Wikipedia talk:WikiProject Mathematics/Archive/2009/Jun

References to Non-Newtonian calculus
References to Non-Newtonian calculus are being added to to the 'See also' section of various articles related to the exponential function. They don't seem relevant enough to warrant inclusion, but what should I put into a comment when removing them - is there a guideline please? Or do you think they are reasonable? Dmcq (talk) 16:01, 30 May 2009 (UTC)
 * The guideline is WP:SEEALSO, although it leaves it mostly up to the judgment of the editor. "See also" is slightly deprecated, in the sense that it is better to weave the items into the narrative. My opinion is that this subject is irrelevant to the exponential function, so I would be bold and delete the links with the comment "remove irrelevant wikilink". --Uncia (talk) 16:36, 30 May 2009 (UTC)
 * Non-Newtonian calculus is the pet project of User:Smithpith. He's identified himself as Michael Grossman, one of the inventors of non-Newtonian calculus, and consequently he has a WP:COI every time he writes about it. In my opinion, the "theory" is a non-notable piece of quackery, but unfortunately the article survived AfD. I would love to see it go away, though. Ozob (talk) 15:32, 1 June 2009 (UTC)

Looking for help with mathematical coincidence
There is current and threatened editorial action on the article mentioned. The article is primarily a list, and I would like to improve its nature. I would also categorize it as a part of mathematics education, if such is possible. I have one citation to "attempted" work by a CalTech Ph.D. at zhurnaly.com/cgi-bin/wiki/CoincidentalTaxonomy that I would like to use or suggest as being used in the article. I also think the article might be re-directed to a larger article on mathematical curiosities. I have my own original results that I deem not to be research that I also would like to place in the introduction or body of the article as well. This is the subject matter you can find at User:Julzes/365.25. The results were found by happenstance, this being my explanation for not regarding them as research, and I have no interest in staking a claim to them.Julzes (talk) 04:40, 31 May 2009 (UTC)


 * Somebody's (or several somebodies) have been having a lot of OR fun. I wouldn't be displeased if it was just deleted.  --C S (talk) 06:05, 31 May 2009 (UTC)


 * Well, I can understand that point of view from someone interested in 4-dimensional topology, but you have to acknowledge that users of lower levels might benefit if such an article were really well-written rather than in its current pathetic state.Julzes (talk) 06:44, 31 May 2009 (UTC)


 * I have no idea what you are going on about. The article is in violation of Wikipedia policies, which is why you've been getting different people commenting likewise on the talk page.  You haven't been around for too long, so you should consider that you aren't really understanding what's viable content or not.  In particular, I recommend thoroughly reading and digesting WP:OR.  And I mean, really trying to understand it, not trying to parse it in a way that justifies your article -- that's a mistake a lot of newcomers make, and not surprisingly, they always parse the policies in a way that justifies their articles that a lot of experienced Wikipedians who have long familiarity with policies don't agree with.  --C S (talk) 06:54, 31 May 2009 (UTC)
 * I've been down this road, and I'm trying to get the exception on routine calculations clarified. You're no help, and it's not "my" article.Julzes (talk) 07:06, 31 May 2009 (UTC)


 * Thanks for pointing out the article. I'll have a quick search with google books if any of the 'fact' ones strike me as interesting but otherwise Wikipedia can't be used as a repository for odd bit of numerology people dream up, it has got to satisfy notability. If nobody can find citations then they should be removed. Dmcq (talk) 07:48, 31 May 2009 (UTC)
 * Don't rush it, though, if that's your attitude. BKell set a two-week deadline a few days ago.Julzes (talk) 10:45, 31 May 2009 (UTC)
 * By the way, in the current article the fact that the square root of 2 plus the square root of 3 is a fair approximation to pi has been arbitrarily removed ahead of schedule (along with one that is more precise but also more complex), and the article does not even contain the coincidence involving simply e and its base-ten representation or that of the common logarithm of 2.  All these things should be in a wikipedia article somewhere, and if not this article then where?  Finding sources for notability's sake should not be top priority.  Fixing things like this should.Julzes (talk) 10:53, 31 May 2009 (UTC)


 * Not all things should be in Wikipedia. It is not an attempt at forming The Library of Babel. Notability is a basic requirement. There's places and in Wikipedia to discuss changing basic things like this but |I don't think you'll get far with this one. Dmcq (talk) 12:17, 31 May 2009 (UTC)
 * Some things are a kind of mathematical common knowledge. Consider if instead of the article in question saying that log102= 0.30103 it were corrected to show how close it is to this.Julzes (talk) 12:48, 31 May 2009 (UTC)

How about transferring this to our sister project Wiki Books? They are using the same software and probably have a lot more tolerance for this type of thing. Of course sometimes the worst things are turned into a fine article by some genius, but I have no idea how this should work in this case. --Hans Adler (talk) 15:21, 31 May 2009 (UTC)
 * Am new and only so far familiar with the encyclopedia.Julzes (talk) 20:31, 31 May 2009 (UTC)


 * I'm surprised h2g2 doesn't have an article on numerical coincidences what with the infinite improbability drive. Dmcq (talk) 13:27, 1 June 2009 (UTC)

Certain external links
user:MrOllie recently deleted these two links from Circumscribed circle, calling them "linkspam" in the edit summary: (In the course of doing this, he left fully intact the previous edit, which was vandalism.) The pages appear to be well written and relevant, unlike cases of linkspam I've seen where the page merely links injudiciously to other places on the web that superficially seem relevant to the topic, for the purpose of advertising. It looks as if they supported by advertising but not created for the purpose of that advertising, again unlike sites of the other sort I've seen. Some of MrOllie's recent edits leave the impression that he spends a lot of time removing linkspam, but may not be capable of judging the quality of the pages that he deletes the links to.
 * Triangle centers by Antonio Gutierrez from Geometry Step by Step from the Land of the Incas.
 * Circumcenter, Circumcircle, and Circumradius Theorems and Problems.

In some cases of this kind, the person deleting the links on these grounds asserts that the person who put the links there has a conflict of interests. In such cases, reinstatement of the links by someone with no such conflict is then found inoffensive, so that it is held there is no grounds for considering them "linkspam". MrOllie has recently deleted lots of links to various pages on geometry on that particular site. It appears that MrOllie may lack either the ability or the willingness to judge the difference between two sorts of sites:
 * Those that are supported by advertising and are competently and professionally done pages on topics unrelated to the thing being advertised, maintained for purposes other than advertising;
 * Those that are created for the purpose of advertising and include either material on some other topic of interest, crudely copied from other web pages, or links to other web pages superficially appearing to be on that other topic of interest, but without professional or competent judgment, or any judgment, as to what material is good and what is worthless crap.

If those whose primary concern is getting rid of linkspam, and any WikiProjects or the like concerned with that, lack the ability or willingness to make this sort of distinction, then people like the denizens of this present WikiProject need to intervene to help them. Michael Hardy (talk) 16:43, 31 May 2009 (UTC)
 * I see no problem with restoring these two external links in the article. An editor who had knowledge of the topic and did not personally have a COI would certainly be justified in putting the links back, under WP:BRD, provided he left a comment on the article Talk and ideally with a notification to the person who had removed them. If MrOllie is doing this all across the geometry articles then he shouldn't keep doing these removals without joining a discussion like the present one. EdJohnston (talk) 17:58, 31 May 2009 (UTC)


 * I removed many links to this site because they are links to an ad supported site and linked by the site owner, who operates a single purpose account for the purpose of adding these links. If anyone who is independent of the site would like to add them back, go ahead and please do so, since we would then be developing a consensus in favor of inclusion. I would request that they be considered case by case - please don't blanket add them all back. - MrOllie (talk) 20:43, 31 May 2009 (UTC)


 * May I ask any editor who restores a link (removed as spam) to please make sure to include an edit summary indicating that you have checked the linked site and believe it to be helpful for the article (and not redundant).
 * Re the issue raised above, I checked the edit claiming "linkspam" and would like to thank MrOllie for taking the time to remove the promotional links added by what is clearly a single purpose account. I wanted to put that on the record here, but may I suggest that further discussion on the general spam issues should take place at WT:Spam. Johnuniq (talk) 11:07, 1 June 2009 (UTC)


 * You also raised this issue at Wikipedia talk:WikiProject Spam (permanent link) ; I have responded to you there. -- A. B. (talk • contribs) 18:11, 1 June 2009 (UTC)

Trivial or relevant?
I would be interested in hearing people thoughts about this. Articles such as 6 (number) generally attract lots of trivia. etc. etc. etc. What are the relevant guidelines on what should be included in such an article? Are there any good or featured articles of this kind that can be used as a model? The most recent inclusion which at least is mathematical if a bit obscure. &mdash; Martin (MSGJ · talk) 09:20, 1 June 2009 (UTC)
 * Six is the name of a character on Blossom.
 * In football (soccer), the number of substitutes combined by both teams, that are allowed in the game.
 * The number of cans of soda or beer in a six-pack.
 * It is the only even perfect number that is not the sum of successive odd cubes.


 * WikiProject Numbers lists some criteria. PrimeHunter (talk) 10:09, 1 June 2009 (UTC)

An editor assistance request
Hello, WikiProject Mathematics! An editor has asked for help concerning a technical mathematical article here, and I wonder if someone who understands these things better than I could advise.— S Marshall  Talk / Cont  21:41, 3 June 2009 (UTC)


 * See also Articles for deletion/Lukaszyk-Karmowski metric. —David Eppstein (talk) 05:05, 4 June 2009 (UTC)

Help Guys!
Guys, i've been Reading this Project for many months, there are many Highly talented Folks here, i really want an answer for this, i Do believe Wikipedia is not a Forum but i really really want an answer for this, please guys don't Delete this here is the Problem:

solve for t-

60√t (sin(t/3))^2 = 150

only t is under root after 60

Please Help! 122.174.74.142 (talk) 17:01, 4 June 2009 (UTC)
 * You'd probably be better of posting this at Reference_desk/Mathematics, but keep in mind that the reference desk will not do your homework for you decltype (talk) 17:11, 4 June 2009 (UTC)

Diagrams of Sheffer operators
User:Lipedia (formerly User:Boolean hexadecimal) added some odd diagrams to two articles; I've removed them. Diffs: Logical NOR and Sheffer stroke. This is not the first set of odd images added by this user; File:Hasse_diagram_of_all_logical_connectives.jpg was a previous one that, in the end, was not used in any articles. Thoughts? &mdash; Carl (CBM · talk) 21:13, 1 June 2009 (UTC)


 * It turns out there was another set at Henry M. Sheffer. &mdash; Carl (CBM · talk) 21:20, 1 June 2009 (UTC)


