Wikipedia talk:WikiProject Mathematics

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Arbcom decision on MHP: OR vs exposition in mathematics

The arbitration of the Monty Hall problem is nearing its decision phase.

Two proposals for the arbitration committee's decision concern Wikipedia policy on mathematical articles, especially original research versus secondary sources. Both proposals endorse editors' use of "arithmetic operations". This language could be of great concern to this project, and deserves your attention. Sincerely,  Kiefer.Wolfowitz  (Discussion) 23:47, 13 March 2011 (UTC)

Yes, it's of real importance to our project, and there are important nuances that neither version captures. But I thought we weren't supposed to edit Arb proposals?

CRGreathouse (t | c) 00:19, 14 March 2011 (UTC)

Editors may comment on proposals on the appropriate talk page. (I can strongly recommend against editing the arbcom pages that have warnings against civilian editing!)

I have asked two wise editors to watch the proceedings and this language, and I am sure that another wise editor already there can also comment effectively. (I commented informally on one arbcom member's talk page, and raised my concerns.) I believe that the most experienced editors should be trusted to advise ArbCom.  Kiefer.Wolfowitz  (Discussion) 00:44, 14 March 2011 (UTC)

Most worrying. Either version appears to make original research out of even routine examples. Sławomir Biały (talk) 01:19, 14 March 2011 (UTC)

Examples make or break articles, on WP and elsewhere. IMHO, we have to have the ability to make simple examples to interest readers, who would never be able to read research or even junior-senior math.

They should not issue any ruling on mathematics exposition. The social problems sufficed to make the MPH talk page a horror. If a mathematics article appears at ArbCom without social disorder on the talk page, then it may be reasonable for ArbCom to invent new principles to guide mathematics exposition. with apologies for being opinionated,  Kiefer.Wolfowitz  (Discussion) 01:33, 14 March 2011 (UTC)

I don't see how the proposed principles interfere with the presentation of routine examples, being routine they will undoubtably be able to be sourced. Paul August ☎ 02:01, 14 March 2011 (UTC)

Having looked closer at this I now have concerns about the proposed language. Paul August ☎ 12:55, 14 March 2011 (UTC)

Copying examples from reliable sources is generally not possible, due to copyright. While it is true that I've often seen people introduce errors into examples, there's not really a great alternative. Dcoetzee 02:27, 14 March 2011 (UTC)

Our examples are often similar to, but not identical with, those in other sources. The proposed mandate would in principle require that we copy sources step for step. Otherwise, it us generally not possible to find sources for each and every particular detail, even if the general principles are well-known. For instance, even simplifying a polynomial at the end of a longer example now requires sources in which the very same polynomial is simplified, which seems to be straightjacketing. Sławomir Biały (talk) 02:43, 14 March 2011 (UTC)

I think that the OR rule together with the Copyright law make coverage of mathematics (or any other subject) impossible. You have to think (commit 'original research') to do mathematics. The only alternative is to blindly copy from 'reliable' sources which violates copyright. Of course, such copying and the verification that the source is indeed reliable also require thought (OR). So the rule against OR is an absurdity which should be repealed.

The reason we have a rule against OR is to try to avoid disputes about what is correct reasoning by appealing to an outside source. Notice that in mathematics, this is usually only necessary when one or more of the disputing parties is a crank or troll. However, refusing to allow an edit on grounds that it is OR is ultimately just an excuse for rejecting what we think is false without having to get the agreement of a crank or troll. JRSpriggs (talk) 03:05, 14 March 2011 (UTC)

This one is fairly complicated. I don't think it true that, outside of mathematics, OR and copyright makes coverage impossible. The problem is that an allowable rephrasing in most fields becomes OR in mathematics, as even a change in notation does not fall in the "routine arithmetic calculation" exemption in Principles 11. However, an expert mathematician's edits may qualify as allowable per se under WP:SPS, but may fail WP:COI. This might lead to weird results as using the diff adding the material as a reference, but it seems to satisfy the rules. I'll comment there if I can think of anything sensible to say. — Arthur Rubin (talk) 04:33, 14 March 2011 (UTC)

To be more precise, if I make an edit to an article on (say) the Axiom of Choice which I consider obvious, and it's reverted as OR, another editor can restore it sourcing it to the diff. — Arthur Rubin (talk) 04:42, 14 March 2011 (UTC)

After David Eppstein and Geometry Guy have alerted ArbCom of concerns about unintended consequences of the proposed wording(s), some ArbCom members have declared that they need some time to think about this issue.

I have followed only a couple of the ArbCom proceedings, but reading those few proceedings, I have impressed with the conscientiousness and intelligence of its members --- it is like a committee made up of Geometry Guys who actually read and think before writing!

Mathematicians should not cluck like a brood of chicken littles on the ArbCom pages. Let us leave our most experienced and articulate volunteers, whose work on WP is known to and respected by some ArbCom members, to discuss calmly the proposals with them. As the original chicken little,  Kiefer.Wolfowitz  (Discussion) 08:49, 14 March 2011 (UTC)

JRSpriggs's comment describes my experience. The WP community is able to control tendentious editing by agreeing that some edits represent OR (often OR by synthesis).

I am worried that the proposed language may influence featured-article and good-article criteria, rendering mathematical articles ineligible if they include examples for lay readers or explain concepts using consensus explanations that cannot be sourced: for the latter, see the example on my talk page, which could be challenged as OR by synthesis, I fear.  Kiefer.Wolfowitz  (Discussion) 09:12, 14 March 2011 (UTC)

Alternative wording suggested by Kiefer.Wolfowitz

I (K.W.) suggest the following changes:

1. Change "arithmetic" to "mathematical".
2. Add "providing context using standard mathematical results or providing elementary examples" to the list of accepted editing activities.
3. Add the following: "Explanations, which use routine mathematical results or reasoning, are not considered "original research by synthesis", even if such routine mathematics are not referenced specifically for the application discussed: The mathematical results should be capable of routine referencing (easily referenced if challenged) and the article's editing should display an overwhelming agreement both that such derivations are routine (rather than original research) and that (to avoid simple OR proofs of important results) the result is unsurprising."

I would suggest that we strive for consensus language here, and then ask our leaders to communicate consensus suggestions to the ArbCom page.  Kiefer.Wolfowitz  (Discussion) 11:34, 14 March 2011 (UTC)

Elen asks for alternative wording

If you guys can get together a variant form of words quickly, and post it on the proposed decision talkpage, it can be put in as an alternative.

