**Stephen P. King** (*stephenk1@home.com*)

*Sat, 31 Jul 1999 21:12:26 -0400*

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Dear Matti,

I am taking a little break to think and read...

Matti Pitkanen wrote:

*>
*

*> On Thu, 29 Jul 1999, Stephen P. King wrote:
*

*> > Matti Pitkanen wrote:
*

*> > >
*

*> > > Dear Stephen,
*

*> > >
*

*> > > I realized that the problem related to how self, say X, experiences
*

*> > > its subselves was trivial. It must experience them as
*

*> > > collection of invididuals. Any self Y containing X (of
*

*> > > course!) experiences the subselves of X as 'average' self, abstraction for
*

*> > > a class of objects. This realizes individuals and classes
*

*> > > crucial for computational description of brain. I am
*

*> > > reading Pinker's book about how brain works and building
*

*> > > TGD:eish version of computationalism.
*

*> >
*

*> > Interesting! :-)
*

*>
*

*> Or some aspects of computationalism. Symbols, representations,
*

*> hierarchical, modular language like structures, program like
*

*> structures as cascades of selves generaated with self.
*

*> Computing defined as deterministic symbol manipulation by fixed
*

*> rules is not in question. I refuse from honour of being robot!(;-)
*

But is it not true that symbols are information when we think of them

as having a "meaning" but are material configurations when we think of

quantities such as charge, mass, spin, etc. ? A robot has all of its

behavior predetermined, it has not free-will!

[SPK]

*> > > > It is logical entailment or implication that "goes backwards" with
*

*> > > > respect to time. This is discussed at length in Pratt's paper ratmech.ps
*

*> > > > If we take the negation: "not A <--- not B", we are just reversing the
*

*> > > > respective arrows. Umm, only in the strict binary boolean case is ~~A =
*

*> > > > A, so it gets a bit complicated when we are using a Chu_[0,1] space to
*

*> > > > represent the interactions of a given pair of LSs, since fuzzification
*

*> > > > allows for ~A \intersect A =/= 0 under certain conditions!
*

*> > >
*

*> > > [MP] This seems to be in conflict with naive ideas about
*

*> > > relantionship between logical and temporal causation.
*

*> > > What about set theoretic representation of logical causation:
*

*> > > could LS:s within LS:s provide fundamental realization for this:
*

*> > > LS:s born withing LS:s as representation of logical
*

*> > > implication sequence?
*

[SPK]

*> > I am trying to point out how material causation is different from
*

*> > logical entailment, or, as you say, logical and temporal causation. The
*

*> > set theoretic representation is usually used to represent material
*

*> > causation. Umm, I
*

*> > am trying to better understand your point of view here. My ideas only
*

*> > seem to make sense in the context of a mathematical duality existing
*

*> > between the material configurations and the information content of an
*

*> > LS. I am saying that logical implication and temporal causality are
*

*> > mathematically dual!
*

[MP]

*> I did not get intuitive grasp about the arrow diagram. Just why
*

*> should the directions of time arrow and logical arrow be different while
*

*> I directly experience them to be same when I think a conscious thought A
*

*> implies B?
*

Think of how logical implication works. Think of what "precedence"

means in terms of logic...

snip

{spk]

*> > Logical entailment act over the states (the information about events)
*

*> > with in the particular observer's quantum jump history in such a way
*

*> > that it selects the particular physical event that is "jumped" to in the
*

*> > temporal causal direction. This is like saying that the particular
*

*> > memory of an observer weights its decision as to which of the paths to
*

*> > take given a menu of many paths in the "garden of forking paths" that
*

*> > the spinoral configuration space represents. This also can be looked at
*

*> > from the point of view of the Everett-Dewitt-Wheeler MUI theory, that
*

*> > Bill mentions in [Time 502] (Thanks for pointing this out, Bill! :-) )
*

[MP]

*> I would see this as follows: each item in sequence A-->B--> ...means
*

*> wakeupe of subself. A or some larger self containing A experiences all
*

*> these wakeups consciously. Depending on what kind of quantum jump is
*

*> involved, conscious experience is that of A implies B .. or object B
*

*> is contained inside object A or something else.
*

The q-jumps define the forward flow of observer's time. I do not

believe that time has any meaning independent of an observer... The

arrow of logical precedence (entailment) goes the other direction...

