On Tue, Jan 15, 2002 at 07:07:47PM -0800, [EMAIL PROTECTED] wrote:
> 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.

I think you probably misunderstood what you read. What's true is that
universal priors based on different Turing machines are close to each
other, up to a multiplicative factor that depends on the pair of universal
priors being compared. But this multiplicative factor is not necessarily
insignificant in terms of practical consequences, and there are other
candidiate measures proposed by Juergen that seem about as attractive as
universal priors (i.e. the less dominant speed prior, and the more
dominant one based on GTMs which I'm not sure has a name).

> 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.

Even though you're inside, you can (and I think in some cases must)
consider your situation from an outside perspective. 

> 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?

One thing you do give up when you abandon the concept of an objective
measure is an explanation of why you are who(/when/where) you are. But I
can't shake the feeling that perhaps the question doesn't really make
sense, because how could you not be who you are? However, if you don't
want to give this up, you can keep the notion of an objective measure just
for the purpose of having this explanation, but adopt an arbitrary
subjective measure for making decision. In other words, even if you think
there is an objective measure, you don't have to care about each universe
in proportion to its measure.

Now suppose you could manipulate the beliefs of your future selfs and not
have them remember the manipulations (e.g. like the protagonist in the
movie Momento). What would you want your future selfs to accept as the
objective measure? Well it would be the same as your subjective measure,
because otherwise you'd be in a situation where the future selfs that you
care a lot about don't have a good explanation for why they are where they
are, while some of the ones you don't care much about do have a good
explanation. And what's the downside to your future selfs believing in
the "incorrect" objective measure? There doesn't seem to be one.

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