Providing examples is not a problem - slotting in different variables to a sourced method is not OR, nor is it really deriving from first principles. Glossing should not be a problem if you have some referencing to show the general applicability of the gloss. I do have concerns with the example Kiefer gave on his talkpage [1], but I'd have more problems with the old version that the new, assuming that somewhere in the sources cited are the two equations, the definition of limits, and the information about strictness in relation to Minkowski sum. It is the old example which seems to have lots of derivations without referencing. --Elen of the Roads (talk) 14:20, 14 March 2011 (UTC)

I refactored and emboldened Elen's request for help, which is most important!  Kiefer.Wolfowitz  (Discussion) 15:12, 14 March 2011 (UTC)

@Elen, I updated the references in the example. For sequential convergence, the most elementary exposition is John Fridy's Analysis:The Theory of Calculus, and I am sure that the results are available in the Green & Heller reference (and probably Arrow & Hahn, Mas-Colell, etc.: I am away from my references this week). Certainly the strictness of the Minkowski sum is covered by Rockafellar (pages given) and also Schneider: I believe that Rockafellar has a sequential discussion of limits, also. The equation (inclusion) appears in Ekeland (pages given).  Kiefer.Wolfowitz  (Discussion) 14:42, 14 March 2011 (UTC)

I made this proposal. It would be best for others to strive for a consensus statement, following Elen's very kind and thoughtful statement of interest.  Kiefer.Wolfowitz  (Discussion) 14:46, 14 March 2011 (UTC)

I've only had a chance to skim most of the Arbcom case, but it seems like the main issue is the detailed derivations from first principles. The language used should more closely reflect the actual problem, rather than casting an overly broad net against anything that could possibly be construed as original research.Sławomir Biały (talk) 16:10, 14 March 2011 (UTC)

I have posted an alternative wording on the workshop page. Geometry guy 22:10, 14 March 2011 (UTC)

Teaching and OR

I don't have much to say about the MHP apart from thanking the people who have commented on the arbcom page. I did want to say something related. Lately, after discussion at WT:TECHNICAL and WT:NOR, and looking at WP:NOT, I have been thinking about the underlying issues that lead to these disagreements. I'm only thinking about articles at the advanced undergrad level and beyond here; articles on basic topics are less problematic because there are plenty of low-level references. But there are few references on advanced topics that are accessible to an untrained reader.

Three points:

• There's a tension between making "reference" articles that are primarily useful for people who already know the topic, and making "didactic" articles that help people who don't know the topic learn it. When WP:NOR is interpreted more strictly, that leads us to favor specialists over learners. WP:TECHNICAL, on the other hand, asks us to lean more towards learners, by explaining things in our own words, using analogies, and giving examples. These two policies are naturally opposed to each other.

• WP:NOT has the same opposition inside it, saying both that articles should not be written for specialists and that articles should not be written to teach people about the topic at hand. For example, it says both "A Wikipedia article should not be presented on the assumption that the reader is well versed in the topic's field." and "The purpose of Wikipedia is to present facts, not to teach subject matter.".

• These disagreements go back all the way to the founding of Wikipedia. There was never a time when all the articles "followed policy" after which time the articles began to "violate policy". Instead, the articles have always been in a state of flux, and the policies have never perfectly captured the balance between the goal to be a reference work and the goal to present material to students who are learning it for the first time.

I think that we do a reasonable job at balancing these things in our articles, both overall and in mathematics. My main point is that if we realize that Wikipedia's goals are sometimes in conflict with each other, it can help us find a middle ground. — Carl (CBM · talk) 13:43, 14 March 2011 (UTC)

Let's not forget IAR

Seems to me we are in danger of becoming too rule-obsessed, hierarchical and obsequious over this. If Arbcom produces a ruling which appears to prohibit simple explanatory examples in mathematics articles, then common sense tells us this cannot be what was intended - either Arbcom have mis-worded their statement or we have mis-interpreted it. As explanatory examples obviously improve the encyclopedia, IAR tells us we can use them anyway. At the same time, we can either ask Arbcom to clarify their ruling, or simply drop them a hint by awarding them a trout. Gandalf61 (talk) 15:50, 14 March 2011 (UTC)

This ruling, percolating through WP like phosphorous from a lava chamber (! ;) !), may make it impossible to get articles approved for feature article status, although it probably would have no effect on most articles.  Kiefer.Wolfowitz  (Discussion) 16:00, 14 March 2011 (UTC)

Personally, I don't think it's worth focusing on featured article status anyway. The goals of the FA wikiproject are not necessarily aligned with our goals, but that's OK. Wikipedia can accomodate both. — Carl (CBM · talk) 16:31, 14 March 2011 (UTC)

New wording

In response to comments made by editors from this WikiProject, Arbitrator Elen of the Roads has proposed an alternative wording of the principle, which caused concern here, for other arbitrators to consider and vote upon. You can comment on the proposed principles at Wikipedia_talk:Arbitration/Requests/Case/Monty_Hall_problem/Proposed_decision. Geometry guy 23:42, 14 March 2011 (UTC)

Thanks again for working with this. — Carl (CBM · talk)

The links being said to show Original Research

Regardless of the OR statement of principle that ArbCom may or may not adopt, I am concerned by what the examples of what they are claiming is OR in their statement of facts -- specifically the three claimed examples cited at Wikipedia:Arbitration/Requests/Case/Monty_Hall_problem/Proposed_decision#Article_has_been_subject_of_original_research Article has been subject of original research.

As far as I can see (more detail on the decision talk page here, here, and here), none of these three examples properly constitute original research.

It seems to me that this is no small issue, because the examples Arbcom cite are going to be the most direct operational indication of what they consider to be OR, and how they mean whatever principles they adopt to be interpreted.

I'd welcome second and further opinions on these examples, and whether we think they are OR or not, because the Arbcom members are refusing to engage on the merits of these links; yet are still happily voting for the proposition. Jheald (talk) 09:55, 15 March 2011 (UTC)

This is extremely concerning for me as well. There are thousands of words on that talk page detailing how horrible these words are, and no one except Elen (which is epically wrong bout what is OR and what isn't) seems to bother reading these concerns. Perhaps we should write message on the arbitrator's talk page to address the concerns raised on the talk page about how the all the proposed wordings are utterly horrible. Headbomb {talk / contribs / physics / books} 21:53, 16 March 2011 (UTC)

WP:CALC seems open to improvement

Even some ArbCom members refused to vote on using its exact current wording in their principles (which they are still struggling to formulate in that respect). So, clearly WP:CALC is deficient. I suggest you guys take this opportunity to improve the wording in the policy, so you won't have to put out this kind of fire in the future. All the best, Tijfo098 (talk) 18:27, 16 March 2011 (UTC)

I don't think wp:calc was ever meant to be used as a guideline for quantitative disciplines, rather the sort of routine calculations that one does in history and biography articles for instance. It's obviously insufficient to cover more mathematical articles, but I don't know if it's worth emending the policy, or just clarifying its intended scope: it doesn't exclude things that aren't just pure arithmetic from the more quantitative articles, provided no original research is committed. Sławomir Biały (talk) 19:00, 16 March 2011 (UTC)