 * I thought we'd been through all this in Talk:Logical connective not so long ago. What has changed between then and now? I notice the German version of the article also removed his diagram recently. Dmcq (talk) 22:12, 1 June 2009 (UTC)


 * Surely there must be a limit to what we need to take seriously and discuss before rejecting. The symbols used are original research, and even apart from this his graphics only make sense with long explanations. From a discussion on his user talk page at de: : "Ja, die Zeichen habe ich entworfen. Quellen außerhalb der Wikipedia bin ich erst dabei zu schaffen, was eine Aufgabe für die nächsten Jahre sein dürfte." I.e., it was he who designed the symbols; he is in the process of creating sources outside WP, which should be a task for the next few years.
 * A look at this user's contribution history shows that this is a single purpose account for pushing alternative conventions for numbers, logic and music. --Hans Adler (talk) 23:37, 1 June 2009 (UTC)


 * My thoughts are that if no reliable source is provided to indicate general usage, these diagrams should be removed without hesitation. Thanks for doing that. Johnuniq (talk) 02:25, 2 June 2009 (UTC)


 * Wow, File:Hasse diagram of all logical connectives.jpg is a 7016×9921-pixel, 5.13-MB JPEG. What an excellent candidate for an SVG (apart from its OR-ness). —Bkell (talk) 08:48, 2 June 2009 (UTC)


 * There seems to be more of it at commons:File:Hypercubeorder.svg. —Bkell (talk) 08:53, 2 June 2009 (UTC)

Quote: ''I thought we'd been through all this in Talk:Logical connective not so long ago. What has changed between then and now? I notice the German version of the article also removed his diagram recently. Dmcq'' Please make sure, you've got the topic, before you add your opinion. Here we speak about the following two diagrams, and about nothing else. (They have never been used in any german articles.)

The same about Hans Adler: The symbols used are original research, and even apart from this his graphics only make sense with long explanations. Which symbols?! (Probably you remember these, but they do not appear in the diagrams we speak about. I've once used them as a means of explanation in the Wikipedia, to visualise the relations between logical connectives, and this was a mistake, indeed.)

Concerning Bkell: Ah ... ordering logical connectives in a Hasse diagram by implication is original research - very interesting. (Maybe you take a look at this homepage.)

Concerning CBM: Nice to meet the user, who removed the set theoretic definition of logical connectives (Added by Gregbard) with the most funny statement: ''It's quite unclear to me what these sets are supposed to represent. It was tagged as possible OR for some time.'' I mention this sentence, because here it seems to be the same.

The diagrams:

Prefix notations like are usual, but nearly unreadable for human beings. At the moment in the NAND article there is a section called Simplification, where the operation is not written, because it's always the same operation, NOR in this case: That's easier, but still hard to read, because it's very difficult to see, which left and right brackets belong together. Combining them to circles is the easiest solution. And that's what you want to call original research? (To express operations by circles surrounding the arguments is nothing special, by the way: It's also done in existential graphs.)
 * NOR(A,B)
 * NOR(NOR(A,A),NOR(B,B))
 * NOR(NOR(NOR(A,A),NOR(B,B)),NOR(NOR(A,A),NOR(B,B)))
 * NOR(NOR(NOR(A,A),B),NOR(A,NOR(B,B)))
 * (A,B)
 * ((A,A),(B,B))
 * (((A,A),(B,B)),((A,A),(B,B)))
 * (((A,A),B),(A,(B,B)))

At the moment these two diagrams are the easiest way to show, how every logical connective can be expressed by only one Sheffer operator. Greetings, Lipedia (talk) 16:34, 3 June 2009 (UTC)


 * Sorry for not noticing that your latest work doesn't feature your symbols. It's still similar enough in most respects. OK, it may not be original research in a strict sense, but it's still idiosyncratic notation on many levels. This includes an odd choice of what to present in great detail, an odd choice of variables, the odd choice of circles, a horrible colour scheme, accessibility problems and the complete lack of printable explanation. Some of these problems are easily fixed, but I recommend that you don't bother.
 * Your attack on CBM shows how detached from reality you are. CBM is a professional mathematical logician with wide-ranging interests throughout logic and an enormous amount of patience. He didn't understand your set notation, and neither do I (a model theorist), although I have a vague idea what it is supposed to be and don't doubt that I could in principle figure it out if I were willing to spend a few minutes on this nonsense.
 * Laying out the 16 binary logical connectives in a Hasse diagram is of course not original research. If we don't have a picture like the first one in your reference, then we probably should. The most important difference to your diagrams is that you stress your idiosyncratic stuff and hide the most important information in a link map. It's the difference between a straightforward illustration and a riddle like the Pioneer plaque. --Hans Adler (talk) 20:31, 3 June 2009 (UTC)


 * I do agree that, if a Lindenbaum algebra of the propositional language generated by two variables is included, it should be clearly labeled as such, rather than as a powerset algebra. But I don't see a good reason to include it.


 * Ultimately, I'm not convinced by unpublished the "Geometry of logic" reference. Certainly Lindenbaum algebras in general are well known, but Lindenbaum algebras are not really very often discussed in context with logical connectives. The relationship appears quite tenuous and unsupported by published work.


 * The final part of the reference, e.g. the part about Steve Vickers, is related to topological methods, not to automorphisms of the 16 element Boolean algebra.


 * The thing that seems to be emphasized in the diagrams is that both the powerset algebra of a four-element set, and the Lindenbaum algebra of a propositional language with two variables, are 16 element Boolean algebras. But this seems to be the sort of trivia that is not really of interest. I mean, we could also associate logical connectives with isomorphism classes of subgroups of Z210 in the same way, but this would not motivate the "group theory of logical connectives"...


 * In fact, the reference admits the lack of a clear link, saying
 * "If, however, the 16 digital labels are interpreted as naming the 16 functions from a 4-set to a 2-set (of two truth values, of two colors, of two finite-field elements, and so forth), it is not obvious that the notion of partial order is relevant. For such a set of 16 functions, the relevant group of automorphisms may be the affine group of A mentioned above.  One might argue that each Venn diagram in Figure 3 constitutes such a function-- specifically, a mapping of four nonoverlapping regions within a rectangle to a set of two colors-- and that the diagrams, considered simply as a set of two-color mappings, have an automorphism group of order larger than 24... in fact, of order 322,560.  Whether such a group can be regarded as forming part of a "geometry of logic" is open to debate."


 * In these cases, I am willing to go along with published sources when they do indeed cover things that might appear trivial. But I haven't seen evidence of that here. &mdash; Carl (CBM · talk) 23:43, 3 June 2009 (UTC)

Just a short note: It's no problem including the connectives names in the diagrams. It's what I first did, but it became too crowded for my taste. The hint, that printable information is desirable is true indeed. Concerning the color scheme: I may choose darker colors, to make the appearance less gaudy. It's just important, that A and B have different colors. I will upload modified versions at the weekend. Greetings, Lipedia (talk) 07:33, 4 June 2009 (UTC)


 * You seem to have ignored my request for any published source that thinks these diagrams are interesting. &mdash; Carl (CBM · talk) 12:10, 4 June 2009 (UTC)

No, I didn't ignore it, but I doubt that it is justified. Content must be verifiable, otherwise it's original research - and the content is undoubted in this case, and verifiable by any source you want. But like every encyclopedia, we should display this verified information in the way, that serves our readers best. An article is good, when the content is verifiable, and as many readers as possible (also non experts) can understand it as easy as possible. So your request aims in the wrong direction: The question is not "Does it appear somewhere in exactly this way?" but ''"Does it help anyone to understand Sheffer operators?".

This is disputable of couse. I think it does:

The article tells, that all sixteen logical connectives can be expressed in terms of NOR and NAND respectively, so I think we should show that - and not only mention some examples, presuming that the reader can easily deduct all others. This could be done in a sixteen row table of couse, but the most helpful way to display logical connectives is not the table (because the neighbour rows have nothing to do with each other) but the Hasse diagram showing all implications. The formulas should be shown in a clear and easy way, so somewhat easier to read than (((A,A),(B,B)),((A,A),(B,B))), the notation used in the Simplification section in the present NAND article. Combining the parentheses to circles for better readability is really not a "idiosyncratic notation" (the Simplification section presumed) but a very simple step. The hint, that "the most important information" should be shown in the diagram itself was justified, so I changed it (and the color scheme as well).

This is how it could show at the end of the articles (= at the end of the Simplification section, which could be included also in the NOR article): Greetings, Lipedia (talk) 12:26, 11 June 2009 (UTC)


 * I think the problem with such diagrams is that it is neither common knowledge nor easy to work out exactly how to read it. As a result, to justify including it into an article for the purpose of helping someone's understanding, it would need to accompanied by an explanation of the notation or a link to an explanation. If, however, such notation is not standard, then it is original research, and hence has no place in Wikipedia. Truth tables, however cumbersome you think they are, are an accepted method of presentation in most mathematical and logic books, and have been for decades.
 * Your comments that such truth tables are not the notation we should be using to represent them may be right; such discussion should be limited to academic books and journals, not on Wikipedia, which is a tertiary source. --Joth (talk) 12:53, 11 June 2009 (UTC)

"it would need to accompanied by an explanation of the notation or a link to an explanation" Please note, that I proposed to include them in the Simplification section in the present NAND article (and its equivalent in the NOR article not yet created). Did you read it? In this section simplified notations like (((A,A),B),(A,(B,B))) meaning NAND(NAND(NAND(A,A),B),NAND(A,NAND(B,B))) are used. In the context of this section the short explanation below the diagram will do. (I wouldn't be so crazy, to include these files in the logical connectives article, and think it could help some reader there. Hope you didn't think that.)

"Truth tables, however cumbersome you think they are" "Your comments that such truth tables are not the notation we should be using" These lines tells me, that you missunderstood something I wrote, or something the others wrote about me. I did not even mention truth tables nor would I say anything against them (I actually love truth tables!). Here we speak about the linking of many equal operations in NOR logic and NAND logic, and what I don't like are unreadable formulas like NOR(NOR(NOR(A,A),B),NOR(A,NOR(B,B))) or even the simplification (((A,A),B),(A,(B,B))). I think these simplified formulas are better readable, when the outer parentheses are bigger and the inner parentheses are smaller.

