the exact same degree of belief to any proposition of the form: ‘I’m the first observer’, ‘I’m the second observer’, etc.
Trying to assign the same degree of belief to infinitely many mutually exclusive options doesn’t work. The probability of being an observer #1 is greater than the probability of being an observer #10^10, simply because some possible universes contain more than 1 but less than 10^10 observers.
I’m not sure how exactly the distribution should look; just saying in general that larger numbers have smaller probabilities. The exact distribution would depend on your beliefs about the universe, or actually about the whole Tegmark multiverse, and I don’t have much strong beliefs in that area.
For example, if you believe that universe has a limited amount of particles and a limited amount of time, that would put an (insanely generous) upper bound on the number of observers in this universe.
Trying to assign the same degree of belief to infinitely many mutually exclusive options doesn’t work.
Yeah, but the class of observers in the Doomsday argument is not infinite, usually one takes a small and a huge set, both finite. So in theory you could assign a uniform distribution.
For example, if you believe that universe has a limited amount of particles and a limited amount of time, that would put an (insanely generous) upper bound on the number of observers in this universe.
Exactly, and that’s an assumption I’m always willing to make, to circumvent the problem of an infinite class of reference.
The problem though is not the cardinality of the set, it’s rather the uniformity of the distribution, which I think is what is implied by the word ‘randomness’ in S(S|I)A, because I feel intuitively it shouldn’t be so, due to the very definition of observer.
Trying to assign the same degree of belief to infinitely many mutually exclusive options doesn’t work. The probability of being an observer #1 is greater than the probability of being an observer #10^10, simply because some possible universes contain more than 1 but less than 10^10 observers.
I’m not sure how exactly the distribution should look; just saying in general that larger numbers have smaller probabilities. The exact distribution would depend on your beliefs about the universe, or actually about the whole Tegmark multiverse, and I don’t have much strong beliefs in that area.
For example, if you believe that universe has a limited amount of particles and a limited amount of time, that would put an (insanely generous) upper bound on the number of observers in this universe.
Yeah, but the class of observers in the Doomsday argument is not infinite, usually one takes a small and a huge set, both finite. So in theory you could assign a uniform distribution.
Exactly, and that’s an assumption I’m always willing to make, to circumvent the problem of an infinite class of reference.
The problem though is not the cardinality of the set, it’s rather the uniformity of the distribution, which I think is what is implied by the word ‘randomness’ in S(S|I)A, because I feel intuitively it shouldn’t be so, due to the very definition of observer.