From: Osher Doctorow osher.domain.name.hidden, Mon. Sept. 23, 2002 12:32PM
I refer readers to
http://www.superstringtheory.com/forum, especially to the
String - M Theory - Duality subforum of their Forum section (membership is
free, and archives are open to members, and many of my postings are in the
archives), during the last few days, in which I have provided literature
references and sites from very recent research mostly that puts Analysis via
determinants and/or negative exponentials at the forefront of science - not
merely the interesting Fredholm type determinants and the Slater
determinants, but determinant maximization in general (with constraints).
Fields crossed by these include quantum theory, general relativity,
information theory, communications theory, experimental design, system
identification, statistics as a whole, geometry, computer programming,
entropy, experimental design, algorithms including path-finding algorithms
for convex optimization, etc.
Let me very briefly recapitulate why determinants are Analysis-based rather
than Algebra-based. The expression 1 + y - x, which can be generalized to
c + y - x for arbitrary real constant c (or even to non-real expressions,
but that is another story) or simply written y - x with incorporation of c
into y or x, is continuous and CRITICAL to outgrowths of Analysis including
probability-statistics (for Rare Event scenarios), fuzzy multivalued logics
(see below for those who believe that logic is algebraic), proximity
functions, geometry-topology based on proximity functions. Determinants
generalize y - x to a finite alternating series. Alternating series in
general generalize determinants. The same site (earlier postings) explains
why fuzzy multivalued logics and logics in general are Analysis-based rather
than Algebra-based, although many mathematical and non-mathematical
logicians unfamiliar with Analysis have believed otherwise.
Osher Doctorow
Received on Mon Sep 23 2002 - 12:45:33 PDT