(In this case the left and right parentheses touch in the middle, and become a circle. If anyone conciders my diagrams to be original research because of this, I can easily make a short break in the middle, so that every circle becomes a pair of semicircles, easily recognizable as a pair of parentheses - than it would be exactly the same like (((A,A),(B,B)),((A,A),(B,B))) and so on.) Greetings, Lipedia (talk) 15:41, 11 June 2009 (UTC)


 * I don't think I have any particular objection to something simple like the first or second diagram in [] being added. I don't think it adds anything but it's not large and can be understood easily and filed away in the mind as a pretty picture. The funny diagrams are just not suitable though, they are large and peculiar and cluttered covering up any sense one might extract and they keep being put in as an alternative to the straightforward text. The straightforward text is what can be maintained easily and moving vital bits of the text to funny diagrams with non-standard tooltips and ways of showing things is just silly. Dmcq (talk) 23:10, 13 June 2009 (UTC)

If something is correct, it doesn't need to be "maintained". Possibly your focus is more on the editor than the reader - in my eyes a fundamental mistake, but it appears to me, that this is quite usual in the Wikipedia. The blame against the first version was to be "a riddle like the Pioneer plaque" because I "hide the most important information in a link map". So I've got this information included, and now the blame is, that the diagrams are "cluttered". Isn't that a bit strange? Looks as if the rejection is more imporant than the reason. I think it's sad, that all this debate is primarily harping on about principles, may they be real or imagined, and the question "Does it help someone?" does not play any role. Is "they keep being put in as an alternative to the straightforward text" really a senseful blame? For me it's too far away from "Does it help someone?" and thus secondary, borderline unimportant. For me an article is good if and only if it helps as many and as different people as possible. Greetings, Lipedia (talk) 15:56, 14 June 2009 (UTC)


 * Well, there's no way we can let the deciding criterion be "does it help someone". A lot of things might help someone.  But throw them all in there and you've got an unreadable mess.
 * The images are, in their way, lovely. But they're too gaudy; they try to pack &mdash; not exactly too much information, because there's not really much there &mdash; but information in too many different ways, into a small space.  In doing so they're more likely to confuse than inform.
 * Most importantly, they are not standard ways of presenting the information. They are idiosyncratic.  This is not a bad thing in general, but it's a bad thing for an encyclopedia. --Trovatore (talk) 19:57, 14 June 2009 (UTC)

Of course I didn't mean someone when I said "someone", but rater a quantity of people worth mentioning. But sadly we have no means to check, what exactly is helpful to how many people. Concerning idiosyncracy I can only repeat what I said before: I can easily make a short break in the middle, so that every circle becomes a pair of semicircles, easily recognizable as a pair of parentheses - than it would be exactly the same like (((A,A),(B,B)),((A,A),(B,B))) and so on. But I'm not going to do that. We can agree that the diagrams don't match in Logical NOR, Sheffer stroke and Henry M. Sheffer and end the discussion. Lipedia (talk) 09:39, 16 June 2009 (UTC)

Hereditary set
Another funny diagram has been added to Hereditary set. At least it's smaller but I think it detracts from what little content there is in the article. A straightforward listing of a few sets would be better and could include some infinite ones. I think the article needs a bit of expansion. For instance a set containing itself and all subsets wouldn't have an ordinal number as far as I can work out. Dmcq (talk) 11:17, 14 June 2009 (UTC)


 * The set P^4({}) = P( P( P(P({})))) respectively it's infinite completition (the union of sets P^n({}) for all n) should be mentioned somewhere in the context of pure sets - but possibly this diagram could match better in Pure countable set.
 * The elements of P^n({}) do not only follow each other (in the way natural numbers do), but they also include each other (in the way Boolean functions imply each other). I don't think the second information is unimportant. Greetings, Lipedia (talk) 14:58, 14 June 2009 (UTC)

Would this project be interested in some collaboration with Wiktionary?
Basically, a significant number of math terms are virtually impossible to define for the layman, usually because the relevant Wikipedia articles are simply unhelpful, even useless (cf. hypoelliptic- wikt: ) to people without knowledge of fairly advanced maths (and yes I fully acknowledge the difficulty of avoiding jargon in many math articles). Another problem often comes in that some terms may be ridiculously hard to give good quotations (i.e. from books or scientific publication), such as sphenic number- wikt:, even though they are clearly in use (in this case, the problem comes with the small amount of truly useful material in google books and google scholar).

Would WPMATH members be interested in answering the occasional requests for help in such cases? Circeus (talk) 02:44, 3 June 2009 (UTC)


 * Sure. Jakob.scholbach (talk) 06:11, 3 June 2009 (UTC)


 * Me too. I guess you could post the requests here&mdash;can anyone think of a better place? Ozob (talk) 15:19, 3 June 2009 (UTC)

Okay, so your first mission, if you accept it (sorry, couldn't help it :p), is to help define hypoelliptic in comprehensible term, and verify whether or not that definition directly relates to the current mathematics definition we have for elliptic. Personally, I'd appreciate some backgroung for dating the term. I find a fair amount of material that discusses or mentions Lars Hörmander's solution (?) ot the things (apparently at some point in the 50s or 60s), but none about when the term started being used (of course it might not have been formally used before Hörmander). A typical example is here. Circeus (talk) 17:32, 3 June 2009 (UTC)


 * The Mathematics Reference desk would also be happy to help. --Tango (talk) 17:52, 3 June 2009 (UTC)


 * I am not quite understanding what is required, but I try to say something. First, "elliptic" in (elementary) geometry is not the same (but related to) "elliptic" in PDE ("partial differential equations"). Second, "hypoelliptic" is a term of PDE (no counterpart in elementary geometry). Third, "hypoelliptic" admits some degeneration ("elliptic" does not), but not too much degeneration. Less technical it is impossible to explain, I am afraid. Boris Tsirelson (talk) 18:07, 3 June 2009 (UTC)
 * And, by the way, wiktionary for now interprets "elliptic" only geometrically (not PDE). Boris Tsirelson (talk) 18:09, 3 June 2009 (UTC)


 * And by the way the definition of an elliptic given at elliptic: "2. (mathematics) Of a function in which the sum of the squares of two variables is constant", is wrong! Paul August &#9742; 18:31, 3 June 2009 (UTC)
 * re:"elliptic" Okay, clearly, we need at least two definitions for elliptic in maths, the current one should be marked as (geometry) and is obviously linked to the general equation cited in ellipse: "Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters. Moreover, any canonical ellipse can be obtained by scaling the unit circle of $$\reals^2$$, defined by the equation $$X^2+Y^2=1$$". There are various other aspects of maths involving the adjective (e.g. elliptic function), and likely the Wiktionary article needs improvement to account them.
 * re:hypoelliptic You have completely lost me already. It is clear to me the relevant sense of elliptic is the one involved in Elliptic operator, but that's as far as I got with it. Circeus (talk) 19:33, 3 June 2009 (UTC)
 * So, which help could I provide about "hypoelliptic"? You understand that it is relevant to elliptic operator, but weaker. Do you want to understand what does it really mean? To which extent? Do you need explanation about "degenerate"? Hypoelliptic operator is allowed to be degenerate at some points, and even at every point, but the direction of degeneracy must change from one point to another in such a way that some properties of elliptic operators still hold in a weakened form. If you want to be more specific here, then you really have to read the article in Wikipedia. Boris Tsirelson (talk) 20:41, 3 June 2009 (UTC)
 * Let me add that "hypoelliptic" is weaker than "elliptic" but stronger than semi-elliptic.Boris Tsirelson (talk) 20:47, 3 June 2009 (UTC)
 * Basically, the only thing I really think I understand (If I had actual understanding of calculus, I wouldn't need to ask!) is that a hypoellictic function (drawing from elliptic function) is a function in the complex plane. Would it be accurate to reverse the relation (in the same way sphenic must be dfined in relation to sphenic numbers, not the other way around) and define hypoelliptic as an adjective related to either hypoelliptic operator or hypoelliptic function? Circeus (talk) 21:08, 3 June 2009 (UTC)
 * Oops, I forgot about elliptic function! No, this is not related at all. This is a third meaning of "elliptic". No, there is no "hypoelliptic function" (as far as I know); only a differential operator or a differential equation may be hypoelliptic. Boris Tsirelson (talk) 04:56, 4 June 2009 (UTC)
 * Wow, there is also Elliptic curve, Elliptic complex etc. Boris Tsirelson (talk) 05:39, 4 June 2009 (UTC)

So, to get back to the question of a dictionary definition of hypoelliptic: Right? —David Eppstein (talk) 06:17, 4 June 2009 (UTC)
 * 1) "Hypoelliptic" is a combination of hypo- (less than or weaker than) and elliptic, and is used to mean something that is like an elliptic thing, but weaker; the only usage of this we've found so far is in hypoelliptic operator.
 * 2) A "hypoelliptic operator" is a differential operator that preserves smoothness. As the name implies, this condition is weaker than the conditions defining an elliptic operator.
 * Right, with three reservations. First, there is also "hypoelliptic differential equation" (just a differential equation whose differential operator is hypoelliptic). Second, "preserves smoothness" is not very clear; but maybe this is the best one can expect from a dictionary. (Rather, the inverse operator preserves smoothness). Third, one could also mention "semi-elliptic". Boris Tsirelson (talk) 07:24, 4 June 2009 (UTC)
 * One extra question, not necessary, just out of my own curiosity: is it accurate that an elliptic operator will be hypoelliptic, but not the reverse (i.e. elliptics are a class of hypoelliptics), or is it that elliptic operators may be hypoelliptic (they merely intersect)? Circeus (talk) 15:41, 4 June 2009 (UTC)
 * Yes, every elliptic operator is hypoelliptic, but not the reverse. Boris Tsirelson (talk) 18:16, 4 June 2009 (UTC)
 * And it is in fact written, see Elliptic operator: "thus, every elliptic operator is hypoelliptic". Though, misunderstandings are possible because of different levels of generality: usually one has in mind second-order differential operators, but sometimes higher order differential operators are also treated, and sometimes only second-order differential operators with constant coefficients are treated. Boris Tsirelson (talk) 18:26, 4 June 2009 (UTC)
 * To be accurate: every elliptic operator with infinitely differentiable coefficients is hypoelliptic. In particular, every elliptic operator with constant coefficients is hypoelliptic. Boris Tsirelson (talk) 19:31, 4 June 2009 (UTC)

Judging by this discussion, some preliminaries on dismbiguation by email might help. You can run things past me offline to get a general sense. Charles Matthews (talk) 10:55, 14 June 2009 (UTC)

Did you know
...that a mitimorphism is a morphism from the power set of a fibre bundle into another fibre bundle?

