that most of the Simple English articles never saw much serious effort put into them. But there are only a handful of "introduction to" articles, so you can easily compare for yourself the English wiki article, "intro" article, and "simple English" article: general relativity (intro, simple); mathematics of general relativity (intro); electromagnetism (intro, simple); entropy (intro, simple); evolution (intro, simple); genetics (intro, simple); virus (intro, simple); quantum mechanics (intro, simple); systolic geometry (intro); M-theory (intro, simple). –jacobolus (t) 02:15, 13 November 2023 (UTC)

The very fact that there are so few of them is a strong indicator that the Wikipedia community does not consider them a good idea. That they are confined to a small number of topics strongly suggests they are the product of a small handful of editors who decided on their own they were a good idea. I'm reminded of some other boondoggles of this sort, like that spate of creating unmaintainable thousands of portals for too-narrow topics, which later got mass deleted. This "Introduction to foo" series seems to be loosely inspired by the "Index of foo articles" series, but lacking the community buy-in to develop it that the index series has. This, plus the fact that the easier-reading language in at least several of the introduction articles would be lead improvements at main articles, is why I like the idea of merging them into main articles.  — SMcCandlish ☏ ¢ 😼  05:12, 13 November 2023 (UTC)

If you think any one of these in particular would be better merged, nobody's stopping you from putting in the work to write the merged article and then try to convince the rest of "the Wikipedia community" that your version is better. –jacobolus (t) 05:36, 13 November 2023 (UTC)

For someone that professes to no longer want to be in an argument with me, you sure seem to expend a lot of energy trying to bait one. This is a discussion, for everyone one; it's not an "I don't like you, so buzz off until you do busywork to personally satsify me (so I can just crap all over it anyway just to stick it to you)" personal social media page of yours.  — SMcCandlish ☏ ¢ 😼  06:49, 13 November 2023 (UTC)

Your proposal is more or less "I don't like this so someone else should go fix it for me". My proposal is: why don't you try to put your own effort where your mouth is? I'm not just trying to harass you; without actually trying to do this, I think you are entirely misunderstanding what these articles are trying to accomplish and grossly underestimating how much work it would take to re-organize them a different way. The only way to get past that is to actually meaningfully engage with the content, rather than having handwaving meta-discussions from the sideline somewhere. –jacobolus (t) 17:44, 13 November 2023 (UTC)

Also, I never said I didn't like you, or that you should "buzz off", or that anyone should "crap" on anything, and nobody wants to "stick it" to you. I earlier asked you what your problem was when you launched a heap of gratuitous off-topic insults at me. I still don't really understand what your problem is as you continue with the hostile and insulting language. I would again urge you to stop. It's distracting to everyone here, counterproductive, and tiresome. –jacobolus (t) 17:52, 13 November 2023 (UTC)

Lots more fight-bait, that I will resist. "I don't like this so someone else should go fix it for me" bears no resemblance to anything I've said. What we have is largely redundant articles that are disused by our readers and do not form a coherent set or category, a consistent editorial approach, but which nevertheless have very valuable content that is often better than what is in main articles (or at least could be used as high-level summary in leads, with more detailed/jargony presentations moved down into article bodies; there's not a binary false dilemma here). My "proposal" is that we need to have a discussion to decide what to do with these articles and more importantly the content in them (either as a class, or mostly as a class with some special cases). I happen to lean toward merging them into main articles on the same topic, for reasoning I've already explained quite clearly, and which you have not substantively addressed. But for all I know, we'd instead emerge with a consensus that such articles are ideal and we need more of them, in a systematic way. Hard to be sure until the discussion proceeds without being trainwrecked.

Lots of things at WP are hard; that doesn't mean we don't do them when they're the sensible thing to do. I'm entirely aware how difficult a good-quality merge (or split) is with complex material, as I perform them in topics in which I have significant competence. I'm perfectly willing to help in some of these cases, but I'm not certain my attempts to help would be useful to or wanted by people who are actual subject-matter experts in these specialties, and running off to do an amateurish job at one of them as a "demo" would probably do more harm than good. (In the more complex topics at which I am highly competent, I can imagine the poor results of someone "casual" in that subject trying to do merge or split operations, and the picture isn't pretty.) Your suggestion that I should just go off and do it all myself comes off as silly trolling and an attempt to derail a discussion which may have an outcome that isn't the "do nothing" one you favor. So, no, I will not be entertaining that idea, and I'm not going to respond to further fight-picking in that direction (or, if I can help it, any other ones). Your central premise boils down to the idea that my view is irrelevant (or worse) because I'm not likely the one to get the bulk of the job done. But everyone here – including you – knows that's fallacious. So is the idea that we can't look at content A and content B and imagine them merged without someone actually doing the merge.  — SMcCandlish ☏ ¢ 😼  18:29, 13 November 2023 (UTC)

I'm telling you that these articles are not "largely redundant", which you would quickly see for yourself if you bothered to go look at them. Some of them (maybe all of them) could plausibly be merged, or reorganized and split up some other way, but it's not a priori obvious that the merged article would be an improvement, and abstractly hand-waving about it is thoroughly unconvincing.

