Chapter 12: The Principle of Computational Equivalence

Section 5: Explaining the Phenomenon of Complexity

Ingredients for complexity

With its emphasis on breaking systems down to find their underlying elements traditional science tends to make one think that any important overall property of a system must be a consequence of some specific feature of its underlying construction. But the results of this section imply that for complexity this is not the case. For as discussed on page 1126 there is no direct structural criterion for sophisticated computation and universality. And indeed most ways of ensuring that these do not occur are in essence equivalent just to saying that the overall behavior exhibits some specific regularity and is therefore not complex.

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From Stephen Wolfram: A New Kind of Science [citation]