I was hoping someone here could clarify whether this newly created article is a hoax, a neologism, or just very obscure. Thanks, decltype (talk) 08:08, 4 June 2009 (UTC)


 * Hmm. 0 Google, Google Scholar and Google Books hits. Interesting editing history of article creator. --Hans Adler (talk) 11:59, 4 June 2009 (UTC)


 * I am under the impression that DYK requires at least one reference for the sentence they put on the main page. &mdash; Carl (CBM · talk) 12:06, 4 June 2009 (UTC)
 * I think DYK was just a humorous way of phrasing the question whether this is a hoax. The article would also fail for insufficient length. It looks to me like a definition made up by a mathematics student who is also a good dictionary game player. But then I have seen a serious definition of a "morphism" from one type of object to another once; not that I would approve of that kind of thing. --Hans Adler (talk) 12:22, 4 June 2009 (UTC)
 * Yes, it was indeed an attempt at humour. Article is now proposed for deletion. Thanks for your input. decltype (talk) 15:57, 4 June 2009 (UTC)
 * An anonymous user from the University of Waterloo,, removed the prod template, saying: "seen it; not sure about the etymology part". Ozob (talk) 19:52, 11 June 2009 (UTC)
 * Since Prod was rebuffed, I've put it forth for a real AfD at Articles for deletion/Mitimorphism. &mdash; Charles Stewart (talk) 20:22, 11 June 2009 (UTC)

Visualization for integration by parts
Could someone look at the geometric argument for the integration by parts? I am thinking to add a section to the article about that and have a couple questions. I used xfig to create the picture, is there a better tool to create pictures like that? I could not find this particular trick in the literature, does it constitute OR if I add this argument to the article? (Igny (talk) 02:20, 5 June 2009 (UTC))


 * It's not OR. Leibniz used this exact argument, but I'm sure there have been countless references to this picture since then.  --C S (talk) 02:39, 5 June 2009 (UTC)


 * I've seen this explanation of integration by parts in several books. The only source I can lay my hands on at the moment is Nelson's Proofs Without Words, see page 42. --Uncia (talk) 03:14, 5 June 2009 (UTC)


 * Nice book, thanks for the reference. (Igny (talk) 17:25, 5 June 2009 (UTC))


 * I think for art like this it would be preferable to use .svg (a vector format) for the graphics instead of .jpg (a bitmap format), if possible. I use Adobe Illustrator for that but it's kind of expensive; the most popular free alternative seems to be Inkscape. —David Eppstein (talk) 02:25, 5 June 2009 (UTC)
 * I will work on creating an SVG pic of good quality. (Igny (talk) 17:25, 5 June 2009 (UTC))

Category:Linear operators?
Category:Linear operators seems a rather strange category. It says that it is for linear operators defined on functions, but this seems rather overly restrictive. What should be done with it? Sławomir Biały (talk) 15:18, 7 June 2009 (UTC)


 * I have posted a more detailed discussion at Category talk:Linear operators. Please direct your input there. Sławomir Biały (talk) 15:46, 8 June 2009 (UTC)

Statistics portal at Featured portal candidates
Portal:Statistics is being considered for featured quality status, at the Featured portal candidates process. Comments would be appreciated at Wikipedia:Featured portal candidates/Portal:Statistics. &mdash; G716  &lt;T·C&gt; 01:26, 9 June 2009 (UTC)

Editor trying to remove talk page requirement from technical tag
See Template_talk:Technical_(expert). User: Debresser has repeatedly tried to remove the talk page requirement, contrary to the explicit instructions in the technical guideline. I pointed out to him that since this tag is scarcely used, Coren's mistaken reformatting of the tag (which changed the template to an ambox, which is for articles) was not reverted, unlike the situation for the regular technical tag, which was reverted. Debresser insists that since Coren's reformatting of the tag as an ambox was unreverted, I must be completely mistaken about the consensus regarding the placement of the technical tag on talk pages. He has not explained why there is this distinction (one technical tag on the article, the other on talk pages) and has refused to read the guideline or its talk page to understand the consensus. Indeed, according to him, since this mistake was unreverted for 2 years or so, his position is the consensus! --C S (talk) 14:32, 11 June 2009 (UTC)


 * This seems to have been resolved amicably through better communication almost immediately after this post, but I guess help with moving the misplaced templates from articles to talk pages would be appreciated. --Hans Adler (talk) 15:37, 11 June 2009 (UTC)


 * No, absolutely not! Certainly all the misplaced templates are due to people who inappropriately tagged the articles and so they shouldn't be moved, rather they should be deleted to save editors wasted time.


 * Also, Debresser has rather foolishly taken the "informal RFC" initiated on the talk page of template:technical (which was never closed!) as a sign of consensus against placing the template on talk pages ("Please notice that the discussion on Template_talk:Technical points to article namespace with 6 against 4").  So he has initiated his own proposal to reverse this.  See Wikipedia_talk:Make_technical_articles_accessible.  --C S (talk) 20:19, 11 June 2009 (UTC)


 * Oh! Sorry for the mistake. --Hans Adler (talk) 22:36, 11 June 2009 (UTC)

"List of arithmetic topics"?
Lo and behold: List of arithmetic topics is a red link. Should we do something about that? Michael Hardy (talk) 03:50, 13 June 2009 (UTC)


 * Notice that List of basic arithmetic topics is a redirect to Outline of arithmetic. JRSpriggs (talk) 08:44, 13 June 2009 (UTC)


 * ...which has a link to an alleged "main" article called List of arithmetic topics, which should be more detailed and extensive, including all Wikipedia articles that fit (just as with the other subjects). Michael Hardy (talk) 20:08, 13 June 2009 (UTC)

License update and PlanetMath
Under the terms of the licensing update being adopted across all Wikimedia sites, WMF projects will no longer be able to add GFDL-only text published elsewhere. Any GFDL text added to Wikipedia after Nov. 1, 2008 will have to be removed as a copyvio. PlanetMath uses the GFDL and hence this could shut down a potentially valuable source of content interaction. In order to avoid that, PlanetMath would need to also relicense to CC-BY-SA as explicitly allowed under GFDL 1.3.

If you have contacts at PlanetMath, or participate there yourself, I would encourage you to discuss this issue with them. See also: Licensing update/Outreach. Dragons flight (talk) 01:14, 14 June 2009 (UTC)

Abbreviations in algebra-related articles
I have a somewhat minor complaint with regards to some of the algebra-related articles. In particular, I find that too many technical terms are abbreviated. For example, although it is reasonable to abbreviate terms like "unique factorization domain" to UFD, or "principal ideal domain" to PID, abbreviations such as BFD, BD, HFD, AD etc... are ambiguous to some extent (try to guess what some of them refer to; I find that this is not at all trivial, even for algebraists). As an encyclopedia, we should aim to be as clear as possible, and abbreviations should only be done if absolutely necessary. Even in this case, the word which is abbreviated should be made clear, along with its abbreviation. I tend to find abbreviations such as ACCP to mean "ascending chain condition on principal ideals" somewhat pointless because along with abbreviations like UFD or PID, it is somewhat difficult to interpret (one may guess ACCP to be some sort of "domain" if he was not familiar with it). Furthermore, such abbreviations can lead to errors. For instance, one may write "UFD domain" instead of "UFD" thus being redundant to some extent. Therefore, although abbreviations of basic terms are OK, we should start defining/linking abbreviations when using them; especially if the term to which they correspond is somewhat unknown. -- PS T  04:44, 14 June 2009 (UTC)


 * I definitely agree. I haven't spotted any of these in algebra articles so far, but when I do, I'll get busy removing them. I think many of the mathematics articles need to have their jargon reduced and accessibility increased; removing pointless axioms is a great way to start this. --Joth (talk) 07:01, 14 June 2009 (UTC)
 * I just had a look at some articles with ACCP in them, and some have the abbreviation, but immediately after writing the term in full (for example in Unique factorization domain. I think it's OK to use such abbreviations in that context. --Joth (talk) 07:04, 14 June 2009 (UTC)
 * Often, abbreviated terms are used in articles which do not describe those terms specifically and exist for another purpose. For instance, a term such as ACCP might be used in an article on Bézout domains (not that it necessarily is) but may not be thoroughly explained there. However, in most cases, articles specific to a term, will pay great emphasis to clarifying ambiguities with respect to its abbreviation (such as UFD in the article on "unique factorization domain").
 * On the other hand, although an abbreviation may be explained in a particular area of an article, readers who do not read this area will not know of the abbeviation (if I read an article, it is usually the lead that I read last, so if the term whose abbreviation is ACCP were defined there, and I had never heard of it, I will most certainly be disadvantaged should I come across ACCP before reading the lead). I agree, of course, that if one uses an abbreviation and one writes the abbreviation in full, there is no problem. However, this must be done every time one uses an abbreviation for otherwise, especially if the article is long, a reader may not notice the one single time where the abbreviation is explained. -- PS T  13:51, 14 June 2009 (UTC)

Citing a footnote more than once
In WP:REFNAME, starting from 14 April 2008, I read: "In subsequent uses of the named tag the use of   is encouraged rather than copying the whole footnote again, as whole footnotes tend to reduce the readability of the article's text in edit mode, which makes finding specific parts of the text when editing tedious."

On the other hand, the short version is more prone to accidents under further edits; if the editor is not careful enough, his/her local edit may have unwanted global effect. See also Wikipedia_talk:Footnotes.

For this reason I have used the long version in unbounded operator. (Initially I did not know about that style recommendation.) I wonder, do we mathematicians agree that the short version is preferable also in our texts? Boris Tsirelson (talk) 12:03, 15 June 2009 (UTC)


 * Basically there are three options:
 * Refer to the previously named footnote
 * Repeat exactly the same unnamed complete footnote
 * Repeat exactly the same named complete footnote
 * I think we should use the same convention as everybody else, and I actually think that 1 is the best. 2 is inferior because it clutters the article; also if only one of two previously identical footnotes gets a correction it looks very unprofessional. 3 is really bad: If you have two footnotes with the same name and change only the first, nothing happens. You may not even notice, or you may get very confused. If you change only the second, you get a surprising regression when the first instance is removed or the two passages are swapped. With 1, when a reference is removed we get bold red text telling us what went wrong so it can be fixed immediately.
 * These arguments are a bit weaker in the case of Harvard referencing as in unbounded operator, but even then I think it's better not to use 3 to avoid puzzling others who are not used to it. --Hans Adler (talk) 12:44, 15 June 2009 (UTC)


 * And if the prominent red bold text is not enough, there's a bot running around fixing these. — Emil J. 13:07, 15 June 2009 (UTC)
 * Does it fix the references by getting them from the page history? That would be great, but I have never observed this. --Hans Adler (talk) 13:25, 15 June 2009 (UTC)
 * Yes, it extracts the references from the page history. See Special:Contributions/AnomieBOT for examples. — Emil J. 14:02, 15 June 2009 (UTC)


 * There are three other options, none of which involve note ids. The first is to avoid the use of notes altogether, in favour of paranthetical references to a proper reference list.  Second, one can use MLA-style notes, where the first version of the reference is given in full, and after that the note is given as a short reference, either the "AUTHOR_LIST, DATE" or "AUTHOR_LIST, SHORT_TITLE", possibly followed by the page ref.  Or last, one can use parenthetical references in notes, rather as if they were short references in notes, which is what the Chicago Manual calls notes plus references style. &mdash; Charles Stewart (talk) 14:12, 15 June 2009 (UTC)


 * I see, thank you all; indeed, "1" is the best for my case. Special thanks to User:Algebraist for his help with "unbounded operator". Boris Tsirelson (talk) 14:43, 15 June 2009 (UTC)

Named footnotes have one disadvantage: they discourage grouping together several references cited in the same sentence. Thus, the degree to whch they shorten footnotes is debateable. Septentrionalis PMAnderson 18:42, 16 June 2009 (UTC)
 * That's true. But of course one may make a conscious choice to group those together that are not reused. --Hans Adler (talk) 19:16, 16 June 2009 (UTC)
 * But unbounded operator has one point where it references three notes, numbered 3, 15, and 5 IIRC; for situations like that, one must do one or the other. I prefer to have one note, which cites all three; the Harvard templates can then link the footnote to the bibliography, if necessary.


