Patrick Leahy writes:
> Sure enough, you came up with my objection years ago, in the form of the 
> "White Rabbit" paradox. Since usage is a bit vague, I'll briefly re-state 
> it here. The problem is that worlds which are "law-like", that is which 
> behave roughly as if there are physical laws but not exactly, seem to 
> vastly outnumber worlds which are strictly "lawful". Hence we would expect 
> to see numerous departures from laws of nature of a non-life-threating 
> kind.

I think the question is whether we can assume the existence of a measure
over the mathematical objects which compose Tegmark's ensemble.  If so
then we can use the same argument as we do for Schmidhuber, namely that
the simpler objects would have greater measure.  Hence we would predict
that our laws of nature would be among the simplest possible in order
to allow for life to exist.

If we assume that a "mathematical object" (never clear what that meant)
corresponds to a formal axiomatic system, then we could use a measure
based on the size of the axiomatic description.  I don't remember now
whether Tegmark considered his mathematical objects to be the same as
formal systems or not.

Hal Finney

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