Log-Rolling and Self-Promotion

The Bactra Review Brainchildren

Dennett talks about patterns in a single instance of a signal; matters are somewhat different, and actually a bit easier, if one wants to reproduce a statistical ensemble. In that case, randomness becomes eminently compressible. (As I've said before, to model coin tossing, toss a coin.) Moreover, there is a technique for constructing a (computationally and informationally) minimal model which has as much predictive power as is available to any pattern based solely on the signal. (There isn't yet a proof that this model is unique, so Quine is saved for another day.) For the technique of pattern-finding, and making highly compressed representations of random ensembles, see James P. Crutchfield, "The Calculi of Emergence: Computation, Dynamics and Induction," Physica D 75 (1994): 11--54; for the optimality results, see James P. Crutchfield and Cosma Rohilla Shalizi, "Thermodynamic Depth of Causal States: When Paddling around in Occam's Pool Shallowness Is a Virtue," Physical Review E59 (1999): 275--283. (I warned you there would be log-rolling and self-promotion.)

Addendum: There is now a proof of uniqueness, up to the way some cases of measure zero are handled: see Theorem 3 of Cosma Rohilla Shalizi and James P. Crutchfield, "Computational Mechanics: Pattern and Prediction, Structure and Simplicity", Journal of Statistical Physics 104 (2001): 817--879, available in PDF here or as cond-mat/9907176. Where this leaves Quine, or for that matter Dennett, I shan't attempt to say.