 * This is, of course, a matter of taste; but we should bear in mind tastes differ. Septentrionalis PMAnderson 23:02, 16 June 2009 (UTC)

First-order logic
I have been working, with help from other editors, to improve the article on first-order logic. If anyone has the time to review the relatively long article and give an outside perspective, it would be greatly appreciated. &mdash; Carl (CBM · talk) 18:01, 15 June 2009 (UTC)

Please look at Dirac delta function page
Can someone take a look at the Dirac delta function page? The editor User:Sławomir Biały may know what he is talking about, but it is beyond my area of expertise. Assuming that he is competent, I wonder if the article is being made unaccessible to anyone below his level of knowledge? PAR (talk) 03:50, 16 June 2009 (UTC)


 * His edits look right. He has also removed some text that seems to think that the Dirac delta function is just "notation", which is a good thing. What he has added can be found in any number of standard texts in functional analysis. It is possible this has made the article less accessible to many (e.g. physicists), however his edits have definitely made the article more accurate. Any attempt to make the article more accessible should start off from where the article is now incorporating the new changes. There were certainly several common misconceptions present in the article before User:Sławomir Biały's changes. Hope this helps. RobHar (talk) 18:13, 16 June 2009 (UTC)

cc-by-sa and citizendium
Some of you may or may know, but Wikipedia has switched its license to cc-by-sa. One consequence is that we are now permitted to import text from citizendium (an encyclopedia project started by a cofounder of Wikipedia). I have just imported a large chunk of text from CZ to Gamma function, which greatly improved the article (in a matter of minutes :) Anyway, I thought you might consider doing something like that. -- Taku (talk) 11:05, 16 June 2009 (UTC)


 * Does anyone know what sort of attribution is required in these situations? with the GFDL we had a well established practice of using a template at the bottom of the article to say we had imported text. What do we do with the new license? &mdash; Carl (CBM · talk) 12:09, 16 June 2009 (UTC)


 * For the time being I have created the Citizendium template parallel to the Planetmath template. I added it to Gamma function in the references section. &mdash; Carl (CBM · talk) 12:17, 16 June 2009 (UTC)

My recent edit to this section seems to have perversely disappeared.

Taku seems to assume we know what "cc-by-sa" is, and doesn't link to it. Here's the link: cc-by-sa. Michael Hardy (talk) 20:32, 16 June 2009 (UTC)
 * Oh: I never actually hit the "save" button on that one. Readers are hereby ordered to ignore my first comment above and read only my second comment. Michael Hardy (talk) 20:36, 16 June 2009 (UTC)


 * More concretely, see Text of Creative Commons Attribution-ShareAlike 3.0 Unported License. JRSpriggs (talk) 07:46, 17 June 2009 (UTC)

Just a side note &mdash; Taku said that WP has switched to cc-by-sa. According to the notice I'm looking at below this text box, that does not appear to be exactly true. Apparently new content is multi-licensed under cc-by-sa and GFDL. I'm not a lawyer but it seems to me that this could get complicated for reusers. Ordinarily, when you make a derivative work from multi-free-licensed content, you can choose the license under which to release the derivative work, at least as I understand it.

But in the case of WP, the content from before the change is not available to be re-licensed under cc-by-sa, unless the authors all consent to this, which as a practical matter seems impossible. For content that WP has copied from Citizendium, this content cannot be relicensed under GFDL without the copyright holders' consent. So apparently the author of a derivative work, to be safe, must also release the work under both licenses, and so on for all derivatives of that work, and this seems contrary to the natural reading of each license separately. Have the lawyers really thought this through? --Trovatore (talk) 09:12, 17 June 2009 (UTC)
 * It's important to note that we haven't relicensed under CC-BY-SA – we've just adopted a dual-licensing scheme with CC-BY-SA and GFDL. &mdash; Anonymous Dissident  Talk 09:21, 17 June 2009 (UTC)
 * Yes, that I understood. That doesn't seem to answer the points I raise above. --Trovatore (talk) 09:28, 17 June 2009 (UTC)
 * I didn't mean to reply to you directly. I was just putting it out there. &mdash; Anonymous Dissident  Talk 09:37, 17 June 2009 (UTC)
 * I thought that one revision of GFDL had been modified to allow people to import text licensed under it to the CC-BY-SA license, and we were only going to use CC-BY-SA hereafter. Right? JRSpriggs (talk) 09:32, 17 June 2009 (UTC)
 * Not quite. All old GFDL wikipedia content has been relicensed as CC (which is permitted under GFDL 1.3, and hence requires no further consent from authors). New text submitted to Wikipedia by the copyright holder must be licensed as both GFDL and CC. New text imported from elsewhere must be CC and may (but need not) be GFDL-licensed also. Thus all text will be avaliable under CC-BY-SA-3.0 and may be available under GFDL 1.3, but a full history trawl is required to work out if a given page is GFDL-compatible. Details at Licensing update. Algebraist 10:49, 17 June 2009 (UTC)

Since the principal motivation behind the license switch is to allow the importation of contents licensed under cc-by-sa, if you couldn't data-dump contents from citizendium, say, I don't see the point of the switch. This page hopefully answers some questions raised above. But to summarize key points: Because of (ii), we can now data-dump contents licensed under cc-by-sa. But the other unintended? consequence is that we are no longer able to data-dump contents from PlanetMath. Since we've been relying less and less on PlanetMath lately, hopefully this doesn't cause much pain. -- Taku (talk) 10:52, 17 June 2009 (UTC)
 * (i) Any "old" contents are now licensed under cc-by-sa. (They are still available under GFDL, the old license, since anything licensed under GFDL stay under GFDL; you can't strip away GFDL.)
 * (ii) But more important, after this update, only dual-licensed content or CC-BY-SA-compatible content can be added to the projects, and GFDL-only submissions will no longer be accepted..
 * In fact, any datadumps imported from PlanetMath since last November must now be removed. Algebraist 11:13, 17 June 2009 (UTC)

More on pi....
A user inserted this into the article on the square root of 2:
 * The square root of two can also be used to approximate &pi;:
 * $$2^m\sqrt{2-\sqrt{2+\sqrt{2+\cdots+\sqrt{2}}}} \to \pi\text{ as }m \to \infty\, $$
 * for m square roots and only one minus sign.
 * $$2^m\sqrt{2-\sqrt{2+\sqrt{2+\cdots+\sqrt{2}}}} \to \pi\text{ as }m \to \infty\, $$
 * for m square roots and only one minus sign.
 * for m square roots and only one minus sign.

I did some simple number-crunching that seems to bear out the assertion. The user has not responded to my inquiry about where to find a proof; I think this user hasn't been around lately. Can anyone tell us anything?

Probably this result should be mention in one or more of the articles related to &pi;. Michael Hardy (talk) 19:57, 16 June 2009 (UTC)


 * (Igny (talk) 20:22, 16 June 2009 (UTC))

This is one of the methods of numerically approximating &pi; attributed to Archimedes — it follows easily from considering inscribed 2m-gons and applying half-angle formulas. Arcfrk (talk) 21:00, 16 June 2009 (UTC)


 * (Edit conflict) Seems closely related to the duplication formula for cosine, in fact. Obviously the gadget with all plus signs under the square root tends monotonically up to 2, and this is related to "how fast". The "how fast" is related to twice cos of some angle you keep halving, according to my algebra. There is something more to prove here, which is why the number is pi. I suspect Euler knew, though. Charles Matthews (talk) 21:05, 16 June 2009 (UTC)

OK, here's a sketch. First, note that &pi; = 2m(&pi;/2m) and that &pi;/2m equals sin(&pi;/2m) with a third degree error term. Then we hit the sine with the half-angle formula:
 * $$\begin{align}

2^m\sin\frac{\pi}{2^m} &= 2^m\sqrt\frac{1-\cos\frac{\pi}{2^{m-1}}}{2} \\ &= 2^{m-1}\sqrt{2-2\cos\frac{\pi}{2^{m-1}}}. \end{align}$$ The half-angle formula for cosine tells us:
 * $$2\cos{\alpha/2} = \sqrt{2 + 2\cos\alpha},$$

which we now apply to the previous equation:
 * $$\begin{align}

2^{m-1}\sqrt{2-2\cos\frac{\pi}{2^{m-1}}} &= 2^{m-1}\sqrt{2-\sqrt{2 + 2\cos\frac{\pi}{2^{m-2}}}} \\ &= 2^{m-1}\sqrt{2-\sqrt{2 + \sqrt{2 + \cos\frac{\pi}{2^{m-3}}}}} \\ &= \cdots \\ &= 2^{m-1}\sqrt{2 - \sqrt{2 + \sqrt{2 + \sqrt{2 + \cdots + \sqrt{2 + 2\cos\pi}}}}}, \end{align}$$ where there are m square root signs. Of course, cos &pi; is &minus;1, so the last term is zero. This leaves us with:
 * $$2^{m-1}\sqrt{2 - \sqrt{2 + \sqrt{2 + \sqrt{2 + \cdots + \sqrt{2}}}}},$$

where there are m &minus; 1 square root signs. Shifting the index by one gives the desired formula.

