Re: Black Hole Bouncing vs Evaporation vs Control

From: OsherD (mdoctorow_at_comcast.net)
Date: 03/11/05 

Date: 10 Mar 2005 17:13:53 -0800

>>From Osher Doctorow

We're beginning to see that there is a good deal of "mysticism"
concerning what exactly is going on in physics with anomalies and
generation of mass and related things, especially when mathematical
group theory is used as it has been together with Lie algebras and Lie
groups and so on. Indeed, Cao points out that both Weyl and Wiggins
were led astray in some important places by group theory in physics,
and something similar happened with the quark Nobel Prize winner at the
Santa Fe Institute whose name is on the tip of my tongue.

Should physicists consult mathematical specialists in algebra (which
includes group theory) to clarify the problems? It never hurts to
consult mathematicians, but algebraists have an especially difficult
time because their field or discipline is in a sense even bigger than
physics. It contains too much "data" and too few "principles".
Almost anything is algebra or can be thought of as algebra. Whereas
geometry is very roughly grounded in pictures and graphs, algebraic
subjects only seem to "end" when another discipline claims priority -
for example, number theory or arithmetic claims priority for real
numbers, integers, modular arithmetic, etc., so algebraists usually
agree that those topics aren't their main foci although texts in
algebra commonly include at least parts of number theory/arithmetic.
Calculus (called analysis and later real, complex, functional,
nonsmooth analysis, etc., in college and onward, although in high
schools or grammar schools the word "analysis" is often used to mean
precalculus!) claims priority in differentiation and integration and
measure and aspects of continuity closely related to them, which
algebraists usually "allow" while still using "derivations" and so on
in their own topics and fighting a "holding action" on continuity.

Category theory is an attempt by algebraists (Saunders MacLane and
William Lawvere) to organize algebra, and like most fads it has turned
out to bias organization in one direction, namely composition of
functions and "generalizing sets to 'objects' " which benefits neither
logicians nor set theorists but provides lots of commuting diagrams to
make simplicity more difficult if more 'organized along the direction
of commuting diagrams', and is very much approved of by many computer
people who are not any better in logic or set theory than most
algebraists.

We are going to turn next to Edward Witten, hopefully. See you soon, I
hope.

Osher Doctorow

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