Subject: categories: re: cracks and pots

From: Eduardo Dubuc <[email-masked]>
Date: Thu, 23 Mar 2006 13:50:45 -0300 (ART)

Hi

To follow are the contents of two postings that Bob (always vigilant, ja!)
thought best to concatenate in only one.

On spite of Robert's erudition and his knowledgeable discourse, I still
think Einstein using differential geometry to develop general relativity
is not at the same level that John Baez using category theory to develop
and/or understand string theory. His arguments are valid in a court of
law, but do not convince me. I imagine John himself is probably the first
to laugh at such a comparison.

But this is not the issue of my present posting. He touches also some
pertinent points that go more to the core of the "cracks_and_pots" debate.

(In between ** are Robert  words)

What Motl says certainly does not make people using category theory in
string theory laugh. Applications of category theory to string (or to
other physical theories competing with string theory ?, see Yetter's
posting, it is all very confusing !!) may be valuable or may not. I (and a
lot of us) can not tel.

** In which case demands that they ($) be read out of the meeting are
premature.
($) papers that claim applications to physics **

This is a difficult question.

Marta was saying (and Bob Walters and others agree) that when a paper was
claiming applications to physics it was easily accepted without
knowledgeable and close examination, and that there were a lot of them.

Probably a lot of them should be read out, but not by policy against (as
it was erroneously interpreted in these postings). Serious refereeing is a
healthy practice that should not be equaled with censorship.

**Remember - in mathematics it's a matter of "In God We Trust,
everybody else must provide a proof."**

This is not so much so. Speculations in math are very difficult. If not
well founded they are vacuous. Only great mathematicians can do them
(example close to us, Grothendieck), the rest of us must provide a proof.

**If the math itself meets mathematical standards of rigor, its
application to physics need surely only meet the standards appropriate to
that subject.**

The math itself must also meet standards of quality, not only of rigor.
Besides that, "standards appropriate to that subject" does not mean "free
for anything". Motl writes:

"I always feel very uneasy if the mathematically oriented people present
their conjectures about physics, quantum gravity, or string theory as some
sort of "obvious facts."

Clearly he is  saying that these standards are not being fulfilled (in his
opinion of course) by claimed applications of math to physics.

Motl  may be wrong or he may be right, what we have not seen yet in these
postings is a convincing or clear answer to the questions he arises. I
would say, not even an answer at all.

These questions triggered Marta's original posting, which in turn was
arising other (not exactly the same) questions. I do not agree necessarily
with Marta's implicit views, what I support is her courage to point out
that they are serious problems in the category theory community (for
example, quality of the publications, abuse of fashionable topics to get
grants, invited speakers in CT meetings).

Best wishes    e.d.

---

From: "Urs Schreiber" <[email-masked]>
Date: Sun, 26 Mar 2006 14:25:16 +0100

Dear Category Theorists,

I have begun trying to compile a list with information (mainly links to
reviews and other literature) on applications of categories in mathematical
physics and string theory. (It is not finished yet, though.) See

http://golem.ph.utexas.edu/string/archives/000775.html .

Best regards,
Urs Schreiber