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.​



> ​> ​
> 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.


> ​> ​
> 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.


> ​> ​
> 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.


> ​> ​
> without external clues.
>

​In other word physical external clues can provide something pure
mathematics can not.​



> ​> ​
>  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.



> ​> ​
> Arithmetic can simulate a silicon processor
> ​ s
> imulating 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. ​


​
>> ​>> ​
>> 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.


​> ​
> 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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