My "proposal" is that we need to have a discussion to decide what to do with these articles – and my counter-claim is that this is a naïve discussion doomed to failure until its proponents try to concretely engage with the content.

not certain my attempts to help would be useful to or wanted by people who are actual subject-matter experts in these specialties – in that case, the appropriate thing to do is go start a specific discussion on a particular page and try to convince these experts that this is a good idea in at least one specific case, or recruit one of them to concretely try this out.

Otherwise, the way I'm imagining this discussion to proceed if you get your way is some kind of bureaucratic mandate (if taken to some bigger forum, maybe backed by a drive-by "consensus" of people who don't intend to work on any of the articles in question) that ends up raining down on a bunch of people who never asked for it. I think that would be actively harmful to the project. –jacobolus (t) 18:50, 13 November 2023 (UTC)

Thanks for engaging; this is more substantive. Rather than repeat the same thing in two spots, I'll try addressing this with the quantum mechanics example, in reply to XOR'easter below.  — SMcCandlish ☏ ¢ 😼  21:06, 13 November 2023 (UTC)

I don't think we can take very fact that there are so few of them as an indicator of much anything, really. They are hard to write, and the people with the knowledge to do the job are (in my experience) more inclined to work on niche topics at a higher level. But being a low priority doesn't make them a bad idea or one that the community has rejected. XOR'easter (talk) 17:14, 13 November 2023 (UTC)

Fair enough, but they don't seem to be something the community is taking up. I'm not sure that's a hair worth splitting very far. Maybe more to the point, these articles are not easy to notice and are disused, so they don't seem to be serving their purpose. The material in them is what is of value, and I would think that the argument to merge that material into the main articles on the topic is pretty compelling, both for getting the material in front of more eyeballs and for making the main articles easier for more readers to parse in the first place.  — SMcCandlish ☏ ¢ 😼  17:29, 13 November 2023 (UTC)

I've advocated for plenty of merges in my day, and I have run into a few different highly-technical corners of the encyclopedia where I thought we'd be better off with fewer and larger articles. But at the same time, I believe that some splits are sensible. To revisit an example I mentioned above: Quantum mechanics is a hard subject, for instance, and trying to cover all the twists and turns of its historical development while also explaining the subject as taught today is a really big job. Spinning off History of quantum mechanics while leaving behind a synopsis in the main article makes organizational sense. Of course, the main article gets much more traffic: 1.5 million annual page views versus less than 100,000 [1]. Does that mean we should try attracting more attention to the history spin-off page? Plausibly yes. Does the traffic disparity invalidate the idea of having the spin-off page in the first place? No, I don't think it can. XOR'easter (talk) 18:07, 13 November 2023 (UTC)

Sure, but how does that relate to Introduction to quantum mechanics largely serving the same basic purpose as Quantum mechanics and covering much of the same ground? All of our top-level articles on all subjects are basically encyclopedic introductions to them, with non-introductory drill-downs like History of quantum mechanics, Mathematical formulation of quantum mechanics, Applications of quantum mechanics, Interpretations of quantum mechanics, broken out to split-off articles. Introduction to quantum mechanics reads to me like a better-worded version of some of the material in Quantum mechanics, the latter of which could be improved by using much of the wording in the former, without losing the detail in many of the latter's sections. The former even has a history-of section and applications section, etc., while also breaking some of the more technical aspects into easily digestible sections or subsections. Just seems like a tremendous amount of effort to basically produce a WP:CFORK that in certain ways is superior to what it forked from (though missing a lot), but which would be even better in re-combined form. When I look at other intro-to articles, I'm seeing a similar pattern. But, flipping this around, if we become sure that the intro-to articles are a great idea, then why aren't we doing lots more of them, with a systematic approach to it? It doesn't seem very practical to just do this very, very spottily at a handful of subjects. I'm inclined toward thinking it's either not a good idea, and should result in merges, or that it something that should become a standardized part of our encyclopedic approach, isntead of being a rare and kind or random "mutant". (And, yes, I lean toward the former; I guess that makes me meta:Mergist in some sense, though this isn't really about "major" versus "minor" topics, more like "comprehensive" versus "basic" approaches to how to write core/introductory material in an encyclopedia.)  — SMcCandlish ☏ ¢ 😼  21:06, 13 November 2023 (UTC)