Clarifying its scope would be my choice too. We don't want editors to start making inferences in other article claiming that "A implies B" from RS1 "B implies C" from RS2 therefore ... because in social science in particular B from RS1 is often not quite the same as B from RS2. Yes, math and a few closely related formal sciences are an epistemic exception, where inferences like the above are possible without much "OR". But I'm not sure how to say that without being too pretentious or too insulting. The current arbcom wording, something along the lines of: it's fine if it has consensus and nobody asks for citation, seems better, and has the elephant standing for it. -) Tijfo098 (talk) 23:29, 16 March 2011 (UTC)

Latest proposal

There is a new proposed wording. It works for me. Does anyone else have any thoughts about it? Sławomir Biały (talk) 14:11, 17 March 2011 (UTC)

It leaves matrix calculus as a dead article, but that may be for the best. The only sourced notation so far provided is misleading, and (IMHO) unusable for real mathematics. — Arthur Rubin (talk) 15:00, 17 March 2011 (UTC)

The essential thing I think that WP:CALC is missing is a reiteration that the methods must not be novel and it must not support a novel conclusion. Basically it shouldn't support original research. An example illustrating a method or a straightforward indication of how a result is obtained is okay. Saying "it is okay because I have only used standard methods to derive it, it is straightforward mathematics" is an immediate red flag. Dmcq (talk) 15:10, 17 March 2011 (UTC)

I see WP:CALC as a separate entity from original research in mathematics. That's meant to cover routine "everyday" calculations (like in a biography or history article), rather than derivations in quantitative articles. I think the Arbitration Committee has, with this last proposal, finally realized that WP:CALC is ill-suited as a criteria for original research in mathematics. There seems to be some support here for clarifying the intended scope of WP:CALC. Sławomir Biały (talk) 15:17, 17 March 2011 (UTC)

Decision

The decision has been publicized.  Kiefer.Wolfowitz  (Discussion) 00:44, 25 March 2011 (UTC)

Square bracket in a link

I was thinking about puttting in a link to interval (mathematics) for things like (−π, π] because people keep 'correcting' it to two round brackets. However there is a little problem in that one then gets three right square brackets or else one has to put in a space or the right bracket is black as in (−π, π]. Any ideas on a good way of getting it looking right thanks? Dmcq (talk)

Create a set of templates {{left half-open interval}}, {{right half-open interval}}, etc. Makes it more difficult to "correct" them (and more obvious why they shouldn't be). —Ruud 16:07, 14 March 2011 (UTC)

well you could always use $(-\pi ,\pi ]$ as long as you're not to picking about Latex within a text block.--Kmhkmh (talk) 16:10, 14 March 2011 (UTC)

Use <nowiki> tags, or any other delimiters: (−π, π] Nageh (talk) 16:20, 14 March 2011 (UTC)

Thanks everybody. I think I'll go with the nowiki or perhaps nobreak so I don't even need the &nbsp; Dmcq (talk) 16:41, 14 March 2011 (UTC)

Just been thinking about the templates left half-open interval etc. It does have the advantage it can be used for later instances that shouldn't be linked. Dmcq (talk) 17:18, 14 March 2011 (UTC)

We had this discussion a while ago (in 2003 or so?) and one of the things that got decided was that the brackets in asymmetric intervals should be enclosed within "nowiki" tags. Has that been neglected lately? Michael Hardy (talk) 17:22, 14 March 2011 (UTC)

I'm afraid so. I have difficulty with last week never mind eight years ago :) Anyway I just set up {{open-closed}} and {{closed-open}} - my first foray into creating templates! I guess I should stick something about it in a math help with formatting page if people like them else just the <nowiki> method. Dmcq (talk) 18:40, 14 March 2011 (UTC)

And I've tried them out on atan2. I've used {{math}} to format the contents rather than just {{nowrap}} as I think π looks better than π. Dmcq (talk) 22:10, 14 March 2011 (UTC)

A similar problem occurs when one tries to put a link to one of our articles into the comment part of an external link. See this edit to Monetary policy where Mattdarst tried to insert a link to Credit Channel into the comment field of an external link where the comment read ""THE STOCK OF CLOSED BANK DEPOSITS, DURATION OF CREDIT CHANNEL EFFECTS, AND THE PERSISTENCE OF THE U.S. GREAT DEPRESSION"". It caused the external link to terminate prematurely. JRSpriggs (talk) 01:27, 15 March 2011 (UTC)

I've seen bots "correct" semi-open intervals and similar mathematical notations. I'm aware of the nowiki solution, but seem to recall that this doesn't always discourage the more vigilant bots. A template solution seems best. Sławomir Biały (talk) 12:35, 15 March 2011 (UTC)

Which bots? Michael Hardy (talk) 18:04, 17 March 2011 (UTC)

Unfortunately, I no longer remember. I also don't know if this issue has since been fixed. It was a few years back that I noticed that some bots would sometimes parse mathematical markup incorrectly, and attempt to "correct" the problem. Sławomir Biały (talk) 18:33, 17 March 2011 (UTC)

I've set up {{open-open}} and {{closed-closed}} as well to complete the set. I hadn't thought about it before but they must be doing some special work to stop things like [1, 2] causing trouble. Anyway I use &#91; and &#93; instead in the templates. Dmcq (talk) 13:36, 15 March 2011 (UTC)

As an example {{open-closed|−π, π}} produces (−π, π] and the eventual code sent out to do this is <span class="texhtml" style="white-space: nowrap;">(−π, π]</span> Dmcq (talk) 14:07, 15 March 2011 (UTC)

I have formatted the argument (complex analysis) article using math type formatting for any inline mathematics throughout. I also set up a {{mvar}} template to do individual variables easily. Any comments gratefully received. Dmcq (talk) 15:14, 21 March 2011 (UTC)

Florentin Smarandache

The article Florentin Smarandache has been nominated for deletion for a 2nd time (AfD here); members of this project may be interested in commenting. Mlm42 (talk) 18:35, 17 March 2011 (UTC)

At least one editor there seems to be laboring under the impression that the subject of that article is a very influential mathematician. It is very frustrating arguing with this person. Sławomir Biały (talk) 01:31, 22 March 2011 (UTC)

Logarithm is up for FAC

Opine here. Jakob.scholbach (talk) 17:59, 21 March 2011 (UTC)

Probability notations

On the suggestion of one of the editors interested in the arbitration on Monty Hall problem, I started a little essay on mathematical notation in probability theory and its applications. First draft is at essay on probability notation; you can talk about it at: probability notation essay-talk. Comments are welcome! Especially if you can tell me that this is all superfluous because it's been done, and done better, before. Richard Gill (talk) 18:21, 21 March 2011 (UTC)

Normal numbers page is broken

I was looking at Normal number and there seems to have been an edit by a well-meaning anonymous user which broke the markup. I would revert his edits, but I don't know enough about the subject to know if he was correcting an error in the article and made a mistake. Could someone with some more math skills than I take at look at the last two edits? Thanks.

