From: Osher Doctorow [log in to unmask], Tues. Feb. 12, 2002 10:13PM

As a member of approximately 350 internet forums/discussion groups, the
question occurs to me as to why probability-statistics, analysis (real,
complex, functional), differential equation, logic, physics, creativity and
geometry forums are more tolerant and open-minded toward new ideas, even of
non-mainstream type, than other forums such as advanced algebra (including
categories, semigroups, algebraic topology), topology, number theory,
computer (including quantum computer), complexity, and history of science.
There are a few notable exceptions.

Ordinarily I do not subscribe to the *Golden Mean* explanation since it does
not usually work, but I think that tolerance may be an exception - that a
golden mean between the very abstract and the very concrete/real/applied
helps tolerance for new and non-mainstream ideas.   Probability-statistics
and physics and differential equations and real-complex-functional analysis
have a long history and tradition of combining theory and experiment or
applications to the real physical/cognitive world (in fact,
probability-statistics came mostly out of real analysis).  Creativity
obviously involves tolerance for new and non-mainstream ideas, and it seems
to involve both abstract and concrete or applied knowledge.

Logic and geometry are a bit more difficult to explain, especially when
compared with the relative rigidity of topologists except in physics
string/brane theory.   I think, however, that they are especially
interesting because topology is more abstract and, outside physics, less
applied/concrete than either logic or geometry.   Geometric objects are what
we see all the time, logic is what we use all the time in mathematics and in
vast parts of the sciences and even humanities.  Topology is rarer in the
sense that it is concerned largely with holes and handles and caps and
stretching-squeezing without tearing/breaking.   Although life does have
many holes/handles/caps and stretch-squeezes, it has far more of everything
else and especially geometry and logic at least on the level that human
beings usually perceive it.

But surely, one might argue, logic is very abstract.   Yet quantum logic,
which is having a major rebirth and was quite important in the 1970s,
indicates now that in a sense logic underlies the entire quantum part of the
universe.   Fuzzy multivalued logics underlie much of human thinking (both
abstract and concrete), and I have even argued quite effectively that they
are more general than quantum logics.

True, there are counteracting tendencies and crossing tendencies even among
the internet forums of the better type that I have mentioned.   Greed within
materialism still probably keeps some probability-statistics forums and even
more probability-statistics people outside the internet from considering
alternative types of non-mainstream probability-statistics because of fear
that they might challenge their monopoly of consulting/grants (an example is
the extreme reluctance of many mainstreamers to incorporate Logic-Based
Probability-Statistics (LBP) into their repertoire of techniques/theories -
even though it only differs from the more mainstream Bayesian Conditional
Probability-Statistics (BCP) by replacing division of probabilities by
subtraction of probabilities.  Anger and fear seem to play major roles in
different nations adopting different agendas in physics and mathematics -
for example, Europe is more oriented toward fuzzy multivalued logics, the
USA toward number theory, Europe tends to be more open-minded about
superluminal experiments, the USA tends to be more conservative about
superluminal experiments (although everybody agrees that the superluminal
group/phase velocities can have practical useful applications).   Ignorance
plays a major role in keeping many scientists/mathematicians following the
footsteps of Founding Fathers instead of changing axioms into a
Non-Euclidean version of almost every discipline (something which
probability-statistics especially could use much of).

As for complexity, I have recently found that all of the internet forums on
the subject that I know of are dominated by exceptionally narrow-minded,
intolerant, controlling people.   This may surprise some who have heard of
the Santa Fe Institute of New Mexico (supported largely by the University of
Minnesota) and its complexity research and rather prominent researchers
associated with Santa Fe Institute including John Casti, Murray Gell-Mann,
Leo Breiman.   I am not particularly impressed with the works of any of
these people, but more important, complexity is an abstraction which is so
far removed from reality that most of its internet forum adherents totally
resist any attempt to define it - they argue that any such attempt will
reduce it to simpler ideas and therefore is illegitimate since complexity is
irreducible.   Santa Fe Institute researchers are usually more cautious in
their public utterances, but it usually comes down more or less to the same
thing when one tries to pin down what they are saying.   The closest they
come to a concrete example is the typical claim that life is complex but
physics is not, and most of them spend their lives modeling life and its
evolution or development on computers.   When you ask them to define life,
they will either tell you that it is what they get on their computer
simulations or that it is undefinable, or they will give you some examples
which you are not allowed to further break down since to do so would be to
*simplify*.

Osher Doctorow
Formerly (and still intermittently in parts) California State Universities
and Community Colleges