Wikipedia talk:WikiProject Mathematics/Archive/2008/Apr

Wiener sausage

has been linked from the main page. Unfortunately this means it is picking up some juvenile vandalism, and could do with watching. R.e.b. (talk) 16:10, 1 April 2008 (UTC)

Werdnabot is back

FYI, according to Wikipedia:Wikipedia_Signpost/2008-03-31/Features_and_admins, Werdna (talk · contribs) and his Werdnabot (talk · contribs) have returned. Werdnabot appears to be archiving again. JRSpriggs (talk) 12:19, 2 April 2008 (UTC)

Combinatorial number theory

I just noticed that we have no article titled combinatorial number theory. Should I be surprised? Michael Hardy (talk) 02:48, 2 April 2008 (UTC)

Not while we have (as far as I can see) no article which even mentions compactness arguments in combinatorics. Algebraist 13:10, 2 April 2008 (UTC)

I'd like to see that article, but I'm not up to the task of writing it. CRGreathouse (t | c) 14:30, 2 April 2008 (UTC)

I second those sentiments. --Cheeser1 (talk) 15:34, 2 April 2008 (UTC)

In the article space, exactly five articles link to combinatorial number theory, and two of those are lists. Michael Hardy (talk) 13:17, 3 April 2008 (UTC)

Area theorem

Right now, area theorem redirects to black hole thermodynamics. But there's an important theorem about conformal mappings called the area theorem. I checked, and there's nothing that links to area theorem. I'm planning on writing an area theorem article. What should I do, just erase the redirect? (I'm a wiki-newbie.) Oded (talk) 05:07, 4 April 2008 (UTC)

If you are sure that the article does not already exist under another name, then change the redirect into a disambiguation page (see Wikipedia:Disambiguation). That page should have links to: your new article (perhaps called area theorem (conformal mapping)), the article on black hole thermodynamics, and any other articles which talk about "area theorems" (such as Heron's formula for the area of a triangle). JRSpriggs (talk) 05:38, 4 April 2008 (UTC)

I've made it into a disambiguation page. Maybe that could use a bit more polishing. Michael Hardy (talk) 19:50, 4 April 2008 (UTC)

Maths Short Cuts

Maths Short Cuts is as clumsily written an article as you'll ever see. Delete? Michael Hardy (talk) 13:15, 3 April 2008 (UTC)

Delete. silly rabbit (talk) 13:18, 3 April 2008 (UTC)

The first revision of the article contained a {{db-nocontext}}, so this is probably a recreation of some sort. I don't think the clumsy style itself should be a concern for deletion (but if the article does stick around, it needs to be moved to appropriate capitalization, it needs a grammatical rewrite, and it needs re-wikification). It is not too hard to imagine a well written article on the topic: there are a reasonable number of articles in math(s) ed. about shortcuts, and process versus understanding, so one could have a nice section surveying the ed. literature, using one of Polya's books perhaps as a guide. Similarly, there is a huge business worldwide in "cram schools", "crib sheets", etc. and one could have a section surveying the business aspects, perhaps including links to series such as Schaum's outlines, or Kaplan's preparation things.

None of this precludes deleting the current article, which is unsourced (and nearly blank after removing unsourceable material and WP:NOT#Textbook problems). The current editor is probably not signing in, but still working from changing IPs in the 59.* range. JackSchmidt (talk) 13:33, 3 April 2008 (UTC)

The page was created before, by the same author, with the same content, and deleted once. My personal opinion is that we want to avoid making a "list of ways to guess the answer to a math problem." Unless someone has an idea of what an encyclopedia article on this topic could contain, I also would agree with deletion. But we should contact the author as well to explain this. Also, remember that issues with English presentation can be easily fixed later, so it's really only issues of content that should be relevant to deletion. — Carl (CBM · talk) 13:43, 3 April 2008 (UTC)

Generally I would agree that poor Englsh can be fixed in an otherwise useful article. But the problems with this article run much deeper than grammar and spelling. How do you even begin to make sense of a sentence such as "To know the nature of a triangle,just assume the angles keeping in the mind that the sum is 360⁰". This particular article is such an incoherent jumble that it is unfixable. Anyway, I had already attached a prod tag before I saw this discussion. But if it is a recreation of a previously deleted article, that is sufficient grounds for speedy deletion isn't it ? Gandalf61 (talk) 21:25, 4 April 2008 (UTC)

No, {{db-g4}} requires that the article was deleted after an afd process. Since it was a speedy deletion, it doesn't apply. Cenarium^Talk 16:33, 6 April 2008 (UTC)

Delete + salt = 360⁰ⁿ⁺¹. --Cheeser1 (talk) 21:58, 4 April 2008 (UTC)

Contested prod, nominated for deletion, see Wikipedia:Articles for deletion/Maths Short Cuts. If you think that you can make a decent encyclopedic article on the subject, you have 5 days. However, it will certainly still fails WP:NOT#MANUAL and WP:N, so it will be deleted anyway. Cenarium^Talk 15:40, 6 April 2008 (UTC)

I agree with all of you.Thanks a lot for your response.But my purpose of starting this article is to help EAMCET aspirants in wikipedian way.As wikipedia users increasing in India are incresing,shortly it will be found to be a very useful page.Undoubtly, talented lecturers will contribute to this page,IF IT IS NOT DELETED.Many students in India are craving for Maths Short Cuts as succeeding in the test is a do or die problem for them.If you encourage this article,including my self and many others will start to make this a very useful page.Feel free to delete if still it is felt useless.Thank you--Chintapalli David Raju (talk) 16:36, 6 April 2008 (UTC)

The problem is that Wikipedia is an encyclopedia, and the primary purpose of a page is not to be useful for some people, but to be an encyclopedia article. Internet is vast and diversified, I'm sure that EAMCET aspirants can find specific help on other sites. Cenarium^Talk 16:49, 6 April 2008 (UTC)

Hadamard finite part integral

The new article titled Hadamard finite part integral uses the word "hypersingularities". I don't know what those are, so I searched for hypersingularity and hypersingularities and found nothing. Should we edit this to say [[hypersingularity|hypersingularities]]? Michael Hardy (talk) 19:45, 4 April 2008 (UTC)

Hypersingular integral equations are integral equations whose kernel has a singularity of an order greater than one. They arise in the study of spatial problems in air and fluid dynamics, elasticity, the theory of diffraction of electromagnetic and acoustic waves, ecology, etc. Usually, hypersingular integral equations are obtained as a result of reducing Neumann boundary value problems for the Laplace or Helmholtz equation to integral equations by means of the double-layer potential. 81.249.161.2 (talk) 08:47, 6 April 2008 (UTC)

Well, I see that we had no page titled singular integral equation, so I created it as a redirect to integral equation. Now a question is whether to do the same with hypersingularity? Or can that term also be used elsewhere than in integral equations? Michael Hardy (talk) 14:54, 6 April 2008 (UTC)

If the page for the technical term frobnitz redirects to Frotzian, then I think the term frobnitz should be introduced somewhere on the target page.  --Lambiam 16:52, 6 April 2008 (UTC)

If so, that's not a reason not to introduce the redirect BEFORE the mention of frobnitz is on the target page. Instead it's a reason to add some mention of frobnitz to the target page. And if the added material is extensive enough, in some cases the mention should be a link to the redirect page which should then get converted into an article. Michael Hardy (talk) 16:55, 6 April 2008 (UTC)

Only if frobnitz will get mentioned in a reasonable amount of time after the redirect is created. The page Frobnitz has been a redirect page since 11:04, April 24, 2006, but the term is not mentioned on the target page (although in this case actually because someone deleted an existing mention).  --Lambiam 20:52, 6 April 2008 (UTC)

Shall I propose Hypersingular Integral Equations and Their Applications by I.K. Lifanov, G. Vainikko, L. N. Poltavskii, MG.M. Vainikko (Taylor & Francis, Inc. publisher) 2003 - ISBN-13: 9780415309981 and Hypersingular Integrals and Their Applications by Stefan G. Samko, Samko Samko (CRC Press) 2001 - ISBN-13: 9780415272681 as possible references to hypersingular integral equations? 81.249.161.2 (talk) 21:57, 6 April 2008 (UTC)

Axiom schema of replacement

The article on the Axiom schema of replacement is so poorly written that I cannot bear to even look at it. Too many versions are discussed and the formulas and explanation are all awful. JRSpriggs (talk) 14:06, 30 March 2008 (UTC)

What do you think of this formula (from Axiom of infinity):

$\exists \mathbf {N} \forall n(n\in \mathbf {N} \iff ([\forall k\in n(\bot )\lor \exists k\in n(\forall j\in k(j\in n)\land \forall j\in n(j=k\lor j\in k))]\land$

$\forall m\in n[\forall k\in m(\bot )\lor \exists k\in n(k\in m\land \forall j\in k(j\in m)\land \forall j\in m(j=k\lor j\in k))]))\,?$

 --Lambiam 20:53, 30 March 2008 (UTC)

Perhaps JRSpriggs is referring to the fact that both formulae in the 'variants' section are incorrect? Algebraist 21:11, 30 March 2008 (UTC)

That was a temporary error as I was editing the page to try to help JRSpriggs edit it again. I copied and pasted some improved LaTeX code but didn't remember to fix it before I hit save. Things are better now, in every sense. — Carl (CBM · talk) 21:12, 30 March 2008 (UTC)

Sorry, I missed that. That is an improvement. Algebraist 21:14, 30 March 2008 (UTC)

To CBM: Thank you for your edits. The article is much better now. JRSpriggs (talk) 10:44, 31 March 2008 (UTC)

I've had the same experience before - I open a page, look at it, and can't bear to look at it any more. I've been through that process with Propositional logic more than once. — Carl (CBM · talk) 18:26, 31 March 2008 (UTC)

Open the page, make one very small change, then don't come back to it for a month. Repeat for the next five years, or until satisfied. linas (talk) 02:29, 8 April 2008 (UTC)

To Lambiam: As you know, I wrote that formula in the axiom of infinity. Obviously, it is correct and written in the best style of formal language. However, it is difficult to understand because it is entirely formal using the element relation and equality rather than derivative concepts. There also was an English rendering which is much clearer. To help you and others, I just added another rendering of intermediate formality. JRSpriggs (talk) 11:01, 31 March 2008 (UTC)

I did some more work on the axiom of infinity. I hope you like it better now. JRSpriggs (talk) 06:08, 1 April 2008 (UTC)

We have no notational convention for quantifications, and indeed the notations are all over the place in different articles. Personally I find

$\exists \,\mathbf {I} :\emptyset \in \mathbf {I} \,\land \,(\forall x\in \mathbf {I} :x\,{\cup }\,\{x\}\in \mathbf {I} )$

easier to read than

$\exists \mathbf {I} \,(\emptyset \in \mathbf {I} \,\land \,\forall x\in \mathbf {I} \,(\,(x\cup \{x\})\in \mathbf {I} )).$

Since the formal language of ZFC has not been presented, it is not obviously meaningful to state that one formal formula is more formal than another formal formula, and presenting the allegedly more formal version to the reader serves no clear purpose.  --Lambiam 09:03, 1 April 2008 (UTC)

Do you know where the colon notation comes from? I see it in a few place on WP. There is a well established standard in contemporary mathematical logic, and I think it's reasonable for us to use that standard here. The convention is that in general we quantify θ like so: $\forall x(\theta )$ or $\forall x\theta$, depending on whether the scope of the quantifier is clear. I don't think I've ever seen a contemporary mathematical logic text that uses commas, periods, or colons to delimit formulas. Of course this isn't an issue of being "more formal", it's just a convention for syntax of first-order formulas. — Carl (CBM · talk) 12:17, 1 April 2008 (UTC)

I see the style with the colon often, but perhaps not in logic textbooks as such. I'll check Enderton when I get home. CRGreathouse (t | c) 13:43, 1 April 2008 (UTC)

I have Enderton's book here, and he doesn't use colons. Neither do Mendelson's or Kleene's undergraduate texts (Mendelson does use the older (x)(Ey) notation). I also looked at a few set theory books: none of Jech, Kanamori, Kunen, or Levy use colons, periods, or commas.

