Wikipedia talk:WikiProject Mathematics/Archive 7

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

Contents

Other_names_of_large_numbers

I find Other_names_of_large_numbers a rather dubious article. Google will only find a lot of the names here inside this article. --R.Koot 00:02, 1 August 2005 (UTC)

hmm, it does seem pretty arbitrary --MarSch 17:57, 14 August 2005 (UTC)
I concur -- Arthur Rubin 22:13, 16 August 2005 (UTC)

meta: help formulae

Has anyone else noticed what's happened at http://meta.wikimedia.org/wiki/Help:Formula? Someone has added a whole bunch of stuff which might be reasonable but I don't think it's the right place for it. It's certainly not what people should see when they go looking for help on TeX markup. I'm not really sure where it should go though. Dmharvey Image:User_dmharvey_sig.png Talk 20:50, 1 August 2005 (UTC)

You might have noticed that I moved it to the talk page. The suggestions contain a lot of tweak factors, which are probably very specific to the browser and configuration. They are totally out of place at meta:Help:Formula and to be honest, if he can't be bothered to put them in the right place, neither can I. -- Jitse Niesen (talk) 17:00, 4 August 2005 (UTC)
I agree that they don't belong there at all. I think that was the point, though. Wanted them to be seen. Who's in charge of TeX markup, anyway? - Omegatron 17:05, August 4, 2005 (UTC)
The m:Developers are in charge of the software and hence also of the TeX markup (no surprise here). As far as I can see, there has been very little work done on it in the past two years, so I guess nobody is taking responsibility for the TeX markup specifically. That's why I'm pretty confident that just putting some comment on m:Help:Formula will anger people but not yield any improvements. -- Jitse Niesen (talk) 17:22, 4 August 2005 (UTC)
So no one in particular? Just kind of this thing that's there but no one ever touches or has anything to do with? - Omegatron 17:55, August 4, 2005 (UTC)

E (mathematical constant) moved to Euler's number

Ed Poor has moved E (mathematical constant) to Euler's number. Is everyone ok with that? I have no strong feelings either way, but the move has created a lot redirects which should be fixed (especially the double redirects). I don't know as yet if Ed intends to to do that. I'd be willing to help with the redirects, but i want to be assured that we have a consensus for the name change first. Please respond on Talk:Euler's number. Thanks, Paul August 19:55, August 2, 2005 (UTC)

Why should it be moved? I think I'll move it right back. Charles Matthews 20:01, 2 August 2005 (UTC)
No, I'm not happy with the move. It is rarely called Euler's number, I think. Bubba73 20:06, August 2, 2005 (UTC)
Good move. Leave it at Euler's number. - Omegatron 20:56, August 2, 2005 (UTC)

I think it would be best if everyone responded at Talk:Euler's number. Thanks Paul August 21:08, August 2, 2005 (UTC)

blahtex version 0.2 released

Blahtex is a new LaTeX to MathML converter designed specifically for MediaWiki.

More information is available at m:Blahtex.

At the blahtex download page may be found an interactive demo, samples of equations from Wikipedia, and the source code.

I invite everyone to participate in the discussion on how on earth to make MathML work in MediaWiki.

This message will be cross-posted on Wikipedia:Village pump (technical) and on the Wikitech-l mailing list (as soon as I figure out how it works).

Cheers Dmharvey Image:User_dmharvey_sig.png Talk 13:37, 3 August 2005 (UTC)

Deletion of VfD

This isn't strictly an issue for this project, but I thought it was about such a fundamental part of Wikipedia that it should be widely publicized. It concerns the Vfd process (and as it turns out this page has been involved in several VfDs recently). There has been considerable recent discussion about possibly eliminating VfD see:

Paul August 15:19, August 3, 2005 (UTC)

Ongoing discussion at Wikipedia:Deletion reform and its subpages; my proposal is on Wikipedia:Deletion reform/Proposals/Speedy redirect Septentrionalis 01:29, 24 August 2005 (UTC)

Inline PNG formulas - a poll requested

There was a discussion right above about PNG-fied TeX vs HTML. It looks to me that the arguments for inline PNGs there were the same as in Wikipedia talk:WikiProject Mathematics/Archive4(TeX), but that the consensus nevertheless seemed to be that HTML is preferred to PNG.

However, the issue does not seem to die out, with some kind of silly revert war going on at cardinal number. I would like to see an informal poll to figure out what people think and if there is some consensus about it; and whether the issue is that important at all. I for one prefer HTML formulas inline if the TeX formulas become PNG images, unless HTML is unable to render the formulas correctly. Oleg Alexandrov 15:27, 3 August 2005 (UTC)

I've gone both ways on this. At first I put equations in as HTML if they were simple enough and used TeX for the more complicated stuff. However, it didn't look good to me to have some equations in one and some in the other, since they look so different. Secondly, in some fonts at least (including the one I use) the HTML Greek letters are not very close to the way I'm used to seeing them. Therefore, if some of the equations on a page were in TeX I want to do all of them in TeX. A drawback if TeX is that the characters are thin and not of uniform thickness, at least on my system. Bubba73 15:45, August 3, 2005 (UTC)
*sigh* — if only MathML was working, we could leave this debate behind.... (hint hint see above :-) Dmharvey Image:User_dmharvey_sig.png Talk 15:52, 3 August 2005 (UTC)
Yes we know that MathML will cure all the ills. :) But it is at least 5 years away I would say. What is your position on inline PNGs in the meantime? Oleg Alexandrov 15:35, 4 August 2005 (UTC)
Haven't we been through this?
I can see both. Ideally we would use math tags for everything, and the inline PNGs and HTML and mathML generated from that code would look good no matter what. See m:Help_talk:Formula#Maynard_Handley.27s_suggestions for more about inline TeX tweaks, including appropriately-sized PNGs that resize along with text, etc. - Omegatron 15:41, August 4, 2005 (UTC)
Oleg, you're much more pragmatic than me :-) My position is: both inline PNGs and HTML look awful, but I am forced to concede that inline PNGs are worse. Therefore, in the current software environment, I think inline PNGs should be forbidden under all circumstances. As displayed equations, they are fine (if a little rough around the edges). I also think that inline HTML should be avoided if at all practical. Such equations should be made displayed if at all possible. In other words, I really don't like any of the options currently available for inline equations.
In response to some other points: (1) I'm not sure exactly what you're referring to when you saying that MathML is five years away. There are browsers out there that do a half-decent job. (Perhaps not decent, but half-decent anyway.) Besides, there are moves afoot. For example, the Stix fonts project is supposed to reach a major milestone later this year. (2) I'm concerned about the portability of Maynard Handley's ideas. I would like to see them up and running on a test wiki, so that I can try them out in a few browsers. Dmharvey Image:User_dmharvey_sig.png Talk 16:10, 4 August 2005 (UTC)
In response to (1) and (2). What matters is when Microsoft's Internet Explorer will have default and goood MathML support. And I doubt that will happen soon. Oleg Alexandrov 22:13, 4 August 2005 (UTC)
I agree that IE won't have default MathML support soon (if ever). That's a shame. I also agree that the current plugin support (i.e. MathPlayer) leaves a lot to be desired. However, I don't think requiring a plugin is necessarily a bad thing in itself. For example, lots of people view PDFs in their browser, even though browsers generally don't have default support. (Correct me if I'm wrong about this.) There is some mechanism that lets the browser inform you when you need an appropriate plugin for something.
Yes you are right. :) So let us hope MathPlayer will work soon, and work not only for IE. Oleg Alexandrov 23:47, 5 August 2005 (UTC)
May I add that my position on inline PNG would change drastically if Wikipedia had MathML support enabled. If MathML was there and working, I would *encourage* people to do inline equations in <math> tags, and hope that this encourages people viewing those pages to switch to a better (!) browser. Dmharvey Image:User_dmharvey_sig.png Talk 22:32, 4 August 2005 (UTC)

Separated from other text, I think TeX looks a lot better than HTML. However it's use inline is problematic. I usually try to avoid inline TeX, and I think there has been a consensus for this view. But to me it is also problematic to mix inline HTML with non-inline TeX, so sometimes when I want to use non-inline TeX, I also sometimes use inline TeX (for example for variable names, see absolute value). I would hate to see a hard and fast "rule" about this. Paul August 16:39, August 4, 2005 (UTC)

Agree about not wanting a hard and fast rule about it. But why would one use as in cardinal number the PNG \{1,2,3,\dots\} instead of simply the html {1, 2, 3, ...}? Oleg Alexandrov 22:13, 4 August 2005 (UTC)
I agree that doesn't make a lot of sense. Paul August 02:51, August 5, 2005 (UTC)

Please see my comments on this issue at: Wikipedia_talk:How_to_write_a_Wikipedia_article_on_Mathematics#Too_much_HTML.3F. - Gauge 03:48, 21 August 2005 (UTC)

The blind, with screen reading software and with some kinds of HTML enabled software, have some hope of making sense of the page if HTML us used. Unless appropriate "alt=" attributes are required, they have no hope with PNG. Nahaj 02:35:26, 2005-09-08 (UTC)

If you would have checked yourself, the TeX in math tags is in the alt text. Dysprosia 02:41, 8 September 2005 (UTC)
The section is PNG formulas, and I understood the question to be HTML or PNG. Since my browser doesn't speak TeX, I'll guess you are referring to a PNG produced from the math tags? And I give, how is it that you expected me to tell PNG from a PNG produced from the tags so that I would have noticed this? Nahaj 02:51:08, 2005-09-08 (UTC)
I think you are misunderstanding how PNG formulae are generated. The formulae images are not manually created, users do not upload regular images of formulae. Formulas are written in the TeX language and are placed inside <math> tags. If the formula is very simple, the TeX representation of the formula is converted into HTML and displayed. Otherwise, if it is complicated, the TeX representation of the formula is converted into a PNG image and is displayed. The alt text of the PNG image is the TeX representation of the formula. For example, the PNG formula S_{\mathbf{p}}(\mathbf{a})=\alpha\mathbf{v}_1+\beta\mathbf{v}_2 will have "S_{\mathbf{p}}(\mathbf{a})=\alpha\mathbf{v}_1+\beta\mathbf{v}_2" as the alt text. So the issue of 'appropriate "alt=" tags' is responded to, and thus some provisions at least are made for accessibility.
If you would have investigated this issue yourself, by either playing around in the sandbox, or having a look how some mathematics articles are typeset, and viewing the alt text of PNG formulae, you would have found out all this yourself.Dysprosia 10:40, 8 September 2005 (UTC)

Ten thousand articles waiting to be written ...

