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> But the definition of computation is physical. A lot of mathematics is inspired by physical considerations, but mathematical concepts are themselves not phys
by catnaroek 10y ago
> But the definition of computation is physical.
A lot of mathematics is inspired by physical considerations, but mathematical concepts are themselves not physical. In particular, computation is just having state transitions, not necessarily in a physical system. (Just like recursion is any form of self-reference in any definition, not necessarily procedure definitions.)
> The Church-Turing thesis is a physical hypothesis.
Then let's not mention it, and stick to what can be dealt with mathematically.
- pron 10y ago> A lot of mathematics is inspired by physical considerations, but mathematical concepts are themselves not physical. I'm not sure I understand your point. It is true that any computation can be modeled mathematically, but so can any other physical process. Also, computation does not require a specific physical implementation and is an abstract concept, but so what? Gödel, Turing and von Neumann were very well aware that computation is a physical/philosophical concept described mathematically, not a purely mathematical one. > Then let's not mention it, and stick to what can be dealt with mathematically. But the definition of what is computable and what isn't depends on the Church-Turing thesis.