Return-Path: <JulioHuato@aol.com>
Delivered-To: andy@mira.net
From: JulioHuato <JulioHuato@aol.com>
Date: Sat, 20 Dec 1997 10:15:24 EST
To: andy@mira.net
Subject: Re: Complexity, Mathematics and Dialectics
Organization: AOL (http://www.aol.com)

Andy,

I believe that you have drawn the proper conclusions from complexity.  And the
way you present them is very clear.  I must admit that your reading of these
simulations as EXERCISES IN LOGIC (setting the limits of formal logic) was
entirely unexpected to me.  But since you first expressed it, I became
convinced that this was indeed their main (rational) result.  As to your text,
I have marked a few corrections to likely typos (in brackets).

I understand that the focus of your site and list is, and should be, Hegel.
The generality of the Logic makes it impossible to avoid being thrown in every
direction.  People approach Hegel from all angles, and my angle is still
economic theory.  You may wish to split the list according to individual
interests, etc.

In any case, I guess I should try to develop a web site dedicated to the
critique of modern economic theory.  In a sense, if it takes off, it will be
an offspring of your site.

J.

PS:  A friend of mine gave me a book on the saga of Fermat's Enigma.  I read
it in a few hours, nonstop.  I'm sure you have thousands of readings waiting
in line, but if you get interested, I can ship it to you.

-------------
<<Complexity, Mathematics and Dialectics

Over the past decade, a new science has emerged known as "Complexity". This
science uses computer simulation to empirically investigate the outcome of
very simple formal rules governing the interaction of a large number of
component sub-systems, or individuals, in a system.

The need for an empirical science to study these phenomena is explained by a
corollory of Gödel's Theorem discovered by Alan Turing, the founder of
Computer Science: that in any computational system there [is] at least one
algorithm, the results of which cannot in priciple be predicted. This is a bit
of [a] truism for anyone who has prog[r]ammed a complex computer system!

The implication for understanding the relation of formal and dialectical logic
is profound. In any complex (i.e. real) system, the phenomena exhibited arise
out of the relations of the component systems in a way which cannot in
principle be deduced by formal logical analysis; and this is true even where
the atomic relations are absolutely simple and static. 

Such complex systems fall initially into two kinds: those where the atomic
relations lead to a static or repetitive structure in the mass, where the
mechanical application of formal logical analysis is valid, and those that
lead to chaos, where the Law of Large Numbers and probability theory is valid.
A simple measure derived from the atomic relations indicates whether the
system is likely to be structured or chaotic. But there is also a third case,
the border-line or transition case, where the atomic relations lead to
"complex behaviour", rich in form, leaps, sudden transformations and dynamic
structures, all in principle unpredictable from the standpoint of formal
logic.

Furthermore, it has been empirically established that where the sub-systems
have the capacity to replicate and mutate in some way (the normal condition of
any significant "real" system), thus modifying the balance of the atomic
relations, the system will in time either "die", or gravitate to a complex
transition system, from a chaotic or structured state to a complex one, from a
stable, predictable system to one giving rise to complex, "revolutionary"
phenomena. Empirical computer simulation has reproduced analogues of systems
(neurological or social) which learn, the origin of life from a "primeval
soup", punctuated evolution, etc.

The scientists who are doing this work have expressed serious concerns about
the state of the world economy, especially after the end of the relatively
stable Cold War Period, and have tended to become fans of Heraclitus or
Taoism; interestingly, none of them have so far recognised that a very precise
science of the logic of complexity already exists in the Logic of Hegel. >>