It must be that someone uses colons; maybe it's common in some other field? — Carl (CBM · talk) 13:53, 1 April 2008 (UTC)

To Linas: The changes (by CBM and myself) to both axiom schema of replacement and axiom of infinity as a result of this discussion were substantial, not minor. JRSpriggs (talk) 07:54, 8 April 2008 (UTC)

Knaster–Tarski theorem vs Kleene fixpoint theorem

The second page has no reference at all and the result is a direct consequence of the first one. The two pages should probably, at least, be merged. 81.249.161.2 (talk) —Preceding comment was added at 07:51, 7 April 2008 (UTC)

Bieberbach conjecture

Copied from User talk:Oleg Alexandrov

Requested move: De Branges' theorem --> Bieberbach conjecture

I left a comment on the talk page a couple years ago:

So the article says it was formerly called the Bieberbach conjecture. I found that odd as I've always thought of it as Bieberbach conjecture, and heard it often referred that way. Do specialists really call it de Branges' theorem? A preliminary look through MathSciNet, seems to indicate that "the de Branges theorem" actually refers to a more general theorem that implies (among other important stuff) the Bieberbach conjecture. --C S (Talk) 07:36, 15 April 2006 (UTC)

I looked through search results on Google Scholar, and I don't find any reference to De Branges' theorem other than those refer to either other or more general results. It appears the name is still "Bieberbach conjecture".

--C S (talk) 18:48, 7 April 2008 (UTC)

Any comments on this? I can easily do the move on the technical grounds using the admin buttons but perhaps people familiar with the topic in question can comment on this first. Thanks. Oleg Alexandrov (talk) 05:51, 8 April 2008 (UTC)

I am somewhat familiar with the topic albeit as an observer. My impression is that the term "Bieberbach conjecture" is still widely used, and the people working in the field have not switched to "de Branges' theorem". The wiki entry should certainly be entitled "Bieberbach conjecture", his distasteful sympathies for nazism notwithstanding. Katzmik (talk) 10:53, 8 April 2008 (UTC)

I agree that it is still mostly reffered to as the Bieberbach conjecture. However, both names are legitimate. It is somewhat of an editorial choice at this point. If we think that it should be called de Brange's theorem, then that's what we should call it. Oded (talk) 15:00, 8 April 2008 (UTC)

According to the naming conventions we should use what is the most common name, and not what we think it ought to be.  --Lambiam 20:18, 8 April 2008 (UTC)

Bieberbach conjecture is definitely the common name. Both names were mentioned in the complex analysis courses I took, and the preferred name was always B.c. Neither of the men involved have bland histories, so trying to chose a name that gives the most "dignity" is not likely to succeed for this article. JackSchmidt (talk) 20:28, 8 April 2008 (UTC)

If that's the common name, then it should be moved back. Whether it should be called "de Branges' theorem" is completely irrelevant; we are not in the business of language reform. When and if that becomes the accepted name, it can always be moved again. --Trovatore (talk) 20:58, 8 April 2008 (UTC)

One could make the point that the situation in mathematics is different and that the discussion in naming conventions does not apply. The issue here is not like the distinction between using the common dog rather than the scholarly Canis lupus familiaris. In mathematics, naming a result is also a way of attributing (and often mis-attributing) credit. The discussion in naming conventions does recognize that exceptions are sometimes beneficial. Oded (talk) 21:00, 8 April 2008 (UTC)

It is not our job to correct historical injustices. We reflect the common usage in the field. This is by no means a unique situation -- for example Zorn's lemma was not, or at least not essentially, original to Zorn (and he never claimed it was). --Trovatore (talk) 21:02, 8 April 2008 (UTC)

Agreed. L'Hôpital's rule being another classic example. --Cheeser1 (talk) 21:17, 8 April 2008 (UTC)

Incidentally, do we have an article listing such cases (misattributed names in math)? I imagine it would be rather large, but interesting to peruse. Hamming number might be another example of this. CRGreathouse (t | c) 03:51, 9 April 2008 (UTC)

I seem to recall that maybe there is such a list. In my opinion, though, there should not be. It's too subjective. --Trovatore (talk) 03:55, 9 April 2008 (UTC)

Sounds like one of many places to edit war about who stole calculus from whom. Not to make any WP:BEANy suggestions. --Cheeser1 (talk) 04:44, 9 April 2008 (UTC)

List of misnamed theorems. —David Eppstein (talk) 04:45, 9 April 2008 (UTC)

OK, I performed the move. The move can be of course undone should in the future be agreement about it. Oleg Alexandrov (talk) 02:46, 9 April 2008 (UTC)

Dubious math

Don't know if this is the best way of handling this, but on Random article patrol I came across Straferunning, about a technique in video-gaming. My math is a bit rusty, but I've a feeling that the "Mathematical proof" in this article is a hoax...input appreciated... Camillus (talk) 00:07, 9 April 2008 (UTC)

Although I go by a preliminary, brief glance here, I concur: this seems to be a collection of mathematical phrases such as "tangent", thrown together with some nice formatting. Particularly, "df = tan (ψ) / cos (ψ), when df = 0 then ψ = 0." seems completely irrelevant with regards to video-gaming. I have wiped the dubious material. Anthøny 00:27, 9 April 2008 (UTC)

I don't claim the proof is not a hoax or a joke, but it is more or less correct. It appears to be appealing to calculus to prove an elementary statement about real numbers or even more intuitive statement about right triangles: the hypotenuse of a right triangle is longer than either its adjacent or opposite side. The calculus is standard, if f(0) >= 0 and f'(x) >= 0 for 0 < x < 1, then f(x) >= 0 for 0 < x < 1. The proof apparently iterates this method to avoid doing any analysis on trig functions. In my opinion the proof given in the lead is just fine, or if one wanted to be formal, quote the pythagorean theorem. JackSchmidt (talk) 00:41, 9 April 2008 (UTC)

I have heard of this issue elsewhere. In some games that limit speed independently for forward and sideways movement, you can get a higher maximum speed by running both forward and sideways at the same time. This is a simple consequence of vector addition (or, as JackSchmidt says, the Pythagorean theorem). — Carl (CBM · talk) 17:49, 9 April 2008 (UTC)

If you can also move diagonally, it just means the game has the Chebyshev distance as its metric, so then that is "normal" in the game's virtual world. If you use a screen on which the pixels are 2mm by 2mm instead of 0.2mm by 0.2mm, do you go ten times faster than normal?  --Lambiam 18:18, 9 April 2008 (UTC)

This is off-topic, but: games like this keep track of each player's position using some internal coordinates, not based on pixels. Distance between players is measured in the ordinary Euclidean metric for purposes like telling how long it takes for a projectile from one player to reach the other player. So outrunning other opponents is important, which is why people learn to do things like run diagonally in order to get a competitive edge. The archetypal technique of this sort is probably circle strafing. — Carl (CBM · talk) 18:31, 9 April 2008 (UTC)

New template for talk pages, expecially the larger ones

{{Unanswered}} Some pages, such as this one have lots of post, and it requires some work to see what has been answered or acknowledged. therefore I have helped make the {{Unanswered}} template that can be put above a section allowing one to quickly glimpse what has been answered. If you were waiting for an answer but never got one as the post in somewhere in the middle tag it! please voice any queries or comments in the talk page ofTemplate:Unanswered (links, talk) and not here. Cheers --Squidonius (talk) 15:12, 13 April 2008 (UTC)

Wanted: Ring theorists and abstract algebraists

Hello math people. I have been working to reconstruct the article about Emmy Noether on my drawing board. I have completed her biography and have now come to the part where I must explain (briefly, but in some detail) her contributions to mathematics and theoretical physics.

However, I – as an English teacher who dropped out of pre-calculus in high school – can't understand a single word of the math involved. I'm hoping one of you is willing (or can recommend someone) to help me write these final sections about Ms. Noether's work in the fields of ring theory, abstract algebra, Galois theory, and algebraic geometry. If so, please leave a note here (I'll watch the page) or – preferably – on my talk page. I thank you in advance and will now recede to my lair of Balzac and Achebe. – Scartol • Tok 00:18, 14 April 2008 (UTC)

The drawing board has now been shipped out to the main article. Scartol has done a great job and has asked me (among others) to help with the math. Although I can probably wax lyrical about Noether's theorem and Noetherian rings, I'm not a physicist or an algebraist, so I would encourage anyone here, especially those who have expertise in these areas, to dive in! Geometry guy 21:02, 15 April 2008 (UTC)

WP:Featured article candidates/Emery Molyneux

There's an FAC here with math related content (Emery Molyneux) which needs content-expert input. Can editors here provide some? Thanks, Geometry guy 00:28, 16 April 2008 (UTC)

Introduction to M-theory

An AfD debate: Wikipedia:Articles for deletion/Introduction to M-theory.

I would really, really like to have WP policy changed so that AfD debates could take place under the guidance of specific wikiprojects, rather than be open to general debate. This latest AfD is not unlike previous drive-by deletes, where those voting for deletion are non-mathematicians who have no clue or interest in the topic, and those voting to keep are the usual crowd you'd see here.

I think this wikiproject is entirely capable of self-policing, and of deleting bad articles. At the same time, we mostly don't run around trying to delete articles on pokemon or high-schools. Thus, I'd really like to see a policy where non-wikiproject editors would be discouraged from "meddling" in wikiproject affairs, including the deletion of good/bad articles. linas (talk) 03:15, 16 April 2008 (UTC)

Reposting from WP:Physics:

Introduction to M-theory was completely rewritten in 2004 by an editor who included large swaths of text copied verbatim from the book Turn of the Century. The article was brought up for concerns about no references being cited in such a large article and the general format of 'introduction to...' articles when the copying was noticed (see Wikipedia:Administrators' noticeboard/Incidents#X for Dummies fork). Due to the volume of the material copied, and subsequent wording changes being derivatives of the copyrighted text, all revisions of the article since January 2004 were deleted. Since this was a lengthy article, I would appreciate it if members of this wikiproject could get it back up to speed. Four years is a long time to miss things in most theoretical science fields :) -M^ask? 09:00, 14 April 2008 (UTC)

---

There is Wikipedia:WikiProject Deletion sorting. I notice that this project has yet to include any science categories. I don't know if there are other Wikipedia initiatives to categorize deletion discussions. It seems like a good idea. Better, at least, than having someone post here every time there is a deletion discussion within the scope of the project. silly rabbit (talk) 14:03, 16 April 2008 (UTC)

"Formal Laurent series" redirect to .... ?

