- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

From: Osher Doctorow <osher.domain.name.hidden>

Date: Mon, 23 Sep 2002 12:31:32 -0700

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

Date: Mon, 23 Sep 2002 12:31:32 -0700

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

*
This archive was generated by hypermail 2.3.0
: Fri Feb 16 2018 - 13:20:07 PST
*