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New Scientist (02/26/05) Vol. 185, No. 2488, P. 32; Buchanan, Mark
Earthquakes, ecosystems, economies, and other inherently complex systems and
events long regarded to be mathematically irreducible could be more
measurable then previously thought, according to research into cellular
automata, which are computer programs that can form complex patterns by
following simple rules. University of Illinois at Urbana-Champaign
researchers Nigel Goldenfeld and Navot Israeli applied pattern analysis via
"coarse-grained" models to cellular automata. Such analysis, in which the
models concentrate only on the most relevant details of the pattern-forming
process, has demonstrated that similar logic principles apply to completely
different situations. Goldenfeld and Israeli established that in 240 out of
256 cellular automata outlined by mathematician Stephen Wolfram, rules that
generated relatively simple and predictable patterns roughly mirrored the
behavior of rules that led to computationally irreducible patterns. This
rule also held for automata notorious for their computational
irreducibility. Meanwhile, Santa Fe Institute physicist Jim Crutchfield
believes connections between the past and future for virtually any system
could be predicted with a "computational mechanics" approach he has
developed. He reasons that the various histories of a system can be sorted
into classes, so that the same outcome applies for all histories in each
class. This means that many details of the underlying system may be
inconsequential, so that an approximate description much like Goldenfeld and
Israel's coarse-grained models can be organized and used to make
predictions. Crutchfield and Goldenfeld agree that coarse-graining could
help tackle deep scientific problems.
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