DavidSol (talk) 01:34, 22 March 2011 (UTC)

I just noticed that Lindelof space was broken in much the same way for no apparent reason. It appeared to be caused by an edit adding a Korean interwiki, but now I wonder instead if it's a software problem. Sławomir Biały (talk) 01:43, 22 March 2011 (UTC)

Please note: Lindelöf space and Lindeloef are essentially identical spellings, whereas Lindelof is different (and incorrect). So if you can't type the umlaut, then write Lindeloef. Michael Hardy (talk) 02:51, 22 March 2011 (UTC)

At the time I was more concerned with having a link to the right place than valid typography, Michael. And yes, I can't type an umlaut at the moment. Sławomir Biały (talk) 10:46, 22 March 2011 (UTC)

I think it's just the wiki software getting confused. The anon at normal number undid his/her own change. The article got better after I tried purging it. I've seen similar issues with other unrelated pages today as well. —David Eppstein (talk) 01:45, 22 March 2011 (UTC)

Duffin–Schaeffer conjecture

I've put an "orphan" tag on Duffin–Schaeffer conjecture, so get busy and think of a few (dozen) articles that should link to it. Michael Hardy (talk) 02:49, 22 March 2011 (UTC)

DYK: Criss-cross algorithm for linear optimization

A new article on the Criss-cross algorithm for linear optimization has been nominated for Did You Know?:

• ... that, while the criss-cross algorithm visits all 8 corners of a cube when started at a worst corner, it visits only 3 more corners when started at a random corner?

Corrections and comments are especially welcome. Best regards,  Kiefer.Wolfowitz  (Discussion) 03:48, 22 March 2011 (UTC)

Article should be in mathematics project?

Pick's theorem seems pretty applicable to your project. You might want to examine it and tag it if appropriate. Cliff (talk) 05:50, 22 March 2011 (UTC)

I added the project rating to the discussion page. Sławomir Biały (talk) 11:12, 22 March 2011 (UTC)

The article was already on List of mathematics articles, as well. That is the master list of articles in the project. — Carl (CBM · talk) 11:18, 22 March 2011 (UTC)

MathJax update

Just to let you know, I have updated my mathJax user script to recent version 1.1 of MathJax. Notable change is the support for webfonts via CDN (i.e., no local font installation requirements). Details at the user script documentation page. Feedback welcome. Nageh (talk) 21:37, 23 March 2011 (UTC)

Minimal negation operator

While this unreferenced article looks cool, I can't find anything in google books to support it. WP:OR? Tijfo098 (talk) 05:21, 25 March 2011 (UTC)

The talk page there seem to indicated I'm right (the creator is now indef blocked for something similar.) Tijfo098 (talk) 05:23, 25 March 2011 (UTC)

Looks pretty original to me. — Arthur Rubin (talk) 06:32, 25 March 2011 (UTC)

Wow. A Jon Awbrey article lavishly illustrated by Lipedia. Unfortunately it appears that Peirce never wrote about anything else with a similar name. In that case we might have hit a logic crankery jackpot. Let's take this to AfD. If this was a real notable topic, some mathematician would have noticed through all the years and especially since 11 August. Hans Adler 06:59, 25 March 2011 (UTC)

I just had a look through Awbrey's contributions and the following just strike me as being iffy. Some are redirects, others are just bits of Pierce's writings that probably could be a paragraph somewhere else I think. Things like boolean domain I just cant see the point of a separate article from boolean but logical matrix I can see is probably okay. Others like sign relation I just plain don't understand. Semeiotic seems to be some variant spelling of Semiotic by Charles Saunders Pierce.

• Ampheck
• Boolean domain
• Boolean-valued function
• Categorical set theory
• Comprehension (logic)
• Continuous predicate
• Descriptive science
• Entitative graph
• Finitary boolean function
• Formal sciences
• Hypostatic abstraction
• Hypostatic object
• Logic of Relatives (1870)
• Logic of Relatives (1883)
• Logic of information
• Logic of relatives
• Logical graph
• Logical matrix
• Multigrade operator
• Normative science
• Parametric operator
• Pragmatic maxim
• Prescisive abstraction
• Projection (mathematics)
• Projection (set theory)
• Relation construction
• Relation reduction
• Relative term
• Semeiotic
• Semiotic information theory
• Sign relation
• Sole sufficient operator
• Zeroth-order logic

I guess most of these are perfectly okay but is there some that even someone familiar with Charles Saunders Pierce isn't familiar with or thinks is unnecessary? Dmcq (talk) 18:50, 25 March 2011 (UTC)

I recognize most of these terms as being used by Peirce in his logical writings. Peirce's preferred spelling "semiotic" as "semeiotic", as you suspected.

I have only an amateur understanding of his logic. Peirce had an anti-Fisherian approach to terminology, where he thought it bad sport to use an existing word for a new idea (and would have denounced the Fisherian vice of switching between the two, e.g. "information", etc.). This explains why Peirce introduced so much novel terminology, and why he was less successful as a salesman than Fisher.  Kiefer.Wolfowitz  (Discussion) 20:47, 26 March 2011 (UTC)

Logical graph is a nebulous article that could use work. I think the term existential graph has been used more recently, and perhaps even by Pierce. Tijfo098 (talk) 04:09, 30 March 2011 (UTC)

Currently on the Main Page ...

... is John Milnor, who has been awarded the Abel Prize. The article is OK as such, but could obviously be expanded quite a bit. Charles Matthews (talk) 09:43, 25 March 2011 (UTC)

Drinker's paradox

There seems to be a bit of hostility to the newly-listed article Drinker's paradox on the article's discussion page. Various editors are grumbling about deletion, original research, etc. I thought perhaps someone in the project should investigate. Sławomir Biały (talk) 12:16, 25 March 2011 (UTC)

You mean Drinker paradox, right? Most of the opposition seems to be about the title; it is argued that it is not a "paradox". Which, as far as it goes, I would agree with, but it can still be an interesting and possibly notable illustration of some tension between the mathematical tradition of using English to express logical formulae, and what English sentences usually mean in an everyday setting. –Henning Makholm (talk) 12:31, 25 March 2011 (UTC)

This sort of thing is covered by WP:COMMONNAME. This is clearly the common name as it is found in a number of books, which by the way also means it will not be deleted. Whether it is actually a paradox or not is only slightly relevant and certainly would not trump the common name criterion in this case. Lots of people have this funny idea that a title is the article whereas it is simply a way to find the article which is what common name is all about. Dmcq (talk) 13:00, 25 March 2011 (UTC)