Looking for something to do? WikiProject Missing encyclopedic articles has made a list of missing science topics, containing articles on Weisstein's MathWorld that have no corresponding Wikipedia article. There are more than ten thousand entries (but a considerable number is due to different capitalization conventions), including the intriguing Algebra of Chinese Characters (unfortunately, it is just an empty article on MathWorld). On a side note, remember that there is also the PlanetMath exchange. -- Jitse Niesen (talk) 22:39, 3 August 2005 (UTC)

CiteSeer citations

I've created a template you can use for CiteSeer citations. If they ever change the URL again, only the template needs to be updated.

{{citeseer|View-based and modular Eigenspaces for face recognition|pentland94viewbased}}

View-based and modular Eigenspaces for face recognition

--R.Koot 22:28, 4 August 2005 (UTC)

I've also created one for links to MathWorld
{{mathworld|Register machines|RegisterMachine}}
Eric W. Weisstein, {{{title}}} at MathWorld.

--R.Koot 03:33, 5 August 2005 (UTC)

The second one duplicates Template:MathWorld - Fredrik | talk 19:09, 6 August 2005 (UTC)
Did I say Template:Mathworld? I meant Template:ScienceWorld ofcourse. ;) --R.Koot 19:29, 6 August 2005 (UTC)

minus or negative infinity?

"linearly towards minus infinity" or "linearly towards negative infinity" or "linearly towards −∞"? - Omegatron 22:35, August 4, 2005 (UTC)

Negative infinity sounds right to my non-native speaker ear. Oleg Alexandrov 00:41, 5 August 2005 (UTC)
I think either of the first two are ok. The second sounds slightly more formal, but I once had a professor who couldn't stand people even saying "negative three", it was only "minus three" for him. Dmharvey Image:User_dmharvey_sig.png Talk 00:56, 5 August 2005 (UTC)
I use minus infinity in speech, which sounds better, but that may only be so because it's closer to what it is in Dutch. I think I prefer negative infinity in writing, however. --R.Koot 01:02, 5 August 2005 (UTC)
I am a native speaker (UK English), and only ever use "minus", be it three or infinity. (I doubt I am Dmharvey's professor!). --stochata 21:32, 6 August 2005 (UTC)
To me, "negative three" sounds like the script of a Holywood B-grade. I'm a "minus 3" type of person. --Zero 13:43, 11 August 2005 (UTC)
IMO, they are different. minus infinity is a number, negative infinity is a place. -- SGBailey 22:04:53, 2005-09-08 (UTC)

Jitse's math news page

I don't know if you noticed, but Jitse Niesen made a bot to output the following page each day: User:Jitse_Niesen/goim. Here, listed are new math articles in the list of mathematical topics and list of mathematicians, new requests for math articles, fulfilled requests for math articles, articles in need of attention/on vfd, etc.

I believe this page should be a very useful resource for math articles editors (that is, us). I would suggest adopting this page to the project, that is, renaming it to Wikipedia:WikiProject Mathematics/recent changes or something, but I can't come up with a good name.

Any ideas of what else such a page can contain or what other things itchy bot writers like Jitse and me could do to improve the math wikiproject? Oleg Alexandrov 00:41, 5 August 2005 (UTC)

how about Wikipedia:WikiProject Mathematics/Current activity?
I've sometimes wondered whether it would be possible to write a "non-reciprocated link finder" script. If A links to B then in many cases B should link to A. Would be nice to find these more easily. But I can think of lots of reasons that it wouldn't really work. Dmharvey Image:User_dmharvey_sig.png Talk 01:00, 5 August 2005 (UTC)
I could write such a script, and generate a list of pairs of math articles which have links going on only in one direction. Is that what you want? Oleg Alexandrov 23:47, 5 August 2005 (UTC)
I guess I would be interested to see that. My only reservation is that I expect there to be a very large number of links that we discover only really make sense in one direction, and that the links we are really interested in are actually hard to spot within such a list, and therefore that you'd be spending a lot of time writing a script that turns out not to be useful. So if your best guess is that it wouldn't be worth the effort, then don't bother. Otherwise, please go right ahead! (by the way, where is some information on how to write such robots? I might be interested in trying my hand one of these days.) Dmharvey Image:User_dmharvey_sig.png Talk 23:51, 5 August 2005 (UTC)

To write the script would be very easy. It will not be a bot, rather a perl script analyzing all the math articles which I have stored locally on my machine (and I have all of the articles in the list of mathematical topics, updated daily). But I am not myself sure how helpful that would be. The total number of pairs would be in the tens of thousands. Maybe we should sleep on this idea for a while, and wonder if anything useful will come up. Oleg Alexandrov 00:05, 6 August 2005 (UTC)

I agree. Leave it for now. Dmharvey Image:User_dmharvey_sig.png Talk 00:34, 6 August 2005 (UTC)
I moved User:Jitse_Niesen/goim to Wikipedia:WikiProject Mathematics/Current activity. Did you know that 2451 of the 8979 articles are (marked as) stubs? Rather depressing, really. -- Jitse Niesen (talk) 01:48, 6 August 2005 (UTC)
How did you find 8979 articles? I count 8227. Oleg Alexandrov 02:06, 6 August 2005 (UTC)
My first guess is that I include List of mathematicians and you do not. This gives me 746 links, and 8227 + 746 = 8973, which is close enough. I can send you the complete list if you want. -- Jitse Niesen (talk) 13:00, 6 August 2005 (UTC)

other languages

hi I'm just wondering if there are math(s) project pages like this in other languages? It sounds like a lot of people who hang around here actually are quite multilingual. I speak only English (and a pathetic amount of mandarin chinese). Dmharvey Image:User_dmharvey_sig.png Talk 01:28, 5 August 2005 (UTC)

I could not find anything in Romanian or Russian. Oleg Alexandrov 02:22, 5 August 2005 (UTC)
Dutch: no mathematics project.
German: http://de.wikipedia.org/wiki/Diskussion:Portal_Mathematik.
French: http://fr.wikipedia.org/wiki/Discussion_Wikip%C3%A9dia:Projet%2C_Math%C3%A9matiques and http://fr.wikipedia.org/wiki/Discussion_Wikip%C3%A9dia:Projet%2C_math%C3%A9matiques_%C3%A9l%C3%A9mentaires (both not very active.) --R.Koot 02:40, 5 August 2005 (UTC)
Italian: http://it.wikipedia.org/wiki/Wikipedia:Progetto_Matematica
Spanish: http://es.wikipedia.org/wiki/Wikipedia:WikiProyecto_Matemáticas
Swedish: http://sv.wikipedia.org/wiki/Wikipediadiskussion:Projekt_matematik
Japanese: http://ja.wikipedia.org/wiki/Wikipedia:ウィキプロジェクト_数学
Some are, inevitably, more active than others. And some of them were already linked together, I would never have been able to find the Japanese one myself. —Blotwell 13:08, 7 August 2005 (UTC)

request

Could an admin exchange Random Access Machine and Random access machine for me, please? Thanks, --R.Koot 02:40, 5 August 2005 (UTC)

Done Paul August 03:00, August 5, 2005 (UTC)

Another one: Mathematical reviews should go to Mathematical Reviews as it is the title of a journal, see Talk:Mathematical reviews. -- Jitse Niesen (talk) 12:25, 7 August 2005 (UTC)

Done Paul August 23:58, August 8, 2005 (UTC)

EXTRAPOLATION METHOD I would be grateful if the mathenaticians would be kind enough to look at my extrapolation method on www.AIDSCJDUK.info to determine whether it is suitable for a link from Wikipedia. Copy of earlier E-mails with Wiki. are below. Edward G. Collier MBCS CITP

Unfortunately, it seems that one cannot paste E-mails into this area. My method was devised in 1987 and wasexplained in detail at a Royal Statistical Society special meeting on AIDS forecasting that year. It was briefly written up in the Jornal of that Society Vol 151 Part 1 1988 Although the professors, statisticians and epidemiologists present also explained their proposed methods, my simple (but not simplistic) mathod was the only one that ever produced any viable forecasts and is still being used today as can be seen from the web site. I also have used the method for several years in forecasting variant CJD in the UK. The SEAC sub-committee with responsibility for overseeing the progress of vCJD asked me to get the method published. However, the various mathematical bodies and journals that I approached declined to publish it as I had no references. As a retired engineer and not an academic, I had no way of finding appropriate references and in any case I had not referred to any as the idea came into my own head. I am sure that there are many people who could make use of the method - even in control engineering- if you can publicise it in the excellent Wikipedia. Thank you, Edward G. Collier Edwardhfd@aol.com

