On 26 Dec 2012, at 20:58, meekerdb wrote:
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.
That's the fate of ALL universal number. They have NEVER enough
memories. The available 'tape' is always too much short. They always
feel like having something more to say. And they always make mistake,
unless they are ideally correct, a condition which is met only in the
universal number's mind.
Computable does not mean, concretely computable. That would makes
addition and multuplication NOT computable, as nobody can add the
10^10000 first digits of PI.
Bruno
Brent
Bruno
http://iridia.ulb.ac.be/~marchal/
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