Could you add references to some of that number of books to the article? I found it strange that the only source it gives is to Smullyan's book, which according to the article itself called it the "drinking principle" rather than the "drinker paradox". So the title is currently unsourced, which is not good when it has been seen to cause contention. –Henning Makholm (talk) 13:31, 25 March 2011 (UTC)

maybe make a redirect from "drinker principle" too? regards "difference between [propositional logic] and what English sentences usually mean": no. there is no difference there. the grammar, syntax,, AND semantics is exactly the same; it is a perfectly ordinary sentence and the meaning of it is no different whether you address it with formal logic or with "ordinary interpretation". the difference lies in what happens after the sentence has been linguistically parsed and what not converted into formal relations. up to that point nothing has diverged, and at that point you will have the same thing in either case. once in the form of formal relations, however, differences of two types are introduced: 1.) implicit assumptions, and 2.) rules of logical manipulation. regarding 2.), a person untrained in logic is more likely to use the rules given to them by instinct, which are incorrect. well, in a certain sense. they are not designed to be correct, they are designed to be quick, and to be decent approximations, and to the end they serve well. but, fundamentally, there are incorrect. regarding 1.) the sentence as is gives incomplete information, from a logical point of view, eve. do you mean just right now? this round? ever? here logic differs from conventional usage, in filling in this missing information: logic always refers to the instant, unless otherwise explicitly noted. whereas conventionally we fill in this missing information with "...ever...". and this is how one gets to the difference in conclusions. they are both actually correct, it is simply a matter of how you fill in the missing information. Kevin Baas^talk 13:40, 25 March 2011 (UTC)

I suppose in that sense it is a "paradox", because most (if not all) so-called "paradoxes" really just appear as such because there was a missing piece of information that we didn't realize was missing. really when you include the missing information you see that there is no paradox at all. nature simply does not do "paradoxes". Kevin Baas^talk 13:43, 25 March 2011 (UTC)

I just tried out "Drinker paradox" | "Drinker principle" in Google books and scholar and there's two pages of references, some to principle, some to paradox and various ones having a 's after the first word! At least there's paradox ones predating the article, I keep worrying that somebody will stick a wrong title in and that takes over from what people were actually using :) Dmcq (talk) 14:14, 25 March 2011 (UTC)

A paradox is an *apparent* nonsensical or *apparently* false statement, which on careful consideration can be seen to be correct after all. So it seems to me that the drinker paradox is a paradox indeed! Or: it shows that ordinary logic is maybe not so appropriate to logical reasoning in everyday life, as most of us thought. Quite a few paradoxes in mathematics can be seen as symptomatic of inadequacies of the "usual axioms* of present day mathematics. But either way, this is the sort of thing that is usually called a paradox, so I see no problem at all with the nomenclature. Richard Gill (talk) 16:07, 25 March 2011 (UTC)

The term paradox is fairly informal. Any puzzling statement may be called a paradox. Paradoxes are not a big deal, because they can be resolved. A paradox that is a big deal, and that cannot be resolved (easily) is called an antinomy. In order to resolve an antinomy, one has to forsake an important part of one's intellectual heritage. The Barber paradox is resolved by accepting that, well, there just isn't such a village with such a barber. In order to resolve an antinomy, one may have to reject long standing accepted fundamental principles. Over the course of history antinomies eventually become mere paradoxes because our knowledge and language catches up with them.Greg Bard (talk) 16:37, 25 March 2011 (UTC)

Tai's method

Apparently someone rediscovered the trapezoidal rule and managed to get it published. See Tai's method. Just an article about the trapezoidal rule under another name? Or an article about how something weird like that can happen? Either way, is the article in some way worth keeping? Michael Hardy (talk) 03:49, 26 March 2011 (UTC)

It is claimed that more than 100 works cite the article. Michael Hardy (talk) 03:53, 26 March 2011 (UTC)

If the claimed citations do check out, I'd say it is ok to keep it. Also imho this is partially not a math issue, but a question for the applied field/domain in which the "discovery" was made (here biology, medicine I guess). Many apllied sciences have there own names and versions of math theorems and though I can't think of another example on top of my head, I'm pretty sure there is quite a number of such cases. If the name/method in question is well known/established enough (not among the math community but in the domain in which it originated), WP should provide an article or a redirect. Which of the 2 options is better needs to be judged on a case by case basis.--Kmhkmh (talk) 13:21, 26 March 2011 (UTC)

Use of maths symbols in html

The 'Math and logic' symbols in the editor include a load of special symbols. Is it okay to use all these in maths articles? For instance can I say ℝ rather than $\mathbb {R}$ in inline maths? And by the way I don't believe I should bold that as in ℝ, would that be right too? Dmcq (talk) 12:56, 26 March 2011 (UTC)

The WP:MOSMATH, which can always be revisited, recommends the ordinary boldface R to the blackboard bold ℝ, due to the latter being potentially unsupported in some browser configurations. I agree that ℝ is wrong (in fact, I don't think this can be typeset in LaTeX easily either). I really don't like the way inline PNG looks in the middle of running text, so I would avoid using the <math> form in any case. Sławomir Biały (talk) 13:41, 26 March 2011 (UTC)

Well I guess I better raise something at MOSMATH then because it seems silly to have them prompted in the editor and then deprecate them. I think I'd prefer to have the text and the stand along formulae match up better and having those symbols available would help greatly with that but it really needs to be checked. Dmcq (talk) 15:49, 26 March 2011 (UTC)

"Inline" as opposed to "displayed" use of TeX within Wikipedia has always been problematic. Things like the following can happen:

blah blah blah $e^{x^{3}}\,$ blah blah blah.

Obviously the e should be at the same level as the surrounding text and the x³ should be in superscript, but that's not what happens. Also on some browsers, the part in math tags looks comically gigantic. You can also get siuations like this:

There are examples (such as $\int {\frac {\sin x}{x}}\,dx$

) in which etc. etc. etc.

The right parenthesis is on the next line! It also happens with periods, commas, etc. "Displayed" TeX, on the other hand, generally looks quite good:

$\int _{0}^{x}{\frac {\sin u}{u}}\,du.$

So I generally prefer non-TeX notation in an "inline" setting. Michael Hardy (talk) 00:54, 27 March 2011 (UTC)

N-dimensional space

Over at Talk:N-dimensional space we're having a traditional merging discussion. The issue is that these articles (and probably others) all contain redundant material: Space (mathematics), Vector space, Dimension, Dimension (vector space), Basis (linear algebra), Euclidean space, Manifold (mathematics), N-dimensional space. So I thought I'd bring it up here.

My opinion: Each kind of space (vector, Euclidean, manifold, etc.) obviously deserves its own article. Additionally the Space (mathematics) and Dimension articles seem useful as catalogues/overviews. But Dimension (vector space) could be merged into Basis (linear algebra) and/or Vector space, and N-dimensional space could be merged into Space (mathematics) and/or Dimension.

Any comments? Mgnbar (talk) 16:39, 26 March 2011 (UTC)

Special case

Special case is currently a stub article that could use a lot of work, both within the article and in other articles that should link to it. Get busy. Michael Hardy (talk) 00:45, 27 March 2011 (UTC)

QUERY - Aren't changes on a page supposed to be reported????????????????

Hi! I use Wikipedia very often and thought for sure that a policy of yours was to add in a "page history" page that showed any changes to an article and by whom for that page?

