Computation and the Brain

Abstract
Two very different insights motivate characterizing the brain as a computer. One depends on mathematical theory that defines computability in a highly abstract sense. Here the foundational idea is that of a Turing machine. Not an actual machine, the Turing machine is really a conceptual way of making the point that any well-defined function could be executed, step by step, according to simple 'if-you-are-in-state-P-and-have-input-Q-then-do-R' rules, given enough time (maybe infinite time) [see COMPUTATION]. Insofar as the brain is a device whose input and output can be characterized in terms of some mathematical function -- however complicated -- then in that very abstract sense, it can be mimicked by a Turning machine. Given what is known so far brains do seem to depend on cause-effect operations, and hence brains appear to be, in some formal sense, equivalent to a Turing machine [see CHURCH-TURING THESIS]. On its own, however, this reveals nothing at all of how the mind-brain actually works. The second insight depends on looking at the brain as a biological device that processes information from the environment to build complex representations that enable the brain to make predictions and select advantageous behaviors. Where necessary to avoid ambiguity, we will refer to the first notion of computation as algorithmic computation, and the second as information processing computation.
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