On 22 Jan 2014, at 20:05, Stephen Paul King wrote:
Dear Bruno,
On Tuesday, January 21, 2014 8:51:14 AM UTC-5, Bruno Marchal wrote:
On 20 Jan 2014, at 21:17, Alberto G. Corona wrote:
> Computation is understood as whatever made by a digital computer or
> something that can be emulated (or aproximated) by a digital
computer.
OK. That's a good definition, and it is correct if ... we assume
Church's thesis.
> So everything is a computation.
Goddam! Why. Even just about what is true in arithmetic cannot be
emulated by any computer.
I am afraid you might not really grasp what a computer is,
conceptually. See my answer to stephen yesterday, which shows wahy
Church thesis entails that most attribute of *machines* cannot be
computed by a machine.
Or think about Cantor theorem. The set of functions from N top N is
not enumerable, yet the set of *computable* functions is enumerable.
That is a theorem that takes certain axioms as true... We can build
theories with other axioms...
Always. But that would made sense only if you provide the other axioms.
I wish to escape the prison of the Tennenbaum Theorem!
This looks non sensical to me. But even if there were some sense here,
I remind you that I gave you two days ago, a constructive proof of the
existence of non computable functions, based on a constructive
diagonalization procedure (unlike the one by Cantor), (and Church's
thesis).
Just that with Cantor's result, it is more easy.
Bruno
> That is a useless definition. because
> it embrace everything.
For a mathematician, the computable is only a very tiny part of the
truth.
>
> Everything is legoland because everything can be emulated using lego
> pieces? No, my dear legologist.
Not veything can be emulated by a computer. few things actually in
usual math. Some constructivist reduces math so that everything
becomes computable, but even there, few agree.
In Brouwer intuitionist analysis he uses the axiom "all function are
continuous" or "all functions are computable", but this is very
special approach, and not well suited to study computationalism (which
becomes trivial somehow there).
>
> What about this definition? Computation is whatever that reduces
> entropy.
It will not work, because all computation can be done in a way which
does not change the entropy at all. See Landauer, Zurek, etc.
Only erasing information change entropy, and you don't need to erase
information to compute.
> In information terms, in the human context, computation is
> whatever that reduces uncertainty producing useful information and
> thus, in the environment of human society, a computer program is
used
> ultimately to get that information and reduce entropy, that is to
> increase order in society, or at least for the human that uses it.
The UD generates uncertainty (from inside).
>
> A simulation is an special case of the latter.
>
> So there are things that are computations: what the living beings do
> at the chemical, physiological or nervous levels (and rational,
social
> and technological level in case of humans) . But there are things
that
> are not computations: almost everything else.
That is the case with the definition you started above, and which is
the one used by theoretical computer scientist.
Bruno
http://iridia.ulb.ac.be/~marchal/
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