I ask because your page on Summation had early in its write-up an image of an example of Induction ( http://upload.wikimedia.org/math/5/d/1/5d1ba66a7aca2c258985399ff22410ef.png ) ... odd that that very image wasn't there just a few days ago for another image that was the exact same equation but in different form.

I looked for the history of why and who changed that image because its odd I been coincidently writing a paper on the example of Induction used of the original image and linking this very page for that image and sending that paper to leading Set Theory specialists and other university piers and that image was very helpfull in dealing with the issues the paper regarded. Now suddenly someone changed the image to a different example of Induction and I find the timing very peculiar. It doesn't change anything about my paper except for it to be easier to understand for anyone needing to see the example of Induction I was using from here but is now changed. I only linked to the page on Summation.

Anyways, how did that image change on the Summation page without anyone ever knowing it happened or why in the pages history?? — Preceding unsigned comment added by G2thef (talk • contribs)

The history of summation is here. The sum you mention was put into the article on April 17, 2010, in exactly the same form it is there now. It is possible that some time in between then and now, someone changed it into the form you prefer and that is was then soon after changed back, but that sort of thing is much harder to find since it would take scanning all the changes to the article rather than simply doing a binary search. —David Eppstein (talk) 20:50, 27 March 2011 (UTC)

Montante's method

Is this a notable article? Jakob.scholbach (talk) 21:19, 27 March 2011 (UTC)

It's entirely unreferenced, and there are no google scholar hits. I am suspicious of the supposed origin of this algorithm as well: the attribution feels like self-promotion and original research. At any rate, there is a well-known fraction-free algorithm called the Bareiss algorithm from 1968 that predates the date of 1973 given here. As far as I can tell, the two algorithms are the same or very nearly the same. Sławomir Biały (talk) 21:34, 27 March 2011 (UTC)

Eswiki has an article about the supposed discoverer. Doesn't look quite like run-of-the-mill self-promotion (modulo my lack of knowledge of Spanish). Could possibly be a case of people naming the result after the one among several independent discoverers that they identify with the most. If it's really the same thing, it ought to redirect to a common article, which then should document the various names. –Henning Makholm (talk) 22:08, 27 March 2011 (UTC)

But there is no evidence of anyone calling it Montante's method, and I can't find any reference to Montante regarding the method. The interview here refers to apparently unpublished papers by Montante Pardo, in which he apparently calls it the "Método Montante". That's more than a little questionable, and does look very much like self-promotion and original research to me. Sławomir Biały (talk) 22:21, 27 March 2011 (UTC)

There are some Google hits in Spanish that look like the algorithm is taught under that name at various institutions in (mostly) Mexico: [2] [3] [4] [5]. These links appear to be too different to all be self-promotion.

It feels at least plausible that some Spanish-speaking project member would be able to dig up a reliable source for the name. Anyone have access to a collection of Mexican linear algebra textbooks? –Henning Makholm (talk) 22:52, 27 March 2011 (UTC)

Perhaps Google scholar and Google books don't index Spanish-language books, but there is an utter absence of any kind of relevant hits for "Metodo Montante" or "Montante's method", and variants in reliable published sources. This very algorithm appeared in a widely cited article by Bareiss five years before Montante allegedly came up with it. It seems to be a neologism that should be avoided. Sławomir Biały (talk) 23:09, 27 March 2011 (UTC)

So, should it be merged into the article on the Bareiss algorithm and attributed to him? JRSpriggs (talk) 09:30, 28 March 2011 (UTC)

Since the article seems to be of rather low quality, I nominated it for deletion. Jakob.scholbach (talk) 19:46, 31 March 2011 (UTC)

The assistance of WikiProject Mathematics requested

In looking over some project work I did for an undergrduate computing degree I noted that the academic supervising me had come up with what he called a 'slew' transform.

I've put a rough note in my userspace at Wikiversity (because of concerns about verifability here) The link is : http://en.wikiversity.org/wiki/User:ShakespeareFan00/Slew_transform

I'd appreciate someone from the WikiProject that understand 3D transformation stuff, to help provide a better citation , or indeed a creative commons licensed proof that will show what's stated is correct.

A 'slew' transform is a transform where 'distances' parrallel to an axes before a 'slew' are preserved, as opposed to a 'shear' where they are not.

I'm also trying to understand how to abstractly define a 'grid'. ( The best definition I can think of for 2D is that a 'grid' is a regular arrangement of points and lines that fills a plane.

For a 'cubic' style of grid, this regular arrangement can be more formally considered as a (Lattice Graph?) formed by the Cartesian product of 2 path graphs, representing lines perpendicular to each other. However, I'm thinking I need to put in some kind of constraint on where the grid points can be placed, and I'm not entirly sure how I specfiy that constraint in an abstract math way...

A 'polar' style of grid is however more complex, being the Cartesian product of a number of path graphs(?) with some kind of cycle graph , ( aka a Prism Graph?). Again some kind of constraint would need to be defined on where grid points can be placed..

And finally Has this sort of thing been done before in a textbook a math noob can understand? Sfan00 IMG (talk) 22:36, 27 March 2011 (UTC)

Regarding your first request, I am not clear exactly what the text on that page is trying to say, but I do not see how the examples can be correct, as they claim to modify the Z or Y axes but do nothing in those directions.

Regarding your second request, I think you want lattice (group).

Also, I suggest you ask these types of questions at Wikipedia:Reference desk/Mathematics in the future. Ozob (talk) 23:23, 27 March 2011 (UTC)

Thanks, re the 'slew' transform, can you leave some thoughts on my Wikiversity talk page ?

The context of the slew transform by the way in the original project was based on being able to convert a 'cubic' lattice to be transformed into a 'heaxagonal' or 'parallelogrammic lattice' one (in 2 dimensions).

Can you suggest a better way to describe what a slew transform appears to be doing, because I'd like to be able to explain it clearly to other people? Sfan00 IMG (talk) 09:52, 28 March 2011 (UTC)

You might find the explanation at Affine transformation#Affine transformation of the plane more helpful. The problem you mention is a special case of what is talked about there. Charles Matthews (talk) 10:17, 28 March 2011 (UTC)

Boolean algebra content forks?

