Wikipedia talk:WikiProject Mathematics/Archive 20

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This is the archive file "Wikipedia talk:WikiProject Mathematics/Archive20". It is for December 2006.

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

1 Equations gone
2 Stablepedia
3 completing the square
- 3.1 A variation on the theme: the middle term
4 Geometry portal
5 Scientific citation guidelines
6 templates at ω-consistent theory and related
7 New MathSciNet template
8 Uppercasing again
9 Complete lattices (and Boolean algebras) and varieties
10 Possible vandalism in Taylor series
11 New "undo" function
12 Wikipedia:Release Version 0.7
13 Continued fractions
14 Sylvester's sequence listed as Good Article
15 Slashdot of previously deleted transreal number
16 Template:Calculus footer
17 A new article about continued fractions
18 Suggested move of List of mathematics articles
19 Simple Introduction
20 Area of a disk
21 Proofs of trigonometric identities
22 "Big" articles
23 Problems at exponentiation and empty product
- 23.1 Bullying
24 Manifold Destiny
25 Need advice
26 Representing probability
27 Luigi Fantappiè
28 Symbol for differential
29 Word problem (mathematics education)
30 Polar coordinate system
31 Wikipedia:What is a good article?
32 Renaming Exclusive disjunction Exclusive or
33 Vector Notation
34 Calculus footer
35 Featured article Regular polytope up for review
36 User:WAREL again?
37 Dispersive PDE Wiki
38 GurchBot 2 messed up our archives! But I have repaired them.
39 Writing about math
40 Lobachevsky Article
41 Where do graph theory articles go?
42 Writing about math (2)
43 Congratulations to Paul August
44 Articles with the greek letter mu in their titles
45 Wikipedia Day Awards

Equations gone

Any one know what is up with the equations on WP? I recently browsed one of my pet articles (Kt/V)-- and all the equations are gone despite that there were no edits. The equations in Navier-Stokes equations are also gone. Interestingly, the equations in Standardized Kt/V are still there. It looks like there's some error with the equation interpreter-- perhaps due to recent changes discussed above? Nephron T|C 20:40, 25 November 2006 (UTC)

Strange... no sooner had I posted the above and they re-appear. Nephron T|C 20:43, 25 November 2006 (UTC)

Stablepedia

Beginning cross-post.

See Wikipedia talk:Version 1.0 Editorial Team#Stablepedia. If you wish to comment, please comment there. ★TWO YEARS OF MESSED ROCKER★ 03:47, 26 November 2006 (UTC)

End cross-post. Please do not comment more in this section.

completing the square

An edit-warrior, wishing to give his arguments ONLY in edit summaries, has twice deleted a new section I added to completing the square. He says

“

Incidental mathematics, although clever, is not relevant. The wording ('this may be considered completigng the square') shows this.

”

Could we have some third (and fourth...) opinions? Michael Hardy 03:50, 26 November 2006 (UTC)

Here's the new section, with a typo fixed (I should have said "equal to −2"): Michael Hardy 03:54, 26 November 2006 (UTC)

A variation on the theme: the middle term

By writing

$x + {1 \over x}$

$= \left(x - 2 + {1 \over x}\right) + 2$

$= \left(\sqrt{x} - {1 \over \sqrt{x}}\right)^2 + 2$

one sees that the sum of a positive number x and its reciprocal is always greater than or equal to 2, with equality only when the last parenthesized expression vanishes. That happens if and only if x = 1. By adding the middle term, equal to −2, one gets a perfect square; thus this may be considered a sort of completion of the square.

I do not want an edit war. I would like additions like this to be supported by consensus before they are added. This addition is not directly related to the point of the article. Broadness is fine. Math with no apparent purpose is not. I don't think the addition adds anything of substance to the article, and it makes the article more confusing (at least to me). IF there were consensus, I would not object. Michael, thank you for putting out the request. Michaelbusch 03:58, 26 November 2006 (UTC)

It seems to me that Michael Hardy's example is no more and no less valid as the other examples in the article. And demanding that all additions to articles are first discussed on a talk page is just not how the wiki idea works. However, I would be concerned that there are too many examples in that article already − seeing such a density of formulas might give a newcomer the mistaken impression that there is something deep and complex going on here, which is not true. Henning Makholm 04:37, 26 November 2006 (UTC)

One of the guidelines for good writing is to focus on a clear purpose. Reading over this article and the proposed addition, I see one benefit, and a problem or two.

The new section points out that we can complete a square in a second way, which might be good to know. However, the "middle term" will be a constant only when the outer terms are reciprocals. That is, if we are given x²+y², the completion will add 2xy. Frankly, the "at least two" proof is too special-case to be motivating. Any other use steps out into more general algebraic manipulation. If that's where we want to go, then we need another example.

Meanwhile, the article needs a face lift; the formatting could be much nicer with the new "align" ability. --KSmrq^T 04:59, 26 November 2006 (UTC)

User:Michaelbusch is in the wrong here. Reasonable people can disagree about quite how many examples an article such as this should contain. But such disagreements should not be carried out by deletions: the Talk page is for such discussions. Charles Matthews 07:49, 26 November 2006 (UTC)

Lest there be any confusion, my previous remarks were not meant to say Michaelbusch did the right thing. On a more positive note, I took the opportunity to reformat, reword, and reduce the article. Maybe the proposed addition will fit more comfortably now. --KSmrq^T 09:20, 26 November 2006 (UTC)

I apologize for jumping the gun. I've probably been reverting too much vandalism and developed bad habits. Michaelbusch 01:08, 27 November 2006 (UTC)

OK, since the issue's been raised: can anyone contribute some good examples besides the one I used? Michael Hardy 00:47, 27 November 2006 (UTC)

I've put the new section, somewhat revised, back into the article.
Some decent additional examples could help. Michael Hardy 01:35, 29 November 2006 (UTC)

In case anyone cares: I've now added another example to the article: factoring the simple quartic polynomial.

$x^4 + 4.\,$

We get

$(x^4 + 4x^2 + 4) - 4x^2 = (x^2 + 2)^2 - (2x)^2,\,$

and this factors as a difference of two squares to get

$(x^2 - 2x + 2)(x^2 + 2x +2).\,$ Michael Hardy 20:18, 30 November 2006 (UTC)

I care, and I like it. My only suggestion is to use a constant term other than 4, to more clearly separate the contributions of different pieces. With that in mind, I replaced the 4 with 25. I also removed extra blank lines in the multiline equation; to my eye they space the lines too far apart. --KSmrq^T 01:40, 1 December 2006 (UTC)

Geometry portal

Flarn2005 has created a Geometry portal. At the moment is a bit bare bones-ish, so it would be useful if people could contribute to it. Tompw 00:08, 27 November 2006 (UTC)

Scientific citation guidelines

Discussion of the proposed Scientific citation guidelines seems to have simmered down. I suspect the guidelines have consensus among math and physics editors. If you have strong feelings about the guidelines, please comment on the talk page. CMummert 01:50, 1 December 2006 (UTC)

templates at ω-consistent theory and related

Need mediation at these articles (the other party is Gene Nygaard). I think the {{lowercase}} and {{wrongtitle}} templates are frequently misused, but this is one case where they are genuinely important. Using the Latinizations is wrong; the articles clearly should start with the Greek letter ω, but starting them with Ω would be worse, as that could be interpreted as being related to Ω-logic. --Trovatore 01:48, 25 November 2006 (UTC)

What is the exact controversy? Do you yourself prefer {{wrongtitle|ω-consistent theory}} or {{lowercase|ω-consistent theory}}? You believe that Gene Nygaard opposes the use of both of these templates? EdJohnston 02:05, 25 November 2006 (UTC)

Yes, I think he's against both of them. I guess {{wrongtitle}} is more precise for that one. Many of the disputed articles are actually redirects, where I have to admit it's a pretty puny issue, but I still think the templates should be there for tracking purposes. I feel strongly that, while there are decent arguments for automatically uppercasing titles that are in the Latin alphabet, there are no good arguments for automatically uppercasing titles that start with a non-Latin character. When that restriction is lifted, as it should be, we should have a way of finding these redirects and correcting them. --Trovatore 02:09, 25 November 2006 (UTC)

I understand that you want to use {{lowercase}} in redirects. I do see evidence of an edit war on the [Ω-consistent theory] redirect. So I went to Template:lowercase and did 'What links here', but did not see any pages listed with Greek initial letters. So:

Do we know that the Javascript-lowercasing trick works with Greek letters?
Do redirects show up in a 'What links here' request? Unless at least one of these is true, I'm not sure what the benefit is. EdJohnston 05:35, 25 November 2006 (UTC)

Redirects do show up in "what links here". Probably you didn't look far enough down the page. (There used to be a category for articles including this template; that seems to have been deleted, which I thought was a bit unfortunate.)
Redirect titles also show up at the top of the page, showing you from where you've been redirected. That, unfortunately for these articles, is automatically uppercased.
I haven't looked into the javascript thing. Personally I'm not happy with any solution that requires having javascript turned on in the user's browser (turning it off is the more secure practice). I really think we should agitate to remove the automatic uppercasing in the case of titles that start with non-Latin characters; I see no justification for uppercasing Greek letters. --Trovatore 05:49, 25 November 2006 (UTC)

Oh, now I see what you mean. I hadn't realized the javascript thing was automatic. Given that, I think we should move omega-consistent theory to ω-consistent theory and use {{lowercase}} (which does seem to work with Greek letters). It's not as good a solution as removing the auto-uppercasing for non-Latin letters, but it's probably the best available now. Unfortunately ω-consistent theory has too much of an edit history and won't permit a move on top of it, so I guess I'll need some help on that. --Trovatore 06:27, 25 November 2006 (UTC)

I used my magic stick to move the page. -- Jitse Niesen (talk) 08:27, 25 November 2006 (UTC)

Thanks, Jitse. "Your kung foo is the best." But it really is a seriously imperfect solution; I hope you'll support my proposal to remove auto-uppercasing for articles that start with non-Latin (or at least Greek) letters. (See section below.) --Trovatore 08:33, 25 November 2006 (UTC)

Is that magic stick a "three foot black rod with a rusty star on an end"? I used to have one of those, but I dropped it in a twisty passage and could never find it again. --KSmrq^T 09:14, 25 November 2006 (UTC)

It shouldn't have been moved anyway. There is nothing improper about the title as it existed, and it did not need any "wrongtitle" tags. Having them there was just plain flat-out wrong, and moving it so that it can be justified on the basis of the usage of a Greek letter as the initial letter of the article name is even worse nonsense. Gene Nygaard 01:56, 3 December 2006 (UTC)

And it most certainly didn't need the "lowercase" template, which is the one which it had and the one I removed. Gene Nygaard 02:04, 3 December 2006 (UTC)

And, lest anybody is dumb enough to be fooled by the Java-script shenanigans with the display on this articles page, just go follow the links to the one real non-stub category in which this article can be found, and come back and tell us exactly what sort of nonsense you see when you get there. Not only what you see for the article name, but also what letter you find it listed under.

Just where the fuck do you find it, anyway? Off in oblivion, somewhere after the Z.

I'll hold off on fixing the sort key properly until at least a few of you get a chance to see how you are squirreling away this information, hiding it so that is is unfindable.

If you aren't competent enough to deal with those templates and fix the problems they cause, then just stop using them. Gene Nygaard 02:16, 3 December 2006 (UTC)

The move was certainly not intended to justify the template. Rather, the javascript trick made it possible to put the article at the correct title. The title with Latin "omega" was flat-out wrong; you won't find that in the literature, except possibly in some popularization somewhere.

