I don't know how you expect me to respond to this.
> Before even talking about Turing computability and infinite set atheism (which rule out a continuous, infinite configuration space), configuration space is folded on itself around the identity axis.
Infinite set atheism is basically Yudkowsky's reason for denying Hilbert space, so I don't know why we should talk before it.
Read the comments on "The Quantum Arena" -- Yudkowsky didn't even know whether the thing he was railing against as an uncountably infinite set was indeed infinite! (Presumably he has updated by now.)
> Unless you think (a,b) is not the same configuration as (b,a)
Well, it depends on the situation. I assume you're talking about the configuration space of the position of two indistinguishable particles, in which case of course I think they're the same configuration (that's what 'indistinguishable' means) and you're just beating down a straw man. If wavefunctions in general are members of a Hilbert space, then so are symmetric wavefunctions.
> Overall, I'm not sure what you're talking about. Can you be more explicit, or provide some links?
All of the wavefunctions for two particles described within are elements of L^2(R^2); the subset of physically realizable wavefunctions forms a subspace which is also a Hilbert space (answering your question about "permutable" spaces).
Well… I agree. But then again, I don't think he really was trying to teach it. The way I see it, he just lifted confusions you would have if you start to really learn QM.
> Before even talking about Turing computability and infinite set atheism (which rule out a continuous, infinite configuration space), configuration space is folded on itself around the identity axis.
Infinite set atheism is basically Yudkowsky's reason for denying Hilbert space, so I don't know why we should talk before it.
Read the comments on "The Quantum Arena" -- Yudkowsky didn't even know whether the thing he was railing against as an uncountably infinite set was indeed infinite! (Presumably he has updated by now.)
> Unless you think (a,b) is not the same configuration as (b,a)
Well, it depends on the situation. I assume you're talking about the configuration space of the position of two indistinguishable particles, in which case of course I think they're the same configuration (that's what 'indistinguishable' means) and you're just beating down a straw man. If wavefunctions in general are members of a Hilbert space, then so are symmetric wavefunctions.
> Overall, I'm not sure what you're talking about. Can you be more explicit, or provide some links?
http://galileo.phys.virginia.edu/classes/252/symmetry/Symmet...
All of the wavefunctions for two particles described within are elements of L^2(R^2); the subset of physically realizable wavefunctions forms a subspace which is also a Hilbert space (answering your question about "permutable" spaces).
TL;DR: Don't try to learn QM from EY.