Re: cracks and pots

["Robert J. MacG. Dawson" <rdawson@cs.stmarys.ca>]

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