As for the sort key -- frankly, I can't see why the article shouldn't appear after Z. It's no more "unfindable" there than any other article not on the first page of the category listing. Where else ought it to appear, exactly? --Trovatore 02:46, 3 December 2006 (UTC)

It's not just the sort key; it appears in the cat as Ω-consistent theory. (I'm using an IE machine. Septentrionalis 03:10, 3 December 2006 (UTC)

Yeah, I know, and probably in watchlists too and who knows what else. It's not an ideal solution, but IMHO it's way better than "Omega-consistent theory". Brion Vibbers was not at all receptive to the idea of distinguishing between Latin and Greek letters for the purpose of case sensitivity (well, I was trying to give him extra work after all; I'm a programmer myself and know how that goes), but he did say that eventually we'll be able to mark articles as starting with lowercase. Presumably then the categories and so on will respect that. --Trovatore 03:14, 3 December 2006 (UTC)

New MathSciNet template

I just created a new template, {{MathSciNet}}. Hope you all find this helpful! —David Eppstein 06:34, 1 December 2006 (UTC)

Looks awesome. Well done! --King Bee 19:50, 2 December 2006 (UTC)

Good idea! But could you briefly explain the difference between the two kinds of id numbers, the one that's merely an integer, and the one that begins with 96f:....? For the WP reader, is there any advantage of one over the other? Also, I notice you recently updated the Leonidas Alaoglu article's references with the new template, and you explicitly added a JSTOR link to each entry there. Will this continue to be needed? Certainly getting the first page from JSTOR is beneficial for those readers who don't have an institutional subscription to MathSciNet. Also, for post-1995 articles, should we still be trying to find a DOI as well, even when an MR link is present? Reply on my Talk page if this question is too specific for the project Talk. EdJohnston 20:27, 2 December 2006 (UTC)

The 96f:etc numbering is an older style of MR identification, that lets one determine the year and MSC classification from the id. They've switched to a newer system involving meaningless integer ids. Both work equally well in terms of creating a working link to mathscinet, but perhaps the new system should be preferred as it's the way records on the system identify themselves when you view them. One can often get the jstor or doi link from the mr link (even without a subscription to mathscinet) but I think if a direct link is possible it should be included as well so that WP's content is more self-contained. I am only planning to include mr links for papers that have an actual review available at that link; I don't see the point in linking to mr for the ones that say "no review of this item is planned" and then just send you on to the article itself. —David Eppstein 20:33, 2 December 2006 (UTC)

Uppercasing again

The javascript thing is sort of nice, but not sufficient to allow different articles on Ω-logic and ω-logic, which we really ought to be able to have. I've left a note at Wikipedia:Village pump (technical)#Uppercasing of non-Latin letters (including references for the two logics that should be treated, or at least treatable, distinctively). See what you think. --Trovatore 07:32, 25 November 2006 (UTC)

We can't solve all the world's problems, including the foibles of some of the terminology used. Assuming that there are distinguishable concepts there, how do the fools who are silly enough to try to make a distinction of two concepts on the basis of the capitalization of a Greek letter used as a symbol deal with disambiguating them in speech? That might give us a clue as to whether it is a problem even worth our attention, and how to deal with it if it is. Gene Nygaard 11:53, 4 December 2006 (UTC)

Complete lattices (and Boolean algebras) and varieties

This comprises a few questions related to the concept of κ-complete lattices and Boolean algebras (where κ is an arbitrary cardinal number), and universal algebras with infinitary (or proper class) signatures.

Where should statements about κ-complete lattices appear? -complete lattice? A section of complete lattice? A section of lattice (order)? Something else?
In my Ph.D. thesis, I note that κ-complete Boolean algebras can be looked as as a variety (universal algebra) with respect to an infinitary signature. (I know of no other source, but I've never been contacted to say that it was in error. A reference in my thesis does apply universal algebra to infinitary algebras, but I don't know if I kept a copy of the reference.) Where (and if) should this information appear in Wikipedia. (I'll have to go over my thesis to see if I mentioned κ-complete lattices. I think it's in there, although it may only be for κ-complete κ-distributive lattices.)
Also in my thesis, I noted that complete Boolean algebras can be thought of as a variety with the signature being a proper class. (I'm almost certain no one else has dealt with that, but not absolutely certain).
Also in my thesis, I extended the concept of free algebra to those with a proper class of operations, and noting that the free complete Boolean algebra on an infinite set of generators does exist in that sense, but is a proper class.

What to do, what to do? I don't want to violate WP:OR or the extension of WP:AUTO to my work, but my thesis is a WP:RS, I suppose. — Arthur Rubin | (talk) 15:56, 4 December 2006 (UTC)

It's an important principal point. The WP:OR sums up Articles may not contain any unpublished arguments, ideas, data, or theories; or any unpublished analysis or synthesis of published arguments, ideas, data, or theories that serves to advance a position.; and in the fuller explanations states This policy does not prohibit editors with specialist knowledge from adding their knowledge to Wikipedia, but it does prohibit them from drawing on their personal knowledge without citing their sources. If an editor has published the results of his or her research in a reliable publication, then s/he may cite that source while writing in the third person and complying with our NPOV policy. I do not at all this excludes you from citing your own thesis; or any other to write about their own work (if it does fulfil the WP:RS guidelines and is of encyclopedian intetrest). Perhaps, we should be a little extra careful about our own work, because (a) we may risk to exaggerate its general interest, and (b) we may underestimate the troubles for others to follow the exposition of ideas. Apart from that, I find the 'who do you think you are' attitude extremely distasteful, and rather counterproductive. (I noticed you've had an attac of that kind on your talk page; you have my deepest sympathy and support in this matter.) The researchers also often do have experience of explaining their ideas to wider auditoria, and putting them into context. IMO, it would be an extremely stupid waste not to accept contributions of this kind.

Concretely, if you are asking 'Is κ-completeness of sufficient interest for the WP?', my personal answer is yes. However, I'd not like it to be written as parts of articles such as Complete lattice, since as far as I understand a complete lattice is κ-complete for 'each' κ (excuse my usage of 'naïve set theory'), not the other way around; and since I think at least one important result is not extendable from the theory of complete lattices to the κ-complete ones. (Namely, a complete semilattice is a lattice; but does this hold for e.g. $\alef_0$ -complete semilattices?) So, I'd prefer separate articles. I also think giving the basic definitions and a few main properties should be enough; and sensible links and categorisations.--JoergenB 18:41, 4 December 2006 (UTC)

Technical point; it's clear that an ℵ₁-complete semilattice is not necessarily an ℵ₁-complete lattice, even if it is a lattice. But there's still the naming problem to deal with. There is a PlanetMath article at κ-complete, but that's just wrong for a name. (Being ℵ₀ complete is trivial, under those definitions, which I believe are standard.

Possible vandalism in Taylor series

This article contains the text

Third, the (truncated) series can be used to compute function values approximately (often by recasting the polynomial into the Chlemloid's form and evaluating it with the Chlemshaw's algorithm).

I cannot find any Google hits for Chlemloid's form or Chlemshaw's algorithm anywhere but in this article or its mirrors. Could this be sneaky vandalism? -- 80.168.226.41 02:45, 6 December 2006 (UTC)

Zipping back many, many edits finds an older version of this text:

Third, the (truncated) series can be used to compute function values approximately (often by recasting in the polynomial into the Chebyshev form and evaluating it with the Clenshaw algorithm).

I've reverted to this version of that sentence: it looks at least plausible, given the context. -- 80.168.226.41 02:50, 6 December 2006 (UTC)

New "undo" function

From Wikipedia:Wikipedia Signpost/2006-11-27/Technology report:

It is also now possible to undo edits other than the last one, provided that no intermediate changes conflict with the edit to be undone. The interface used is more akin to "manual revert" than rollback: on diff pages, an "undo" link should appear next to the "edit" link on the right-hand revision. When this link is clicked, the software will attempt to undo the change while preserving any changes since then, and will add the result to the edit box to be reviewed or saved. (Andrew Garrett, r17935–r17938, bug 6925)

There is a new button labelled "(undo)" which appears on the right under the edit summary when you look at the diff in a vandal's contributions. This allows you to remove a change without disturbing subsequent changes to the same page. I just found out about it. Have not had an occassion to try it yet. JRSpriggs 10:18, 29 November 2006 (UTC)

By the way, the author of this feature, Andrew Garrett, is perhaps better known as User:Werdna who also created User:Werdnabot. JRSpriggs 12:22, 3 December 2006 (UTC)

Correction, I should have said:

There is a new button labelled "(undo)" which appears on the right on the top line, e.g. "Revision as of 17:15, 5 December 2006 (edit) (undo)", when you look at the diff. This allows you to remove a change without disturbing subsequent changes to the same page.

I have used it now and it is very convenient. Try it out! JRSpriggs 06:36, 7 December 2006 (UTC)

Wikipedia:Release Version 0.7

The next round of nominations for the Wikipedia:Release Version is now open, these are articles which are to go on a CD-release of wikipedia. I've nominated 19 new mathematics articles.

Number - Pythagorean theorem - Eigenvalue, eigenvector and eigenspace - Fermat's Last Theorem - Polar coordinate system - Euclidean geometry - Derivative - Integral - Regular polytope - Cartesian coordinate system - Chaos theory - Circle - Real number - Complex number - Decimal - Infinity - Polynomial - Statistics - Gottfried Leibniz

which are generally our higher importance topics and of at least B+ status. I guess most of these could do with some a bit of love and care. There may be other articles I've missed which others think should also be nominated. --Salix alba (talk) 11:09, 2 December 2006 (UTC)

I'm curious, what work do you think the derivative page needs? It's already a GA. --King Bee 22:33, 4 December 2006 (UTC)

So good that someone just vandalized it to say that the derivative is "defined as the poopie of a cow." Isn't anonymous public editing fun! For as appalling as such vandalism is, I have to tell the truth and say that this particular expression got a chuckle out of that corner of my brain where my junior high self still lives. (BTW, how does one go about reverting a change without messing up other edits that have taken place later? I was hesitant to try it myself since I figure someone out there knows how to do it better than I do. But I'd really like to know if there's some fancy trick for it.) VectorPosse 23:09, 4 December 2006 (UTC)

Never mind. I figured it out. This new "undo" feature is the bomb! VectorPosse 23:23, 4 December 2006 (UTC)

Actually, that is kind of funny that you checked it right after my comment. =) --King Bee 00:18, 5 December 2006 (UTC)

As you asked, compare the German version de:Differentialrechnung which is an FA. History is very brief, the critical points min/max could do with an illustration, only one application, taylors theorem could do with expansion, week on functions which fails to be continuous, no mention of C-infinity fuctions. Newton-Raphson methods missing (as an example of why derivatives are useful). The generisations section is written at too high a level, using a lot of technical terms the lay reader would not understand, a simple example of a function of more than one variable would help. Week on referencing. Differential equations could do with a mention. Generally OK as a how-to for single valued case, but peters out towards the end. Theres some more comments on Talk:Derivative#GA_Review and Wikipedia:Good_articles/Disputes/Archive_7#Derivative. --Salix alba (talk) 20:35, 6 December 2006 (UTC)

Continued fractions

I want to add some new articles about particular varieties of continued fractions to Wikipedia (S-fractions, J-fractions, the continued fraction of Gauss, etc). Unfortunately the definition given in the basic article is so restrictive that the mathematical objects I want to discuss have been defined right out of existence! There are already some 250 links to the existing article, so renaming it is probably out of the question. My plan is to rewrite the existing definition and tweak the rest of the article so it's still logically consistent. Here's the definition I'm working with right now.

In mathematics, a continued fraction is an expression of the form

$x = b_0 + \cfrac{a_1}{b_1 + \cfrac{a_2}{b_2 + \cfrac{a_3}{b_3+\,\cdots}}}$

where the a_i and the b_i are numbers. The a_i are the partial numerators of the continued fraction x. The b_i are the partial denominators, and the ratios a_i / b_i are the partial quotients.

If all the partial numerators are 1 and all the partial denominators (except b₀) are positive integers, the continued fraction is a simple continued fraction, expressed in canonical form. Most of this article is devoted to simple continued fractions – see this related article for a more general discussion.

I'm posting this for comment. Is this definition sufficiently general? I suppose I could define a continued fraction as the composition of a (possibly infinite) sequence of Möbius transformations, but that wouldn't be very accessible, for the general reader.

Oh -- I also have a question. I'm not an expert on TeX. The ellipsis in the formula above is not quite right – it really should be replaced with three dots that descend to the right. Does anybody know the name for one of those?

Your feedback is welcome. I'll check back here regularly, or you can contact me on my talk page. DavidCBryant 16:13, 30 November 2006 (UTC)

Why don't you just add a section on Generalizations? The "absurdly narrow" definition includes all real numbers, which is broad enough to start with. Septentrionalis 17:50, 30 November 2006 (UTC)

Well, I thought of that, but then I looked at generalized continued fraction, where I read:

In mathematics, a generalized continued fraction is a generalization of the concept of continued fraction in which the numerators are allowed to differ from unity. They are useful in the theory of infinite summation of series.

