Due to an editing error on my part some of you will have received four posts from Jim Stasheff with no subject line, and in some cases (as Nimish Shah pointed out to Jim, who also alerted me) spam filters will have prevented delivery. With apologies to Jim, these messages are repeated below (except for some of the material repeated from earlier posts). Since I will be away from email access there will be an interruption in postings to this list until Wednesday starting a little more than 24 hours from now. Several new items in the current thread will be posted shortly, and responses to them arriving in the next day will be posted, but I would encourage you not to submit further items for posting until after Wednesday. best wishes, Bob Rosebrugh ----------------------------------------------------------------------------- Date: Wed, 15 Mar 2006 20:53:54 -0500 From: jim stasheff <jds@math.upenn.edu> Subject: categories: Re: cracks and pots Mostly well said, David I would only modify/deform ;-) what you say by doubting therte are that many physicists who are anti-cat theory (not pro-) but watch out once some leader of the school adopts it the school will follow - much faster than if they were mathematicians jim David Yetter wrote:
Dear Marta,
My reaction to the blog posts you cite is that this is a sting theorist holding his breath and refusing to learn category theory. My guess is that Motl wouldn't want to learn the heavily categorical formulations of mirror symmetry that Yan Soibelman uses, even though they are motivated by string theory. Basically categorical ideas aren't part of the standard bag of tricks physicists use (even though they often give much more elegant, concise, and insightful formulations of some of those tricks), and the proverb about 'old dogs' and 'new tricks' applies to physicists as well.
... Date: Wed, 15 Mar 2006 20:58:45 -0500 From: jim stasheff <jds@math.upenn.edu> Subject: categories: Re: cracks and pots Marta Bunge wrote:
I was trying to elicit an open response from those who *do* know about the value (or lack of it) of categorical string theory. In particular, I would like to have an answer to this question. Why is it that anything which even remotedly claims to have applications to physics (particularly string theory) is given (what I view as) uncritical support in our circles?
Best, Marta
It's not so much the applications that seduce some of us but rather the *new* structures the physicists suggest that turn out to have neat mathemaical, e.g. categorical, aspects. e.g quantum groups jim Date: Wed, 15 Mar 2006 21:07:25 -0500 From: jim stasheff <jds@math.upenn.edu> Subject: categories: Re: cracks and pots
I was aiming at the fact that there is a certain trend within category theory (when did it start?) to consistely give center stage to anything that claims to have connections with physics (in particular string theory). Is this because (it is believed that) the state of category theory is now so poor (as "evidenced" by the lack of grants) that they (the organizers of meetings) want to repair this image at any cost? Also, by so doing, are we not becomeing vulnerable? Are we not pushing students to work on a certain area on the grounds that it is fashionable and likely to be funded, even if those students may lack the motivation and sound background knowledge? I feel that this is dangerous for category theory (and mathematics in general), as it may lead (is leading?) to narrow developments of any subject that is approached with these objectives in mind. I did point these concerns of mine already, in response to the posting by Robert MacDawson, whom I also thank for giving me the opportunity to make clearer what my real concerns are.
Consider instead what happened in algebraic topology in the last century (or in invariant theory of polynomial forms in the previous one): classic internal problems e.g. homotopy groups of spheres ground on and on while the enthusiasm and excitement of `application' motivated problems died with a lack of such problems (I have in mind vector fields on spheres and allsorts of diff geom motivations).
On the subject of what constitutes good mathematics, Ronnie Brown has pointed out to me a beautiful expose (with Tim Porter) which you can find in www.bangor.ac.uk/r.brown/publar.html I urge you to read it.
Exactly - if it's good math, it's not tainted by being invented by physicists. jim Date: Wed, 15 Mar 2006 21:08:42 -0500 From: jim stasheff <jds@math.upenn.edu> Subject: categories: Re: cracks and pots For that remember (if any are as old as I) matrices good, groups bad the gruppenpest jim Krzysztof Worytkiewicz wrote:
The blog in question is indeed more than dubious. Besides the "scientific" manicheism (group good, monoid bad...), what to think about ranking countries according to a "civilization index"? The blogger also claims he was mastering differential geometry and particle physics at age of 15, so he obviously was too busy and missed the provocative phase. Not a reason however to try to catch it up as an "adult".
Cheers
Krzysztof