On 27 Dec 2012, at 20:13, meekerdb wrote:
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
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.
It makes "concretely computable" an approximate notion.
Computable, on the contrary, is made 100% mathematical, once we
assume Church's or Turing's thesis.
Your laptop, and your brain can be said to approximate the immaterial
machine(s) you are, in the comp picture. Like a quantum field
approximates your brain, and arithmetic approximates the quantum
We still have to understand why the quantum fields seems to get the
But then that breaks the chain of inference that fundamental physics
is inconsistent with CTM.
Fundamental physics has not been shown inconsistent with CTM.
Metaphysical physicalism has been shown inconsistent with CTM, and
this by using the mathematical non approximate use of computable.
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