On 07 Oct 2015, at 03:58, John Clark wrote:
On Tue, Oct 6, 2015 at 3:17 PM, Bruno Marchal <[email protected]>
wrote:
> Sigma_1 complete provability is Turing universal,
But the proof or that can't compute one damn thing! No proof
can.
That is false. Sigma_1 provability can compute what any other
universal system can compute, and even in the same way/algorithm.
> the problem is that in "computation done physically", what do
you mean by computation?
As I've said over and over and over again. I mean the process
of finding a specific answer to a specific problem.
That is "solving a problem", not computing a function. But that stoo
can exist in arithmetic, and is a-handled more with the RE sets (the
w_i), than with the phi_i. In that case, you still rely oin the purely
mathematical theory. No physical assumption is needed, still less
metaphysical materialist assumption.
> If you mean it in the usual standard sense, then
I mean the sort of computation that people are interested in,
the sort they will pay money for, the sort of computations that
INTEL does.
OK? but that is not the standard one.
> no Turing machine can aver distinguish an arithmetical
computation from a physical one,
That's not all it can't do! Unless the machine is made of matter
that obeys the laws of physics no Turing machine can distinguish
ANYTHING, and the blueprints of a 747 can flt you across the
Atlantic either.
False. true only if you add physical as a quality for the result.
> without external clues.
In other word physical external clues can provide something pure
mathematics can not.
If computationalism is correct, the physical is an epitsemological
reality, not an ontological one.
> I was talking on the computations in arithmetic.None of them
are physical
There are no computations IN arithmetic, computations are always
done TO arithmetic by physics.
Physical computations might do that. But arithmetical computations,
which can emulate *all* computations (with Church-Turing thesis- does
not assume anything physical.
> Arithmetic can simulate a silicon processor simulating a
Turing machine,
You've got it exactly backwards. The simple must simulate the
complex not the reverse, otherwise there would be no point in doing
simulations. A silicon processor is vastly more complex than a
Turing machine.
All universal beings can simulate all universal beings when doing
computations.
It go in both direction.
>> And yet for some strange reason INTEL still uses
silicon and not diophantine degree four polynomial. How odd.
> No, that is not odd. INTEL sold machine for physical
computations.
And INTEL makes machines like that because billions of people will
happily pay trillions of dollars for physical computations, but they
won't spend a nickle for a non-physical computation. Maybe those
billions of people know something you don't.
By definition, if those computations did not exist in arithmetic, they
would not exist in the physical reality either. INTEL needs both
mathematicians and physical engineers. The notion of computation has
just nothing to do with physics. read the book by Davis with the
original papers for god sake.
Bruno
> You are the guy who has been shown believing that 0 = 1,
remember?
No, I do not remember and that is surprising. Zero being equal to
one would be big news and I would have thought I would have
remembered that.
John K Clark
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