User talk:Dmharvey/Archive1

This archive is from May 2005 to May 2006.

Welcome

I saw you already found Wikipedia:WikiProject Mathematics. Its talk page is good to have on the watchlist, as there a lot of the math-related issues on Wikipedia re discussed. Enjoy! Oleg Alexandrov 17:19, 24 May 2005 (UTC)

Welcome to Wikipedia! linas 00:22, 3 Jun 2005 (UTC)

Re: Wallpaper group

Agreed, the geometric proof for 2D cannot be used unchanged for all dimensions. However, the linked page seems adequate for wallpaper groups, and it is explicit about its limits:

We will give the proof for ℝ². The proof for ℝ³ is similar. It is harder for higher dimensions!

One generic proof depends on the transformation matrix having only integer entries in terms of a lattice basis. But one of the nice properties of your edits is the introduction of a great deal of visual material, and the 2D geometric proof, though more limited, seems more in line with that style.

Two dimensions of tension are apparent in content of this nature: abstract mathematics versus concrete examples, and specific (2D only) versus general (such as 3D crystallographic groups). Given the topic of the entry, it seems wise to stick with specific and not worry about higher dimensions. As for mathematics, readers may be young or inexperienced, and we'd hate to give them a bad taste, to make them feel like this material is unpleasant or too difficult. A matrix proof might do that.

KSmrq 21:25, 5 Jun 2005 (UTC)

Cantor's first uncountability proof

You wrote:

"Cantor's first proof" is new to me, and I have to say it's delightful. I agree that mathematicians generally believe the diagonal argument to be Cantor's first. However, I'm not completely convinced that this isn't really a diagonal argument in disguise. I need to think about this a bit.

I don't think anyone claimed that it's not really a diagonal argument in disguise, nor does that matter, IMO. Anyway, I've added a reference to the paper in which the argument was published in 1874. Michael Hardy 22:57, 7 Jun 2005 (UTC)

If you want I could e-Mail you MS Word files of my complete counter-arguments to Cantor's infinity theorems . . . BenCawaling@Yahoo.com [21 June 2005]

The village pump thing

I saw your message on Wikipedia talk:How to write a Wikipedia article on Mathematics just now. My point was, when you have a question mathematicians don't know how to answer; you can post it on the village pump, and hope somebody else will know the answer. So, good luck with Wikipedia:Village pump (policy) Oleg Alexandrov 00:16, 8 Jun 2005 (UTC)

testing edit

can I edit at the moment?

Fermat's Little Theorem Response

(moved to relevant talk page) Dmharvey File:User dmharvey sig.png Talk 5 July 2005 11:50 (UTC)

Fermat's Little Theorem coincidence

An eerie thing just happened; I bumped into your work again, quite by chance. As often happens on the Web, and even within Wikipedia, I was randomly surfing, free associating, when I came to the Fermat Little Theorem page. Noticing it was partially broken, I checked to see when it had happened. I found that a string of edits had recently occurred, with the result that the page was worse than before! Since the only purpose seemed to be replacing "equal to" with "congruent to", I backed out those changes and used Unicode. After all that, I found your note on the talk page saying you were working on a new version. Wish I had seen that first. Ah well, I heartily agree the existing article falls far short of what it ought to be. To warn future editors, I have inserted a note at the beginning of the wiki source, suggesting a visit to the talk page.

Aside from this random touch-up, I recently devoted (too much) time writing a proper page for point group, which had been redirecting to crystallographic point group. It seems a bit too densely written and incomplete, but at least it covers the basics. I deliberately included a link to crystallographic restriction theorem, as a reminder that we shouldn't leave that as just an off-site link in the wallpaper group article. Did you ever find a proof (or two) you liked, at least for 2D and 3D? KSmrq 2005 July 5 04:55 (UTC)

Hi there KSmrq, nice to run into you again. Your unicode edits are good. That proof now looks presentable. I think I prefer my new exposition (I especially think the "example" section is important to include), but it's a much closer thing than before. I might use that unicode symbol in a few of my inline equations, I'm not happy with their current rendering.

That point group is a great start, well done.

