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From: <hal.domain.name.hidden>

Date: Tue, 15 Jan 2002 19:07:47 -0800

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

Received on Tue Jan 15 2002 - 19:16:15 PST

Date: Tue, 15 Jan 2002 19:07:47 -0800

Wei writes:

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

Received on Tue Jan 15 2002 - 19:16:15 PST

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