Talk:Main Page

Way to synchronize equation numbering in Transcluded text?
I have had to fix up equation numbering problems on several pages (i.e., Definition:Sturm-Liouville Equation, Sturm-Liouville Theory and Orthogonality of Solutions to the Sturm-Liouville Equation with Distinct Eigenvalues) as material was moved from the main article into a Definition. This raises a pertinent question. Are there templates for equation numbering that would solve these kinds of problems? I imagine this synchronization requirement is not limited to the pages I work on. Dan Nessett 16:48, 29 March 2012 (EDT)


 * No there's not, but it hasn't been seen as a problem before. It is rare that a train of thought is so long as to stretch over multiple pages (transcluded or not), as (has been explained before) the nature of this site is more as a dictionary (short pithy entries) than as an encyclopedia (longer discursive entries).


 * TL;DR - If equation numbering breaks under the influence of refactoring, it's just one of those things that will need fixing. --prime mover 16:57, 29 March 2012 (EDT)


 * Maybe this is something that can be fixed; some ideas drip in that may allow for the extension being developed to cover this (but I imagine that it will be hard to cover things like $(3')$ and $(1a)$ which occur now and then. Should I put some more thought into it? --Lord_Farin 17:21, 29 March 2012 (EDT)


 * If you think you have a strategy, then it's worth exploring. For one, I'd suggest a template "eqno" or something equally pithy, which might also contain a means of directly linking back to the original equation in the same / similar way that "eqref" etc. works in a conventional $\LaTeX$ work.


 * But the question is bigger. Pure maths is one thing, where the expositions are short, and there is no need for lengthy pages. However, applied maths and mathematical physics may require that the descriptions are considerably longer (thinking ahead to the delights of the analysis of the behaviour of waves and ripples on the surface of a body of liquid is filling me with anticipation as I type) and so, as with S-L Theory, a new approach will need to evolve.


 * The challenge will be in the crafting of short, self-contained but transcludable, pages like Definition:Sturm-Liouville Equation such that any page referencing it will be able to either link to it or, as necessary, transclude it, without the need to copy-paste or any otherwise repeating material.


 * Another challenge: if several pages are so transcluded, what if the equation numbers clash? --prime mover 17:32, 29 March 2012 (EDT)

Good point, and nice elaboration on the challenges we are coming to face with the advent of more applied systems and research fields. The only possible ways I see to solve this problem are by using eg. an optional unique identifier (like 'eqnaboutblabla') or allowing only for a possible subscript to be added to a number (eg. where 'a' yields $(na)$, and "'" gives $(n')$ with $n$ as appropriate). But these are bound to be fiddly and will put up a wall of syntax for new aspiring editors. Maybe this last point isn't really big because the convention could be applied in a 'only-when-required' fashion. In any case, the amount of documentation I would deem necessary will demand a lot of time, time I seem not to have in the coming few months.

But then, I haven't even spoken about what to do with things like 'Axiom $(2)$' or 'Equation $(3)$ on "somepage"' as references; I haven't got a solution for that yet (maybe we needn't look, as this is of relatively small impact, on crystallised pages). --Lord_Farin 17:45, 29 March 2012 (EDT)


 * I thought about this problem a bit and I now think it will be difficult (but perhaps not imposssible) to provide the requisite functionality even with an extension. What I think is needed is a way for equations transcluded from a page to be tagged with a number based on their context on the referencing (not the transcluded) page. For example, an equation labeled (1) on a source page might require labeling as equation (3) on the referencing page.


 * Achieving this would seem to require global state on the referencing page that figures out where the first reference to the equation occurs and then assigns it a number. That number would then be assigned for each reference to the equation. This is a bit like citations implemented by the Cite extension, but with dynamic numbering.