Formal Laurent series now redirects to formal power series. I can imagine it redirecting to Laurent series. I can also imagine it being a page with links to both of those and little else until someone decides to make an article of it, but then someone might be tempted to call it a "disambiguation page" and of course that's not what it would be. What is the best thing to do with that page? Michael Hardy (talk) 03:03, 17 April 2008 (UTC)

It could redirect to the section Formal power series#Formal Laurent series. PrimeHunter (talk) 03:13, 17 April 2008 (UTC)

Problem editor

I am sick and tired of User:Mathsci making snide, disparaging, factually inaccurate, and incivil comments in the edit summaries (as well as on talk pages) any time I happen to be editing an article that he considers his own. He apparently believes that no sentence he has ever breathed upon can be changed without his sanction. I have ceased working on several articles because I do not appreciate being personally attacked in return for my efforts to improve Mathematics coverage at Wikipedia, which includes correcting errors made by people who don't believe that they could make an error and rearranging material to be helpful to the reader, not the author. If anyone else here thinks that his attitude runs contrary to the spirit of Wikipedia (or even violates some policies that we have here), will that person or persons be so kind as to let it known to him? In the meantime, I'm withdrawing from Wikipedia. All the best, Arcfrk (talk) 23:04, 6 April 2008 (UTC)

It's hard to tell exactly which edits or articles you're looking at. A quick scan turned up this edit, but there must be more than that to be this distressing. These things are often better handled by discussion talk pages, rather than edit summaries, even though it seems like the least efficient way at times. — Carl (CBM · talk) 23:29, 6 April 2008 (UTC)

This has been reported before: at the ANI. But I don't have the time now to read through it at all. --Cheeser1 (talk) 23:37, 6 April 2008 (UTC)

Such editors are not that uncommon indeed. Arcfrk, I'd suggest you don't give up on editing, and please notify us on this page if in the future you need extra opinions on how something should be written (from my experience just going back and forth with the same editor and no outside input is not always a productive way of doing things). Oleg Alexandrov (talk) 01:15, 7 April 2008 (UTC)

The only recent edit summary I can find that Arcfk might be referring to is [1], but that's over 2 months ago. Both of you appear to have made valuable contributions to Wikipedia. There are bound to be some personal(ity) clashes in any community but it's a shame if they cause valued people to leave. YoMaybe a short wikibreak would be enough? Qwfp (talk) 05:25, 7 April 2008 (UTC)

A fellow mathematician just told me that this was going on. I am unaware of any serious content dispute that User:Arcfrk has had with me in mathematics. He did propose splitting up the Orbifold article, but with little or no attempt to discuss or justify the matter on talk pages. Is it possible that I might have blinded him with science? (BTW, Cheeser, we are not discussing my edits to Marseille and Aix-en-Provence here, where I am still apparently being wikistalked by the Australian User:Michellecrisp.) For those that are interested, I have had a wikibreak while giving a graduate course in the UK, but will now probably be preparing articles on Weyl-Kodaira theory and spherical functions for SL(2,R) and SL(2,C), with applications to the Selberg trace formula. With no history of prolonged edit conflicts or revert wars in mathematics articles (or elsewhere), I have no idea why User:Arcfrk has brought his complaints here. No diffs were provided from mathematics articles and there's probably quite a simple explanation for that :) Differences are usually easily resolved in advanced mathematics articles (for example the slight clarification to the lead in Kazhdan's property (T) following CBM's intervention). Mathsci (talk) 20:33, 9 April 2008 (UTC)

For the record, the name just rang a bell, I have no familiarity with or opinion on this issue - old or new. Just providing a link to anyone who cares to click it, in the interests of transparency. --Cheeser1 (talk) 22:29, 9 April 2008 (UTC)

Transparency? I have no idea what you could mean by that; nor can I pretend to compete with you for visibility on WP:AN/I. Mathsci (talk) 20:12, 11 April 2008 (UTC)

I'm afraid I can't help you learn common definitions of English words, although you might try the OED entry for transparent, meaning 2a. As to whether or not you and I are more "visible" on the ANI, that is I'm afraid, not an appropriate nor relevant point of discussion. Excuse me if I have somehow struck a raw nerve by providing a helpful and at least somewhat, if not completely, relevant link. --Cheeser1 (talk) 23:35, 11 April 2008 (UTC)

I think this is a problem in communication, arising partially from anonymity. Some people aren't as careful with their words as they may be in real life. There is, in fact, a way to tell someone they're wrong nicely. Some people find the lack of authority in anonymity troubling. Additionally, consistently hinting of one's real life authority will usually only serve to annoy others (especially in contexts to bolster one's arguments). There are lessons for all involved parties here. But there is no "problem editor" here, I think. Thank goodness. A candidate for "problem editor" is more likely to be found at Talk: complex number, although s/he doesn't really compare to the last time I recall a section called "problem editor" here. --C S (talk) 02:15, 10 April 2008 (UTC)ic

Even on that page, I think that everyone involved has the interests of the article in mind. The pages on elementary topics such as number systems, functions, etc. have a well deserved reputation for being more difficult to work on, but I think it is more due to the bike shed effect than to bad intentions. I try to limit my own participation on those articles to balance stress against benefit. — Carl (CBM · talk) 02:28, 10 April 2008 (UTC)

In fact, in the article on the Surfaces, there was no account at all of Gauss' contributions (differential geometry), even though most of this is often regarded as undergraduate material (if, following Gauss, connections are not used). I added the standard classic material and did not object when User:Arcfrk split off the material. However, he failed to provide a short summary of the material removed from Surfaces, which therefore has not improved the article. (I pointed this out on the talk page of the article, but there was no response.) Moreover the lead he wrote for the newly-formed Differential geometry of surfaces was a short essay in WP:OR which bore no relation at all to the actual considerable content and was unsourced: it did not even mention the name of Gauss. I therefore altered the lead to reflect what was actually covered by the article, which at that stage was all my own work. I have no idea why he decided to add unsourced personal material in the lead, but that is possibly a problem with his editing. In Boundedly generated groups he seemed not to want the the now classic 2 page "automaton" counterexample of Grigorchuk to be cited. He also does not seem to allow sufficient time to discuss these splits before making them. Instead of moaning here, why doesn't User:Arcfrk write a mainspace article on the Gromov boundary? Mathsci (talk) 07:10, 10 April 2008 (UTC)

Aha, caught in the act: [2]! But seriously, regardless of what you may think of Arcfrk's style, I think Wikipedia is much better off with his/her contributions than without them. My suggestion is that the two of you should make amends. You are both valuable to the project. It's unfortunate that this thread is a referendum on you personally, and it is understandable that you would become defensive. But I myself see no evidence that you are, or have ever been, a problem editor. Same with Arcfrk. silly rabbit (talk) 22:09, 11 April 2008 (UTC)

If you examine the edit history, prior to Arcfrk deciding on the move, you will see that I wrote all of the lengthy main text. Arcfrk's lead did not reflect the content of the article, was unsourced and possibly WP:OR. He should get out of the habit of chopping up articles so hastily. As you will see on the talk page of Surfaces, I was not against the move. However, as I've said above he did not even bother to summarise the material excised from Surfaces. I don't think that is very helpful for Wikiproject Mathematics. Mathsci (talk) 08:09, 17 April 2008 (UTC)

We seem to be singing from the same hymsheet, silly rabbit (even citing the same edit). Glad to see you're still around too! (Red sig is a cute trick..)Qwfp (talk) 23:11, 11 April 2008 (UTC)

The only things that MathSci has blinded me with are his bad manners, amount of bile he spits into the edit summaries and comments on the talk pages, and his unjustified cockishness. Ah, sorry, forgot the scale of his hypocrisy. I first encountered him when he was engaged in an ugly dispute with another editor concerning the spelling of von Neumann's name, making his trademark insinuations about the level of intelligence and/or professional knowledge and ordering another editor not to touch his article. One of the things he said then was

But I am a little upset that you choose to be rude to mathematicians. They are only the people who could have created this article.

— obviously, not the principle he would follow himself. He complained ad nauseam about the widely supported split of the "Differential geometry of surfaces" that I had performed, opting for attacking my rather extensive edit for the epsilon that it was lacking, instead of "graciously accept"ing (another of his free advices to others that he doesn't like to follow himself) the consensus to fork, and helping to smoothen it (incidentally, "Differential geometry of surfaces" is one of the articles that badly need improvement but which I wouldn't touch given the inevitable attacks on anyone who dares to emend MathSci's "all my own work").

Those interested can look over his talk page archives to test the validity of his statement about "no history of prolonged edit conflicts or revert wars in mathematics articles (or elsewhere)", as well as the talk page of "Orbifold", where his non sequitur response to my forking off proposal included an attack on my mathematical competence. Although to this day he did not condescend to write a substantive reply, he (hypocritically) accused me of "little or no attempt to discuss or justify the matter on talk pages" in this very thread! I am far from surprised, though, given the belligerent spiel that he posted on my talk page after my earnest attempt to clean up "Boundedly generated group". And so on, and so forth. Instead of calling my well-founded concerns "moaning", why doesn't he look in the mirror, and apply the same standards to himself as he does to the others?

Sorry for the long ramble, and I do wish that we were spending the time more productively, by adding new content and improving the quality of existing articles through editing and reasoned discussion that does not involve personalities of the editors. I reckon I was dreaming. Arcfrk (talk) 07:34, 13 April 2008 (UTC)

Arcfrk seems to be attempting to prolong a non-existent drama. Meanwhile, off-wiki the Weyl-Kodaira article is coming along apace :) Mathsci (talk) 08:09, 17 April 2008 (UTC)

Arcfrk, I agree with many of your sentiments, seems like Mathsci enjoys disparagaing behind my back here on the maths page. Look at this talk page (some of it has been archived), quite a few editors have complained to him about his behaviour especially when he doesn't get his way, he accuses legitimate editors of vandalism or trolling. Look at my contributions, I am neither a troll nor a vandal, and contribute to a wide range of location articles all around the world. Mathsci tried to strongly discourage me from contributing to any French place articles in a display of WP:OWN. Michellecrisp (talk) 13:13, 17 April 2008 (UTC)

Mathsci's accusation of wikistalking is absolute WP:KETTLE when he himself has engaged in it against me. He has only ever edited one Australian article (while I have edited many French and European locations)...Mount Isa straight after I edited it, he did this nonsensical edit [3] which another editor clearly saw as deliberately disruptive [4]. Classic wikistalking if I ever saw it. Michellecrisp (talk) 15:54, 17 April 2008 (UTC)

What are you doing here on this mathematics wikiproject page, unless you are wikistalking me? As far as I am aware, you have little or no familiarity with higher mathematics. Stop trying to create wikidrama. You tried completely unsuccessfully to complain about me on WP:AN/I with no result whatsoever. (Apart from you and me, there was only one brief comment by another editor on that thread, which you needlessly prolonged.) What on earth are you doing here, apart from yet again trying to disrupt WP? Mathsci (talk) 18:59, 17 April 2008 (UTC)

But since you are here, let me point out a consistent failure in your use of logic. In mathematics it is usually not possible to prove things by producing one example. Similarly on the WP, we have a three revert rule. As far as I am aware I reverted something you wrote once in my wikipast. On dear. You claimed that I WP:OWN French place articles: however, again this was something you were unable to support by a reasonable number of diffs. Since I also occasionally help in stopping misguided edits to Prime number, perhaps you consider I also own that page too. I would be interested to hear your thoughts on vandalism to Prime numbers, since you have strayed to this page. (How did you find this page, unless you looked at my list of contributions?) Mathsci (talk) 19:09, 17 April 2008 (UTC)

User_talk:Michellecrisp#Random_comment.2Fquestion Djk3 (talk) 19:35, 17 April 2008 (UTC)

Thank you. The community at work as usual :) Mathsci (talk) 19:43, 17 April 2008 (UTC)

Some irony perhaps (failure in the use of logic)... ;] Tparameter (talk) 12:03, 18 April 2008 (UTC)

Since this is really a page for discussing math, I have to point out that the statement, "in mathematics it is usually not possible to prove things by producing one example", is false. In fact, there are as many proofs by counter example (one example) as there are real numbers. There are as many proofs using 'one example' as there are any other thing you can imagine. Tparameter (talk) 07:49, 19 April 2008 (UTC)

OK I'll come clean. It's all my fault. --CSTAR (talk) 16:49, 17 April 2008 (UTC)

Or von Neumann's :) Mathsci (talk) 18:59, 17 April 2008 (UTC)

As I member of the community I am always glad to help. Since effort had been made to mention Michellecrisp's name in a discussion she was not a part of, I thought it only fitting to invite her to the conversation. While I wouldn't call you a problem editor, you do seem to go "straight for the jugular" when it comes to mathematical prowess. When you use phrases like "you are simply completely out of your depth" you shouldn't be surprised people get insulted. Thenub314 (talk) 00:49, 18 April 2008 (UTC)

