As I write, I have open in front of me an article by
Gregoire Nicolis entitled "Physics of far-from-equilibrium
systems and self-organization" which appears in "The New
Physics", Paul Davies, ed.
I also have open a textbook by Yaneer Bar-Yam entitled
"Dynamics of Complex Systems" and a second textbook by
Kondepudi and Prigogine entitled "Modern Thermodynamics -
From Heat Engines to Dissipative Structures".
The Prigogine textbook doesn't mention "complex" or
"complexity". The Nicolis article mentions both structural
and behavioral complexity and suggests that algorithmic
complexity is the correct way to quantify both. The
transition, as a system moves farther from equilibrium, from
a spatially simple state to a self-organized spatially
structured state is described, and it is explicitly noted
that this transition results in the appearance of "a modest
complexity". The source of this increment of complexity in
spontaneous symmetry breaking is explained. He then goes on
to extrapolate: "We can therefore say that we have literally
witnessed the birth of complexity thru self-organization.
True, the type of complexity achieved is rather modest, but
nevertheless it presents characteristics which were usually
ascribed exclusively to biological systems." Later in the
article, he describes a second kind of spontaneous
transition that takes place farther from equilibrium - the
appearance of chaotic dynamics. Here, he notes that while
the structural complexity is still not particularly high,
the behavioral complexity is, in some sense, no longer even
finite - a trace of the system's behavior through any
parameter results in the continual appearance of new
information. He speculates that if this information is
somehow "remembered" by the system, then even the structural
complexity can be driven to high levels. And that, he
believes, is the explanation for biology.
The Bar-Yam textbook also defines structural and behavioral
complexity using the notion of algorithmic complexity -
mentioning the name of Kolmogorov. But it also defines a
"complex system", as distinguished from a "simple system".
So, here we have a basis for Dr. Holtzer's binary viewpoint.
So, what is "complex" in Bar-Yam's view? It actually has no
obvious to do with scalar "complexity". Instead, a "complex"
system exhibits emergence, whereas a simple one does not.
Bar-Yam promises to tie together this idea of a complex
system to the metric ideas of complexity. IMO, he fails
utterly to deliver on this promise.
Tim suggests the reading of "complex" as "complicated" -
that is, difficult to understand. IMO, this is much of the
explanation of the fascination that this collection of ideas
has. Because, however they define "complex", the
promulgators of this viewpoint do all agree on what ideas
belong in an article or textbook on "complexity theory".
Prigogine's thermodynamics, Feigenbaum's logistic maps,
strange attractors, Turing's morphogenetic fields,
renormalization, and a whole lot of handwaving are the
standard menu. All of these ideas are just complicated
enough, and just related enough, that in a mist of partial
understanding there is a tantalizing hallucination that some
grand synthesis is just over the horizon.
IMO, while there may be some philosophical interest in
explaining complexity, complexity is not part of the
explanation for any phenomenon of interest to biology,
chemistry, or any other natural science. Some systems of
great structural complexity have simple behaviors, some have
complex behaviors, some have chaotic behaviors. But the same
can be said of systems that are quite simple structurally.
The notion of emergence is useful, but it is an idea much
older than the rest of "complexity theory" and it is not
really conceptually connected to any of these newer ideas.
