To categories@mta.ca Subject: categories: Re: cracks and pots In-Reply-To: <E1FJfCK-0003LO-EL@mailserv.mta.ca> Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Sender: cat-dist@mta.ca Precedence: bulk Status: RO X-Status: X-Keywords: X-UID: 61
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
I end with a quote from the end of David Yetter's posting in reply to mine. "If (I suspect when) the string theory emperor turns out to have no clothes, category theory will suddenly become de rigeur in physics". I share his optimism.
Most cordially, Marta Bunge
************************************************ Marta Bunge Professor Emerita Dept of Mathematics and Statistics McGill University 805 Sherbrooke St. West Montreal, QC, Canada H3A 2K6 Office: (514) 398-3810 Home: (514) 935-3618 marta.bunge@mcgill.ca http://www.math.mcgill.ca/bunge/ ************************************************
From: "John Baez" <baez@math.ucr.edu> To: categories@mta.ca Subject: categories: Re: cracks and pots Date: Tue, 14 Mar 2006 11:56:09 -0800 (PST)
Hi -
I just came across the following pages
http://motls.blogspot.com/2004/11/category-theory-and-physics.html http://motls.blogspot.com/2004/11/this-week-208-analysis.html
written by Lubos Motl, a physicist (string theorist). Some of you may find these articles interesting and probably revealing.
Are we category theorists as a whole going to quietly accept getting discredited by a minority of us presumably applying category theory to string theory?
I can't tell if you're kidding. I'll assume you're not.
There's nothing wrong with applying category theory to string theory. The papers by Michael Douglas and Paul Aspinwall cited above by Motl are some nice examples of using derived categories to study D-branes.
Further examples: the Moore-Seiberg relations turn out to be little more than the definition of a balanced monoidal category, and the Segal-Moore axioms for open-closed topological strings are nicely captured using category theory here:
http://arxiv.org/abs/math.AT/0510664
There were a lot of nice talks on the borderline between category theory and string theory at the Streetfest.
Perhaps more to the point, Lubos Motl is famous for his heated rhetoric. He doesn't like me, or anyone else who criticizes string theory. The articles you mention above are mainly reactions to my This Week's Finds.
He's actually being very gentle - for him. He even says "the role of category theory can therefore be described as a `progressive direction' within string theory".
I'm sure you'll all be pleased to know that. :-)
It is surely not too late to react and point out that this is not what (all of) category theory is about.
I would urge everyone not to react - at least, not until they are well aware of what a discussion with him is like. See his blog and his comments on Peter Woit's blog if you don't understand what I mean. For example:
http://pitofbabel.org/blog/?p=51
Please give a thought about what we, as a community, can urgently do to repair this damaging impression.
Since Motl's personality is well known, any damage will be minimal. I think we should relax and take it easy.
Best, jb