An example of a measure in this context would be the complexity measure that Tegmark mentioned, as long as we agree on a way to encode mathematical structures (the nonuniqueness of representation is one of the issues that Tegmark brought up).
Whether this is an appropriate measure (i.e., whether it correctly “predicts conditional probabilities for what an observer should perceive given past observations”) is unknown; if we knew how to find out, then we could directly resolve the measure problem!
An example of a context where we can give the explicit measure is in the many-words interpretation, where as I mentioned, the Born probabilities resolve the analogous measure problem.
An example of a context where we can give the explicit measure is in the many-words interpretation, where as I mentioned, the Born probabilities resolve the analogous measure problem.
So you are saying that the “Born probabilities” are an example of an “appropriate measure” which, if “postulated,” rebuts Egan’s argument?
The Born probabilities apply to a different context—the multiple Everett branches of MWI, rather than the interpretative universes available under dust theory. If we had an equivalent of the Born probabilities—a measure—for dust theory, then we’d be able to resolve Egan’s argument one way or another (depending on which way the numbers came out under this measure).
Since we don’t yet know what the measure is, it’s not clear whether Egan’s argument holds—under the “Tengmark computational complexity measure” Egan would be wrong, under the “naive measure” Egan is right. But we need some external evidence to know which measure to use. (By contrast in the QM case we know the Born probabilities are the correct ones to use, because they correspond to experimental results (and also because e.g. they’re preserved under a QM system’s unitary evolution)).
I would guess you are probably correct that Egan’s argument hinges on this point. In essence, Egan seems to be making an informal claim about the relatively likelihood of an orderly dust universe versus a chaotic one.
Boiled down to its essentials, VincentYu’s argument seems to be that if Egan’s informal claim is incorrect, then Egan’s argument fails. Well duh.
An example of a measure in this context would be the complexity measure that Tegmark mentioned, as long as we agree on a way to encode mathematical structures (the nonuniqueness of representation is one of the issues that Tegmark brought up).
Whether this is an appropriate measure (i.e., whether it correctly “predicts conditional probabilities for what an observer should perceive given past observations”) is unknown; if we knew how to find out, then we could directly resolve the measure problem!
An example of a context where we can give the explicit measure is in the many-words interpretation, where as I mentioned, the Born probabilities resolve the analogous measure problem.
So you are saying that the “Born probabilities” are an example of an “appropriate measure” which, if “postulated,” rebuts Egan’s argument?
Is that correct?
The Born probabilities apply to a different context—the multiple Everett branches of MWI, rather than the interpretative universes available under dust theory. If we had an equivalent of the Born probabilities—a measure—for dust theory, then we’d be able to resolve Egan’s argument one way or another (depending on which way the numbers came out under this measure).
Since we don’t yet know what the measure is, it’s not clear whether Egan’s argument holds—under the “Tengmark computational complexity measure” Egan would be wrong, under the “naive measure” Egan is right. But we need some external evidence to know which measure to use. (By contrast in the QM case we know the Born probabilities are the correct ones to use, because they correspond to experimental results (and also because e.g. they’re preserved under a QM system’s unitary evolution)).
I would guess you are probably correct that Egan’s argument hinges on this point. In essence, Egan seems to be making an informal claim about the relatively likelihood of an orderly dust universe versus a chaotic one.
Boiled down to its essentials, VincentYu’s argument seems to be that if Egan’s informal claim is incorrect, then Egan’s argument fails. Well duh.