>From Osher Doctorow [EMAIL PROTECTED], Tues. Dec. 3, 2002 1326

Tim May gives a very detailed account of his ideas on category and topos
theories, and I will only comment on a few of his ideas and some of Ben
Goertzel because of space and time limitations.

I think that Tim and I, and hopefully Ben, do not differ on the extreme
usefulness of being able to generalize concepts across many different fields
and subfields.  MacLane and Lawvere's category theory TRIED to do that, and
the effort is certainly commendable.   Perhaps it is more than commendable.
As one who seldom receives commendations, I may tend to give them less often
to others than I did when I started out in mathematics/science.

Nevertheless, I perceive or understand what Ben refers to as a certain lack
of deep results in category theory as compared with my Rare Event Theory for
example - although Ben understands it relative to his own experiences.  The
theorems that Tim has cited are one counterexample class to this, but where
are the great predictions, where is there anything like the Einstein Field
Equation, the Schrodinger Equation, Newton's Laws, Fermat's numerous
results, Maxwell's Equations, the Gauss-Bonnet Theorem and its associated
equation that ties together geometry and topology, Non-Euclidean/Riemannian
Geometry, Euclidean Geometry, the Jacobsen radical, Gauss-Null and related
sets in geometric nonlinear functional analysis, Godel's theorems, or even
Hoyle's Law or the Central Limit Theorems or the almost incredible theorems
of Nonsmooth Analysis and Kalman filters/predictors and Dynamic Programming
and the Calculus of Variations and Cantor's cardinals and ordinals and
Robinson's infinitesimals and Dirac's equations and Dirac's delta functions
and Feynmann's path history integrals and diagrams and the whole new
generation of continuum force laws and on and on.

Sure, category theory can go in to many fields and find a category and then
take credit for the field being essentially a category, and I can go into
many fields and find plus and minus and division and multiplication analogs
and declare the field as an example of Rare Event Theory [RET] or Fairly
Frequent Event Theory [FFT or FET] or Very Frequent Event Theory [VFT or
VET] or a plus field or a minus field or a division field or a
multiplication field.   And both Category and RET-FET-VET theories can show
that many of their concepts cross many fields.   This is very commendable,
although to me it is old hat to notice that something like a generalization
of a group crosses many branches of mathematics, whereas RET-FET-VET classes
such as GROWTH, CONTROL, EXPANSION-CONTRACTION,
KNOWLEDGE-INFORMATION-ENTROPY tend to cross not only branches of mathematics
but branches of physics and biology and psychology and astrophysics and on
and on.

But string and brane theory are suffering from precisely what category
theory is suffering from - a paucity of predictions of the Einstein and
Schrodinger kind mentioned in the second paragraph back, and a paucity of
depth.  Now, Tim, you certainly know very very much, but how are you at
depth [question-mark  - my question mark and several other keys like
parentheses are out].

I will give an example.  Socrates would rank in my estimation as a Creative
Geniuses of Maximum Depth.    The world of Athens was very superficial,
facially and bodily and publicly oriented but with relatively little depth,
and when push came to shove, rather than ask what words meant, it preferred
to kill the person making the inquiries.   What it was afraid of was going
deep, asking what the gods really were, why so-called democracy ended at the
boundaries of Athens and even was inapplicable to all people in Athens, what
democracy really was, why the individual and the group/humanity were not
equally important, when the Golden Mean and the Golden Extreme as I would
call it [for example, valuing Knowledge rather than compromising between
Knowledge and Ignorance] applied.

You mentioned, Tim, that the Holographic Model is still very hypothetical.
Are we to understand that G. 't Hooft obtained the Nobel Prize for a very
hypothetical idea [question-mark] among others.   I have actually
generalized the Holographic Principle and it follows from RET-FET-VET
Theory.   But it happens to be an example of DEPTH of a type that Category
Theory does not know how to handle.  It says that LOWER DIMENSIONS CONTAIN
MORE KNOWLEDGE-INFORMATION THAN HIGHER DIMENSIONS - IN FACT, ALL OF IT, with
appropriate qualifications.

I will conclude this rather long posting with an explanation of why I think
Lawvere and MacLane and incidentally Smolin and Rovelli went in the wrong
direction regarding depth.  It was because they were ALGEBRAISTS - their
specialty and life's work in mathematics was ALGEBRA - very, very advanced
ALGEBRA.  Now, algebra has a problem with depth because IT HAS TOO MANY
ABSTRACT POSSIBILITIES WITH NO [MORE CONCRETE OR NOT] SELECTION CRITERIA
AMONG THEM.   It is somewhat like the Ocean - if an explorer worships the
Ocean, then he will go off in any direction that Ocean seems to be leading
him, and at least half of the time he will be wrong in terms of applications
and predictions and usefulness and depth and so on.   ANALYSIS, on the other
hand, uses algebra and geometry and topology and number theory, but its core
ideas are LIMITS [ONE- OR TWO-SIDED], MEASURES, CHANGE, and a few other
things, and how these relate to geometries and topologies and algebras.
Rovelli and Smolin and Ashtekar and Schwarz and Witten are slightly
different types of algebraists - they are either ALGEBRAIC GEOMETERS or
ALGEBRAIC TOPOLOGISTS, with PHYSICS thrown in of course.   Their string and
brane and knot and loop theories have about the same depth as those of
MacLane and Lawvere in terms of not predicting new things.  Oh, they do
marvellously at REINVENTING THE WHEEL, at reconstructing QM and QFT, etc.

Osher Doctorow



----- Original Message -----
From: "Tim May" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, December 03, 2002 11:30 AM
Subject: Re: Applied vs. Theoretical



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