User talk:William Hart

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Tasks: start a new article • add basic, wanted or requested articles • add definitions • add metadata • edit new pages

Welcome to the Citizendium! We hope you will contribute boldly and well. Here are pointers for a quick start, and see Getting Started for other helpful "startup" links, our help system and CZ:Home for the top menu of community pages. You can test out editing in the sandbox if you'd like. If you need help to get going, the forum is one option. That's also where we discuss policy and proposals. You can ask any user or the editors for help, too. Just put a note on their "talk" page. Again, welcome and have fun!

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Kind Regards, Robert Tito | Talk 08:09, 15 February 2007 (CST)

ID

Hi William, thanks for the start on intelligent design. Could you give us a bio please? --Larry Sanger 09:07, 15 February 2007 (CST)

Apologies for not realising this was a better place for questions about bio details. You've answered the point of my question pertinently and appropriately. I intend to delete my remarks from the talk page on the article (but will revert if you'd prefer they remain there). David Tribe 07:54, 17 February 2007 (CST)

Sure, no problems. I was never a big WP contributor, so I don't really know much about the best way to do things. You're welcome to delete the comments from the discussion page along with my response if you want, or leave it there as you wish. You could even transfer it all to this page if you wanted. But maybe it isn't that important. To further answer your questions, I'm actually considering not contributing much more to the article, just to see how it develops from here. I think it is fairly neutral (apart from the Popper comment, which I think Gareth contributed), and I'm just curious to see how it "evolves" under the "intelligent" direction of future contributors. Your summary for your single edit to the article was pretty funny by the way. I feel that my piles and arthritis were perfectly designed to achieve their end. :-) William Hart 08:06, 17 February 2007 (CST)

I'm relieved that I have'nt seriously offended you. I'm sill thinking of relegating Popper name to the footnotes.!I really welcome much your copy edits on HGT ( I have since installed Firefox 2 with its spell checker and those issues will go away now I hope. I've slapped a To Approve tag on V 1.1, 24 hours time limit. More seriously and genuinely, I've reflected further about your credentials for ID, ans on the basis or neutrality now see that you may be ideally qualified. I hope that you take my clumsiness as a disincentive to participate further. The story cries out for an ending. I might sometime find time to do the flagella bit. I had to stay away the last 24 hours David Tribe 15:48, 18 February 2007 (CST).

PS As far as rules, I think that getting to know each other is a phase that we'll go thru; puzzeling remarks become less worrying after that occurs. Ive genuine jokes can be misinterpreted. Be aware that dealing with odd situation here requires the wisdom of Solomon. BTW I learnt that the correct term for an organism in the Domain Archaea is archaeon (noun) and Ive got to find my error on this somewhere and correct it! David Tribe 15:56, 18 February 2007 (CST)

Thanks for the encouragement to continue adding to the article on ID. I'm a bit worried about being the person who "finishes the story". I'd really like to see some other qualified individuals add something. As for it being a story, I'm not so sure I can make it so. I've always struggled with writing compelling prose (comes from being a mathematician). To me, the story needs a list of the principal arguments from the ID camp and a list of the primary scientific objections to those arguments (with citations where possible). Trouble is, that takes the article out of the woolly beginning it currently has and into the realm of "oh, I have to actually do lots of extra reading to make a good job of this". I mean, I know the basic story, but I have higher standards than that, and I'm just not sure I have the time to invest. I might consider adding intermittently as I find the time. I'd particularly like to add something about the No Free Lunch theorem and Dembski's search spaces. It's a concept that WP doesn't even mention IIRC. But understanding Dembski's papers, even for a mathematician, is a non-trivial task!! I understand what he's getting at, but understanding the actual mathematics is somewhat of a chore. Separating the philosophy from the mathematics which models it is also quite difficult.

As for being neutral, it isn't that hard for me as an academic without much invested in the issue. I'd like to see ID presented in a completely neutral way. ID is portrayed by its adherents in such a positive light and by its opponents as such a hindrance to progress that it is hard to sit back and truly assess it for what it is, on intellectual grounds. Very few people but academics and intellectuals with nothing to lose by doing so, actually want to consider the issues on intellectual grounds. Most people actually don't care if the concept has content or not. They only care if the idea of an intelligent designer makes them happy or angry. William Hart 18:11, 18 February 2007 (CST)

Based upon my reading of your entries on the talk page, I think your arguments on making the article neutral are a good start. Stephen Ewen 15:41, 23 February 2007 (CST)

fundamental domains in elliptic curves article

Hi - thanks for all the corrections in this and in the hyperelliptic curves article. However, in one of them we are in disagreement: the fundamental domain of the uper-half plane under PSL_2 cannot be a closed set: we can take only half the points on the boundary. Do you agree ? I want to change it back.--dlehavi 22:36, 22 February 2007 (CST)

Hi David - I'm not so sure... Usually the fundamental domain is as I have defined it, i.e. it is a closed region for which every z \in H is PSL_2(Z)-equivalent to a point of the domain, but for which no two points in the interior are PSL_2(Z) equivalent (two boundary points are permitted to be equivalent).

A standard reference for the definition as I give it is Neal Koblitz "Introduction to Elliptic Curves and Modular Forms", or Serge Lang, "Introduction to Modular Forms" or Anthony Knapp, "Elliptic Curves", etc. In particular, note that Wikipedia (according to these sources) is incorrect in its definition. I also believe William Stein uses the same definition as me, and he is a recognized authority. I understand why one may wish to exclude half the boundary, but convention has the terminology apply to a closed (and usually simply connected) region. If not, one has to choose which boundary to remove.

