Stephen P. King (stephenk1@home.com)
Thu, 29 Jul 1999 18:51:38 -0400
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! :-)
> > > [MP]
> > > > By the way, motion in zero modes occurs as hopping quantum jump by
> > > quantum
> > > > jump:
> > > >
> > > > x1-->x2--x3---
> > > >
> > > > Just like Brownian motion. In fact, I believe that Brownian motion
> > > > indeed corresponds to this kind of motion. The possibility to
> > > > Brownian motion to move faster than light would not be a
> > > > result of nonrelativistic approximation but real physical
> > > > effect.
> > [SPK]
> > > Yes! WE need to look at this very carefully! I say that the
> > > forward jumps ... -->x1 --> x2--> ...
> > > are dual to "backward jumps" ... i2 <-- i1 <-- ... of logical
> > > implication (following Pratt). It looks like this:
> > >
> > > ... -->x1 --> x2--> ... Time
> > > | |
> > > ... |g |h ...
> > > | |
> > > ... <--i2 <-- i1<-- ... Logic
> > >
> > > were g and h are infomorphic bisimulations...
> > >
> > > [MP] The problem is that logical causation and temporal causation
> > > seem to have different directions unless one replaces A--> B with
> > > not A <--- not B.
> >
> > 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!
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...
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! :-) )
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". 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]
> > > I would take only the upper part of the diagram:
> > >
> > > ... -->x1 --> x2--> ... Times for generation of subselves x1, x2
> > >
> > > and denote selves by x1, x2,.... Since x2 is subself of x1
> > > implication x1-->x2 is realized as set-theoretical inclusion.
> > > Subself is implied by self and in correct temporal order!
[SPK]
> > Yes, but I am trying to discuss how the ordering by inclusion is
> > constructed. If we just assume that the ordering is a priori, then we do
> > not have to deal with the question as to why the selves (or more
> > generally, observations) are ordered as they are. It is this assumption
> > that exists in the classical model of space-time and is in severe
> > contradiction with facts, such as those illustrated in the EPR and
> > delayed choice situations.
[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! 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 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.
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.
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". 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).
[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.
[MP]
> > > There are several interpretations depending on the nature
> > > of quantum jump: interpretation as logical causation
> > > or as genuine set theoretic inclusions: selves as representation
> > > for objects of figure. Entire figure as big self, background and
> > > objects of figure as subselves containing smaller objects
> > > as subsubselves.... Or tree like
> > > structure of linguistic expression...
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"! 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. 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.
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.
snip
> > > [MP] There are objections agains simple rule that unentangled
> > > subselves are experienced as average subself by self
> > > containing them. Probably the subselves must have large
> > > enough mutual resemblance before they are averaged. Perhaps
> > > they must have same p-adic prime, belong to same spacetime sheet:
> > > something like that. Must think about.
[SPK]
> > I think that a situation is required such that a "large enough"
> > sampling of the possible actions of the selves can be had so that a
> > winner can be reasonably predicted. We see an example of this in
> > political elections in a democratic country. The individual electorate
> > (representing the individual subselves) vote and a sample of these are
> > polled by the media to form a statistical sample of the whole and this
> > sample is used to predict the outcome "sooner than the actual counting
> > of the ballots can occur". I think that the situation involved with
> > "selves" is a continuous voting/polling situation since the "elections"
> > occur at every quantum jump!
> > The p-adic prime looks to me to well model the size of the sample
> > population!
[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]
> > > [MP] In TGD framework causality is not involved at level of experiencing.
> > > It is involved at the dynamics determining spacetimes as
> > > absolute minima of Kahler action: that is at the level of configuration
> > > space geometry. In your approach situation is obviously different.
[SPK]
> > I say that since the determination of the particular experience is not
> > modelable locally, as it involves an entire light-like hypersurface, the
> > causality not considered as an experience itself. Only the results of
> > the determination enter into the "picture". So I agree this you here. My
> > only question is in the nature of the "absoluteness" of the minima of
> > the Kaehler action. Umm, what are the quantities involved in the Kaehler
> > action? Is there an associated Lagrangian or Hamiltonian? What
> > "information measures" are related to it?
[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? 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! 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". :-)
> 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! :-)
> 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?
> 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!)
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!
Onward,
Stephen
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