Peer review is not a perfect process, but Wikipedia is explicitly not supposed to be a way around it. See WP:NOR. --Trovatore 20:06, 13 September 2005 (UTC)

Project subpages

As some of you have noticed, partly in honor of Jitse's great new Current activity page — way to go Jitse! — I have created a new section on the project page to list and describe the various project subpages. I know they are all mentioned somewhere else on the page, but I thought it would be good to also list them together. At any rate that got me to thinking about these pages:

Should these also be subpages of this project? I could see some benefit to bringing these all under one banner so to speak. Paul August 17:38, August 6, 2005 (UTC)

Guidance on style
Manual of Style
Supplementary manuals

Abbreviations
Biographies
Capital letters
Command-line examples
Dashes
Dates and numbers
Headings
Legal
Links
Lists of works
Mathematics
Music
Pronunciation
Spelling
Text formatting
Titles
Trademarks
Writing about fiction

Special article styles

Disambiguation pages
Arabic transliteration
China-related articles
Ethiopia-related articles
Ireland-related articles
Islam-related articles
Japan-related articles
Korea-related articles
Latter Day Saints
Medicine-related articles
Portugal-related articles

Other guidance

How to edit a page
Guide to layout
Captions
Categorization
Categorization of people
Cite sources
Explain jargon
Footnotes
Writing better articles
Lead section
Lists
Music samples
Naming conventions
Overlinking
Picture tutorial
Proper names
Sections
Sister projects
Summary style
Technical terms
and definitions

Words to avoid

I think we should not make them subpages, as these pages are not just about our project. So, our style manual, Wikipedia:How to write a Wikipedia article on Mathematics, might be better off standing on its own rather than
Wikipedia:WikiProject Mathematics/How to write a Wikipedia article on Mathematics.
I agree though that it is better to list some of those pages together, as there is quite a bit of duplication now on the project page, with things listed multiple times.
On a more general note, I would think the project page needs a bit of overhaul. Wonder what people think. Oleg Alexandrov 19:35, 6 August 2005 (UTC)
YES. Dmharvey Image:User_dmharvey_sig.png Talk 12:29, 7 August 2005 (UTC)
On a related note, I think the name of the style manual, Wikipedia:How to write a Wikipedia article on Mathematics, is rather long and not so pretty. Maybe a renaming it to something else could be a good idea. Oleg Alexandrov 19:35, 6 August 2005 (UTC)
Actually, I think it could well be a subpage, like Wikipedia:WikiProject Mathematics/style. Or rename it to Wikipedia:Manual of Style (mathematics). Anyway, please do something, as I rarely type the title correctly at the first attempt. The other two pages should not become subpages: Wikipedia:Naming conventions (theorems) falls into the Wikipedia:Naming conventions (...) series and Wikipedia:Algorithms on Wikipedia is more computer science than mathematics. I also agree with Dmharvey above. -- Jitse Niesen (talk) 12:49, 7 August 2005 (UTC)
The shorter the better. :) I hope more opinions will come in as how to rename it, since it is an important document. Oleg Alexandrov 23:24, 7 August 2005 (UTC)
I agree that Wikipedia:Algorithms on Wikipedia should not be a project subpage. I hadn't really looked at it, just copied it from the project page —now I'm wondering if it belongs there either? Also I like either of the page titles Jitse suggested for the "How to …" page. Paul August 17:23, August 7, 2005 (UTC)
What about just Wikipedia:Mathematical writing or Wikipedia:Writing mathematics Dmharvey Image:User_dmharvey_sig.png Talk 19:36, 8 August 2005 (UTC)
I think if we do not want to make it a subpage of this project, then it should probably be called Wikipedia:Manual of Style (mathematics) (per Jitse) since that would be consistent with other "Supplementary Manuals of Style" listed on Wikipedia:Manual of Style (see table to right.)

I agree with Paul and Jitse about naming it Wikipedia:Manual of Style (mathematics). By the way, I truly hope that the fat style template to the right will not make its way in our manual of style, it is just so long, and not so helpful (for example, why would we need in our manual of style a link to how to write China-related articles).

Oh, and we can make the shortcut WP:MSM point to the new location, to save some typing when referring to it. Oleg Alexandrov 20:30, 8 August 2005 (UTC)

Agree that Wikipedia:Manual of Style (mathematics) is good. Dmharvey Image:User_dmharvey_sig.png Talk 01:51, 9 August 2005 (UTC)

Moved. Oleg Alexandrov 20:37, 9 August 2005 (UTC)

blahtex: now compiles on linux

Blahtex 0.2.1 has been released. It now compiles and runs on Linux thanks to Jitse Niesen.

Jitse has had some initial success with integrating blahtex into mediawiki: check it out.

Source code, online demo and samples here.

More info and bug reports at m:Blahtex.

Dmharvey Image:User_dmharvey_sig.png Talk 01:53, 9 August 2005 (UTC)

Style: *-algebras

I was editing the *-algebra, B*-algebra, C*-algebra etc. pages for consistency of style and I noticed some pages had <sup> tags around the * in these expressions, thus giving (e.g.) C* rather than C*. This looks horrible (and increases leading) on my browser (Netscrape 7) and the majority of pages didn't have it, so I took out those I found. But I assume someone had a reason for putting them in: is there any browser for which this looks better? Our proposed style guide should address this one way or the other. (This is different from the superscripting issues discussed at Wikipedia:How to write a Wikipedia article on Mathematics already because it relies on the * character appearing superscripted by default.)

And while I'm here: our preferred spelling seems to be C*-algebra (not C* algebra, C-star algebra, C star algebra, etc.) The exception is that our page on *-algebras is currently at star-algebra. Is there any reason for this, for example, is it usually spelled this way in the literature? —Blotwell 04:58, 9 August 2005 (UTC)

mentions of categorical considerations

I wrote the section on morphisms in the article on projective spaces, and it occurred to me that while using the language of category theory to describe maps between projective spaces is extremely convenient, it might be off-putting for the undergrad who's never studied any category theory, and just wants to know about projective spaces. -Lethe | Talk 07:13, August 9, 2005 (UTC)

I agree. I don't think you can assume that the person reading about projective spaces knows about category theory. However, that doesn't mean you should throw out what you've done. I think the article needs both versions. (The baby one first.) Dmharvey Image:User_dmharvey_sig.png Talk 11:03, 9 August 2005 (UTC)
I agree with Dmharvey, we can have our category theory and eat it too! (of course this come from someone who was a categorical topologist in a past life ;-) Paul August 19:55, August 9, 2005 (UTC)

But the thing is, for the example I'm thinking of, there aren't "two versions". I just say "in the category of ____ the morphisms are ____". there really isn't any category theory there that can be separated out. just some terminology that can be used or not used. -Lethe | Talk 22:07, August 9, 2005 (UTC)

Hmmm. A question: what title would you give the section if you chose to write it without categorical language? Would you still call it "morphisms"? Or something like "Projective linear transformations"? Are you worried that without the categorical language, it is difficult to motivate why these particular types of maps between projective spaces are important? Dmharvey Image:User_dmharvey_sig.png Talk 22:16, 9 August 2005 (UTC)
It seems like only someone with category theory in mind would, immediately after describing a new mathematical construction, then describe maps between such constructions. I imagine that if I didn't have that language available, I also wouldn't have the mindset to take time out to describe the maps. So I guess it's probably OK this way? -Lethe | Talk 22:59, August 9, 2005 (UTC)
I'm not convinced. I think that for a reader interested in learning about projective spaces, but without the category theory background, it is still useful for them to hear the fact that the "right" kind of maps between such spaces are the projective linear ones, even if they don't quite have the context to understand what "right" means. Anyway, why is this the right category? What about algebraic maps between projective spaces? Dmharvey Image:User_dmharvey_sig.png Talk 14:33, 10 August 2005 (UTC)

Sub and super markup feature request

I've requested that markup be added to simplify entering sub and superscript at Bug 3080. It's just TeX markup with mandatory brackets. I think it will clean up the markup and be a lot easier to type than HTML.