I tried to skim both introduction to quantum mechanics and quantum mechanics with a medium level of care (definitely not a detailed close read), and my strong impression is that these two articles are almost entirely different, serving different audiences with largely different needs. Intro QM is entirely non-mathematical and makes up non-technical pseudo-examples to introduce some of the main concepts which have a lot of prerequisites to tackle as found in even the simplest examples in a college textbook, while QM is full of tensor products of Hilbert spaces, the time evolution of quantum states, commutation relations, Fourier transforms, unitary matrices, Gaussian wave packets, etc. If you try to merge the articles, the intended audience for one of the two is going to end up in trouble: either (a) the intended audience of intro QM is going to be left baffled by an article too full of formulas and advanced concepts for them to follow, or (b) much of the technical content will be stripped out and more expert readers will need to go somewhere else to figure out how to find answers to more technical questions. –jacobolus (t) 22:05, 13 November 2023 (UTC)

To echo the above reply: Quantum mechanics and Introduction to quantum mechanics don't serve the same basic purpose. And as to why we don't have more "Introduction to..." articles? Well, quite possibly we should, but people need to be motivated to do it. I think that improving the main articles on big subjects and judiciously creating less-technical offshoots would both be beneficial. However, the volunteers with the expertise necessary all have a thousand and one other things demanding their time. XOR'easter (talk) 22:34, 13 November 2023 (UTC)

I guess I don't see a problem with writing one paragraph that begins with something like "In simple terms, ..." then gives the non-mathematical analogies, followed by "More technically, ..." and the more proper examples with actual math in them. Readers of both sorts would quickly learn to skip over the parts that don't directly address their needs. I'm left wondering, if these "Intro to" articles are meant to be extra-basic, even more so than our main articles, then why are they at this project instead of at Simple (with whatever wording tweaks would be needed there), or at Wikiversity as part of an intro to science topics course, or at Wikibooks in an e-book form. It's just weird and counterproductive, to me, for en.WP to be hosting competing articles that serve as topical introductions. Maybe that's just too bad and there's nothing to to done for it. But I'm skeptical that this is the only answer the community could come up with.  — SMcCandlish ☏ ¢ 😼  22:51, 13 November 2023 (UTC)

Answering editors objections to making articles more understandable

I was surprised by all the pushback from expert editors against making articles easier to understand in the thread Yes, they are too hard to understand. No, really above. Although most of this stuff is already in the article, maybe it would help to put a list of their objections, and answers, in the guidelines. Here are some --Chetvorno^TALK 06:50, 9 November 2023 (UTC)

• "Some articles are about topics too advanced to make them comprehensible to general readers; it is a waste of time to try"
  Look at the Encyclopedia Britannica entry for the topic: a good encyclopedia writer can explain any topic to general readers. A concept can always be made more comprehensible. And even if the concept can't be fully explained in the introduction, it should include context: What categories does this concept fit in? Does it have any analogies to simpler concepts? What properties does it have? What are some simple examples? Who discovered it? When? What is it used for? Why is it important? This is a large part of what general readers want to know. Context is a major part of understanding. --Chetvorno^TALK 06:50, 9 November 2023 (UTC)

  It is simply not true that there are some topics that can be made comprehensible to general readers, especially without serious violations of our content policies and guidelines. (E.g., Galois cohomology.) Articles should be written in a way that complies with our content policies and guidelines. If no source exists that explains a topic for general readers, then it is typically the case that a Wikipedia article cannot either, without at the very least engaging in original research, and at worst being completely wrong. For articles about very abstract mathematical concepts, often the best "introductory" sources available are the AMS Notices "What is..." columns, written by subject experts for a "general mathematical" audience (i.e., graduate students already working in the area or mathematics PhDs who are not specialists.) That's often the best we can hope for. Tito Omburo (talk) 12:31, 10 November 2023 (UTC)

  A subject of interest primarily to e.g. math PhDs working on unsolved problems, lawyers working in the corners of inter-state contract law, or industrial chemists trying to eke an extra percent of yield in some obscure reaction can still usually be made accessible to advanced undergraduates or early grad students. I think we can often do better at accessibility than the "What is..." columns for mathematical topics, but those are indeed in many cases more accessible than what we currently have at Wikipedia, so are a good source to take inspiration from and cite. –jacobolus (t) 15:35, 10 November 2023 (UTC)

  There are often no sources as good as "What is..." columns, particularly for abstract subjects that are only of interest to specialists. Our own coverage should of course aim to be as accessible to as wide a likely audience as possible, but the expectation needs to be tempered. Firstly, Wikipedia follows sources. That is policy, and there is a policy against original research. To some extent, this is relaxed for explanations aimed at making things accessible, but still it is a policy demanding some deference. You can find examples (like homology theory) where there are loads of accessible sources out there. I think the typical editor fails to appreciate that this tends to be the exception rather than the rule, and expectations should be set appropriately. Tito Omburo (talk) 16:17, 10 November 2023 (UTC)

  "Follow the sources" doesn't mean you can't ever put a brief definition of a jargon term inline, can't include examples or pictures, can't describe historical/mathematical context, etc. –jacobolus (t) 17:37, 10 November 2023 (UTC)

