Dear Bruno,
Thank you for you kind and thoughtful comments. Interleaving...
From: Bruno Marchal
Sent: Saturday, January 22, 2011 4:05 AM
To: [email protected]
Subject: Re: A paper by Bas C. van Fraassen
Hello Stephen,
On 21 Jan 2011, at 23:15, Stephen Paul King wrote:
Dear Bruno,
Thank you for writing further on this. I can understand the metaphor of
“dreams shared by a continuum of running machines, and they can define (non
constructively) notion of worlds, and proximity of worlds” and agree with it if
I weaken the definition of the word “machine” to be something far removed from
the concrete idea that most persons have.
[BM]
Yes. A machine is just a number interpreted by a universal number. A universal
number is a number u such that there is an arithmetical relation R with R(u, x,
y, z) <-> phi_x(y) = z provable in PA (say).
[SPK]
Is there a commutative diagram for that relation? I can better understand
complicated equations expressed in Category Theory terms.
**
The concern that I continue to have is how do our models represent 1) a
plurality of distinct 1-p (merely postulating a plural 1-p is insufficient
reasoning for me.), 2) the evolution of those 1-p.
[BM]
The plurality comes from the fact that the UD, or the true (and thus provable)
Sigma_1 relation generates them all. easy consequence of Church thesis and
Mechanism.
The evolution comes from the fact that (Sigma_1) arithmetic emulates their
(infinitely many) computable evolution.
[SPK]
I have no difficulty whatsoever with the UD per say, I just fail to see how
the mere existence of Sigma_1 (or Sigma_n) –> evolution of 1-p. This is a
“bridge to far for me” as it tells me nothing of the vertical relations between
UD (existing in Platonia) and 1-p (existing at the immediate finite expression
of the individual observer (the entity that reports to having 1-p)). This
reminds me of Julian Barbor’s attempts to eliminate time from physics by using
the H=0 relation of the “universal wavefunction” to “prove” that time does not
exist. His thesis fails because there is a little thing called computational
complexity that makes his machinery grind to a halt by proving that the
computational resources (walls of Platonia are not enough!) will always be less
than what is needed to compute the infinite NP-Complete problem which is the
generation of the contents of the “time capsules” that his theory requires to
replace time’s flow”.
This problem can be traced even back to Leibniz’ Monadology where the
“pre-ordained harmony” upon which Leibniz’ Monadology rests its explanation of
how all of the internal evolutions of the Monads will be synchronized with each
other. OTOH, we can still use the Monadology if we replace the need for a
computation of the 3-p “initial conditions necessary” with a plurality of
ongoing 1-p type computations within each Monad that act to continuously align
pairs of Monads with each other. This is the distinction between 1 computation
that must occur prior to the existence of Monads and many computations that
co-exist with the monads.
I can see that we can reword this idea into a form that is identical to
your UD and UDA, but there is still an infinite tower structure that connects
each individual 1-p with the ideal 3-p. One thing that proves this to me is
that at the limit of the 3-p we find that our structure is identical to a “zero
information system”, as any part of it is isomorphic to any other part and to
the whole. There is no “difference that makes a difference” there.
I see your theory as a very sophisticated form of idealism
[BM]
No problem. I agree with term, because I think that numbers are ideas, indeed.
relatively to universal numbers, numbers are ideas creating ideas, even
analytical ideas.
[SPK]
OK, let me ask the question another way: How can numbers interact with each
other without the interface that physicality allows? Numbers are like bosons in
a condensate, they have no separable existence from each other nor any thing
like causal efficacy. They merely exist. That they encode relationships is not
a surprise, that is the essence of their existence! Perhaps we have been lead
astray by the mathematization of the idea of causality based on an unrealistic
toy model. We can say that X causes Y, if and only if Y occurs only when X is
present, but this neglects to mention that X and Y are not unique singletons in
the universe of possibilities. This Humean model presumes that there is only a
single instantiation of objects that somehow escapes the reality of the
plurality of the 1-p.
Just as we can prove that there exist an infinite number of equivalent
physical Machines that can code the same computer program, there are infinitely
many X_i and Y_j where i =/= j, this is the heart of the NP-Complete problem
that I mentioned above. I propose Pratt’s “process dualism” as a way to cut
this Gordian knot, but I am only weakly able to explain someone else’s theory.
What the mathematics of special and general relativity (and quantum field
theory) tells us is that for any physical object there are an infinite number
of 3,1 dimensional coordinate frames that can instantiate an object and the
mapping (diffeomorphism) between these was proven to be NP-Complete.
Until and unless we can show that Integers are non-commutative then we
cannot treat them as if they obey the same kind of statistics as fermions. But
there is hope, fermions need bosons to interact with each other and bosons need
fermions to be distinct from each other. We can play with Supernumbers, but
they are dualistic and do not have a natural Monotonicity!!!!
**
that still suffers from the problem of epiphenomena. I say this because I
cannot figure out how your theory explain a common illusion of a physical world
necessarily emerges within the dreams of the “running” machines. How do the
many dreams have sufficient structure to act to supervene inertia?
[BM]
They have too. That is the point of the UDA.
They can. That is the point of AUDA.
The fact is that the number relations are highly non trivial, especially when
you realize that from the point of view of the machine, even when ideally
correct, they are unable to relate the different internal views (p, Bp, Bp & p,
Bp & Dp, Bp & Dp & p + their G/G* splitting).
[SPK]
Then it is my failing to understand how to get UDA and AUDA to prove P=NP,
for that is what you are in essence proposing!
**
I have been re-reading the Mauldin paper and trying to figure out how the
Movie Graph idea is not being used a device to amplify a refutation of Comp in
the paper.
[BM]
Maudlin and me gives different proof that mechanism is incompatible with
materialism. We show that
~MEC v ~MAT
equivalently MAT -> ~MEC, or MEC -> ~MAT.
You can use the movie-graph to refute MEC starting from MAT, or to refute MAT
starting from MEC, or to prove that MAT and MEC are logically incompatible,
starting from nothing (= classical logic and arithmetic).
[SPK]
OK, but please understand that this proof is just a restatement of the
epiphenomena problem that any monism will have. Unless we have some form of
duality at some level the “hard” problem will remain. Just because Descartes
screwed up with his version of "substance dualism” does not necessitate that
all forms of dualism suffer the same problem! We can see that the dualism will
vanish at some appropriate level into a neutral monism, but the dualism need
not self-stultify so long as we have a model of interaction that is not
inconsistent at all levels. We can get MEC and MAT to co-exist peacefully if we
use Pratt’s idea, but to do so will require us to give up on our hopes for a
single theory of everything that can be finitely encoded on a T-shirt that
beautiful Olympia can model for us.
Onward!
Stephen
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