Isn't this just WP:SPADE? Why waste time trying to analyse other editors' personalities? That is not what WP is about. Isn't it enough that experts are willing to spend time adding useful mathematical content to the WP project? Mathsci (talk) 10:51, 18 April 2008 (UTC)

No, it's not enough. Not when an expert may chase away other experts with a confrontational attitude. It's not just Arcfrk; I just realized a day ago when editing free group that you had a hand in encouraging Jim Belk to not contribute as much as he would have. The talk page discussion seems to me to be a good example of why people may find you difficult. Just like any other open source project, sometimes it is more beneficial in the long run to turn away some experts who cannot learn to work with others. It has happened more than a few times before on math Wikipedia, and I'm sure it'll happen again. I don't think you deserve all or even many of the harsh remarks that have come your way, but I think you ought to realize there's a reason you've aroused such anger in your fairly limited time and interaction on Wikipedia. --C S (talk) 12:29, 18 April 2008 (UTC)

I was not analyzing your personality. I was not trying to offend you. I was just pointing out one reason why I think you tend to make people angry. I think C S remarks are well put. And I agree the answer to your question is clearly no. Thenub314 (talk) 21:27, 18 April 2008 (UTC)

I agree with thenub314, they indeed informed me as the subject of discussion here. I am here to defend myself and accusations on my character on Wikipedia. If this is a violation of Wikipedia policy then report me. I am concerned over Mathsci's behaviour on Wikipedia and it seems that I'm not the only one. Threats like this [5] don't help either. Especially as the Mount Isa example above demonstrates stalking behaviour that he so detests. I have also been contacted by another editor on another topic area concerning Mathsci's behaviour. Certainly, if we can all stick to the assumption of good faith this would be a better place. Michellecrisp (talk) 02:59, 18 April 2008 (UTC)

Meanwhile I have now started the task of writing Spectral theory of ordinary differential equations. If Michellecrisp wants to help write the section on Inverse Scattering Theory (Gelfand-Levitan) at some later stage she is free to pitch in. Otherwise I suggest she discuss my single edit to Mount Isa somewhere else where it might possibly have some relevance. Mathsci (talk) 10:47, 18 April 2008 (UTC)

Such a patronising comment (am I surprised?). I have as much interest in maths articles on Wikipedia as you have in Mount Isa. Michellecrisp (talk) 11:15, 18 April 2008 (UTC)

Under a thread about your snide remarks - a thread where you implicitly invited Michellecrisp to participate (by making an accusation of stalking) - I'm not sure if a random challenge to an intellectual bench-press contest on some specialized topic in math goes to support your side very well. Tparameter (talk) 12:12, 18 April 2008 (UTC)

Tparameter, I think now-vanished user User:Cheeser1, who recently disgraced himself on WP:AN/I, brought up Michellecrisp. Please could you use this page for making comments on mathematical edits: this is not WP:AN/I, no matter how much you might want it to be. BTW, on a different note, it was a great pleasure to encounter User:OdedSchramm helping with the lede to Differential geometry of surfaces. Sigh. Anyway back to Titchmarsh, Kodaira and good old Hermann Weyl. Are people on this page interested in writing mathematics articles or just in scoring points? Mathsci (talk) 20:02, 18 April 2008 (UTC)

For the record, I have never commented in, participated in, or paid any attention whatsoever to any WP:AN/I activity of any kind, so let's not let conspiracy theory get the better of us. Anyway, back on topic - all I'm saying is that if you accuse a user of some random infraction (for example, the aforementioned Michellecrisp stalking accusation that you made), then expect them to reply directly. Tparameter (talk) 00:23, 19 April 2008 (UTC)

I agree with Tparameter, Mathsci, you referred to off topic claim of wikistalking by me, first and here on this page and now say it should be restricted to maths only discussion. True, WP:KETTLE if I ever saw it. Then you tell me not to discuss it on your talk page [6] If someone is accused of violation of Wikipedia policy it should be discussed before further action is taken. Seems like Mathsci thinks he is always right on everything and no correspondence shall be entered into. Michellecrisp (talk) 04:15, 19 April 2008 (UTC)

Let's end this discussion now. I think there is wide concensus that (a) Mathsci is doing good editing work, (b) he/she tends to offend people and (c) we all ask him/her to be more considerate in the future. Let's try to put this behind us. Oded (talk) 17:36, 19 April 2008 (UTC)

Seems he hasn't learned to be considerate after Oded's message here, besides still complaining about me [[7], Mathsci accuses me of vandalism today [8] for this good faith edit [9]. Michellecrisp (talk) 08:00, 21 April 2008 (UTC)

Michellecrisp - you are being disruptive. You regrouped the Municipal library and the Friche visual arts centre under a section that you headed "Opera and Theatre" in Marseille. That was a capricious edit. An unjustified and unhelpful edit like that gives the impression of someone idly trying to make a suoerficial content-free change to the page, possibly to be provocative. And for Aix-en-Provence you included a reference to a claimed "cultural centre", citing a one sheet tourist guide as your only reference. This guide has no mention of a cultural centre, either in the french and english versions (usually available as rubbish on the streets of Aix). However, as I know, because I have attended performances at both places, there is a new "Grand Theatre de Provence" (already mentioned in the article) and a new "Pavillion Noir" for dance (this has been added to the article with a link to its website). Michellecrisp, you are vandalising articles, trolling, forum shopping, following me around (to other editors' talk pages) and disrupting the WP project. In future avoid capricious edits and find references that amount to more than a one-sheet fold out guide. Do you really have nothing better to do with your time? I will be forced to report you on WP:AN/I if you continue following me around. As I have said your persistent attempts to generate incidents artificially (eg as you have just done) does not place you in a very good light. Please stop making WP:TROLLish WP:POINTy edits to articles to provoke other editors. It gives the appearance of a scheming busybody.

Please also stay off this Wikiproject Mathematics page, unless you have comments to make on mathematics. I am still eager to here any of your thoughts on Fredholm determinants or Spectral theory of ordinary differential equations (which I fear, even unfinished, is too long, but that is partly because the articles on bounded variation and spectral theory are not quite up to par). Perhaps you think you can besmirch my mathematical reputation by heckling from the gallery, who knows. Mathsci (talk) 11:09, 24 April 2008 (UTC)

(ec) Here is the diff [10] that Michellecrisp was referring to. She is misrepresenting the edit summary which I include in full here.

rv capricious edit - restore previous form - Municipal library and the Friche Arts Centre have nothing to do with either theatre or opera

Nothing about vandalism. I also left a message on her talk page, not here, but she didn't see fit to mention that. In Michellecrisp's case it is very hard to assume good faith any more. As an act of kindness, mathematical editor User:R.e.b. tried to remove one of her provocative edits from my talk page (where she had left a comment about something that was none of her business). She rudely reverted it. [11] How can one assume good faith in such circumstances? Mathsci (talk) 11:38, 24 April 2008 (UTC)

Nothing about vandalism? you use that exact word here [12] Michellecrisp (talk) 11:44, 24 April 2008 (UTC)

I said "effectively vandalism" on your talk page, because you had effectively vandalised the article by making a foolish edit. I will try to get a mathematics adminstrator to archive this discussion to stop your trolling. The Municipal library is not a theatre, Michellecrisp. A visual arts centre is not a theatre or an opera house, Michellecrisp. Yet that is what your edits implied. You now come her complaining that somebody reverted these edits as "capricious". Kindly stop trolling and gaming the system. Resume your mainspace editing and stop wasting other people's time. Mathsci (talk) 12:01, 24 April 2008 (UTC)

Report me if you think I have violated Wikipedia policy because you keep wanting to, not sure why you haven't already, that's unless you're gaming. Others (not just me) above have commented on your lack of consideration and civility. I have not engaged invandalism or trolling, check the article in question or edits of any article that I've edited. the Aix reference seemed to be an official tourist guide not some "rubbish" this is where you really display lack of good faith and display WP:OWN by saying I've been there, therefore I am better. If it is an unsatisfactory reference then edit it out and let it be, not persist with this personal vendetta. your statement regarding "unless you have comments to make on mathematics" is another classical piece of WP:KETTLE, because you've spent the previous paragraph discussing your French article edits. I have made some contribution in terms of references to both the Aix en Provence and Marseille articles such as this [13] that have not been removed. Anyone else see the aggression and personal attacks in Mathsci comments? And let's not forgot his wikistalking on the [14] Mount Isa article. Michellecrisp (talk) 11:24, 24 April 2008 (UTC)

What is it that you don't understand that you don't understand about, Please stop following me around? Leaving gratuitous "busybody" messages here and on my talk page seems like provocative disuption. Please stop this, no matter how much pleasure it may give you. I'm still extremely busy editing mathematics articles. Get on with your own mainspace editing instead of making a nuisance of yourself here. Mathsci (talk) 11:44, 24 April 2008 (UTC)

You basically character assassinate me above accusing me of trolling and vandalism yet not reporting me, and I see fit to defend myself with evidence, that is permitted. Perhaps if you never even wrote about this today (seems you had the time to write a few paragraphs), I wouldn't have responded. simple. Michellecrisp (talk) 11:49, 24 April 2008 (UTC)

The diffs I provide above, with explanations, tell WP editors all they need to know about your currently not-quite-rational and seemingly emotional behaviour. I also would ask you please to leave this page if you only want to discuss edits to Aix-en-Provence and Marseille. You are deliberately trying to prolong a discussion ended by Oded Schramm. BTW I have never made any attempt to analyse your character, only your edits. Mathsci (talk) 12:13, 24 April 2008 (UTC)

P.S. It was you who posted after Schramm's winding up. What you wrote was nonsense, Now please just go away. I am currently preparing the section on hypergeometric functions from the original article in German. Your trolling here is a completely unwanted and irritating distraction. Mathsci (talk) 12:17, 24 April 2008 (UTC)

"Formally defined"

Many maths articles contain a phrase like "X is formally defined as Y". Does this have a different meaning than just "X is defined as Y", or is the word "formally" noise? Its use here does not correspond to any of the meanings listed under Formal#Mathematics.  --Lambiam 20:55, 8 April 2008 (UTC)

Can you give a few examples? I can imagine that in some situations one would say "X means this and that, but is formally defined as Y", because the first definition, while not entirely precise, might be helpful in conveying some intuition better than "Y". Oded (talk) 21:09, 8 April 2008 (UTC)

I think "formally defined as" is shorthand for "if you're looking for a high-level explanation, go ahead and skip this part". --Trovatore (talk) 21:10, 8 April 2008 (UTC)

I tend to agree it's often just noise, and in those cases I remove it as part of copyediting. For example,

A function is injective if distinct inputs are always mapped to distinct outputs. Formally, this means that if f(a) = f(b) then a = b.

Here the "formal" definition is no more or less formal than the other definition, it is just written using symbolic notation. I think it's a misperception among some writers that mathematics can't be rigorous or formal without using a lot of complicated symbols.

