From: Osher Doctorow [log in to unmask], Sat. Feb. 16, 2002 10:29AM

On http://www.superstringtheory/forum under various subcategories, I have
been expressing Max Born's Quantum Probability in terms of
Logic-Based-Probability (LBP) and other probability-statistics analogs of
fuzzy multivalued logics.   The essence of this is that quantum
probability-statistics can now be considered to be a subclass of fuzzy
multivalued logics or their probability-statistics analogs LBP and so on.
Abstracts of part of this are also at http://www.transhumanist.com under the
June 1-30, 2002 Online Symposium on Practical Cosmology and elsewhere.

I am now doing some cross-posting only by subclass of the subject matter, so
that in this posting I am sending to statistics or real-complex analysis
forums or places where these are applied.

The technicalities of the results can be examined at the above sites for
those who are interested, but here I want to emphasize a few general
conclusions and open problems.

1.  The leading branches of mathematics with physical and biological and OR
applications now appear to be probability-statistics, fuzzy multivalued
logics (NOT quantum logics in their usual formulation), geometry, and
real-complex analysis (including PDEs and ODEs), although only within
physics and other applied sciences would I also add geometry-topology.
Although advanced algebra (including category theory and semigroups) is a
valuable field, and similarly abstract topology and number theory and
computers (theoretical and practical), in my opinion in view of my above
results they are not leading at present in the most rapid and most deep pure
and applied results.   This will probably category theorists in particular,
who have considered themselves to be in the forefront of algebra if not
beyond, but without further generalization of categories (especially beyond
commuting diagrams and functors), and in view of their slow progress in the
quantum vs macroscopic (general relativity, etc.) applications, this is my
conclusion.

2. Probability-statistics has made deep and basic mistakes in not looking
for a revolution comparable to geometry's revolution when Non-Euclidean
Geometry changed one axiom and forever expanded the old mainstream Euclidean
Geometry's monopoly of methods to diverse methods and theories.   My wife
Marleen's and my introduction of LBP in 1980 changed such a
probability-statistics axiom, namely the axiom of (Bayesian) conditional
probability-statistics (BCP for short here) that dependence/influence of
events is expressed by division of probabilities to the axiom that it is
expressed by subtraction of probabilities.   The present results and
numerous others since 1980 are the consequence of this simple change in one
axiom.

3.  Real and Complex Analysis must in my opinion return to a reconciliation.
The habit of quantum and neo-Einstein relativistic physicists of using
complex analysis alone may have been justified in early physics, but the
newer results indicated above suggest that more will be learned by being
able to translate or relate real and complex analysis than by remaining
exclusively with one.  My own preference is real analysis from which
probability-statistics of most types developed, but it is clear from the
results that it is very useful to relate real to complex analysis instead of
remaining exclusively in real analysis.

4. Exclusive concentration on physics or OR or chemistry or engineering or
biological science or other fields would probably not have enabled the newer
results which I have been presenting.  INTERDISCIPLINARY is the new keyword
in my opinion, not INTRA-DISCIPLINARY, although the latter is obviously very
important.

5. Making logical operations EXPLICIT in the STATEMENT of theorems/theories
and not merely in proofs or derivations of corollaries or even theorems is
key to the new methods.   Quantum logicians even of the old school
recognized intuitively that logic was key to the universe, and fuzzy
multivalued logics now appear to be key to logic.   I myself was originally
discouraged by thinking that *fuzzy* just imitates poor human thinking and
recommended against research into fuzzy logics in the late 1970s, but I have
found otherwise quite rapidly.  It is true that poor human thinking is one
application of fuzziness, but it is one of the smaller applications.  The
very structure of a large part of the universe itself appears to involve
fuzzy multivalued logics not as *poor thinking* but as partial thinking or
*partial life* even more generally.   This is not the same as partial
information of AI (artificial intelligence), which tends to be exclusively
formulated in old mainstream probability-statistics terms and theories, but
such partial information could be reformulated in terms of fuzzy multivalued
logics.

Osher Doctorow