user talk : jacobolus

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Again, welcome! --Lst27 (talk) 23:54, 15 Jan 2005 (UTC)

Dialogue and talks in Wikipedia

[... clipped; see 2024 archive and Talk:Function (mathematics) ... ]

Indeed, that's why I decided terminating my yearly visit to this article (over the past 10 years I have seen no progress), and coming back in 2025. As regards the codomain issue, since the 1980s I've been regularly asking mathematicians using codomains why they might want it. The answer always amounted to "tradition in certain fields" or "it's a convenience" (without a technical justification). Yet, most definitions for composition of functions with codomains are very restrictive. Of course, since the term codomain exists, it must be covered by an article meant to be encyclopedic, but a solid technical justification would be a genuine added value.

If you have the incentive to continue working on this article, you may find Rogaway's remarks very helpful [1], in particular his remark #18: 'Definitional choices that don't capture strong intuition are usually wrong, they may come back to haunt you". As for the of informal introduction, I recently found very high praise for the educational style of Michael Spivak's Calculus (now in its 4th edition, freely available on the web). Since the perspective of the article must be far wider than calculus (ideally, all of mathematics) the intuitive discussion on functions must also be wider. A suitable preamble to the formal definition might run as follows (after a few examples). (begin excerpt) In our examples, we have been writing f(x) for the "output value" of the function f for a given "input value" x. This immediately raises two questions: (a) for which values of x is f defined? and (b) if x is such a value, what, then, is the value of f(x)? (end excerpt). Answering those questions provides the justification for a simple formal definition to follow.

I hope this helps. Other work currently prevents me from providing more input or even having an occasional look at these pages. Boute (talk) 09:17, 3 March 2024 (UTC)

The most obvious purpose I can see is to avoid extra bookkeeping. It's easier to say e.g. a square matrix represents a function from $\mathbb {R} ^{n}\to \mathbb {R} ^{n}$ and not worry up front about noting that the image might be some restricted subset in degenerate cases. Etc. –jacobolus (t) 09:46, 3 March 2024 (UTC)

Was reading through this talk page out of curiosity and might have something helpful to add. When talking about functions $\mathbb {R} ^{n}\rightarrow \mathbb {R} ^{m}$ you don't want to exclude maps that only map to subspaces. Also the transpose map turns the codomain of a matrix $M$ into the domain of $M^{\top }$. I think the category theorists quite appreciate the codomain for these reasons and others. Anyway happy late new year I guess. Shoe Deceiver (talk) 21:36, 7 January 2025 (UTC)

Oh and also the preimage map of clearly depends on what the codomain is. Shoe Deceiver (talk) 21:48, 7 January 2025 (UTC)

Subtended angle intro

Hi,

Obviously it's disappointing to have clarified something for the worse, but I'm happy to go with your reverting of it.

What I'm wondering, though, is whether there's a way to introduce readers in a really clear way to the central idea first, rather than (as it seems to me) hit them straight away with several definitions in succession, all applied to different situations, and a large number of wikilinks? That's the problem I was trying to solve, really, and it's clear from the talk page that at least one visitor had trouble understanding the article when they visited in 2019, though I've not checked what it looked like back then. Musiconeologist (talk) 21:13, 5 January 2025 (UTC)

Afterthought: maybe a better diagram would go some way. Show one angle, with a a line segment, an circular arc and an arbitrary curve all subtending it (and having the same endpoints?). We can also say the line segment subtends both the arcs if we want, and everything subtends the angle. Musiconeologist (talk) 21:44, 5 January 2025 (UTC)

Moved to Talk:Subtended angle § Subtended angle intro

Fundamental theorem of calculus

• User:Dedhert.Jr/sandbox/1

Might be planning to implement it anyway. But do you think the introduction of differentiation and integral seems superfluous and somewhat unrelated before the fundamental theorem of calculus? I somehow managed to relate those two with the fundamental theorem in order to describe it mathematically. The second theorem's proof is the only problem I could not comprehend anymore. Dedhert.Jr (talk) 04:30, 6 January 2025 (UTC)

I'm not quite sure what the question is, or what you mean by "implement it". If you are asking whether it is worth giving a quick introduction about what derivatives and integrals are in the article about the fundamental theorem of calculus, I would say yes. Some readers who are not familiar with calculus might be curious about it. I think we should if possible give a (brief) explanation at the start which is accessible to e.g. high school students taking an algebra or trigonometry course who have not yet seen any calculus. But we also shouldn't belabor it, as that may be distracting for more expert readers. –jacobolus (t) 23:57, 7 January 2025 (UTC)

Reordered Formulas

Hi, I reordered the formulas on the page about stereographic projections because I think sums are nicer if they don't lead with a minus. It's also more consistent since, as it stands, the formula for the polar form has both $1+R^{2}$ and $R^{2}+1$ in the denominator. That said I won't contest. Shoe Deceiver (talk) 10:42, 7 January 2025 (UTC)

@Shoe Deceiver: There are a wide variety of different variants in use in different sources, but it's typical to put the 1 first. If it were up to me we'd use a north-pole centered stereographic projection, in which case the relevant quantities end up as ⁠${\tfrac {1}{2}}(1+x^{2}+y^{2})$⁠ and ⁠${\tfrac {1}{2}}(1-x^{2}-y^{2})$⁠. (If I ever manage to get the time and energy for a substantial rewrite I might put this one in place. It also has the beneficial property of not reversing the orientation of the sphere. I think it's easier to make sense of, it accords better with the conventional spherical coordinates which measure the polar angle from the north pole as 0, and it generalizes better to uses such as taking the tangent of half an angle or taking the stereographic projection of unit quaternions as a representation of rotations ["modified Rodrigues parameters"].) –jacobolus (t) 19:59, 7 January 2025 (UTC)

Disambiguation link notification for January 10

An automated process has detected that when you recently edited James Ivory (mathematician), you added a link pointing to the disambiguation page Lemma.

