twisting chaos/science

P8475423 at vmsuser.acsu.unsw.EDU.AU P8475423 at vmsuser.acsu.unsw.EDU.AU
Tue Aug 29 16:01:07 MDT 1995


Chris's statement on which Jerry asks for clarification:
> Paradoxically chaos theory may give insights into this. Despite its
> dramatic name, chaos theory shows that non-linear systems are *usually*
> stable, with only occasional phase changes.

Is that right? I don't really think it is, but I will allow others to
elaborate.
...
is a bit of an overstatement. and also a question of definition.
Stable in Chris's sense is, I think, "doesn't break down"; I think
Jerry sees stability in terms of "doesn't have crises", where in
economic terms a crisis might be an inflationary and unsustainable
boom, or a deep depression.

A system can have booms or depressions without undergoing a breakdown,
hence the semantic confusion.

A good example of what Chris means is, from what I have been told
by medicos, the heart. It can be modelled as a nonlinear process--
is a nonlinear process--but most of the time it operates within
stable parameters. However, in some critical ranges, it can be
pushed from normal operation into cardiac arrest. The latter
type of behaviour is rare, as Chris says--fortunately.

The reason for this is that a truly complex evolved system tends
to have a number of "homeostatic feedback loops", where tiny
changes to inputs have considerable power to control the otherwise
unstable nonlinear processes. I have a demonstration of the same
in my JPKE paper, when I incorporate a government sector: what was
a potentially unstable system (in Jerry's sense) becomes one which
is very stable (I meant in Chris's sense, pardon me: it would
undergo complete breakdown for some interest rate levels without
a government sector, it wouldn't break down regardless of interest
rates with a government sector).

"Artificial life" modellers have come to argue that life itself
is something which exists on the "edge of chaos"--they see a
region between the apparent complete randomness of chaos, and
sterile stability, where self-organisation rules. This is
where most nonlinear systems actually exist.

Cheers,
Steve K


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