Forgive me, Iâm probably being stupid again đŹ.
On efficient computability being necessary for reality: Iâm not sure I understand the logic behind this. Would you not always get diagonalization problems if you want supervening ârealâ things to be blessed with R-efficiently computability? For example, take R to be something like a Solomonoff induction. R-efficiently computable there means Turing computable. For our M which supervenes on R, instead of Minds, letâs let M be the probability p of a given state. The mapping function g: R->M, mapping states to the probability of states, cannot be R-efficiently computed (no matter what sort of Turing machine or speed prior you use for R) for diagonalization reasons. So the probabilities of states arenât a ârealâ thing? It seems like a lot of natural emergent things wouldnât be R-efficiently computable.
On homomorphic encryption being un-reversible: quantum computers are reversible, right? So if you say physics is as powerful as a quantum computer, and you want homomorphic encryption to be uncomputable in polynomial time, you have to make Pâs physics âstateâ throw quantum information away over time (which it could, in e.g. Copenhagen or objective collapse interpretations, but does not in e.g. many worlds) or maybe restrict the size of the physical universe youâre giving as state to not include information we radiated away many years ago (less than 62.9 billion light years).
Hmm⌠I think with Solomonoff induction I would say R is the UTM input, plus the entire execution trace/âtrajectory. Then M would be like the agentâs observations, which are a simple function of R.
I see that we canât have all ârealâ 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 âeffectiveâ, being âproduced somewhereâ⌠so I infer they are probably âcomputed in realityâ in some sense (although thatâs not entirely clear). They have access to their beliefs/âobservations 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, itâs 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. (Shouldnât matter too much anyway if natural supervenience is local, then mental states couldnât be affected by far away physical states anyway)
Hereâs a pure quantum, information theoretic, no computability assumptions version that might or might not be illustrative. I donât actually know if the quantum computer Iâm talking about could be builtâIâm going off intuition. EDIT I think this is 2 party quantum computation and none of the methods Iâve 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, youâll 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 awayâhow can we know if someone looked at Bob? What if we separate Alice and Bob past each otherâs 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 heâs 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 Iâll note that for me, this version, like the homomorphic version, is mostly saying that your description of a quantum physics state shouldnât 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. Iâm not sure how the âprovably random noise from bothâ 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 donât know how to generalize that to computation in general.
I think some of the non locality is inherited from âno hidden variable theoryâ. Like it might be local in MWI? Iâm not sure.
Forgive me, Iâm probably being stupid again đŹ.
On efficient computability being necessary for reality: Iâm not sure I understand the logic behind this. Would you not always get diagonalization problems if you want supervening ârealâ things to be blessed with R-efficiently computability? For example, take R to be something like a Solomonoff induction. R-efficiently computable there means Turing computable. For our M which supervenes on R, instead of Minds, letâs let M be the probability p of a given state. The mapping function g: R->M, mapping states to the probability of states, cannot be R-efficiently computed (no matter what sort of Turing machine or speed prior you use for R) for diagonalization reasons. So the probabilities of states arenât a ârealâ thing? It seems like a lot of natural emergent things wouldnât be R-efficiently computable.
On homomorphic encryption being un-reversible: quantum computers are reversible, right? So if you say physics is as powerful as a quantum computer, and you want homomorphic encryption to be uncomputable in polynomial time, you have to make Pâs physics âstateâ throw quantum information away over time (which it could, in e.g. Copenhagen or objective collapse interpretations, but does not in e.g. many worlds) or maybe restrict the size of the physical universe youâre giving as state to not include information we radiated away many years ago (less than 62.9 billion light years).
(Donât feel obligated to reply)
Hmm⌠I think with Solomonoff induction I would say R is the UTM input, plus the entire execution trace/âtrajectory. Then M would be like the agentâs observations, which are a simple function of R.
I see that we canât have all ârealâ 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 âeffectiveâ, being âproduced somewhereâ⌠so I infer they are probably âcomputed in realityâ in some sense (although thatâs not entirely clear). They have access to their beliefs/âobservations 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, itâs 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. (Shouldnât matter too much anyway if natural supervenience is local, then mental states couldnât be affected by far away physical states anyway)
Hereâs a pure quantum, information theoretic, no computability assumptions version that might or might not be illustrative. I donât actually know if the quantum computer Iâm talking about could be builtâIâm going off intuition. EDIT I think this is 2 party quantum computation and none of the methods Iâve 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, youâll 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 awayâhow can we know if someone looked at Bob? What if we separate Alice and Bob past each otherâs 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 heâs 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 Iâll note that for me, this version, like the homomorphic version, is mostly saying that your description of a quantum physics state shouldnât 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. Iâm not sure how the âprovably random noise from bothâ 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 donât know how to generalize that to computation in general.
I think some of the non locality is inherited from âno hidden variable theoryâ. Like it might be local in MWI? Iâm not sure.