A generalized continued fraction is an expression such as:

$x = \cfrac{b_1}{a_1\pm\cfrac{b_2}{a_2\pm\cfrac{b_3}{a_3+\,\cdots}}}$

where all symbols are integers. [emphasis added]

So I can't even write about "generalized" continued fractions unless I change this definition. Opening up a "generalization of generalized continued fractions" seems like a bad idea for some reason, and if I'm stuck with cleaning up a bad definition, I might as well go whole hog.

Call me cranky if you like, but the existing definition of a cf on Wikipedia does not reflect the way mathematicians use this term. DavidCBryant 18:18, 30 November 2006 (UTC)

It seems to me like the correct thing to do would be to modify the generalized continued fraction article to fit your definition and discuss the various special cases there. The definition given at continued fraction seems to be the most common one and should probably remain the same. -- Fropuff 19:00, 30 November 2006 (UTC)

And why stop at numbers? There are extremely useful continued fractions where the coefficients are functions; most of the useful generalizations are proven by evaluating these. But do please leave the basic definition at the head of continued fractions; the urge to plunge into the greatest possible generality immediately should be resisted for the sake of comprehensibility. Septentrionalis 20:17, 30 November 2006 (UTC)

I proposed stopping at numbers because that's what most people think of when they think of addition and multiplication. I do understand that continued fractions of functions can be formed. And it's certainly possible to define continued fractions with differential operators, and with a whole lot of other objects that are the elements of a field, or even of a division ring. I'm not sure how useful such things would be ... that kind of stuff is not my bag. Anyway, I'm clearly a minority of one at the moment ... I read some other talk pages where others raised similar concerns, but they've apparently been driven away from Wikipedia. One poor guy named q analogue apparently tried to work on this before I did, without much success. Another guy, Hillman, apparently took some abuse from somebody -- I can't tell easily because his user page has been protected.

Arithmonic is apparently still around, but he seems to be keeping a low profile at the moment. I looked at his web site; he has written a book about generalized continued fractions and claims to have found periodic representations of cubic irrationalities. That's a pretty amazing advance, if he's right. LaGrange proved the bit about periodic continued fractions and quadratic irrationals about 200 years ago. So here's a guy who maybe made this huge advance in number theory, and you guys apparently don't even want to talk to him. "Original research", I suppose. (This is part of a message signed by User:DavidCBryant 01:07, 6 December 2006 (UTC) -- the original signature appears below, after some interpolated comments.)

No, sheer fantasy, like most "original research" around here; all periodic continued fractions are quadratic. The proof is in Hardy and Wright; briefly, if x is the value of the whole continued fraction, and r the value of the tail.

$x=\frac{h_nr+h_{n-1}}{k_nr+k_{n-1}}\,$

and by comparing this equation for n and m a period apart, and solving each for r, we get a quadratic equation for x. Septentrionalis 03:10, 6 December 2006 (UTC)

I'm familiar with the proof that an infinite periodic continued fraction in the traditional form (where each element of the cf is just a complex number) converges to a root of some quadratic polynomial if it converges at all. Not every infinite periodic cf is going to converge, though ... it's pretty easy to build [0; z, z, z, z, ...] and see that it's divergent for certain complex z, all of which lie on an open segment of the imaginary axis from −2i to 2i. For instance, just plugging in i for z generates a periodic sequence of convergents with a period of 3, and every third convergent is the point at infinity. You can get similar "orbits" of any length by plugging in other (pure imaginary) values of z. That's not what Arithmonic is talking about on his web site.

Arithmonic has devised a generalized continued fraction (a "fractal fraction") in which each partial numerator and partial denominator is itself a ratio between a finite continued fraction and one of those Engel expansion things. He has a whole lot of "1"s appearing as numerators, and positive integers as denominators. Anyway, his doodad looks sort of like a Christmas tree of integers arranged in a very complicated pattern, so it's only a "continued fraction" in a very general sense. I really don't think the proof mentioned above applies to Arithmonic's Christmas tree, because the recurrence relations he mentions involve the preceding 3 convergents, not just the previous 2. You _can_ get a third-degree polynomial out of a longer recurrence relation like that.

I haven't really figured out how that Christmas-tree-like structure works. But I did see his claim, which is that when you plug a "3" into this thing -- that's it, just a "3" everywhere a denominator occurs -- it converges to the (real) cube root of 2. I can't really say if he's right or not ... the web site doesn't provide enough detail for me to follow exactly what's going on. And I'm not ready to buy his book and try to plow through it right now. But I'm not ready to dismiss his claim as "sheer fantasy". I've looked at his stuff closely enough to understand that there just might be something unusual hidden inside the "fractal fractions" he's talking about. DavidCBryant 17:10, 6 December 2006 (UTC)

Anyway, I know when I'm licked. If you want to read any more about what I really think, try this link. DavidCBryant 01:07, 6 December 2006 (UTC)

What DCB really thinks is that

We should include

$\pi=3 + \cfrac{1}{6 + \cfrac{9}{6 + \cfrac{25}{6 + \cfrac{49}{6 + \cfrac{81}{6 + \cfrac{121}{\ddots\,}}}}}}$

in continued fraction

That we are preventing this by advising him to leave the definition there as that of "simple continued fractions".

He never said this; I'm going to surprise him. I agree that we should include it; I disagree that we need to fiddle with the definition. Septentrionalis 03:19, 6 December 2006 (UTC)

Well, thanks for reading my rant, PMA. That's nice of you. I do appreciate it. But your solution doesn't make a lot of sense to me, because now you've displayed an object in the article that is not one of the objects the article defines at the outset. I think some readers might find it confusing, the way it stands. But hey, what's a little inconsistency here or there? After all, the article about complex analysis says that a function of a complex number is itself a real number. Set of all sets, here we come! (Or was that "Bertrand Russell, here we come!" I forget now.)

Anyway, I'm tired of arguing about the difference between a "continued fraction" and a "simple" or "regular" continued fraction. I'm going to concentrate on some other topics for a while. DavidCBryant 17:10, 6 December 2006 (UTC)

I've just added the continued fraction for π given above to the List of formulae involving π (so I hope it's correct!). Michael Hardy 00:36, 8 December 2006 (UTC)

Thanks, Michael. The formula is already in the article about Pi, in the "Continued Fractions" subheading. So you're not on the hook, if it's wrong. It is correct, though. It doesn't converge very quickly ... it's reminiscent of Wallis' continued product for Pi, in a quaint sort of way. Anyway, just to allay any concerns you may have, the first 12 convergents are 3/1, 19/6, 141/45, 1321/420, 14835/4725, 196011/62370, 2971101/945945, 50952465/16216200, 974212515/310134825, 20570537475/6547290750, 475113942765/151242416325, and 11922290683065/3794809718700. (I know that numerical evidence does not constitute a proof. But at least you can see that this thing is tending in the right direction ... 3, 3.167, 3.133, 3.14524, 3.13968, 3.1427, 3.14088, 3.14207, 3.14125, 3.14184, 3.14141, 3.14174, ...) DavidCBryant 03:55, 8 December 2006 (UTC)

Sylvester's sequence listed as Good Article

Sylvester's sequence has been listed as a Good Article, thanks to a proposal by User:Anton Mravcek and a review by User:Twinxor. I'm a little surprised, given its low density of inline citations and our recent experiences with GA reviews, but pleasantly surprised. —David Eppstein 16:32, 6 December 2006 (UTC)

Happy news. Light and reason have pushed back dark and chaos, at least for a day. Another positive sign is that Wikipedia:Scientific citation guidelines has elevated status.

I'm sure the illustration helps. (People like pretty pictures, even if they don't understand them.) The topic will be unfamiliar to almost all readers; curiously, that can help. (Every day or so our geometry article is vandalized.)

One weakness that catches my eye is the lack of ISBNs. For the second edition of Concrete Mathematics, we should have

ISBN-10: 0-201-55802-5; ISBN-13: 978-0-201-55802-9; Published: 1994-02-28.

(I don't know if the exercise cited has changed from the first edition.) For Computational Recreations in Mathematica, we should have

ISBN-10: 0-201-52989-0; ISBN-13: 978-0-201-52989-0; Published: April 1991.

A reminder: We are but three weeks away from the big ISBN switch. From ISBN.org:

On January 1, 2007, the book industry will begin using 13 digit ISBNs to identify all books in supply chain.

However, any ISBN is better than none. (The online converter is handy for hyphenation, validation, and conversion.) A quick way to find a number if the book is not in front of you is to do a web search with the title in double quotation marks and 'ISBN'. Example: '"Concrete Mathematics" ISBN' (without the single quotation marks). Usually the top hits are Amazon and AbeBooks; often the ISBN is visible in the list of search results without clicking further.

We could also use ISSN ids. These are harder to find, but an AMS site can help with this, and with expanding abbreviated journal names. Thus we find

Acta Arith. is Acta Arithmetica; Polish Acad. Sci., Warsaw; ISSN 0065-1036.
Amer. J. Math. is American Journal of Mathematics; Johns Hopkins Univ. Press, Baltimore, MD; ISSN 0002-9327.
Enseign. Math. is Enseignement des Mathématiques (The Teaching of Mathematics); Masson, Paris; ISSN 1269-7842.
Enseign. Math. (2) is L'Enseignement Mathématique. Revue Internationale. IIe Série.; Enseignement Math., Geneva; ISSN 0013-8584.

I'm guessing that the second series is intended for the Erdős and Graham article.

Quibbles aside, it's nice to see a small technical article appreciated. --KSmrq^T 08:09, 7 December 2006 (UTC)

Good to see the guidelines have a greater status. I've now started a thread on Wikipedia talk:What is a good article? discussing the issue. At least some of the GA people are quite supportive of changing the criteia as soons as the agidelines have been accepted.

Nice to see Sylvester's sequence get through. The one point I'd make is that the caption could be expanded. I'd probably turn it round by 90 degrees and add a labels for 0 and 1, so its more obvious that the things are summing to 1. --Salix alba (talk) 14:02, 7 December 2006 (UTC)

Thanks for the quibbles; I added the ISBN-10's and a longer caption. To my mind ISSN's do not belong on individual article references but rather the reference should wikilink the journal name (as the ones in this article already do) and the ISSN should go into the article about the journal. If I had a DOI link I'd include that, though. —David Eppstein 16:19, 7 December 2006 (UTC)

Slashdot of previously deleted transreal number

FYI, slashdot.org has evoked transreal number which is a recreate of a previously deleted article. I think its an prime example of mathematical illiteracy. Oh well. Afd, fix or delete. linas 19:46, 7 December 2006 (UTC)

For the morbidly curious, the Slashdot article is here. Perspex machine has been AFDed, too; I prodded James Anderson (mathematician). Lunch 23:30, 7 December 2006 (UTC)

Template:Calculus footer

A new {{Calculus footer}} has been created. A discussion about it is going on at Talk:Calculus#Re: Addition of Template:Calculus footer. Oleg Alexandrov (talk) 17:30, 9 December 2006 (UTC)

A new article about continued fractions

Hi, all!

I just put a new article out in the big namespace. Please take a look at it and tell me what you think -- either here, or on my user talk page.

