Re: Applied vs. Theoretical

From: Osher Doctorow <osher.domain.name.hidden>
Date: Sun, 1 Dec 2002 12:48:37 -0800

>From Osher Doctorow osher.domain.name.hidden, Sunday Dec. 1, 2002 1243

Sorry for keeping prior messages in their entirety in my replies.

Let us consider the decision of category theory to use functors and
morphisms under composition and objects and commuting diagrams as their
fundamentals. Because of the functor-operator-linear transformation and
similar properties, composition and its matrix analog multiplication
automatically take precedence over anything else, and of course so-called
matrix division when inverses are defined - that is to say, matrix inversion
and multiplication.

It was an airtight argument, it was foolproof by all that preceded it from
the time of the so-called Founding Fathers in mathematics and physics, and
it was wrong - well, wrong in a competitive sense with addition-subtraction
rather than multiplication-division. There is, of course, nothing really
wrong with different models, and at some future time maybe the
multiplication-division model will yield more fruit than the
addition-subtracton models. And, of course, each model uses the other
model secondarily to some extent - nobody excludes subtraction from the
usual categories or multiplication from the subtractive models.

What do I mean when I say it was relatively wrong, then, in the above sense
[question-mark].

Consider the following subtraction-addition results - in fact, subtraction
period.

1. Discriminates the most important Lukaciewicz and Rational Pavelka fuzzy
multivalued logics from the other types which are divisive or identity in
their implications.
2. Discriminates the most important Rare Event Type [RET] or Logic-Based
Probability [LBP] which describes the expansion-contraction of the universe
as a whole, expansion of radiation from a source, biological growth,
contraction of galaxies, etc., from Bayesian and Independent
Probability-Statistics which are divisive/identity function/multiplicative.
3. Discriminates the proximity function across geometry-topology from the
distance-function/metric, noting that the proximity function is enormously
easier to use and results in simple expressions.

It sounds or reads nice, but the so-called topper or punch line to the story
is that ALL THREE subtractive items above have the form f[x, y] = 1 plus y -
x. ALL THREE alternative division-multiplication forms have the form f[x,
y] = y/x or y or xy.

Category theory has ABSOLUTELY NOTHING to say about all this.

So where are division and multiplication mainly used [question mark]. It
turns out that they are used in medium to zero [probable] influence
situations, while subtraction is used in high to very high influence
situations.

Come to your own conclusions, so to speak.

Osher Doctorow


----- Original Message -----
From: "Tim May" <tcmay.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Sent: Sunday, December 01, 2002 10:44 AM
Subject: Applied vs. Theoretical
Received on Sun Dec 01 2002 - 16:04:06 PST