I should be cleaning out the fridge. She's going to kill me. Ozob (talk) 23:57, 16 June 2009 (UTC)

Albert Einstein
...is at peer review. Help get it back to FA. Casliber (talk · contribs) 11:33, 17 June 2009 (UTC)
 * Why should anybody care about FA?
 * The demotion was pedantic and semi-literate; the recent FAC is a joke which complains that it does not cite printed sources, when it cites many. (This diff is immediately before the nomination; it hasn't changed much.)
 * Any support for deleting Featured Articles altogether? It does real, if minor, services for Wikipedia; but as an article evaluation system, it could be profitably replaced by a random number generator. Septentrionalis PMAnderson 16:15, 17 June 2009 (UTC)


 * I suppose that you do not care about ever seeing a mathematics article on the Main page again? JRSpriggs (talk) 04:30, 18 June 2009 (UTC)
 * I propose to take a longer road. Replace FA, or fix it, and the mathematical features will follow. I would prefer to see nothing on the front page than a good many FAs; it's one of Wikipedia's public embarrassments.Septentrionalis PMAnderson 17:34, 18 June 2009 (UTC)


 * I for one certainly don't care about that. But even though I have no desire to participate in the FA and GA processes, I have no objections if other people do. &mdash; Carl (CBM · talk) 04:46, 18 June 2009 (UTC)


 * Articles that are meant to serve a broad audience benefit from the kind of feedback you get from the GA and FA process. Articles of more specialist interest probably don't.  I certainly want to get the Logic article to reach the GA/FA criteria.  I can't think of any other articles that (i) I care about and (ii) I think are worth the effort.  Maybe, someday, Mathematical logic and Arthur Prior, but they are harder sells.  Einstein looks like a better bet, but I don't care enough to get involved. &mdash; Charles Stewart (talk) 08:38, 18 June 2009 (UTC)


 * Logic seems to be coming along very well. I spent some time on Mathematical logic last year, and it is not in bad shape. I know of several lingering defects in that article, and I am sure there are more that I don't know. But I think it would require someone with quite a bit of background to give a truly thorough review of the article. &mdash; Carl (CBM · talk) 13:55, 18 June 2009 (UTC)


 * Thanks. There's much, much more to be done, though.  several lingering defects &mdash; I know that feeling very well. &mdash; Charles Stewart (talk) 14:05, 18 June 2009 (UTC)


 * I think Charles' comment about the intended audience and the value of encyclopedia wide reviews like FA and GA is insightful. Would there be any value in the mathematics project having it's own review process? Paul August &#9742; 15:16, 18 June 2009 (UTC)
 * We have WikiProject Mathematics/A-class rating. Algebraist 15:20, 18 June 2009 (UTC)


 * We do/did have the A-class review process, but it is defunct now.


 * After reflecting on that process, and my general experience with WP, my thought is that the sort of process we developed for A-class review has systemic problems that prevent it from working. To give a thorough review to an article such as First-order logic would require a comparable amount of effort to peer-reviewing a journal paper. The PDF version of that article is 22 pages long.


 * Few editors have the time and energy to do that type of intensive review for a never-ending list of articles. I certainly do not have the energy. Also, discussion page format for reviews is more suited for drive-by comments than to slow, thorough reading. The limiting resource here is reviewer time per article. &mdash; Carl (CBM · talk) 15:23, 18 June 2009 (UTC)


 * The discussion of FAC for this article may be moot; it's certainly premature. As noted at the peer review, the present coverage of Einstein's scientific work is not close to A- or FA-class; an NPOV assessment would probably put it at a high C-class.  Until some editors with scientific knowledge devote themselves to improving that coverage, it probably shouldn't be listed as a Good or A-class article.  Proteins (talk) 18:15, 18 June 2009 (UTC)

Euclidean algorithm on the Main Page
Hi, just an friendly heads-up that a mathematical article, Euclidean algorithm, will be featured on the Main Page in a few hours. Since Main-Page articles are usually a magnet for vandalism, it would be great if you could add it to your watchlists for the day and fix things as you happen to notice them. Others will undoubtedly be watching as well. My own schedule is very busy, however, so I'll have only a limited time to help out. Thanks! Proteins (talk) 20:29, 17 June 2009 (UTC)

Collaboration en.wp et fr.wp in mathematics
I've just posted a comment on the French WikiProject here and the German one. Are there currently any "institutionalized" means of collaborating with the guys there? For example, the French site is also using a grading scheme similar to the one used here, but nonetheless the actual article quality is not automatically comparable. I'd like to spot articles in French or German whose English equivalent is worse (or the other way round, but that's more relevant to fr.wp and de.wp). Any ideas about that? (Obviously, the same holds true for other languages, but I think it is a start to deal with these two.) Jakob.scholbach (talk) 19:51, 13 June 2009 (UTC)
 * Generally en is most complete and that the quality here is also generally better, I believe. (Otherwise I would be working at de or fr.) Translations from en to the other languages are going on throughout Wikipedia, all the time – this doesn't seem to require coordination, or at least not a new initiative. Some other points to consider:
 * Since it's relatively rare for the French or German version to be better, we normally don't look there. The only times I have found myself on fr or de looking for maths articles were when something had gone seriously wrong (e.g. wrong title for years, such as prametric) and I wanted to see how they dealt with it. They are bound to know when their version is better. If they would notify us after significant improvements, that would be a great help for us.
 * They might also have developed ways of presenting sets of articles that we could import and then keep synchronised.
 * What can we give back?
 * --Hans Adler (talk) 20:41, 13 June 2009 (UTC)
 * Actually, I find that some of the articles in these languages are of a decent quality. For instance, manifold in the French language is a feature article and appears to be reasonably well-written. On the other hand, I have also noticed languages in which the articles are featured, although of poor quality. Lumbaart seems to be notorious for this. Perhaps the reason why many people edit the articles in English is that more people collaborate here. There is also the obvious reason that the articles are of a better quality. -- PS T  04:53, 14 June 2009 (UTC)
 * There are some French articles you should read if you can : fr:périmètre, fr:théorème du minimax de von Neumann, fr:théorème de d'Alembert-Gauss, fr:théorème du point fixe de Brouwer, fr:énigme des trois maisons for example. Maybe some of them deserve translation into English. --El Caro (talk) 08:44, 14 June 2009 (UTC)
 * Definitely. --Hans Adler (talk) 09:07, 14 June 2009 (UTC)
 * The French featured good [I was confused about the French system Hans Adler 07:05, 21 June 2009 (UTC)] article on the Brouwer fixed point theorem is interesting. Plenty of ideas, history, pictures. No mention of Sperner's lemma, though, which I would say was a failure of NPOV, since it gives a whole lot of space to the later work of Nash, thus favouring a famous American mathematician over an obscure German one. The German article on Brouwer is much superior to ours. Charles Matthews (talk) 10:48, 14 June 2009 (UTC)
 * If anyone has trouble following Charles about the differences between Brouwer fixed point theorem and the French version, it's because the translation is in progress. --Hans Adler (talk) 14:08, 14 June 2009 (UTC)
 * I have no opinion on NPOV and Sperner's lemma, but as a general comment: It's hard to get NPOV right when you are basically the only author and the featured good article discussion looks like this: fr:Discussion:Théorème du point fixe de Brouwer/Bon article. --Hans Adler (talk) 22:24, 14 June 2009 (UTC)
 * Jakob's idea seems very good, but what can we do concretely? --El Caro (talk) 19:25, 17 June 2009 (UTC)
 * I am not sure what we can do by way of organised co-operation, but it seems a good way to start is to do more cross- and trans-wiki work. So far I have translated two small maths articles into German, and I am currently translating a French featured article into English. (It's probably going to be a GA here.) If topic X has a strong affinity to language L ≠ English, e.g. Nicolas Bourbaki to French, then it's probably worth keeping the articles on X in English and in L synchronised to ensure that all improvements in one version make it into the other version. The other Wikipedias can then simply translate the English or L version. What I like about this approach is that we, the large English Wikipedia with its many native speakers of other languages, help some of the other Wikipedias to grow and get something back in return. --Hans Adler (talk) 11:40, 18 June 2009 (UTC)
 * I think that is a googd idea, but I think that you could add en.v and fr.v for collaboration fr:v:Projet:Mathématiques and v:School:Mathematics Regards, Otourly (talk) 10:25, 20 June 2009 (UTC)

GA Reassessment of Special relativity
I have done a GA Reassessment of the Special relativity article as part of the GA Sweeps project. I have found the article to need quite a bit of referencing. I have placed the article on hold for a week pending work. I am notifying all interested projects of this review which can be found here. If there are any questions please contact me on my talk page. H1nkles (talk) 17:59, 19 June 2009 (UTC)

Higher-dimensional algebra in need of attention
I gave it a preliminary cleanup, but the article seems unfocused and unsure of what to cover. Lots of redlinks (which could be redirects or piped, but I lack knowledge here). Also seems to draws heavily from one author (R. Brown).Headbomb {{{sup|ταλκ}}κοντριβς – WP Physics} 14:24, 20 June 2009 (UTC)


 * Higher-dimensional algebra certainly lacks motivation (I don't really count wanting to be general) and orthodix organisation. Charles Matthews (talk) 15:30, 20 June 2009 (UTC)


 * What a depressing article. I had never heard of the term "higher-dimensional algebra", but Baez and Brown seem to be using it. Judging from the description, a "supercategory" might just be an n-category for some n. But then why are only 2-categories mentioned? Since there are technical problems with the definition of n-categories I suspect it's one of the competing variants. There are no links between this article and the apparently closely related article n-category. The applications in mathematical biology sound like a hoax based on an accidental use of the word "supercategory" in that field. I am not saying it is a hoax, but without any explanation it's hard to tell. Esquisse d'un Programme could serve as a motivation for studying n-groupoids (Grothendieck says they capture all of "tame" geometry, or something like that) but only appears under "see also". Hans Adler 16:28, 20 June 2009 (UTC)


 * Seifert–van Kampen theorem has some problems. One might go through the math articles citing Brown and see if there is a systematic coi/bias problem.  JackSchmidt (talk) 16:33, 20 June 2009 (UTC)


 * This external link to Higher Dimensional Group Theory may or may not shed light on things. Charvest (talk) 02:41, 21 June 2009 (UTC)
 * Oh, I see the article already links to that page. Never mind. Charvest (talk) 02:45, 21 June 2009 (UTC)

François Viète
Hello, a lot of good faith information has been added to the page by someone who is French I believe, and it is therefore in dire need of cleanup. More importantly for this WP, it lacks inline citations, although it does have references. I wouldn't know if did find references for some statements, so if someone with more knowledge could look into it... it also makes some fairly heavy claims, that a) aren't sourced and b) sound fairly disputable. I know little of the history of algebra, but 'He was the first mathematician to have represented the parameters of an equation by letters' sounds like a big claim. Since the contributor has added a lot of information, it could be a really good page, so I suggest anyone who can should get involved. On another point, New algebra didn't exist until the contributor created it, which seems quite odd. Considering the title may be a direct translation, or not use English terminology, could someone who fully understands the subject, and knows what pages exist check that the page doesn't already exist. Factual correctness would be great, but as I said, the edits are in good faith. - Jarry1250 (t, c, rfa) 15:55, 21 June 2009 (UTC)
 * He was the first mathematician to have represented the parameters of an equation by letters is perfectly true (indeed, it hedges too much; Diophantus was doing something quite different). Septentrionalis PMAnderson 17:47, 21 June 2009 (UTC)
 * I wasn't suggesting it was an incorrect claim, I was just checking, and it should probably have a reference. - Jarry1250 (t, c, rfa) 18:30, 21 June 2009 (UTC)
 * http://sci.tech-archive.net/pdf/Archive/sci.math/2009-01/msg03978.pdf : "Viète introduced arbitrary parameters into an equation and distinguished these from the variables of the equation. But his notation was only *partly* symbolic and was still ultimately based on Euclidean geometry. But for the first time, one could speak of a general quadratic equation, not just certain particular equations with particular numerical values." --El Caro (talk) 18:54, 21 June 2009 (UTC)

