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Turing personally addressed the question of analog computation and determined that they add nothing over discrete machines, as discrete computers can compute anything an analog computer would do to the desired precision that matters to you. He even discussed the subject in his 1936 paper, when he introduced his model. He wrote that eventually one would need to distinguish between two states, and so a model where states can be arbitrarily indistinguishable adds nothing, so you may as well discretize. When he wrote about the operation of the brain he said that it shouldn't matter if the brain is continuous or discrete; its operation could be simulated to arbitrary precision by a discrete process. He did wonder about quantum effects, though (he understood quantum entanglement when he was 16, Hodges writes).

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