As I've been learning, WP is the most advanced timesink technology known to humankind. At the moment I'm trying to focus my WP energy on fermat's little theorem. When I'm satisfied with that, I might come back to the point group/wallpaper group constellation of articles. Unfortunately my list of "intended edits" to other articles is getting rapidly very long. Dmharvey File:User dmharvey sig.png Talk 5 July 2005 11:57 (UTC)

Question on one of your goals

What do you mean by "...comprehensive. Even an expert in the area should not find anything new?"

Well I'm not sure how to make myself clearer than I already have. (I welcome your suggestions.) I guess I mean that if there's some piece of knowledge X out there, then WP should somehow include X. Obviously it's the most ambitious goal on the list. Keep in mind my preface: "They are of course, merely ideals." Dmharvey File:User dmharvey sig.png Talk 8 July 2005 16:49 (UTC)

I that by saying even an expert shouldn't find something new implies there may be more out there that isn't in the article to me. The wording seems self contradictory.Guardian of Light 9 July 2005 17:18 (UTC)

Would you prefer "… should not find anything missing."? KSmrq 2005 July 9 18:58 (UTC)

But by my definition of "comprehensive", all the expert's knowledge is already included in WP. :-) Dmharvey File:User dmharvey sig.png Talk 9 July 2005 18:18 (UTC)

ok hopefully that's settled it Dmharvey File:User dmharvey sig.png Talk 23:59, 9 July 2005 (UTC)

Yes. I realize it seems minor, but your message is conveyed well with the word missing as user KSmrq put it. Anyway, nice to have you on board! Guardian of Light 13:14, 11 July 2005 (UTC)

Response to goals

Here's a little reminder list I keep for myself.

To effectively teach mathematics, we would do well to include these elements:

• Theorem(s)
• Proof(s)
• Intuition

---

• Example(s)
• Counter-example(s)
• Connections

---

• Exercise
• Teaching

---

• Pictures
• Humor

By "connections", I mean to explicitly tie the topic under discussion to other topics, preferably several, preferably already familiar to anyone, preferably of interest in themselves. By "exercise", I mean that to learn mathematics we need to use it. By "teaching" I mean that an excellent way to better understand a topic is to try to explain it to someone.

The two most unusual items are "counter-example(s)" and "humor". It is not uncommon to see examples of a theorem, but seeing what can happen when a condition is not met helps make the conditions as memorable as the conclusion. This also ties in to the next point, because it's inhibiting to only see everything go right, and we need to be able to relax and risk being wrong — and laugh when it happens. Humor not only attracts me, but it's also something I've observed in the very best of teachers. Put succinctly,

When we laugh, we learn.

Retaining, or inserting, humor in writing is a constant challenge, especially since mathematics-as-written has picked up a bad habit of being far stiffer than mathematics-as-taught. At the very least, it reminds me to write with a light heart, to convey the joy of the material.

What's not on the list, and harder to describe, is organization. A good presentation feels natural, inevitable, but also surprising. It should come in bite-size pieces, a goal in tension with overall brevity. If an argument is too long, we can lose the thread before we reach the end. The reader should never feel lost, but always know where we are, where we're going, and why. And that "why" should be compelling, so they want to go there. The language should concentrate nouns and verbs in active voice, to drive the narrative forward.

Maybe the single most important guideline is to never, ever, forget that we're writing for complete human beings, for whom sex, dinner, and dirty laundry can be as important (or more important) than our topic! :-) KSmrq 2005 July 9 06:19 (UTC)

Hey KSmrq there are some very useful comments. Especially concerning humour. The funny thing, and I've just noticed this since you've pointed it out, is that I make a lot of use of humour in the classroom, but I don't do it when I write about mathematics. I'll have to think about this a bit. It seems much harder in writing, because you go through so many versions trying to make it perfect, which doesn't happen in teaching (at least not over the same time scale). One of my favourite examples of using humour to communicate about a definitely unfunny topic is the film Life Is Beautiful, have you seen it? Dmharvey File:User dmharvey sig.png Talk 9 July 2005 12:46 (UTC)

