Suppose there is a 2^(-n) chance of universe U_n with n people for n > 0. Initially, there's nothing paradoxical about this. SIA converges. But look at the evidence you get from existing. Call that E.

P(U_n|E) = knP(U_n) for some k

P(U_n|E) = P(U_n&E)/P(E)

P(U_n|E) < P(U_n)/P(E)

P(E) < P(U_n)/P(U_n|E)

P(E) < P(U_n)/(knP(U_n))

P(E) < 1/kn

Since k is constant and this is true for all n, P(E) = 0

So, existence is infinitely unlikely? Or we must assume a priori that the universe definitely doesn't have more than n people for some n? Or P(U_n&E) is somehow higher than P(U_n)?

Right. In a sense, P(E) is one over the number of possible people in the universe (scaled by how much of configuration space 'you' are).

Observing your existence only changes your probabilities if your nonexistence was also, causally, an option. In order for there to be an infinite number of possible people in the universe, but only this exponential prior distribution, the probability that any given chunk of stuff is 'you' has to go to zero.

This kinda confused me, I think because P(E) does not represent what I'd colloquially expect - I'm pretty sure now that it's a sampling probability, not a global probability.

Open thread, Dec. 15 - Dec. 21, 2014

by Gondolinian 1 min read15th Dec 2014309 comments


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