[SPK]

*> > The key idea, I think, that we must do is find a conceptual way of
*

*> > making sense of how the "inside-outside" differences of LS:s works,
*

*> > following Hitoshi's theory, as this gives us a way of understanding the
*

*> > dual relationship. On the "outside" of an LS, we have the view
*

*> > point of an observer, who "sees" the LS as a cm point-like particle,
*

*> > that behaves "classically", e.g. it is impossible to observe the QM
*

*> > behavior that goes on "inside".
*

[MP]

*> In TGD approach LS would see those sub-LS:s, which are awake as
*

*> representations for objects of external world or internal world.
*

Ok, but I don't fully understand what you are thinking here...

snip

[SPK]

*> > The problem I see is that the assumed identification of a self with a
*

*> > set must be considered very carefully!
*

[MP]

*> Actually identification as quantum subsystem 'able to stay awake' in in
*

*> question. Tensor factor of state state. This identification is induced
*

*> from definition relying on the identification of spacetime sheet as
*

*> subsystem. This problem is very intricate and I do not claim of having
*

*> understood all of it. I wants to pretend that all is understood but
*

*> I do not believe it(;-).
*

Let's discuss it further...

[SPK]

*> > Since the ordering of quantum
*

*> > jumps is not an a priori given, we have a situation that is like saying
*

*> > that the winner in each match in a tournament will advance to the next
*

*> > stage, but we are unable to predict which one that will be. The "winner"
*

*> > is, of course the one that has the most extremal MNP in the "given
*

*> > situation", but this is just like saying that the winner is the one that
*

*> > scores the most goals!
*

[MP]

*> I am not sure what you meant with 'the ordering of quantum jumps is not an
*

*> a priori given'. It is! There is only ordered heap of ticks with new
*

*> tickes added on this heap 'all the time'. What is not given except in
*

*> statistical sense, is the ordering of psychological times associated with
*

*> quantum jumps for a given self: psychological time can also decrease
*

*> occasionally. The ordering of quantum jumps is what gives subjective
*

*> time absolute arrow and induces arrow of psychological time.
*

*> In second time scale this arrow is absolute. 10^40 events make
*

*> statistics excellent!
*

I am talking about the order of the "ticks", like how would they be

labeled 1, 2, 3, ... The "heap" of then "exists" for sure, but the order

in which individual q-jumps are taken from the heap is, I am arguing,

not a priori given. Umm, my thinking of this is "weird" since the

ordering is "fixed" only within a finite "window" that constitutes an

observer (with is why I cal an observer a poset of observations), is is

dissipative... Umm, nothing is truly fixed, only relatively fixed...

[SPK]

*> > I am trying to look at more subtle situations, namely the way that the
*

*> > non-local light-cone structure defines a causal structure and
*

*> > considering how it is constructed. The matter of logical consistent
*

*> > implication is normally not considered in physics! It is just assumed
*

*> > that only a single Absolute set of geodesics exist (e.g. a single
*

*> > lightcone structure M^4) and it is these that define the paths of
*

*> > motions of particles.
*

[MP]

*> Yes. The question is: which is the correct framework for
*

*> discussing logical implication in physics. In Einstein's times it would
*

*> have been considered at the level of spacetime and this is what you are
*

*> suggesting.
*

Not really, I am saying that space-time is a subjective notion, a

framing within which the particular observations are related for each

other. This is very different from the classical thinking.

*> I suggests that neither statespace or spacetime is the correct
*

*> framework. Logic is aspect of mind and consciousness and therefore it
*

*> is *quantum jump* which defines the correct framework.
*

*> This suggests that connection with lightcone causality comes only
*

*> through the concept of psychological time. Already the phenomenon
*

*> of quantum tunneling (breaking of lightcone causality) suggests that this
*

*> is the case.
*

Yes! We are so close! Because of the mathematical duality between the

dynamics of the logical entailment of information contained in q-jumps

and the light-cone causality defining material motions, the change in

one of these "complementary" aspect is reflected in the other. More on

this later...