Thanks! DavidCBryant 02:10, 12 December 2006 (UTC)

Or the article talk page. Septentrionalis PMAnderson 04:03, 13 December 2006 (UTC)

Simple Introduction

Some science articles are starting to produce introductory versions of themselves to make them more accessible to the average encyclopedia reader. You can see what has been done so far at special relativity, general relativity and evolution, all of which now have special introduction articles. These are intermediate between the very simple articles on Simple Wikipedia and the regular encyclopedia articles. They serve a valuable function in producing something that is useful for getting someone up to speed so that they can then tackle the real article. Those who want even simpler explanations can drop down to Simple Wikipedia. What do you think?--Filll 22:55, 12 December 2006 (UTC)

I am completely sympathetic with the need to have good pedagogical material. At the same time these articles seem out of place in what is supposed to be an encyclopedia. An encyclopedia should be a reference work that provides a succinct overview of a given topic, not a textbook from which to learn. It also seems detrimental to divide the effort of editors amongst multiple articles on the same topic. In my view it would be more appropriate to move the introductions you mention and others like them to Wikibooks. We can and should provide links to that material from Wikipedia. -- Fropuff 04:17, 13 December 2006 (UTC)

I find the introductory versions for the physics articles refreshing and worthwhile. I can agree with many of the points made by Fropuff, especially about dividing up editors' efforts, but I do believe there is a place in an encyclopedia for such material. I have expressed the opinion here in this forum before--and perhaps I am in a minority here--that we ought to be flexible about what is "allowed" or "disallowed" instead of being too dogmatic about what is "encyclopedic". In other words, I believe good pedagogy can be a guiding principle and not a secondary consideration. VectorPosse 05:19, 13 December 2006 (UTC)

I can appreciate the need not to divide the efforts of a few editors. However, I have a few comments:

this is not a zero sum game. There are more editors joining all the time. There are roughly 30,000 editors now on Wikipedia and more will come if things continue
providing accessible materials will actually enable more editors to contribute in areas in which they are not specialists but can come up to speed, increasing the number of available editors
Encyclopediae are only useful if they can be used with a minimum of hassle. If I look in some subject I am not an expert in and it is too much trouble to even read the introduction/lead of the article, I will probably give up and look someplace else
Encyclopedia Britannica provides something of a gold standard in encyclopedias. Encyclopedia Britannica has multiple articles on many subjects at different levels of sophistication:
- "Britannica Discovery Library" for preschool children
- "My First Britannica" encyclopedia for 6 to 12 year olds
- the single volume Britannica Concise Encyclopædia
- macropedia
- micropedia
- ready reference volumes

and this does not include the propedia. So Britannica might have 6 or more articles at different levels aimed at different audiences. I am not suggesting that Wikipedia attempt to equal their efforts, but 2 or 3 does not seem excessive when the most famous competitor has recognized the need for 6 or more. And the criteria they have is utility, because if it is not useful, they cannot sell encyclopediae.

I have no objection to Wikibooks, but that seems like the wrong format for shorter articles that are somewhat focused.
The lead parts of many articles on Wikipedia are completely unhelpful to nonspecialists. In real print encyclopediae, I do not find this to be the case. They pay more attention to accessibility, and we should too. An introductory article is just an extended lead article, or primer that can be used as an aid to reading the regular article.
Succinct and terse is a great goal, but it is not one I have noticed being met here on Wikipedia often enough. That still does not preclude the requirement of the material being accessible.--Filll 05:47, 13 December 2006 (UTC)

I don't know if I agree that simple intro articles are out of place. But I do think the concern of dividing up effort is a very valid one. I would agree that editing is not a "zero sum game", but I think that's the wrong thing to bring up. I think what Fropuff was referring to is the dividing up of expertise. Sure there are editors joining everyday, and if somebody puts in less effort, people will join who will pick up the slack. Unfortunately, that doesn't really address expertise. When one person, expert on a particular topic, stops editing, progress in that area may stop for a very long time (and errors start creeping in). It's not like there's a uniform distribution of experts joining, let alone a uniform distribution of expertise in the different areas.

I find it doubtful that even doing an incredible job would significantly increase the expertise level of editors. To really gain significant expertise takes considerable effort and dedication. People with that desire will want to study the material out of books. What Wikipedia offers is a useful synthesis of materials. I don't think a scenario where someone learns exclusively off Wikipedia is viable, even assuming a radical improvement.

One thing I want to point out about Brittanica and paper encyclopedias is that they really do a careful job of selection. By doing so, they can focus on fewer articles and ones in which it is much simpler to write well. Wikipedia does not have this advantage. Its strength is in large coverage. So it's really unfair and unrealistic to compare.

Since I got on this soapbox, I do want to say one thing about accessibility however. A common refrain is "Only a specialist can understand it and why would he or she need to read this?" This is wrong. The mistaken assumption is that because the reader did not understand it, the article is esoteric and cannot be understood by anyone other than an "expert". This leads to the tagging of numerous mathematical articles as being too technical. Of course, in reality, there are many people and many levels of expertise and many levels of mathematical maturity. A person adept in one technical subject can often learn something in another because of a high degree of maturity and understanding of how to cull the main ideas out.

Being too technical is an issue that we should be concerned about, but probably if there was less of what I just described, math editors would probably take these concerns more seriously. We try nonetheless.

Having said that, this concern has been raised before, again and again. There's been more of a focus on improving what we have, rather than extending it. People, with the desire, have improved articles such as mathematics and manifold. It took a great deal of effort and time. Right now I've been working on a rewrite of knot theory. It's taking a lot of time, and I certainly can't put in that much time regularly. There are also a few things I promised, but never got done. So the spirit is willing, but the flesh, as usual, is often weak. --C S (Talk) 18:57, 13 December 2006 (UTC)

Chan-Ho raises some good points about how best to split our time, the sheare quantity of mathematical articles can be intimidating. levels of expertise can also be intermidating, when an undergraduate user joins the project, he is greated with a big list of very experiences mathematicians, which may give the feeling of "what can I contribute". The answer is plenty, we have a lot of articles which don't require PhD's to edit, indeed these are often our most visited articles.

Its just occured to me that it might be worthwhile to set up a /High school mathematics work group and /Degree level mathematics workgroup where those with those levels of qualifications could congrigate. The workgroups could have their own list of articles to work on and possible participants lists. It might help in setting up some sub communities where people feel more able to contribute.

Also Wikipedia:WikiProject Mathematics/Participants could do with a prune. Many of the people who are listed there are no longer active. I had a start at this at User:Salix alba/Sandbox2, moving those who had not contributed in the last three months to a hall of fame section.

We do have a good recruiting oportunity at the moment, the Wikipedia:Articles for deletion/Transreal number‎ and related debates have seen a lot of new people, maybe some of these could be encouraged to work on some of the mathematics article. --Salix alba (talk) 20:02, 13 December 2006 (UTC)

Things like knot theory and category theory are not places for amateurs. I would agree completely with that. However, if you do have a lot of editors with lower skill levels, I hope you can employ them in constructive ways.

Another value of having things as accessible as possible is that many scientists actually visit Wikipedia as one of their starting places when doing research on an unfamiliar topic. And many people interested in applications regularly try to mine mathematics for ideas and machinery to use in applied disciplines. These people might have an impressive level of sophistication in some other area, but need a helping hand or even a guide to the literature to help them get started. This is a function that Wikipedia can fill. --Filll 20:25, 13 December 2006 (UTC)

I've now created a Hall of Fame section in /Participants for users how have not editted in the last three months. There were some who had not edited since 2004. A reasuring number on the participants list are still active editors which is encouraging. --Salix alba (talk) 23:32, 13 December 2006 (UTC)

Actually, I think knot theory is a good field for amateurs. That's why I picked knot theory to improve, since I expect it's an article that can be widely read and digested. Mentioning it in the same breath as category theory is kind of misleading, although of course, some very advanced aspects of knot theory are very abstract and even category theoretical. There have been several editors with an "amateur" interest in knot theory that have made big contributions to the knot theory portion of Wikipedia. But some left, one passed away, and it's difficult to replace dedicated editors in general.

The goal of accessibility is a good one, and I hope some of Richard's proposed mechanisms will help that along. More direction would be beneficial, I think. ---C S (Talk) 04:52, 14 December 2006 (UTC)

Area of a disk

The article area of a disk could use some work. It may be the only Wikipedia article justifying the familiar πr² expression, so it wouldn't hurt to bring it up to civilized standards. Michael Hardy 01:09, 13 December 2006 (UTC)

I've reproduced the proof by Archimedes on the talk page. (But without the obvious figures.) The article page scares me! Maybe later. --KSmrq^T 00:22, 14 December 2006 (UTC)

Proofs of trigonometric identities

Proofs of trigonometric identities is, in its present form, a horrible mess. Please help clean it up. Michael Hardy 19:12, 13 December 2006 (UTC)

I slapped it into Category:Article proofs, which, by definition, only allows messy, horrible articles. :-) linas 02:55, 14 December 2006 (UTC)

"Big" articles

I'm encountering some concern about the size of the article Areas of mathematics. I saw a reference to a 64K (= 65,536 byte) limit in somebody's message (Oleg's?) recently.

Anyway, I want to learn more about that. Does anyone know where to look it up? Does the limit apply to the wiki markup file that an author/editor can access? Or does it apply to the XML file (sans images) that the server serves up? I'm certain the 64K limit doesn't count graphics ... I tried to load the Mandelbrot set article the other day, and my poor little box choked on it somewhere between 1.0 and 2.0 Mbytes. :(

Thanks for the help! DavidCBryant 20:53, 13 December 2006 (UTC)

Wikipedia:Article size is the relavant guideline. AoM is less than 64K, so I think its probably OK. As this is a list type article much of the guideline is not really relavant, and the problems with older browsers has mostly disapeared. Mandelbrot is one if the most image rich pages about, but I am suprised that your prowser chocked. You must have quite an old machine. --Salix alba (talk) 22:18, 13 December 2006 (UTC)

AMD K6, 300 MHz. Dial-up connection. I paid $50 for it, OS and all. I'm a Neanderthal. ;^> Thanks for the reference! DavidCBryant 11:45, 14 December 2006 (UTC)

I agree that AoM is not a place to enforce teh article size rule, unless it gets truley huge, and its very nature should make that avoidable. (I have a Cerelon 333, an even worse processor. However, even with broadband, info arrives at the computer slow enough for my ancient computer to deal with it... internet connections are far slower than internal data transfer - even the original IDE standard from 1994 ran at 3.3MB/sec = 26.4Mb/sec, over three times faster than the most turbo-charged broadband around in the UK today) Tompw (talk) 13:30, 14 December 2006 (UTC)

Problems at exponentiation and empty product

Yes, it's the infamous 0⁰ debate again, and from many aspects I regret that I stepped in it, because it's really kind of a silly argument that doesn't matter much. However it does matter, at least a little, that the two mentioned articles asserted a consensus that does not exist.

(Precis of my position, which is not really the point, but just so you know where I'm coming from: The arguments for 0⁰=1 make perfect sense for exponentiation as defined on the naturals, or even when the base is ineterpreted as a real and the exponent as a natural, because then we are indeed discussing an empty product. However they cease to convince in the context of real-number-to-real-number exponentiation. The natural number 0 and the real number 0.0 are distinct kinds of thing, and there is no reason 0.0^0.0 must be defined, merely because 0⁰ is.)