  No, but not every subject has a picture that explains it (most don't). Some jargon terms require still more jargon terms to define them. The article Galois cohomology you recently complained about has historical context out the wazoo. An explanation of cohomology as "cocycles modulo coboundaries" is unlikely to be availing, a Galois group as "group of automorphisms of a field fixing a subfield", etc. One has to be reasonable, and to communicate with other wikipedians that in many cases an article will not be understandable at all to someone without a good background in mathematics (and certainly not without doing OR). I'd like you to at least acknowledge this point. It seems like it should be pretty uncontroversial. Tito Omburo (talk) 18:15, 10 November 2023 (UTC)

• "Explaining things in simple terms is 'dumbing down' the article"
  Adding simple explanations does not mean removing any of the advanced content. Many expert editors regard any simplified explanation as ‘lies to children’. This is probably too extreme (and haughty) a view. Simplified explanations given in introductory-level textbooks should be acceptable, as long as the ways it is inadequate are mentioned. --Chetvorno^TALK 06:50, 9 November 2023 (UTC)

  Many many topics are not covered in "introductory-level textbooks" (and certainly not for textbooks you would consider "introductory": for example, the book "Modular forms and Galois cohomology" is an introductory level textbook on Galois cohomology, but I doubt a non-expert would recognize it as such). If topics are covered in (what you're thinking of as) introductory textbooks, it is certainly possible to give introductory descriptions of them. But otherwise, probably not without violation policies at best, and being completely wrong at worst. Tito Omburo (talk) 12:31, 10 November 2023 (UTC)

  The article Galois cohomology makes very little effort to be accessible beyond a trivially tiny audience of specialists. Its accessibility could be dramatically improved without sacrificing any usefulness to a specialist audience. –jacobolus (t) 15:38, 10 November 2023 (UTC)

  That's just not true. The lede and most of the article is perfectly understandable to a non-specialist. If there are reliable sources that do a better job of introduction, they can be used to improve the presentation. Tito Omburo (talk) 15:44, 10 November 2023 (UTC)

  The lead section consists entirely of jargon. Someone who hasn't yet taken a course in homological algebra is going to be able to make no sense of it whatsoever. Edit from after the following comment: Worse, if someone clicks through to group cohomology, homological algebra, Galois module, Galois group, Field extension, Galois representation (redirects to Galois module), or Exact functor, they get an equally inaccessible description. This entire cluster of articles is a mess from an accessibility perspective. The article Homology (mathematics) stands out for being much better than any of those, but e.g. a curious undergrad physics student arriving at Galois cohomology is never going to manage to make it there. –jacobolus (t) 15:52, 10 November 2023 (UTC)

  Look, the context-setting in the article is at a more accessible level than Serre's introductory textbook on the subject, and Hida's introductory book, and even the encyclopedia entry at EoM. In fact, arguably our article should include more technical detail to be useful to as wide an audience as possible (e.g., transcribed from [2]). The problem with a topic like this is that what is one to explain in a short lede section? All of homological algebra? All of cohomology theory? All of Galois theory? Actions of groups on modules? The lede even leaves out any discussion of class field theory (which is actually quite essential), so in this way is pitched "one level down" from an intended readership. At some level it's going to be "turtles all the way down". Understanding the lede (or even the rest of the article) does not require a detailed understanding of homological algebra, contrary to your contention. Tito Omburo (talk) 15:57, 10 November 2023 (UTC)

  arguably our article should include moretechnical detail – this would also be fine. These two motivations are not in conflict here. This article has plenty of space to grow to serve all of these audiences. –jacobolus (t) 16:49, 10 November 2023 (UTC)

  What I'd like to see out of all of these articles listed above is for someone who just finished a typical introductory undergraduate abstract algebra course to be able to either directly understand the majority of the lead section, or else be linked within 1 hop to articles about the prerequisite jargon such that those articles' introductory sections are largely understandable.

  My experience is that mathematicians in particular have this problem more than almost anyone else I have run into, that they forget what it's like to not already know the meanings of the technical terms they spent years of toil making sense of, so take it for granted that other people will be able to understand a long string of conceptually sophisticated jargon without any assistance. –jacobolus (t) 17:06, 10 November 2023 (UTC)

  One hop from a specialist article is a non-specialist, not someone who just finished an undergraduate algebra course. Tito Omburo (talk) 17:16, 10 November 2023 (UTC)

  When I say "trivially tiny audience of specialists" above, what I mean is "people with math PhDs", and when I say "general audience", I mean e.g. physicists, economists, computer programmers, and undergraduate math students. Wikipedia's advanced math articles, on the whole, do a very poor job at including a wide audience. They are written largely for people who already know the subjects under discussion in detail, and could in most cases be made at least somewhat legible to a much wider audience (like 100x as many people) without much compromise. –jacobolus (t) 17:19, 10 November 2023 (UTC)

  Perhaps the mathematicians, who have spent their lives explaining mathematics to others, might actually be right? I'd like you to at least entertain this possibility rather than simply dismissing it by saying they are doing a "very poor job".