We seem to have three articles on the same subject:

• Boolean logic
• Boolean algebra
• Boolean algebra (logic)

Does anyone know why? Are there any objective reasons to have three articles on this relatively elementary topic? — Carl (CBM · talk) 00:49, 29 March 2011 (UTC)

FWIW, I had redirected Boolean logic to Boolean algebra because (1) it was clear after doing my research for the lead for Boolean algebra that it's the same topic, and (2) there wasn't much in boolean logic that isn't in boolean algebra; Venn diagrams are in, and even google queries. The only thing that is not in are SQL queries, but there aren't conceptually different (not when restrcited to discussion about boolean operators), and there are thousands of programming languages (PL) out there, why SQL in particular? There's a CS-ish article on boolean expression that could cover that, but as you can see from its stubby nature, nobody (except StuRat) thought the syntactic difference in how boolean expressions are written in various PLs matter much. Tijfo098 (talk) 02:15, 29 March 2011 (UTC)

Enough reasons for merging Boolean logic yet again (!) can be seen at the talk page section Talk:Boolean_logic#Entire_Article_Rewrite and following section Talk:Boolean_logic#Problematic_article. Hans Adler pointed out at the time that StuRat was in violation of WP:OWN and WP:POVFORK. At the time StuRat had reverted the merging of his article by reviving it. Just now he's reverted Tijfo098's merge of it. In view of the many circumstances mitigating against this abysmally badly written article that StuRat owns, I've undone that revert. If StuRat wishes to reinstate his article a third time, we can offer him the choice of whether he prefers to be blocked for WP:OWN, WP:POVFORK, or WP:3RR. --Vaughan Pratt (talk) 03:26, 29 March 2011 (UTC)

Actually, StuRat promptly reverted my redirect, so I've started an official RfC on Talk:Boolean logic to attract opinion from previously uninvolved editors (and perhaps non-WPM editors as well to avoid some sort of systemic bias) as WP:DR recommends. Tijfo098 (talk) 05:55, 29 March 2011 (UTC)

Now, Boolean algebra (logic) needs more attention. There may be some material there worth merging (particularly the bibliography), but it seems too WP:NOTTEXTBOOK, e.g. explaining in detail how some expression is different if read as a Boolean rather than numeric. But even CS101 classes would give students a basic idea of type system. Tijfo098 (talk) 02:15, 29 March 2011 (UTC)

I do not own Boolean algebra (logic). It is true that I wrote more than 95% of it, but I have no objection to merging it with Boolean algebra. I'm all for anything to reduce the mess that the absurd proliferation of articles on Boolean algebra has become. --Vaughan Pratt (talk) 03:26, 29 March 2011 (UTC)

Actually, that article is well-written, so perhaps there is a way to keep it available to the public on WikiMedia servers. I don't now much about that, but I think Wikiversity would accept that page as-is. Although Wikiversity doesn't get the same google juice as Wikipedia, we could link it from Boolean algebra; I'm not sure what are the standards for that. Perhaps someone here has experience in that area? Tijfo098 (talk) 12:21, 29 March 2011 (UTC)

I was going to suggest as an alternative to move it to Introduction to Boolean algebra, but there's already yet another (introductory?) article on the same topic there. Actually, except for the lead, that article is nearly indentical to what Boolean algebra has now, so it's conceivable to move Boolean algebra (logic) over it. (Some care is needed to probably attributed the current content of [[bolean algebra, so, perhaps the current Intro should be moved to a subpage of Boolean algebra first.) Tijfo098 (talk) 09:48, 30 March 2011 (UTC)

I would guess it is in the natural order of things to delete Boolean algebra (logic) which (at first view) is subsumed by the new Boolean algebra as far as coverage is concerned and which extra details can be either added to the current "Boolean algebra" page or moved to specialized pages. However, it would be a pity to just dispatch its contents and delete it. So maybe, as it was suggested above by Tijfo098, that might be a good article to Wikiversity (that I don't know well actually how it works but that might be an alternative if some people think it is relevant). --Hugo Herbelin (talk) 20:19, 30 March 2011 (UTC)

There are several options:

• It could fill in wikiversity:Topic:Computer logic#Boolean Algebra, although I guess it is just too big for that.
• It could replace wikiversity:Boolean algebra (an abandoned page with nothing worth preserving).
• It could make a new chapter of wikibooks:Formal Logic.

I guess the second option would be best because that's an isolated page where it wouldn't be immediately surrounded by inferior stuff. Another option would be to move it to Citizendium. It doesn't have a Boolean algebra article yet. Of course in none of these locations it would get much attention. Hans Adler 20:46, 30 March 2011 (UTC)

The second option is fine by me. The upshot as I understand it is that Boolean algebra (logic) would (for now) become merely a redirect to Boolean algebra (later it might be expanded to Main article status parallel to Boolean algebra (structure). Its former text can go to wikiversity:Boolean algebra if that's kosher according to everyone involved. It's fine by me---as I said, although I wrote almost all of it, I don't own it, Wikipedia does. Or maybe it does: does Wikipedia continue to own text that has been deleted? There should be a mechanism whereby Wikipedia abandons deleted text after a suitable grace period in order to allow others to claim or reclaim it.

While on the subject of lightening up, I propose to put a merge tag on Boolean algebras canonically defined aimed at merging its source-able parts into Boolean algebra (structure) which is in dire need of more substantive material.

In the opposite direction, I'm considering writing a new article Boolean algebra (presentations) as a Main Article covering the many presentations of both Boolean operations (featuring in particular Post's completeness characterization as it appears in Boolean algebras canonically defined, along with complexity results about relative succinctness of different bases) and Boolean axiomatizations (featuring complemented distributive lattices and Boolean rings and why both are important, but also listing some of the more impressively succinct axiomatizations such as Huntington's axiom, Robbins's axiom, Wolfram's axiom, etc.). Boolean algebra is unusual among equational theories in having a great many presentations. Suggestions, objections, etc.? --Vaughan Pratt (talk) 00:57, 31 March 2011 (UTC)

Looking again at Boolean algebra (logic) I notice a section on derivation that could form the nucleus of another Main-article subtopic of Boolean algebra, namely Boolean algebra (proof systems) or something like that. --Vaughan Pratt (talk) 01:00, 31 March 2011 (UTC)

I think they should rather be called something like proof systems in Boolean algebra or presentations of Boolean algebras. If they're sourceable, that is, and not original synthesis. --Trovatore (talk) 01:09, 31 March 2011 (UTC)

I think that a List of equivalent definitions of Boolean algebras (or whatever the title) would be very useful and I would indeed recommend it to be not too much pure original research nor too much textbook-style (and possibly not at all of this kind). Such an article could typically also include non-equational, e.g. order-based presentations.

About a "proof system" article based on Boolean algebra (logic)#Derivations, I'm a bit skeptical. Part of this section should better go to a new page equational reasoning which (in my opinion inappropriately) links to universal algebra but which I think deserves both a larger and more operational approach, for instance by connecting it to rewriting.