I'm guessing that what you are aiming for is a moduli space, which is presumably the fundamental domain as I define it, with the edges identified. I see you are an expert in such matters so I'll leave *that* up to you.

Just as a general note, I see that the elliptic curves article reads very much like an algebraic geometry article, i.e. is quite technical and studies the algebraic geometry of elliptic curves. I wonder if this is the best way to introduce the subject, given that historically it didn't develop this way. And by the way, the hyperellitic curve article is a great improvement over what exists in WP. William Hart 03:19, 23 February 2007 (CST)

Hi, My reference is Herb Clemenes's "scrapbook of complex algebraic curves", but indeed the discussion in that part is geared twords moduli spaces. It seems that its algebraic geometers on one side and modular forms/number theorists on the other, so lets keep your edit.

I plan to give the modular forms/elliptic integrals a fair handshake (this part is mostly written - are you inetersted in writing it?). I think that starting with it is not a good idea with what today's target audience knows. Many people today (not only mathematicians) have seen pictures of plane cubics. In the middle level of the target audience graduate students see homology groups and line bundles very early in their carrier, independent on their experties; allmost nobody knows today what abelian integrals are, and only people working in related fields know what a modular form is.

Thanks for the help (and the complement). BTW should we move this discussion to the article talk page ? --dlehavi 08:10, 23 February 2007 (CST)

I see. There are a few issues here. One is whether to use the algebraic geometer's definition or not. The other is whether the article on elliptic curves etc should be treated from an algebraic geometer's point of view. Obviously the answer to the former question depends on the answer to the latter. I think you are right, most (American) graduate students see cohomology before they see the integers, so your point of view might be the right one for a technical audience. Another way of doing things might be to split elliptic curves into two articles, one called Elliptic_Curves_Algebraic_Geometry and Elliptic_Curves_Number_Theory. I'd be greatly in favour of doing this and I think the CZ people have suggested such things before in other situations, so it wouldn't be without precedent.

I have to admit I planned on adding some articles to algebraic number theory before treating things like elliptic curves and modular forms, so any article on elliptic curves from a number theorist's perspective would have to wait if I were writing it.

We can move this discussion to the talk page if you like, but the issues here probably go beyond just that one article. There is significant overlap between algebraic geometry and number theory and a number of articles might benefit from having dual presentations. What do you think?

Incidentally, I know Christoph Ritzenthaler from my time in Leiden. I notice he was a coauthor of yours. William Hart 09:10, 23 February 2007 (CST)

I agree that the main issue is indeed the "waht viewpoint do we take", but I think that the seperation solution is a bit extreme. I think that in an encyclopedia we should give all the view points, and stress the connections between these viewpoints (in the paper at hand Weierstrass form and p function, tau and the j-invariant). Idealy, as I see it, this would be a joint work of a function theorist, and number theorist and a geometer. I worked with paople who swear by different (mathematical) gods than my own before, I'd hate to break this tradition in an encyclopedia article of all places - its math after all, not mideast pllitics :)--dlehavi 17:10, 23 February 2007 (CST)

Oh, my inclination to separate the article had nothing to do with believing the article to be controversial. After all, we don't have any cranks trying to tell us what they think elliptic curves are yet. Rather my concern was one of mathematical elegance. It seems to me that each section of the article will need to be written three times, once from each point of view. For example I imagine you will want to introduce modular forms as sections of line bundles or whatever they are, whereas I will want to introduce them as functions invariant under the action of certain Fuchsian groups. Others will want to speak about GL_2 of the adeles and start discussing tne Langland's correspondence. Anyhow, if you don't want to split the article, we won't. At some point I might try and interweave some function theorist/number theorist perspectives throughout the article. Relating those ideas to what you have been written might be difficult though. Anyhow, I want to have a go at algebraic number theory first. William Hart 19:59, 23 February 2007 (CST)

hyperelliptic curves article

Hi, Modulo (probably serious) cleanup I think I finished the hyperelliptic case article. care to comment (as at seems we are the only two people who care :) )--dlehavi 22:42, 26 February 2007 (CST)

Hi David. Yes, it looks like a lot of work has gone into the article. Well done. I'll have a bit of a fiddle to correct some spelling and clean up the references at some point if you don't beat me to it, but it is looking really nice. I'm particularly looking forward to the article on Abelian Surfaces if you are going to write it. This is a topic I know almost nothing about, and have wanted to know something about. So it should be good to have some of the basics about that topic in CZ. William Hart 06:11, 27 February 2007 (CST)

Hi, William - tried to fix what you suggested in the HE , but I'm not sure I'm the best person to write the non-technical introduction. Did my best though. Nice paper on number theory--dlehavi 14:23, 3 March 2007 (CST)

Many thanks

Thanks for your very kind words. You make a very good point about perfection in design, and I will take a fresh look when I get a minute. I was prompted to include that after looking through the wiki on the Discovery Institute site, and some of the entries, on junk DNA for example, seemed to recognise that they felt that the existence of so much junk in human DNA seemed incompatible with intelligent design; those entries highlighted recent work that suggests that much of this might in fact be functional as evidence thereby supporting ID, or at least more compatible with it. But you're right, there is no reason why intelligent design has to be perfect.

I haven't read Behe's book unfortunately, but will try to find out more.Gareth Leng 08:03, 6 July 2007 (CDT)