  Regarding the example of the Galois cohomology article, what would you propose we add to the lede to make it more accessible to your hypothetical undergraduate? Would the following be adequate? "Historically the first, and one of the most basic applications of Galois cohomology is to describe the structure of the group of elements of norm one in a cyclic field extension of degree $n$, that is, an extension field where the Galois group $G$ is generated by a single element $\sigma$ of order $n$. The cohomology group $H^{1}(G,L^{*})$ with values in the group of non-zero elements of $L$ can be described as the quotient of the cochains by the coboundaries of dimension one. A cochain is a group homomorphism from $G$ to $L^{*}$, which is completely determined by its value on $\sigma$, say $b=f(\sigma )\in L^{*}$, such that the product $b\sigma (b)\cdots \sigma ^{n-1}(b)=1$. This product is just the relative norm of the element $b$. A coboundary is an element of the form $b/\sigma (b)$. Hilbert's theorem 90 states that every such cochain is a coboundary, i.e., $H^{1}(G,L^{*})=1$ is the trivial group. Therefore, every norm one element of the field $L$ can be expressed as $b/\sigma (b)$." Tito Omburo (talk) 17:44, 10 November 2023 (UTC)

  My impression is that mathematics teachers (as a broad social group under their current societal constraints; I'm not calling out any specific person here) don't generally do a good enough job of explaining mathematics: the field is notorious for chasing away promising and interested students by making them feel stupid and not giving them enough support, at every level from primary school up through grad school. It's very much a sink-or-swim go-figure-it-out-for-yourself kind of subject.

  My impression is that the world's best mathematical expositors and popularizers are mostly not writing Wikipedia articles (because they are busy doing something else), and most of the people writing math articles on Wikipedia at every level are not in general making legibility to the broadest reasonable audience one of their top priorities. But I think it should be.

  Galois cohomology was your example, not mine, and is probably not the best place to start since this is a topic that has a lot of prerequisite concepts, even in the best case is only going to be vaguely comprehensible to non-mathematicians, and only gets about 20 page views per day. Energy directed at making lower-level topics legible will have better payoff.

  But if a hypothetical physics undergrad did want to figure out even roughly what Galois cohomology was talking about, and they tried clicking through any of the jargon words in the first two sections, the prerequisite articles they'd arrive at are all equally inscrutable, as are the prerequisites to those; our hypothetical student would have to go probably 5+ hops deep in any given direction to get to a page they could make any sense of at all. That's unfortunately pretty exclusionary. Most of our more basic articles like field extension, normal subgroup, exact sequence, automorphism group, etc. etc. etc. are still written in a very spare and inaccessible style.

  If you want to figure out if a particular explanation is clear enough, the best people to try it on would be some students who are a few years away from taking the course in question. Ask them if they can figure out what all the jargon roughly means, see if they can restate the main idea in their own words, etc.

  might actually be right? – what does this mean? I claim that our articles within 1–2 hops of your original example are almost entirely inaccessible to anyone who isn't at least a math grad student. Is your claim that any other result is impossible? You think this is the best we can do? –jacobolus (t) 19:14, 10 November 2023 (UTC)

  Again, you're dismissing not just mathematics researchers but even mathematics pedagogy as inscrutable. You start to sound like a classic crank. I'm just trying to inject some realism into this discussion. Can we do better? Certainly. Can we make everything accessible to everyone? Absolutely not.

  Regarding the examples of hops, the articles homological algebra, Galois group, field extension, and even group cohomology do include an accessible description in all cases. Definitely not enough to understand what a Galois group or field extension "really is" (because that requires knowing what a field is, what a group is, what an automorphism is). But they set their topics in context, and include links for further browsing. I don't claim that any of these are perfect, but blanket claims that everything is terrible strike me as very overwrought.

  Also, I am still curious whether you think my proposed addition to the Galois cohomology article enhances its accessibility, which you seem not to have addressed. Tito Omburo (talk) 19:25, 10 November 2023 (UTC)

  What you call "accessible description" I call "completely illegible to anyone who isn't already a math grad student". There's a very wide gulf between this state and making "everything accessible to everyone", a straw man which nobody is proposing. I urge you to go hand a printout of the first couple sections of any of these articles to randomly selected undergraduates in technical subjects or technical professionals from other fields (or even advanced math undergrads), and directly ask them whether they can make sense of them. I would expect almost none of them to find these articles legible. This is not just my personal opinion; people complaining about how illegible math articles are on Wikipedia is so common it has become cliché. As for your proposed addition, I'm not the person to ask about this. I don't know or care too much about algebraic number theory, and it's been 15 years since I last spent any time learning about cohomology or Galois theory. –jacobolus (t) 19:55, 10 November 2023 (UTC)

