On 12 Nov 2012, at 20:29, Stephen P. King wrote:
On 11/12/2012 11:18 AM, Bruno Marchal wrote:
On 11 Nov 2012, at 23:35, Stephen P. King wrote:
On 11/11/2012 10:34 AM, Bruno Marchal wrote:
On 10 Nov 2012, at 12:32, Roger Clough wrote:
Hi Bruno Marchal
Plato says that we all live in a dark cave, seeing only
shadows on the wall, eager to see the light outside.
So there is at least a duality which I call platonia (heaven)
and contingia (earth).
OK. For example with heaven played by the truth of all the
propositions. But earth, with comp, belongs to heaven, or at
least on the path of going back to the one, among many path. The
existence of the paths are necessary, but the memory of the path
is half in heaven, and half in particular contingent geographico-
historical context.
Platonia contains the necessary stuff, the dark cave we live in
contains the contingent stuff.
The dark cave might be the physical universe. It is the border
of the universal mind reality. An object whose mathematics is
amenable to number theory, or computer science.
We cannot experimentally make the difference between a law, or an
instantiation of a deeper law. We cannot separate experimentally
geography and physics, but we can define physics by what gives
the universal prediction by different universal beings, and with
comp this is enough to define a precise indeterminacy domain from
which the universal beings can seen aspects of the universal
border.
Comp reopens the debate between Plato and Aristotle. At the
least, it shows that science has not decided this, and it
illustrates, by listening what the machines can already say about
them, another rationalist conception of reality, which gives
sense to the Pythagorean neoplatonist negative theology.
Bruno
Dear Bruno,
This is wonderful! Now, all I want from you is that you consider
the idea that "knowledge is not free".
It is fuzzy, but as far as I can interpret this favorably, I do
agree.
There is a cost in resource utilization (or entropy generation) to
gain knowledge.
I can still agree. Then the comp consequence is that the physical
resources are derivable from a notion of arithmetical resource.
Dear Bruno,
Could you explain this idea of arithmetical resource in depth?
Just imagine the universal dovetailer. It generates and implements,
and execute all programs. The infinite resource of arithmetic is just
that we agree that for all x, there is a y with y > x. It is trivial.
PA proves AxEy(x < y & x ≠ y)
May be you are still skeptical that the elementary arithmetical
relations implement all computations, but this is the big thing
discovered by Post, Church, Kleene, and others and which is the base
of computer science.
Matiyasevitch extended such result by showing that for getting the
Turing universality, the diophantine polynomial of degree four are
enough.
Bruno
I hope to have a more coherent formula involving the Blum measure
soon.
You can consult "Conscience and Mechanism" where I use Blum measure
for the "theory of intelligence". Blum measure is a quite general
notion of arithmetical or computer science theoretical measure
indeed.
OK, I will study this. I will use the Google Translate service. ;-)
--
Onward!
Stephen
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