Hmm… I think with Solomonoff induction I would say R is the UTM input, plus the entire execution trace/trajectory. Then M would be like the agent’s observations, which are a simple function of R.
I see that we can’t have all “real” things being R-efficiently computable. But the thing about doxastic states is, some agent has access to them, so it seems like from their perspective, they are “effective”, being “produced somewhere”… so I infer they are probably “computed in reality” in some sense (although that’s not entirely clear). They have access to their beliefs/observations in a more direct way than they have access to probabilities.
With respect to reversibility: The way I was thinking about it was that when the key is erased, it’s erased really far away. Then the heat from the key gets distributed somehow. Like the information could even enter a black hole. Then there would be no way to retrieve it. (Shouldn’t matter too much anyway if natural supervenience is local, then mental states couldn’t be affected by far away physical states anyway)
Here’s a pure quantum, information theoretic, no computability assumptions version that might or might not be illustrative. I don’t actually know if the quantum computer I’m talking about could be built—I’m going off intuition. EDIT I think this is 2 party quantum computation and none of the methods I’ve found are quite as strong as what I list here (real methods require e.g. a number of entangled qbits on order of the size of the computation).
You have two quantum computers, Alice and Bob, preforming the same computation steps. Alice and Bob have entangled qbits. If you observe the qbits of either Alice or Bob in isolation, you’ll forever get provably random noise from both of them. But if you bring Alice and Bob together and line up their qbits and something somethingmumble, you get a pure state and can read off their joint computation.
Now we have all sorts of fun thought experiments. You run Alice and Bob, separating them very far from one another. Is Alice currently running a mind computation? Provably not, if someone looked at Bob last year. But Bob is many many light years away—how can we know if someone looked at Bob? What if we separate Alice and Bob past each other’s cosmic horizons, such that the acceleration of the expanding universe makes it impossible for them to ever reach each other again even if they run towards each other at the speed of light? Or send Bob to Alpha Centauri and back at close to the speed of light so he’s aged only 1 year where Alice has aged 8. Has Alice been doing the mind thing for the past 7 years? Depends on whether you look at Bob or not.
(but I’ll note that for me, this version, like the homomorphic version, is mostly saying that your description of a quantum physics state shouldn’t be purely local. A purely local description must discard information, something something mixed state Von Neumann entropy)
Yeah that seems like a case where non-locality is essential to the computation itself. I’m not sure how the “provably random noise from both” would work though. Like, it is possible to represent some string as the xor of two different strings, each of which are themselves uniformly random. But I don’t know how to generalize that to computation in general.
I think some of the non locality is inherited from “no hidden variable theory”. Like it might be local in MWI? I’m not sure.
Hmm… I think with Solomonoff induction I would say R is the UTM input, plus the entire execution trace/trajectory. Then M would be like the agent’s observations, which are a simple function of R.
I see that we can’t have all “real” things being R-efficiently computable. But the thing about doxastic states is, some agent has access to them, so it seems like from their perspective, they are “effective”, being “produced somewhere”… so I infer they are probably “computed in reality” in some sense (although that’s not entirely clear). They have access to their beliefs/observations in a more direct way than they have access to probabilities.
With respect to reversibility: The way I was thinking about it was that when the key is erased, it’s erased really far away. Then the heat from the key gets distributed somehow. Like the information could even enter a black hole. Then there would be no way to retrieve it. (Shouldn’t matter too much anyway if natural supervenience is local, then mental states couldn’t be affected by far away physical states anyway)
Here’s a pure quantum, information theoretic, no computability assumptions version that might or might not be illustrative. I don’t actually know if the quantum computer I’m talking about could be built—I’m going off intuition. EDIT I think this is 2 party quantum computation and none of the methods I’ve found are quite as strong as what I list here (real methods require e.g. a number of entangled qbits on order of the size of the computation).
You have two quantum computers, Alice and Bob, preforming the same computation steps. Alice and Bob have entangled qbits. If you observe the qbits of either Alice or Bob in isolation, you’ll forever get provably random noise from both of them. But if you bring Alice and Bob together and line up their qbits and something something mumble, you get a pure state and can read off their joint computation.
Now we have all sorts of fun thought experiments. You run Alice and Bob, separating them very far from one another. Is Alice currently running a mind computation? Provably not, if someone looked at Bob last year. But Bob is many many light years away—how can we know if someone looked at Bob? What if we separate Alice and Bob past each other’s cosmic horizons, such that the acceleration of the expanding universe makes it impossible for them to ever reach each other again even if they run towards each other at the speed of light? Or send Bob to Alpha Centauri and back at close to the speed of light so he’s aged only 1 year where Alice has aged 8. Has Alice been doing the mind thing for the past 7 years? Depends on whether you look at Bob or not.
(but I’ll note that for me, this version, like the homomorphic version, is mostly saying that your description of a quantum physics state shouldn’t be purely local. A purely local description must discard information, something something mixed state Von Neumann entropy)
Yeah that seems like a case where non-locality is essential to the computation itself. I’m not sure how the “provably random noise from both” would work though. Like, it is possible to represent some string as the xor of two different strings, each of which are themselves uniformly random. But I don’t know how to generalize that to computation in general.
I think some of the non locality is inherited from “no hidden variable theory”. Like it might be local in MWI? I’m not sure.