Coarse-graining, symbolic dynamics and collective coordinates: How physicists deal with large, complex systems, and why cognitive scientists might care

Many systems in statistical physics admit multiple levels of  description, from microscopic molecular detail up through very  broad macroscopic features. The higher-level descriptions are  "coarse-grainings" of the lower levels, and the higher-level  variables are generally collective properties of many lower-level objects. Not every coarse-graining leads to a "good" set of  macroscopic variables; those that do have certain statistical  properties. These properties, in turn, have important  information-theoretic implications, and, when the coarse-graining is discrete ("symbolic dynamics"), the system can be modeled by  stochastic automata. After sketching these ideas, I suggest some  ways they might help cognitive scientists relate symbolic or  computational descriptions to neural, dynamical ones.