I've seen some of the end of the film, not the whole thing. It's amazing and moving, if a little unrealistic; between starvation, forced labor, and the like, merely surviving was a challenge. (Isn't it interesting that much of the strength of U.S. mathematics today is built on mathematicians that the Nazis didn't want?) However, I'm familiar with one true story of survival involving music rather than humor, for women in a Japanese prison camp. I attended a performance of this music by the Peninsula Women's Chorus, and it was an unforgettable experience. KSmrq 2005 July 9 18:58 (UTC)

Euclidean plane isometry

At long last I have added some illustrations of "mirror algebra" to the Euclidean plane isometry article. Here's a news flash: Creating illustrations is a bigger time sink than writing text. But since each picture saved me a thousand words, maybe it will pay off. :-) KSmrq 2005 July 9 05:11 (UTC)

looks great! The text really needed that. (see talk page) Dmharvey File:User dmharvey sig.png Talk 9 July 2005 12:38 (UTC)

Hmette welcome

(moved to User_talk:Hmette) Dmharvey File:User dmharvey sig.png Talk 14:09, 10 July 2005 (UTC)

Crystallographic restriction theorem

The new crystallographic restriction theorem article was fun, and now with dancing girls vectors! :-)

I was sorely tempted to make the Busby Berkeley allusion more explicit, by using images of comely maidens rather than clumsy vectors to illustrate the geometric proof, but my nerve failed. Part of the fun was bringing together in one place bits and pieces of insight from a variety of sources. The dancing vector proof could be honed to its essentials, as in the external link, but the polygon version (inspired by The Centre For Conceptual Sculpture) strikes me as more memorable. I have not come across a proof of the k-dimensional restriction, nor taken the time to do it myself; but I'm delighted to be able to state the full theorem at last.

So, at long last, the dangling reference in wallpaper group is properly resolved. Enjoy. KSmrq 06:15, 2005 July 18 (UTC)

Wow. I've only had a brief look. I don't have time right now to read it carefully let alone do any editing, but I will put it on my list, and I will be back. Looks like a great start, excellent work. Here's just a few brief comments: (1) perhaps need to be more specific in the intro about the distinction between the full crystallographic group (including translations) and just the point group. (2) the general theorem applies to any orthogonal transformation fixing the origin, not just rotations. I'm not sure whether the composite of two rotations around mutually orthogonal axes in four dimensions is called a "rotation", but this needs to be clarified. More importantly, the term "rotation" doesn't cover orientation-reversing transformations, which the CR theorem does apply to. The k dimensional proof goes something like this: Suppose T is our transformation in R^k with exact order n. Write it as a matrix with respect to the basis generated by the lattice it preserves, so T has integer entries. It satisfies T^n - 1 = 0, so has one of the primitve nth roots of unity as an eigenvalue. But its minimal polynomial has integer coefficients, so the conjugates over Z are also eigenvalues. There are phi(n) of these, so k >= phi(n). (I feel like I'm missing some critical detail, but I think it's the basic idea.) Dmharvey File:User dmharvey sig.png Talk 11:44, 18 July 2005 (UTC)

Glad you like it; after all, it's your fault it exists (by creating a red link in wallpaper). We could discuss your comments on the article talk page; but I've made minor edits to address them. It'd be great if you could flesh out the proof idea and amend the article. Meanwhile, I'm noticing the amount of work left to be done on the wallpaper group page, still an inviting timesink. :-) KSmrq 07:25, 2005 July 19 (UTC)

FWIW

Yes. and, FWIW, my current favorite is what Tigger says to Pooh when he leaves: TTFN linas 00:29, 10 August 2005 (UTC)

TTFN = ? My Pooh cultural background is very weak. Have you ever read TLA? Very amusing. Dmharvey File:User dmharvey sig.png Talk 00:46, 10 August 2005 (UTC)

AcronymFinder works for me. KSmrq 23:56, 2005 August 10 (UTC)

Hmmm. Didn't seem to work in this case. Dmharvey File:User dmharvey sig.png Talk 23:58, 10 August 2005 (UTC)

Not \newcommand... symbol!

The work on blahtex seems great. In its page I read you plan a newcommand functionality but didn't do it yet. Well... hold on... why not avoid this terrible awkwardness that (La)TeX is actually a programming language ?

I mean (La)TeX is notoriously hard to parse in its entirety and has never been specifed except as... a program (as far as I know). So why not take the chance to define symbols instead of defining any forms of commands ?

