Hi Stephen,
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.
Gosh. Categories with *partial* functions, as needed for Turing
universality, are hard to manage, for me at least. Not sure I can even
build the product and coproduct!
You might take a look at the dominical categories of Di Paoloa and
Heller: see
http://www.jstor.org/pss/2274352 (The Journal of Symbolic Logic ©
1987 Association for Symbolic Logic)
But you might just add difficulties to recursion theory, which is
already not so easy. In my opinion.
**
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 is unclear. You allude to the general problem of indexical.
Remember that my assumption is mechanism. From that you are conscious
here and now because some Sigma_1 proposition is true (and thus
provable, even by tiny RA (Robinson arithmetic). Now the problem we
have to solve is that we have to isolate a measure on the Sigma_1
proposition true proposition, actually, on their proofs. They are
accessed by the UD an infinity of times, through an infinity of
computations. This is handle technically by the logic of Bp & Dp (& p)
with p restricted to Sigma_1 proposition. Bp & Dp is definable and
third person (the intelligible matter), and the first person
"matter" (sensible matter, physical sensations) is handled by Bp & Dp
& p, which is not definable by the person. This should give the
qualia, including the "qualia of time". Formally, this works, but
leads to open problem in logic.
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 do not interact. But universal numbers simulates, even
emulate, everything Turing emulable, including interacting bodies.
Physical reality emerges from the gluing of those emulation, as
observed by the internal machine. That universal numbers exist is just
due to the turing universality of a tiny part of arithmetic. It is
long to prove, but is already in Gödel's 1931 paper. You need the
fundamental theorem of arithmetic, the remainder chinese lemma,
Gödel's beta function, etc.
Numbers are like bosons in a condensate, they have no separable
existence from each other nor any thing like causal efficacy.
Cute analogy. But analogy in interdisciplinary fields can be very
misleading.
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.
Each hypostases defines a notion of causality, by B(p->q), with B the
modal operator corresponding to the hypostase.
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!!!!
**
You substantialise the numbers too much.
Remember that I am using numbers because they are taught in high
school. I would talk to computer scientist, I would use the S and K
combinators. The point is that with comp the laws of physics are
invariant for the change of the basic "ontology". Any first order
specification of a universal system will do. Numbers are quite cute
for doing that, but they are not intrinsically important at the start.
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 no clue what P=NP has to do with all this. Machine's theology
need the whole arithmetical hierarchy and beyond.
Also. Matter is not an epiphenomenon. Matter just don't exist. Think
of arithmetic as a video game, or Matrix. Except that we are
distributed in it, in a very complex way.
I show ~MEC v ~MAT.
But the form MEC -> ~MAT is constructive. It explains why matter is
phenomenologically observed by persons.
Only with MAT consciousness becomes epiphenomenal. This usually ends
up with the elimination of the person. Brrr...
**
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.
Only material monism has that problem, because materialist postulate a
primary-material world causally closed, so that consciousness is an
epiphenomena.
But immaterial monism has no epiphenomena. Primary matter really don't
exist att all (unlike consciousness before the materialist becomes
eliminativist!), only numbers (or combinators, fortran programs,
choose your favorite basic universal ontology) and their "execution"
relative to universal numbers). Consciousness is then related to the
natural belief in a reality which grows when universal numbers looks
inward and get Löbian. It is a sort of "Dt?", with the "?" being
unconscious or instinctive. And this gives a fundamental role of
consciousness: the relative speeding universal execution. Useful for
"self-moving" entities and persons. It makes consciousness playing a
fundamental role, even in the origin of the physical role, and this
without any kind of magic.
There is still matter, but matter is not substancial. It is a
persistent observable, explained by a precise phenomenology. That
phenomenology explains the first person plural sharable quanta and the
first person non sharable qualia.
I am not saying that this is true, only that this follows from the
assumption that "I" am Turing emulable and the use of the classical
theory of knowledge.
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.
By changing the definition, we can attribute new meaning to terms. If
by matter you mean the taste of coffee, the smoothness of velvet, the
perfume of flowers, ... There is no worry. That abounds, from the
point of view of relative numbers, in Platonia, including typhoons and
taxes (alas). If by matter you mean any reification of particular
universal numbers (like in Digital physics approach) then that does
not exist, if my reasoning is correct, in the MEC frame. If you mean
by matter any sort of primitive substance, then that exists even less
(if I can say).
With comp there is a rather precise theory of mind (computer science/
number theory), and any universal machine/number can find it by
itself. The mind body problem is then reduced to the body problem
(UDA). And bodies appears as sum on all the computations going through
the mind states. If we impose the negation of solipism, this entails
we share computations and thus are multiplied collectively. This is
testable, and this gives an Everett-like sort of physics. In that
sense, Everett's formulation of QM confirms COMP + ~solipsisme. To
extract the first person plural from comp is more difficult, but seems
very reasonable, from the S4Grz1, X1* and Z1* logics. But such an
extraction has nothing to do with the fact that IF we are machine, we
*have to* do it to get the correct theory of both qualia and quanta.
I have discovered that in some people attributes me a proof of MEC ->
PHYSICS, when I have only proved the much more modest MEC ->
B(physics) where B = the modal necessity box, here. People confuse p -
> q with p -> Bq. It is radical (coming back to Plato's idealism),
but modest: we are just at the beginning. I only provide jobs for an
infinity of future mathematicians :)
Best,
Bruno
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