I don't know what a more-senior-than-me wikipedian would say here, but my impression is that wikipedia also needs experts like you for consolidating the existing articles and for weaving more connections between articles. An easy road map in this direction would precisely be to merge the "canonically" article, without losing the technical content (creating e.g. an Examples of Boolean algebras subtopic) and ideally adding the new technical contents mentioned in previous discussions: atomicity, completeness, freeness, saturation. --Hugo Herbelin (talk) 23:11, 31 March 2011 (UTC)

Jacob Barnett

There is a deletion discussion under the auspices of our project that could benefit from its input. Sławomir Biały (talk) 00:21, 31 March 2011 (UTC)

Fourth Dimension

An editor is insisting in marking the lead of Fourth dimension as dubious in "In mathematics, the fourth dimension, or a four-dimensional ("4D") space,^{[dubious – discuss]} is an abstract concept derived by generalizing the rules of three-dimensional space". They say a four dimensional space could be any sort of space not necessarily Euclidean whereas others have said it referes in this instance to an extension of Euclidean 3-space. I would like to remove the dubious tag or otherwise resolve this. This is a bit similar I guess to the N-dimensional space business mentioned in a section above but as far as I can see there has been no real follow up to that, also I think they are a bit different in that N-dimensional space is actually used for many other things like configuration spaces whereas four-dimensional space is rather specific. Talk is at Talk:Fourth dimension#Title?. Dmcq (talk) 11:00, 31 March 2011 (UTC)

A mathematician could use the term 4-dimensional space in any discussion of a "space" that has "dimension" 4. For example, a vector space (over any field) with a basis consisting of 4 elements, a manifold whose charts map to R⁴, a manifold whose charts map to C⁴, a topological space of Hausdorff dimension 4, etc. So I feel strongly that 4-dimesional space should not be restricted to 4-dimensional Euclidean space. Mgnbar (talk) 12:57, 31 March 2011 (UTC)

The definite article seems out of place in that article's lede. CRGreathouse (t | c) 13:12, 31 March 2011 (UTC)

My understanding is that it's a historical usage, and the name of the article was taken from the book The Fourth Dimension by Charles Hinton (1912). — Carl (CBM · talk) 13:14, 31 March 2011 (UTC)

@Mngbar: If you ask a mathematician about "a point in 4-dimensional space", with no qualifiers and not saying "a four dimensional space", she will immediately assume you mean 4D Euclidean space. The term "4-dimensional space" as a proper noun is completely tied to Euclidean spaces in ordinary mathematical usage. We have to add other words to make it clear when we mean some other sort of four-dimensional space. — Carl (CBM · talk) 13:14, 31 March 2011 (UTC)

You raise a good point. Out of context, it would be unlikely for the mathematician to be referring to a particular complex manifold or topological space. However, I argue that "a point in 4-dimensional space" would just as commonly refer to an element of a four-dimensional vector space. In teaching, we often draw pictures of vector spaces, even when we have not assumed any Euclidean structure on them. Furthermore, a major point of contention at Talk:Fourth dimension is whether "four-dimensional space" should default to Euclidean or Minkowski space. There is a strong physics influence here, and maybe there should be. Mgnbar (talk) 13:43, 31 March 2011 (UTC)

Looking at the lead again the 'a' in 'a four dimensional space' looks out of place to me but the 'the' in 'the fourth dimension' is correct in the context of referring to 4 dimensional Euclidean space. The lead does talk about that physics deals with four dimensional spacetime but doesn't say strongly enough that the article is just dealing with a mathematical space rather than spacetime. The fourth dimension is also referred to in things like 'The Time Machine' where they mean something like a four dimensional Euclidean space where we are confined to a layer like in Abbot's book Flatland rather than anything like the modern conception of spacetime. Dmcq (talk) 20:44, 31 March 2011 (UTC)

Lightstone

A. H. Lightstone is on sale here: http://en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/A._H._Lightstone Tkuvho (talk) 15:20, 31 March 2011 (UTC)

Gauss–Codazzi equations vs. Gauss–Codazzi equations (relativity)

I have no idea what these two are about exactly, but these two articles seems to be about the same thing. Opinions on what should be done? Headbomb {talk / contribs / physics / books} 19:16, 31 March 2011 (UTC)

They're the same, but both articles suffer from irreconcilable notational incompatibility. Sławomir Biały (talk) 21:35, 31 March 2011 (UTC)

Making sense of 0.000...01

Our page http://en.wikipedia.org/wiki/Talk:0.999.../FAQ lists a number of frequently asked questions about 0.999... One of the answers to these questions deals with the "number" 0.000...01 (with an implied infinity of zeros before the last digit). The answer asserts, correctly, that this number is meaningless as a real decimal. I added a brief parenthetical comment here to the effect that one can make sense of such a number in a proper extension of R, providing a link to a page where this is discussed. The parenthetical remark was apparently too much for the guardians of purity at 0.999... and was reverted, most recently here. I would appreciate some input. Tkuvho (talk) 20:24, 31 March 2011 (UTC)

I think that is likely to just confuse people more. I don't have anything against the hyperreals, but I think that when people are already confused about something that's part of the grade school curriculum (real decimal expansions), we should be particularly hesitant to point them at even more difficult things that are not even part of the usual undergraduate curriculum (hyperreal decimal expansions). So I think the point of the FAQ is to be very simplistic. The article itself does discuss infinitesimals, as I think it should. — Carl (CBM · talk) 20:30, 31 March 2011 (UTC)

Are infinite decimals part of the grade school curriculum?? You are lucky if you get them in high school in many cases. The purpose of a FAQ page is not to address a particularly young segment of our readership, but to attempt to answer typical questions that might arise on the talk page. A number of inexperienced editors have reacted with interest to the suggestion that infinitesimals have a role to play here. Frankly, I don't see why the talk page is any less of a legitimate place to discuss infinitesimals than the 0.999... page itself. Tkuvho (talk) 21:00, 31 March 2011 (UTC)

I have seen grade school curricula with the fact that 0.999... = 1 (specifically, the 10x - x = 9x proof). Ozob (talk) 21:28, 31 March 2011 (UTC)

You mean, "the 10x - x = 9 proof". --Boris Tsirelson (talk) 07:01, 1 April 2011 (UTC)

The fact that only rational numbers have repeating decimal expansion, and the algorithm for finding the corresponding rational from such an expansion, are common topics. Here is an NCTM worksheet that puts that skill in middle school. [6]. — Carl (CBM · talk) 21:47, 31 March 2011 (UTC)

Those are extremely useful formulas, indeed. From the point of view of a wider continuum, they hold up to an infinitesimal error if the infinity of periods is interpreted in terms of an infinite hypernatural. From the real view point, all such infinitesimal differences are erased by an application of limit or standard part. None of this contradicts the fact that student intuitions about "0.000...1" have a fruitful mathematical implementation. Tkuvho (talk) 04:56, 1 April 2011 (UTC)

The readability of articles

I have just been reading a mathematics article about the Halting Problem (Turing et al) and found it to be very difficult to read. A lot of text books on subjects particularly in the field of science and maths have been written in this style and it leaves the reader frustrated and confused. Surely an encyclopedic article should be accessible to the widest audience possible? I think some simplification of the language with perhaps more steps and examples would help to get across to the reader some of the concepts involved. Readers are generally not stupid people (else why would they be there) but the knowledge should be communicated better. Language, next to knowledge, is the most important asset an encyclopedia can have.

Sam- Helsinki, Finland