Basically, there are three key ideas that keep reappearing throughout
the book. Each idea is relatively simple in principle, but all three
must be presented within the context of the entire book in order to be
appreciated since all of them make some reference to the contents of
the five book parts: computation,
fractals, chaos, complex systems, and adaptation.
Taken in order, these three ideas roughly build on one another, so it
helps to consider them in the following order:
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By this I mean that the topics of computation, fractals, chaos,
complex systems, and adaptation are far more interesting considered
together than by themselves. Each of the topics is related to the
others in a non-trivial way; moreover, each can be seen as the result
of a few simple principles such as recursion, parallelism, and
nonlinearity.
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``Beauty,'' i.e., that which makes something interesting, is related
to a mixture of regularity and irregularity. When things are too
regular, we usually find them to be uninteresting because they yield
no surprises for us. Complementary to this, highly irregular things
are often uninteresting because they make no sense. In the middle,
between regularity and irregularity, lies a place where things can be
understood, but not completely.
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The interesting things mentioned
above are often found to have computationally profound qualities. For
instance, even if you had a perfect model or theory of how something
worked, chances are that it would still be impossible to perfectly
predict the future of that which you have modeled. A related result
guarantees just the opposite: regardless of how much ``data'' one
collects, it's not always possible to build a perfect theory. Taken
together, these two results insure that there will never be an end to
science, or suprises.
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