Le 21-juil.-12, à 20:04, Stephen P. King a écrit :
On 7/21/2012 7:57 AM, Bruno Marchal wrote:
Hi Stephen,
I appreciate very much Louis Kauffman, including that paper. But I
don't see your point. Nothing there seems to cast any problem for
comp or its consequences.
Why not read the MGA threads directly, and address the points
specifically?
I already did. My contention is that computational universality is
NOT the separation of computations from physical systems, it is the
independence of a given computation from any one particular physical
systems.
Computational universality is an arithmetic notion. You don't need UDA
to separate it from physics, you need only a good intro to computer
science. This critics is wrong at the very start.
The independence of a given computation from any particular physical
system is obviously part of the comp assumption, and should not be
confused with the impossibility of any physical system to capture or
produce consciousness, which is related to the mathematical and the
theological by comp, and that is the consequence of UDA including MGA.
By addressing MGA, I meant you to quote that text, and that text only,
and tell me were you disagree, and for what reason.
The former Seperation is categorical in that one has seperate
categories with no connection between them whatsoever. The latter is a
duality between a pair of categories in that for the class of
equivalent computations there is at least one physical system that can
implement it and for a class of equivalent physical systems there is
at least one computation that can simulate it. (Equivalent between
physical systems is defined mathematically in terms of homologies such
as diffeomorphisms) This idea was first pointed out by Leibniz and
known as Leibniz equivalence. See
http://plato.stanford.edu/entries/spacetime-holearg/
Leibniz_Equivalence.html
This makes sense in Aristotelian physics, which, that is the point,
does not make sense if comp is true. Unless you can find a flaw. May be
you have a problem with what a proof consists in. Proofs does not
depend on the interpretation of the terms and formula occurring in it.
A proof in math, and in applied math, is always complete in itself.
Keep in mind that comp does not presuppose any theory of physics. It
assumes only that the physical reality is Turing complete at least. If
not, asking for an artificial digital brain would not make sense.
Bruno
Bruno
Le 20-juil.-12, à 05:34, Stephen P. King a écrit :
Hi Bruno and Friends,
Perhaps this attached paper by Louis H. Kauffman will be a bit
enlightening as to what I have been trying to explain. He calls it
non-duality, I call it duality. The difference is just a matter of
how one thinks of it.
Onward!
Stephen
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<Laws of Form and the Logic of Non-Duality.pdf>
http://iridia.ulb.ac.be/~marchal/
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Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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