Subject: categories: cracks and pots

From: "Marta Bunge" <[email-masked]>
Date: Sun, 12 Mar 2006 17:29:42 -0500

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
[email-masked]
http://www.math.mcgill.ca/bunge/
************************************************

---

From: David Yetter <[email-masked]>
Date: Tue, 14 Mar 2006 01:08:49 -0500

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

---

From: Eduardo Dubuc <[email-masked]>
Date: Tue, 14 Mar 2006 11:55:07 -0300 (ART)

I congratulate Marta for her posting, I just read Motls's

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

---

From: "Robert J. MacG. Dawson" <[email-masked]>
Date: Tue, 14 Mar 2006 12:05:43 -0400

Marta Bunge wrote:
> 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

---

From: "Marta Bunge" <[email-masked]>
Date: Tue, 14 Mar 2006 11:30:21 -0500

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

---

From: Robert Seely <[email-masked]>
Date: Tue, 14 Mar 2006 18:18:56 -0500 (EST)

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 =-

-- 
<[email-masked]>
<www.math.mcgill.ca/rags>

---

From: Dominic Hughes <[email-masked]>
Date: Tue, 14 Mar 2006 15:26:31 -0800 (PST)

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