Re: Turing vs math

From: Marchal <marchal.domain.name.hidden>
Date: Fri Oct 29 03:07:14 1999

Juergen Schmidhuber wrote:

> The UTM theory predicts that everything including QM superposition
> is quantizable. According to it there is nothing like Super-Turing
> computability in our universe. Justification: at the moment there is
> no data that forces us to believe in continua. Recurring question: why
> assume more than necessary?

The UD dovetails on all the initial segments of the reals.
The first person point of view is independent of the delays of
(virtual) reconstitution. So personal histories are linked
to c infinite computations.

This entails also that any machine looking at itself at a level
which is below its level of substitution will "observe" non
computable thing. (What I call now "the Galouye effect").

Note that this is empirically confirmed by QM.

So we have that 3-locality and 3-determinisme (3-computability)
entails 1-indeterminisme, 1-nonlocality (1-uncomputability).

In fact 3-discreteness of the observer entails 1-continuum spectrum.

(I have argue elsewhere why locally these 1-uncomputability are still
3-communicable---because the UD "duplicates" entire collection of
entangled computational histories. I called them 1plr-person
point of view (1plr = first-person PLuRal)).

When Juergen say that "...there is no data that forces us to believe
in continua", this is slightly misleading.
I would say there is no data who forces us to believe in some
material or substancial continuum, but there is no data who forces us
to believe in any form---even discrete---of substance !
Now, to extract the laws of physics from a theory of mind we cannot
dispensed with the necessary 1-appearance of some continuum.
So even if comp makes the discrete ontologically more primitive than
the continuum, the appearance of discrete objects could still be (and
probably are) derived from the "behavior" of a continuum.

I guess Juergen believes in some physical computationalism
a la Jacques M Mallah. At least Jacques M Mallah seems aware of
a very hard "implementation" problem for such type of
computationalism.

With the pure comp I am advocating, we must "just" find the right
measure on the computational histories, extract the physics, and compare
with the empirical evidence. In case of difference we must abandon
comp. In case of confirmation, we are free to accept arithmetic as a
TOE.

This shows also that the Turing vs Math debate is a false debate.
Current Number theory relies on the theory of complex functions, and,
in a somewhat similar way, computertheory relies on the whole
Cantor paradise.

To paraphrase Kronecker again, God has created only the natural numbers,
all the rest, universes and continua are (universal) numbers dreams.
And the laws of physics are reductible with the objective laws of
the mergeable UTM's dreams.

Bruno
Received on Fri Oct 29 1999 - 03:07:14 PDT