Wei writes:
> This brings up the question: Which measure is evolution making us try to
> maximize? The answer is none. It only appears that way because people who
> try to maximize their measures according to some measure function will
> tend to have large measures according to that measure function. So if
> you sample the multiverse according to some measure function,
> you'll likely find people who appear to be trying to maximize their
> measures according to that measure function. But if you then sample the
> multiverse according to a second measure function, you'll likely find
> people who appear to be trying to maximize their measures according to the
> second measure function.

This makes sense in a formal, mathematical way.  Given a sheaf of
universes you can apply any weighting function you want.  But I still
think you are taking too many degrees of freedom here.  My intuition is
that there must be some kind of constraint which keeps you from adopting
arbitrary measures.  But I don't have a good idea yet for what that
might be.

A couple of possibilities occur to me.  One is that it might be
irrational to adopt other measures (for some definition of rationality).
For example, rationality might impose some consistency conditions on your
weighting function.

Another possibility is that mathematics says that there is really only
one measure function, the universal measure, for all but an insignificant
fraction of worlds.  That is, all measure functions are arbitrarily
close to the universal measure, in the limit.  I thought I remembered
reading that this was a property of the universal measure.  If so then
it would mean that you can't really depart from it very much.

There is also the point I and others have made, that you are not just an
observer from outside the universe, but a participant inside.  This ties
you to the universe in a way which might constrain you.  I think your
argument above makes more sense if you think of yourself as an observer
of a multiverse in which you are not participating, say some kind of
computer simulation.  Then the idea of measure seems pretty arbitrary.
However once you are inside you are influenced by the reality of measure.
I don't see how you can reconcile the notion that measure is arbitrary
with the observation that the laws of probability work.  Aren't these
phenomena tied together?  Living here in this world, aren't you forced
to either believe that the universe is fantastically improbable (because
we live in an extremely low-measure universe for some arbitrary measure),
or else that we do in fact live in a high measure universe, meaning that
measure is not arbitrary?

I think you have answered this last objection already but I need to think
about it some more.  I don't know if any of these proposals really work.

Hal

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