Re: another paradox and a solution

From: Wei Dai <weidai.domain.name.hidden>
Date: Tue, 24 Feb 1998 13:20:22 -0800

On Tue, Feb 24, 1998 at 04:12:38AM +0000, Nick Bostrom wrote:
> Can't this be explained by saying that: if all superposed states
> actually exist, then there are a lot of instances of the
> experimenter and a lot of instances of the assistant. By the
> arrangement you describe, the instances of the experimenter and
> the instances of the assistant conspire to kill a subset of the
> instances of the experimenter and share the prey between the
> instances of the assistent and the surviving instances of the
> experimenter. So the money don't appear out of nowhere; in some senes
> they come from the killed instances of the experimenter. But it is
> not a matter of transfering something from one branch of the
> universal wave function to another; rather it is a matter of
> selectively eliminating "poverty-branches" (or at least making them
> observerless) by linking them to suicide mechanisms. That will have
> the effect of increasing the consentration of wealthy brances. This
> is somewhat analogous to killing the poor people in the world in
> order to thereby raise the average standard of living.

I think this is a good way to think about the situation. But regardless of
how you think about it, there is something wrong with a theory that says
playing Russian roulette is rational. If nothing else the number of people
who believe the theory will dwindle very quickly. (Note that this is a
different paradox from the one we've been talking about. Here the
experiment itself is a choice, not just the bet.)

> What, more exactly, do X and Y stand for? A perception is an object,
> but strictly speeking, so far as I can see at least, probabilities
> apply only to propositions. Saying that these propositions are of the
> form "There will be an experience of type A." might not be enough;
> for that proposition would be true whether there is one or several
> instances of experiences of type A, and you seem to want to
> distinguish these cases. "I will have an experience of type A." might
> not do either, since at t=0 there is no fact of the matter as to
> which future instance of your mind will actually be "you". "There
> will be n instances of experiences of type A." might be the right way
> to go.

The P(X|Y) notation comes from Tegmark's TOE paper. It means the
probability that I will perceive X after subjective time t, given that
I've perceived Y so far. A problem with the AUH is that it is not at all
clear how to define probabilities for general propositions, or that such
probabilities would mean anything. This is especially true for my more
radical AUH which says binary strings are the fundamental objects that
have independent existence, and universes are interpretations of certain
collections of strings. How would you define the probability for "There
will be n instances of experiences of type A."?

I am uncomfortable with the definition of probability that I proposed
since it seems very radical to have probabilities that are greater than 1.
I would love to see an alternative if it also solves the problems I've
mentioned with Tegmark's definition.
Received on Tue Feb 24 1998 - 13:21:02 PST