• Symbols would have a semantic, they should probably be output with a link to another wikipedia entry (and a tooltip maybe and...)
• Symbols would be invoked somewhat like a macro but... also as operators (with precedences)
• Symbols can be defined, they should be so along with possible notations
• Notations should be choosable (by an author, maybe by a user, maybe by...).

A program very similar to blahtex seems to be QMath (see [1]). The latter is doing the conversion from a textual unicode-based input to OpenMath (which is equivalent to content-MathML but more extensible).

How does it sound ?

polx 2005-08-10 23:00 CEST

Hi polx, thanks for your interest and encouragement. May I take this opportunity to invite you to help out by finding as many bugs in blahtex as you can, and to check out Jitse's work on integrating blahtex with mediawiki!

I'm afraid I don't understand what you mean by "symbol". Could you give a few specific examples?

A few other comments, which may or may not address some of what you were asking:

The reasons I want input as close to LaTeX as possible are: (1) backward compatibility for existing equations in wikipedia, (2) To make it as comfortable as possible for professional mathematicians/scientists to contribute to wikipedia. LaTeX is the de facto standard that these people already know.

I don't intend to produce Content MathML at all. Only Presentation MathML. Therefore I don't think OpenMath is appropriate. We are aiming for the simpler task of encoding visual output, not encoding mathematical semantics. Please correct me if you think I'm misguided. Dmharvey File:User dmharvey sig.png Talk 00:07, 11 August 2005 (UTC)

Hi dmharvey...

(I will take the time to look at your example page but MacOS support is quite poor as you know, have you tried it with TechExplorer?)

Regarding Mac OS support. You may be surprised to hear that I work primarily on a Mac, and that I'm quite a fan of the OS. As you say, the options for MathML support are right now very limited, I think "non-existent" would be a better term. "Luckily" I have a available a windows machine on which I can test the MathML output. I actually tried out techexplorer (on the mac) for the first time a few days ago, I can't say I was impressed, in fact I could barely get it working at all. Maybe I'm doing something wrong. I wrote a few comments on m:Blahtex/Bugs_in_browser_MathML_support. If you can tell me how to get it working, I'd be interested to hear about it.

I remember my tests were also frustrating until David Carlisle made the hint that the embed tag should be used and that's one that worked... look in the archive of www-math@w3.org for a pointer, I think. Sorry not be able to provide more... I'll be offline for two weeks in less than 20 hours... Btw... announcing blahtex milestones on this list would be more than sensible, it'd also get the help of people involved with such tools.

Examples of symbol could be for the usage of the tangent space or tangent bundle of a manifold. In LaTeX, you write it $T_pM$ but no-one tells you the semantic of this notation, the symbol T... is... maybe just a variable whereas, I think, one understands symbol to have a semantic. A similar example would be the absolute value sign, used to be written as a pair of pipes: if someone finds itself in front of such a graphical presentation (e.g. by web-navigation), it has no way to know what it means... whereas linking to this symbol could be offered. Being able to specify that the notation of the pair of pipes (in LaTeX source) is a bracket is also great because it should then be sure to stretch the pipes... With \newcommand, well... you can make \abs{x+y}.

Well, I think providing semantic content is just too hard. Let's look at $T_p M$ for an example. How much semantic content to provide? Does the markup need to specify that $M$ is a manifold? A topological manifold or a differentiable manifold or something else? Does it need to indicate that p is an element of M? Does it need to specify that the whole object $T_p M$ is a vector space, and further that it's part of a whole bundle of vector spaces on the manifold? Even worse, does $T_p M$ refer to just a single vector space at a particular point $p$, or is it a function of $p$? I think to specify an extension of LaTeX that could capture some or all of that would be a major undertaking in itself.

This ideal world you are describing where all the types are known and well declared is not here, indeed, i.e. is too hard to expect from Wikipedia content. However, you do a little bit and just hook to the symbol tangent-space the description of which probably would tell you that you expect a point of the manifold and a manifold. That symbol explanation should also be decorated with definitions which, at least for a while, would only happen to exist for differentiable manifolds...