Examples:

  • x^{3} → x3 (powers)
  • CO_{2} → CO2 (carbon dioxide symbol)
  • 1^{st} → 1st (ordinals)
  • ^{2}H_{2}O2H2O (isotopes)

I can't think of anything this would conflict with, can you? Vote for it if you like it. Suggest a different syntax if you don't. Other syntaxes were suggested, which I really don't like. - Omegatron 19:39, August 9, 2005 (UTC)

I am not really happy with new notation. You can just use math tags to do the same thing. Oleg Alexandrov 20:25, 9 August 2005 (UTC)
There are lots of uses for super and subscripts that aren't math, like CO_2\,\! or "1^{st}\,\! place". There's really no need to type 17 characters to output 3. My markup is 6 characters; shorter and quicker and easier than both math and HTML markup. Math markup isn't appropriate for everything, and there's a lot of contention about whether it should be used inline with text at all.
And regardless of whether math markup is the way things should be done, HTML markup is the way things are done, in most cases (as in these featured mathematics articles: 1, 2).
This could save time and effort for those reading and writing the markup this way. - Omegatron 21:25, August 9, 2005 (UTC)
I agree that for things like CO2 and 1st it would be nice to have simpler markup. I disagree in the case of x^3, since this should have the semantics of a mathematical expression, but let's not go there, because that always seems to open up a can of worms :-). However, I'm quite uneasy about adding your modifications to the wiki markup. How are you going to handle the fact that there are probably quite a few ^ and _ and { and } characters hanging around in existing articles? Dmharvey Image:User_dmharvey_sig.png Talk 22:25, 9 August 2005 (UTC)
It doesn't matter if there are ^, _, {, or } characters hanging around in the markup. It only matters if there are ^{ ... } or _{ ... } hanging around outside of math tags. If there are, I doubt there are many. The only article I can imagine having them is m:Help:Formula. There aren't even any in the TeX, ASCII art, or obfuscated code articles. (I checked!) I'm sure whoever would implement this also has the capability to search for the few that might be out there and surround them with nowiki tags first (or math tags, since they're probably mistakes). - Omegatron 23:46, August 9, 2005 (UTC)

FWIW, I like it, seems like a good idea. As to the stray-markup issue, what about articles that contain sample source code? I thought I saw an article that showed how to compute factorials in 18 different programming languages. linas 00:00, 10 August 2005 (UTC)

I have to admit it's starting to sound tempting. Have you suggested this to the people who work on chemistry articles? Dmharvey Image:User_dmharvey_sig.png Talk 00:30, 10 August 2005 (UTC)
Yeah, I suggested it at Wikipedia:WikiProject Chemistry. :-)
As for stray markup, just track it down and put <nowiki> tags around it before implementing the markup filters. I'm not sure how that works for preformatted text, though:
Testing testing 12 3<sup>4</sup> 5^{6} 7^{8}
Looks like it works for those, too. - Omegatron 02:47, August 10, 2005 (UTC)

AKS primality test cleanup

I've expanded the article with information about the algorithm itself, and some detail about the proof. I'm not happy with the look of the <math> sections though - this is my first attempt at a significant amount of mathematical markup - so some help in cleanup would be appreciated.

Eventually this article should probably include the full algorithm in programming terms (rather than only in mathematical terms), and describe the complete proof. But I need to learn a bit more about finite fields and group theory before I can hope to do that myself.

As far as I can see, the only markup forcing things to PNG are the use of \sqrt(r) and \equiv. Hv 13:39, 10 August 2005 (UTC)

Thanks. It's an important algorithm, which caused quite a stir when it appeared. I cleaned it up a bit. In particular, you should use \log for logarithms in <math> mode, and \ge instead of >= (incidentally, \ge and \le are other commands that force PNG, which is rather strange as they can be rendered rather easily in HTML). Look at my changes for details. Oh yes, if you reference articles like Lenstra 2002, they should also be put in the references. Cheers, Jitse Niesen (talk) 15:05, 10 August 2005 (UTC)
Thanks; I didn't know about \log, but I've noticed that I tend to miss the < and > operators; the references to more recent papers are not mine (though among my next tasks is to track those down and try to read them).
I'm not convinced I like the mix of <math> and inline HTML, but I accept there is no ideal solution at the moment - Bubba73's comments in the Inline PNG formulas discussion above resonated strongly with me. Hv 16:59, 10 August 2005 (UTC)
As I say in that discussion, I usually don't change PNG to HTML (though I do make the change sometimes when I don't think enough), but since you made the request, I thought it would be okay. Anyway, I changed it back. I hope you don't mind my changing the \forall in text. Sorry about assuming that you put the references in there; I should have checked that. -- Jitse Niesen (talk) 17:20, 10 August 2005 (UTC)
Apologies if my lack of clarity here caused you to waste time. I can claim only ignorance and foolishness; I'm trying to catch up with the options and arguments on formatting, but I haven't located consensus yet on anything beyond no current solution is ideal, and wouldn't it be nice if MathML were here already, and it's a mess.
In summary, I don't know what is best for that page, and don't trust that what's best for me (my browser, my OS, my installed fonts) would be best for the majority, so I can only hope for and defer to someone better able to judge. Hv 18:10, 10 August 2005 (UTC)

Move of Inclusion (mathematics) to Inclusion map

I am proposing moving Inclusion (mathematics) to Inclusion map. For my reasons and how I plan to go about it see Talk:Inclusion (mathematics). If you have any thoughts on this move please comment on that talk page. Thanks. Paul August 18:42, August 10, 2005 (UTC)

I found this on VfD

Mathematics and space

Over at the Talk:Space#On arranging stuff in this article page there's a discussion about whether the section on Mathematics and space could be rewritten to contain a brief summary of how space works in maths, as at the moment it is pretty much a list of links. Could someone take a look at Space, which it is hoped will be a big picture article taking in the various uses of the concept of space, and see if work can be done on the Mathematics and space section. Thanks for any help or thoughts. Steve block talk 07:58, 11 August 2005 (UTC)

VfD for Mathematics and God

The article Mathematics and God is up for deletion. I voted to keep, here's the VfD page: Wikipedia:Votes for deletion/Mathematics and God. — Paul August 19:36, August 11, 2005 (UTC)

Of course, anybody watching Wikipedia:WikiProject Mathematics/Current activity would have discovered this a few days ago (sorry for the shameless plug, but Paul gave me a perfect opportunity). I moved the section "Articles on VfD" up to make it more prominent. By the way, it quite worries me that the article got a dozen delete votes and none of them bothered to comment on the reasoning brought up subsequently — I understand Ed Poor's frustration better now. -- Jitse Niesen (talk) 11:37, 12 August 2005 (UTC)
Yes that's how I discovered it by checking up on Wikipedia:WikiProject Mathematics/Current activity (I had forgotten to put it in my watchlist) And I agree about the comment on VfD. Paul August 16:50, August 12, 2005 (UTC)
BTW, its not showing up on Wikipedia:WikiProject Mathematics/Current activity any more ... maybe the time limits should be increased to more than a week? When I'm not in wiki-holic mode, more than a week can pass before I look at stuff. linas 23:58, 16 August 2005 (UTC)
The idea is that VfD discussions are supposed to last only seven days, so I thought it wouldn't be useful to list it longer. However, as you noticed, some discussions are not closed after that period, so now VfD pages are kept for ten days. I'm still trying to find the right balance on how long to keep the material. Of course, you can always look in the history of the page. -- Jitse Niesen (talk) 17:33, 17 August 2005 (UTC)
The VfD is closed. Keep won, though I'd hardly call it a concensus. The NPOV tag remains in the article itself (correctly, in my view). China, India, and the Arabic world have produced more notable mathematicians than just Ramanujan; those who voted to keep might help by finding quotations from other non-Western voices. Mathematicians like Russell and Clifford are well-known for their writings on God; I have added their remarks, and would invite others to add more of the kind. Especially nice would be more fun contributions like Erdős and (my addition) Hardy. --KSmrq 20:01, 2005 August 19 (UTC)

Category:Mathematician Wikipedians

I created Category:Mathematician Wikipedians as a subcategory in Category:Wikipedians by profession and categorized myself in there. Company is welcome. :) Oleg Alexandrov 23:28, 11 August 2005 (UTC)

What about Category:Wikipedian mathematicians? --R.Koot 23:56, 11 August 2005 (UTC)

Will people list themselves there or can anyone list them there? If the former, the list may be so incomplete as to be useless. Michael Hardy 21:28, 18 August 2005 (UTC)

If anybody is willing to go through mathematicians user's pages and add them to one or the other category, I will not mind. :) Oleg Alexandrov 01:28, 19 August 2005 (UTC)
Do you think that the others would? I think a directory is a great idea but perhaps the listing should be voluntary. Or maybe you could just leave someone a note on their talk page when you have added them (to give them the option to be unlisted). What do you think? --Kooky | Talk 19:13, 19 August 2005 (UTC)
To rephrase myself, if anybody is willing to go through mathematicians talk pages and mention to them about one or the other category, I will not mind. :) Oleg Alexandrov 19:56, 19 August 2005 (UTC)

There must be only one. If we do not merge these now, someone will do it later and more clumsily, and with much more work. There seems to be no standard, and Category:Wikipedian mathematicians is more idiomatic to my ear, so I propose we use that one. Septentrionalis 14:01, 19 August 2005 (UTC)

Category:Wikipedian mathematicians also fits better with Category:Wikipedians by profession. My vote is with Septentrionalis. I've added Wikipedian mathematicians to Category:Wikipedians by profession, so at least it is now obvious there are two conflicting page titles. --stochata 20:05, 19 August 2005 (UTC)
Don't know about you folks, but my profession seems to change every few years. (Three years ago, I was a "businessman". Now I'm an "engineer".) Classification by areas of interest, past and/or present, might be more accurate than whatever (non-)career is one is fated to, given the caprecious winds of the economy and slipperiness of the rungs of the social climbing ladder. linas 21:31, 19 August 2005 (UTC)

According to this, WP is not a directory. However, many categories for Wikipedians already exist. Since all the listings appear to be voluntary ones, I have no further comment on the subject. Oleg: Sorry about the misinterpretation. =) --Kooky | Talk 22:32, 19 August 2005 (UTC)

OK, I moved myself to Category:Wikipedian mathematicians. If more people feel to prefer this one, we will need to nominate Category:Mathematician Wikipedians for deletion and move the other people in there to Category:Wikipedian mathematicians. Oleg Alexandrov 05:48, 20 August 2005 (UTC)

I've now nominated Category:Mathematician Wikipedians for deletion. Note that the yokels don't seem too happy about the other page either (as per Koooky's comment above). --stochata 15:34, 26 August 2005 (UTC)

stochata, thanks. It seems there is a likelyhood both categories will be deleted, so you could go vote on that. Oleg Alexandrov 16:08, 27 August 2005 (UTC)

Announcing Jise's RfA

I would like to announce that I have nominated Jitse for adminship, and I am here shamelessly encouraging everyone to vote (in support I hope ;-). To vote or comment go here: Wikipedia:Requests for adminship/Jitse Niesen. — Paul August 16:58, August 12, 2005 (UTC)

Paul's nomination was successful, so I have now access to the admin tools. Thanks to everybody for voting. -- Jitse Niesen (talk) 12:28, 20 August 2005 (UTC)
Jitse, shouldn't you update your blurb in the participants list to reflect your newly elevated status? ---CH (talk) 00:04, 24 August 2005 (UTC)

PNG rendering improvements

Maynard Handley has put up a wiki demonstrating some improvements he has made to the LaTeX => PNG rendering process.

