Steven Strogatz says in the epilogue to his new book SYNC :
"Every decade or so, a grandiose theory comes along,
bearing similar aspirations and often brandishing an
ominous-sounding C-name. In the 1960 it was cybernetics.
In the '70s it was catastrophe theory. Then came chaos
theory in the '80s and complexity theory in the '90s."
He continues in the epilogue with
"Chaos theory revealed that simple nonlinear systems could
behave in extremely complicated ways, and showed us how to
understand them with pictures instead of questions.
Complexity theory taught us that many simple units
interacting according to simple rules could generate
unexpected order. But where complexity theory has largely
failed is in explaining where the order comes from, in a
deep mathematical sense, and in tying the theory to real
phenomena in a convincing way [..]
I think we may be missing the conceptual equivalent of
calculus, a way of seeing the consequences of the myriad
interactions that define a complex system."
Can we explain where the order and organization in complex
systems comes from ? W. Brian Arthur has identified three
means by which complexity tends to grow in the evolution of
complex systems : increase in "species/niches" diversity,
in structural sophistication and increase by "capturing software".
Based on these three basic mechanisms, I have examined the
emergence of complexity in a new article, which contains
51 Pages, 30 Figures, 12 Tables and 97 References. It
can be found at my website (PDF 745 KB, PS 1,91 MB)
http://www.geocities.com/einstein702000/complexity.pdf http://www.geocities.com/einstein702000/complexity.ps I have tried to gather as many interesting pieces from
the giants of the science of complexity as possible and
assemble them to a coherent picture how complexity
emerges in complex systems. These giants are
Philip W. Anderson, Murray Gell-Mann, W. Brian Arthur,
Stuart A. Kauffman, Stephen Wolfram, John H. Holland,
Peter Schuster, John Maynard Smith, Harold Morowitz,
Steven Strogatz, Chris Langton and others.
This does not mean that I have "discovered vastly more than I ever
thought possible" and it does not "touch almost every existing area
of science, and quite a bit besides", as Stephen Wolfram formulates
in his NKS book. If I discovered one thing it is that I am much
more stupid than I ever thought possible. But maybe the one or
other idea is a small part of a much larger body of thought and
provides a step or a hint for what's coming next in the study of
complex adaptive systems.
Best Regards,
Jochen Fromm
Locked