More importantly, having all this extra markup is going to make it very difficult for a casual editor to work on articles, since they need to know all the content markup to make sense of it all. It's going to be orders of magnitude more complicated than understanding the ordinary wiki markup (like "== headings ==" and stuff).

In the ideal world. There should be good ways to make this completely unaware of the authors as long as they don't wish to declare new symbols or notations. Such syntax as polynomials and differential calculus can, I think, mostly be written semantically interpetable. I can only agree that we cannot afford full semantic right-away... but partial one should be easily reachable soon (e.g. the processor would give the pipes the semantics of absolute-value only if it can analyze it correctly...)

Can I also mention another related issue involving "\newcommand". Currently, because of technical limitations in the mediawiki software, it is not possible to have a "newcommand" at the top of an article which applies to an equation later in the article. That is, the only way a "\newcommand" could possibly work right now is in the equation itself. As you can probably work out for yourself, this is not very useful. This is the main reason I am not planning newcommand functionality at the moment.

Well, this is a common problem with the definition (and management) of input-notations... this needs to be somewhere in the header... or in a metadata... don't know.

That you wish to stay close to LaTeX is acceptable for the compatibility reason, I believe. That you wish to stay close to something like LaTeX is sane because of the wide-usage of LaTeX but note: this wide-usage is at the academic level... teachers tends to prefer the evil office suites, it seems.

But declaring stuck to LaTeX is dangerous since it is not a standard, a specified language, or anything such. There's many forms of LaTeX... much too many! If blahtex starts constraining soon its form of LaTeX, it will have a more restricted set of sources needing to be supported, and, maybe partially support mathematical symbols.

You'll have to explain this a bit more. I don't know enough about the various forms of LaTeX. Do you mean different versions of LaTeX itself (like LaTeX 2e etc) or different packages that get added on, or something else?

I think packages are the most dangerous ones... I also think one can judge this by the complete unavailability of complete alternative LaTeX parsers (whereas the wish is definitely there).

If you do not wish to go for MathML content, my talk is maybe useless... why not consider the possibility of added value of such? At least, say, to provide navigation using mathematical symbols (maybe tooltips) and mathematical search ?

I definitely agree with you here. This is something I have in mind for the more distant future, i.e. after we actually get any MathML working at all :-). I would eventually like to add some LaTeX markup which simply turns part of the equation into a wiki-link. For example, an equation in which the symbol "congruent to" appears might have an appropriate link to Modular arithmetic. MathML has specs for specifying hyperlinks for portions of an equation, so this is not beyond the realms of possibility. Dmharvey File:User dmharvey sig.png Talk 13:44, 14 August 2005 (UTC)

then we're on common tracks! -- Polx 13:56, 16 August 2005 (UTC)

blahtex

I'm interested in your MathML efforts, and possibly in contributing. Is there a way to track plans, test progress, make suggestions, and so on? Also, how does this compare to the other such tools that already exist, such as those listed at the W3C MathML site? There are parallel wiki efforts, such as UniWakka, that seem ahead of Wikipedia. As I understand it, the major obstacle for WP (MediaWiki) is not generating MathML for the mathematics bits, but generating valid XML for everything else. What is the status of that, and what can be done to move it along? --KSmrq^T 20:32, 2005 August 25 (UTC)

Mate we need all the help we can get!!

That Uniwakka site is very interesting. They seem to have solved lots of the problems that we're trying to solve. I haven't looked at it in detail yet, but I will.

In summary, the "MathML in Wikipedia" problem can be divided into three chunks.

1. Having a LaTeX => MathML converter
2. Integrating the converter into mediawiki
3. As you point out: Getting the rest of mediawiki to generate valid XHTML, in a way that is compatible with all the major browsers.

Item (2) should be pretty straightforward.

Item (1) is what I am personally focussing on; I intend blahtex to be such a converter that can stand alone as well as mesh well with mediawiki. We have the additional problem of writing a converter that is compatible with some of texvc's slightly strange behaviours. As you mention, there are existing converters already out there. My opinion, based on my playing around with them at some length, is that they have some serious deficiencies, and I want to write one that is better. Whether I will succeed is yet to be seen :-) Try typing in "a := b" or "\mathbf\lambda" into any existing converter and you'll get an idea of the subtleties involved. As far as I'm concerned the output should be as close to LaTeX as possible. Blahtex version 0.2.1 (the currently available version) should not be seen as my intention of what the output quality will eventually be; it was just something to generate a bit of momentum. I am currently working on 0.3, which should be quite an improvement.

