[time 677] Re: [time 673]Stephen's duality theory, Plus Infinite Products = Infinite Worlds

Stephen P. King (stephenk1@home.com)
Mon, 06 Sep 1999 01:56:04 -0400

Dear Bill et al,

        I apologize for being brain dead for a while. I ask that you all have a
bit of patience with me. I am sorry that I have been cranky!

WDEshleman@aol.com wrote:
> Stephen,
> [WDE]
> Stephen, restate your duality theory, in 100 words or less,
> then I will comment. :-]
> [SPK]
> > I am still in the formative stage of my thinking of the duality theory.
> > I use a strange combination of graph theory, category theory and other
> > formalisms that I have picked up here and there...
> > This is a very bad sketch of what comes to mind right now. It is not
> > even wrong as it is here presented! I intend it to be fixed as we
> > discuss the ideas further. :-)
> [WDE]
> 100 words, not 1029 words (yes I counted them)!!!

        Sorry, It is that is is very hard to describe my picture in one hundred
words or less! There is so much background info required so that I can
juts say "U = ~~U, iff U =|/=| ~~U" and ~~U |=/|= U. End first
restatement of my duality.
        Let me try again: The matching of every question to every answer
concerning the question "What/when/were/why/how/who am I?", with regards
to all possible question/answer pairs, requires an infinite fair game to
be possible. Problem" An infinite fair game can neither start nor end.
Since it takes forever to verify that all is equivalent the game can not
start. Since it takes for ever to play a fair game, it can not ever end!
So it has to be Eternal. End second restatement
        All particles of matter, forgetting for a second about their wave
complements, can encode information via their spatial and temporal
configurations. The equivalence class of particle configuration spaces
is dual to the equivalence class of messages encoded in the
configurations of the particles. Matter is not information and
information is not matter, but not not information = matter and not not
matter = information. This is a fundamental duality, the duality of
Being and Nothingness.
End third restatement
        Thought:... Curvature is the deviation from the mean of zero curvature
e.g. x^2 + y^2 = z^2. What is "the mean of kinetic energy"? zero
curvature = zero energy? Exactly, what is energy?
> [SPK]
> > Simply put, the Universe U is the totality of Existence and as such is
> > infinite (with a "undecidable" cardinality). It is everything that
> > exists and this existence is tenseless. The particular subsets u_i of
> > the Universe form a powerset U^U that admits any possible decomposition,
> > e.g. any possible combination of u_i is contained in U^U. The u_i are
> > singletons that may be {0} under certain circumstances that I still need
> > to work out. :-).
> [WDE]
> I suspect that the entropy (S) of U^U is k*U or { U * log(U) } ???
> And that the probability of being found in u_i is:
> P_i = u_i / (U^U) ??? So that,
> S = U * log(U) = sum{ -P_i * log(P_i) : i = 1, infinity} ???

        I don't know of the top of my head. :-( I will try to find out. I think
that it is, basically: That is the change of a given configurations of
particles have of exactly matching isomorphism with a given description
of a configuration of particles? If it is 1, then we have a monism, it
it is 0, we have a infinite pluralism. How many dualities (binary
related pairs) that are disjoint are possible? How many ternary
relations? How many 4-ary? ... How many are 1/2-ary? How many are
1/3-ary? ... What is 1/n-ary mean?
        What sounds right to you?
> [SPK]
> > I believe that the u_i can be considered in two ways, as "independent
> > sets" or "complete graphs". These are complements in that the complement
> > of a graph G which has all nodes connected to each other is a graph with
> > no edges connecting them. I am identifying clusters of material
> > "particles" with the independent sets and the information "content" of
> > them with the complete graph. I am identifying the complete graph with
> > Complete Atomic Boolean Algebras (CABAs). These denote the n-ary
> > relations that exist between the u_i. Note that any u_i by itself is
> > isomorphic with U.
> > I am considering all subsets are dynamical systems when we allow for
> > the identification of the elements in one u_i (the 'independent set')
> > with the relations (the 'complete graph') among the elements of another
> > u_i. This identification is at least symmetrical iff they share an
> > element in common. The subsets can evolve to become identical to each
> > other and thus U by stepwise changing their relations, this collapses
> > the CABAs into singletons as Pratt describes in ratmech.ps. The key is
> > "how many steps does it take to collapse all possible CABAs into
> > singletons, given an infinite number of them?" (Remember that singletons
> > are identified with the subsets of U.) Tentative answer: Forever!
> > ...
> > Now, the english version of this: The Universe is all that could
> > possibly exist. So we get an infinity of "existents" or "possibilities".
> > At this level we have no time or motion or change of any type, thus no
> > mass, charge, or any other property other than mere existence.
> > The Universes is identical to the powerset of its existents and is an
> > element there of (as the empty set {0}, I think). The possible subsets
> > contained in the Universe can have elements in common. These constitute
> > the subsets of the Universe. The allowance that the subsets of the
> > Universe can have elements in common allows for the definition of n-ary
> > relations between the subsets. I identify the n-ary relations with that
> > is called information and the subsets themselves with material
> > particles.
> > The "evolution" of the subsets of the Universe is given by the
> > possibility that the relations can connect subsets, converting them into
> > singletons, such that they become identical to the Universe itself. This
> > evolution is seem most clearly in thermodynamic entropy, where material
> > events evolve such that they become identical to each other. This
> > "evolution" has a directionality to it that is identified with the
> > "directionality" of time. One key implication of the duality theory is
> > that for every change there is a dual one such that the two add to zero
> > change, thus the evolution of material particles is dual to the
> > evolution of the information "content". This evolution is called logic
> > and it defines the chaining of inference of the bits of information.
> > The subsets take forever to accomplish the task of becoming identical
> > to each other, and thus this gives us an Eternity of time to experience
> > "what it is like to experience some sequence of particular
> > observations".
> > I will quit here before I cause even more confusion!
> >
> > references:
> > http://one.ececs.uc.edu/cs543/4-22.html
> > http://www.askdrmath.com/problems/randazzo3.19.96.html
> > http://www.cs.utwente.nl/amast/links/v02/i03/AL0203.html
> > the paper: ftp://ftp.daimi.aau.dk/pub/BRICS/LS/95/1/BRICS-LS-95-1.ps.gz
> [WDE]
> When you can say this in 100 words or less, then you will know whether
> you are right (consistent) or wrong (inconsistent).

