Stephen P. King (stephenk1@home.com)
Sat, 31 Jul 1999 21:12:26 -0400
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
> > > > 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.
[SPK]
> > 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!
[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
> 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.
I think so too!
Onward!
Stephen
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