Wei Dai wrote:
> I agree that if a solution exists, this will be a key part. But I don't
> think it's enough. In the outside view of AUH, there is a matter of fact
> about how any decision is made in each universe. How do you define the
> effects of making any particular choice? WIthout AUH you can define the
> effects of a choice as the set of events that would not have occured had
> you not made that choice. But with AUH this definition no longer makes
> sense, because there is no possible meta-universe where you do not make
> any particular choice or make that choice with a different frequency or
> measure.
Why can't there be any meta-universes where I make that choice with
a different frequency or measure?
> > I was assuming that by this time the copies have received some extra
> > differentiating information, however slight. One copy might have
> > heard the sound "alpha" and the other "beta". Then the one that has
> > heard "alpha" could say to himself: "The probability that the copy
> > who heard alpha (me) will see heads when he opens his eyes is p."
> > However, I now realize that in principle, the copy could calculate
> > whether it was the alpha-copy or the beta-copy that will see tail. So
> > the probability would be 1 or 0 if the copy in question could compute
> > this; but if there are practical limitations on his computational
> > abilities then the above reasoning might still give the copy useful
> > probabilistic information.
>
> I'm not sure i understand your setup here. Can you be more explicit about
> how the "alpha" and "beta" fit into the situation that we're talking
> about?
Ok:
At time 0 the experiment starts. At time 1 a coin is flippend and
observerd by the experimenter. At time 2 a second coin is flipped
(but not observerd by the experimenter). At time 3 the experimenter
is duplicated iff both coins show heads.
Now, I add the following feature:
At time 3.5, everybody is showed a card with a different colour,
randomly. (Say, one is showed a blue card, one a green card and one a
red card.)
At time 4, everybody is told the following: "You exist at time 4.
What is the probability that you will see the second coin showing
heads when you open your eyes and observe it?".
So on the AUH, at time 4 there will be one guy, A, who remembers
having seen (tail, tail); B remembers having seen (tail, heads); C
(heads, tail); D(heads, heads) and E(heads, heads). In addition, each
if these guys has seen a different colour. Hence, if a guy has seen
yellow, he can meaningfully ask: "What is the subjective probability
(relative to my knowledge) that the guy who saw a yellow card will
see heads when he opens his eyes?"
It is true that if this guy had unlimited processing power, then he
could solve the theory of everything and deduce that with probability
one or zero, the guy who say yellow will see heads. But if
intellectual restrictions make this infeasible, he can make the
following reasonable guess: "The guy who saw yellow remembers having
seen the first coin showed heads. There are three guys who remember
having seen the first coin showed heads. Two of these will see the
second coin showing heads when they open their eyes; the third won't.
Since I don't have any other info that I know how to take into
account, I estimate the subjective probability that the guy who saw
yellow (i.e. me) will see the second coin showing heads is 2/3.
This is one way in which the AUH, given my interpretation (with
standard probability & decision theory) gives a useful way of making
predictions.
_____________________________________________________
Nick Bostrom
Department of Philosophy, Logic and Scientific Method
London School of Economics
n.bostrom.domain.name.hidden
http://www.hedweb.com/nickb
Received on Sun Apr 12 1998 - 19:04:48 PDT