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posted 01. February 2002 12:05
Dynamical Complexity and Regularity
by Richard A. Johns
johns@interchange.ubc.ca
ABSTRACT—The aim of this paper is to provide a mathematical basis for the plausible idea that regular dynamical laws can only produce (quickly and reliably) regular structures. Thus the actual laws, which are regular, can only produce regular objects, like crystals, and not irregular ones, like living organisms.
1. The dynamical complexity of an object is defined. This is something like its algorithmic information content, but I use a dynamical system in place of a universal Turing machine. A dynamically-complex object is, roughly speaking, one that the dynamical laws have little or no tendency to produce from a random initial state. A "GIGO" theorem is proved, that an object with dynamical complexity n bits requires time 2^n to be generated, so that highly-complex objects effectively cannot be generated spontaneously.
2. The term "regular dynamical law" is defined, in such way that the known dynamical laws of physics are regular. The irregularity of an object is defined, and then I try to show that the dynamical complexity of an object s, with respect to a regular law, always exceeds the irregularity of s. It seems clear that living organisms are highly irregular, in the sense defined, so (if this result holds) they must be dynamically complex as well. It would then follow that living organisms could not have been produced, from a random initial state, by the known dynamical laws.
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[ 18 July 2002, 10:15: Message edited by: Moderator ]
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