On the other hand, sometimes an article will have a nice intuitive explanation in the lede, and a more technical definition lower down. In that situation, it makes sense to indicate that the first "definition" is only intended to be approximately correct, and that the other one is the "formal definition". Combinatorial species and Universal property are examples of this type of article. — Carl (CBM · talk) 22:06, 8 April 2008 (UTC)

I can point to Matrix (mathematics)#Matrices without entries (which I contributed) where it says that "matrices should formally be defined, [...] as quadruples (A, r, c, M), where A is the set in which the entries live, r and c are the (natural) numbers of rows and columns, and M is [...] the matrix in the usual sense". A clear case where the formal definition is meant to coexist with, and differ from, the usual definition Marc van Leeuwen (talk) 07:16, 9 April 2008 (UTC)

An example is the first sentence of Complex number: "In mathematics, a complex number is a number which can be formally defined as an ordered pair of real numbers ...". This cannot be a case of a more precise definition after an intuitive one. (Personally I also think this is a bad way of introducing the concept; I once wrote a beautiful lede, but unfortunately other editors were not capable of recognizing its beauty.)  --Lambiam 17:26, 9 April 2008 (UTC)

That's a good example of a bad use of "formally defined". Although complex numbers can be represented as pairs of reals, there are other ways of defining the complex numbers (some are discussed lower in the complex numbers article) that don't require first defining real numbers. So to say they "are defined" that way is misleading. — Carl (CBM · talk) 17:45, 9 April 2008 (UTC)

To say that something "is defined" in a certain way never means that that's the only way to do it. And complex numbers do very frequently get defined in that way. Michael Hardy (talk) 17:47, 9 April 2008 (UTC)

It's a matter of context. If I say that a group "is defined" to be a set with an associative binary operation with identity and inverses, what I am trying to convey is that, for all practical purposes, this is the only definition of a group that one is likely to encounter. (Of course there are other definitions, such as a category with one object and every morphism invertible, but they are much less common). But that isn't true for the complex numbers; the representation as pairs of real numbers is akin to taking coordinates, but a coordinate-free viewpoint is equally important. Anyway, in that article, it is easy to rephrase the lede in a way that I think everyone can agree with. — Carl (CBM · talk) 18:20, 9 April 2008 (UTC)

To me it seems like a typical case of a precise definition that might follow a more intuitive one (but what precedes it in this case, I don't know; I haven't looked yet). Michael Hardy (talk) 17:46, 9 April 2008 (UTC)

I'm surprised by Carl's observation that complex numbers can be defined without first defining real numbers (although if one really wants to it is not hard, for instance as a topological closure of the "Gaussian rationals", but I cannot see any reason why one should do so). Note that Complex number#Characterization as a topological field is about characterising complex numbers, not about defining them, and nothing else I saw inthe article tries to forget about real numbers first. But this is probably beside the point of the current discussion. Probably you just meant to say complex numbers can be defined in other ways than by defining arithmetic operations on R², which of couse is quite true. Marc van Leeuwen (talk) 12:07, 11 April 2008 (UTC)

Every definition is, ultimately, no more than a characterization that fixes the definiend up to isomorphism.  --Lambiam 00:09, 12 April 2008 (UTC)

Is that definiendum or definiens? JRSpriggs (talk) 06:40, 12 April 2008 (UTC)

Definiend is an English form for Latin definiendum, like operand for operandum, solvend for solvendum, and so on.  --Lambiam 19:58, 12 April 2008 (UTC)

Hi, I am new to this section, having only very recently started to venture beyond spelling/grammar copyedits into deeper problems such as where rigour might rigourously require a 'form' (representation) that might not be strictly correct English grammar/spelling.

Right here right now what draws me into this piece of the page is wondering whether formal refers to form as in such things as G. Spencer Brown's "Laws of Form", or in such ideas as tokens, symbols, and representations?

Because, if it does, then the English gloss which is followed by the use of the term 'formally' and a representation in a 'form' (maybe even a 'formal system' in a Godelian sense???) makes sense to me, as it seems potentially to be saying that the English representation is not, or might not, be as 'formal' (in a Godelian sense even, maybe? Executable? Machine-readable? Machine-executable?) as the (possibly rigourous???) representation by means of a 'form' involving symbols rather than words.

Mind you, this ambiguity or potential ambiguity might be addressable by means of writing 'represented in [label of formal system aka 'form in the G. Spencer Brown sense'] as' instead of using the token or word 'formally'.

That is, maybe a distinction could be useful between 'formally' and 'in a form' (aka in a specific 'form', such as algebraic form or LISP form or FORTRAN form or C++ form or oilpainting form or whatever form one is about to use...)

Knotwork (talk) 10:59, 18 April 2008 (UTC)

Definitions in mathematics

Although this is a reply to a remark above I prefer to start a new section, as I am drifting away from the original discussion. I quote the remark:

Every definition is, ultimately, no more than a characterization that fixes the definiendum up to isomorphism.  --Lambiam 00:09, 12 April 2008 (UTC)

I disagree here, whether really every definition is meant, or just those of the complex numbers. For one, this gives too much importance to category theory, as if it were that one cannot define something before one has introduced a category first in which it is to live (so that "up to isomorphism" makes sense). As for the complex numbers, I'm not sure what that category should be; topological field seems to capture most uses of complex numbers, but I would hesitate to claim it allows expressing all important aspects of complex numbers. Second, there is a difference between on one had definitions of the complex numbers like R² equipped with a ring structure, or as R[X]/(X²+1), or as a subring of the real 2×2 matrices, and on the other hand characterisations like being the algebraic closure of the real numbers, or a particluar kind of topological field. The former are three really different definitions, even though one could do with any one of them because correspondences between the representations are easily established. The latter are two different characterizations of the complex numbers as an object in two different categories, and each determines the complex numbers only up to isomorphism in that category (and not even up to canonical isomorphism, because neither caracterization distinguishes complex conjugates). A characterization does not necessarily prove that anything exists that meets its requirements (even if often, as in case of algebraic closures, one knows this to be true). One of the points of category theory is that in many cases one does not have to, or want to, worry about which precise definition is used, since many questions only require knowing the object up to isomorphism; this is why one often characterizes structures as universal objects. But not everything in mathematics takes place within category theory, and in certain cases there is a choice between constructions that does not appear to related to isomorphisms in any particular category (think of constructions of the natural numbers or the real numbers).

There is an important lesson to learn here for wikipedia. Whether for reasons of category thoery or other reasons, one is in mathematics often less interested in what things are than how they behave (or are related), so several viewpoints about the former question can peacefully coexist (one one may even hold that it is immaterial what something is). However a wikipedia article, and particularly its lede, normally focusses on its subject itself, rather than on the context in which it appears, which gives a conflict with what one would like to do mathematically. I've seen long discussions along these lines in Talk:Polynomial and Talk:Complex number and they probably exist for other articles as well. However, I don't see any easy solutions; if one wants to cater for a broad and not necessarily knowledgeable public, one cannot just begin with saying that the structure is really all that matters: I'm sure that starting "A polynomial is an element of a polynomial ring" would put a lot of people off. (In the case of polynomials there is a separate article on polynomial rings, but there seems no point in having a separate article on the field of complex numbers.) It would maybe be interesting to have a discussion about guidelines how to handle this kind of question in general. Marc van Leeuwen (talk) 12:30, 12 April 2008 (UTC)

One issue I find interesting is that for certain objects, such as natural numbers, we begin with a naive understanding, and formal definitions are only valid to the extent that they accurately represent the naive version. This is particularly blatant for topics like 1 (number). It would be absurd to start that article with the sentence:

In mathematics, 1 is the set $\{\varnothing \}$.

even though that is an extremely common and important formal definition of the number 1. At a certain level of sophistication, which I don't think it precisely defined, we no longer have naive understandings of things, and so the definition and the object itself become identified. Banach algebra is at this level of sophistication.

The first sentence from Natural number makes me smile:

In mathematics, a natural number (also called counting number) can mean either an element of the set {1, 2, 3, ...} (the positive integers) or an element of the set {0, 1, 2, 3, ...} (the non-negative integers).

Despite being circular from a technical point of view, I think this sentence is able to convey the naive understanding of natural number to almost every reader. — Carl (CBM · talk) 17:58, 12 April 2008 (UTC)

Category theory offers a way of formalizing many situations, but certain observations about mathematical constructs that can be conveniently expressed in the language of category theory do not depend on category theory for their validity. Whatever the "behaviour" of complex numbers, the blue complex numbers are not behaviourally distinguishable from the red complex numbers, and in he ordered-pair representation we can have (a,b) in one representation for (b,a) in another – and isn't (a,b) actually {{a},{a,b}}, or is it {{0,a},{1,b}}?

Although articles usually start with a definition of the subject, it is usually not a definition in the mathematical sense. Rather than following some format mechanically, I'm all in favour of the presentation that best brings the essence across. If that requires a variation on the "X is Y" format, let's be flexible about it.  --Lambiam 20:42, 12 April 2008 (UTC)

Part of what brought me to this project is that the structure of the math pages I wandered into from the quantum mechanics pages has so far subjectively seemed to require maybe too many pages open in my browser at a time due to so darn many terms I need to grasp to get anywhere in all this sea of knowledge. It has started to seem to me that it would help if there were a more blatantly obvious way to get enough overview into me faster. I seem to vaguely recall way back when, once upon a time, somehow Wikipedia had managed to reasonably succinctly get across to me some kind of general idea of the shape of the dependency tree of the math terms such that I was reading about rings and ring theory and entanglement and so on nice and easy. Now I have over thirty pages open digging deeper and deeper looking to grasp this stuff and still have not come across anywhere where it maps out for me some kind of an 'up to' sequence that would allow me to navigate it all better. It seems to me this is part and parcel of the general problem of mathematicians assuming too much background on the part of the reader instead of developing concise succinct background-providing preambles that will bring the reader up to speed as efficiently as possible.

It occured to me that I might be a good example of a kind of person the pages should be accessible to, yet for some reason this year I am finding them less accessible than they were a year or few ago.

Maybe motivation is part of it. When I click to a page I am motivated by the page I am actually trying to read, whereas the page I have clicked through to might have such a totally different motivation that it maybe doesn't nicely address the reader who was sent from where I was sent from. I am not ready to go so far as to suggest that it would help to have dynamic pages that re-arrange themselves based on the referring URL so as to be maximally useful to someone who has just come from that specific referring URL, but by mentioning this hypothetical prescription I might get across a sense of part of the problem I am having. I am pretty sure by now, having already closed many more pages than I still have open, that this process of clicking a hypothetically explanatory link is looking like a non-converging algorithm: it does not seem to be leading me toward an understanding of what motivated my click, instead it seems to be exploding out farther and farther from relevance to where I started.

Part of that will be me having a hyperactive reticular activating system or some such: my own reaching too far into irrelevance. But gosh darn it isn't there at least some kind of heirarchy or collection of different proposed heirarchies for what is really needed to understand which parts of what? I wonder if the 'up to' idea, or something like it, might help sequence the portions of maths pages, so that (for a hand-waving not necessarily good example) as you read down the page you don't reach "up to isomorphism" until you read far enough down the page ('down to isomorphism'? ;)). Heck, no use I have yet seen of the phrase "up to isomorphism" has even taken the trouble to inform me as to whether that is farther up than "up to simple arithmetic", "up to computability", "up to long division", "up to multiplication", "up to the discovery of calculus" ("by Issac Newton in such and such a century"? ;))", and so on. Like, how far up is isomorphism? What is next up from it, what is one down from it, what is left of it or beside it etc etc etc? (Which direction is up?!?!?! Is there a sequence, order, heirarchy, or graph indicating what is upward, downward, whateverward of what?)

Maybe the pages should go like "up to primary school, blah blah blah; up to high school etc etc etc; up to 1984 (Bell et al) etc etc etc; whereas if allowed down to Godel then of course (complete? formal? etc)" and so on (up to the bleeding edge... ;))

Knotwork (talk) 11:47, 18 April 2008 (UTC)

No abbreviations! (?)

At Wikipedia talk:Citing sources, under the heading "We shouldn't abbreviate journal names", I posted this:

We often read that something was published in J. Am. Phys. Soc. or something like that. That's standard in scholarly journals. I'd prefer to have a policy against such abbreviations, in favor of writing Journal of the American Physical Society instead. Wikipedia does not have the limitations of print journals, and hence doesn't have the need for such abbreviations, and often there can be uncertainty about the name of the journal, especially when it's not in one's own field. If such a policy were established,[...]