(Opt-out instructions.) --DPL bot (talk) 19:53, 10 January 2025 (UTC)

Notice of edit warring noticeboard discussion

Hello. This message is being sent to inform you that there is currently a discussion involving you at Wikipedia:Administrators' noticeboard/Edit warring regarding a possible violation of Wikipedia's policy on edit warring. Thank you.---Wikaviani ^{(talk) (contribs)} 16:53, 5 February 2025 (UTC)

I replied at Wikipedia:Administrators' noticeboard/Edit warring § User:Jacobolus reported by User:Wikaviani (Result: No violation) –jacobolus (t) 18:55, 5 February 2025 (UTC)

Sine and cosine

Did you mean to remove the Van Brummelen citation in this edit? XOR'easter (talk) 18:36, 13 February 2025 (UTC)

@XOR'easter, Whoops, no I had just added it and did not mean to immediately remove it. I started working offline on reworking that section a bit, but have been a bit busy. –jacobolus (t) 18:43, 13 February 2025 (UTC)

Archiving

Talk:Hindu–Arabic numeral system is currently 158k bytes, which is more than the 75k that the guidelines suggest as a line for archiving. It is one of the largest talk pages.[2] Usually when talk pages calm down, large closed discussions are archived. The top two or three topics are a year old and done with. Is it not time to archive them? Manually perhaps? Wizmut (talk) 08:02, 18 February 2025 (UTC)

If you aren't a participant in discussions on this topic, why do you care so much? The problems with the page are still persisting and are not really "done with". This page and related pages are a serious mess. –jacobolus (t) 15:14, 18 February 2025 (UTC)

Please assume good faith. I'll try to articulate the problems I see.

Is there current work being done pursuant to these topics? There does not appear to be. Such large and wide-ranging discussions, some parts of which led to consensus and others not, are very hard to pick apart. Guidelines (WP:TALKSIZE) suggest starting new topics rather than bumping old ones. The new topic could focus on one problem and summarize points made earlier. Absent archiving, topics that probably shouldn't be replied to directly could make use of {Discussion top} and {Discussion bottom}.

There are also parts that devolved into personal attacks (not talking about you specifically) - someone trying to catch up on maintaining the page would see a lot of dirty laundry. Even worse, there are productive comments mixed right in, which often get lost. So it goes... I recognize some of the names.

I understand that some of these points may not be entirely persuasive. I will leave it to you to keep the talk page maintained. I would ask, however, that you consider the guidelines I mentioned earlier, as well as the perspective of any editor that is new to the article and who may want to understand what work is currently being done on it. Regards, Wizmut (talk) 19:34, 18 February 2025 (UTC)

@Wizmut – I'm not assuming bad faith. I'm asking why you personally are affected. (For example: if you wanted to start a new talk page discussion about this topic but felt overwhelmed by the talk page, that might be a good reason to try to do something about it.) It seems likely to me that you are going through some auto-generated list of big talk pages and trying to "fix" them in order from largest to smallest. In my opinion this activity has very limited value, and I would recommend spending your time on something else.

dirty laundry – This is helpful context for readers, because it shows that the obvious problems in the article are a subject of discussion, not just being swept under the rug. –jacobolus (t) 19:39, 18 February 2025 (UTC)

"Dirty laundry" was referring to all of the comments that were not about improving the article. Comments about editors, rather than content. Such comments are very unhelpful to incoming editors. Indeed, they probably set a bad example.

For the concern of trying to hide problems. New topics can always be created. Old ones can be linked to. In fact that's what should happen; a new editor replying to one of the monoliths currently available would just make it hard to follow the flow of discussion.

My recommendations about talk page maintenance come from examining over a thousand talk pages, and the actions that are usually taken to help them along. They also come from reading guidelines. There is no requirement that I be personally affected in order to maintain an article. Indeed, it is often better to have an impartial point of view. Wizmut (talk) 20:13, 18 February 2025 (UTC)

History of calculus

In the section of Early precursors of calculus of India subsection it states that

They applied ideas from (what was to become) differential and integral calculus to obtain (Taylor–Maclaurin) infinite series for sine, cosine and arctangent.

What does it mean? Myuoh kaka roi (talk) 14:32, 18 February 2025 (UTC)

I'm not particularly satisfied with the description there, but it's hard to give a short and accessible but nuanced summary. For more see Kerala school of astronomy and mathematics, Madhava of Sangamagrama, Madhava series. (Or better, try reading some of their references.) –jacobolus (t) 15:10, 18 February 2025 (UTC)