On 20 Sep 2015, at 03:17, John Clark wrote:
On Sat, Sep 19, 2015 , Bruno Marchal <marc...@ulb.ac.be> wrote:
>> Theorems don't make calculations, physical microprocessor
chips do.
> Physical computer are implementation, in the math sense, of
turing universality by physical devices.
What makes you so certain that Turing machines aren't just man
made descriptions (and approximate descriptions at that) of physical
computational devises?
because they compute exactly the same thing that what you can compute
assuming only classical logic and elementary arithmetic, or by
assuming the identity axioms and Kxy = x and Sxyz = xz(yz).
very different way to get the computable functions, with quite
different assumpitions leads to the same class of functions.
Then there is the fact that the set of partial computable function is
close for the diagonalization of Kleene, making arithmetic (and
combinators, Turing machines ...) which makes that notion as much
solid as the notion of natural numbers. So, as I don't think that the
natural numbers is a human invention, I don't think the notion of
Turing machine is a human invention. You can prove their existence
from the K and S axioms given above, or from addition and
multiplication + a bit of logic.
Usually the simpler thing simulates the more complex thing, but a
physical computer is far more complex than a Turing Machine, so is a
microprocessor implementing a Turing machine or is a Turing
Machine implementing a microprocessor?
Yes, arithmetic can simulates a Turing machine, a quantum computer,
etc. It can, and it does, actually.
But a primary physical reality, well I have already not much clue what
that can be, and if it behaves like the primary matter which should
appear to exist with computationalism, then a priori, such matter can
only approximate the real thing, not really simulate it.
> Does prime number needs paper to exist in the logico-
mathematical sense of existence?
It doesn't matter, prime number don't make calculations,
I was just saying that the prime number, or the order relations, or
the range of polynomila equation exist like the prime numbers, etc.
That prime number does not compute is not clear for me.Such a question
might depend from Riemann hypothesis. If the Hilbet- Montgommery
hypothesis is correct (that the zeta non trivlal zeroes describe a
quantum spectrum, it might be that the prime numbers already emulates
a quantum computer).
physical microprocessors do.
Locally, but if quantum field theory is correct, it is an analog
imitation of the digital. You need to make precise your theory of
primary matter to proof that it can emulates all computations, like
arithmetic or the combinators. That is not an obvious question.
And all numbers may exist, but if the computational resources of the
entire physical universe is finite then the set that contains all
the prime numbers and only prime numbers may not.
I don't believe in that type of God, to be sure. It does not work with
either computationalism, nor quantum mechanics.
> a person can do a computation too, and they are not
necessarily physical
In the history of the world a no person lacking a physical brain
has ever made a calculation, and it is very easy to understand why
if physics is more fundamental than mathematics. But if mathematics
is more fundamental then that fact is quite odd.
You can prove in PA the existence of all terlminating computation, and
the existence of many non terminating computations, and RA already
emulates them all.
> you might read the book "Inexhaustibility" by Torket Franzen,
which explains this with some details.
Books by Torket Franzen do not make calculations, physical
microprocessors do.
Starw man! Nobody said that a book makes computation. I said just that
if you study that book you will grasp why computations are realized in
the arithmetical reality, or any model of a Turing universal theory.
> Physical water, like any physical stuff does not rely on one
computations, but on an infinity of them,
Nobody knows if that is true or not, maybe only an astronomical
number of calculations would be required to perfectly simulate
water, but if you're right and a infinite amount of mathematics
would be required to do what just a small amount of matter can do so
effortlessly then it's game over and physics is more fundamental
than mathematics, and mathematical models can never be more than
just approximations of the real deal.
Not at all, as this is *derived* without any phsyical assumption other
that the physical can emulate locall the universal digital machine.
>> Definitions don't make calculations, physical
microprocessors do.
>Definition does not but relation does.
Only if the relations are about the orientation of PHYSICAL
things.
In the theory Kxy = x & Sxyz = xy(zy), no assumption of object, still
less of oriented object is made. You are not using the standard notion
of computation.
> Indeed a computation is a digital relation, and it does not
depends on any physical assumption. Just read a book in theoretical
computer science.
No book in theoretical computer science can make a calculation,
Read what I wrote.
but a physical microprocessor chip can.
You don't know that, but infer it empirically. But the existence ofthe
computation is arithmetic is a theorem provded in the book mentionned.
It is well done in Epstein and Carnielli, or in Bollos, Jeffrey and
Burgess, or discussed in Franzen's book, or deepened in Matiyazevic's
work and book.
>> I don't assume anything but I do know 4 things for
certain: 1) Simulated water can not quench my thirst.
> That is ambiguous.
If that is ambiguous then EVERYTHING is ambiguous, and without
contrast words have no meaning
> you need to grasp step 3 before I can explain more on this.
There is nothing in step 3 to grasp, there is no there there.
> Proofs don't make calculations,
> Sigma_1 proof and calculations are the same thing.
Then then I really REALLY don't understand why you don't start
the Sigma_1 Proof Computer Hardware Corporation and become the
richest man who ever lived.
> Like fortran calculations are the same as algol calculations.
Yes, without physical hardware to run them on both FORTRAN and
Algol are indeed the same, both are just squiggles on paper.
Confusion between the finger and the moon.
> comp is a theology,
Maybe, but I no longer care what "comp" is.
I stop here as you play dumb again.
Bruno
> When I prove the existence of a computation in the theory
RA [...]
I don't need the the theory RA to prove to me that
computations exist, I already know that they do, what I want is for
the theory RA, or anything else, to make a computation without the
use of matter that obeys the laws of physics. And I don't want a
proof, and I don't want a axiom, and I don't want a definition, and
I don't want a book; I want a computation.
> you need to get step 8 for this.
Until you fix step 3 any higher step is meaningless.
> Their argument is that a physical computer can only be an
approciamation of the mathematical one, like a physical circle can
only approximate a mathematica circle.
A physical circle, like one drawn by hand with ink on paper, if
far far more complex than a mathematical circle; so you tell me,
which is a approximation of which?
>>> that prime number existence does not depend on its
computation,
>> I think maybe it does depend on the physical possibility
of it being computed in the universe, although I could be wrong.
> That would make Euclid's wrong,
If so he wouldn't be the first ancient Greek that was dead
wrong.
> Where John Clark is = where his body is,
So you think consciousness has a position, does consciousness have
a velocity too, or a temperature, or a pressure, or a mass, or a
magnetic moment?
John K Clark
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