On 04 Jun 2015, at 18:11, John Clark wrote:
On Thu, Jun 4, 2015 , Bruno Marchal <[email protected]> wrote:
>> A real physical device is much more complex, that is to say has
many more attributes, than any of our algorithms. So if you have a
simple thing and a complex thing you tell me which is making a
simplified approximation of which.
> The supplementary attribute that the physical device possesses
have nothing to do with the algorithm
And an algorithm has nothing to do with the supplementary attributes
of the physical device.
Exactly.
The physical device is far more complex than the algorithm,
astronomically more complex, so you tell me which is a simplified
approximation of which.
The physical device is no more relevant to the algorithm than any
other universal system. You can implement the factorial in fortran,
and you can implement fortran in lisp, and you can implement lisp in
the physical, at least approximatelly, as in the mathematical realm,
you don't have to add the default hypothesis: no asteroids. The level
of complexity is not relevant here. two apples is far more complex
than the number 2, which is an atemporal immaterial notion or
(universal number) idea.
You could say that a real circle is only an approximation/
simplification of a real physical circle, which is made of ink
molecules, etc.
Yes, a curve of ink molecules lying on top of a layer of cellulose
molecules is astronomically more complex than the set of xy points
that solve the equation (x-h)^2 + (y-k)^2 = r^2. So if a
mathematical circle is only a simplified approximation of a (sorta)
circle drawn on a paper why isn't a mathematical Turing Machine a
simplified approximation of a physical electronic computer?
That is because you conceive an application of math to a physical
world. In that case we can say that the sphere is only an
approximation of the Earth surface. But with a computer, we go in the
other direction. We have a clean mathematical concept (the circle) and
we need to approximate it with the physical (the wires).
The point is just that the notion of computation, once you agree with
Church-Turing thesis, is made into a purely arithmetical notion. You
can define computable and finite piece of computation by one precise
combinators, or one precise number, or one precise diophantine
polynomials, etc.
Turing discovered all this in a context of foundation of mathematics.
The discovery of the universal machine is a mathematical discovery.
They exist in the relative way in arithmetic like prime numbers
exists, and all computations (except the physical one) are mapped on
semi-computable number relations.
You are the one invoking some God (Matter) capable of making some
computation more real than others.
And you are not completely wrong, given that computationalism will
distinguish the physical from the psychological by making the physical
relying on the infinities of computation below the machine
substitution level. But this, with comp, explains the physical, from
machine self-referential properties, and so can be translated in
arithmetic to give the proposition logic of physics.
Bruno
John K Clark
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