Question: Wouldn't under SIA we'd be expected to be in a universe with a high number of observers? Yet this isn't actually what we're seeing. Our universe is pretty much completely lifeless outside of Earth, at least based on what we have discovered so far.
What if we're in one of the universes with a small number of observers? Wouldn't that go contrary to the assumptions in the SIA? And if we're in one of the universes with a small number of observers, even though the SIA predicts otherwise, how can we trust the SIA to predict the fact that we'd be in a multiverse with a huge number of observers?
"The Sleeping Beauty problem is a puzzle in decision theory in which whenever an ideally rational epistemic agent is awoken from sleep, they have no memory of whether they have been awoken before. Upon being told that they have been woken once or twice according to the toss of a coin, once if heads and twice if tails, they are asked their degree of belief for the coin having come up heads."
In the case she is woken twice is she asked to identify the coin twice? it is unclear from this wording. If she is asked twice on tails and once on heads then thirding is obvious, if she is only asked the second wake on tails then halving is obvious.
I guess I should’ve clarified it further heh, but I was almost sleeping yesterday
What I meant is that’s really really hard to make a consistent a priori probability distribution in both cases. E.g. in jackets example it’s not quite obvious why you should be able to make any claims about the two hypotheses a priori
Maybe the first one is the second one with additional 100 jackets included with some probability, if the two jackets parts are independent
Maybe it’s not and there are just way more possible explanations for the first case than for the second
In the second case maybe you should give finite and infinite universes totally equal a priori probabilities
Or, maybe each one of finite universes with size X should be equally as likely as the infinite one
Maybe you should consider different ordinals for the infinite universe. Maybe not, maybe it doesn’t matter as long as the infinite universe is infinite
Still, it’s a pretty strange thing to a priori give only one possible probability distribution for each question
Question: Wouldn't under SIA we'd be expected to be in a universe with a high number of observers? Yet this isn't actually what we're seeing. Our universe is pretty much completely lifeless outside of Earth, at least based on what we have discovered so far.
What if we're in one of the universes with a small number of observers? Wouldn't that go contrary to the assumptions in the SIA? And if we're in one of the universes with a small number of observers, even though the SIA predicts otherwise, how can we trust the SIA to predict the fact that we'd be in a multiverse with a huge number of observers?
"The Sleeping Beauty problem is a puzzle in decision theory in which whenever an ideally rational epistemic agent is awoken from sleep, they have no memory of whether they have been awoken before. Upon being told that they have been woken once or twice according to the toss of a coin, once if heads and twice if tails, they are asked their degree of belief for the coin having come up heads."
In the case she is woken twice is she asked to identify the coin twice? it is unclear from this wording. If she is asked twice on tails and once on heads then thirding is obvious, if she is only asked the second wake on tails then halving is obvious.
She's asked twice if tails, but thirding is still controversial
I guess I should’ve clarified it further heh, but I was almost sleeping yesterday
What I meant is that’s really really hard to make a consistent a priori probability distribution in both cases. E.g. in jackets example it’s not quite obvious why you should be able to make any claims about the two hypotheses a priori
Maybe the first one is the second one with additional 100 jackets included with some probability, if the two jackets parts are independent
Maybe it’s not and there are just way more possible explanations for the first case than for the second
In the second case maybe you should give finite and infinite universes totally equal a priori probabilities
Or, maybe each one of finite universes with size X should be equally as likely as the infinite one
Maybe you should consider different ordinals for the infinite universe. Maybe not, maybe it doesn’t matter as long as the infinite universe is infinite
Still, it’s a pretty strange thing to a priori give only one possible probability distribution for each question
Reply to both examples is that undefined probability distribution can lead to random results
???
Re jackets and presumptuous philosopher’s cases
It’s quite hard to intuitively get reasonable probability distribution on whatever thing you just imagined
Yeah, that's a good article.
The presumptuous archeologist seems crazy, as do a lot of the other objections to SSA. What do you make of the bare probability point?
That SIA is just the normal way to do probability for all other events.