Anyway as I say my position is beside the point. The point is that there are editors (well, one in particular, a difficult fellow whom some of you have encountered in the past) who want to preserve the articles in a state where they assert a consensus that does not in fact exist among mathematicians. I think you'll all agree that's wrong, whatever your views on the underlying "issue", if we can dignify it with that name. Please come and work on a broader-based approach. --Trovatore 17:06, 15 December 2006 (UTC)

Isn't 0⁰ an indeterminate form; i.e., I can make it equal to whatever I like if it shows up in a limit? How does it make sense to define 0⁰ = 1? --King Bee 17:20, 15 December 2006 (UTC)

Please, let's take discussion on the merits somewhere else -- this talk page would quickly become unusable. (See talk:empty product, for example -- my fault, I concede, but let's not repeat the problem here.) --Trovatore 17:25, 15 December 2006 (UTC)

Agreed. --King Bee 17:32, 15 December 2006 (UTC)

I left a comment to Bo Jacoby on the talk page of empty product. I encourage others to come and make a comment. --C S (Talk) 11:39, 16 December 2006

For reference, some of the previous problems with this editor (Bo Jacoby) are recorded at Wikipedia talk:WikiProject Mathematics/Archive16#Problem editor. Editors dealing with him should be aware that he has a history of wanting to use Wikipedia to promote his own (invented) notations and preferred conventions, and no amount of editors or argument has been able to convince him otherwise. —Steven G. Johnson 17:28, 18 December 2006 (UTC)

Bullying

Judging by this and other past "wars" with Bo Jacoby, it seems that he is really nothing more than a big bully. (And I don't feel like I'm resorting to an ad hominem attack when I say so. The evidence speaks for itself.) I worry about editors leaving the project over such things. I know I, for one, refuse to play into his specious and tangential arguments, since he seems to thrive on getting impassioned responses to his silliness. But if we all ignore him and choose to leave the debate, it seems he gets his way. Is there no recourse for dealing with bullying like this? VectorPosse 20:31, 16 December 2006 (UTC)

So far, it appears that nothing has happened except for a vigorous discussion on two talk pages. All that needs to happen to correct the articles is for someone to rewrite the appropriate parts with a neutral viewpoint, using pedantic references that leave no stone unturned. Many editors will recognize quality writing and complain if it is reverted. CMummert 22:13, 16 December 2006 (UTC)

Fair enough, although I was refering to repeated problems in the past by Bo Jacoby, not just this particular discussion. I'd have to do a little research to find all the past problems--I'm relying a little on memory here. But my question is more general anyway. I have read of people leaving the project over this kind of thing before; editors willing to shout louder and longer than anyone else can be quite discouraging. At what point does this vigorous discussion become inappropriate and problematic? It may not have crossed that line in this case, but if there's a history of such aggression.... Anyway, your point about watching for POV reverts and then complaining is well-taken. VectorPosse 01:06, 17 December 2006 (UTC)

If you feel impelled to it - and I can't say his manners appeal to me -, it will be more useful at WP:RfC, the section on user conduct, not here. Do tell us so we can all chime in on the mathematical points though. Septentrionalis PMAnderson 01:14, 17 December 2006 (UTC)

Bo Jacoby has already been reported here as a problem editor. In past episodes one recurring passion was "improving" notation. Just revert as much as you need after leaving one brief comment on the talk page. If you have 3RR concerns, feel free to ask here for other editors to join in. I'd recommend against extended talk page engagements with Bo; he seems to feed on that.

The American Heritage Dictionary of the English Language defines ad hominem as

"Appealing to personal considerations rather than to logic or reason",

and includes in its usage note the observation that

"[T]he homo of ad hominem was originally the person to whom an argument was addressed, not its subject. The phrase denoted an argument designed to appeal to the listener's emotions rather than to reason. … The phrase now chiefly describes an argument based on the failings of an adversary rather than on the merits of the case"

It is perfectly acceptable to object to how someone behaves at Wikipedia, and it is also acceptable to question the content of edits. We do want to be careful about confusing the two, as in "Johnny doesn't play nicely with others, so what he just said is wrong." By contrast, it's OK to say, "Johnny doesn't play nicely so I don't want to play with him", or "Most of Johnny's edits contain nonsense and this one looks like more of the same."

Within Wikipedia, as in the real world, the real challenge with problem people is to decide how we will respond. Suppose, for example, Melchoir does something unhelpful and annoying, again. (Substitute the "problem person" of your choice — me, if you like!) Can we rewire his brain? Can we correct his sense of humor? Can we bring him to his senses? No, no, and probably not. The only person we might control is ourselves, and even that is uncertain. I cannot offer a sure recipe; I can offer quotations:

Never attempt to teach a pig to sing; it wastes your time and annoys the pig. — Robert A. Heinlein
One ought never to turn one's back on a threatened danger and try to run away from it. If you do that, you will double the danger. But if you meet it promptly and without flinching, you will reduce the danger by half. — Winston Churchill
I learned long ago never to wrestle with a pig. You get dirty, and besides, the pig likes it. — George Bernard Shaw
I like pigs. Dogs look up to us. Cats look down on us. Pigs treat us as equals. — Winston Churchill
Don't be too hard on me. Everyone has to sacrifice at the altar of stupidity from time to time, to please the Deity and the human race. — Albert Einstein
It is a dear and lovely disposition, and a most valuable one, that can brush away indignities and discourtesies and seek and find the pleasanter features of an experience. … It is a feature that was left out of me at birth. And, at seventy, I have not yet acquired it. — Mark Twain
Always look on the bright side of life. — Eric Idle

Draw your own conclusions! :-D --KSmrq^T 04:06, 17 December 2006 (UTC)

When I saw this subsection start up, I knew it was only a matter of time. I simply don't deserve this. Please show some decency. Melchoir 05:04, 17 December 2006 (UTC)

Don't be so hard on yourself; you do deserve a good laugh. I don't know how many banana peels must be sacrificed, but it will be worth it. Try reading the Eric Idle quotation in full; it's bound to cheer you up! --KSmrq^T 06:12, 17 December 2006 (UTC)

Okay, ha ha ha! What a card that KSmrq is; when he calls me unhelpful and annoying I know it's all in good fun and he doesn't mean it. He wouldn't embark on a campaign to tarnish my name on every forum available to him if he thought he might actually influence anyone's opinion. And since it's implicitly understood that he respects me as a human being, there's certainly no need for him to act like it. It's all a joke! Whee, I pass the test! Everybody in a three-parsec radius gets a cookie! Melchoir 06:59, 17 December 2006 (UTC)

Thanks Melchoir. Paul August ☎ 18:43, 17 December 2006 (UTC)

I'm here all week — try the veal. Melchoir 19:02, 17 December 2006 (UTC)

It's distressing that somehow this section on "bullying" actually contains some. --C S (Talk) 10:32, 17 December 2006 (UTC)

I'm curious how many cookies you passed out, Melchoir. Surely not as many as $\aleph_0$ , but probably quite a few. How fast were they moving when you let fly (to cover a 3-parsec radius, I mean)? Is your arm sore? And why didn't I get one? ;^> DavidCBryant 12:17, 17 December 2006 (UTC)

I'm missing all the jokes here, but in any case if Melchoir is on non-standard time, and cranks out one cookie at every 1/N second, he/she can crank out N cookies p/second. For N non-standard, the standard cardinality of the hyperinteger interval 1..., N is $2^{\aleph_0}$ . —The preceding ~~unsigned comment was added by CSTAR (talk • contribs) 17:38, 18 December 2006 (UTC).~~

Oops forgot to sign--CSTAR 17:42, 18 December 2006 (UTC)

At that rate, Melchoir's not only going to have a sore arm; he'll be falling-down dizzy in nothing flat, to boot. And what a windmill! Katrina was just a baby zephyr. This wind will blow the atmosphere right off the planet, along with most of the houses! ;^> DavidCBryant 19:44, 18 December 2006 (UTC)

How is it that the disputes in Mathematics are so much more civilized than those in the rest of Wikipedia? I am somewhat stunned to realize how much cooler and calmer things are after reading a bit. Especially when I think about some of the Mathematicians I know in real life...--Filll 14:08, 17 December 2006 (UTC)

Sorry, I only cranked out a couple dozen before running out of butter. (Really!) Who knew there'd be such a rush? Melchoir 17:29, 17 December 2006 (UTC)

Why "disputes in Mathematics are so much more civilized"? Because there is no reason to care at all about mathematics unless you care about getting things right (as opposed to getting your own way, say). This shared dedication to the standard of truth and esthetic beauty keeps us from fighting each other too seriously. JRSpriggs 07:15, 18 December 2006 (UTC)

Manifold Destiny

A well-meaning, new editor has been making some additions to this article. I don't believe these follow NPOV, but I no longer have the energy to talk to this person. I tried explaining NPOV doesn't mean putting out one argument followed by counterargument, but somehow this person doesn't seem to understand and takes everything as an accusation of some type. His/her grasp of the facts and circumstances also seems tenuous. --C S (Talk) 23:57, 18 December 2006 (UTC)

Need advice

I need an advice on how to group entries in List of operators. Any thoughts?--Planemo 13:26, 10 December 2006 (UTC)

This is a little out of my area, but I feel that you need more explanation of these transformations. What do the variables mean? What is the transformation used for? It is good that you have pointers to articles for some of them, but every one of them should have a pointer (even if it is a red-link). You described them as "This list includes the most widespread transformations of analytical functions of one argument.". In what sense are they "analytical"? If you mean that they are defined on the complex plane and have complex derivatives everywhere, then you should put them in a category that deals with complex numbers. JRSpriggs 04:56, 11 December 2006 (UTC)

I added some boilerplate and various links that perhaps addresses JRSpriggs' comments. A merge with list of transforms might be contemplated. There are some generic transforms that don't easily fit in this list. linas 06:44, 11 December 2006 (UTC)

I would strongly recommend the merge. List of operators is where I would look for unary and binary operators (+,- *,/, absolute value). Septentrionalis PMAnderson 16:00, 11 December 2006 (UTC)

They are functions, not operators and already covered in "left composition" entry ( $f\circ y \,$ )--Planemo 17:32, 11 December 2006 (UTC)

And these are functionals; so? Septentrionalis PMAnderson 18:48, 11 December 2006 (UTC)

No they all are particular cases of left composition operator.--Planemo 18:52, 11 December 2006 (UTC)

The question is how to group the entries better: by properties (i.e. linearity) or by branch of mathematics where they are used? But where to place such operators as composition or derivative then? Should the functionals be separated or not? Or to create a special section for binary operations such as composition, convolution and inner product? Or maybe group by type of coordinates/parametrization?--Planemo 11:39, 11 December 2006 (UTC)

IMHO, having such a "list" is not that good an idea. the term "operator" is used in a hell of a lotta places in mathematics, making a comprehensive listing difficult and somewhat pointless. and having an incomplete list, as that article is right now, is misleading, unless one is very specific about the context and what is meant by an "operator". right now it looks rather like an ungainly collection. for instance, an operator theorist would find few items on that list to be of interest; in any case, they are well-covered elsewhere. i am sure such examples abound from other fields, say the boundary operator from homology. also, some entries in the list seem rather funny, e.g. taking the inverse of a function is listed, so is the arc-length of a curve and the L^2 norm. sure one can use whatever terminology one wants, but calling every trivial thing an "operator" doesn't help the credibility or the utility of the "list". Mct mht 18:25, 11 December 2006 (UTC)

I agree the term is too broad, but the list is dedicated to the certain meaning. And what's wrong with arc-length or inverse function? Maybe that they are not liner while most "specialists in operators" work with linear ones?--Planemo 18:47, 11 December 2006 (UTC)

What's wrong with the non-linear operators is that there are just about zero operator-theoretic results, theorems or facts about them. Taking some random thing and calling it "an operator" seems pointless to me, as it does not suddenly offer new insight, nor does it allow some general theorem to be applied to obtain new results. By contrast, the linear opers have a rich theory and many general theorems that can be applied. Thus, I'd recommend discarding the entire non-linear section. But perhaps this discussion should be taken to the article talk page. linas 03:24, 14 December 2006 (UTC)

in light of the fact that the article has undergone further edits. i would like to state again that, if one insists on having such a list, one must be very specific about what's meant by an operator, in what particular context(s). right now it's a rather incoherent collection, including the see also links. a case might be made that an article listing all common integral transforms has a place in WP. but calling, say, the L² norm an "operator" is not a good idea. i doubt there's single piece of literature that uses that terminology. there are quite a few such misleading examples in that list right now. Mct mht 12:23, 20 December 2006 (UTC)

Representing probability

I need to represent the following probability mathematically using the correct wikicode/syntax.

A person is presented with 7 questions and 7 answers. What are the odds of them correctly pairing off 4 of them?

perfectblue 09:15, 19 December 2006 (UTC)

I'm not sure I understand your request. You've already stated the problem without needing any special syntax. The answer will, of course, be a number, also not requiring anything special. Are you saying that you need to know how to type up the solution to the problem using proper mathematical notation? Are you intending to put this in some article? In that case, maybe you could post what you have in the article and then someone could help you format it properly. Otherwise, this forum isn't really in the business of solving math problems, especially since we have no way of knowing if this is a question on a take-home exam or something like that. (Not to suggest that you're cheating on an exam or anything; I'm just pointing out a reason why it might not be a good idea for people in this forum to solve other people's math problems without knowing what they're for.) VectorPosse 09:31, 19 December 2006 (UTC)

The problem needs a bit more in order to be stated unambiguously. To define the probability of the outcome, we need to know more about the process by which the outcome is produced. If you ask a bunch of mathematicians seven questions like 24+13 = ?, 11+58 = ?, ..., and you give them the seven answers, like 37, 69, ..., but in some different order, then almost all will get all seven correctly paired off. At the other extreme is when people would not have a clue, like you give them seven phone numbers picked at random from the white pages of the Manhattan telephone directory, and the names of the subscribers, and you ask them to pair them off. To avoid a possible accidental bias, you randomize each time the order in which these items are presented to the subjects. Then the pairings will, on the average, have 1 correct pair and 6 incorrect pairs. So let us assume that the process is that the pairing is picked at random out of the 7! = 5040 possible pairings, each with equal probability of 1/5040. Letting p_c stand for the probability of having exactly c correct pairs, we have then: p₀ = 1854/5040; p₁ = 1855/5040; p₂ = 924/5040; p₃ = 315/5040; p₄ = 70/5040; p₅ = 21/5040; p₆ = 0/5040 = 0; p₇ = 1/5040. So the probability of having exactly 4 correct pairs is 70/5040, which is about 1.39%. The probability of having at least 4 correct pairs is p₄ + p₅ + p₆ + p₇ = (70+21+0+1)/5040 = 92/5040, which is about 1.83%. --Lambiam ^Talk 12:13, 19 December 2006 (UTC)

It's for a wiki entry the I'm drafting about the paranormal (User:Perfectblue97/Natasha Demkina), and I don't know how to write it up properly as I am neither a mathematician, nor a regular user of wikisyntax.

