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I came to my conclusion independently by observing that computing the time evolution of most physical systems to arbitrary precision is impossible in finite tim

by atroyn 9y ago

I came to my conclusion independently by observing that computing the time evolution of most physical systems to arbitrary precision is impossible in finite time. More formally, the state space grows much much faster than polynomial time. Finding out if we can do better with quantum computing is an active area of research. I haven't read Searle/Penrose

simonh 9y ago
If humans can't do that either, and we cant't, why would you conclude that it's necessary to be able to do that in order to match human intelligence? Or are you specifically talking about perfectly simulating human brains? Human brain emulations are only one very specific and narrow form a strong AI might take. But even in that specific subset of possible AIs, we have no real idea how precise the simulation might have to be. It might be perfectly acievable without even simulating individual molecules.
- atroyn 9y ago
  I don't agree with your assertion that humans can't do that. Whether or not human cognition is a superset of computation is an unanswered question. That aside, even if human cognition is a computable function, there are no guarantees that the physical process giving rise to human cognition is computable, nor that any process giving rise to cognition is computable.
  - naasking 9y ago
    > Whether or not human cognition is a superset of computation is an unanswered question Unless something in physics changes drastically, human cognition is a finite state automaton. See my other reply on the Bekenstein Bound.
naasking 9y ago
> More formally, the state space grows much much faster than polynomial time The growth has an upper bound which means it's ultimately computable: https://en.m.wikipedia.org/wiki/Bekenstein_bound https://en.m.wikipedia.org/wiki/Bekenstein_bound
- atroyn 9y ago
  This says nothing about the time evolution of the state space of a system, only that the entropy as it relates to _the current state of the system_ is bounded - indeed the bound is on the entropy of a finite volume of fixed energy. Even if we expand the volume to encompass the entire universe, the bound informs only the _maximal_ entropy at any given time. As this relates to the human brain, and even omitting any quantum weirdness (of which there is probably a lot), all we can say is the total state of the brain at time t requires at most N bits, where N is the bound over volume of the brain. It says nothing about the (information theoretic) entropy of the _dynamics_ of the brain, which is where the process of cognition actually occurs. In fact many (if not most) physical processes have infinite entropy. For an example of a deterministic system that exhibits such behavior, Consider the logistic map at r~5.7. There exist some coarse partitions [0] of the state space such that the trajectory that can be expressed in a finite number of bits, but this is not in general the case, even though any _given_ state of the system can be expressed in a finite number of bits. Other examples include the double pendulum, three-body orbits, and in fact most real physical systems. In fact it is not in general true that a system with N bits of state can be always simulated with <= N bits. We can obey the Bekenstein bound without necessarily being able to simulate the process, even a complete description of the state at time t. For the time evolution of the state space of a system, the Lyapunov Time [1] and the Lyapunov Exponent [2] are much more informative. If the time required to reach another bit of precision grows faster than polynomial time, no Turing machine can hope to simulate that physical system in a practical amount of time. In fact we also have physical bounds on how much memory we have to work with, and how fast we can flip bits for a given volume of space - simply enumerating all possible state transitions of the brain using a Turing machine will require a volume of space much larger than the brain itself if the time evolution of the system produces large Lyapynov exponents (which it absolutely does). This should come as no surprise - known NP-hard problems have the same behavior. I would also add, even if the brain turns out to have a representation in N bits, and the state transition is (somehow) computable in polynomial time, it may still be physically infeasible to do so without just building and 'running' an actual brain. [0]http://tcode.tcs.auckland.ac.nz/~corpus/logistic.html http://tcode.tcs.auckland.ac.nz/~corpus/logistic.html [1]https://en.wikipedia.org/wiki/Lyapunov_exponent https://en.wikipedia.org/wiki/Lyapunov_exponent [2]https://en.wikipedia.org/wiki/Lyapunov_time https://en.wikipedia.org/wiki/Lyapunov_time PS: To me all of the above suggests that whatever the universe is doing when it's doing physics, it certainly isn't computing in the Church-Turing sense.

by atroyn 9y ago

simonh 9y ago

If humans can't do that either, and we cant't, why would you conclude that it's necessary to be able to do that in order to match human intelligence? Or are you specifically talking about perfectly simulating human brains? Human brain emulations are only one very specific and narrow form a strong AI might take. But even in that specific subset of possible AIs, we have no real idea how precise the simulation might have to be. It might be perfectly acievable without even simulating individual molecules.

atroyn 9y ago
I don't agree with your assertion that humans can't do that. Whether or not human cognition is a superset of computation is an unanswered question. That aside, even if human cognition is a computable function, there are no guarantees that the physical process giving rise to human cognition is computable, nor that any process giving rise to cognition is computable.
- naasking 9y ago
  > Whether or not human cognition is a superset of computation is an unanswered question Unless something in physics changes drastically, human cognition is a finite state automaton. See my other reply on the Bekenstein Bound.

naasking 9y ago

> More formally, the state space grows much much faster than polynomial time The growth has an upper bound which means it's ultimately computable: https://en.m.wikipedia.org/wiki/Bekenstein_bound https://en.m.wikipedia.org/wiki/Bekenstein_bound

atroyn 9y ago
This says nothing about the time evolution of the state space of a system, only that the entropy as it relates to _the current state of the system_ is bounded - indeed the bound is on the entropy of a finite volume of fixed energy. Even if we expand the volume to encompass the entire universe, the bound informs only the _maximal_ entropy at any given time. As this relates to the human brain, and even omitting any quantum weirdness (of which there is probably a lot), all we can say is the total state of the brain at time t requires at most N bits, where N is the bound over volume of the brain. It says nothing about the (information theoretic) entropy of the _dynamics_ of the brain, which is where the process of cognition actually occurs. In fact many (if not most) physical processes have infinite entropy. For an example of a deterministic system that exhibits such behavior, Consider the logistic map at r~5.7. There exist some coarse partitions [0] of the state space such that the trajectory that can be expressed in a finite number of bits, but this is not in general the case, even though any _given_ state of the system can be expressed in a finite number of bits. Other examples include the double pendulum, three-body orbits, and in fact most real physical systems. In fact it is not in general true that a system with N bits of state can be always simulated with <= N bits. We can obey the Bekenstein bound without necessarily being able to simulate the process, even a complete description of the state at time t. For the time evolution of the state space of a system, the Lyapunov Time [1] and the Lyapunov Exponent [2] are much more informative. If the time required to reach another bit of precision grows faster than polynomial time, no Turing machine can hope to simulate that physical system in a practical amount of time. In fact we also have physical bounds on how much memory we have to work with, and how fast we can flip bits for a given volume of space - simply enumerating all possible state transitions of the brain using a Turing machine will require a volume of space much larger than the brain itself if the time evolution of the system produces large Lyapynov exponents (which it absolutely does). This should come as no surprise - known NP-hard problems have the same behavior. I would also add, even if the brain turns out to have a representation in N bits, and the state transition is (somehow) computable in polynomial time, it may still be physically infeasible to do so without just building and 'running' an actual brain. [0]http://tcode.tcs.auckland.ac.nz/~corpus/logistic.html http://tcode.tcs.auckland.ac.nz/~corpus/logistic.html [1]https://en.wikipedia.org/wiki/Lyapunov_exponent https://en.wikipedia.org/wiki/Lyapunov_exponent [2]https://en.wikipedia.org/wiki/Lyapunov_time https://en.wikipedia.org/wiki/Lyapunov_time PS: To me all of the above suggests that whatever the universe is doing when it's doing physics, it certainly isn't computing in the Church-Turing sense.