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No, there is no reason to think that the human brain is capable of computing anything that isn't Church-Turing computable. Luckily no translation actually requi
by frostburg 8y ago
No, there is no reason to think that the human brain is capable of computing anything that isn't Church-Turing computable. Luckily no translation actually requires a "general solution" of the problem formally.
- yters 8y agoHow do you know this is true?
- frostburg 8y agoTexts have finite length.
- yters 8y agoCan you expand the missing premise? 1. Texts have finite length. 2. ____ 3. Therefore, the halting problem does not impact machine translation.
- frostburg 8y agoSorry, missed this. I'll try to explain. A real computer doesn't actually have an infinite tape (memory) like a canonical Turing Machine, it's actually a finite state machine with a vast amount of possible states that we conveniently think about as analogous to a Turing machine, hence the the halting problem is actually solvable (just not in practice) for real hardware. Given content that can be expressed in two languages in a text of finite length, you could in theory enumerate all the possible translated texts.
- yters 8y agoIf it is not solvable in practice, I don't see how finiteness addresses my objection...