Yeah, using a simplicity prior is appealing for this kind of questions. A related idea, which I haven’t really seen anywhere, is that it might solve Loschmidt’s paradox.
The paradox comes from realizing that, since the laws of physics are time-symmetric and our most likely future has higher entropy, our most likely past (conditional only on the present) also has higher entropy than the present. All your memories are lies, and the glass of milk just assembled itself from a broken state a second ago! The usual solution is by conditioning on both the present and a hypothetical low-entropy distant past, which is known as the “past hypothesis”. Then the mystery is why the distant past had such low entropy, which is neatly resolved by a simplicity prior saying some highly ordered states have very short descriptions. For example, a uniform density of gas in space which can collapse into stars etc. would be a nice starting point.
Your last paragraph is interesting. Maybe the simplicity prior indeed leads to a penalty for larger universes! Or maybe not, if the idea of finding observers in a universe is itself simple, and we just need to say “find observer #2345671 in universe #3”. This whole thing makes me very confused.
I’m not sure my memories being lies is actually all that likely even taking Loschmidt into account. I don’t expect my memories to get scrambled in the near future, so I also shouldn’t expect my memories to recently have spontaneously unscrambled. Is that how it works? Hm, but on the other hand, does the asymmetry of my memories provide sufficient evidence that the past was low-entropy? If you have a max-entropy prior over states of matter in the universe, no, absolutely not. You’d need some kind of simplicity prior or similar. So I guess you’re totally right :)
Yeah, using a simplicity prior is appealing for this kind of questions. A related idea, which I haven’t really seen anywhere, is that it might solve Loschmidt’s paradox.
The paradox comes from realizing that, since the laws of physics are time-symmetric and our most likely future has higher entropy, our most likely past (conditional only on the present) also has higher entropy than the present. All your memories are lies, and the glass of milk just assembled itself from a broken state a second ago! The usual solution is by conditioning on both the present and a hypothetical low-entropy distant past, which is known as the “past hypothesis”. Then the mystery is why the distant past had such low entropy, which is neatly resolved by a simplicity prior saying some highly ordered states have very short descriptions. For example, a uniform density of gas in space which can collapse into stars etc. would be a nice starting point.
Your last paragraph is interesting. Maybe the simplicity prior indeed leads to a penalty for larger universes! Or maybe not, if the idea of finding observers in a universe is itself simple, and we just need to say “find observer #2345671 in universe #3”. This whole thing makes me very confused.
I’m not sure my memories being lies is actually all that likely even taking Loschmidt into account. I don’t expect my memories to get scrambled in the near future, so I also shouldn’t expect my memories to recently have spontaneously unscrambled. Is that how it works? Hm, but on the other hand, does the asymmetry of my memories provide sufficient evidence that the past was low-entropy? If you have a max-entropy prior over states of matter in the universe, no, absolutely not. You’d need some kind of simplicity prior or similar. So I guess you’re totally right :)