RE: The edge of Chaos

From: Ben Goertzel (
Date: Mon May 05 2003 - 11:35:33 MDT


The "edge of chaos" is an interesting concept, which unfortunately it has a
checkered history.

If you take a complex system, and chart the "chaoticity" of its behavior
against its control parameters, most of the time you will NOT find a simple
portrait in which there's an orderly regime separated from a chaotic regime
by a "fine line" representing the edge between order and chaos.

The "edge of chaos" meme was started by a research paper by Chris Langton,
in the early 1990's (I think -- coulda been the late 80's) , which purported
to show this kind of portrait derived from the space of 1D cellular
automata. Other researchers tried to replicate these results and did not
succeed. Nevertheless the phrase stuck, presumably because of its evocative
poetic quality.

What you really see when you study complex systems is a lot more, well,
complex.... You see fractal mish-mash patterns of orderly regions, chaotic
regions, and complex regions ["complex" meaning having nonrandom patterns
that nevertheless aren't repetitive]. The "edge" is actually a whole bunch
of edges, on different scales and with different properties in different
parts of the space...

What this means is that self-regulation is key in many complex systems --
but not necessarily self-regulation with avoidance of excessive order or
chaoticity as the primary goal. Optimizing for degree of order/chaos may be
much harder than optimizing for other things that are roughly correlated
with this degree. It's true that in many cases an adaptive complex system
wants to avoid excessively repetitive or excessively unstructured
("chaotic") behavior. But this can often be achieved implicitly, by
self-regulating for other qualities rather than degree-of-chaoticity. To
take an example drawn from our recent Novamente work, if a dynamical
computational reasoning system adapts its parameters so as to provide the
highest-quality conclusions, it will *automatically* set its parameters to
values that will result in behavior that isn't too orderly or too chaotic --
because neither excessive order nor excessive chaos is near optimal for

-- Ben G

> -----Original Message-----
> From: []On Behalf Of Simon
> Gordon
> Sent: Monday, May 05, 2003 1:12 PM
> To:
> Subject: The edge of Chaos
> This is a reminder that the most interesting systems
> exist on the very fine line between Chaos and Order,
> this includes intelligent systems.
> When trying to design and develop artificial
> intelligent systems we should always check the orderly
> behaviour of the system versus its chaotic behaviour.
> If the system displays chaotic behaviour then we need
> to adjust it to perform more orderly and if the system
> displays orderly behaviour then we need to adjust it
> again to perform more chaotically. We need to keep
> iterating this process (with progressively finer
> increments) until we arrive at the "edge".
> Think liquid crystals.
> Simon.
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