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? It is surely not too late to react and point out that this is not what (all of) category theory is about. Please give a thought about what we, as a community, can urgently do to repair this damaging impression. Unless we are prepared to wait until things change by themselves within our lifetime. Hopefully disturbing your weekend, Cordially, Marta ************************************************ 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/ ************************************************
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. His attack on Baez is fairly standard stuff: in the mode of "string theory is the theory of nature, so we don't want to think about alternatives like loop quantum gravity." It is a polemical defense of a scientific theory that hasn't produced a testable prediction in the 40 plus years since its inception, and worse than that, unless one adds bells and whistles to fix it (in the manner of 'gaseous Vulcan' or Ptolemaic epicycles), predicts the existence of a massless scalar field *not observed in nature*. It really has nothing at all to say about category theory, which is after all a mathematical theory which stands irrespective of its extra-mathematical applications. Categorical ideas are absolutely central to several competitors to string theory: the Barrett-Crane model of quantum gravity (and to a lesser extent 'loop quantum gravity' with which the BC model is often conflated) and Connes' recovery of the Standard Model from non-commutative geometry (a part of mathematics which has obliged reluctant mathematicians to think about categorical ideas deeper than they originally were comfortable with). There is nothing cracked or crackpot about either. It is simply a fact we have to live with that our subject has found legitimate uses in physics, but uses which are unpopular with the dominant school of physics in the North America. If (I suspect when) the string theory emperor turns out to have no clothes, category theory will suddenly become de rigeur in physics. (As it should, since categorical expressions of physical ideas are the logical conclusion of 20th century physics drive to express everything in coordinate-free terms.) Best Thoughts, David Yetter On 12 Mar 2006, at 17:29, Marta Bunge wrote:
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? It is surely not too late to react and point out that this is not what (all of) category theory is about. Please give a thought about what we, as a community, can urgently do to repair this damaging impression. Unless we are prepared to wait until things change by themselves within our lifetime.
Hopefully disturbing your weekend, Cordially, Marta
************************************************ 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/ ************************************************
I just posted a notice of a special session on Categorical Logic and Quantum Computation in the upcoming ASL meeting at UQAM - although the preparation for that session goes back many months, and it was always my intention to post a schedule for the session here, I was reminded to do so upon reading Marta's message; in a sense I see it as a partial reply (even if the applications to physics are not those of the postings Marta quoted). I think the mathematics of that session will be of a high standard - we hope many of you will attend to judge for yourselves! -= rags =- -- <rags@math.mcgill.ca> <www.math.mcgill.ca/rags>
I congratulate Marta for her posting, I just read Motls's http://motls.blogspot.com/2004/11/category-theory-and-physics.html and find it very revealing as Marta said, and more than that, I find it a very clear exposition (by way of philosophy and by way of examples) about what is good science and mathematicas and about what it is not. Marta is right about that it concerns all of us category theoricist. I will like to see here a debate about Motls's writing quoted above. Just about this writing, NOT ABOUT Motls himself or other things he may have done or represent !! I do not feel capable to say something because in particular am ignorant of physics, but many of you are not. I think in Bill for example. So long Eduardo Dubuc
Marta Bunge wrote:
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? It is surely not too late to react and point out that this is not what (all of) category theory is about.
I don't see that we have any more need to do this than (for instance) algebraic topologist, group theorists, or differential geometers have when somebody floats a perhaps-too-conjectural theory using those branches of mathematics. Heck, physicists have managed to come up with what are now generally seen as dubious theories using nothing more than elementary arithmetic (Dirac's Big Numbers hypothesis, say.) Do the number theorists have to protest this? Big problems in physics have tended to be solved only after a lot of attempts that look pretty strange in retrospect (think of some of the early models of the atom!) But correct theories (or at least theories that represent a major improvement in understanding and prediction) can also look pretty strange; think how general relativity, or even special relativity, must have looked in their day. I seem to recall that the periodic table was originally considered at least as dubious as Bode's Law - and if they had been able to measure molecular masses more accurately in Mendeleev's day, they would have seen that the main idea was actually _wrong_, and its acceptance would probably have had to await the technology to separate individual isotopes, which do have (reasonably) predictable masses. Quaternions were fashionable in Victorian days to represent motions in space, dropped out of fashion when people decided that the restriction of their applicability to three-dimensional space was parochial, and dropped back in again when people realized that in fact a three-plus-one-dimensional spacetime had some rather special properties. Mathematics, like the phone service, is a "common carrier". We develop it; we use it; but we have neither the right nor the obligation to police how others apply it (unless they get the mathematics itself wrong?). Moreover, given the historical difficulty of recognizing good physical theories ahead of time, it would be impossible to do so wisely even if we had the right. I do not see how anybody can possibly discredit category theory by applying it to string theory, even inappropriately, any more than "The da Vinci Code" discredits classical geometry and number theory. -Robert Dawson
Dear Robert, I agree with most of what you say, and I was not suggesting that we police how categorists choose to apply their field. Nothing further from my mind.
Mathematics, like the phone service, is a "common carrier". We develop it; we use it; but we have neither the right nor the obligation to police how others apply it (unless they get the mathematics itself wrong?). Moreover, given the historical difficulty of recognizing good physical theories ahead of time, it would be impossible to do so wisely even if we had the right.
But organizers of meetings in category-related subjects can certainly direct attention to certain trends in category theory, thereby promoting certain areas over others, and this they can easily do by their choice of invited speakers of (series of) lectures. They may have neither the right nor the obligation to do so, but they certainly have the power to do so. If this happens consistently, then the outcome is predictable. Students (and their advisors) might flock to certain areas of research just because they are fashionable and can thus get funding that otherwise will not be easily obtained. This may lead to narrow developments of any subject that they approach with this objective in mind, and that is dangerous for the future of category theory (of mathematics, in general). That is my main concern. My posting tried to call attention to what I think is a sad state of affairs in category theory, when it need not be. Best wishes, Marta
Roger Penrose, page 960 of "The Road to Reality - A Complete Guide to the Laws of the Universe": Another idea that may someday find a significant role to play in physical theory is *category* theory and its generalisation to n-category theory. [...] It would not altogether surprise me to find these notions playing some significant role in superseding conventional spacetime notions in the physics of the 21st century. Dominic http://boole.stanford.edu/~dominic
participants (6)
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David Yetter -
Dominic Hughes -
Eduardo Dubuc -
Marta Bunge -
Robert J. MacG. Dawson -
Robert Seely