A woman is given 7 cards each bearing 1 person's medical record, and is sat before 7 people (1 card per person). She is asked to use her paranormal powers to match each card to the correct person. She does this correctly 4 times. The odds of her doing this (4 matches out of 7) by pure chance are about 1 in 50 (2%).

I would like to know how to write this up in the form of a mathematical formula using wiki syntax (so that it comes up like an image, rather than as written text).

perfectblue 12:18, 19 December 2006 (UTC)

There is no truly standardized way of doing this. After having explained that C denotes the random variable that gives the number of correct pairings for a pairing drawn from a uniform distribution (discrete) on all 7! possible pairings, you could write:

$\Pr(C \geq 4) = \frac{23}{1260}.$

However, this does not add any weight or credibility beyond the statement in plain English that the probability of getting at least 4 correct pairings by pure chance is 23/1260, which is less than 2%, and you introduce the risk that readers who understand the formulation in natural language might not understand the mathematical formula. --Lambiam ^Talk 14:57, 19 December 2006 (UTC)

<math>\Pr(C \geq 4) = \frac{23}{1260}?</math>

I don't know why, but I thought that there was a way of doing this where you fed in the data and the equation, and it calculated it on the server and presented it to the user.

perfectblue 15:20, 19 December 2006 (UTC)

That would be cool: a computer algebra system integrated with Wikipedia. In this case I don't know a formula, and rather than deriving one it was easier to (let a simple program) enumerate all 5040 possibilities. --Lambiam ^Talk 17:22, 19 December 2006 (UTC)

You should not consider a random process for comparaison but rather the results obtained in average by people choosen at random. As soon as one can see the people and have (even a short) look at the records, the pairing is far from being random. pom 15:32, 19 December 2006 (UTC)

Do you mean Cold reading? That was something that was determined best dealt with by setting a margin for success on the outcome based on Bayesian inference (or so I'm told). In this case, the margin was determined to be 5 out of 7. Significantly higher than could reasonably be expected through either random chance or educated guessing. Needless to say that some people have accused the margin of being set too high.

perfectblue 15:47, 19 December 2006 (UTC)

It really depends on what the hypothesis is you are testing. If the hypothesis is that the subject did better than purely random, and we had picked a moderately strict value of 2% for the size of the test, then we should conclude that the null hypothesis ("not better than random") is to be rejected. If, however, the hypothesis is that the subject does better than a control group of comparable (same age group, same background) but otherwise randomly selected people, then the necessary data for hypothesis testing is simply not there. (It might still be possible to acquire such data if the test conditions can be recreated.) In this specific case, it would actually have been more relevant to take a control group of general practitioners, and I don't understand why that was not done – it would have been easy enough to organise. If the aim was to potentially support an extraordinary claim, then I must say that 7 for the length of the run is rather low. --Lambiam ^Talk 17:22, 19 December 2006 (UTC)

Unfortunately, we're not talking about a fully fledged experiment carried out by serious scientists. All they did was to get two statisticians to decide that 5 out of 7 was a good score based on Bayesian inference, and then they ran the experiment with that. There was no null hypothesis (the only criteria were that 5,6 or 7 were good and any lower number might as well be 0 because they determined that 4 or less represented chance or cold reading), no control group, and no attempt to take the experiment any further. It wasn't exactly good science, but then it was conducted fro a TV documentary by SCICOP.

perfectblue 18:43, 19 December 2006 (UTC)

Without knowing the experiment, your characterization surprises me. The former CSICOP (correct spelling), now CSI, used (according to your writeup) the likes of Persi Diaconis — who surely understands statistics, and Ray Hyman — who is thoroughly familiar with proper experiments and controls involving human subjects. Unless the organization and these two minds have rapidly deteriorated in recent years, I would expect them to get their statistics right for a documentary they produced. --KSmrq^T 18:31, 20 December 2006 (UTC)

If all 5040 permutations of the seven answers are equally probable, then the answer is given in the article titled rencontres numbers as 70/5040 = 1/72. Michael Hardy 20:38, 19 December 2006 (UTC)

Michael Hardy's answer is correct for a purely random choice of a permutation of 7. But this is far from random. Medical records contain an enormous amount of identifying information which the woman could use (asside from the name), such as: age, sex, race, weight, height, medical conditions which have obvious effects on a person's appearance, etc.. Perhaps we should be amazed that she only got four of them right instead of all seven. And 1/72 = 0.0138888... . JRSpriggs 07:10, 20 December 2006 (UTC)

P.S. Also one should probably calculate the probability of getting at least four correct, rather than exactly four. Or perhaps another value. But I do not know enough about statistics to know for sure which is the correct probability to use. JRSpriggs 07:15, 20 December 2006 (UTC)

The relevant criterion should be of the form at least C correct, for some predetermined value C. --Lambiam ^Talk 12:15, 20 December 2006 (UTC)

The 1/72 for exactly four and the value for at least four were already given above by Lambiam. Actually, it seems that in this experiment she did not have medical records, but had to identify each of 7 medical conditions (including "none", the "control") with the correct person. This is less information than a medical record, but still not random. I don't know anything about how the 5/7 threshold was determined, but saying that statisticians had decided that and used it hardly shows that it wasn't carried out by serious scientists. The only question is whether there is an argument for saying that 4 or less could be chance/cold reading, and so a "failure". Since the aim was to determine whether or not further study was worthwhile, it is hardly surprising that a "failure" resulted in no attempts to take it further. JPD (talk) 11:05, 20 December 2006 (UTC)

To Lambiam: I am sorry that I did not notice that you had got the answer first. If you are correct about using a predetermined value, then presumably that would be the five correct that the "experts" called for. Then the probability would be, using your figures, (21+0+1)/5040 = 22/5040. However, then she failed the test, so I do not know how relevant that probability is in the case of failure. JRSpriggs 12:25, 20 December 2006 (UTC)

I haven't studied the rationale for picking the number 5. In general the criterion should depend on the hypothesis tested, which I don't know for this case. But it is indeed a matter of statistical hygiene to determine in advance the criterion for what shall and what shall not be deemed significant. Otherwise the temptation to pick the criterion afterwards that best supports your favourite hypothesis may prove irresistable. If you are to guess my telephone number and you tell me you can probably get the last two digits right, well, by pure chance that is 1 on 100, so if you then manage to pull that off, it is like wow (or you must have spotted it on a label on one of my suitcases). If instead you get the last one right, as well as the first digit, while the one-but-last is only off by 1, well, the probability of just that happening is actually less, but if you offer that as a replacement criterion afterwards I'm not going to go for it. The relevance, if any, of 22/5040 is that it is a pretty small (although not impossibly small) probability for some pre-agreed remarkable event to come about by pure chance. --Lambiam ^Talk 13:00, 20 December 2006 (UTC)

Luigi Fantappiè

Luigi Fantappiè could stand a cleanup job. It seems a touch heavy on the uncritical adoration. Anville 23:49, 19 December 2006 (UTC)

Symbol for differential

Lseixas (talk · contribs) has been going around changing the symbol for differential, e.g. "dt" to "\mathrm{d}t" inside Tex expressions at General relativity and elsewhere. If I remember correctly, KSmrq (talk · contribs) told us to do the exact opposite. Is there an agreed standard symbol for the differential? JRSpriggs 09:59, 20 December 2006 (UTC)

I have not seen this. The closest thing I know of is that sometimes "\mathbf{dx}" is used for vector quantities, as in:

$\mathbf{dx} = ( dx_{1}, dx_{2}, dx_{3} ).$

But this seems not to be the case here. VectorPosse 10:18, 20 December 2006 (UTC)

The d signs in ∫x³dx and dy/dx are primarily syntactic operators, like the λ in the lambda expression λx.x². Rendering them in the same font as normal variables may be confusing (what is the derivative of of sin(ωd) w.r.t. d). Therefore a good case can be made for using a distinctive font for this syntactic operator, and if we were to redesign the current hodgepodge of mathematical notation in a more rational way I'd be all in favour of that. The fact is, however, that this operator is conventionally rendered in italics, just like Euler's constant e and the imaginary unit i. This makes it impossible, for example, to use i as the summation variable in $\sum_{k=0}^{n-1} e^{2 \pi i k/n}$ . Oh well, such is mathematical life. In any case, it is not up to us Wikipedians to redesign mathematical notation, however irrational. We should stick to the conventional common use: italic d operators. --Lambiam ^Talk 12:36, 20 December 2006 (UTC)

In one of my papers, the publisher changed my italic d 's to roman d's in expressions like $\frac{\mathrm{d}}{\mathrm{d}t}\Big|_{t=0} f(t)$ and $\int f(t)\mathrm{d} t$ . I also own some books that follow this "roman d" convention (less than 10% of my total books, though, most seem to use italic), so the usage of italic d's is not universal. Kusma (討論) 13:10, 20 December 2006 (UTC)

This has been discussed before. I'm behind a dial-up connection now, so I won't look for it, but it's somewhere in the archives (the most extensive discussion was mostly about roman versus italic i for the imaginary unit). As Kusma says, roman d does definitely exist, mostly in Europe, but italic d is used more often. The previous discussion led to the conclusion of treating this the same as the difference between American and British English: articles should be consistent and the first contributor gets to decide which convention to use. For the record, I like the roman convention. -- Jitse Niesen (talk) 14:10, 20 December 2006 (UTC)

Believe it or not, but there's actually an ISO standard for this: a roman "d". See, for example, Beccari's article in TUGBoat (Volume 18, Issue 1, pp39--48, 1997). But mathematics articles and monographs haven't ever really followed the standard... My two cents, Lunch 21:01, 20 December 2006 (UTC)

The most recent comment I made was on the mathematics reference desk, where I recommended using the italic "d" when writing articles. We have a never-ending struggle with the variations in mathematical conventions. As Jitse says, there are parallels to the differences between American and British English. Our "offical" page of mathematical conventions is mute on this topic, though it has been briefly discussed on its talk page. Perhaps we should move this dialog there, for the benefit of future editors.

Those who have mostly seen basic calculus may not realize all the different roles dx can play. Some examples (not exhaustive):

Part of a differential operator, such as ^d⁄_dx f.
The variable of integration, such as ∫ f(x) dx.
A total derivative, such as ^d⁄_dx(f+g) = ^df⁄_dx+^dg⁄_dx.
In differential geometry, a vector in the cotangent bundle, such as 3dx+2dy.
In exterior algebra, part of a differential form, such as dx∧dy.
An exterior derivative operator acting on a differential form, such as ddx = 0.
In algebraic geometry, a boundary operator acting on a chain complex, such as d_n : A_n→A_n−1.

Those familiar with these applications will appreciate the important connections between them, so the parallel notation is not totally capricious. Yet each use is formally different.

In some of these cases dx is best considered a "diphthong", not a d acting on an x. For example, Herbert Goldstein, in Classical Mechanics, 2/e (Addison-Wesley, 1980, ISBN 978-0-201-02918-5), has a footnote (p.169) saying

“It cannot be emphasized too strongly that dΩ is not the differential of a vector. The combination dΩ stands for a differential vector, i.e., a vector of differential magnitude. Unfortunately, notational convention results in having the vector characteristic applied only to Ω, but it should be clear to the reader there is no vector of which dΩ represents a differential. As we have seen, a finite rotation cannot be represented by a single vector.”

