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Uncomputability

The kinds of behaviours seen in models of complex systems are the result of following a set of rules. This is because these models are embodied in computer programs, which must necessarily follow well-defined rules. By definition, any behaviour seen in such worlds is the outcome of following the rules encoded in the program. Although computing machines are de facto rule-following devices, there is no a priori reason to believe that any of the processes of nature and humans are necessarily rule-based. If uncomputable processes do exist in nature--for example, the breaking of waves on a beach or the movement of air masses in the atmosphere--then these processes will never fully manifest themselves in the surrogate worlds of their models. Processes that are close approximations to these uncomputable ones may be observed, just as an irrational number can be approximated as closely as desired by a rational number. However, the real phenomenon will never appear in a computer, if indeed such uncomputable quantities exist outside the pristine world of mathematics.

To illustrate what is at issue here, the problem of whether the cognitive powers of the human mind can be duplicated by a computing machine revolves about just this question. If human cognitive activity is nothing more than rule-following, encoded somehow into our neural circuitry, then there is no logical obstacle to constructing a silicon mind. On the other hand, it has been forcefully argued by some that cognition involves activities that transcend simple rule-following. If so, then the workings of the brain can never be captured in a computer program.

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