Re: Patriarchy: Re: What Matriarchy?

Stephen Barnard (
Wed, 14 Aug 1996 21:06:01 -0800

Joel and Lynn Gazis-Sax wrote:


Let's try to get on a civil basis, OK? I enjoy a flame war now and
then, but I'm tired of it. I'm sorry if I've offended you in any way,
and I promise not to question your motives, call you nasty names, be
really sarcastic, or any of that stuff, if you will do the same.

Here's the deal about chaos theory, in a nutshell, as I understand it.
It is *not* the case that chaos is equivalent to uncertainty, as you
seem to believe, although there is a connection. Some *well-defined*
dynamical systems (which can be either discrete or continuous) exhibit
trajectories in their phase space (the space of all possible states)
that are extremely complicated, unlike relatively simple periodic or
quasiperiodic dynamical systems that we're used to (like a pendulum).
They have the property that any uncertainty in the initial condition
(the starting point) grows with time. James Gleick (not sure of the
spelling) wrote the runaway best-seller, Chaos, which popularized this
idea. Some people got carried away with it, but its a very good book.
It's accessible to non-mathematically inclined people and it tells a
good story about the scientists and mathematicians behind the theory.
(The technical literature is nearly incomprehensible to anyone but a
specialist or a math whiz.)

There is, IMHO, a very interesting concept that is popular in the new
field of Artificial Life (bogosity alert!). It's called "life on the
edge of chaos". The idea, roughly, is that there is a continuum of
types of systems, from very simple systems with fixed, periodic, or
quasi-periodic attractors (trajectories, more-or-less), up to completely
random systems with attractors that fill their phase spaces (they can
take on any state with about equal probability). At the interface are
chaotic systems -- not really simple, but not completely random either.
"Life at the edge of chaos" claims that evolution takes place at this
interface. It isn't as crazy an idea as it seems at first.

Eric says he's an expert on ergodic systems, so maybe he can elaborate.

I hope this isn't too confusing. Gleick's book is very good. I
recommend it highly.

Steve Barnard