Intrinsic curvature
Hi, that link redirects to Curvature. Which in turn directs you to Curvature of Riemannian manifolds. This article appears to be missing its first sentence dealing with expression but without, or skipping, definition? It has been unchanged for years (I know nothing about it myself) ~  R . T . G  16:24, 21 June 2009 (UTC)


 * The main problem is the lack of an introductory article on intrinsic curvature. Once you know what curvature is and what Riemannian manifolds are (we have that article), then you don't really need too much of a definition of the phrase "curvature of Riemannian manifolds", you can just get on with discussing the technical aspects. --Tango (talk) 18:28, 21 June 2009 (UTC)


 * If the question is where does one go to find out the meaning of intrinsic curvature, then at the moment (given the absence of the introductory article that Tango refers to above) as far as I can tell, the best place for that is "Curvature" not "Curvature of Riemannian manifolds". I think part of the problem is that "Curvature" links the first use of the term "Intrinsic curvature" to the article "Curvature of Riemannian manifolds", leading the reader to believe the reverse. Paul August &#9742; 18:59, 21 June 2009 (UTC)


 * Well, the onus is on we editors to use a lead to describe every article as can be broadly understood. As a suggestion to anyone who knows different curvatures, what is the difference between circular curvature, elliptical curvature and Riemannian curvature? Could you say (if that is what it is) "A Riemannian curvature is, similar to a wave, an increasingly inclining curvature, one that smooths out, linear on the circle or the ellipse, a 3d swirling curvature or a difficult to describe combination of curves like that?" It is probably a straight line for all I know but if I read it in a book I would probably take a look at Wikipedia. ~ R . T . G  20:35, 21 June 2009 (UTC)
 * Riemannian curvature is simply the concept of curvature for Riemannian manifolds, so I think the definition is in the name. We have a problem with maths articles because it is often not practical for articles about advanced mathematics to be understandable to the layman, especially as a stand-alone article. Anyone trying to read curvature of Riemannian manifolds without having read Riemannian manifold is not going to get very far, and there isn't much we can do about that. --Tango (talk) 21:00, 21 June 2009 (UTC)


 * Okay but there is a way to describe it (of course if I come up with that I will write it all down!!) ~ R . T . G  13:20, 22 June 2009 (UTC)

All "propositions" are proven????
I noticed that Proposition and Proposition (mathematics) both say "... proposition is used for a proven statement ...". As a universal proposition, this is false according to my understanding and as "proposition" is used in propositional calculus, propositional formula, proposition (philosophy), and implicational propositional calculus. JRSpriggs (talk) 18:11, 21 June 2009 (UTC)
 * It is one meaning of Proposition: the statements in a textbook are often called Theorem 2.5, Proposition 2.6, Lemma 2.7.... The claim that Lemmas are harder proofs than Propositions is not my experience; indeed, it seems to me backward; but the entire discussion might be better at Wiktionary, since it is about the word, not the concept. Septentrionalis PMAnderson 18:17, 21 June 2009 (UTC)
 * I make no claim that my usage is standard, but in the one instance I can recall in which my co-authors introduced "propositions" as well as lemmas and theorems into one of my papers, they were intermediate between lemmas and theorems: proved statements that summed up a series of technical lemmas into a more general and simpler form, but that we did not want to claim as the main results of our paper. —David Eppstein (talk) 18:20, 21 June 2009 (UTC)
 * My understanding of the usual usage of the terms is that a Lemma is a result used to prove something else and a Proposition is an interesting result in its own right, but a fairly minor one when compared to a Theorem. These terms are all very subjective and depend on context, of course. What's a Lemma to one person may be a major result to another. --Tango (talk) 18:24, 21 June 2009 (UTC)
 * Like the trivial corollary of the modularity theorem for semistable elliptic curves. Dragons flight (talk) 06:53, 22 June 2009 (UTC)


 * I've prodded the article, on the grounds it belongs at Wiktionary; the principal sense of "proposition": a statement which can be true or false, (or the meaning of such a statement) is at proposition (philosophy) and the chief effect of this article has been to attract links which should go there. Septentrionalis PMAnderson 18:34, 21 June 2009 (UTC)
 * I've unprodded it, I think the article should either be kept or merged into somewhere, not deleted. It contains useful content. --Tango (talk) 18:52, 21 June 2009 (UTC)
 * I don't think that the contents of Wiktionary are useless, and that's where it should go - unless you can find a better place here. Septentrionalis PMAnderson 19:05, 21 June 2009 (UTC)
 * I have to agree with Sept here. I doubt there's anything encyclopedic to be said about the distinction between propositions (in the sense of mini-theorems) and lemmata.  Really proposition in this sense is hardly ever used stand-alone &mdash; it's just part of a labelling scheme, allowing you to write things like we now finish the proof of Theorem 3.3 by a straightforward application of the method used to prove Proposition 3.1.
 * On the other hand, the default meaning of proposition in mathematics is "statement that is either true or false". So proposition (mathematics) absolutely should redirect to proposition (philosophy), because it's the same usage.
 * I'm not in principle opposed to merging content from the existing article, but I didn't actually see anything worth merging. I'm willing to be persuaded otherwise, if I've missed something. --Trovatore (talk) 20:33, 21 June 2009 (UTC)
 * We currently have a section, Theorem, which makes an attempt at explaining the differences. I think there could be a full article on this topic, explaining the history of this way of structuring papers, explaining any differences in how it is done in other countries, etc. An article specifically on propositions doesn't make much sense, but it would be good as part of a larger article on the subject. --Tango (talk) 21:06, 21 June 2009 (UTC)
 * Well, could be, but I still don't see anything worth saving from the current article. --Trovatore (talk) 21:29, 21 June 2009 (UTC)
 * In any case the article proposition (philosophy), at least in its current state, has nothing to do with "Proposition 3.1", and in fact I have difficulty seeing much of a connection with mathematics. I think the "Proposition 3.1" sense is dominant in mathematics in general compared to the propositional formula or propositional variable sense, and that in turn is certainly more common than the proposition (philosophy) sense. Trovatore has redirected to proposition (philosophy), and I think that's totally unacceptable. I think that was way too bold and the previous situation, while not at all good, is at least not totally confusing. Therefore I have reverted. Hans Adler 00:31, 22 June 2009 (UTC)
 * So first of all, the "Proposition 3.1" sense may well be the one with the highest total count of occurrences. But this is a very poor target for anything called proposition (foo), because it doesn't mean anything.  It's just a label, the way some streets are called "lane" and come are called "place", but there's no time you'd want to say that such and such a street "is a lane" or "is a place".  This sense has encyclopedic value approximately zero; I don't think it ought to enter into this discussion at all.
 * As for propositional variables and so on, again I don't think you would ordinarily call these propositions. They're propositional variables or propositional what-have-yous, but not propositions.  So again I don't think this sense enters into the discussion.
 * On the other hand, how are you going to describe, say, the continuum hypothesis? You can't call it a "theorem" in the contemporary sense (Hilbert did, apparently intending theorem in the sense of "part of a theory" or some such, but that sense of the word is hardly understood nowadays).  It's not really a hypothesis or a conjecture, because most people don't think it's true.  You could call it a "sentence", I suppose, but that seems overly syntactic; it won't work if I'm talking about the meaning of the sentence.
 * But you can very well call it a proposition. And in fact you can argue about whether it really is a proposition or not.  This, I would say, is truly and by far "the dominant sense" of the word proposition in mathematics, when the word is being taken seriously as opposed to simply used to organize a paper. --Trovatore (talk) 03:36, 22 June 2009 (UTC)
 * By the way, in Russian "proposition" as in "Proposition 3.1" is "предложение", while "proposition" as in "a proposition is either true or false" is "высказывание". I wonder, what happens in other languages? Boris Tsirelson (talk) 06:33, 22 June 2009 (UTC)
 * In German, the meanings related to logic are called Aussage, while the numbered things are a bit rarer than in English and called Proposition. Hans Adler 09:27, 22 June 2009 (UTC)
 * I think when the CH is referred to as a "proposition" it is not usually appropriate to link this to proposition (philosophy). Perhaps in a philosophy of mathematics context – but otherwise it's no more than a synonym for "statement". A dedicated article for "Proposition [3.1]" is inappropriate, but an article on mathematical terminology, and in particular theorem/lemma/proposition/remark/corollary is certainly encyclopedic, although it's obviously a bit hard to find the appropriate sources that no doubt exist somewhere.
 * Without such an article we have the philosophical meaning and the technical meaning in mathematical logic. With it we have 3 mathematical meanings. Keep in mind that proposition (mathematics) is already partially disambiguated. We can't start proposition (philosophy) with a hatnote saying:
 * Proposition (mathematics) redirects here. For other meanings in mathematics see Propositional formula and Mathematical terminology
 * Therefore as it's ambiguous it must be either a disambiguation page or an article that can contain a hatnote pointing to the other meanings in mathematics. If proposition (mathematics) were a redirect to proposition (philosophy), then there would be no reason to link to proposition (mathematics). If there are no appropriate incoming links anyway, I don't see why it can't be a disambiguation page. I think there should be a general principle that if "X (A)" is still ambiguous, it should not be a redirect to a completely disambiguated article "X (B)". I can't find anything relevant in WP:Disambiguation or the archives of its discussion page, though. Hans Adler 09:27, 22 June 2009 (UTC)
 * (left) We have a dab page; it's at proposition. When there is a common meaning of a word about which we have no article (verbs, for example), dab pages will often mention it, but not link to it, or else offer a cross-wiki link to Wiktionary. That's what we should do here; we can update proposition as soon as this discussion is over.


 * Almost all the links to proposition (mathematics) (I don't see any exceptions, but I may have missed some) mean proposition (philosophy); that is the sense with mathematical content. This includes Lemma (mathematics), which defines a lemma as a "proven proposition"; if the textbook sense were meant, a lemma would not be a proposition, and "proven proposition" would be redundant.


