Subject: categories: Re: cracks and pots

From: Eduardo Dubuc <[email-masked]>
Date: Wed, 15 Mar 2006 18:00:07 -0300 (ART)

Hi:

I will put quotations from different postings or Molt's writing in between
two "**"

Well, I can see the classical reaction of some groups when one of its
members points out that something is really wrong with the group.

Marta will suffer all kind of "polite" (nothing of the sort of the
Benabou-Taylor confrontation) attacks, but not for this less devious or
sanguine. Typically she will be taken out of context, or get answers to
questions she never had asked, or be treated ironically or in disbelief
(**I can't tell if you're kidding.  I'll assume you're not **)

There are two principal points here:

1. The real value of some contributions of category theory to physics.

2.  The lot of rubbish written using category theory and which is
fashionable because it claims to have applications to physics.

Marta was forced to explicit some of the questions we can clearly see in
between lines in her original posting:

** 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 remotely claims to have applications to physics (particularly
string theory) is given (what I view as) uncritical support in our
circles?

Best,
Marta **

I will like to see a clear answer to this question. Or a clear refutation
proving that it is not the case.

Notice that the existence of point 2. above is perfectly consistent with
the existence of really valuable contributions of category theory to
string theory, which is one of the points treated by Motl.

** 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.**

This make us think that they may be some valuable contributions, but this
possibility is also left open by Motl himself.

Quoting myself:

** 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 !! **

No luck, just discredit Motl, not refute his sayings:

**  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. **

** 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.**

The following is  better in answering Motl:

** 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. **

I am unable to judge, but it seems to me this gives category theory strong
support But does not go against what Motl says concerning category
theory. Neither against Marta's warning that category theory is being
discredited by many (she says a minority) category theory people.

Motl writes:

** I've asked the same elementary questions to many people who've been
trying to explain me derived categories - some of them with some success,
most of them with no success whatsoever: Are these notions and statements
of category theory something that you can prove - or at least check in
many situations - to be valid for string theory as we know it, or is it
just an unproven conjecture that derived categories describe D-branes? **

Can somebody give a an answer ?

He also 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". **

I would say that any serious scientist or mathematician would feel the
same way !!, and also that this seems to be a common practice in many
papers that claim applications of category theory to physics.

** I have this image of differential geometers saying to each other, a
century ago, "Don't you think somebody ought to tell that Einstein to
stop trying to use differential geometry to explain gravity, before our
whole field gets a bad name?" **

Well, Einstein was not "trying to", he was using it, and presented this
use as an accomplished fact.

Also, you forgot to mention that he flunk a high-school exam or something
of the sort proving by this very fact that a lot of people were stupid,
just as they are those which have doubts about the real value of some
applications of category theory to physics !

** 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. **

** Since Motl's personality is well known, any damage will be minimal.
I think we should relax and take it easy.**

Well, rubbish category theory always discredits the whole of category
theory, specially given the fact that it is not yet a prestigious and
established subject (think in SGA4 and the introduction of SGA41/2)

It will be nice to relax and take it easy.

Will all of us do so  ?

I hope we will read in this cat-list some valuable considerations about
Motl's questions and doubts, and about Marta's courageous warnings.

e.d.