  I don't have much contact with undergraduates these days. But if I were to compare our article on group cohomology to the entry in the eom, or Serre's book, or, pretty much any other source that discusses the topic, ours is easily more accessibl, informing the reader that it studies groups using methods of topology by regarding groups as spaces. That's accessible! Similarly, our article on homological algebra informs the reader that the subject uses techniques from topology (homology theory, an article you recently praised) to study algebraic structures. That's accessible! (The eom article unhelpfully tells the reader that it is the study of derived functors.) The article Galois group appropriately points a reader to the more elementary account in Galois theory, but the first sentence eludes some technical details (without telling lies to children). You say I am attacking a staw man, but you seem unable to assess an appropriate level of accessibility for a technical article. In my experience, most Wikipedians suffer the same deficiency. People regularly complain that articles on technical subjects are technical. If they want to make them less technical, and have the expertise to do so, they are welcome to. But instead you have collectively dismissed the expertise of those that do have the expertise to do so as doing a "very bad job", or even those responsible for mathematics pedagogy (!), dismissing their expertise in such matters, even when more often than not such people are telling you they're doing the best they can. (Omg cut it out with the stupid templates, is there any evidence that a block of text at the top of a technical article improves its accessibility by obscuring the article contents?) That attitude is very counterproductive, and often leads to misguided threads like this one. Tito Omburo (talk) 21:21, 10 November 2023 (UTC)

  I will certainly agree with you that we're less opaque to the uninitiated than Serre's book (wide accessibility was clearly not among Serre's goals), and I will also agree with you that these Encyclopedia of Math articles by V.E. Govorov / A.V. Mikhalev and L.V. Kuz'min also don't do a good job at this. But "less inaccessible than some completely inaccessible sources" is not really where anyone should be aiming.

  Calling people who are frustrated by articles they can't read "deficient" isn't very welcoming. But note that these "deficient" people even include professional mathematicians sometimes: Math is so big that nobody understands every corner of it from top to bottom, it's of general benefit to all of us to make every article as broadly accessible as practical, even if it takes adding a couple extra paragraphs of introductory explanation that seem a bit redundant, or going out of our way to write overview articles that do more hand-holding than any advanced textbook would bother with.

  I don't doubt page authors are generally "doing their best", but writing for broad legibility takes significant dedicated effort and if it isn't a priority it just won't happen. I don't mean offense, and am not trying to call out anyone specific or "dismiss" anyone's efforts. There's just a significant gap between where we currently are and an encyclopedia that strongly prioritizes helping non-experts make sense of unfamiliar topics.

  I don't understand what you mean by "block of text" or what templates you are referring to. If you are talking about navigation templates, I typically find those to be space and attention wasters, and never add them to articles. Some people seem to like them though. –jacobolus (t) 22:55, 10 November 2023 (UTC)

  It appears to be a widely held belief that templates such as {{technical}} improve the accessibility of technical articles, but I am confused how that is supposed to work. A block of irrelevant text before the lede of an article does not seem to be an improvement for accessibility (or otherwise). Tito Omburo (talk) 23:41, 10 November 2023 (UTC)

  I don't think adding banners has ever helped any article. Cf. User:Jorge Stolfi/Templates that I sorely miss. –jacobolus (t) 23:46, 10 November 2023 (UTC)

  Looking at the group cohomology article, I'd guess that a third- or fourth-year physics undergraduate would get as far as tools used to study groups before giving up. There's a parenthetical before the bold text which is at least as obscure as the article name itself. The first sentence ends by mentioning algebraic topology, which just looks like the combination of two math words to make an even mathier word. The second sentence brings in group representations, which are an advanced undergraduate or early graduate topic, then drops in the term G-module. It could be worse, but it's not easy going.

  I share the concern voiced above that focusing on articles that get infrequently read and are targeted at the highest levels of education may be misplaced effort. I'd like to see Wikipedia have really top-notch coverage of math topics taught in high school and the first couple years of college. To me, that seems the way to aim for benefiting a wide population (and the people learning things at even younger ages probably aren't looking them up in an encyclopedia). This means Pythagorean theorem, quadratic formula, sine and cosine, linear equation, ..., on up through calculus, Matrix (mathematics), Eigenvalues and eigenvectors, and the like. XOR'easter (talk) 02:06, 11 November 2023 (UTC)

• "Mathematical articles require equations in the introduction":
  Even if true, that doesn't mean it should not also include a simple word explanation. One technique is after giving the equation, to rephrase it in words for nonmathematicians. --Chetvorno^TALK 06:50, 9 November 2023 (UTC)

  For an article about an equation, it is important to include the equation in the lede. The lede should be a capsule version of the article, as accessible as possible, but also useful to likely readers of the article (which can include experts, graduate students and other researchers, etc, in more technical areas). Tito Omburo (talk) 12:31, 10 November 2023 (UTC)