With his permission I offer you the URL: http://name99.org/wiki99/. It will disappear within about a week so check it out soon.

In my opinion, some of the improvements are great (Wikipedia should definitely use them), some are so-so, and some are, let's say, ambitious.

I'd like to hear some opinions. Dmharvey Image:User_dmharvey_sig.png Talk 21:39, 12 August 2005 (UTC)

The rendering looks worse to me. Dysprosia 03:21, 13 August 2005 (UTC)
Those are all terrible on my system (Firefox on KDE/linux with 1024x768 res) -Lethe | Talk 03:35, August 13, 2005 (UTC)
Correct link to the zip-file: wiki99.zip
There is a particular, uncomfortably large, font size at which the rendering is readable (although still worse), otherwise the rendering is unreadable (Firefox 1.0.4 and IE 6 SP2 on Win XP HE SP2, LCD screen 1680x1050). I think the way it scales with font size is cool though. --nosfractal 04:21, 13 August 2005 (UTC)
The auto-scaling feature is indeed interesting, but the actual rendering, as noted above, does resemble an atrophied 16th century manuscript. (I'm using Konqueror.) linas 22:42, 16 August 2005 (UTC)
Having a stronger TeX->HTML conversion would make autoscaling irrelevant, however. A good first step has been taken in ensuring that the HTML text is the same font as the rest of the document, but the conversion is still so weak as to render less than signs in PNG and not use HTML (iirc). Dysprosia 22:52, 16 August 2005 (UTC)
Actually, in my browser (Safari 2.0, also with Firefox 1.0.4 for mac), xyz is rendered (via HTML) in a different font to xyz. Am I doing something wrong? Dmharvey Image:User_dmharvey_sig.png Talk 23:18, 16 August 2005 (UTC)
Dave, go to User:Dmharvey/monobook.css and add
span.texhtml { font-family: sans-serif; }
See User:Jitse Niesen/monobook.css for an example. Unless anybody disagrees that this is a good idea, I will try to get this in the site-wide stylesheet. -- Jitse Niesen (talk) 10:24, 17 August 2005 (UTC)
Looks like your skin. It looks quite nice and consistent in Cologne Blue, where math is in the same font as italics. Dysprosia 11:45, 17 August 2005 (UTC)
Not for me, if I switch to Cologne Blue, then xyz (<math>xyz</math>) is rendered in a different font than xyz (''xyz''). Perhaps a browser thing, or something to do with the browser settings? More research needed. -- Jitse Niesen (talk) 11:59, 17 August 2005 (UTC)
That's quite bizarre. The fonts should be the same, anyway. Dysprosia 12:15, 17 August 2005 (UTC)
Hmmm. I've applied Jitse's suggestions (about User:Dmharvey/monobook.css). Now I get matching fonts in Firefox, but not in Safari. I've tried clearing caches and restarting the browser, and as far as I can tell Safari isn't trying to apply its own style sheets, so I have no idea what's going on. Ah well, no big deal. Incidentally, I don't often use Firefox, but now I'm looking at it, the italics in normal text look awful. The spacing after a word in italics is much too small. Dmharvey Image:User_dmharvey_sig.png Talk 12:32, 17 August 2005 (UTC)

Number articles up for deletion

The aforementioned article is up for deletion. Uncle G 15:42:27, 2005-08-16 (UTC)

I've voted to delete this article. I agree with the sentiments expressed here: User:Uncle G/Wikipedia is not infinite. Paul August 16:59, August 16, 2005 (UTC)

New section: "Mathematics featured articles", comments?

I've added a new section: "Mathematics featured articles" to the project page. I might expand it a bit with some information on "Featured articles" and the FAC process. It might also be nice to track down and add the date when each article became an FA. Comments? Paul August 18:48, August 16, 2005 (UTC)

Ok I've made some changes to the "featured articles" section. In particular I:

  1. added a list of "former features articles"
  2. added the date when each article was "featured" and "de-featured"
  3. linked the date to the "featured" or "de-featured" discussion (for those I could find, older articles don't have nicely organized and archived discussions)
  4. used a tabular format rather than a list format.
  5. changed the section title to reflect the addition of "former" articles.

Paul August 20:28, August 18, 2005 (UTC)

Mathematical notation in articles

I'm new here, and I'd like clarification about use of mathematical notation, specifically in set theory and mathematical logic. For example, my new stub of Transitive set uses the ∈ (&isin;) symbol, which the guidelines suggest should be replaced by the text "is in". Arthur Rubin 00:29, 17 August 2005 (UTC)

Generally speaking, you would want to follow the guidelines. However, my opinion in your case is that using ∈ is fine, essentially because the audience for that article would be expected to be familiar with standard set-theoretic notations already. Dmharvey Image:User_dmharvey_sig.png Talk 03:23, 17 August 2005 (UTC)
Two distinct concerns apply, both of which argue for "is in". The first is whether a reader can properly view the character in their browser. This would not be a problem for a PNG image, but that's ugly inline. The second concern is audience comprehension. For this brief article there is little to be gained by technical notation; "is in" may invite more readers.
The implications of these two concerns vary among articles. We can only hope that the character set problem will go away soon, but meanwhile the list of "Insert" characters below the edit window is considered safe. In the case of a long, technical article like Kripke semantics, proper notation is essential, so use it — though as little as possible in the lead paragraphs, and in <math></nomath> brackets elsewhere. --KSmrq 04:46, 2005 August 17 (UTC)
Good points by Dmharvey and KSmrq. Oleg Alexandrov 15:16, 17 August 2005 (UTC)

more about improving inline PNGs

I've been trying to improve on what Maynard Handley did with the PNGs.

There are still severe problems (mostly relating to Windows), and it's not good enough for deployment, but I think it's starting to get somewhere, and I'd appreciate some opinions.

Check out User:Dmharvey/Inline_PNG_discussion.

Dmharvey Image:User_dmharvey_sig.png Talk 17:15, 17 August 2005 (UTC)

Requested move

Could an admin move Menelaus theorem to Menelaus' theorem? Note that the page's principal author User:Tokek has left a note on talk:Menelaus theorem regarding the choice of title, but as I read it it doesn't seem that Tokek would find this change objectionable. —Blotwell 06:57, 20 August 2005 (UTC)

I did it. Now Menelaus theorem is a redirect to Menelaus' theorem. Hope that was a correct move. --Zero 08:28, 20 August 2005 (UTC)

Framed box around formulas

Yesterday I removed with my bot framed boxes around formulas wherever I could find them. I mean, boxes of the form:

This is a theorem, or a formula.

I based my reasoning on the discussions at Wikipedia_talk:WikiProject_Mathematics/Archive10#Dotted_framebox_around_formulas and Wikipedia_talk:WikiProject_Mathematics/Archive6#A_little_note_on_using_purple_dotted_boxes but Paul rightly pointed out that a preliminary discusion would have been good. So, belately, I wonder, what do people think of these boxes? Thanks. Oleg Alexandrov 18:46, 20 August 2005 (UTC)

I don't feel strongly one way or the other, but I never use the boxes. I think they should probably be left out unless something really needs to be emphasized. Bubba73 19:28, August 20, 2005 (UTC)
I don't much like them. I think it would be good to remove them, at least in the cases I've seen. Perhaps there might be a use for some more visually pleasing way (not purple dotted lines) to set off certain text. But it would be best to use such devices sparingly, if at all. Paul August 19:36, August 20, 2005 (UTC)
I think the borders are gaudy and obtrusive, but I'm not going to bend anyone's arm either way. --Kooky | Talk 20:28, 20 August 2005 (UTC)
Can we have hot pink with circulating neons? --Zero 02:44, 21 August 2005 (UTC)

Characterizing Notability of Mathematicians

Hi all, I am a non-member dropping by to alert you all to an ongoing VfD discussion.

The issue is: which mathematicians should have biographies in the Wikipedia? I think a simple and common sense rule of thumb (the title is a joke; of course I don't expect a mathematically precise criterion) should be:

a wikibiography of mathematician M, which claims no non-mathematical notability for M, should explain or at least describe at least one clearly notable mathematical achievement of M.

I am no doubt hardly the first to point out that with thousands of person obtaining a Ph.D. in math every year, and gadzillions of math professors around the world, and tens of thousands of members of SIAM, AMS, MAA, and other mathematical societies around the world, simply earning a Ph.D. or publishing some research papers probably shouldn't qualify one for a biography.

Here is a more bizarre possibility: suppose the article claims that M is notable because he won the Y Prize, it should link to the formal English language Y prize citation for M. If that doesn't exist (in English), at the Y Foundation website, and if there is no other grounds for M's alleged notability, I question whether M should have an entry in the English language Wikipedia.