Similarly, William L. Burke dedicates Applied differential geometry (Cambridge University Press, 1985, ISBN 978-0-521-26929-2) “[t]o all those who, like me, have wondered how in hell you can change $\dot{q}\,\!$ without changing $q\,\!$ .” (This also serves to remind us of the contrasting conventions of Newton and Leibniz.)

I am not bold enough to demand a universal convention, nor even a case-by-case dissection. However, I would highly recommend that the first two instances, which are elementary calculus, use the italic "d". This is partly because it seems to be the most common convention, partly to respect the diphthong, and partly because it frees up other typographical variations for the other cases. It is especially important to have variants available when describing connections, to avoid wild confusion. --KSmrq^T 21:35, 20 December 2006 (UTC)

If there's a controversy about this subject, including verifiable sources such as the ISO convention mentioned above, shouldn't something of the history of this controversy be mentioned in Leibniz's notation for differentiation? And why is that article separate from Leibniz notation, and why do those two articles use two different versions of the convention? —David Eppstein 21:47, 20 December 2006 (UTC)

With regards to the ISO standard, I think it's mostly meant to be applied to physics and engineering. I think IUPAC chimed in at one point or another with a similar standard for chemistry. On the other hand, like I mentioned above, mathematicians have never really gone along with all of it. ( So ppppppthtthhthththth! ;) Lunch 22:15, 20 December 2006 (UTC)

It seems that there are strong references for roman d: CBE manual (Scientific Style and Format 6ed 1994 CUP cf p208) and Swanson's Math into Type. pom 23:22, 20 December 2006 (UTC)

Those who would like to read the 1997 TUGBoat article about the ISO and IPU conventions can find it online. Please note that the introduction says

“I will discuss here those few tricks that physicists and engineers, not mathematicians, must know in order to satisfy the international regulations and to distinguish similar symbols with different meanings and, ultimately, in order to cope with the ISO regulations and the recommendations issued by the International Union of Pure and Applied Physics (IPU).”

(His emphasis!) He later says

“The house style of the majority of publishing companies, where the differential operator is a common italic ‘d’, was evidently set up under the influence of the tradition of pure mathematical typesetting before the ISO regulations were published; … while the modern world is so attentive to international standards, this particular one is almost completely neglected.”

The only other significant comment on d occurs on page 8, in regards to spacing. It has been almost a decade since the article was published; I do not know how standards and practices have changed in that interval.

Beccari spends most of the article dealing with constants and physical quantities, and that context explains the desire of the standards to distinguish the "e" indicating an electron from the "e" indicating the base of natural logarithms, or the "d" indicating crystal lattice plane spacing from the "d" indicating a differential. The needs of pure mathematics articles are rather different, though we cannot completely separate ourselves.

Consider a discussion of the electrical field surrounding an electron. A mathematician would confine the charge in a sphere and use the observation of Gauss that we can substitute an integral over the boundary for an integral over the interior. We would consider this a special case of the generalized Stokes' theorem, which concerns itself with differential forms.

$\int_M \mathrm{d}\omega = \int_{\partial M} \omega.\!\,$

Thus we see this as integrating a form, either ω or dω, over either a manifold, M, or its boundary, ∂M. Here the roman "d" indicates an operator, the exterior derivative, on forms. But if we consider a planar variant of this situation, where this theorem specializes to Green's theorem, we would use dx and dy, with italic "d", not roman. For example, suppose we wish to find the center of mass of a uniform density simple polygon region, R, with border P. Its coordinates are merely the average x and average y positions.

$\begin{align} \bar{x} &{}= \frac{1}{A}\iint_R x \, dx\,dy & \qquad \bar{y} &{}= \frac{1}{A}\iint_R y \, dx\,dy \\ A &{}= \iint_R dx\,dy \end{align}$

We can compute each of these three integrals using the theorem, which here we would write

$\iint_R \left( \frac{\part F}{\part x} - \frac{\part G}{\part y} \right) \, dx\,dy = \int_P G\,dx + \int_P F\,dy ,$

where F = F(x,y), G = G(x,y). In this context dx and dy should be viewed as parts of a differential form, because we are concerned with the broader theorem, which is stated in those terms. (Readers not familiar with this method are urged to discover the beautifully efficient computations in term of the polygon vertices for themselves. For example, to find the area integral we can let F(x,y) = x, G(x,y) = 0. The integral along P is the sum of the integrals along each of the edges.)

In this example, we would prefer not to use a roman "d" with two entirely different meanings. --KSmrq^T 03:38, 21 December 2006 (UTC)

If I may put this in cultural terms: it appears that WP engineering and some undergrad level physics articles prefer the roman d, while the math and especially the postgrad math articles prefer the italic. I beleive tha this is because the engineering/physics textbook authors are taking considereable pains to distinguish vectors from scalars, and differentials from derivatives, and all of those issues undergrads struggle with, and are placing that emphasis on the notation. Thus, undergrads are exposed to this meticulousness, and will edit on WP in this fashion. The (pure) mathematicians have "gotten over it", and have a different way of dealing with such issues ('by abuse of notation'), and are thus happier with the italic d, as it is visually prettier on the page: it doesn't screem out "look at me, I'm important" like the roman d does. linas 00:20, 21 December 2006 (UTC)

This "cultural" analysis is right on. I'm a pure math guy, and the expression $\int f(t)\mathrm{d} t$ screams at my eyeballs! :) VectorPosse 00:48, 21 December 2006 (UTC)

Mine too. Let's try a variation:

$\int f(t)\,\mathrm{d} t$

That looks a little bit better, but still

$\int f(t)\,dt$

is what I'm accustomed to and is what I see in most books, every day. If one must use the Roman "d", one should still have the space between "f(t)" and "dt". Thus: \int f(t)\,dt. Michael Hardy 01:16, 21 December 2006 (UTC)

Well, Lseixas (talk · contribs) did about 75 edits on 19 December 2006 alone, almost all of which were changing the italic form to the roman form (often many formulas in a single edit). JRSpriggs 05:29, 21 December 2006 (UTC)

I very much prefer the plain dx notation to \mathrm{d} t, and either way, I think mass conversions are a bad idea. I reverted a bunch of them. Oleg Alexandrov (talk) 20:47, 21 December 2006 (UTC)

Word problem (mathematics education)

There's a really interesting discussion going on about this article. The main problem seems to be that it is very difficult to explain what this is. Unfortunately, currently the article reads something like a diatribe on how the notion of "word problem" is nonsense. This article seems to have been in this kind of state for over three years. --C S (Talk) 19:57, 20 December 2006 (UTC)

Polar coordinate system

I'm thinking of putting this article as a FAC, but before I do so, I would love the opinion of a few math editors, so I can get the article even better before letting it be the subject of the scrutiny of the rest of the Wikipedia community. As I've never been through the featured article process before (nor have I been involved in it), any comments/help with the article would be greatly appreciated. —Mets501 (talk) 21:50, 20 December 2006 (UTC)

It looks good to me, I could not see any specific flaws on a brief scan. Much improved from a couple on months ago. --Salix alba (talk) 23:23, 20 December 2006 (UTC)

Great! Michael Hardy has done some nice cleanup, so I think I'll give others a chance to input here and then I'll submit it. —Mets501 (talk) 23:57, 20 December 2006 (UTC)

I see many tiny problems, but no big ones. The worst problem is that it is never made clear what subset of R×R the polar coordinates (r,θ) are supposed to range over, and the difficulties at r = 0 are completely ignored. Then there are many statements that are just not quite right; for example in the lead: "For many types of curves, a polar equation is the simplest means of representation; for others, it is the only such means." (my emphasis). The last part is indefensible. If a curve is given by a polar equation F(r,θ) = 0, then we can also describe the curve by a Cartesian equation G(x,y) = 0, where G(x,y) is defined by G(x,y) = F(radius(x,y), angle(x,y)) for suitable functions radius and angle. Finally, several of the citations are to sources that have no authoritative value. At some time there used to be a maths article of the week improvement drive or something like that; perhaps that could be revived. --Lambiam ^Talk 00:27, 21 December 2006 (UTC)

I left some comments at Talk:Polar coordinate system. -- Fropuff 00:51, 21 December 2006 (UTC)

Wikipedia:What is a good article?

This is being revised, especially the infamous section 2b about inline citation. It seems to me that even the edits I did not do are in a sensible direction; after some jumping up and down at Wikipedia:Good articles/Review#Johann Sebastian Bach (where it is perhaps clearer than on mathematical articles what sort of points are at issue), some mutual understanding may have been attained. Please come help. Septentrionalis PMAnderson 04:40, 21 December 2006 (UTC)

Renaming Exclusive disjunction Exclusive or

If you have an opinion about whether the article should be named "Exclusive or" or "Exclusive disjunction", come on down to Talk:Exclusive disjunction and share your opinion. Samboy 09:09, 21 December 2006 (UTC)

Vector Notation

Recently the vector notation on a huge number of pages was changed from bold style ( $\mathbf{B}$ ) to arrow style ( $\vec{B}$ ), in an effort to make notation on wikipedia more homogeneous. In paticular the Maxwell's Equations section has been changed.

Is this such a good idea? To begin with, mathematical notation is not in fact consistent, with different persons, groups, countries and even continents often using quite different notation. What is more appropriate to some may be less aprropriate to others. Notation vary's across fields as well. It doesn't seem wise to impose a single notation for all of Wikipedia when no over all consensus exits. ObsessiveMathsFreak 15:18, 21 December 2006 (UTC)

Wide sweeping changes to alter notation are generally frowned upon (and often reverted). There are numerous such notational issues which have been argued to death on this page (see above and almost any archive page). The upshot always is as long as an article is consistent in its notation don't change it simply because you prefer an alternative notation. We treat differences in spellings (British vs. American) the same way. In Wikipedia, as in life, we need to respect our differences. -- Fropuff 18:00, 21 December 2006 (UTC)

The latter is nice for one reason: It uses semantic markup. However, in the physics, math, and engineering I've seen, bold is more widely used. Perhaps a high-level admin could redefine \vec to produce bold, leaving \overrightarrow to produce $\overrightarrow{B}$ ? —Ben FrantzDale 18:21, 21 December 2006 (UTC)

Calculus footer

I find the {{Calculus footer}} template to be rather ugly, either with stuff hidden or stuff shown. I would suggest that it be rewritten keeping only the most relevant calculus topics, instead of the huge amalgam of links, whether they show up or are hidden. Comments? Oleg Alexandrov (talk) 20:32, 21 December 2006 (UTC)

I personally like it. It is well-organized and quite comprehensive. Relegating it to the end of the article keeps it from being obtrusive. Making it more attractive is worthwhile, but I wouldnt delete any content. - grubber 20:48, 21 December 2006 (UTC)

This template is very nicely put together, kudos to the editors. It is non-obtrusive in any way to the articals, and doesn't force people to scroll through links and links, looking for what they are looking for; This is much better than having to look in a page of links for what you are looking for. Just one click on the side for a list of pages with your topic. It is very nice, useful, and complete; it is good to have that much information organized that way. - 'Lord Nikon' --00:37, 22 December 2006 (UTC)

Just like the roman d vs. italic d discussion above, I will insist that footers are another cultural thing. I vaguely remember discovering "cheat sheets" for the first time in high-school, and they seemed to be brilliant way of organizing knowledge. Years later, entering grad school we had to pass "comprehensives", and we were allowed one page of notes. The top-of-the-class, all-grade-A honors student, a girl, came in with the most tightly packed, carefully designed cheat-sheet I'd ever seen, and ace'd the thing, of course (I myself couldn't remember the formula for coriolis forces). There is a debate going on now at WP:physics about a cheat-sheet arrangement of (nasty ugly) collection of thermodynamics formulas; in defense of this ugliness is the argument that the CRC does it this way too. So while I know that the overwhelming majority of mathematicians here absolutely deplore and despise these footers and nav-bars (as I do), I think that, perhaps, in a certain class of articles, these footers are an aid to understanding, and should be allowed instead of being busted down. Live & let live. linas 03:44, 22 December 2006 (UTC)

Nevertheless the purpose of these footers is different from crib sheets. I support the suggestion of keeping such navigation aids focussed on the most relevant topics. The people who need such navigation aids most are not served by an indiscriminate collection of links to vaguely related articles; before you know it they need a metanavigation aid to navigate the footer. That is simply a matter of being bold: if a link offend thee, pluck it out, and cast it from the template. What would bother me is if such a template gets plastered over all articles involving some calculus, but that isn't the case yet and will hopefully remain so. --Lambiam ^Talk 09:52, 22 December 2006 (UTC)

Featured article Regular polytope up for review

Hi. I have nominated the FA Regular polytope to be review to see if it still complies with the featured article criterias. You are welcome to comment at Wikipedia:Featured article review/Regular polytope.