[SPK]

*> > The problem becomes obvious when we consider that the uncertainty
*

*> > principle tell us that the notion of a priori actualized geodesics is
*

*> > impossible! We can only consider a spectrum of "possible" geodesics as a
*

*> > priori existing, the one that is "actually" followed depends on "glocal"
*

*> > conditions, and these vary with the observer's history.
*

[MP]

*> This would be true if you would quantize metric of spacetime just as it
*

*> is quantized in GRT. In TGD nothing like this is attempted.
*

*>
*

*> a) Association X^3-->X^4(X^3) *fixing geodesics* but is by no means in
*

*> conflict with uncertainty principle since the construction of
*

*> configuration space spinor fields reduces to the construction of their
*

*> values on the space of 3-surfaces located on lightcone boundary times
*

*> CP_2. Values of configuration space spinor fields elsewhere are fixed
*

*> by Diff^4 invariance.
*

But, what about the problem that Hitoshi points out that Diff^4

invariance prohibits the construction of clocks, and without clocks it

is impossible to measure time.

*> b) One can construct representations of Diff^4 invariant Poincare
*

*> algebra parametrized by lightcone proper time parameter a and these
*

*> representations reduce to representations of ordinary Poincare
*

*> algebra for a---> infty.
*

*>
*

*> c) Uncertainty principle forces states to be *superpositions of
*

*> spacetime surfaces X^4(X^3)* but does not make the concept of
*

*> classical goeodesic nonsensical.
*

After reading Prigogine's work I am not so sure! He points out that it

is impossible to define individual trajectories, e.g. geodesics...

*> This is important difference: when I realized that classical physics in
*

*> sense of X^3--> X^4(X^3) association is exact part of quantum theory, not
*

*> some approximation resulting from formal functional integral formalism
*

*> which actually does not work at all, I experienced quite
*

*> many thrills in my spine! When your spine begins to make matter-mind
*

*> type quantum jumps and finds itself in state of oneness, you know that you
*

*> are on right track(;-)!
*

:-) I know that feeling!

[SPK]

*> > When we look out into the night's sky we notice that the further out a
*

*> > point of light is observer to be, the "farther back in time" the event
*

*> > "occurred".
*

[MP]

*> Classically yes.
*

*>
*

*> > We usually consider that any other observer's perception can
*

*> > be constructed by a continuous transformation of framings, e.g. by a
*

*> > Lorentz transformation of our set of observations, and thus conclude
*

*> > that the is just a single night sky for all. It is not "obvious" and
*

*> > "naive" notion that I am disputing! We should say that there exists an
*

*> > equivalence class of "night skies" and there exists a mapping between a
*

*> > given observer and a particular "night sky". The particular
*

*> > identification does not follow from just a binary set theoretic
*

*> > inclusion, there is an optimization process involved that takes into
*

*> > consideration the particular past history of the observer and this
*

*> > selects the particular mapping (or identification).
*

[MP]

*> Here I think that we understand each other's positions. I have
*

*> real night sky and infinity of p-adic nights skies, one for each
*

*> self in this infinite universe(;-).
*

Yes!

[SPK]

*> > > > We can just say that temporal orderings are given by the MNP of the
*

*> > > > quantum jumps, but I am trying to understand the details better. I think
*

*> > > > of this as asking what decides the winner in a tournament; while we can
*

*> > > > not say with certainty 1 who will win. All we can do is to set up
*

*> > > > "pay-off matrixes", etc.
*

*> >
*

*> > The key problem we are facing here is how to "draw" the boundary of the
*

*> > set, how is it decided with elements are "inside the set" and which are
*

*> > "outside"!
*

[MP]

*> Yes. Let me see this from my viewpoint. I have definition of self as
*

*> quantum subsystem: the geometric definition
*

*> underlies it. The event horizons associated with wormholes (metric
*

*> determinant vanishes since metric changes from 1-1-1-1 to -1-1-1-1
*

*> signature are natural boundaries of selves.
*

I do not understand your thinking here. How do you know that it is a

metric chance involved in the boundary of a self?

