Maybe I don’t understand your idea yet. You started with the question whether probabilities are a “reality fluid”, a “measure of caring”, or something else. How would you answer this question for the probabilities of a quantum coin in our universe?
I didn’t mean to address the question of what probabilities are in full generality, just on the level of abstraction of metaphysics / Tegmark IV / UDASSA / etc. I guess for a quantum coin in our universe (which is a more “zoomed in” context), I don’t really have anything new to say—just whatever quantum mechanics does, which is an integral over a measure in some way, I think? And then you derive your actual betting odds from your preferences if necessary, e.g. in Sleeping Beauty. (so I guess it’s kind of a combination of a reality fluid and a caring measure).
Ok, I think I understand it a bit better now. But one thing I’d like to note is that UDASSA wasn’t “zoomed out”. One cool feature of the UD is that, given enough observations from our universe (but not the laws of physics), it’ll reconstruct the right distribution for more observations from our universe. It doesn’t need separate levels for “universes” and “stuff within a universe”, it just does everything on one level. So if you replace it with a two-level system, that might be a bit unsatisfying.
Yeah, that’s a good point—I should clarify that. Technically, I’m not summing over universes either (that’s why I said “roughly speaking” earlier), but over all possible computations that lead to my observations, just like UDASSA.
The crux in whether this reconstructs reasonable actions / betting odds (e.g. that it generally converges with quantum mechanics) too is what I mentioned in the post—whether it reconstructs some version of a simplicity prior.
Maybe I don’t understand your idea yet. You started with the question whether probabilities are a “reality fluid”, a “measure of caring”, or something else. How would you answer this question for the probabilities of a quantum coin in our universe?
I didn’t mean to address the question of what probabilities are in full generality, just on the level of abstraction of metaphysics / Tegmark IV / UDASSA / etc. I guess for a quantum coin in our universe (which is a more “zoomed in” context), I don’t really have anything new to say—just whatever quantum mechanics does, which is an integral over a measure in some way, I think? And then you derive your actual betting odds from your preferences if necessary, e.g. in Sleeping Beauty. (so I guess it’s kind of a combination of a reality fluid and a caring measure).
Ok, I think I understand it a bit better now. But one thing I’d like to note is that UDASSA wasn’t “zoomed out”. One cool feature of the UD is that, given enough observations from our universe (but not the laws of physics), it’ll reconstruct the right distribution for more observations from our universe. It doesn’t need separate levels for “universes” and “stuff within a universe”, it just does everything on one level. So if you replace it with a two-level system, that might be a bit unsatisfying.
Cool, thank you for putting in the effort!
Yeah, that’s a good point—I should clarify that. Technically, I’m not summing over universes either (that’s why I said “roughly speaking” earlier), but over all possible computations that lead to my observations, just like UDASSA.
The crux in whether this reconstructs reasonable actions / betting odds (e.g. that it generally converges with quantum mechanics) too is what I mentioned in the post—whether it reconstructs some version of a simplicity prior.