I am going with the original post’s apparent belief that in the presence of infinities, probabilities are meaningless. This presumably derives from the observation that there are equally many even numbers and numbers divisible by eight, even though a probability distribution derived from taking the limit as the range goes to infinity would conclude that the probability of the one is four times higher than the other.
The OP was careful, it seems, to avoid that issue. (Infinite set agnosticism?)
In any case, our perceived history matches the Born rules too well for it to be reasonable that “probabilities are meaningless”, so either the universe is OK with measures on infinite sets or it’s somehow finite after all. (I incline strongly toward the former hypothesis, for reasons of mathematical elegance— thoroughly finitary versions of Hilbert spaces are hack-ish.)
our perceived history matches the Born rules too well for it to be reasonable that “probabilities are meaningless”, so either the universe is OK with measures on infinite sets or it’s somehow finite after all
I like this; it is an excellently compact way of putting it.
The OP was careful, it seems, to avoid that issue. (Infinite set agnosticism?)
I don’t see this. I am referring particularly to this paragraph:
No, this view of reality claims that your current observer-moment is repeated infinitely many times, and looking forward in time, all possible continuations of (you,now) occur, and furthermore there is no fact of the matter about which one you will experience, because the quantum MW aspect of the multiverse has already demolished our intuitions about anticipated subjective experience.
I agree with you that the Born rules imply meaningful probabilities; but it seems to me that the OP does not believe this, at least in the part I’ve quoted.
Probabilities over infinite sets are not at all meaningless. If a set is countable, they have to privilege some objects (in the sense that not everything can have the same probability). If the set is uncountable (say the real numbers between 0 and 1) then there’s no problem with having a very well-behaved probability distribution. (I’m skipping over some details. The fact that not every set is measurable means that one needs to be very careful when one talks about meaningfulness of probability).
I am going with the original post’s apparent belief that in the presence of infinities, probabilities are meaningless. This presumably derives from the observation that there are equally many even numbers and numbers divisible by eight, even though a probability distribution derived from taking the limit as the range goes to infinity would conclude that the probability of the one is four times higher than the other.
The OP was careful, it seems, to avoid that issue. (Infinite set agnosticism?)
In any case, our perceived history matches the Born rules too well for it to be reasonable that “probabilities are meaningless”, so either the universe is OK with measures on infinite sets or it’s somehow finite after all. (I incline strongly toward the former hypothesis, for reasons of mathematical elegance— thoroughly finitary versions of Hilbert spaces are hack-ish.)
I like this; it is an excellently compact way of putting it.
I don’t see this. I am referring particularly to this paragraph:
I agree with you that the Born rules imply meaningful probabilities; but it seems to me that the OP does not believe this, at least in the part I’ve quoted.
Probabilities over infinite sets are not at all meaningless. If a set is countable, they have to privilege some objects (in the sense that not everything can have the same probability). If the set is uncountable (say the real numbers between 0 and 1) then there’s no problem with having a very well-behaved probability distribution. (I’m skipping over some details. The fact that not every set is measurable means that one needs to be very careful when one talks about meaningfulness of probability).
Yes, I understand this, but as noted in my comment above, it appears that the OP is using a different assumption.