 * It wouldn't be hard to uniquely identify equations based on a page name and a number on that page, but then to map that into a dynamically allocated number on the referencing page would require MW parser functionality that doesn't exist. In the past I wanted to write templates that did arithmetic on citation numbers for a similar purpose, but discovered that the parser simply doesn't support this. The MW parser is a big mess, but not particularly sophisticated from a computer language point of view. So, achieving the goals of dynamically allocated equation numbering is probably a bridge too far.


 * By the way. In regards to transcluding individual equations from other pages, it might be useful to install the Labeled_Section_Transclusion extension. Just a thought. Dan Nessett 18:46, 29 March 2012 (EDT)


 * Sounds like a good idea to me. This may be particularly useful when we might want to transclude more than one section of a given page - at the moment (or when I last tried it) when you have more than one "onlyinclude" section in a page it doesn't work properly. --prime mover 02:00, 30 March 2012 (EDT)


 * Labeled section transclusion is superseded by the (PW-tailored) extension in development, which will allow for customisation of the header levels under transclusion. To achieve this I am already working with global states; I think it's possible, albeit with a special, to-be-written parser function that outputs $(3)$ (because it's possible that one would like to write $(3)(4)$ to indicate multiplication (though this is disallowed by house style, I think that the distinction should be made clear) and thus simply fetching the occurrences of $(n)$ (and then, which one of the occurrences labels the equation itself? 'see equation $(n)$ below' would cause problems) would be too simple an approach). --Lord_Farin 03:12, 30 March 2012 (EDT)

Laugh and a half
Here's a wally who thinks you can copyright $\frac 1 3 = \frac 1 2 - \frac 1 4 + \frac 1 8 - \frac 1 {16} + \cdots$

http://en.wikipedia.org/wiki/User_talk:WIKI-1-PIDEA#Angle_trisection

How we laughed! --prime mover 15:20, 30 March 2012 (EDT)

Category:Disproofs
Just today, Restriction of Non-Reflexive Relation is Not Necessarily Non-Reflexive was posted. I would argue it belongs in the category Category:Disproofs and maybe some more specialised category linking to Proof by Counterexample. The title could then maybe even be:


 * Disproof:Restriction of Non-Reflexive Relation is Non-Reflexive

I'm bringing this up as the 'not necessarily' in the title shows that it isn't really a 'proof' in some intuitive, emotional sense. What do you think? I haven't bothered practical objections like the linking structure on the site. --Lord_Farin 10:56, 1 April 2012 (EDT)


 * Possibly ... but then there are going to be some borderline cases (can't think of any) which are perhaps proofs of a negative result, etc. Proofs by counterexample may already exist as a category (like "direct proofs" and "proofs by induction") but I've never been a fan of such categorisation strategies so I haven't kept them up to date. --prime mover 14:39, 1 April 2012 (EDT)


 * That's what redirects are for. I noticed that the categories expressing kinds of proofs aren't very popular, and I don't care enough to change that. --Lord_Farin 18:25, 1 April 2012 (EDT)

Source works
Before I just delete the offending line, what's the thoughts of others on a discussion in a maths forum as an appropriate "source work" for a given page? I expect you may be able to guess which page(s) I'm talking about. The forum consists of the contributor raising hypotheses which other contributors to that forum are either disproving immediately or expressing scepticism about. --prime mover 17:58, 4 April 2012 (EDT)


 * I'd rather have no source. --Lord_Farin 18:06, 4 April 2012 (EDT)

Axiom of Countable Choice
As concern had been expressed about the inability to adequately discuss results depending upon the Axiom:Axiom of Countable Choice, I have put together Template:ACC which can be included, in a similar way to Template:AoC, at the bottom of any result which requires the ACC for its validity.

However, I am unfamiliar with the philosophical implications of ACC (they're nowhere near as widely discussed as those of AoC) so can't do justice to the wording.

Is there anyone out there who knows (and is philosophically liberal) enough about this to be able to make a better job of wording it? --prime mover 03:47, 5 April 2012 (EDT)