Wei Dai writes:
>What is the set of all possible universes? Max Tegmark says its the set of
>all mathematical structures, and Juergen Schmidhuber says its the set of
>all Turing machines, but neither gives much justification. I tend to agree
>with Schmidhuber, if only because Tegmark's definition does not seem to
>lead to an effective theory. For example, what does a uniform distribution
>on all mathematical structures mean? However it would be nice to have some
>stronger justifications for assuming that only computable universes exist.
I need to get back to even more basic basics.
1) There's a certain elegant simplicity to the claim "all possible universes
exist", at least if "possible" is interpreted as broadly as possible, i.e.,
"not logically inconsistent". But if you start substituting other meanings
for "possible", I think the elegance quickly disappears. You'd then still
have to explain why other non-logically-inconsistent universes don't exist,
and you'd have a bunch more weird universes to explain why we don't easily
I find the many worlds theory of quantum mechanics elegant, but not because
it can be thought of as equally the above claim with a certain odd quantum
definition of "possible". I find it elegant because it seems simpler than
the known alternatives which account for the empirical data.
2) I can see why you might want some sort of prior over universes, so you
can make inferences about what universe you are in. But why should your
difficulty in choosing such a prior be an argument against universes
existing? Just because you have trouble thinking about a universe doesn't
mean it doesn't exist.
3) My basic problem with the "all possible universes exist" claim is that
I find it hard to figure out whether my actions have any consequences.
If all possible universes exist, then for any me in one universe choosing
one action, there is another me in another universe choosing another action.
In a global sense I can't choose actions anymore. All possible actions get
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