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


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