By Sebastian Brock
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Extra resources for A syriac life of Saint Maximus the Confessor
Since biological brains are excessively noisy, stochastic environments, and since they have to have arisen by evolution, it seems very far-fetched that such models have anything to do with intelligence or mind. The upshot of all these investigations, then, is that it seems apparent that the brain as well as any reasonable physical device can be simulated by a Turing machine. Turing was of course unaware of these later investigations into mathematical physics, but neither did he suggest that his analysis of the proof process of the mathematician was mathematically rigorous.
The ordinary computer will need to do only as many logical operations as the brain did, in total, just as we can simulate the actions of a parallel computer with a serial computer. Moreover, because we can in principle map from one su‰ciently powerful model of computer to another with no loss of power, we can switch back and forth from model to model. If we want to talk about using artificial neural nets (a model of computing discussed in chapter 4), we can talk about programs on an ordinary computer.
The way this works is simple. A’s tape is simply initiated with a description of B’s lookup table and B’s program. As the machine A reads the tape and follows the instructions in its lookup table, it goes through a sequence of operations. For every configuration that machine B goes through, machine A has an exactly corresponding configuration that it goes through. When eventually B halts (assuming it does), A halts in its corresponding configuration with an exactly corresponding message written on its tape.