• "It is essential to use the correct terminology (i.e. jargon) in the introduction"
  Okay, but a brief plain-language explanation of jargon terms should also be included. --Chetvorno^TALK 06:50, 9 November 2023 (UTC)

  Sometimes that would take many pages of explanation and background. Tito Omburo (talk) 12:31, 10 November 2023 (UTC)

I think this is a good point to bring up from time to time. It's not easy to distill one's own expertise into a simple explanation for lay-people. One example in overcoming that, I think we've managed to make a small improvement to the introduction of Mandelbrot set with a couple lay-person friendly sentences, when it used to start very technically. I'm a fan of taking the WP:IMPERFECT approach on such issues in general, working to improve things as we can. —siroχo 08:33, 9 November 2023 (UTC)

One sentence of context-setting is good. But two things stand out. First, there is a vast chasm between being able to set the context for a topic in one sentence, and making the topic accessible to a "general audience" (which is often impossible). Secondly, the Mandelbrot set (or similar article) is a topic for which there is a superabundance of sources aimed at a general audience. But this is not the case for most concepts in the mathematical sciences. I agree that we need to temper our expectations about what is possible, and in particular nip the "everything can be made accessible" fiction in the bud. Tito Omburo (talk) 12:41, 10 November 2023 (UTC)

Let's look at Bijection. I assert that the third sentence of the lede, with minor modification, should be the first sentence. As follows:

"In mathematics, a bijection is a relation between two sets, such that each element of one set is paired with exactly one element of the other set, and vice-versa."

Is that an accurate statement?

Consider the linked terms of jargon currently in the first sentence that are eliminated (they can be introduced later):

function, injective, surjective, codomain, domain of the function.

My revision would retain "set" as a linked term, but the word is recognizable to everyone as an expression for collection of things. Unless my reworking of this lede is completely wrong, I assert that ledes of all mathematical articles can be similarly simplified by removal of much opaque jargon from the first one or two sentences and the substitution of plain English, which is very often found later in the same article. DonFB (talk) 21:59, 10 November 2023 (UTC)

Whether you call a bijection a "function" or a "relation between sets" doesn't really make much difference in how understandable the concept is, in my opinion. I'll agree that "injective (one-to-one) and surjective (onto)" can probably be deferred by a few sentences. This article would also benefit by putting a couple examples in the lead section, by explaining how a function (or pairing) can fail to be a bijection, and by giving short inline definitions of some of the other terms used. –jacobolus (t) 23:03, 10 November 2023 (UTC)

My purpose here was to show that an opening sentence with what I believe to be unnecessary jargon can be written to be instantly understandable to everyone. I'm not a mathematician (probably obvious), so I would defer to those who are in matters of accuracy, while urging and trying to demonstrate that more accessible language can be used. In this example, I used "relation between", which seems even more apparent in its meaning than "function". I looked up function and find its opening paragraph to be...difficult. The second paragraph begins with what I've understood the word to mean, although it uses "originally":

"Functions were originally the idealization of how a varying quantity depends on another quantity."

For my money, that's how the article should start, (with some adjustments), unless more recent standadization has made it truly obsolete. I offer this as another example of how I think it is possible to use plain English at the very start of an article and defer the techno/jargon/lingo/formula to a position later in the article, or the lede, when that's necessary. DonFB (talk) 00:00, 11 November 2023 (UTC)

My impression is that people most commonly think of a bijection as an invertible function. While it's true it can also be thought of as a pairing between two sets, I feel like it's a bit less obvious to put that version first.

I'm not really sure if "binary relation" is more likely to be understood than "function". The concept of functions is usually discussed at length in high school while the concept of a binary relation is (while not inherently any more complicated) a bit more obscure I would guess.

In the case of "bijection" per se, I don't think the concept of a function as one varying quantity depending on another quantity is really the right concept to think of. The concept of a function as an abstract machine that turns an input into an output is probably more useful here, but the abstract mathematical definition in terms of ordered pairs of set elements is probably also alright. –jacobolus (t) 01:23, 11 November 2023 (UTC)

Ok, to show a little more of what I'm getting at, consider the statements:

"think of a bijection as an invertible function"

"can also be thought of as a pairing between two sets"

I submit that the second statement is a lot more accessible than the first. Disclosure: I never heard of bijection until today, hopping among various math articles while reading the discussion above. I'm guessing that "mathematicians most commonly think of a bijection as an invertible function", but most people, like me, don't know the term at all. DonFB (talk) 02:22, 11 November 2023 (UTC)

I took a crack at rewriting the first couple of paragraphs of bijection. Does that help? –jacobolus (t) 23:45, 10 November 2023 (UTC)

