Yup! You aren’t allowed to put a uniform distribution over an infinitely long set. Doesn’t work outside of anthropics either.
I think a pretty reasonable thing to do is to start penalizing Sleeping Beauties based on how complex the universe with her in it has to be. This is not the same as saying “well 1 is only 1 bit and 100 is like 7 bits, so Beauty #100 is exponentially less probable” because we can compress the number of Sleeping Beauty into the function that takes that number and extrapolates what’s going to happen in the universe. But for really, really, really big number Sleeping Beauties, eventually the iron law that there’s only a limited number of simple numbers catches up to you.
If we modify SIA by weighting on the complexity of the universe, what would be the conclusion for the original sleeping beauty problem? Isn’t the Tail world marginally more complex than the Head world?
Maybe, but this is really hard to evaluate. Because what we’re comparing the complexity of isn’t just the numbers “1” vs “2,” it’s Sleeping Beauty’s entire predictive model of what’s going to happen in the world after waking up in room 1 vs. 2.
Yup! You aren’t allowed to put a uniform distribution over an infinitely long set. Doesn’t work outside of anthropics either.
I think a pretty reasonable thing to do is to start penalizing Sleeping Beauties based on how complex the universe with her in it has to be. This is not the same as saying “well 1 is only 1 bit and 100 is like 7 bits, so Beauty #100 is exponentially less probable” because we can compress the number of Sleeping Beauty into the function that takes that number and extrapolates what’s going to happen in the universe. But for really, really, really big number Sleeping Beauties, eventually the iron law that there’s only a limited number of simple numbers catches up to you.
If we modify SIA by weighting on the complexity of the universe, what would be the conclusion for the original sleeping beauty problem? Isn’t the Tail world marginally more complex than the Head world?
Maybe, but this is really hard to evaluate. Because what we’re comparing the complexity of isn’t just the numbers “1” vs “2,” it’s Sleeping Beauty’s entire predictive model of what’s going to happen in the world after waking up in room 1 vs. 2.