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Figure 4.14.
rule 30 cellular automaton. time steps move from the top down-
ward; 1s are denoted by black cells, starting from a single 1. the transfor-
mation rule is shown at the bottom. source: wolfram 2005, 4. (image courtesy of
wolfram research, inc. [] and stephen wolfram llc, as used in stephen wolfram's
new Kind of Science
©
2002.)
computational irreducibility. And that's why traditional theoretical science
hasn't been able to make more progress when one sees complexity. There are
always pockets of reducibility where one can make progress, but there's always
a core of computational irreducibility.
The classical sciences thus address just those “pockets” of the world where the
traditional shortcuts can be made to work, while the reference of NKS is to all
of the other aspects of the world where brute complexity is the rule, and much
of Wolfram's work has been devoted to bringing this ontological perspective
down to earth in all sorts of fields: mathematics; a sort of crystallography (e.g.,
snowflake structures); studies of turbulence; biology, where Wolfram's discus-
sion echoes Kauffman's.
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Having compared the patterns on mollusc shells to
those generated by various CAs, Wolfram notes that (22)
it's very much as if the molluscs of the Earth are little computers—sampling
the space of possible simple programs, and then displaying the results on their
shells. You know, with all the emphasis on natural selection, one's gotten used
to the idea that there can't be much of a fundamental theory in biology—and
