Solomonoff’s method of induction seems like a good fit for a mechanist view of 
things. For instance, it could be used to assign a relative probability to the 
universe being generated by a universal dovetailer: 2^(-K) * m, where K is the 
Kolmogorov complexity of the universal dovetailer and m is the measure the 
dovetailer assigns to universes like ours.

This formula implies that a (more complex) non-universal dovetailer might be 
preferable _if_ it assigned a much higher measure to universes like ours. Such 
a dovetailer might, for instance, output only (or mostly) habitable worlds, 
instead of outputting mostly uninhabitable worlds as the standard UD does, and 
the higher resulting measure would offset the increased Kolmogorov complexity.

If we live in a highly “atypical” universe, that might also affect how we 
should do Solomonoff induction. For instance if we knew that we lived in a 
universe with much less suffering than an “average” inhabited universe, that 
could imply we were generated by a dovetailer that doesn’t like suffering. If 
the opposite is true and we live in a “mean world”, that means we might be 
generated by a sadistic dovetailer, etc.

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