Item (3) is the part of the project which I would like to leave almost entirely to others. I don't really have the background (or honestly the inclination) to work out how to get this stuff right. Currently Jitse Niesen is the guy to speak to about (3), he's been making some progress, and seems quite keen on seeing the job through. You should get in touch with him if you'd like to help out in that department.

There are further problems to be solved, like improving Firefox's MathML support, which is pretty solid but a bit buggy, but maybe that's beyond the scope of what we should be trying to do.

If you want to "track plans" you should put m:Blahtex, m:Blahtex/Bugs_and_feature_requests, m:Blahtex/Bugs_in_browser_MathML_support, m:Blahtex/How_to_make_MathML_work_in_MediaWiki on your watchlist. Also, major progress will always be reported on the mathematics project talk page. In terms of "making suggestions", please put them on m:Blahtex/Bugs_and_feature_requests or m:Blahtex/Bugs_in_browser_MathML_support, or anywhere you feel like really!

If you're looking for something more specific to do which would save us some time, you could

1. Clean up the bug reporting page a bit, especially the browser rendering bugs page, since I would soon like to bring the attention of the browser developers to this page.
2. Do the task described at m:Blahtex#Other miscellaneous fun things.

Dmharvey File:User dmharvey sig.png Talk 22:56, 25 August 2005 (UTC)

What you are doing is good, worthwhile, and very much appreciated. -Anonyme 14:21, 29 November 2005 (GMT)

Thanks. It's nice to have some positive feedback. Please be assured that there is still a lot of work going on in the background -- not just me, others too -- and we will have something more concrete to deliver in the next few months. Dmharvey 23:29, 29 November 2005 (UTC)

Anonymous math writers at Wikipedia

Check out Talk:Symmetry. It seems we may have another "Robert Stewart". Cullinane 01:18, 1 September 2005 (UTC)

Update: A dispute has been submitted to the Wikipedia:Third opinion list of active disagreements:

• Talk:Symmetry Dispute over whether or not to delete a link in "Symmetry in mathematics" section of article on symmetry. See history of Talk:Symmetry for reverts. Actually, primary dispute at the moment is whether reverts are to be allowed in Talk:Symmetry. Dispute over link in main article cannot be resolved until dispute over Talk:Symmetry reverts is resolved. 05:22, 1 September 2005 (UTC)

You're of course welcome to join in, as third-opinion-giver or as Talk participant, but I don't blame you if you don't. Maybe it will bring back some fond memories? Cullinane 06:25, 1 September 2005 (UTC)

Sorry Steven, I just don't have the time right now. These things tend to use up a lot. Dmharvey File:User dmharvey sig.png Talk 11:52, 1 September 2005 (UTC)

OK, no problem. I was wrong, it seems, in thinking I was dealing with a sockpuppet at Talk:Symmetry. I deleted the dispute from the list of active disagreements. It seems to be settled for now. Cullinane 12:22, 2 September 2005 (UTC)

Please vote on list of lists, a featured list candidate

Please vote at Wikipedia:Featured list candidates/List of lists of mathematical topics. Michael Hardy 20:28, 13 October 2005 (UTC)

I've added a section to that page devoted to answering your question by giving examples. I'll probably add more to it later. Michael Hardy 20:15, 18 October 2005 (UTC)

thanks for an excellent explanation

Hi Dmharvey. I guess I failed to follow-up with you on your nice explanation about the continuity of evaluation for non-Hausdorff spaces, and now it's gone off the page. So I wanted to just come here and thank you. Obviously the example works great, I made a dumb mistake when following it through the first time, but it's clear now. It's a nice example. Thanks again. -lethe ^talk 13:50, 14 December 2005 (UTC)

No problem mate. It was fun trying to come up with that example. I hadn't actually realised there was an ambiguity in my working definition of "locally compact" until it was brought to my attention here. I would be interested to know if there is a less stupid counterexample involving, for example, the zariski topology on an algebraic variety. Dmharvey 15:22, 14 December 2005 (UTC)

