On 12/27/2012 3:40 AM, Bruno Marchal wrote:

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.


Right, it makes 'computable' an approximate notion. But then that breaks the chain of inference that fundamental physics is inconsistent with CTM.


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