        Well, did it make any sense at all?
> > > The paper is over 1 mB zipped; thanks
> > > for figuring out what I'll be doing for the future. And that is
> > > exactly the point I'm trying to make about 1/(1 - x). You may
> > > think it is contrary to common sense when I propose that
> > > NOW is NOT "pushed" from the PAST by a PAST operator,
> > > but that the PAST was attracted to all possible NOW's by
> > > an operator that only becomes evaluated in the NOW.
> >
> [SPK]
> > I see these NOW's as the related observations of other observers (the
> > simultaneity frames).
> >
> [WDE]
> > > Another way of saying this is that NOW is attracted to
> > > all FUTUREs by an operator to be measured in the FUTURE.
> >
> >
> > Oh, I agree completely with this thought! We are "pulled" into the
> > future ( a common future)! It is as if we are being pulled toward a
> > singularity, all time arrows of those observers that we can communicate
> > effectively with are pointing in its direction. In a black hole, all
> > motions are restrained to point to the singularity, but this is a
> > space-like restriction. In the former case we appear to have a time-like
> > restriction. I am curious about how it is that the particular observers
> > are given, or in other words, why these observers? I think that is is
> > because they have a minimum amount of overlap in their respective sets
> > of observables and thus can communicate with each other (via
> > bisimulation). BTW, does the bisimulation concept make sense to you?
> >
> [WDE]
> I think of your bisimulation as being more analogous to interference
> than to interaction.

        Umm, "interference = interaction", Sounds right! This is my thinking.
If two systems wish to interact in some particular way, the pair must
have some aspects in common. We takes the fact that we can both kick the
same "big blue marble" that you have a universe in common. If we think
of the situation that creates a holographic interference pattern as the
"interaction of a "reference beam" and a copy of the reference beam
bounced of a target as a model of a fundamental measurement... Yes! You
are correct! Thank you, Bill!
        It is my thinking that bisimulation is another way of saying: that a
pair of waves generating interference patterns when they are superposed
is dual to a information acquisition zero sum game played between any
given observer and all other possible observers O_n, n of which are
well-ordered, and 1(1-n) are not... n = x ... ????????!!!!!!!!
Implications?! Each O_n can be called a Nature or set of Physical Laws
or their Langrangians! Exactly what are Langrangians?
        Thought: Is a space-time manifold that is completely empty of
momentum-energy realizable?

> > > My disclaimer is that this state of affairs is due to a subjective
> > > limitation of the observer and by "psychophysical parallelism",
> > > all objects are observers.
> >
> [SPK]
> > I also consider this as fundamental! I am a bit more specific in
> > thinking that all objects are definable as quantum mechanical Local
> > Systems, and as such are observers, if only of nothing at all!
> >
> [WDE]
> > > And, that the underlying objective
> > > structure has been programmed to subjectively mimic an
> > > attraction to the FUTURE by objectively requiring every
> > > augmentation of state in a given world to be accompanied by
> > > related augmentations in a majority of other worlds. That is,
> > > ( 1 + x ) objectively in multiplicity leads to a subjective
> > > reality where the FUTURE seems to attract the PRESENT.
> >
> [SPK]
> > Yes, this follows, for me, from a consideration that the act of
> > bisimulation itself, is given in terms of the changes that occur within
> > an LS, by the propagator, is "accompanied by related augmentations in a
> > majority of other worlds" which are the posets of observations of LSs
> > that have at least one state in common. (I think that this relates to
> > the formal concept of a fixed point!)
> > This corresponds to the idea that the LSs are evolving toward
> > equilibrium with each other. Thus, if two LSs are at equilibrium, they
> > are identical in information content. Metaphorically put: If two persons
> > are exactly the same, their minds are exactly the same.

        Did this make any sense?
> [WDE]
> > > My infinite products are simply candidates for role of the
> > > objective multiplicity that subjectively offers the seemingly
> > > non-intuitive conclusions drawn above.
> [SPK]
> > I think that the infinite product offer a way to construct coordinate
> > systems that are "subjective" yet can be "shared". It is as if each
> > framing of observations by any observer (object) is constructed from the
> > observations of all of the other objects that it can bisimulate (read
> > "interact with").
> [WDE]
> Sounds good to me...except that I prefer "bisimulate (read "INTERFERE with")"

        How would you explain it? Do you get the "game" idea?


> Sincerely,
> Bill

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