Fred -Chess 22:57, 21 December 2006 (UTC)

Regular polytope has been nominated for a featured article review. Articles are typically reviewed for two weeks. Please leave your comments and help us to return the article to featured quality. If concerns are not addressed during the review period, articles are moved onto the Featured Article Removal Candidates list for a further period, where editors may declare "Keep" or "Remove" the article from featured status. The instructions for the review process are here. Reviewers' concerns are here. Sandy (Talk) 23:27, 21 December 2006 (UTC)

User:WAREL again?

this change at Perfect number by Chikushi (talk · contribs) looks a lot like User:WAREL. It's his first edit, and the formula is byte-for-byte identical to this edit by MIYAJ (talk · contribs), blocked as a sock puppet of User:WAREL. Did I do right in reverting it? — Arthur Rubin | (talk) 20:41, 13 December 2006 (UTC)

Definately. Well spotted! :-) Tompw (talk) 01:01, 15 December 2006 (UTC)

There have also been a sequence of WAREL-like edits to perfect number recently by Sugakusha (talk · contribs), Kotobakarihakirai (talk · contribs), Goodboy Johnny (talk · contribs), and InterCommunication (talk · contribs). Each of those names is a new account that only has edits to perfect number. The first one has been blocked and marked as a suspected sock but the other three have not yet. Given this repeated abuse, and evasion of repeated blocks, would protection for perfect number be in order? —David Eppstein 18:22, 23 December 2006 (UTC)

All blocked. Perhaps semi-protection is in order? -- Jitse Niesen (talk) 20:20, 23 December 2006 (UTC)

I agree that semi-protection makes more sense than full protection. —David Eppstein 20:57, 23 December 2006 (UTC)

Done. -- Jitse Niesen (talk) 15:20, 24 December 2006 (UTC)

Dispersive PDE Wiki

bumped into the above article, apparently on AfD for non-notable, and thought maybe it should be brought to attention here. if that Terrence Tao is indeed a (sufficiently regular) contributor, as claimed, seems to me it is very possible that the website is well-known or becoming so, among specialists. if that's the case, non-notability certainly gets disqualified as a reason for AfD, in my opinion. Mct mht 05:37, 17 December 2006 (UTC)

hm I just browsed a few articles there, looks like Terrence Tao is indeed a substantial contributor. some pages are written entirely by him. credibility is certainly not in question here. seems to me that whether that article is notable or nor should be decided by specialists from the PDE community. the first few votes seem to indicate that's not the case. Mct mht 05:45, 17 December 2006 (UTC)

more follow up, i don't mean to be harsh but the AfD is carelessly brought about. first a bot tags as an article related to Wikipedia:WikiProject Physics, which it is not really. then the bot's owner proposes AfD. the AfD debate is not categorized as mathematics but as (Web or internet), circumventing proper attention. Mct mht 05:57, 17 December 2006 (UTC)

~~I'll go add it to Wikipedia:WikiProject Mathematics/Current activity~~, although in fact the AfD listing is as much notice as most AfDs get. Septentrionalis PMAnderson 20:43, 17 December 2006 (UTC)

The bot got it; not a problem. Septentrionalis PMAnderson 20:48, 17 December 2006 (UTC)

The result of the AfD was keep (no consensus).

For follow on, those who visited the wiki seemed impressed with the quality and extent of its content, so I have a thought. I don't work on PDEs; perhaps someone who does would like to entice participation in an exchange program, like that with PlanetMath. This could both improve our PDE content, and help allay the concerns of those who felt the wiki was insufficiently notable to deserve an article. --KSmrq^T 07:13, 26 December 2006 (UTC)

GurchBot 2 messed up our archives! But I have repaired them.

GurchBot 2 (talk · contribs) moved all archives with non-standard names to standarized names. E.g. changing "Archive12" to "Archive 12" and leaving a redirect behind. By so doing, GurchBot 2 has messed up the archives at Wikipedia talk:WikiProject Mathematics and Wikipedia talk:WikiProject Physics and probably many others which use Werdnabot to archive their talk pages. It did not change the Werdnabot invocations to show the new file name for the current archive so Werdnabot added the archived material to the redirects which were left behind. Also, a minor point, GurchBot 2 did not change the archive lists to point at the new file names so they are now all going thru the redirects. This is a real mess. JRSpriggs 03:58, 26 December 2006 (UTC)

I have repaired this problem for the Mathematics Project and intend to do so for the Physics Project, but the others will have to fend for themselves. I adjusted our Werdnbot invocation and list of archive file names to reflect the new names given to the files by GurchBot 2. JRSpriggs 04:28, 26 December 2006 (UTC)

Apologies to everyone in this WikiProject for messing up your archives. I intended to change the archive lists and werndabot instructions soon after running the bot, but Christmas got in the way. If anyone notices any other pages that are wrong, feel free to fix them; I will try to find time later today to fix things and everything should be OK within 24 hours – Gurch 12:59, 26 December 2006 (UTC)

Writing about math

I am working on a guideline, Wikipedia:Writing about math. Can you people please look at it? --Ineffable3000 23:33, 25 December 2006 (UTC)

I changed a bunch of "it's"s to "its"s. It's pretty ironic to have grammatical errors in an article about how to write math; you should check for more of this. Ryan Reich 23:52, 25 December 2006 (UTC)

Thanks. Math is not english though. --Ineffable3000 02:21, 26 December 2006 (UTC)

"Each mathematics article should have an esoteric explanation." Really? --Lambiam ^Talk 00:53, 26 December 2006 (UTC)

You wouldn't want to write an article about continuity just saying "continuity is when you can draw a line without lifting the pencil". You would want to talk about "open ball in Domain --> open ball in range", etc.. In my opinion, a simple explanation is necessary too for the noobs. --Ineffable3000 02:21, 26 December 2006 (UTC)

"Each article about a proven theorem or lemma should contain a proof." Also for the Four-colour Theorem and the Poincaré conjecture? --Lambiam ^Talk 01:11, 26 December 2006 (UTC)

I said proven theorem. There is no analytical proof for the Four-colour theorem. The Poincare conjecture is a conjecture not a theorem. --Ineffable3000 02:21, 26 December 2006 (UTC)

No, they are both proven. Lambiam's point is that the proofs of these are generally considered fairly complicated and would take a lot of space. This is not an uncommon aspect of proofs of major theorems. --C S (Talk) 01:49, 27 December 2006 (UTC)

I don't see what the problem is! It's easy enough to include a proof by intimidation for each of your examples. --C S (Talk) 01:35, 26 December 2006 (UTC)

That would work. Proof by algorithm / computer-proofs are proofs also and should be included. A link to a script (if available) would be good. --Ineffable3000 02:21, 26 December 2006 (UTC)

I think you missed my joke entirely. --C S (Talk) 01:49, 27 December 2006 (UTC)

Comments should be added at Wikipedia_talk:Writing_about_math. I have my own doubts about all this, which I added there. --C S (Talk) 01:39, 26 December 2006 (UTC)

Are you aware that we already have written guidelines? (See WP:MSM.) Also, I have posted some tips here in the last few months. I suggest instead of writing your own guide, you study existing ones. --KSmrq^T 01:42, 26 December 2006 (UTC)

I did read over WP:MSM and I am proposing that we merge some of my ideas into there as a result of this discussion. --Ineffable3000 02:21, 26 December 2006 (UTC)

Lobachevsky Article

I think that the Nikolai Ivanovich Lobachevsky article should be switched from the scope of wikiproject Russian history to wikiproject mathematics since his importance is in the history of mathematics not the history of Russia. NikolaiLobachevsky 06:35:01 12/26/2006 (UTC)

It can be in both; I'm adding it to WP Mathematics. grendel|khan 16:20, 26 December 2006 (UTC)

Where do graph theory articles go?

There are a number of graph theory articles that I was going to put a {{maths rating}} template on, but I couldn't find the right category. Does it go under topology? I couldn't find any graph theory articles already tagged. grendel|khan 16:11, 26 December 2006 (UTC)

Category:Graph theory or its subcategories. —David Eppstein 16:33, 26 December 2006 (UTC)

No, no, I mean the field parameter of {{maths rating}}; which field are graph theory articles in? grendel|khan 22:36, 26 December 2006 (UTC)

Oh, that. "discrete". Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Discrete mathematics. —David Eppstein 23:07, 26 December 2006 (UTC)

Thanks! grendel|khan 07:27, 27 December 2006 (UTC)

Writing about math (2)

This post recently appeared on the "Portal:Mathematics" talk page. I've taken the liberty of copying it over to this page, where it will probably get more attention. DavidCBryant 17:08, 26 December 2006 (UTC)

I am working on a guideline, Wikipedia:Writing about math. Can you people please look at it? --Ineffable3000 23:35, 25 December 2006 (UTC)

It is also on this page, 4 sections up. --Lambiam ^Talk 18:55, 26 December 2006 (UTC)

Congratulations to Paul August

Paul August, with enthusiastic support, has found a seat on the Wikipedia Arbitrary Committee. (Did I spell that right? ;-D) He joins Charles Matthews, another mathematician. (Why these two fine editors would prefer to settle squabbles rather than write mathematics articles, I cannot imagine.) I congratulate Paul on his success, and look forward to many excellent, even-handed decisions. --KSmrq^T 22:20, 26 December 2006 (UTC)

I did ask Paul why he was standing ... congratulations to him on his fine showing. Charles Matthews 11:19, 27 December 2006 (UTC)

I tried to call, but all I got was this recorded message telling me to rotate my phone by 90 degrees. ;0) Anyway, congratulations Paul! capitalist 06:26, 28 December 2006 (UTC)

Articles with the greek letter mu in their titles

Duja (talk · contribs) has just moved "Mu-operator" to "μ-operator". This is the third (or is it the fourth?) time someone has done this; on the earlier occasions the move was reversed. My understanding was that we had an agreement to keep the Latinized spelling of the Greek letters in the titles of mathematics articles. Please someone (an administrator) reverse this. JRSpriggs 10:55, 29 December 2006 (UTC)

Actually, I even suspect he wrote “µ operator” (with a MICRO SIGN), not “μ operator” (with a GREEK SMALL LETTER MU), and that Wikipedia normalizes Unicode strings in KC form. If this conjecture is true, this would make the letter μ particularly vulnerable to this sort of zealousness, because the symbol µ is generally simple to type and most people aren't aware of the difference (especially if KC normalization will, indeed, render them identical!). --Gro-Tsen 16:51, 29 December 2006 (UTC)

Wikipedia Day Awards

Hello, all. It was initially my hope to try to have this done as part of Esperanza's proposal for an appreciation week to end on Wikipedia Day, January 15. However, several people have once again proposed the entirety of Esperanza for deletion, so that might not work. It was the intention of the Appreciation Week proposal to set aside a given time when the various individuals who have made significant, valuable contributions to the encyclopedia would be recognized and honored. I believe that, with some effort, this could still be done. My proposal is to, with luck, try to organize the various WikiProjects and other entities of wikipedia to take part in a larger celebrartion of its contributors to take place in January, probably beginning January 15, 2007. I have created yet another new subpage for myself (a weakness of mine, I'm afraid) at User talk:Badbilltucker/Appreciation Week where I would greatly appreciate any indications from the members of this project as to whether and how they might be willing and/or able to assist in recognizing the contributions of our editors. Thank you for your attention. Badbilltucker 18:18, 30 December 2006 (UTC)

Categories: Wikipedia talk archives