With all due respect, no. I'm sure it's accurate, but I believe my first sentence version is immediately understandable to anyone in comparison to the current version, or your offer. With the caveat, of course, that what I wrote is accurate in the broadest sense. But really, I'm not here to debate particular articles; I'm only trying to show how I think the beginning of articles on abstruse topics can be written in plain English. DonFB (talk) 00:22, 11 November 2023 (UTC)

This is still not really "plain English" though. The concept of a set in this context is at least a bit tricky (we're talking about potentially infinite collections, e.g. of numbers, lists of numbers, functions, geometric transformations, ...), and a binary relation is concept that is not usually encountered by students until college (and turning it into the undefined term "relation" just makes it ambiguous rather than particularly more accessible IMO). It probably would be worth trying a few versions on e.g. high school students to see which ones were easiest for them to decipher while giving a correct understanding of the concept.

You could well be right that first describing a bijection as a pairing between set elements would be gentler than describing it as a function. –jacobolus (t) 01:38, 11 November 2023 (UTC)

@DonFB okay, I tried again. How about this version? –jacobolus (t) 02:26, 11 November 2023 (UTC)

That (almost) works for me. I would drop "binary pairing" from the first sentence and introduce it later. No need for a speed bump in the first sentence; it doesn't help. Also, some garble seems to exist: "element of each set is paired..." Not "the either set." DonFB (talk) 02:41, 11 November 2023 (UTC)

I'm also a little confused by the text example (1,2 etc); does not look consistent with the graphical example. DonFB (talk) 02:47, 11 November 2023 (UTC)

If considered as a pairing per se, the graphical example could be likewise written as {(1, D), (2, B), (3, C), (4, A)}. Thinking of it as a function, you might instead write {1 ↦ D, 2 ↦ B, 3 ↦ C, 4 ↦ A} or {f(1) = D, f(2) = B, f(3) = C, f(4) = A}. –jacobolus (t) 03:26, 11 November 2023 (UTC)

I put in a ↦ notation instead, but looking at it I'm not sure it's any better. One issue with it is that general binary relations don't necessarily have a single output for any input. That is, this notation works for bijections but not "pairings" in general. It's also not as common, which might leave some people confused. –jacobolus (t) 03:50, 11 November 2023 (UTC)

Articles covering math topics up through early undergrad level

@XOR'easter I wonder if there's a good venue for coordinating on "top-notch coverage of math topics taught in high school and the first couple years of college". I'd also like to see this happen, but it could be nice to organize some group effort rather than individual contributors trying to take each one as a one-off, perhaps something along the lines of the old "collaboration of the month" or the like. I think even aiming for green checks or gold stars shouldn't be the top priority, but just getting all of the most common pages to a consistently decent "B class" kind of standard, with special focus on the lead sections. I feel like the math Wikiproject isn't quite the venue (or rather, it plausibly could be, but I feel people might get annoyed if the traffic there increased a lot discussing a wide set of such articles).

I personally have been trying to put in the research to further improving (or write where they don't yet exist) the articles about spherical geometry and its history, spherical trigonometry, the most common map projections, and more generally some other kinds of geometry topics that could (but typically don't) appear in school. But while these topics have plenty of applications to industry (GIS, attitude control, kinematics, etc.) they're at least somewhat obscure compared to stuff right in the main line of the school curriculum. I wouldn't mind spending some time looking up sources, drawing or redrawing diagrams, etc. for high-value articles. I wonder if there's a good way to e.g. get a page view summary of all articles currently in the math wikiproject and pick out a few that are important and high traffic but currently mediocre. –jacobolus (t) 05:21, 11 November 2023 (UTC)

To get a sense of where things stand, I grabbed the list of level-3 "Vital articles" in mathematics and looked up their 30-day page view counts. The winner? 0, with 241,262. XOR'easter (talk) 21:01, 11 November 2023 (UTC)

Thanks. I have a medium-term interest in cleaning up in particular polygon, triangle, line (geometry), circle, angle, area, trigonometry, and complex number, among various other articles not on your list (most especially sphere, spherical geometry, history of spherical geometry, history of trigonometry, spherical trigonometry, spherical triangle (currently a redirect), spherical circle, great circle, spherical distance, antipodal point, solid angle, stereographic projection, gnomonic projection, tangent (trigonometry) (currently a redirect), half-tangent, tangent addition, complex logarithm, conformal map, Lorentzian plane, Galilean plane, hyperbolic plane, de Sitter plane, anti de Sitter plane, (anti-Euclidean plane, anti-Lorentzian plane – these don't really have a clear name, but I mean planes with flat angle measure and curved elliptic or hyperbolic concept of distance), Laguerre geometry, hyperboloid model, inversive distance, Cayley transform, ...). If anyone wants to collaborate on any of these, I've been chipping away here and there, figuring out how to draw decent diagrams, gathering sources about several, doing my basic reading, .... –jacobolus (t) 01:36, 12 November 2023 (UTC)