I actually think that A is the most intuitive option. I don’t see why it should be possible for something which knows the physical state of my brain to be able to efficiently compute the contents of it.
Then again, given functionalism, perhaps it’s the case that extracting information about the contents of the brain from the encrypted computation is not as hard as one might think. The encryption is just a reversible map from one state space to another. If an omniscient observer can extract the contents of a brain by assembling a causal model of it in un-encrypted phase space, why would it struggle to build the same casual model in encrypted phase space? If some high-level abstractions of the computation are what matter, then the difficult part is mostly in finding the right abstractions.
I don’t see why it should be possible for something which knows the physical state of my brain to be able to efficiently compute the contents of it.
I think you meant “philosophically necessary” where you wrote “possible”? If so, agreed, that’s also my take.
If an omniscient observer can extract the contents of a brain by assembling a causal model of it in un-encrypted phase space, why would it struggle to build the same casual model in encrypted phase space?
I don’t understand this part. “Causal model” is easy—if the computer is a Turing machine, then you have a causal model in terms of the head and the tape etc. You want “understanding” not “causal model”, right?
If a superintelligence were to embark on the project of “understanding” a brain, it would be awfully helpful to see the stream of sensory inputs and the motor outputs. Without encryption, you can do that: the environment is observable. Under homomorphic encryption without the key, the environmental simulation, and the brain’s interactions with it, look like random bits just like everything else. Likewise, it would be awfully helpful to be able to notice that the brain is in a similar state at times t₁ versus t₂, and/or the ways that they’re different. But under homomorphic encryption without the key, you can’t do that, I think. See what I mean?
To be clear in path A I’m imagining that the omniscent observer knows not just physics, but all of reality. By step 10 we already have that physical omniscience + physical (BQP) computation isn’t enough to derive mental states. (So it’s a question of whether the mental states / abstractions are “real”, encoded somewhere in reality even if not properly in physics)
I think the extra difficulty with encrypted phase space is the homomorphic encryption presumably makes it computationally intractable? If it really is intractable then “search over the right abstractions” is going to be computationally hard.
It’s possible to alter a homomorphic computation in arbitrary ways without knowing the decryption key.
An omniscient observer can homomorphically encrypt a copy of themselves under the same key as the encrypted mind and run a computation of its own copy examining every aspect of the internal mental states of the subject, since they share the same key.
If there are N homomorphically encrypted minds in reality then the omniscient observer will have to create N layers of homomorphic computation in order for the innermost computation to yield the observation of all N minds’ internal states, each passed in turn to a sub-computation, and relying on the premise that homomorphically encrypted minds are conscious for the inner observer to be conscious.
The question is whether encoding all of reality and homomorphically encrypting it necessarily causes a loss of fidelity. If yes, one of the trilemmas still holds. Otherwise there’s no trilemma and the innermost omniscient observer sees all of reality and all internal mental states. I’d argue that for a meaningful omniscient observer to exist it is the case that encoding of reality (into the mind of the observer) must not result in a loss of fidelity. There could be some edge-cases where a polynomial amount of fidelity is lost due to the homomorphic encryption that wouldn’t be lost to the “natural” omniscient observer’s encoding of reality, but I think it stretches the practical definition of omniscience for an observer.
I think the argument extends to physics but the polynomial loss of fidelity is more likely to cause problems in a very homomorphically-encrypted-mind-populated universe.
Hmm… I’m not sure if I’m imagining what you are, but wouldn’t the omniscient observer need to know the key already to encrypt themselves? (If reality somehow contains the key, then I suppose omniscience about reality is enough, but omniscience about physics isn’t.)
It is true that being more encrypted is more compatible with being omnsiscent. It’s strange because base physics is often thought of as the more omniscent layer. Like, I still think you get “mind exceeds physics” (hence the trilemma) since the omniscient observer you’re positing isn’t just working in base level physics, they have somehow encrypted themselves with the same key (which is not tractably available). But it seems if they knew the key they wouldn’t even need to encrypt themselves to know anything additional.
To perform homomorphic operations you need the public key, and that also allows one to encrypt any new value and perform further hidden computations under that key. The private key allows decryption of the values.
I suppose you could argue that the homomorphically encrypted mind exists ala mathematical realism even if the public key is destroyed, but it would be something “outside reality” computing future states of the encrypted mind after the public key is no longer available.
Oh, maybe what you are imagining is that it is possible to perceive a homomorphic mind in progress, by encrypting yourself, and feeding intermediate states of that other mind to your own homomorphically encrypted mind. Interesting hypothetical.
I think with respect to “reality” I don’t want to be making a dogmatic assumption “physics = reality” so I’m open to the possibility (C) that the computation occurs “in reality” even if not “in physics”.
After doing some more research I am not sure that it’s always possible to derive a public key knowing only the evaluation key; it seems to depend on the actual FHE scheme.
