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before returning to a state it had visited before—were surprisingly short. He
estimated, for example, that a network having a million elements would “pos-
sess behavior cycles of about one thousand states in length—an extreme lo-
calization of behavior among 2
1,000,000
possible states” (446). And beyond that,
Kauffman's computer simulations revealed that the number of distinct cycles
exhibited by any net was “as surprisingly small as the cycles are short” (448).
He estimated that a net of one thousand elements, for example, would possess
around just sixteen distinct cycles.
On the second, Kauffman had investigated what happened to established
cycles when he introduced “noise” into his simulations—flipping single ele-
ments from one state to another during a cycle. The cycles proved largely
resistant to such exogenous interference, returning to their original trajecto-
ries around 90% of the time. Sometimes, however, flipping a single element
would jog the system from one cyclic pattern to one of a few others (452).
What did Kauffman make of these findings? At the most straightforward
level, his argument was that a randomly connected network of idealized genes
could serve as the model for a set of cell types (identified with the different
cycles the network displayed), that the short cycle lengths of these cells were
consistent with biological time scales, that the cells exhibited the biological
requirement of stability against perturbations and chemical noise, and that
the occasional transformations of cell types induced by noise corresponded
to the puzzling fact of cellular differentiation in embryogenesis.
66
So his ide-
alized gene networks could be held to be models of otherwise unexplained
biological phenomena—and this was the sense in which his work counted as
“theoretical biology.” At a grander level, the fact that these networks were ran-
domly constructed was important, as indicated in the opening quotation from
Kauffman. One might imagine that the stability of cells and their pathways
of differentiation are determined by a detailed “circuit diagram” of control
loops between genes, a circuit diagram laid down in a tortuous evolutionary
history of mutation and selection. Kauffman had shown that one does not
have to think that way. He had shown that complex systems can display self-
organizing properties, properties arising from within the systems themselves,
the emergence of a sort of “order out of chaos” (to borrow the title of Prigogine
and Stengers 1984). This was the line of thought that led him eventually to the
conclusion that we are “at home in the universe”—that life is what one should
expect to find in any reasonably complex world, not something we should be
surprised at and requiring any special explanation.
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This is not the place to go into any more detail about Kauffman's work, but
I want to comment on what we have seen from several angles. First, I want to
