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The Tree of Knowledge

The Limits of Computation

Apostolos Syropoulos goes back to BASICs to consider whether the human brain is a computer.

There is a school of thought that assumes that all intellectual problems can potentially be solved by computers [for example, see ‘The Future of Philosophy is Cyborg’, by Phil Torres in Issue 141]. However, is this really the case? Here I will try to explain why we do not know where the limits of computability are, and how this lack of knowledge affects our understanding in a number of areas.

Roughly, we can say that a computable (or solvable) problem is any problem that can be solved by a finite set of simple actions. Alternatively, we could say that a computable problem is anything that can be reduced to a mathematical equation and solved accordingly. For example, if someone has to travel to a number of towns and has to schedule her trip so that she has to go through each town only once, this is a mathematical problem.

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