No, I didn't make that up. This is exactly the argument some nonmathematician made in a VfD. (Quick now: has anyone here ever heard of the Zois Prize? Before reading the preceding sentence?)

Yesterday, I happened across several biographies listed in Category:Algebraic graph theory which I think violate my simple rule:

  1. Aleksander Malnic
  2. Dragan Marusic
  3. Tomaz Pisanski

I have nominated them for deletion as non-notable. I think the first two are clear cases, the third maybe a bit less clear. Just to be clear, in each case, I would be equally happy with either of the following outcomes:

  1. the article is deleted on the stated grounds,
  2. someone comes up with a useful description of a truly notable mathematical achievement of the subject.

I hope many of you will drop by those pages and vote one way or the other, but I'd also like to see any comments on the bigger issue raised in the subject line: how can one characterize which mathematicians are notable?

In retrospect, I probably should have considered trying to contact authors/editors of these articles before making my VfD nominations. Has anyone had some good experiences along these lines to share? Or advice on how to proceed if a similar situation arises in the future?

Someone raised another issue: these three men all happen to appear on a List of Slovenian mathematicians, so there might be some, er, patriotic rationale for creating these biographies. I don't want to get involved in Balkan politics, so I'd just say that I did recognize one name on that list, Josef Stefan, and I would certainly agree that Stefan is notable and should have a biography here. I'd like to see the others include an explanation of some clearly notable mathematical accomplishment, or else I think they should probably go.---CH (talk) 21:50, 22 August 2005 (UTC)

Oh dear: to forestall misunderstanding, of course I did not mean to imply that whether or not I recognize a name is an adequate criterion for mathematical notability. But if none of the members of this project know anything about mathematician M, and the biography doesn't help, I would say that biography should probably go.

Another thing: I overlooked another name I recognize: Josip Plemelj. Ironic I missed that, because I am gearing up to write about something he was involved with.---CH (talk) 22:04, 22 August 2005 (UTC)

P.S. Someone commented in the VfD to the effect that the fact that some towering figure doesn't yet have a biography, while some lesser figures already have ones, is not by itself grounds for deleting anything. I agree; clearly, Wikipedia's growth is haphazard so this will be a not infrequent occurrence. The balance issue raised in these three cases goes far beyond that, I think, but all I am really trying to say is that, IMO, the average reader of a biography on Wikipedia should not be left with serious doubt that the subject is indeed notable, as I was after reading these three biographies. Again, I'd be happy if someone who knows more than I do about them can convince me I am wrong by telling us all (by expanding the biographies) about some clearly notable accomplishment. But some prize I have never heard of? Doesn't help me. Some very rough analogies (not very serious):

  • earned a Ph.D.: made the local Little League baseball team
  • serves on the math faculty at some uni: plays minor league professional baseball
  • won tenure or an obscure award: got a pat on the back from the team after a big game
  • made a major contribution to mathematics: set a significant major league baseball record
  • won an internationally known mathematics award: won the MVP award
  • won the Field's Medal: entered the Hall of Fame

(I should confess that I don't know much at all about baseball, I'm just trying to, er, play along with a favoriate analogy among Wikipedians.)---CH (talk) 23:58, 22 August 2005 (UTC)

JYolkowski has suggested several times (if I understand him correctly) that the mere verifiability of stated facts in an biography is sufficient grounds for keeping it (see my talk page). This doesn't make sense to me: name person X, birthdate, and birthplace, and someone can probably verify that information. Does that alone qualify X for inclusion? I think it should be rather the notable substance of stated facts (or lack thereof) which qualifies X (or not) for having a biography here.

I seem to be trying to summarize, er, notable comments recieved elsewhere. I have to take the blame for this. Due to the accidental way I got into this (and my inexperience in Wiki discussions of this kind), various useful (or bizarre) comments are now scattered over the talk pages of the three articles, my user talk page, and the vfd pages. Sorry for the confusion!---CH (talk) 00:35, 23 August 2005 (UTC)

Jitse actually found the citation (in Slovenian, I guess) of some obscure award to Marusic :-) So I did the obvious thing and awarded the very first Biographical Barnstar for Brain-numbingly Obscure Web Research to Jitse Niesen. Congrajulations, Jitse! This is such an obscure award that until a few minutes ago it didn't even come with a bronze plated pewter star. But you can verify that Jitse won it!-- just look here! Anyway, if some kind person can translate this well enough, maybe I will change my own vote. Even better, said kind person can add a description (in English) of Marusic's notable achievement in the original article.---CH (talk) 01:02, 23 August 2005 (UTC)

Hi CH, by posting here, you are now officially a member. You might be interested in considering the positions of the Association of Inclusionist Wikipedians as well as the Association of Deletionist Wikipedians. There are some serious philosophical battles on these issues. Amazingly, WP is filled with oodles of non-encyclopedic, non-notable material, e.g articles on ancient soviet submarines, underwater electrical cables, television shows, Pokemon characters, and rock-n-roll bands. linas 04:57, 23 August 2005 (UTC)
Hi CH, to add to what Linas said above, the issue of notability on Wikipedia is unsettled, see: Wikipedia:Notability, Wikipedia:Importance, and Wikipedia talk:Fame and importance. Since Wikipedia is not paper, I lean toward the inclusionist idea that "verifiability" is the more important concept, since it is a necessary condition to be encyclopedic, and being that it also implies a certain minimal amount of notability, is arguably sufficient. (For what it is worth, I believe this is the view held by Jimbo Wales). Paul August 16:11, August 23, 2005 (UTC)

OK, some anon has translated the now notorious Zois prize citation of Marusic, which led me to guess that if he is internationally recognized, some papers by him would appear in a review paper I happened to have at hand. This turned out to be the case, so I changed my own vote in the VfD to a lukewarm keep.

I'd like to try to summarize a few more valuable points which came up:

  • if someone knows of a mathematician who rarely if ever publishes in English but has done extraordinary work (every mathematician can think of examples), of course we all agree that this person should have a biography in the English language Wikipedia, because such a person has clearly made a notable contribution to the body of human knowledge.
  • exhaustive lists of Lusitanian mathematicians might be appropriate in the Lusitanian language Wikipedia, but should be discouraged in the English language Wikipedia, which clearly has a special responsibilty to students all over the world because English currently plays the role of the scholarly lingua franca.
  • the problem with exhaustive lists is that they impede navigation by the generic reader, who wants to find and absorb information on a specific topic; particuarly in a deeply and confusingly interconnected subject like mathematics, eliminating cruft is essential if these pages are to become (remain?) a valuable resource for students and the general public all over the world, which I take it is our goal in the EN language Wikipedia.
  • the sports metaphor breaks down here, because reading about mathematics is far more challenging and daunting than reading the sports pages, and we have a special responsibility to help people find useful and intriguing information about mathematics, which inevitably means taking them places they didn't expect in other parts of the math pages. We must avoid disorienting them or landing them in a huge and amorphous category. So if exhaustive lists "for the sake of keeping exhausting lists" must be kept out, or at least in special categories.
  • how ironic (if unsurprising) that the mindless drones are not the mathematicians--- who were alleged in the popular culture of the first part of the last century to spend their time poring over long lists of meaningless numbers--- but the sports fans! The mere fact that no non-mathematicians expressed surprise at our concern for organization, sanity, good judgement and balance, might suggest that the general public now knows better, or has a new set of misconceptions about us, but probably it only means that the non-mathematicans who dropped by weren't in a contemplative mood.
  • a prize citation by itself means little; mention in a review paper by an international authority is a much more reliable indication that person X, working in some field in which one is not oneself expert, is a major player.

Paul August: up above I think I expressed my take on inclusion; fine by me as long as it doesn't intrude upon the learning experience of the generic user. My concern is to keep that from happening. A mixture of discouraging cruft (hopefully by the art of gentle persuasion) and segregating it is probably the best answer.

Two points, first, "providing a learning experience" for our readers is a noble goal, but strictly speaking, that is not the mission of an encyclopedia, and second, If we are sufficiently creative, having subjects with low notability, should not "intrude" upon such a goal anyway. Paul August 23:02, August 23, 2005 (UTC)

Linas: OK, I'm adding back my name, but I need to focus on the GR WikiProject at least for the rest of this year, because I promised to get some serious work done on that. Yes, I'm talking to you, and all is forgiven, but Linas, I really hope that in the future, you in particular will pay attention to clues that you might be getting on my nerves (or keep an eye on the wikistress meter on my user page), OK? If that happens, I'm sure I'll try to tell you, so if you just remember to be a good listener when interacting with me all should be fine.---CH (talk) 22:27, 23 August 2005 (UTC)

Can more people help me out?

