On 21 Jan 2014, at 17:45, Platonist Guitar Cowboy wrote:
On Tue, Jan 21, 2014 at 2:51 PM, Bruno Marchal <[email protected]>
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 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.
Like the guys from Erlangen and Lorenzen. I gave myself some time
with this, until I decided it was just prohibition/denial: "We just
all pretend that weird stuff does not exist. Only not-weird stuff is
real because we have clarity", is what I remember...
It is a nice way to look at this.
I am still amazed by how popular and how much support this seemed to
get. Difficult to stay open and build understanding of these
approaches for me. PGC
I think it is a form of solipsism, and Brouwer was openly solipsist.
Intuitionism is almost the logic of the first person, which is
solipsist about its own mental space. It is the logic of the guy who
think he is "really" in W, and not in M, which is correct from the 1p
view, (well, in W), but non communicable, as his doppelganger in M
will confirmed.
But this shows that intuitionism and solipsism have some interest in
psychology. I agree yet, that they become empty and non sensical when
they are transformed in theory of everything. We can't deny the
others, despite that notion is not constructive.
Bruno
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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