Hmm. Bear with me while I ramble on a bit. So, what I took out of our conversation was that if we have the stronger version of local compactness (every point has a local base of compact neighborhoods), then we don't need Hausdorff. Does strong local compactness imply Hausdorff? I think it does not (consider indiscrete case). Therefore I can have a non-Hausdorff but still strongly locally compact space, and evaluation should still be continuous, right? OK, so then my next question would be: is Zariski strongly locally compact? So lemme think about that. For example, on the real line, the Zariski is the cofinite topology. It's compact, and so locally compact in the weak sense. Is it locally compact in the strong sense? Well, yes, I think it is: every neighborhood is compact, so any local base is a local base of compact neighborhoods. I'll have to think about whether all Zariski topologies are strongly locally compact, but my hunch is that they are. Trying develop a geometric intuition about Zariski spaces has always made my head hurt though.  :-)

So if Zariski isn't a less stupid counterexample, what is? It fails for the Hilbert cube, right? For the same reasons as your example. The Hilbert cube is kinda stupid too though. I'll think about it some more. -lethe ^talk 17:15, 16 December 2005 (UTC)

I think you're right. If the space is "strongly locally compact" as described above, but not necessarily Hausdorff, then you get a continuous evaluation map. I wouldn't stake my -- ahem -- reputation on this, but I certainly remember that being the only part of your initial argument which was troubling me. Dmharvey 17:49, 16 December 2005 (UTC)

你好

我是中文维基人（wikipedian）,看到您在学习中文，并且很惊讶您可以在短短两年之内学的这么好，我学习了七八年的英文，还感觉不如您的中文这么流畅，希望可以我们可以互相学习，你可以通过wikipedia系统的邮件联系到我，或者用superszheng [at] gmail.com--user:super109:04, 16 December 2005 (UTC)

对不起，我花了太多时间回答你的问题。我还看懂汉字看得很慢。现在我很忙，我努力做维基百科的软件（请看到这儿，才没有从英文到中文翻译 :-)）。可能我多有时间的时候，我用维基百科练习中文。。。谢谢您！ Dmharvey 17:55, 22 December 2005 (UTC)

Wonderful! To learn Chinese, you can find a good amount info from [2].

Just learning

Thanks for the positive feedback & advice re elementary algebra. Is this the way I leave a message specifically for you ? I am just learning but interested in helping make wiki into encyclopedia galactica ! I teach secondary school so I thought I would start with trying to make the maths articles start with common usage and basic concept summary before getting into deep detail. Was assuming that anything less than 5% (?) change was minor. Will try to start reading some wiki policy docs sometime. PS is this automatically signed ? I wonder NO !! Have to insert code manually ? --Diggers2004 00:37, 23 December 2005 (UTC)

Cool torus image

I just noticed Image:Torus-with-seven-colours.png. It's really illustrative, I haven't seen anything like it before - thanks for contributing it. Deco 22:48, 12 January 2006 (UTC)

You're welcome! Dmharvey 02:34, 13 January 2006 (UTC)

Blahtex

Thanks for the award. My first! --Salix alba (talk) 15:12, 9 February 2006 (UTC)

Blahtex compatibility project

Thank you for your message. I passed on your support to User:LutzL, who did approximately the other half of dewiki. It would be quite useful to have updated lists to find overlooked errors and get an overview of the progress in the different languages.--gwaihir 21:35, 19 February 2006 (UTC)

Excellent work! I fully intend to make updated error lists available as soon as possible. Unfortunately the database dumps are a bit stuck at the moment (e.g. http://download.wikimedia.org/dewiki/ and http://download.wikimedia.org/enwiki/), and the latest ones were made *before* you guys got started. I'm checking the dumps every day, and I'll let you know when I put up new lists. Dmharvey 21:47, 19 February 2006 (UTC)

p3 wallpaper group

You're right, that picture of the Polish stones is wonderful. Not only is it a p3, but it's a really beautiful arrangement. I don't know who would make such a thing, but they must have known what they were doing. Ryan Reich 04:31, 3 March 2006 (UTC)

Image Tagging Image:Dharwadkers-theorem.png

This media may be deleted.

