I’m still confused about what you’re trying to say about QM, though. I start with m. Then Omega tells me “QM is true”. Now, I have E which is the set of worlds in which QM is true. But you’re saying QM being true affects m(u) and thats what I don’t grok.
I think it was a mistake to define m on U (the set of possible worlds, before restricting it to E); it can work even if you do it like that, but it’s less intuitive.
Try this: suppose your U can be partitioned two classes of universes: those in Q are quantum, and those in K are not. That is, U is the union of Q and K, and the intersection Q and K is empty.
A reasonable strategy for defining m (in the sense that that’s what I was aiming for) could go like this:
You define m(u) as a product of g(u) with s(u).
s is a measure specific for the class of universes u is part of. For (“logically possible”) universes that come from the Q class, s might depend on the amplitude of u’s wave-function. For those that come from K, it’s a completely different function, e.g. the Kolmogorov complexity of the bit-string defining u. Note that the two “branches” of s are completely independent: the wave-function doesn’t make any sense for K, nor does Kolmogorov complexity for those in Q (supposing that Q implies exact real-valued functions).
The g(u) part of the measure reflects everything that’s not related to this particular partitioning of U. It may be just a constant 1, or it may be a complex function based on other possible partitioning (e.g. finite/infinite universes).
The important part is that your m includes from the start a term for QM-related measure of universes, but only for those where it makes sense.
When Omega comes, you just remove K from U, so your E is a subset of Q. As a result, the rest of the calculations is never dependent on the s branch for K, and always depends on the s branch for Q. The effect is not that Omega changed the m, it just made part of it irrelevant to the rest of the calculations.
As I said in the first sentence of this answer, you can just define m only on E. But E is much more complex than U (it depends on every experience you had, thus it’s harder to specify, even if it’s “smaller”), so it’s harder to define a function only for its values.
Conceptually it’s easier to pick a somewhat vague m on U, and then “fill in details” as your E becomes more exact. But, to be clear, this is just because we’re handwaving about without actually being able to do the calculations; since the calculations seem impossible in the general case it’s kind of a moot point which is “really” easier.
I misread the computability bit, it makes sense.
I’m still confused about what you’re trying to say about QM, though. I start with m. Then Omega tells me “QM is true”. Now, I have E which is the set of worlds in which QM is true. But you’re saying QM being true affects m(u) and thats what I don’t grok.
I think it was a mistake to define m on U (the set of possible worlds, before restricting it to E); it can work even if you do it like that, but it’s less intuitive.
Try this: suppose your U can be partitioned two classes of universes: those in Q are quantum, and those in K are not. That is, U is the union of Q and K, and the intersection Q and K is empty.
A reasonable strategy for defining m (in the sense that that’s what I was aiming for) could go like this:
You define m(u) as a product of g(u) with s(u).
s is a measure specific for the class of universes u is part of. For (“logically possible”) universes that come from the Q class, s might depend on the amplitude of u’s wave-function. For those that come from K, it’s a completely different function, e.g. the Kolmogorov complexity of the bit-string defining u. Note that the two “branches” of s are completely independent: the wave-function doesn’t make any sense for K, nor does Kolmogorov complexity for those in Q (supposing that Q implies exact real-valued functions).
The g(u) part of the measure reflects everything that’s not related to this particular partitioning of U. It may be just a constant 1, or it may be a complex function based on other possible partitioning (e.g. finite/infinite universes).
The important part is that your m includes from the start a term for QM-related measure of universes, but only for those where it makes sense.
When Omega comes, you just remove K from U, so your E is a subset of Q. As a result, the rest of the calculations is never dependent on the s branch for K, and always depends on the s branch for Q. The effect is not that Omega changed the m, it just made part of it irrelevant to the rest of the calculations.
As I said in the first sentence of this answer, you can just define m only on E. But E is much more complex than U (it depends on every experience you had, thus it’s harder to specify, even if it’s “smaller”), so it’s harder to define a function only for its values.
Conceptually it’s easier to pick a somewhat vague m on U, and then “fill in details” as your E becomes more exact. But, to be clear, this is just because we’re handwaving about without actually being able to do the calculations; since the calculations seem impossible in the general case it’s kind of a moot point which is “really” easier.