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Complexity & Choas

Nov 12, 1994 07:20 PM
by Jerry Schueler

John <Not to be too technical, but there are a number of
different formulations of exactly what "Complexity Theory" really
is.  I have come at it from economics, and among those I
discourse with, complexity theory would probably be described
simply as the study of complex systems moving in
multidimensional, multiscalar spaces.>

Agreed.  I have absolutely no background in economics, and will
assume you are correct in those areas.

John <Some of these systems seem to cycle back and forth between
states of (relative) order and chaos, others seem to remain
perched on the "edge of chaos" (as Stuart Kaufmann so poetically
put it).  Chaos theory, then, is the study of one aspect (a
"subset") of a complex system...the behaviour of the system in
its chaotic phases.>

I believe the term for the first type is intermittency - one of
the three "routes to chaos" (the other two being crisis and
period-doubling).  There is certainly a lot of ongoing work
looking at systems in their chaotic phases, but how systems
evolve to chaos is also an area of concern.  To some extent,
there is even disagreement about when full chaos is reached.
Different systems tend to display chaos differently.

John <The Santa Fe people are perhaps the best known, but are
certainly not the only ones studying complexity.>

Agreed.  One of the strongest voices against AI is probably Roger
Penrose.  I just bought his latest book about this, but haven't
had time to read it yet.

John <The Institute itself was begun by a few people who had
studied chaos theory, and a good number who had not.  In fact, I
believe the original impulse came from (if I remeber correctly)
an initial conference composed of a group of economists and a
group of physicists who had sat down to discover whether there
were points of possible conversation between their very different
disciplines.  Many of them had never worked with chaos theory.>

True.  I was being overly simplistic.

John <I'd like to talk with you more about complexity/chaos'
application to not only psychology but to the "spiritual" realm
in general.>

Wow! I am not sure what you mean here? We will have to define
terms.  I view "spiritual" as that which lies above the Abyss,
which is to say above the Ring-Pass-Not of the human mind.  Chaos
begins in the Abyss, and is reflected 'downward' into matter
throughout the 'lower' planes (I am here using the Gupta Vidya
Model supplied by HPB in the SD Vol I; the Abyss is just above
Globes A and G, and separates the 7 lower Globes from the 5 upper
Globes according to the 12-Globe model presented by G de
Purucker.  The Abyss, the real source of all chaos, is equivalent
to the 11th Sephiroth, Daath, in the Qabala).

John <Let me ask you if you've integrated scaling into your your information "equations".  Information certainly
is delivered to the human awareness at many different (one might
almost say `discrete') scales.>

According to Claude Shannon, the founder of information theory,
information refers simply to the number of possibilities, Z.  So
that information, I, can be expressed as:

      I = log to the base 2 of Z

Shannon used the logarithm to the base 2 because modern
communication works with binary numbers or bits.  The human mind
probably does not work in binary.  However, the idea still holds
that Z will be large, so therefore I will be large.  Shannon also
developed the equation for what is called the Shannon
uncertainty, Shannon entropy, or simply information entropy.  It
consists of a negative constant times the integral of the
probability of information times the log of that probability.
However, Shannon information does not concern itself with
meaning, and it only applies to closed systems.  Of course, like
you suggested, a lot of information comes to us without meaning -
such as the background 'noise' of our environment.  I doubt that
equations will apply to the brain's ability to receive
information like electronic equipment does.  However, a lot is
being done in research today, such as looking at the brain as a
complex of parallel circuits.  And several brain models are being
discussed, but again, even the most simple ones are skimpy with

I agree with you that incoming data must be scaled.  The idea
that I am currently working on is that our brain, as a complex
system, undergoes bifurcations.  I am not so sure about period-
doubling, because there are simply too many variables.  But as
the brain approaches a bifurcation point, only a tiny outside
influence is needed to cause drastic changes.  In some cases, its
rather like the straw breaking the camel's back.  I read all
sorts of horror stories in the newspapers and on TV news, such as
a kid who shoots his parents because they won't but him a radio,
or a 'good' student pulling out a gun and shooting everyone on
campus because he only got a B in some class, and so on.  While
these are dramatic, we all go through bifercations at various
points in our lives, many for the best (they are nothing more
than instances in time where choices must be made; where our
lives go down one particular road rather than another).  Often
these critical points can be detected via 'nuances' and taken
advantage of.  But I am not so sure that we can actually develop
mathematical equations for this kind of thing for individual
people (although statistically we may, as people tend to follow
the Poisson distribution in their collective actions).

I guess one of the things that I am trying to say here, is that
you can't always tell what the scale should be, because the
psyche gives events 'meaning' in a very individual manner, as per
Jung's synchronicity.

Jerry S.

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