Hal Finney wrote:
>
>Jesse Mazer writes:
> > Would you say that because you think running multiple identical copies
>of a
> > given mind in parallel doesn't necessarily increase the absolute measure
>of
> > those observer-moments (that would be my opinion)...
>
...
>
>Suppose we are going to flip a biased quantum coin, one which has a 90%
>chance of coming up heads. We will generate the good or bad experience
>depending on the outcome of the coin flip. I claim that it is obvious
>that it is better to give the good experience when we get the 90% outcome
>and the bad experience when we get the 10% outcome. That's the assumption
>I will start with.
>
>Now consider Tegmark's level 1 of parallelism, the fact that in a
>sufficiently large volume of space I can find a large number of copies
>of me, in fact copies of the entire earth and our entire visible universe
>(the "Hubble bubble"?). When I do my quantum coin flip, 90% of the copies
>will see it come up heads and cause the good experience for the subject,
>and 10% will see tails and cause the bad experience.
>
>I will also assume that my knowledge of this fact about the physical
>universe will not change my mind about the ethical value of my decision
>to give the good experience for the 90% outcome.
>
>Now the problem is this. There are really only two different programs
>being run for our experimental subject, the guy in the simulation. One is
>a good experience and one is bad. All my decision does is to change how
>many copies of each of these two programs are run. In making my decision
>about which experiences to assign to the two coin flip outcomes, I have
>chosen that the copies of the good experience will outnumber copies of
>the bad experience by 9 to 1.
>
>But if I don't believe that the number of copies being run makes a
>difference, then I haven't accomplished what I desired. The fact that
>I am running more copies of the good program than the bad wouldn't make
>any difference. Therefore there is no actual ethical value in what I
>have done, I might have just as validly reversed the outcome of my coin
>flips and it wouldn't have made any difference.
>
>In this way I reach a contradiction between the belief that the number
>of copies doesn't matter, the belief that the existence of distant
>parallel copies of myself doesn't make much difference in what I should
>do, and the idea that there is value in making people happy. Of these,
>the most questionable seems to be the assumption that copies don't matter,
>so this line of reasoning turns me away from that belief.
>
>I can come up with similar contradictions from simpler cases like
>our own observations of subjective probability. The fact that I do
>experience a subjective 90% chance of seeing the quantum coin come
>up heads corresponds very well with the fact that 90% of the copies
>of me will see heads - but only if I assume that the multiplicity of
>the copies matters. After the coin flip, in a certain voume of space
>there are 90 copies of me that see heads and 10 copies that see tails.
>But within the two groups all copies are identical (neglecting other
>quantum events which would further split me). If the multiplicity
>doesn't count, then there are really just two outcomes and I might
>expect to subjectively experience equal probability for them.
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 (note that this
does not mean that all physical processes are a kind of dream in the minds
of high-level intelligent beings like ourselves; I think the mathematical
description of the set of all observer-moments in a theory of consciousness
would probably be something like a set of graphs describing the causal
relationships between events in that observer's 'brain', and even very
simple causal patterns, like those created by the random jostling of
molecules in a rock, could be fellow observer-moments, albeit very simple
ones, which we are observing 'from the outside' just like we can only
experience other people's minds from the outside). Without having any clear
idea of how to do this derivation of an apparent physical universe from the
conditional and absolute measure on observer-moments, I don't really know
what the appearance of multiple physical copies would correspond to in terms
of conditional or absolute measure on observer-moments.
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. 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.
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.
Jesse
Received on Mon Jun 20 2005 - 20:39:02 PDT
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