A somewhat long discussion has gotten underway there. Perhaps some who take part in this WikiProject can contribute their wisdom. Michael Hardy (talk) 20:35, 15 April 2008 (UTC)

Embarassing question: Is there some kind of central online repository of mathematics journal abbreviations? I mean, most of them are obvious. But some of them, particularly the non-English ones, really give me a hard time. silly rabbit (talk) 21:10, 15 April 2008 (UTC)

MathSciNet has such a facility, if you can access it. Ryan Reich (talk) 21:18, 15 April 2008 (UTC)

I think the list is actually publicly released, on this page. — Carl (CBM · talk) 21:23, 15 April 2008 (UTC)

Embarassing question No. 2: Is there some standard for journal abbreviations in science, not just math? Thanks. Jmath666 (talk) 04:10, 16 April 2008 (UTC)

Well, there's the Web of Science list of journal title abbreviations. Not sure if all can access it or only subscribers. Qwfp (talk) 05:39, 16 April 2008 (UTC)

There is no standard. MathSciNet abbreviates "Proceedings of the American Mathematical Society" as "Proc. Amer. Math. Soc.", Zentrallblatt MATH uses "Proc. Am. Math. Soc." and Web of Science uses "P AM MATH SOC". -- Jitse Niesen (talk) 10:36, 16 April 2008 (UTC)

I've seen other lists of abbreviations, as well. I strongly suggest avoiding abbreviations: I've had trouble tracking down citations for just this reason several times, and I don't think I'm unusual in that respect. We can afford the space. CRGreathouse (t | c) 13:54, 16 April 2008 (UTC)

The AMS maintains a list of abbreviations at [15]. 83.112.134.6 (talk) 21:36, 16 April 2008 (UTC)

...and the fact that it is the AMS, a specialized organization, rather than something like the Library of Congress, seems to suggest there is no standard that applies simultaneously to mathematics, geography, theology, sociology, etc., so they're best avoided. Michael Hardy (talk) 00:02, 17 April 2008 (UTC)

Two comments: (1) Acronyms must be expanded on first use; shouldn't abbreviations, too? (2) If they were made into links to each journal's own encyclopaedia-entry page, they could be clicked on to find out not only the full name but maybe even where to find them, how authoritative they are regarded (if not enough to warrant a page of their own why mention them at all?)

Knotwork (talk) 14:37, 18 April 2008 (UTC)

Synergetics coordinates

Synergetics coordinates. Merge into barycentric coordinates? Michael Hardy (talk) 03:26, 17 April 2008 (UTC)

No, correct it instead. From a quick look at Weisstein, Eric W. "Synergetics Coordinates". MathWorld., this seems to be a different thing though somewhat related. Jmath666 (talk) 04:37, 17 April 2008 (UTC)

I've redirected it. Maybe the target page ought to get moved to synergetics coordinates? Michael Hardy (talk) 05:02, 17 April 2008 (UTC)

Does the Bary in Barycentric coordinates have any relation at all to the Bary in Baryon (physics)??? Knotwork (talk) 12:09, 18 April 2008 (UTC)

Seems likely. If we believe Wiktionary, the etymology of baryon is from Greek βαρύς "heavy" and the etymology of barycentre/barycentric is from from Greek βάρος "weight". So the first is a "heavy one" and the second is a "centre of heaviness". Gandalf61 (talk)

Linkifying (e.g. as in s/Consistent/Consistent/)

Recently User:Gregbard apparently decided that it would be a good idea to link every occurrence of the word consistent on Wikipedia to the mathematical logic article Consistent. The user has stopped, but since he was using AWB, there are about 100 edits to revert in my estimation. Anyone want to help out? silly rabbit (talk) 12:04, 18 April 2008 (UTC)

Hmm this sounds like skirting the edge of an idealised need for all words to in principle be clickable (tho not necessarily visually-cued as being so) for details as to which of the definitions in which dictionary the author actually intend{s|ed} by that specific use of that token. If there is any chance that the token/word wasn't meant in the mathematical-logic sense, which sense was it intended in? Is a disambiguation page called for?

Similar to my mention earlier of pages varying based on referring URL, maybe ideally it'd be nice if mathematicians viewing pages that don't mean mathematical-logic consistency when they use that token would automagickally link to whichever other possible interpretation of that token seems most likely to be the default interpretation in general usage within whatever field the article is purported to belong? (Is 'Consistent (International Law)' identical to 'Consistent (Pre-1776 Confederate Law)', 'Consistent (Godel)', 'Consistent (Colloquial English(U.S.A.))', 'Consistent (Colloquial English (Ireland))' etc etc etc?)

Knotwork (talk) 12:19, 18 April 2008 (UTC)

Indeed, in nearly all of the edits, the word was not meant in the mathematical-logic sense. The basic threshhold in the Manual of style (links) is that a link should be relevant to the context. Thus, although consistency in the legal sense may (to a logician) be the same thing as consistency in the sense of mathematical logic, a legal article should not have a wikilink from the term to a logic article. In fact, even in some mathematics articles, the term is used in a completely different sense than the logical one, and this creates a real danger of confusion if the word is linked to another (different) definition. silly rabbit (talk) 12:36, 18 April 2008 (UTC)

response copied from my talk page

[...] I am working through a rather large list at a steady clip. I am not wiki-linking every one. There are some that refer to consistency as texture, consistency in databases, consistent performance at a task, etc. I am avoiding those. Feel free to revert any you think are gratuitous --HOWEVER... I do not agree with a very strict interpretation that only the technical sense is worthy. I would like for people who use logical terminology in common discourse to become more aware of it, and use it correctly. Wiki-linking these common English usages will help bring logical concepts closer to the average person's understanding. Be well, Pontiff Greg Bard (talk) 12:27, 18 April 2008 (UTC)

end of paste

Actually, I am gradually going through the most important terms (Using Template:logic as a rough guide), and making sure that they are wiki-linked as appropriate, as I have done in the past. As usual, my view is not as narrow as some others. Consistency is not exclusively the domain of math (and yes I mean that "consistency"). Be well, Pontiff Greg Bard (talk) 12:46, 18 April 2008 (UTC)

Large-scale edits AWB campaigns like this should, in my opinion, be done with community sanction. Also, please read WP:MOSLINKS for general guidelines on when to make wikilinks, and also see WP:MOSQUOTE (please don't add wikilinks into direct quotes). silly rabbit (talk) 12:59, 18 April 2008 (UTC)

To respond to the other part of your post, although it is true that "consistency" is not exclusively the domain of math, the article consistency is a mathematics and logic article. Links to this article should only be made when the context indicates that the author's intention was for the term to be used in this rigorous sense. silly rabbit (talk) 13:14, 18 April 2008 (UTC)

Neither WP:MOSLINKS, nor WP:CONTEXT has any guideline as narrow as the one you have enunciated. This is not a math encyclopedia, it a general audience reference. It seems to me that an author should mean what he writes. I don't disagree with some of your reverts, but certainly not over 100. That's a narrow view, and I think we are better served by a broader view. Be well, Pontiff Greg Bard (talk) 13:29, 18 April 2008 (UTC)

Gregbard frequently goes through to add links to math articles, and generally the links he adds are just fine. In this case, there were a few articles he linked that I would disagree with (Australia-United States Free Trade Agreement) but most of the links are fine technically. If anyone disagrees with a particular edit they can of course undo it; I think Silly rabbit has undone several.

I agree with Silly rabbit that the math article should only be linked if that is the sense intended - in particular, only if there is a formal system at hand. — Carl (CBM · talk) 13:22, 18 April 2008 (UTC)

this was accidentally deleted, so I restored it at the end.— Carl (CBM · talk) 13:48, 18 April 2008 (UTC)

I like Gregbard's idea that encouraging awareness of the potential for rigour is a nice idea, that is part of why I mentioned the idea of a disambiguation page. That way instead of always reverting links that are not intended to mean mathematical consistency one can turn them into hints that the word is possibly too ambiguous. This need not be a blanket thing for all usages of the token but could be used in regions where a reader might reasonably wonder just how rigourous or colloquial or texture or industriousness -related the term is intended to be or to be taken to be. Basically if someone took the trouble to try to make the token into a link maybe it'd be better to [put in the additional work of making the link be the correct link] than to [revert to no link]. (I hope that is legible. ;)) Knotwork (talk) 16:09, 18 April 2008 (UTC)

I have twice now encountered terms I wanted to know the meaning of, found that the token matched a Wikipedia page if turned into a wikilink, but lacked the formal rigourous content knowledge to know whether maybe the author might even have deliberately not made it a link due to actually not intending the token to be interpreted by means of the article found at that link. For example, look at section 7 of Universal algebra, it uses the term 'free algebra' but does it actually mean free algebra or is it trying to use that token to denote some other notion? In the other instance I went and ranted/rambled/whatever on the talk page of the offending page, and even plugged in that nice new talk-page macro to try to bring it to your attention. But I was not (likely still am not) sure whether its best to mention it here so project people will know, or mention it on the offending page's talk page where anyone and/or their pet might stumble upon it. It even occurs to me the answer might differ depending on whether the offending page has the adopted-by-this-project logo/infobox on it... Knotwork (talk) 16:35, 18 April 2008 (UTC)

Let me clarify. I don't especially object to having a link in articles where the particular usage is relevant, and having a link may enrich the reader's understanding of the subject of the article. However, to automatically link all instances of consistent in a large number of articles using the automated tool auto-Wiki-bot, without any wider community discussion, is to my mind very problematic. This isn't about a special case here or there where a link could be helpful. This is tantamount to a "policy-level" decision: should every occurrence of the word (within certain parameters) be linked? The answer to the latter question is clearly no, in my opinion, and the broad consensus in the past agrees with me. Except in certain special and obviously uncontroversial circumstances (e.g., linking a specific event or a specific person, or fixing links to pages, etc.) automated tools are generally not to be used to insert links for precisely this reason. silly rabbit (talk) 16:42, 18 April 2008 (UTC)

I reverted one in the title of a physics paper that seemed completely irrelevant. If the rest are as bad, he should be told to stop. —David Eppstein (talk) 17:07, 18 April 2008 (UTC)

To answer a specific comment unrelated to the section heading: The usage of "free algebra" in the article on universal algebra is much more general than the usage on the free algebra page. Linking from universal algebra to free algebra would likely be more confusing than useful (roughly equivalent to linking to the article on 65535 (number) instead of the article on number; it is accidental that the most common usage of "free algebra" is more or less a random type of "free algebra" in the universal algebra sense). However, the lead of the free algebra article indicated its usage was all throughout abstract algebra, which should probably have been taken to include universal algebra. I specified the context a bit more narrowly ("ring theory") but left open the idea that it is used more broadly in mathematics (it is, but to refer to the ring theory concept, algebra (ring theory)). JackSchmidt (talk) 17:12, 18 April 2008 (UTC)

Luckily someone had already given a very stub class article on free algebras in universal algebra. I wikified it a little, and put something new in the lead. I'm not sure now if you want to link or not. Right now the article is just an unsourced definition (that I have not checked for accuracy). However, at least now if someone searches for "Free algebra" to see what it means, they will be advised of the two similar usages, and hopefully will manage to click on the right set of wiki links (the ring theory set, or the universal algebra set). JackSchmidt (talk) 17:22, 18 April 2008 (UTC)

Thanks! (unrelated? oops... better now? ;)) :twisted: Knotwork (talk) 17:24, 18 April 2008 (UTC)

Another issue with automatic links is that they can miss context. For example, one link that was added to "relative consistency" should really be to "relative consistency". So the manual approval part of AWB does need to be done right. But in general I have found Gregbard's links are generally fine. They show up on my watchlist from time to time. I think these are an exception to previous edits rather than the normal situation. — Carl (CBM · talk) 17:27, 18 April 2008 (UTC)

Still trying to get an overview of relations/dependencies between terms, I found List_of_first_order_theories and found similar 'should these be links?' issues in the section on second order theories, the tokens involved being 'Robinson arithmetic', 'induction' and 'comprehension'; and ranted/rambled about it at Talk:List_of_first-order_theories Knotwork (talk) 17:57, 18 April 2008 (UTC)

Dwyer function ?

