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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

Date: Sun, 1 Dec 2002 12:48:37 -0800

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

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