I have a question/problem/something-I-don't-understand that has been bugging me for years. I have posted it at the bottom of Talk:Infinity. Thank you already to Paul August. --Lord Voldemort (Dark Mark) 17:20, 23 August 2005 (UTC)

weird vandalism

There have been some rather strange edits to Galois theory in the last few weeks, all emanating from IP address 64.136.26.235, just deletions of large random chunks of text. What is especially odd is that this IP address appears to be making genuine edits to other articles. Any ideas? Dmharvey Image:User_dmharvey_sig.png Talk 18:49, 25 August 2005 (UTC)

This is the IP address of a cache server fom United Online, so is most likely used by a lot of different users. --R.Koot 18:58, 25 August 2005 (UTC)

"Tav (number)" article

Take a look at Tav (number). Is this valid? Salvageable? The original article is credited to an IP (which has no other math-related edits), and subsequent edits by others have left the basic text unchanged. Obviously, this article needs either a rewrite or deletion. — Nowhither 13:50, 26 August 2005 (UTC)

It has a valid basis but is so poorly written as to be incomprehensible. See the footnote on page 3 of this Postscript document. Here is Tav: ת --Zero 14:11, 26 August 2005 (UTC)

Talk:Sigma-algebra

The notations used by the cluster of articles close to sigma-algebra are inconsistent with one-another; I'd like to fix this, but only after some agreement on a unified notation. Please see Talk:Sigma-algebra for details. linas 13:58, 26 August 2005 (UTC)

Sheaf

Almost a million (well, nearly) pages still point to sheaf rather than to the moved sheaf (mathematics). There were good reasons not to move it. Charles Matthews 20:33, 26 August 2005 (UTC)

There's an entry for it on the disambiguation page. What's wrong with that? --Kooky | Talk 20:53, 26 August 2005 (UTC)
Well first, the article at "sheaf" should be about the mathematical kind if that is the "primary" meaning of the word (see: Primary topic disambiguation). Of course that the mathematical meaning is the "primary" one is debatable, but the great number of links to it vs. the others is suggestive that it is (at least for the here and now). But if it is decided that it should stay at "sheaf (mathematics)", then the links to "sheaf" which want "sheaf (mathematics)" need to be changed. Paul August 21:17, August 26, 2005 (UTC)
Actually, there are 109 articles listed on the "what links here", of which TWO are not mathematics-related. I vote to change it back. Dmharvey Image:User_dmharvey_sig.png Talk 21:25, 26 August 2005 (UTC)
to Paul August: I see. That makes sense. I'd be willing to work through all the mathematical articles that point to sheaf and redirect them to sheaf (mathematics). If it were decided later on that the mathematical definition were no longer the "primary" definition, wouldn't it have to be done anyhow? --Kooky | Talk 22:18, 26 August 2005 (UTC)
If you can make a good case that the primary definition of "sheaf" is moving away from the mathematical one, then I might be persuaded to change my mind. However, the overwhelming proportion of wikipedia articles are presently pointing to the mathematical meaning of Sheaf, and this seems to be evidence pointing the other way. Dmharvey Image:User_dmharvey_sig.png Talk 22:42, 26 August 2005 (UTC)
Gauge, who moved it, contributes to mathematics articles, and I see no discussion anywhere calling for a move. So I can't imagine there will be an outcry if we just quietly move it back, or whatever administrators do. --KSmrqT 22:58, 2005 August 26 (UTC)
The meaning to which the most links point should perhaps not always be considered primary. For example, the word sheaf was probably chosen for use in mathematics to be suggestive, precisely because the word has another, non-mathematical meaning. The effectiveness of the mathematical usage to some extent depends on that other meaning. Michael Hardy 22:51, 26 August 2005 (UTC)
Almost no one outside of math actually uses the word sheaf; what, pastoral literature? Move it back. linas 00:37, 27 August 2005 (UTC)
Change it or leave it, it's all the same to me. --Kooky | Talk 01:12, 27 August 2005 (UTC)

Agree to move it back to sheaf. Oleg Alexandrov 16:03, 27 August 2005 (UTC)

Sorry, I don't know how I missed the remaining links. I will contribute to fixing them or moving them back, based on what we all decide here. Regarding the move, I was thinking that "sheaf" is a common enough word that it could have many possible current (and future!) meanings. Personally, I don't see any harm in having a more specific link to the mathematical definition (so long as the remaining links are fixed). However, if you'd like to go back to the old link, that's fine with me too. - Gauge 16:58, 28 August 2005 (UTC)
I have fixed the remaining old mathematical links to point to the new location. Apparently at least a couple of articles have already referred to sheaves in the agricultural sense. - Gauge 04:40, 2 September 2005 (UTC)

Aged requests

Some of you may remember that in August 2003 a user began adding a huge number of missing math topics to Requested articles. There were well over a thousand requests added, but through the labour of our math people all but seven of them have now been filled. These last few requests are now listed on Articles requested for more than two years. Since they have taken so long to be filled they are probably very obscure and difficult to write about, and certainly need some expert knowledge. It would be great if some math people could take a look at Articles requested for more than two years and try to clear these final relics. - SimonP 23:28, August 26, 2005 (UTC)

Math Babel

I've just made a comment on the category deletion pages for Category:Mathematician Wikipedians about a Math version of the Babel project. Then I realised it's actually only an extension of the Babel project. Below are some sample categories for discussion, and we could make up a pretty box template like the babblers:

  • Math native speaker of math. This person works as a math professor or similar role in industry.
  • Math-N near-native speaker of math. This person is either engaged in a math doctorate, or works where a very high level of math is required e.g. as a physicist, etc.
  • Math-3 very high level of math. Works where a high level of math is involved (e.g., actuary, computer science, etc), or is engaged in a higher level degree in math, physics or other math related subject.
  • Math-2 has taken or is taking an undergraduate degree, in math, physics or other math related subject.
  • Math-1 basic mathematical ability and literacy. Typically working in an environment where an understanding of math or logic is desirable, such as an accountant.

If we preferred it could be a proper equivalent of Babel, where statisticians, applied mathematicians and pure mathematicians have their own boxes, and people like me can be Pure Math-1! --stochata 11:12, 27 August 2005 (UTC)

Not sure I like this fine level classification. OK, if one wishes to do that, one could. But those Babel thing are ugly and take a lot of room on the page. Oleg Alexandrov 16:10, 27 August 2005 (UTC)
The only problem I have with that classification is that it doesn't distinguish different types of math-nativeness. For example, I might be classified as "native" myself, but when it comes to articles on algebraic topology, numerical analysis, several complex variables, or any number of other topics, my understanding is really probably somewhere between Math-3 and Math-N at most. In other words, a lot of the time, the level would depend on the particular subject itself. Revolver 21:52, 2 September 2005 (UTC)
I think those categories are setting the bar too high. After all, we don't make up separate categories for "native speaker of english", "native speaker, additionally is studying english literature at PhD level", and "native speaker, additionally teaches english literature and phonics at university level". I think what you have as "Math-3" is the highest level I would be willing to categorise on babel. After that there are just too many problems with specialised areas, as Revolver notes. Dmharvey Image:User_dmharvey_sig.png Talk 22:10, 2 September 2005 (UTC)
I did wonder about the height of the bar, especially as compared with "native speaker of English" (which covers perhaps 300 million+ people), as opposed to perhaps a few thousand math professors in higher education. However, sometimes I feel it is worth knowing that X is actually a math professor, rather than a doctoral student. I also agree that specialised subdomains complicate thing. I would also be Math-3 (alternatively, Graph Theory-N, Number Theory-1, Statistics-2) under this classification, but then I do feel that others are better qualified than me, and would appreciate knowing who is who (and would also like other editors to know that my math isn't always 100%, and needs checking). --stochata 12:33, 4 September 2005 (UTC)
A math(s) professor may advertise themselves as such on their user page without a babel notice, if they so choose. Perhaps what you really want is a "Mathematical Wikipedians, classified by area of specialisation" page. The difficulty is that often people categorise themselves too high because they don't know any better. For example, there would be a fair few high school students who would describe themselves as accomplished in "geometry and algebra", despite not knowing the first thing about what real mathematicians in these areas actually do. Dmharvey Image:User_dmharvey_sig.png Talk 12:54, 4 September 2005 (UTC)

Merge sigma additivity into measure (mathematics)?

The article sigma additivity used to be a redirect to measure (mathematics). As part of the PlanetMath Exchange project I copied over the article "additive" to sigma additivity, replacing the redirect. User:Blotwell is now suggesting that sigma additivity be merged into measure (mathematics). I feel like the topic is deserving of its own article, but this is not my area of expertise, (not that I have one ;-) and I would appreciate if other knowledgeable editors could help decide what the best thing to do is. Please comment here. Thanks — Paul August 19:21, August 27, 2005 (UTC)

New math categories

As part of working on categorizing articles copied from PlanetMath — the PlanetMath Exchange project, I noticed that there might be a need for more math categories from subjects listed in the Mathematics Subject Classification (2000 edition). Here's the categories I have in mind:

  1. Category:associative rings and algebras as subcategory in Category:Abstract algebra, as per MSC 16-xx, Associative rings and algebras
  2. Category:nonassociative rings and algebras as subcategory in Category:Abstract algebra, as per MSC 17-xx, Nonassociative rings and algebras
  3. Category:Difference equations and Category:functional equations as subcategories in Category:Equations, as per MSC 39-xx, Difference and functional equations
  4. Category:Global analysis and Category:analysis on manifolds, subcategories in ???, as per MSC 58-xx, Global analysis, analysis on manifolds
  5. Category:Sequences, subcategory in Category:Mathematics, as per MSC 40-xx, Sequences, series, summability
  6. Category:Mathematical biology as subcategory in both Category:Mathematics and in Category:Biology, as per MSC 92-xx, Biology and other natural sciences

I am aware that the Mathematics Subject Classification is not directly applicable to Wikipedia math articles, still, probably it can give some inspiration. I am most uneasy about the global analysis and analysis on manifolds thing. Any suggestions and discussion of the above are very welcome. Oleg Alexandrov 22:57, 27 August 2005 (UTC)

