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Eliezer_Yudkowsky comments on The Anthropic Trilemma - Less Wrong
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Sounds like a right question to me. Got an answer?
A related problem: If we allow unbounded computations, then, when we try to add up copies, we can end up with different limiting proportions of copies depending on how we approach t -> infinity; and we can even have algorithms for creating copies such that their proportions fail to converge. (1 of A, 3 of B, 9 of A, 27 of B, etc.) So then either it is a metaphysical necessity that reality be finite, because otherwise our laws will fail to give correct answers; or the True Rules must be such as to give definitive answers in such a situation.
I'm afraid I'm not familiar enough with the Born probabilities to know how to approach an answer -- oh, I've been able to quote the definition about squared amplitudes since I was a wee lad, but I've never had occasion to actually work with them, so I don't have any intuitive feel about their implications.
As for the problem of infinity, you're right of course, though there are other ways for that to arise too -- for example, if the underlying physics is analog rather than digital. Which suggests it can't be fiated away. I don't know what the solution is, but it reminds me of the way cardinality says all shapes contain the same number of points, so it was necessary to invent measure to justify the ability to do geometry.
Deeply fundamentally analog physics, ie, infinite detail, would just be another form of infinity, wouldn't it? So it's a variation of the same problem of "what happens to all this when there's an infinity involved?"
To the best of our understanding, there's no such thing as "infinite detail" in physics. Physical information is limited by the Bekenstein bound.
Sorry, I may have been unclear. I didn't mean to make a claim that physics actually does have this property, but rather I was saying that if physics did have this property, it would just be another instance of an infinity, rather than an entirely novel source for the problem mentioned.
(Also, I'm unclear on the BB, if it takes into account possible future tech that may be able to manipulate the geometry of spacetime to some extent. ie, if we can do GR hacking, would that affect the bound or are the limits of that effectively already precomputed into that?)
Yes, that is my position on it.