 * Retaining the article means moving all of them, and policing the page to keep editors from making the natural link. Much easier to get rid of this page, which has no sources, and no encyclopedic content. I have restored Trovatore's link, in the hopes of getting readers to the right place in the meantime; the text is here. Septentrionalis PMAnderson 13:59, 22 June 2009 (UTC)

Inappropriate moving of article
has unilaterally moved Newton's method to Newton–Raphson method. This is contrary to our policy of using the most common name in English. JRSpriggs (talk) 10:45, 23 June 2009 (UTC)
 * Raise this at WT:WPM. Both names are widely used from what I know. Oleg Alexandrov (talk) 10:46, 23 June 2009 (UTC)

<>


 * I know what Newton's method is, but I don't think I have ever heard the name Raphson before. Hoever, this is far from my area and the relevant part of my mathematical education wasn't in English. Hans Adler 11:12, 23 June 2009 (UTC)


 * I don't feel strongly either way, but note that "Newton-Raphson" is the name used by the various GCE exam boards in the UK - see, for example, Q7(b) on this AQA paper, Q4(c) on this Edexcel paper and Q4 on this OCR paper. Is this perhaps a UK/US difference in terminology ? Gandalf61 (talk) 11:35, 23 June 2009 (UTC)
 * The Google popularity test says there's not much in it: combining the search with "numerical analysis" gives 21,500 for "newton-raphson" and 37,100 for "newton's method". Enough to move back, though, I guess. &mdash; Charles Stewart (talk) 12:34, 23 June 2009 (UTC)

I have tended to take the term Newton's method to refer to the one-dimensional case and Newton–Raphson method to mean the case of a function of several variables (but still a one-dimensional range space. But I don't know how prevalent that usage is. Michael Hardy (talk) 19:22, 23 June 2009 (UTC) ...and now I see that there's nothing at all about higher-dimensional domains in the article. Michael Hardy (talk) 19:47, 23 June 2009 (UTC)


 * The Calculus texts I learned from and taught from (circa 1960s -1970s) all used "Newton's method", with no mention of "Raphson", I believe. I think it should probably be moved back. Paul August &#9742; 19:50, 23 June 2009 (UTC)
 * I think that Newton's method is more commonly used in textbooks and in the literature. Although I have heard of the Newton-Raphson method, the occurence of this term was in a negligible source. In particular, I think that this term is used mostly in school curricula. Therefore, the article should be moved back, but only followed by mention that another term exists (to ensure no future moves). -- PS T  01:33, 24 June 2009 (UTC)
 * Newton calculated with specific polynomials of degree 3 and didn't write down a general iteration formula. He expanded the polynomial at the current iteration point and neglected then the higher order terms. What Raphson was doing was to write down the "Newton"-iteration for polynomials of degree 3 with variables as coefficients. It was only Simpson that generalized the method to differentiable functions (note that a function at that time was something that could be calculated, i.e., piecewise analytic). The multidimensional method is sometimes called "Newton-Kantorovich method", but I would be surprised if it wasn't already used before 1940.--LutzL (talk) 05:42, 24 June 2009 (UTC)
 * Well, the history is interesting, but I don't think it is relevant to the article's title. Many concepts are named after people who had little or nothing to do with their development - see Stigler's law of eponymy. The central question with regard to the best title for the article is what is the most commonly used name for this method in English. Gandalf61 (talk) 09:18, 24 June 2009 (UTC)
 * Sure. So if this is to remain Newton-Raphson, which is specific for the real one-dimensional case, one would then need a new Newton's method overview article pointing also to Gauss-Newton and quasi-Newton methods, and a specialized Newton-Kantorovich method article specialized on multidimensional pure Newton.--LutzL (talk) 10:34, 24 June 2009 (UTC)

I have now moved the article back, since I seem inadvertently to have annoyed various editors by the move, for which I apologise. However, in my defence I should say (1) I did not "unilaterally" move the article: as can be seen from the talk page, two others had suggested the move, and it seemed that nobody had objected to the suggestion, so I thought the move was unopposed. I have now realised that there was, in fact, further discussion of the matter, but for some reason somebody started a new section on the talk page, instead of continuing the discussion where it had been started, so I did not realise it was there, and (2) As for the move being "contrary to our policy of using the most common name in English", I am not sure which name is more common: I first learnt the method as "Newton's method" back in the 1960s, but in recent years the majority of references I have seen to it refer to it as "Newton-Raphson". Anyway, it seems that the majority opinion expressed on the matter favours "Newton's method", so I am happy to accept it: I certainly had no intention of going against consensus. JamesBWatson (talk) 21:08, 24 June 2009 (UTC)

Multilinear stuff / neologisms?
requests (at my talk page) a comment about


 * Wikipedia talk:Articles for creation/k-array
 * Wikipedia talk:Articles for creation/Multilinear transformation

I personally have never heard of k-array. Is this a neologism? Also, what about the second? Jakob.scholbach (talk) 17:45, 23 June 2009 (UTC)


 * "Multilinear transformation" seems to miss the point that what tensors do for you is to remove the need for this concept. Not much here, I think. Charles Matthews (talk) 18:38, 23 June 2009 (UTC)


 * Both proposed articles are poorly written and have vague, non-specific sources. "k-array" looks like a neologism. For multilinear transformations we already have multilinear map. I think both article requests should be declined. Gandalf61 (talk) 19:48, 23 June 2009 (UTC)
 * Multilinear transformation shouldn't be a redlink though. It should redirect to multilinear map, and now does. Algebraist 12:00, 24 June 2009 (UTC)

Consensus Please
In the article Physics of the Impossible a single editor removed material that I believe, very much enhanced this article. The other editor’s view is that the removed material was off topic. My view is that it is very much on topic.

The current article is here: (current)

The version which I restored is at my sub page here: (restored)

Everything that was removed is related to the book. This is because, as the author writes: “The material in this book ranges over many fields and disciplines, as well as the work of many outstanding scientists.” There is a two and one half page list of the individuals, “who have graciously given their time for lengthy interviews, consultations, and interesting, stimulating conversations.” Most on this list happen to be scientists. I listed only the first 22 individuals and these are scientists. In addition, I linked their names to their biography on Wikipedia. I also listed each scientist’s fields of specialties. Many on the list in the article have more than one field of specialty (view here), and hence this reflects the breadth of knowledge contained in this book. If you look at this section in the restored article you will see what I mean.

In addition, before this material was removed by the one editor, the article was much more interactive. It was also more in line with the intent of Wikipedia that that the readers (as well as the editors) have a satisfying experience with Wikipedia. One aspect of this more satisfying experience is being able to access the knowledge that is available at Wikipedia on the sciences, and, perhaps, the mathematics. So, I linked not only the names on the list, but also many of their scientific disciplines to the respective Wikipedia article. Accessing this knowledge supports the following WikiProjects and their respective portals: (there are more I am sure)
 * WikiProject Astronomy
 * WikiProject Books
 * WikiProject Physics
 * WikiProject Space
 * WikiProject History of Science
 * WikiProject Science
 * WikiProject Mathematics
 * WikiProject Technology
 * WikiProject Computing
 * WikiProject Computer Science
 * WikiProject Engineering

Also, there were graphics that were removed which support the article and the concepts in the book. I believe these should be restored as well. These are on the restored article page, at my sub page. The captions of the graphics show that the book is grounded in real science. If you scroll through the restored article you will see the variety of graphics. I believe these enhance the article aesthetically, as well as help to give a clearer picture of the concepts contained in the book and the article.

Lastly, there were external links that were removed which reflect the concepts in the book. These external links were removed as though they were not relevant. For example, I will list some of the external links, and then the page number in the book, to which each link is related:
 * Solar sails: pp. 152, 158 - 159, 166, 172…
 * Space elevators: pp. 165 – 169
 * Black holes: 156, 232, 235 – 236…
 * Travel at the speed of light: 159 – 161, 163 – 165, 169 – 170…

Unfortunately the external links that were removed are going to have to be restored one at a time, because they cannot be cut and pasted back from the revision history without some distortion. I think these external links should also, be restored to the article.

I think the bottom line is, let common sense decide. Even Wikipedia guidelines say that they are just guidelines, not letter of the law.

I would appreciate a consensus on whether or not to keep the removed material. Please place your comments here: Consensus please. This is on the talk page of Physics of the Impossible.

Thanks for your time Ti-30X (talk) 13:29, 24 June 2009 (UTC)

Template:Define
I am glad to see that we actually have $$\stackrel{def}{=}$$ as a template; it's currently up for deletion, but I hope that will blow over. If others find this as intuitive (for non-mathematicians) as I do, let's use it more widely. Septentrionalis PMAnderson 00:58, 25 June 2009 (UTC)


 * First, the template doesn't seem to be in a wide use. Second, how does one use it? In practice you usually have some formulae or more likely identities that contain def equal somehow in middle. There is no many opportunities to use this template. The deletion therefore seems to be a natural choice. -- Taku (talk) 10:38, 25 June 2009 (UTC)
 * If you want to put such definitions in-line, it's a natural choice; I think that this is one of the templates that is rare because nobody knows about it. Septentrionalis PMAnderson 19:42, 25 June 2009 (UTC)
 * But TeX shouldn't be used inline, and it looks dreadful: x$$\stackrel{def}{=}$$15. Algebraist 19:47, 25 June 2009 (UTC)

XKCD / "In popular culture"
It seems that inevitably some people like to add an "In popular culture" section to an article whenever the webcomic xkcd happens to make even a passing reference to it. Thus Paul Erdős (Talk), Erdős number (Talk), even Proof that the sum of the reciprocals of the primes diverges, etc. Since this is likely to keep coming up at mathematics articles, I was wondering if we could have a policy page or some centralised discussion to point people at? For what it's worth, my opinion is that mere incidental mentions are not worth recording, but nontrivial uses in popular culture (even on xkcd) might be. (XKCD comic.) No doubt there are others who think that all "in popular culture" mentions are cruft. Shreevatsa (talk) 17:46, 26 June 2009 (UTC)
 * We already do have a guideline on this: WP:TRIVIA. This also provides a good retort whenever this sort of thing comes up. —David Eppstein (talk) 20:03, 26 June 2009 (UTC)

It's a big stretch to call an xkcd mention as being a somehow significant "popular culture" mention. Obviously a number of people that like to edit Wikipedia have a somewhat distorted view of what constitutes "popular culture" (I've noted for a while that the article on Crucifixion seems to devote more space and importance to mentions of crucifixions in anime as compared to those in classic artwork and literature). xkcd, as great as it is, is basically a niche webcomic that is only now starting to emerge more into the mainstream. The most defensible insertion would be into Erdos or Bacon number articles...topics which are inherently about popular culture (although the former is more limited to the geek crowd). --C S (talk) 21:20, 26 June 2009 (UTC)
 * It's likely to be the only mention in nontechnical work of the reciprocals of the primes; but an external link may be a better solution. Septentrionalis PMAnderson 23:17, 26 June 2009 (UTC)