Wei Dai wrote:
> Ok, here's another probability paradox. Suppose in the quantum suicide
> experiment the assistant offers the experimenter a bet. The experimenter
> gives the assistant $2 before he pulls the gun, and in return the
> assistant will give $3 to the experimenter after pulling the gun, if the
> result is a click instead of a bang. The assistant clearly has a positive
> expected return from this bet. But if the experimenter believes she will
> hear a click with 100% certainty, she also has a positive expected return.
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.
> These paradoxes show that the method of computing sensory
probabilities
> suggested by Tegmark is flawed. I think the right method involves removing
> the restriction that
>
> sum_over_X P(X|Y) = 1
>
> where Y is current perception and X is future perception.
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.
_____________________________________________________
Nick Bostrom
London School of Economics
Department of Philosophy, Logic and Scientific Method
n.bostrom.domain.name.hidden
http://www.hedweb.com/nickb
Received on Tue Feb 24 1998 - 10:51:43 PST