the non-zero probability that the universe can support an infinite number of computations means that the expected number of computations we expect to be performed in our universe is infinite.
Where do you get the non-zero probability from? If it’s from the general idea that nothing has zero probability, this proves too much. On the same principle, every action has non-zero probability of infinite positive utility and of infinite negative utility. This makes expected utility calculations impossible, because Inf—Inf = NaN.
I consider this a strong argument against the principle, often cited on LW, that “0 and 1 are not probabilities”. It makes sense as a slogan for a certain idea, but not as mathematics.
Where do you get the non-zero probability from? If it’s from the general idea that nothing has zero probability, this proves too much. On the same principle, every action has non-zero probability of infinite positive utility and of infinite negative utility. This makes expected utility calculations impossible, because Inf—Inf = NaN.
I consider this a strong argument against the principle, often cited on LW, that “0 and 1 are not probabilities”. It makes sense as a slogan for a certain idea, but not as mathematics.
I’m not certain of this, but my guess is that most physicists would assign much great than, say, .0001 probability to the universe being infinite.