The function D(x,y) has been studied by several university project students in Combinatorics & Graph Theory in the context of Euler Circuits and rapidly-increasing functions. They have sought to create and edit pages related to it and the idea use of using the name "Dwyer" was theirs and not mine. For my part (Dwyer) I have read around various mathematical functions pages, including wiki, hoping to suggest any inaccuracies and to make cross references where appropriate, an activity which I would not consider self promoting. [User:Dwyerj]

Fairly new editor User:Dwyerj created a new article called Dwyer Function. The obvious issues with title capitalisation and formatting could be fixed, but my main concern is that article does not cite a reference to show that this function is known by this name. A quick Google search turned up nothing relevant. I put a note on the editor's talk page to suggest that they provide references if they have them. In the meantime, has anyone else heard of this function under this name ? Gandalf61 (talk) 08:24, 18 April 2008 (UTC)

Dwyerj (talk · contribs) appears to be mainly concerned (so far) with writing his own autobiography, John Dwyer (Professor), which might be considered to be a conflict of interest (in addition to his original research on various articles). JRSpriggs (talk) 08:43, 18 April 2008 (UTC)

The algana link duplicate has been notified and should be fixed soon.[User:Dwyerj]

I haven't turned up anything, but the link provided by Dwyer is to papers from March and April 2008. They are apparently self-published or at the least, not reviewed. The first states that it is introducing a new function D(x,y). So apparently this is new. The second introduces the term "Dwyer's function" in the abstract (although the link to the pdf is to a duplicate of the first article). Two possibilities: 1) Dwyer has, in rapid fashion, simply named the function after himself. 2) Dwyer has delayed writing about this function and in the meanwhile some people call it the Dwyer function; however, no mention of "Dwyer function" or "Dwyer's function" (in this sense) appears in the literature because either it or its name is not notable. --C S (talk) 18:05, 19 April 2008 (UTC)

Singular Integral

Singular Integral redirects to singular measure, this seems a little off to me. The phrase "Singular Integrals" usually refers to a subject in its own right. For example, the classic reference is "Singular Integrals and Differentiability Properties of Functions. (PMS-30) by Elias M. Stein (Hardcover - Feb 1, 1971)". Does anyone object to deleting this redirect? —Preceding unsigned comment added by Thenub314 (talk • contribs) 14:31, 18 April 2008 (UTC)

Not at all. Please start this important article, if you feel up to it. The redirect is offbase. silly rabbit (talk) 14:40, 18 April 2008 (UTC)

I spoke too soon. There already is an article singular integral, which is on the subject in question. I have adjusted the redirect. silly rabbit (talk) 14:44, 18 April 2008 (UTC)

Excellent. The authors did good work it is a nice beginning. Perhaps we should set up a redirect from Singular Integral Operator to this page. Some pages seem to have a reference to this not existent page. Well, at least one page did, and I fixed it today. But other pages might, and it sounds like a good idea to me.Thenub314 (talk) 18:53, 20 April 2008 (UTC)

Just a note: article names are case-sensitive (except for the first letter). For instance Differential Operator is a redlink, but Differential operator is an article. Of course, neither Singular Integral Operator nor Singular integral operator is linked (as of this writing). silly rabbit (talk) 18:57, 20 April 2008 (UTC)

I've just created Differential Operator, with a capital "O", as a redirect page. I'd do the same for Singular Integral Operator if there were not an obnoxious policy of considering redirects created before their target pages to be "broken". (The manner in which that policy got established was dishonest, and those who cheated won in this case.) Michael Hardy (talk) 19:06, 20 April 2008 (UTC)

OK, now I've created the latter redirect page. Let's see how long it lasts. Michael Hardy (talk) 19:08, 20 April 2008 (UTC)

Relating important tokens

I seem relatively frequently to have observed recurring tokens, such as class, group, sheaf, function, set, topos, and various others.

Some tokens seemed to, or were even explicitly stated or defined to, provide or implement the relating of tokens or to be useful for relating tokens.

For example at Inventio#Topoi I found 'In classical rhetoric, arguments are obtained from various sources of information, or topoi (from the Greek for "places"; i.e. "places to find something"). Topoi are categories that help delineate the relationships among ideas; Aristotle divided these into "common" and "special" groups.'

Another example: at Literary_topos I found "Ernst Robert Curtius expanded this concept in studying topoi as commonplaces: reworkings of traditional material, particularly the descriptions of standardised settings, but extended to almost any literary meme. Critics have traced the use and re-use of such topoi from the literature of classical antiquity to the 18th century and beyond into postmodern literature", which seems (prima facie?) potentially somewhere in or near the-or-a neighborhood of some kind of WP:V guideline or policy or at least a possible leaning in some such direction. (Hmm, seeds that eventually grew, in one of more of our pastward-lightcones, into such constructs, objects, observables (or some such notion?) as WP:V ???)

At Dispositio I found "The first part of any rhetorical exercise was to discover the proper arguments to use, which was done under the formalized methods of inventio. The next problem facing the orator or writer was to select various arguments and organize them into an effective discourse." and "Finally, dispositio was also seen as an iterative process, particularly in conjunction with inventio. The very process of organizing arguments might lead to the need to discover and research new ones. An orator would refine his arguments and their organization until they were properly arranged."

Might some kind of tables be useful to persons attempting such tasks as discovering the proper tokens (or maybe even arguments) to use? For example at Scheme (mathematics) I found "a scheme is an important concept connecting the fields of algebraic geometry, commutative algebra and number theory", at Inventio I found

Aristotle, in his works on rhetoric, answered Plato's charges by arguing that reason and rhetoric are intertwined ("Rhetoric is the counterpart of Dialectic" is the first sentence of his Rhetoric). In Aristotle's view, dialectic reasoning is the mechanism for discovering universal truths; rhetoric is the method for clarifying and communicating these principles to others. And in order to communicate effectively, an orator must be able to assemble proper arguments that support his thesis. Inventio, therefore, is the systematic discovery of arguments. Aristotle, as well as later writers on rhetoric, such as Cicero and Quintilian, devoted considerable attention to developing and formalizing the discipline of rhetorical invention. Two important concepts within invention were topoi and stasis.

At Inventio#Stasis I found "The procedure known as stasis was another important part of the invention process. This involved the practice of posing and exploring questions relevant to clarifying the main issues in the debate. There were four types of stasis: definitional, conjectural, translative, and qualitative", in which (to my mind 'unfortunately' but what do I know?) the four tokens 'definitional', 'conjectural', 'translative', and 'qualitative' all lacked clickability (aka were not wikilinks/wikilinked), leaving me to wonder what kind of translations, between what categories, groups, sheafs, arithmoquines, or whatevers the token 'translative' might (or might not) denote or refer to translations (or some such notion?) between (aka relations between?)

Imagine a two-dimensional table (e.g. in the HTML sense) such that its rows and columns are labelled using 'offending or potentially offending tokens' and whose cells contain symbols indicating properties of the intersection of their column with their row and/or their row with their column, such that, for example, the labels might include 'common ideas', 'special ideas', 'categories', 'classes', 'sets', 'arithmoquines', etc etc etc, including in particular the four tokens 'scheme', 'algebraic geometry', 'commutative algebra', and 'number theory'. Might the previously-quoted text from Scheme (mathematics) hint that the cells at the intersections of the columns and rows labeled by these four labels might reasonably be expected to be potentially usefully populable with data derived from some such construct as the page located at Scheme (mathematics) ??? The naive intuition here is that if there is, as that page seems to imply, some useful relation or relating possible between those four terms then there might well, in principle, be potential utility in assigning symbols or tokens to relations, types of relations, families, species, geni, groups, categories, or some such notion(s), with which to populate some such table, whereby to construct a reference table succinctly and/or concisely indicating which tokens usefully or potentially-usefully relate to which tokens by what manner (or category, or class, or family, or species, or genus, etc etc etc) of relation.

Knotwork (talk) 04:10, 19 April 2008 (UTC)

Similarly/relatedly, imagine a function, maybe even representable in C or C++ or some such language/representation/form with the ... final argument indicating it could accept more arguments, into which one inputs the tokens one is interested in relating, and that returns as result a (maybe even 'the' in some sense or context or some such notion) token which refers to the art and/or science of relating precisely the tokens that were provided as input... Knotwork (talk) 04:30, 19 April 2008 (UTC)

Now: given such a function, maybe the token 'original research' as used at fictonics can be worked-around by means of plugging the token fictonics or the token ficton ("or some such token"? ;)) into some such function, possibly accompanied by one or more other tokens that might occur to one or more occurrers or occurences or implementations or results ("or some such notion? ;)) of [something?] ??? Knotwork (talk) 04:39, 19 April 2008 (UTC)

KW, not to be too rude, but is there in fact some coherent idea that you think is conveyed by the above mass of text? Or are you just putting us all on, Social Text style? --Trovatore (talk) 04:44, 19 April 2008 (UTC)

Probably more than one, if any. Some candidates might include "research is historically citably purported to be expected in the creation of a text" and "if that research is not original then what is? (are there possible answers other than 'a random agglomeration of tokens' and 'a non-original agglomeration of tokens aka mere quotation and/or plagiarism'?) I gotta go look up Social Text... Knotwork (talk) 05:00, 19 April 2008 (UTC)

Does this have something to do with building an encyclopedia describing standard known mathematical material? If it does, I can't discern what it is. We're not here for philosophical maunderings. —David Eppstein (talk) 15:16, 20 April 2008 (UTC)

I agree. Knotwork, you are welcome to use Wikipedia as a source for learning about mathematics. You are also welcome to learn it from books and then to contribute constructively to Wikipedia articles about things that you have (at least approximately) understood. But I am afraid that's not what you are doing [16]. Now a lot of experts will have to go over your past contributions and remove all your misunderstandings that you have introduced into articles. --Hans Adler (talk) 15:39, 20 April 2008 (UTC) OK, it's not as bad as I thought. I reverted you edits to abstract nonsense, but it seems you have done no damage to other mathematics pages, only grammar corrections. --Hans Adler (talk) 15:49, 20 April 2008 (UTC)

Re "Knotwork, you are welcome to use Wikipedia as a source for learning about mathematics. You are also welcome to learn it from books and then to contribute constructively to Wikipedia articles about things that you have (at least approximately) understood.": My feeling or belief seems to be that I would prefer to learn it from Wikipedia and then to contribute, in which construction adjectives applicable by append not necessarily by prepend to the term 'contribute' might include such adjectives as 'clarity', 'rigour', 'utility', 'computability', 'executability', 'efficaciously' (etc etc etc) Knotwork (talk) 17:49, 20 April 2008 (UTC)

Al? Is that you? silly rabbit (talk) 17:53, 20 April 2008 (UTC)

Taking the last paragraph of the above

Imagine a two-dimensional table (e.g. in the HTML sense) such that its rows and columns are labelled using 'offending or potentially offending tokens' and whose cells contain symbols indicating properties of the intersection of their column with their row and/or their row with their column, such that, for example, the labels might include 'common ideas', 'special ideas', 'categories', 'classes', 'sets', 'arithmoquines', etc etc etc, including in particular the four tokens 'scheme', 'algebraic geometry', 'commutative algebra', and 'number theory'. Might the previously-quoted text from Scheme (mathematics) hint that the cells at the intersections of the columns and rows labeled by these four labels might reasonably be expected to be potentially usefully populable with data derived from some such construct as the page located at Scheme (mathematics) ??? The naive intuition here is that if there is, as that page seems to imply, some useful relation or relating possible between those four terms then there might well, in principle, be potential utility in assigning symbols or tokens to relations, types of relations, families, species, geni, groups, categories, or some such notion(s), with which to populate some such table, whereby to construct a reference table succinctly and/or concisely indicating which tokens usefully or potentially-usefully relate to which tokens by what manner (or category, or class, or family, or species, or genus, etc etc etc) of relation.