Category:Nonassociative algebra would be good. Nobody can remember categories A&B, so let's not have any more. Category:Global analysis was 'big in the 1960s' but I think should probably not be used here - cover by means of other ones (possibly one on infinite-dimensional manifolds, one day). Category:associative rings and algebras is really just ring theory, which we have. Charles Matthews 09:45, 28 August 2005 (UTC)
Charles, should it be Category:Nonassociative algebras, meaning plural? Oleg Alexandrov 15:36, 28 August 2005 (UTC)

(I changed the list to a numbered one, to make referring to it easier). I think (1) and (2) should be under ring theory, as I find it hard to see there being enough articles to justify addiational catergories. Similarly for (3) - I don't think there's enough articles to justify additional catergories. For (4), it seems the seqeunce catergory is broadly equivilant to the catergory you suggest putting it under. On the other hand, I definately agree with doing (5) as you suggested. It is important to remember that the MSC classification is designed to classify maths papers, not maths itself. Tompw 11:50, 28 August 2005 (UTC)

So: Category:associative rings and algebras can be just replaced with Category:Ring theory, and probably Category:Difference equations and Category:functional equations are premature, with Category:Equations being enough. However, I would argue though for creating Category:Sequences. It could contain as subcategories Category:integer sequences and Category:mathematical series. Any comments on this? Oleg Alexandrov 01:54, 30 August 2005 (UTC)

Fibonacci numbers subscript style

I raised this question on Talk:Fibonacci number a while back, but didn't get any comments, and since this also concerns other articles, I'll bring it up here. The Fibonacci number article uses the notation F(n), but my impression is that Fn is far more common in other works (both versions are used more or less randomly around Wikipedia). Which one should it be? Consistency would be desirable. Fredrik | talk 18:56, 28 August 2005 (UTC)

I think I prefer Fn, both PlanetMAth and MathWorld use that notation. And Fibonacci number uses both! I would vote to change it to Fn everywhere for consistency. Paul August 20:15, August 28, 2005 (UTC)
Agree with Fn as the preferred notation. Oleg Alexandrov 20:46, 28 August 2005 (UTC)
I agree too. I think subscripts are preferred when you have them available. some literature uses f instead of F. Bubba73 22:54, August 28, 2005 (UTC)

Both notations are common and should be defined. F(n) notation is better for complex expressions such as F(n-3) or worse I think. For simple expressions I prefer F_n though.--MarSch 16:01, 30 August 2005 (UTC)

Game theory wikiproject

Hello all - In the interest of standardizing and growing wikipedia's coverage of game theory, I have started a WikiProject on game theory. We could use some mathematicians help over there. (For instance, we could use an article on the Kakutani fixed point theorem which is used in the proof of the existence of Nash equilibria.) I hope that some folks will come join in! --best, kevin ···Kzollman | Talk··· 02:22, August 30, 2005 (UTC)

featured math articles template

I've templatized the math FAs, although thanks to Paul it doesn't add much :) Any ideas about this? --MarSch 15:41, 30 August 2005 (UTC)

I have objected on Wikipedia talk:Featured articles. --RobertG ♬ talk 15:41, 30 August 2005 (UTC)
I doubt how much use a template is. Oleg Alexandrov 15:59, 30 August 2005 (UTC)
At the time I created the FA section on our project page, I thought about suggesting this at the FA talk page, and decided not to, since I thought it would be easy enough to maintain our list separately (at least for the foreseeable future). I also figured (correctly as it turns out) Raul wouldn't much like it ;-) Paul August 19:54, August 30, 2005 (UTC)

Math equations to plain english

There is an interesting thread at Wikipedia:Village pump (proposals)#Math equations to plain english. Oleg Alexandrov 19:02, 30 August 2005 (UTC)

Map between AMS math articles classfication and Wikipedia categories

Based on the feedback above, I created a table listing how Wikipedia categories are in correspondence with the AMS Mathematics Subject Classification. Again, this is needed for automatic categorization of articles imported from PlanetMath but would be a curious thing to look at in general. See link at User:Mathbot/Wikipedia categories and AMS MSC classification. Any feedback welcome. Oleg Alexandrov 23:22, 30 August 2005 (UTC)

Are you not aware of areas of mathematics? My only complaint is that it links to articles, when I think it should link to categories. The other complain is a lack of the next level of detail: at one point, I attempted to also add a list of categories corresponding to subcats of MSC 11, but was rebuffed. linas 04:12, 1 September 2005 (UTC)
I am aware of that list, and it was very helpful in compiling my list of categories. No, I would not think that page should link to categories — linking to the article is more informative, and from there the link to category is one click away. But maybe a wider discussion is needed on this. Oleg Alexandrov 04:56, 1 September 2005 (UTC)

Rewrite of Boolean algebra, or new article?

There is a discussion going at Talk:Boolean algebra about rewriting it, or perhaps writing a new article. Several people think the article is too technical and difficult to understand, and User:Plugwash (who says he doesn't understand the current article at all) has made an attempt at rewriting it & mdash; that has been reverted (by me!). Please join in the discussion ;-) Paul August 17:12, August 31, 2005 (UTC)

I've concluded that the article for mathematicians (the current one) needs to be separated from the article for non-mathematicians, which I wrote and placed under Boolean logic. It may need to be moved again, though, as I am getting considerable complaints from PhDs over it's placement there. StuRat 19:45, 18 September 2005 (UTC)

the state of "product/sum" articles

It is my personal belief that all of the "product" articles collectively are in a confusing and sorry shape. Some things are misnamed, some articles have no apparent reason for their content organisation, other things aren't clarified enough, etc. At the heart of the matter seems to be a failure to organise, name, and clarify topics by keeping in mind their category theory meaning. This doesn't mean you have to know category theory to understand anything, but category theory does point a clear direction of how things should be organised, and it's not the direction we're going.

There are 4 major ideas going on in all these articles, based on 2 criteria with 2 options each: first, product or coproduct/sum; second, external or internal. That makes

  1. (External) product
  2. Internal product
  3. (External) coproduct/sum
  4. Internal coproduct/sum

A lot of things are named "sum" that are really products, and a few things that are "internal" aren't clearly identified that way (so could be confused with the "default" external case). For example, direct sum of groups is not about the (external) direct sum, or free product, it's actually about the internal weak direct products of groups. Also, in many cases, you can form the product/sum like you do the sum/product, as objects, but it's not a universal object. Similarly, you can take the "abelian" sum of arbitrary groups, but it's not universal. This is sometimes called the "weak direct product" or "restricted direct product". This distinction between what is an object and what actually is universal is missing in many places. You don't have to mention it directly, but it seems it should guide the presentation. Revolver 21:01, 31 August 2005 (UTC)

The universal and unconditional applicability of category theory is a PoV. I believe the definition complained of is Jacobson's, but I will check. Septentrionalis 01:33, 1 September 2005 (UTC)
After looking around some places, the point is taken. There seems to be a conflict in terminology between researchers in pure group theory and others. Even people writing general algebra books (Jacobson is a bit old to guide current usage, it seems to me), the tendency seems to shy away from "direct sum". But a number of people seem to use it, and for those that use it often, I can imagine how the longer name would get old after a while.
Just to put my comment in context, my first immediate reactions upon reading the term "direct sum of groups" were (honestly)
  1. I've never heard of that before.
  2. There shouldn't be such a thing.
But apparently, the term is used fairly commonly among group theorists. I had no idea about this. For the reasons I said above, I think it may seem counterintuitive or contradictory to many people. Perhaps a strong statement expressing that although the term "direct sum" is commonly used when discussing decomposable groups and so on, it should not be confused with the "direct sum" concept of abelian groups, modules, Banach spaces, abelian varities, representations, etc. which most people are more familiar with. Revolver 05:00, 1 September 2005 (UTC)
Besides direct sum of groups (which does indeed sound crazy at first blush), can you wikilink the other articles you are talking about? Its quite an undertaking to make all the various articles more category-like and at the same time point out the various colloquial flavours in each. A uniformity of style would be better achieved by one person combing over all of these articles, which is no small task. linas 05:12, 1 September 2005 (UTC)
One of the used to be direct sum, which was mostly about direct sums of modules, but also had other stuff. The case of groups was cited as a special case of modules, which isn't true, so I changed it to abelian groups, renamed the article direct sum of modules, and added some other remarks. Direct product seems redundant to me, and could probably be used as a disambiguation page, moving most of the material to separate articles for the cases of groups, vector spaces, and topologies. The only thing distinguishing why these are collected together here vs. others which are not is that they are called "direct product", that's why I think a disambig is good. Beyond this, just a clear distinction between internal/external products in some of the cases, comments on alternative terminology (e.g. I had always heard "weak/restricted direct product", etc.), and checking to see that statements made for the finite case really hold for the infinite case (I already corrected one of these at direct sum of groups.) Revolver 16:46, 1 September 2005 (UTC)
I'm not so much interested in "making them more category-like" then I am about making alternative terminology clear and making the non-category vs. category discussions more clear-cut. For example, in the case of a finite collection of abelian groups, the direct sum and direct product are the same as objects, so in the first discussions of what these terms mean (as objects), there's no need to qualify the statement. But, when moving to the category discussion, it should be pointed out that these are not the same thing, even though the objects are the same. The distinction between objects/limits doesn't belong in the primary discussion, but it should belong somewhere. Revolver 16:53, 1 September 2005 (UTC)
Revolver, I think all of what you are saying is eminently sensible. A lot of work though! :-) Dmharvey Image:User_dmharvey_sig.png Talk 17:29, 1 September 2005 (UTC)
Yes, and being the one who mentioned it, I feel I should try to do something. That's the thing about complaining — it carries responsibility! Revolver 21:52, 2 September 2005 (UTC)