Jesse Mazer writes:
> It's a bit hard for me to come up with a satisfactory answer to this 
> problem, because I don't start from the assumption of a physical universe at 
> all--like Bruno, I'm trying to start from a measure on observer-moments and 
> hope that somehow the appearance of a physical universe can be recovered 
> from the subjective probabilities experienced by observers...

I have a similar perspective.  However I think it will turn out that the
simplest mathematical description of an observer-moment will involve a Big
Bang.  That is, describe a universe, describe natural laws, and let the
OM evolve.  This is the foundation for saying that the universe is real.


> But my speculation would be this: multiple copies only increase first-person 
> measure to the extent that, from a third-person perspective, they are likely 
> to create more *distinct* observers with a memory of the split going one way 
> than of the split going the other. So if we look at some very large region 
> where there are 90 copies of our local region of the universe where the 
> quantum coinflip went one way and only 10 copy of our local region where the 
> coinflip went the other way, then even if those 90 copies run in lockstep 
> for a while, chances are good that eventually random events in each region 
> will cause them to diverge. The end result would be that, after sufficient 
> time, in this very large region you'll have 100 distinct regions which all 
> share the same history up until that coinflip, with 90 having records of the 
> flip going one way and 10 having records of it going the other.

I meant to imply that this kind of differentiation could not occur in
my thought experiment, because the subject involved was a simulation in
a computer.  He is not interacting with the environment, he is running
a deterministic program.  So I can give him a good or bad experience
and he will not split.

Do you think you would say, in that case, that when I flip my 90/10
quantum coin, there is no reason to give him the good experience with 90%
probability and the bad experience with 10% probability?  It would be just
as good to reverse the odds?

Remember, I'm not running copies; I'm just running one program, and
flipping a biased coin to decide what to do.


> And given my 
> views on splits having an "anticipatory" quality (so if you're split into 
> two and then one copy is scheduled to be split 999 times later, that will be 
> reflected in your subjective probabilities in the initial split), I 
> naturally tend to think that this means you'd have a 9 times greater 
> probability of experiencing the coinflip outcome that will later lead to 90 
> divergent copies, even if the 90 copies run in lockstep initially.

This is an interesting idea; one thing that occurs to me though is the
problem of amnesia.  (And let's face it, 99% of what we experience,
we don't remember.)  If you're split into two and experience something
in the one copy that is forgotten before it gets split 999 times, does
that to-be-forgotten experience still gain the benefit of the 999-fold
multiplication?

In other words, is it by virtue of later memory of the event that you
expect the subjective probability to be magnified, or is it a more
metaphysical connection?


> But like I said, it's difficult to make any definite claims about why we 
> experience quantum probabilities the way we do, especially since no one has 
> come up with a way to derive a simple frequentist notion of probability from 
> the universal wavefunction in the MWI.

That is indeed the case.  I hope to write an essay soon about what I
think such a solution would look like (not to offer a solution, merely
to try to clarify what exactly I think it needs to explain).

Hal

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