Re: Many Pasts? Not according to QM...

From: Jesse Mazer <lasermazer.domain.name.hidden>
Date: Sun, 12 Jun 2005 00:30:46 -0400

Hal Finney wrote:
>
>Jesse Mazer writes:
> > But I explained in my last post how the ASSA could also apply to an
> > arbitrary "next" observer-moment as opposed to an arbitrary "current"
> > one--if you impose the condition I mentioned about the relation between
> > conditional probability and absolute probability, which is basically
> > equivalent to the condition that each tank is taking in water from other
> > tanks at the same rate it's pumping water to other tanks, then the
> > probabilities will be unchanged.
>
>One thing I didn't understand about this example: how do you calculate
>the probabilities which relate one observer-moment to a potential
>successor observer-moment?

In my notation, if I'm experiencing observer-moment y, then the probability
that I will next experience observer-moment x is represented as P(y -> x).

>And do they have to satisfy the rule that
>
>p(x) = sum over all possible predecessor OM's y of (p(y) * p(x|y))
>
>where p(x|y) is the transition probability from predecessor OM y to
>successor OM x? In other words, is probability conserved much as fluid
>flow would be in tanks which had constant fluid levels?

Yup, exactly--what you wrote as p(x|y), I wrote as p(y -> x).

>
>I'd be interested in any ideas for how one might calculate a priori the
>p(x|y) probabilities. I and others have offered suggestions for how one
>might calculate p(x), i.e. the probability of a given OM (it amounts to
>just 1/2^KC(x) where KC is the Kolmogorov complexity of x).
>
>The problem I see is cases like some of our duplication thought
>experiments where you get copies created, perhaps even in the past or
>future, or in other universes that are widely separated in the multiverse.
>How do you link all these up into predecessors and successors?

My speculation is that p(y -> x) would depend on a combination of some
function that depends only on intrinsic features of the description of x and
y--how "similar" x is to y, basically, the details to be determined by some
formal "theory of consciousness" (or 'theory of observer-moments',
perhaps)--and the absolute probability of x, since if two possible future
OMs x and x' are equally "similar" to my current OM y, then I'd expect if x
had a higher abolute measure than x' (perhaps x' involves an experience of a
'white rabbit' event), then p(y -> x) would be larger than p(y -> x'). So
let's say p(y -> x) = S(y -> x)*p(x), where S(y -> x) is the "intrinsic
similarity" function. In that case, then for my example involving just 3
observer-moments A,B,C, the condition above about absolute probability
remaining constant becomes:

P(A)*S(A -> A)*P(A) + P(A)*S(A -> B)*P(B) + P(A)*S(A -> C)*P(C) = P(A)
P(B)*S(B -> A)*P(A) + P(B)*S(B -> B)*P(B) + P(B)*S(B -> C)*P(C) = P(B)
P(C)*S(C -> A)*P(A) + P(C)*S(C -> B)*P(B) + P(C)*S(C -> C)*P(C) = P(C)

which simplifies to:

S(A -> A)*P(A) + S(A -> B)*P(B) + S(A -> C)*P(C) = 1
S(B -> A)*P(A) + S(B -> B)*P(B) + S(B -> C)*P(C) = 1
S(C -> A)*P(A) + S(C -> B)*P(B) + S(C -> C)*P(C) = 1

So, the "similarity matrix" operating on the absolute probability vector
would give the unit vector, which might imply that given the similarity
matrix, there is a unique possible absolute probability vector that will
satisfy this condition...and of course, once we have the absolute
probabilities, then if conditional probabilities are just p(y -> x) = S(y ->
x)*p(x), that means all the conditional probabilities would also follow
uniquely from this. And like Bruno, my hope would be that the appearance of
a "physical universe" can be recovered from the probabilities of different
observations by OMs.

Jesse
Received on Sun Jun 12 2005 - 00:41:37 PDT