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Wouldn't an incomputable physical process have serious implications beyond CS? How would a physicist even model such a thing? edit: I guess not, since all you
by sobellian 9y ago
Wouldn't an incomputable physical process have serious implications beyond CS? How would a physicist even model such a thing?
edit: I guess not, since all you need is access to the real numbers which is a strict superset of computable numbers, but this doesn't seem like an "interesting" violation of the SCT.
- chubot 9y agoWhat makes you think physics can model everything? That's the point. Math is FULL of functions that can be described -- have properties X and Y, which are useful to prove theorems -- which nobody has thought about how to compute. (Obviously, there are the ones related to incomputibility like the Godel function, but there are others too... I'd appreciate help from others here :) ) And it might not even be useful or interesting (for the purposes of mathematics) to compute them. Not all math is constructive. Likewise you can describe physical processes without computing them.
- daxfohl 9y agoIf SCT is false then for example it may be possible for a quantum computer to use an uncountable set of inputs to compute in finite time whether an arbitrary turing machine will end. That said, you're right, if all that is required is real numbers, then hypothetically an analog computer is all that would be required. But in a truly quantum world where SCT holds, an "analog" computer is only a computable approximation. (Full disclosure: I guess....)