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.
Bruno
Right, it makes 'computable' an approximate notion. But then that breaks the chain of
inference that fundamental physics is inconsistent with CTM.
Brent
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