Thanks for uploading Image:Dharwadkers-theorem.png. I notice the 'image' page currently doesn't specify who created the content, so the copyright status is unclear. If you have not created this media yourself then you need to argue that we have the right to use the media on Wikipedia (see copyright tagging below). If you have not created the media yourself then you should also specify where you found it, i.e., in most cases link to the website where you got it, and the terms of use for content from that page.

If the media also doesn't have a copyright tag then you must also add one. If you created/took the picture, audio, or video then you can use {{GFDL-self}} to release it under the GFDL. If you believe the media qualifies as fair use, please read fair use, and then use a tag such as {{Non-free fair use in|article name}} or one of the other tags listed at Wikipedia:Image copyright tags#Fair_use. See Wikipedia:Image copyright tags for the full list of copyright tags that you can use.

If you have uploaded other media, please check that you have specified their source and copyright tagged them, too. You can find a list of 'image' pages you have edited by clicking on the "my contributions" link (it is located at the very top of any Wikipedia page when you are logged in), and then selecting "Image" from the dropdown box. Note that any unsourced and untagged images will be deleted one week after they have been uploaded, as described on criteria for speedy deletion. Thank you. Shyam ^(T/C) 17:50, 10 March 2006 (UTC)

SVG images for Catalan numbers

Thank you for your words! I wrote more SVG to replace the PNG image for the binary trees in the article of Catalan numbers in the spanish Wikipedia. You can use the image if you like. I'm a computer student, learning SVG too, tell me if you need help to do something more about that. Jasampler

Diegueins / Diego Saá

conversation moved to User_talk:Diegueins

Compass and straightedge

Please comment. John Reid 14:59, 31 March 2006 (UTC)

WAREL RfC

I've filed an RfC against User:WAREL. I listed you as a person who had attempted resolution with him, but it was called to my attention that it would have been better to let you add your own name if you were interested. So I've removed you from the list. -lethe ^{talk +} 01:14, 4 April 2006 (UTC)

No worries mate. Dmharvey 02:23, 4 April 2006 (UTC)

Image:Dmharvey-wallpaper-test-p6m-cell-6.svg

Reply: I apologise! I didn't realise that what was happening. You may find it easier if you write something more then "test" on the page or other users will assume it's a new user playing around with uploading images. As for the speedy process; an editor marks animage as speedy then an admin will delete it. See WP:CSD for the criteria. The criteria are thngs that don't need a vote like vandalism, accidents, tests, etc. IF a user feels that the page shouldn't be deleted they can put {{hangon}} on the page while they write an explanation on the talk page. That's basicaly it. If you have any questions feel free to ask me, Flying Canuck 03:32, 19 April 2006 (UTC)

Image:4ct-non-counterexample.png

I notice that you created Image:4ct-non-counterexample-2.png and have marked it as public domain. You uploaded a similar image, Image:4ct-non-counterexample.png, but this is marked as fair use. If you created this image also, could you change the licensing? Thanks, Pagrashtak 04:29, 20 April 2006 (UTC)

No problem. Let me know if what I've done in insufficient. Dmharvey 11:46, 20 April 2006 (UTC)

That looks fine, thanks! Pagrashtak 22:58, 20 April 2006 (UTC)

adjunction (field theory)

Hi there, we have recently met on some field theory pages. I just created adjunction (field theory) because I think it deserves its own article and field extension is already too cluttered anyway. You might want to have a short look, as it is closely related to simple extension. I am not too proud of the writing style in adjunction (field theory), so feel free to add improvements. By the way, nice work at Degree of a field extension.MathMartin 18:58, 23 April 2006 (UTC)

I think adjunction (field theory) is a good idea, but there are some things I'm going to change on it when I get some time. Also, if you're not already familiar with it, you should check out the math style guide, in particular probably those $A$'s should be replaced by just A (see wikitext). Dmharvey 19:59, 23 April 2006 (UTC)

Variational number theory

Hi David, could you please have a look at variational number theory and tell us whether that sounds reasonable. Charles suggests on User talk:Linas#Variational number theory that it might not be true. -- Jitse Niesen (talk) 12:04, 7 May 2006 (UTC)

I've replied on Linas's talk page. Dmharvey 12:49, 7 May 2006 (UTC)