What if we fully homomorphically encrypt John Smith’s brain simulation before we start torturing it? We can even throw away our copy of the private keys so that no one, ever, outside the simulation will be able to see the results of the torture even though we can calculate it perfectly for as long as we want.
Does encrypted John Smith have qualia? If so, then isn’t the waterfall argument true? We could choose initial keys with enough entropy such that every possible state of the simulation has a corresponding key that would decrypt it. Our physics simulation just reads the encrypted state of every particle/wave in the simulation, applies the results of physics, writes the encrypted results back and repeats. Our choice of decryption key effectively picks a random universe whose evolution is fully determined by the single series of homomorphically encrypted computations, and it’s no longer the computation that’s creating specific qualia, but our choice of key revealing it. Another interpretation is that a single series of computations is producing all possible qualia. This seems to be a very strong case for the waterfall argument being true; the physical evolution of the universe is producing states that can be interpreted in many different ways, and the interpretation is what matters to us.
In complexity terms, fully homomorphic encryption is expensive but it is polynomial in the size of the key, and simulations are polynomial in the number of elements being simulated. If N is the number of elements and M is the number of bits necessary to represent the state of one element then the key would be NM bits. Current fully homomorphic ciphers encrypt/decrypt one bit at a time, meaning that each bit of the encrypted state would require NM bits of storage, and computations are implemented as boolean circuits using homomorphic operations on encrypted bits. Calculating one step of the simulation would require O( ( N + C(N) ) H(N M) ) time and O( ( N + C(N) ) (N M) ) space where C(x) is the boolean circuit size of a physics simulation for N elements and H(x) is the cost of homomorphic encryption operations on x bits. C(x) is polynomial if the simulation is polynomial in x. H(x) is polynomial. The result is polynomial and smaller than the Θ(M^N) universes that could be decrypted. That implies either that John Smith and his exponentially many parallel selves have qualia and we can create exponential qualia with only polynomial work, or encrypted encrypted John Smith does not have qualia. If only some of the John Smith’s have qualia that would imply the existence of philosophical zombies. If we can create exponential qualia from polynomial work then I think the waterfall argument is basically true.
Nick Bostrom’s paper on Duplication vs Unification claims that we should accept Duplication because otherwise we lose the ability to compare the morality of different actions. If the waterfall argument is true then we probably have to accept Unification. There may still be room for some kind of moral optimization under Unification by finding the simplest perspective/mapping such that we can observe the most good given our computational constraints, but if not then we are left with being morally neutral in cases A-F.
What if we fully homomorphically encrypt John Smith’s brain simulation before we start torturing it? We can even throw away our copy of the private keys so that no one, ever, outside the simulation will be able to see the results of the torture even though we can calculate it perfectly for as long as we want.
Does encrypted John Smith have qualia? If so, then isn’t the waterfall argument true? We could choose initial keys with enough entropy such that every possible state of the simulation has a corresponding key that would decrypt it. Our physics simulation just reads the encrypted state of every particle/wave in the simulation, applies the results of physics, writes the encrypted results back and repeats. Our choice of decryption key effectively picks a random universe whose evolution is fully determined by the single series of homomorphically encrypted computations, and it’s no longer the computation that’s creating specific qualia, but our choice of key revealing it. Another interpretation is that a single series of computations is producing all possible qualia. This seems to be a very strong case for the waterfall argument being true; the physical evolution of the universe is producing states that can be interpreted in many different ways, and the interpretation is what matters to us.
In complexity terms, fully homomorphic encryption is expensive but it is polynomial in the size of the key, and simulations are polynomial in the number of elements being simulated. If N is the number of elements and M is the number of bits necessary to represent the state of one element then the key would be NM bits. Current fully homomorphic ciphers encrypt/decrypt one bit at a time, meaning that each bit of the encrypted state would require NM bits of storage, and computations are implemented as boolean circuits using homomorphic operations on encrypted bits. Calculating one step of the simulation would require O( ( N + C(N) ) H(N M) ) time and O( ( N + C(N) ) (N M) ) space where C(x) is the boolean circuit size of a physics simulation for N elements and H(x) is the cost of homomorphic encryption operations on x bits. C(x) is polynomial if the simulation is polynomial in x. H(x) is polynomial. The result is polynomial and smaller than the Θ(M^N) universes that could be decrypted. That implies either that John Smith and his exponentially many parallel selves have qualia and we can create exponential qualia with only polynomial work, or encrypted encrypted John Smith does not have qualia. If only some of the John Smith’s have qualia that would imply the existence of philosophical zombies. If we can create exponential qualia from polynomial work then I think the waterfall argument is basically true.
Nick Bostrom’s paper on Duplication vs Unification claims that we should accept Duplication because otherwise we lose the ability to compare the morality of different actions. If the waterfall argument is true then we probably have to accept Unification. There may still be room for some kind of moral optimization under Unification by finding the simplest perspective/mapping such that we can observe the most good given our computational constraints, but if not then we are left with being morally neutral in cases A-F.