Yes, they can all contribute, though they can’t all contribute equally, because your total probability has to sum to one, there are an infinite number of possible explanations, and there is no uniform distribution on the integers.
Also, apologies if some of my jargon was confusing. Most of it’s in the second chapter (I think?) of Li and Vitanyi’s textbook, if you’re interested, but really I should have just written with less jargon.
Isn’t that exactly what the ‘takes lots of bits to specify which overserver you are’-part can take care of though? Also I’m not sure what it means for a world to contain literally infinite copies of something—do you mean that on average there is some fixed (non-zero) density over a finite volume, and the universe is infinitely large? I think this issue with infinities is unrelated to the core point of this post.
Yes, they can all contribute, though they can’t all contribute equally, because your total probability has to sum to one, there are an infinite number of possible explanations, and there is no uniform distribution on the integers.
Also, apologies if some of my jargon was confusing. Most of it’s in the second chapter (I think?) of Li and Vitanyi’s textbook, if you’re interested, but really I should have just written with less jargon.
Isn’t that exactly what the ‘takes lots of bits to specify which overserver you are’-part can take care of though? Also I’m not sure what it means for a world to contain literally infinite copies of something—do you mean that on average there is some fixed (non-zero) density over a finite volume, and the universe is infinitely large? I think this issue with infinities is unrelated to the core point of this post.