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ware for mathematical computation. Besides running his company, Wolfram
then spent the 1990s developing his work on cellular automata and related
systems, in his spare time and without publishing any of it (echoes of Ashby's
hobby). His silence ended in 2002 with a blaze of publicity for his massive,
1,280-page topic,
A New Kind of Science
, published by his own company.
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The key insight of the new kind of science, which Wolfram abbreviates
to NKS, is that “incredibly simple rules can give rise to incredibly compli-
cated behavior” (Wolfram 2005, 13), an idea grounded in Wolfram's explo-
rations of simple, one-dimensional cellular automata. “Cellular automaton”
is a forbidding name for a straightforward mathematical system. A one-
dimensional CA is just a set of points on a line, with a binary variable, zero
or one, assigned to each point. One imagines this system evolving in discrete
time steps according to definite rules: a variable might change or stay the same
according to its own present value and those of its two nearest neighbors, for
example. How do such systems behave? The relationship of this problematic
to Ashby's, Alexander's, and Kauffman's is clear: all three of them were look-
ing at the properties of CAs, but much more complicated ones (effectively, in
higher dimensions) than Wolfram's. And what Wolfram found—“playing with
the animals,” as he once put it to me—was that even these almost childishly
simple systems can generate enormously complex patterns.
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Some do not:
the pattern dies out after a few time steps; all the variables become zero, and
nothing happens thereafter. But Wolfram's favorite example is the behavior of
the rule 30 cellular automaton shown in figure 4.14
(one can list and number
all possible transformation rules for linear CAs, and Wolfram simply ran them
all on a computer).
If Kauffman was surprised that his networks displayed simple behavior,
one can be even more surprised at the complexities that are generated by
Wolfram's elementary rules. He argues that rule 30 (and other rules, too) turn
out to be “computationally irreducible” in the sense that “there's essentially
no way to work out what the system will do by any procedure that takes less
computational effort than just running the system and seeing what happens.”
There are no “shortcuts” to be found (Wolfram 2005, 30). And this observa-
tion is the starting point for the new kind of science (31):
In traditional theoretical science, there's sort of been an idealization made
that the observer is infinitely computationally powerful relative to the sys-
tem they're observing. But the point is that when there's complex behavior,
the Principle of Computational Equivalence says that instead the system is
just as computationally sophisticated as the observer. And that's what leads to
