Short Explanations of Observations in Physical Worlds

[This post contributes nothing new.]

Consider the sequence of bits observed by a camera situated within the physical universe (which we can imagine as a CA for concreteness).  If we draw a program uniformly at random (i.e., fixing a universal prefix free encoding) and condition on agreement with this prefix, what does the posterior (over programs) look like?

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Cellular Automata

In the interest of concreteness, I am going to talk about cellular automata (CA) a lot here. They serve as a convenient toy example for talking about computation, and particularly about structures embedded in computations (it is easy to think about how such structures exert control over their environment, although this is just as philosophically problematic as acausal control in general). CA have no relevant mystical properties. You could substitute any other sufficiently complicated program, but CA have the virtue of matching our intuition about physics in several ways (similar notions of space and time, of regular physical law, and so on). Whenever the intuition from CAs seems to get in the way of thinking about what is going on in generality I will abandon them.

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