[SPK]

*> > The use of a hierarchical "gathering of objects together" to
*

*> > model selves, I believe, is correct. Your analysis of how we experience
*

*> > music shows a good "proof by example" of this notion. But we still have
*

*> > the question of how it is that the hierarchy is set up under the myriad
*

*> > of situations.
*

[MP]

*> It is purely dynamical. Quantum jumps generate it. Strong NMP
*

*> gives limits by telling what kind of quantum jump occurs within
*

*> given self: is it matter-mind type quantum jump in which self
*

*> behaves as single self or does it lead to generation of
*

*> a new self candidate (actually two since also complement
*

*> of subself inside self is candidate for self). In this
*

*> case self experiences decay to two subselves whereas in the first
*

*> case it experiences 'oneness'. These
*

*> two types of quantum jumps differentiate between Eastern and Western!
*

*> We have obviously chosen the Western mode and are generating
*

*> complicated hierarchical nested structures of selves (just look
*

*> this mail with all its >:s and >>:s and >>>...:s) and
*

*> feeling very unhappy for most of the time(;-). I am seriously
*

*> considering the possibility of Eastern mode if I ever get
*

*> TGD inspired theory of cs finished.
*

Interesting! I am looking forward to the discussion...

[SPK]

*> > I think that the notion of a competitive tournament is
*

*> > the key; it is easy to see that it defines a hierachy of sets given the
*

*> > winners in each level of the tournament. What remains to be modeled is
*

*> > how the criteria of "what it takes to deside a winner" is given. We need
*

*> > not model each possible situation, of course; we only need to show how
*

*> > such can be defined given a particular situation.
*

[MP]

*> Reading Pinker it becomes clear that AI people also have realized
*

*> the importance of competion: otherwise everything would be drowned
*

*> floodwave caused by by combinatorial explosion. The most interesting
*

*> conscious experiences are experienced: this is the fundamental
*

*> dynamics of conscious information processing. The decision of winner
*

*> in TGD framwork is simple: quantum jumper with maximum entanglment
*

*> negentropy gain is the winner.
*

Yes, I agree. Is the number of players competing (in the q-jump)

restricted to a finite number?

*> Why I regard it as so important is that it gives direct connection
*

*> with quantum measurement theory and is consistent with it. Any principle
*

*> which one postulates, must be consistent with QMT: this is highly
*

*> nontrivial requirement.
*

The only difficulty is that we must be very careful how we interpret

QMT!

*> > It is here that I see both Pratt and Frieden pointing us to the
*

*> > notion of "information aquisition" games and the use of pay-off
*

*> > matrices to define the before-mentioned criteria.
*

*> >
*

*>
*

*> The concept of pay-off matrix is new to me.
*

Can we discuss it?

snip

*> > [MP]
*

*> > > Kahler action is Maxwell action for the Kahler form of CP_2 projected
*

*> > > to spacetime. Connection realizing the parallel transport defined
*

*> > > in CP_2 projected to spacetime surface and realizing parallel
*

*> > > transport in spacetime. Lagrangian exists by definition and
*

*> > > is Maxwell action density.
*

*> >
*

*> > So, are you saying that the CP_2 version of the Maxwell action is
*

*> > projected onto "a" space-time or "the" space-time?
*

*>
*

*> CP_2 Kahler form is projected to generic spacetime surface. One must
*

*> scan over all spaceteime surfaces to identify absolute minimum X^4(X^3) of
*

*> Kahler action= Maxwell action for induced Kahler form going
*

*> through given X^3 on lightcone boundary (this restriction
*

*> for X^3 is possible by Diff^4 invariance).
*

This is still a bit too idealistic for my taste. :-( I do not like

having to postulate a priori ensembles and "generic" structures... But I

can see how it is useful in the model. I have to be sure that we do not

use these "non-observables" to much...

