"edge of chaos"

[Martin Taylor 920325 17:20]
(Jeff Dooley 920324.1900)

It's interesting that you should bring up the "edge of chaos" here. I tried
to do that when I first joined this group, and got shot down for it. I am
hoping that I can bring the mutual understanding of the group to a position
where it can accept it as a natural part of PCT, which I think it is. But
I have been holding fire for a year or so, now, because I think many of the
group will misinterpret it.

I started to write a paper based on entirely different foundations about
three years ago, entitled "Thoughts on the edge of chaos", which argued
that ANY thinking machine that would be said to be "intelligent" would have
to be operating on the edge of chaos, and moreover would have to use
catastrophe functions that were the "elements" of the "critical landslide"
(to use the metaphor chosen by whoever wrote the Scientific American article
last year). The catastrophe functions correspond to "categories" in
perception, and are the only things that permit psuedo-logical operation
in physical systems. (In computers, the catastrophe functions are built-in
at the lowest level, and do not have a fractal structure, which makes real
"artificial intelligence" very hard to achieve).

Anyway, I never finished the draft paper, because it was intended for
Behavioral and Brain Sciences, and Freeman got his chaos paper in first.

For PCT people, the key point will be that there must be same-level connections
in the hierarchy, but we are yet a long way from having developed an agreed
substrate for developing that understanding. We'll get there, I hope, before
another year passes.


[From: Jeff Dooley 920324.1900]

(Rick Marken 920324.0820)

On Stuart Kauffman's notion of the "edge of chaos."

Rick, first a mention of what I take Kauffman's mission to be.
Kauffman appears to argue a case for: (1) a dynamics of
spontaneous organization in complex systems--organization arising
out of complexity alone (as I read it) and not as a function of
some ontogenetic structure or blueprint (like a gene)--and (2) a
taxonomy of the "sources" of self-organization in complex systems
and an understanding of how such order may enable and/or
constrain efficacy in natural selection. (Burian-Richardson)
(references below)

Kauffman (Univ of Penn) has elaborated these arguments in his
forthcoming, _The Origins of Order: Self-Organization and
Selection in Evolution_, Oxford, 1992.

A major thesis of this work, according to reviewers Burian and
Richardson, is that the properties of order resulting from the
self-organizing process in biological and non-biological systems
are independent of selection. Kauffman asks, "Must selection
have struggled against vast odds to create order? Or did that
order lie to hand for selection's further molding?" ("Sciences of

So far as I can gather, it is these properties of order or
organization which, in species, drive the ensemble to and keep it
at equilibrium (absent fatal perturbations) within a range of
adaptability he calls "the edge of chaos." It appears to be
precisely Kauffman's point that this edge-of-chaos zone is the
one in which (to use a PCT term) the reorganizing system deals
most effectively with perturbations and constraints by exhibiting
the most resilience under perturbation. So he feels it is no
wonder that the organizing function of complex systems seeks
equilibrium in this zone. The upshot of this is that selection
is not to be held the sole source of order in biology. In fact,
Kauffman suggests that in case selection may slightly displace
evolutionary vectors of generic order in species, those vectors
will still "shine through" as manifest properties, not *because*
of selection but *despite* it. It follows from this that
ontogenetic variation, for Kauffman, is not the whole (or even
the most part) of evolution's story. This appears to be about as
monumental a gestalt switch for biology as PCT is for S-R

Ok, now to your question: what is "the edge of chaos?"

Kauffman offers this thesis: "Complex adaptive systems achieve,
in a lawlike way, the edge of chaos ("Sciences of Complexity").
They do this through a process of self-organization whose lawlike
progression is a function of the complexity of individuals and
ensemble together.

The edge of chaos appears to be a (razor-thin) zone of optimal
adaptability within a fitness landscape or vector space. The
organizing function of the ensemble seeks equilibrium at this
spot. Here is Kauffman's description of the vector space:

". . . complex adaptive entities achieve the edge of chaos
because such systems can coordinate the most complex behavior
there. Deep in the chaotic regime, alterations in the activity
of any element in the system unleashes an avalanche of changes,
or "damage", which propagates throughout most of the system. . .
The butterfly in Rio changes the weather in Chicago. .
.Conversely, deep in the ordered regime, alteration at one point
in the system only alters the behavior of a few neighboring
elements. Signals cannot propagate widely throughout the system.
Thus, control of complex behavior cannot be achieved. Just at
the boundary between order and chaos, the most complex behavior
can be achieved." (Sciences of Complexity) Ensembles self-
equilibrated at the edge of chaos, therefore, promise the most
robust ability for phenotypic change (controlling-behavior!) in
the event of deformations (perturbations) in the landscape.

Bill P. has been suggesting recently that some kind of control
process may be at work in evolution. As I was reading his posts
I was also reading the "Sciences of Complexity" paper and
somewhere in there the lightbulbs just started popping.


Stuart Kauffman, "The Sciences of Complexity and 'Origins of
Order'," _Philosophy of Science Association 1990_, Volume 2, ed.
Fine, Forbes, Wessels, (East Lansing: PSA, 1991).

________, _Origins of Order: Self Organization and Selection in
Evolution_, (Oxford: Oxford U Press, 1992 (July))

Richard Burian and Robert Richardson, "Form and Order in
Evolutionary Biology: Stuart Kauffman's Transformation of
Theoretical Biology," _PSA 1990_, Vol. 2.

jeff dooley