**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Fri, 30 Jul 1999 08:02:47 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 505] Music scales and 2-adic numbers"**Previous message:**Stephen P. King: "[time 503] Re: [time 500] Observation models"**In reply to:**Matti Pitkanen: "[time 500] Re: [time 495] Re: [time 494] Observation models"

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

*> Dear Matti,
*

*>
*

*> This is very interesting!
*

*>
*

*> 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!(;-)

*>
*

*> > >
*

*> > > 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?
*

*>
*

*> 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!
*

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?

*> If we ignore this duality and assume identity between the two, my
*

*> argument makes no sense.
*

*> Thus I do need to better define my reasoning for positing a duality. I
*

*> admit that the discussion of Descartes' duality has caused a great deal
*

*> of confusion! I apologize for this. I, mistakenly have assumed, that
*

*> upon reading Pratt's ratmech.ps paper, that the differences between
*

*> Pratt's notion and that of Descartes would be obvious! I guess that I
*

*> need to be more explicit; I will have to deal with this later...
*

OK

*> 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! :-) )
*

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 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".
*

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

representations for objects of external world or internal world.

*> Another difference is in the
*

*> dimensionality and geometry. Inside, the LS has NxR^6 dimensions (where
*

*> N is the number of QM particles that compose the LS and are entangled)
*

*> and the geometry is Euclidean. There is no "time" per say inside an LS
*

*> other that that defined by the scattering propagator that represents the
*

*> evolution of the behavior of the QM particles inside the LS. There is no
*

*> space-time, there is only a Hilbert space here... This represents the
*

*> "internal" states of an observer, and is not explicitly modelable.
*

*> Outside the LS, the situation is very different! We get into the
*

*> question of what type of geometry is used to act as a base space that we
*

*> fiber with LS:s... I think that it might be a Weyl manifold and that a
*

*> particular observation partitions out a Reimannian region from it, but I
*

*> can not back up my intuition right now...
*

*>
*

*> [MP]
*

*> > You are certainly right. At spacetime level this does not work, which
*

*> > again supports the view that subjective time and geometric time
*

*> > are basically different things. Ordering of implication is most
*

*> > naturally induced by the ordering of quantum jumps.
*

*>
*

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

*> set must be considered very carefully!
*

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(;-).

*> 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!
*

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 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.
*

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.

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.

*> 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.
*

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.

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.

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(;-)!

*> 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".
*

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).
*

*>
*

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(;-).

*> [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"!
*

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.

*> 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.
*

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.

*> 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.
*

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 siple: quantum jumper with maximum entanglment

negentropy gain is the winner.

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.

*> 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.

*> snip
*

*>
*

*> [MP]
*

*> > I found stupid blunder in my thinking. Everything
*

*> > is extremely elegant. Self X experiences its subselves as separate
*

*> > objects independent of their structure. Of course. The
*

*> > self Y at the *next* level of hierarchy containing X experiences
*

*> > the subselves of X as an abstraction, kind of average defining
*

*> > what it is to be self. If X contains mouse and house as
*

*> > subselves Y indeed experiences what it is to be mouse-house.
*

*>
*

*> This situation is what we see in Hitoshi's theory! :-) The Self's
*

*> experience of its "subselves" is, as you say, an "abstraction". This
*

*> follow from the way that other LS:s are abstracted as cm point
*

*> particles. The Self Y experiences X only as a model of X. The
*

*> "averaging" is weighed by the particular history of experiences that Y
*

*> "went through" (i.e. quantum
*

*> jumps).
*

*> Thus the particular "mouse-house" is only given in terms of the
*

*> particular experiences (information structures involves within the poset
*

*> of quantum jumps). In other words, I would think of a mouse-house that
*

*> has a small version of a people-house with a shingled roof and plywood
*

*> walls, while another might think of a mouse-house as a little version of
*

*> a bird-nest, etc.
*

*>
*

*> > Entanglement in turn binds subselves to structures and solves
*

*> > whole-parts problem. If entanglement between apple and mom
*

*> > is reduced in quantum jump the associateion apple<--> mom
*

*> > is experienced.
*

*>
*

*> Yes! :-)
*

*>
*

*> 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 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!
*

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.

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 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).

*> 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". :-)
*

*>
*

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).

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.

*> > 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.
*

*>
*

*> 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! :-)
*

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.

*>
*

*> > 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.
*

*>
*

*> 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?
*

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.

*>
*

*> > 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.
*

*>
*

*> 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!)
*

*>
*

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(;-)!

*> snip
*

*>
*

*> [SPK]
*

*> > > Since we have many observers, it is natural to consider that there are
*

*> > > 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
*

*> > has its own subjective reality defined by quantum jump and besides this
*

*> > objective reality is replaced by new one in q-jump.
*

*>
*

*> I agree completely, this is that I have been trying to communicate all
*

*> 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
*

*> role!
*

*>
*

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.

Associatism, connectivism, neural nets, whatever is

one version of computationalism and entanglement provides very

attractive realization of associative learning. When entanglement

between subselves is reduced in quantum jumps association is experienced.

There is also second, more classical realization of associationism:

grandma and apple pie get associated since the selves representing them in

my head learn to co-operate and keep each other in wake-up (read 'alive'!)

state.

Best,

MP

**Next message:**Matti Pitkanen: "[time 505] Music scales and 2-adic numbers"**Previous message:**Stephen P. King: "[time 503] Re: [time 500] Observation models"**In reply to:**Matti Pitkanen: "[time 500] Re: [time 495] Re: [time 494] Observation models"

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