[SPK]

*> > This is a crutial
*

*> > difference for me! Since I think that the space-time notion is a
*

*> > subjective framing of an observation and there are more than one
*

*> > observer possible in the Universe, to say "the" space-time would imply
*

*> > that all observers share a common space-time and this would imply that
*

*> > an absolute M^4 structure defines the causal choices for all possible
*

*> > observers. This is the Newtonian-Laplacean myth!
*

[MP]

*> It is. But I do not define observers in this manner.
*

*> I do not define observers=selves as spacetime level
*

*> concepts. Observer=self is purely quantal concept: self corresponds to
*

*> a tensor factor of infinite dimensional state space, counterpart
*

*> of state space of quantum field theories. This is very important
*

*> point.
*

I am saying that the space-time framing is "how" an observer observes.

Hitoshi calls it: " "glasses to look at the world" Yes, the self is

purely quantum mechanical. We agree, we just stumble over words... :-)

*> Definition of observers as spacetime level concept was certainly natural
*

*> approach before the advent of quantum theory. Not
*

*> after advent of quantum theory and even less after the idea
*

*> of quantum theory of consciousness. I start from the definition of
*

*> observer as 'self', unit of consciousness described by quantum theory of
*

*> consciousness.
*

I agree!

*> I do not try to say anything about consciousness or observers
*

*> using mere classical physics or classical spacetime concepts.
*

*> Neither do I try to reduce causal choices of observers to geometry
*

*> of spacetime. Their choices occur at completely different level.
*

*> Selfs select between quantum superpositions of spacetime surfaces.
*

*> Not inside spacetime. They are not subject to lightcone causality
*

*> (tunneling phenomenon).
*

I agree with Hitoshi that classicality is subjective, it is "what" is

observed. It is the illusion that is necessary!

[SPK]

*> > What is the
*

*> > alternative? To consider that there are multiple a priori possible
*

*> > projections of the Kahler form of CP_2 and each defines a Maxwell action
*

*> > uniquely for each observer. This is what "observation defines physics"
*

*> > implies and what Frieden claims.
*

*> > I understand that you have philosophical "issues" with this, so I hope
*

*> > that the can discuss this and come to some understanding or at least
*

*> > "agree to disagree". :-)
*

[MP]

*> No. Induction procedure and projection of CP_2 Kahler
*

*> form to spacetime surface is completely unique. The map of
*

*> real spacetime surface to p-adic spacetime
*

*> surface defines observer dependent spacetime as a p-adic version of
*

*> spacetime surface satisfying p-adic field equation (absolute minimization
*

*> of Kahler action).
*

Ok, On this I agree, but it is not what I am asking about! I am

thinking about how the minimization of the Kaehler action is not a

global action, it is local to the particular observer, thus each

observer would have their own "absolute minimization of the Kaehler

action", since every observer has their own light-cone structure. I

point to a generalization of the principle of equivalence: "every

observer always is at rest with respect to their local framing". When

interaction occurs between observers the space-time framing is changed

by the q-jump, and thus the particular minimization configuration of

changed. This is the act of computation that I am thinking of!

*> I would say that absolute minimization of Kahler action and informational
*

*> time development (Schrodinger evolution) define classical and quantum
*

*> physics. Strong form of NMP plus real to p-adics for various
*

*> geometric structures defines what is observed and how observes
*

*> consciously.
*

Sure!

[MP]

*> > > Hamiltonian formalism exists only formally: one can calculate
*

*> > > canonical momentum densities but due to the extreme nonlinearity and huge
*

*> > > vacuum degeneracy one cannot solve time derivatives of
*

*> > > imbedding space coordinates in terms of canonical momentum
*

*> > > densities uniquely. Canonical quantization of TGD fails totally:
*

*> > > this was the deep reason for configuration space geometry.
*

[SPK]

*> > I do not understand this! :-) Is it really necessary to have "unique"
*

*> > canonical monentum densities? What is the conjugate of this quantity?
*

*> > Does this have to do with the lack of a time-energy operator in QM? If
*

*> > so, Schommers outlines one that works also for the Frieden method, I
*

*> > think! :-)
*

[MP]