So the trilemma may be unaffected by this hypothetical. There’s also the question of duplication vs. unification for an observer that has the option to stay at base level reality or enter a homomorphically encrypted computation and whether those should be considered equivalent (enough).
I actually think that A is the most intuitive option. I don’t see why it should be possible for something which knows the physical state of my brain to be able to efficiently compute the contents of it.
Then again, given functionalism, perhaps it’s the case that extracting information about the contents of the brain from the encrypted computation is not as hard as one might think. The encryption is just a reversible map from one state space to another. If an omniscient observer can extract the contents of a brain by assembling a causal model of it in un-encrypted phase space, why would it struggle to build the same casual model in encrypted phase space? If some high-level abstractions of the computation are what matter, then the difficult part is mostly in finding the right abstractions.
I think you meant “philosophically necessary” where you wrote “possible”? If so, agreed, that’s also my take.
I don’t understand this part. “Causal model” is easy—if the computer is a Turing machine, then you have a causal model in terms of the head and the tape etc. You want “understanding” not “causal model”, right?
If a superintelligence were to embark on the project of “understanding” a brain, it would be awfully helpful to see the stream of sensory inputs and the motor outputs. Without encryption, you can do that: the environment is observable. Under homomorphic encryption without the key, the environmental simulation, and the brain’s interactions with it, look like random bits just like everything else. Likewise, it would be awfully helpful to be able to notice that the brain is in a similar state at times t₁ versus t₂, and/or the ways that they’re different. But under homomorphic encryption without the key, you can’t do that, I think. See what I mean?
To be clear in path A I’m imagining that the omniscent observer knows not just physics, but all of reality. By step 10 we already have that physical omniscience + physical (BQP) computation isn’t enough to derive mental states. (So it’s a question of whether the mental states / abstractions are “real”, encoded somewhere in reality even if not properly in physics)
I think the extra difficulty with encrypted phase space is the homomorphic encryption presumably makes it computationally intractable? If it really is intractable then “search over the right abstractions” is going to be computationally hard.
It’s possible to alter a homomorphic computation in arbitrary ways without knowing the decryption key.
An omniscient observer can homomorphically encrypt a copy of themselves under the same key as the encrypted mind and run a computation of its own copy examining every aspect of the internal mental states of the subject, since they share the same key.
If there are N homomorphically encrypted minds in reality then the omniscient observer will have to create N layers of homomorphic computation in order for the innermost computation to yield the observation of all N minds’ internal states, each passed in turn to a sub-computation, and relying on the premise that homomorphically encrypted minds are conscious for the inner observer to be conscious.
The question is whether encoding all of reality and homomorphically encrypting it necessarily causes a loss of fidelity. If yes, one of the trilemmas still holds. Otherwise there’s no trilemma and the innermost omniscient observer sees all of reality and all internal mental states. I’d argue that for a meaningful omniscient observer to exist it is the case that encoding of reality (into the mind of the observer) must not result in a loss of fidelity. There could be some edge-cases where a polynomial amount of fidelity is lost due to the homomorphic encryption that wouldn’t be lost to the “natural” omniscient observer’s encoding of reality, but I think it stretches the practical definition of omniscience for an observer.
I think the argument extends to physics but the polynomial loss of fidelity is more likely to cause problems in a very homomorphically-encrypted-mind-populated universe.
Hmm… I’m not sure if I’m imagining what you are, but wouldn’t the omniscient observer need to know the key already to encrypt themselves? (If reality somehow contains the key, then I suppose omniscience about reality is enough, but omniscience about physics isn’t.)
It is true that being more encrypted is more compatible with being omnsiscent. It’s strange because base physics is often thought of as the more omniscent layer. Like, I still think you get “mind exceeds physics” (hence the trilemma) since the omniscient observer you’re positing isn’t just working in base level physics, they have somehow encrypted themselves with the same key (which is not tractably available). But it seems if they knew the key they wouldn’t even need to encrypt themselves to know anything additional.
To perform homomorphic operations you need the public key, and that also allows one to encrypt any new value and perform further hidden computations under that key. The private key allows decryption of the values.
I suppose you could argue that the homomorphically encrypted mind exists ala mathematical realism even if the public key is destroyed, but it would be something “outside reality” computing future states of the encrypted mind after the public key is no longer available.
Oh, maybe what you are imagining is that it is possible to perceive a homomorphic mind in progress, by encrypting yourself, and feeding intermediate states of that other mind to your own homomorphically encrypted mind. Interesting hypothetical.
I think with respect to “reality” I don’t want to be making a dogmatic assumption “physics = reality” so I’m open to the possibility (C) that the computation occurs “in reality” even if not “in physics”.
After doing some more research I am not sure that it’s always possible to derive a public key knowing only the evaluation key; it seems to depend on the actual FHE scheme.
So the trilemma may be unaffected by this hypothetical. There’s also the question of duplication vs. unification for an observer that has the option to stay at base level reality or enter a homomorphically encrypted computation and whether those should be considered equivalent (enough).