If I understand correctly you would like to develop some sort of taxononomy of mathematical content. While this is a laudable aim, it is a giant undertaking and beset by problems. Indeed I would say that neither the universe of mathematics nor the world at large fits neatly into such a scheme. You might like to have a look at Ontology (information science) and related articles. Perhaphs Category theory may be to your liking. There is some attempt at structuring data in wikipedia but it is limited, possibly Lists of mathematics topics may be the most structured thing we have.

Should we include such a taxomony in wikipedia, in general I would say not. Wikipedia's primary representation method is links, which provide a graph structure, and the category system, which form a directed graph. This less formal systems is one of the strengths of wikipedia and considerably more flexible. Then we have the issue of original research if such a systems were developed it would amount to original research, unless it was a well established system used by wider mathematical world.

So if you wish to work withi the wikipedia system, by all means add links, articles, lists and work on improving our category system. Beyond that it is probably better developed off wiki. --Salix alba (talk) 18:26, 20 April 2008 (UTC)

Managing prerequisites?

Hello everyone. I have a suggestion that might take a lot of work to implement, but I think it would be a tremendous improvement if implemented. Basically, it would be really nice if there was someway to manage the prerequisites needed to read a particular article. Basically, to read a lot of math articles on Wikipedia often require you to understand a number of concepts, abbreviations, even symbolic conventions in order for you to understand the article. Now, I'm fine with clicking on links in order to find the information, but in many cases this spirals out of control. For example, to understand article M, I need to read article N; to understand article N, I need to read article P; to understand article P, I need to read article Q, and so on. And, in even worst cases, this becomes circular: M requires N, N requires P, and P requires M.

What I have in mind is if you divide up all the math articles into a set of subjects: for example, elementary algebra, arithmetic, calculus, linear algebra, and so on. Then, within each of the subjects, you have a set of *base articles* which are then assumed to be understood as a prerequisite for all the other articles within that subject. Any concepts or conventions that haven't been introduced in any of the base articles would then need to be explained within any article that wants to use them. This can even be hierarchically arranged, so that calculus might depend on the base articles under algebra.

I think the arrangement of articles should be pedagogically based rather than mathematically based. That is, for the fourth-grader looking for help factoring a number into primes, he doesn't need to read what, for him, are confusing terms about matrices and polynomials.

Anyway, just a suggestion. — Preceding unsigned comment added by Parody of Language (talk • contribs)

"And, in even worst cases, this becomes circular: M requires N, N requires P, and P requires M": Just as in the real life. This is one the reasons why learning at school proceeds in a spiral fashion and it takes quite a few trips around to get to complicated concepts. WP:NOT. Same frustration here when I am trying to look up something I am not ready for. Still Wikipedia does a quick introduction into almost anything better than anything else I know.

Lead paragraphs should play the role of introducing the subject, at the level accessible to a fourth-grader, if possible. Or a section like Elementary description for this purpose.

Jmath666 (talk) 01:54, 21 April 2008 (UTC)

Induced homomorphism

Induced homomorphism (meaning the homomorphism of fundamental groups induced by a continuous function of topological spaces) has been nominated for deletion. As it is now, it's just a dictionary-definition stub; it was even worse before I cleaned it up. If anyone thinks it's worth keeping as a separate article, I think adding some actual content beyond the definition (and references supporting that content) would be the way to go; right now, the same material is covered better in Fundamental group#Functoriality. —David Eppstein (talk) 18:38, 20 April 2008 (UTC)

I think this one should go. Induced homomorphism could mean so many different things in different contexts. For example, a proper coloring of a graph by k colors induces a graph homomorphism into the complete graph on k vertices. However, there is a more general issue (which I'm pretty sure must have been discussed): it is often the case that while writing an article you need to refer to some notion which does not warrant an article but does require a definition, and the insertion of the definition in the present article would not work well. The obvious solutions, such as having an article containing only a definition or having the definition as a subpage run contrary to WP style conventions, if I understand them correctly. Is there an established recommended solution to this issue? Oded (talk) 18:53, 20 April 2008 (UTC)

Actually, I would like to see an article on this. Admittedly, that's not necessarily an argument against deletion -- maybe there should be an article, but a clean start would be better. CRGreathouse (t | c) 20:33, 21 April 2008 (UTC)

Substitution principle/substitution rule

Can someone (with a background in math) write a rigorous proof of the "substitution rule" or "substitution principle"?

As far as I know this principle applies everywhere... except for special cases in integration. I vaguely remember that one needs to use trigonometric identities to properly integrate certain trigonometric functions. Is there another case where it doesn't apply?

• I started an article called Substitution principle (mathematics).
• I redirected Substitution rule to it -- it previous redirected to integration by substitution.
• I disambig'ed substitution principle -- as it was occupied by a sustainability stub.
• It is interesting to note how many math articles link to substitution rule --see: Special:WhatLinksHere/Substitution rule.
• I think it might be related to the article here: Substitution -- Equality (mathematics)... perhaps a merge is in order.

Thanks, Nephron  T|C 19:26, 20 April 2008 (UTC)

I have a background in math, but it is not clear what you want this article to be. Every thing I checked (approx 1/4 of the articles) that liked to this article really should have been linking to integration by substitution. I am guessing all should. Correct me if this is wrong. Your article seems trying to make the point that in algebra we may give names to quantities and operates with names as we would with the quantities. I was not aware this had a formal name.

Thenub314 (talk) 20:52, 20 April 2008 (UTC)

I agree. I have reverted Nephron's change to the redirect at substitution rule. Gandalf61 (talk) 12:05, 21 April 2008 (UTC)

References for "Shallow water equations"

Shallow water equations includes a striking picture that has "featured" status, but the article has a "no references" tag. Does someone know what the most suitable references are? Michael Hardy (talk) 16:51, 21 April 2008 (UTC)

I can't answer your question, but I noticed the picture before and that there is no information at all about how it is produced. I really should go after it and either get somebody to fill some more details or get the featured status removed. -- Jitse Niesen (talk) 20:10, 21 April 2008 (UTC)

Substitution principle (mathematics)

Sigh..................... Please look at Substitution principle (mathematics) and improve it if it's worth improving. Michael Hardy (talk) 05:24, 21 April 2008 (UTC)

I am strongly in favor of deleting the article. Thenub314 (talk) 11:44, 21 April 2008 (UTC)

It has been {{prod}}-ed. silly rabbit (talk) 11:52, 21 April 2008 (UTC)

Yes, I prod-ed it. I think it is a neologism - I have never heard this operation in elementary algebra called the "substitution principle", and a quick Google search showed up no relevant hits. Happy to be proved wrong if anyone can add a reference to the article !

User:Nephron created the article when they renamed the previous "substitution principle" article to substitution principle (sustainability). They also changed the redirect at substitution rule to point to substitution principle (mathematics), which was completely wrong, as "substitution rule" is used as a synonym for integration by substitution - as pointed out by Thenub314 above. So I fixed that redirect too. Gandalf61 (talk) 12:02, 21 April 2008 (UTC)

Perhaps it is a confused and poorly done attempt to make an article on the substitution property of equality or the instantiation of universals? JRSpriggs (talk) 06:40, 22 April 2008 (UTC)

I doubt this would satisfy the author of that article. I think the article is not really about mathematics, but rather about the kind of operations that one can perform while doing mathematical calculations without messing them up. In some sense, mathematical logic does that too, but the logic treatment of the subject would not be comprehensible to the target readership. Oded (talk) 14:21, 22 April 2008 (UTC)

Another "wave"-topic featured image question

Frequency dispersion in bichromatic groups of gravity waves on the surface of deep water. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red dot overtakes two green dots, when moving from the left to the right of the figure.
New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front.
For gravity surface-waves, the water particle velocities are much smaller than the phase velocity, in most cases.

Here's an image found in group velocity. It's not visually stunning like some "Featured" images, but its purpose is to make a concept clear rather than to hit you between the eyes before you've read anything. This seems like a perfect example of a well-explained picture being worth a very large number of words. Should this one have "Featured" status? Michael Hardy (talk) 20:47, 21 April 2008 (UTC)

I say yes. This is a very nice and illuminating animation. –Henning Makholm 20:37, 22 April 2008 (UTC)

As much as animation does add to articles, I find it can also be quite distracting. Does it seem like a good idea to suggest in the manual of style that a potentially distracting image should be placed into a show/hide box (defaulted to [show])? Once upon a time there was Template:Linkimage, which served roughly this purpose, but defaulted to [hide]. (It was deleted because of censorship concerns, which quite frankly I find a bit unconvincing.) silly rabbit (talk) 20:48, 22 April 2008 (UTC)

I doubt that a collapsible box would significantly enhance the usability of the encyclopedia (in proportion to the visual clutter and monitor real estate taken up by the box itself) unless it defaults to "collapsed". However, isn't that a quite orthogonal discussion? The fact that the image may, in the context of a specific article, be presented in a collapsible box, does not prevent the image itself from being featured, does it? –Henning Makholm 21:38, 22 April 2008 (UTC)

Is there a way to have a show/hide box around the image in just one chosen article without constraining the use of the image in other articles? JRSpriggs (talk) 01:47, 23 April 2008 (UTC)

Oh yes, the collapsible box is markup of its own that must be inserted in the page that includes the image. See examples in Fictitious force -- one of the collapsed animations is used without a enclosing box at Talk:Centrifugal force. –Henning Makholm 01:59, 23 April 2008 (UTC)

The problems with the show/hide box are: (1) the image repeatedly freezes for a moment and then starts moving again, and (2) the image now covers part of the text, which can now be seen only when the box gets collapsed. Michael Hardy (talk) 03:11, 23 April 2008 (UTC)

Oh. The comment above was intended to apply to the picture in shallow water equations. Someone's put that one into a collapsible box. I notice that it's now been further edited so that it doesn't cover up the text. But it still seems to move more slowly than it did before. Michael Hardy (talk) 13:50, 23 April 2008 (UTC)

Huge set of pictures of mathematicians available

Good news for authors of biographies of mathematicians. The Mathematisches_Forschungsinstitut_Oberwolfach features a huge photo collection of mathematicians (roughly 10,000) and has recently allowed the use of the majority of them in wikipedia. A large set of pictures has already been uploaded to wiki commons and is available at commons:Category:Pictures from Oberwolfach Photo Collection.--Kmhkmh (talk) 11:04, 24 April 2008 (UTC)

See #Photographs from the Oberwolfach photograph collection for the caveats. --Hans Adler (talk) 12:00, 24 April 2008 (UTC)

Thanks I completely overlooked that a note regarding this was already posted.--Kmhkmh (talk) 13:58, 24 April 2008 (UTC)

Taxicab geometry and more

This is list of mathematical and chess topics you may want to consider within the scope of WikiProject Mathematics.

• Taxicab geometry, Eight queens puzzle, Eight queens puzzle solutions, Knight's graph, King's graph, Longest uncrossed knight's path, Mutilated chessboard problem, Rook polynomial, Shannon number, Wheat and chessboard problem.

SunCreator (talk) 14:47, 24 April 2008 (UTC)

Thanks for the note. I think you will find most or all of those articles are already listed on the List of mathematics articles. If you would like to add a mathematics project template to the talk pages, please feel free; remember to fill in the quality, importance, and field parameters, using the instructions at Template:maths rating. But the talk page template is not necessary for making the list of mathematics articles. — Carl (CBM · talk) 15:19, 24 April 2008 (UTC)

Okay, glad they are already listed. SunCreator (talk) 20:15, 24 April 2008 (UTC)