On 12/26/2012 1:45 AM, Bruno Marchal wrote:


On 24 Dec 2012, at 19:30, meekerdb wrote:

On 12/24/2012 2:36 AM, Bruno Marchal wrote:
We don't have to bet the brain is (Turing universal), we can prove it.

Can we? How would you prove than every person's brain can compute every computable function?

By teaching them to reduce combinators, which is very simple, or by teaching them to play the Game Of Life, or to interpret a LISP Expression, or more simply by teaching them how to add and multiply natural numbers. If they succeed in one of those task, they can emulate any Universal Turing Machine, and are proved to be themselves Turing Universal. With comp that is enough to conclude that their brain is Turing universal.

But that doesn't show they can compute every computable function; some functions will take too much memory space and some computations are very long so there will inevitably be mistakes.

Brent


Bruno


http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>



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