*> The uniqueness of canonical momentum densities is absolutely crucial
*

*> for the approach. Without this you do not have unique Hamiltonian
*

*> and quantization fails down totally!
*

*>
*

*> Canonical momentum densities are canonical conjugates of dynamical
*

*> variables: now 4 suitably chosen imbedding space coordinates as
*

*> function of spacetime coordinates. Actually situation becomes
*

*> completely catastrophic for vacuum extremals, in particular
*

*> M^4_+ imbedded as surface for which CP_2 coordinates are constant.
*

*> Canonical momentum densities vanish identically for them!
*

*>
*

*> This problem is purely TGD:eish and due to the extreme nonlinearity of the
*

*> action and vacuum degeneracy which corresponds to Abelian U1 gauge
*

*> invariance and gives rise to spin glass analogy and cognitive spacetime
*

*> sheets and padicity and.... The failure of canonical formalism
*

*> reflects all new concepts and new mathematics characteristic for
*

*> quantum TGD.
*

*>
*

*> Well, I am not sure what you mean with time-energy operator...
*

*> Even the unique existence of energy operator, Hamiltonian
*

*> fails.
*

We need to study Schommers work! He shows how to deal with this!

[MP]

*> > > Information measures for conscious experience can be
*

*> > > constructed by taking some quantity, say Kahler function.
*

*> > > Kahler function is mapped to its p-adic counterpart
*

*> > > and unique pinary cutoff appears in this map.
*

[SPK]

*> > The p-adic counter part looks like a filter, that only allows certain
*

*> > quantities through... I have been reading Frieden's book over and over
*

*> > and a thought occured to me. Let's see, I'll quote a section that
*

*> > relates to what I think you are saying here:
*

*> > "A major step of the information principle is the extremization and/or
*

*> > zeroing of a scalar integral. The integral has the form
*

*> >
*

*> > K \equiv \integral dx L [q, q', x],
*

*> >
*

*> > x \equiv (x_1, ..., x_m),
*

*> >
*

*> > dx \equiv dx_1, ..., dx_m, q, x Real,
*

*> >
*

*> > q \equiv(q_1,..., q_n),
*

*> >
*

*> > q_n \equiv q_n(x),
*

*> >
*

*> > q' \equiv \part q_1/\part x_1, \part q_1 /\part x_2, ..., \part
*

*> > q_n/\part x_m
*

*> >
*

*> > (0.1)
*

*> >
*

*> > Mathematically, K \equiv K[q(x)] is a 'functional', i.e. a single number
*

*> > that depends upon the values of one or more functions q(x) continuously
*

*> > over the domain of x. Physically, K has the form of an 'action'
*

*> > integral, whose extremization has conventionally been used to derive
*

*> > fundamental laws of physics. ... Statistically, we will find that K is
*

*> > the 'physical information' of an overall system conisting of a measurer
*

*> > and a measured quantity. The limits of the integral are fixed and,
*

*> > usually, infinite. The dimension M of x-space is usually 4 (space-time).
*

*> > The functions q_n of x are probability amplitudes, i.e., whose squares
*

*> > are probability densities. The q_n are to be found. They specify the
*

*> > physics [pattern of behaviour] of a measured scenario. Quantity L is a
*

*> > known function of the q_n, their derivatives with respect to all the x_m
*

*> > and x. L is called the 'Langrangian' density. ... It also takes on the
*

*> > role of an information density, by our statistical interpretation." pg.
*

*> > 5, Physics from Fisher Information.
*

*> >
*

*> > Now, what happens when we map the functions (here valued as Reals) to
*

*> > its p-adic counterpart? How would this affect your statement below?
*

[MP]

*> In principle the approach works quite generally. Mapping involves
*

*> also mapping of configuration space of dynamics but in principle
*

*> everything is straightforward. When real solutions
*

*> of variational principle are mapped to their p-adic counterparts
*

*> with some maximal resolution defined by pinary cutoff,
*

*> p-adic field equations can be satisfied.
*

Interesting!

