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Why do we need a theory of complex systems?
And how dare the author (with his publisher's consent, no
less) give this book such an audacious title as How Nature
Works? While many theories have been proposed to describe
individual complex systems, self-organized criticality is
the first general theory of complex systems with a firm
mathematical basis.
This book, written by the discoverer of
self-organized criticality, describes for general readers
a concept that has become increasingly important in science.
Many seemingly disparate aspects of the world, from the
formation of the landscape to the process of evolution to
the action of nervous systems to the behavior of the economy,
all share a set of simple, easily described properties.
While it is standard to think of these as "emergent
properties," clearly the explanation cannot end there.
What defines an emergent property?
Punctuated Equilibrium. There are
long periods of relative stasis punctuated by crises ("avalanches")
of various sizes. These avalanches can be literal, as in
a sand pile, or they can be mass extinctions, stock market
crashes or rallies, solar flares or cellular automata.
Power Laws. The relation between
the sizes of these avalanches can be expressed in a simple
exponential equation. There are no singular explanations
for large events: the same forces that made the Dow Jones
average drop five points yesterday also caused the Crash
of 1987.
Fractal Geometry. Where a system
exists in space, it is self-similar on all scales. (Think
of a major river and its tributaries.)
1/f Noise. When a system evolves
over time, the record of the evolution is also fractal.
These properties are all so similar, Bak
writes, that "they make us wonder if they are all manifestations
of a single principle. Can there be a Newton's law, an f=ma,
of complex behavior? In How Nature Works he argues
that self-organized criticality, the spontaneous development
of systems to a critical state, is the key to such a principle.
Few books offer such a compelling glimpse into the science
of the future as this one.
Per Bak is currently Professor in the
Physics Department of Brookhaven National Laboratory. He
has published over 150 papers, including articles in Scientific
American and New Scientist.
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