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Lots of possibilities allowed by general relativity (e.g. computers orbiting black holes and information traveling backwards through time) that may or may not c
by cwzwarich 14y ago
Lots of possibilities allowed by general relativity (e.g. computers orbiting black holes and information traveling backwards through time) that may or may not correspond to our universe allow for computation beyond that of a Turing machine. Until we understand quantum gravity it seems premature to write off those possibilities.
Even simpler, there is the question of whether the universe allows for arbitrary precision measurement of a physical quantity. If it does, then it may turn out that an observable physical quantity (e.g. the mass or charge of a fundamental particle) is a noncomputable real number. If it doesn't, then it may be possible to represent a neural network with noncomputable real weights, but impossible to actually measure them to enough accuracy to simulate the network on a given input.
- bermanoid 14y agoLots of possibilities allowed by general relativity (e.g. computers orbiting black holes and information traveling backwards through time) that may or may not correspond to our universe allow for computation beyond that of a Turing machine. Until we understand quantum gravity it seems premature to write off those possibilities. But that's completely irrelevant when it comes to the functioning of the brain, which operates in the oh so mundane medium size, medium velocity, medium energy scale which modern physics is able to model extremely accurately. I know that a few folks (Penrose, most notably) think that quantum gravity may be relevant to the brain, but that's an extreme fringe opinion, and in Penrose's case it's practically earned him full fledged crackpot status despite his numerous indisputable successes in physics.
- cwzwarich 14y agoWhile it seems unlikely that relativistic effects would play a role in the brain, the original argument also said that the same logic should apply to anything in the universe, e.g. a solar system or a galaxy, which is why I mentioned it.