[MP]

*> > > The number of pinary digits appearing in cutoff
*

*> > > value of Kahler function is measure for the information
*

*> > > contained by the value of Kahler function. The quantum
*

*> > > average of this p-adic integer defines information
*

*> > > measure for quantum history. The value of
*

*> > > p depends characterizes the self in question.
*

[SPK]

*> > So, you are using the prime number with the "identity" of the self? Can
*

*> > we think of this in an algebraic way and consider the prime number
*

*> > "labeling" the self as the algebraic identity of the algebra of the
*

*> > behaviour of that "self"? ( I am just wildly speculated!)
*

[MP]

*> There is infinite hierarchy of p-adic number fields and topologies
*

*> labelled by primes. p-Adic prime p of observer fixes the
*

*> effecitive p-adic topology obeyed by this observer spacetime sheet
*

*> and, as I assume, the effective topology of the spacetime,
*

*> and universe, as experience by the observer. The larger the value of p,
*

*> the more intelligent observer (maximum information gain in cs experience
*

*> behaves as log(p)*p). Everything is experienced as 'grainy' and p
*

*> and pinary cutoff defines the degree of 'graininess'. 2-adic
*

*> observers are the most 'grainiest' selves. Amusingly, computer technology
*

*> works with bits and all engineering acievements are very squareish:
*

*> just like the 2-adic fractals in my homepage. This would suggests
*

*> that our technology reflects the lowest possible level of p-adic
*

*> evolution(;-)!
*

Have you ever heard of "relative primes"?

(http://www.askdrmath.com/problems/athena11.24.97.html,

http://www.dacafe.com/Book/CH02/CH02.17.htm,

http://www.cs.washington.edu/homes/gjb/doc/philmath.htm)

snip

*> >
*

*> > [SPK]
*

*> > > > Since we have many observers, it is natural to consider that there are
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*> > > > many observational experiences to be considered. The notion of a single
*

*> > > > objective reality only makes sense IFF the class of observables is
*

*> > > > strictly sharp (binary certainty). The problem I see is that only a
*

*> > > > prediction can be made up to the accuracy allowed by the p-ary cut-off
*

*> > > > (\epsilon of accuracy). So the smearing of "reality" that QM predict is
*

*> > > > no surprise!
*

*> > [MP]
*

*> > > Actually I have two kinds of nonuniqueness. Each self
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*> > > has its own subjective reality defined by quantum jump and besides this
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*> > > objective reality is replaced by new one in q-jump.
*

[SPK]

*> > I agree completely, this is that I have been trying to communicate all
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*> > along! Why do we need the second nonuniqueness, e.g. "objective reality
*

*> > is replaced by new one in q-jump"? I see this "objective reality" as
*

*> > being defined in terms of the intersection of a finite set of
*

*> > "subjective realities" and is a relativistic notion. Umm, I think that
*

*> > the way that subselves are bound together in the p-adic hierachy plays a
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*> > role!
*

[MP]

*> Actually entanglement provides the mechanism of binding of p-adic selves
*

*> such that they lose their own subselves. This is nothing but
*

*> formation of bound states. Parts--> wholes is nothing but
*

*> formation of entangled states.
*

I think this is true also!

*> Associatism, connectivism, neural nets, whatever is
*

*> one version of computationalism and entanglement provides very
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*> attractive realization of associative learning. When entanglement
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*> between subselves is reduced in quantum jumps association is experienced.
*

*>
*

*> There is also second, more classical realization of associationism:
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*> grandma and apple pie get associated since the selves representing them in
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*> my head learn to co-operate and keep each other in wake-up (read 'alive'!)
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*> state.
*

I think so too!

Onward!

Stephen

**Next message:**Matti Pitkanen: "[time 508] Re: [time 505] Music scales and 2-adic numbers"**Previous message:**Stephen Paul King: "[time 506] Re: preprint: Physical Limits to Communication"**Next in thread:**Matti Pitkanen: "[time 509] Re: [time 504] Observation models"

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