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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