I note that the Occam prior connects more closely to neuroscience than
the PI, in that there are plausible arguments the brain uses an
"energy minimization" heuristic in some cases. Read Montague makes an
argument in this direction in:
http://www.amazon.com/Why-Choose-This-Book-Decisions/dp/0525949828
Ahhh.. for those whose physics is rusty: Note that, in standard
equilibrium thermodynamics, energy minimization is equivalent to
statistical entropy maximization.
So, Montague's approach actually comes very close to asserting that
the brain uses a maxent prior (which has the PI as a special case).
However, I think Zurek's notion of physical entropy as combining
statistical entropy with algorithmic information needs to be factored
in here.
Far from equilibrium, I suspect, to get equivalence with energy
minimization you probably need to include both of Zurek's terms. So,
Montague's energy minimization might be equivalent to a combination
maxent/Occam prior. But I would love to get confirmation (or
refutation) of this from a physicist...
-- Ben
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