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According to halting problem, there is no algorithm which can decide if another algorithm and its input will halt or not. Suppose human intelligence can be simulated in a computer. Also suppose than human can determine if an algorithm will halt for its input.

Then, the simulated brain, which is a program in a computer hence another algorithm, must be able to solve the halting problem which is impossible.

Then, either the human intelligence cannot be simulated in a computer or humans themselves cannot solve halting problem.

On the other hand simulation of brain as a collection of particles is doable at least in principle. Which leaves us with the only option which is human themselves cannot solve halting problem. Am I right?

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marked as duplicate by Evil, David Richerby, Tom van der Zanden, Raphael Sep 5 '16 at 8:08

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  • $\begingroup$ There was already such question (I do not have link right now), but it goes like this: if you have algorithm than human and computer alike will solve the problem. If there cannot exist algorithm to solve the problem (undecidable) for all inputs, than it does not matter what (or who) performs it. The main problem here is the definition of "undecidable" and the algorithm - it cannot work for all inputs, but there is no problem to work on some of them. $\endgroup$ – Evil Sep 4 '16 at 22:29
  • $\begingroup$ "Also suppose than human can determine if an algorithm will halt for its input." That's a rather bold assumption. I wrote an algorithm to find an even number ≥ 4 that is not the sum of two primes; so far all the great mathematicians of the world haven't managed to prove or disprove that it halts. $\endgroup$ – gnasher729 Sep 5 '16 at 21:27
  • $\begingroup$ @gnasher729. Then, it means that there are problems that we cannot solve them never ever! $\endgroup$ – MOON Sep 6 '16 at 10:07