Matti Pitkanen (matpitka@pcu.helsinki.fi)
Wed, 28 Jul 1999 14:13:10 +0300 (EET DST)
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.
See below.
On Mon, 26 Jul 1999, Stephen P. King wrote:
> Dear Matti,
>
> Focusing on two notions...
>
> Matti Pitkanen wrote:
>
> snip
>
> > [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 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!
>
> 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.
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 mosta
naturally induced by the ordering of quantum jumps.
> 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.
>
> > 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...
> >
> snip
>
>
> > snip
> > [MP]
> > > > Actually the measurement can be said to be disjoint in well
> > > > defined sense. Separate selves mutually unentangled.
> > [SPK]
> > > > Yes! This is why separate selves have separate indentities! I say that
> > > > experiences are "almost disjoint" since they differ in at least the
> > > > "point of identity". The notion of a fixed point under a given set of
> > > > transformations is what I considered before I has educated by Peter's
> > > > work. The Self, within Peter's formalism, is a greatest fixed point, I
> > > > think. Umm, I need to review his paper:
> > > > http://www.cs.brown.edu/~pw/papers/math1.ps
> > [MP]
> > > Quantum entanglement is what destroys selves. For instance, could
> > > it be that the separate notes in chord correspond to
> > > frequency-selves which have entangled to form chord-self?
> > > This would explain why we do not hear separate notes but entire
> > > chord.
> >
> > This is why we can not do a "Vulcan Mind Meld"! It would be
> > impossible to unentangle the two minds!
> >
> > [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.
>
> 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.
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.
> snip
> [SPK]
> > > > How is the information content of this localization given? This is an
> > > > infinite NP-Complete problem that requires ETERNITY to compute! It can
> > > > not be given a priori!
> > [MP]
> > > TGD generously provides this eternity! The quantum computation defined
> > > by informational time development operator lasts infinite amount
> > > of lightcone proper time (not our psychological time which
> > > is quite different thing).
> >
> > Yes! :-) I just try to think about how each observation involves
> > its own lightcone of causality...
> >
> > [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.
>
> 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?
>
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.
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 therms of canonical momentum
densities uniquely. Canonical quantization of TGD fails totally:
this was the deep reason for configuration space geometry.
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 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.
> snip
>
> > [MP]
> > > I understand what you are saying. This is probably the only possible
> > > consistent philosophy in the framework in which one does not introduce
> > > quantum jump and replace single objective reality with all
> > > possible objective realities allowed by physical theory.
> >
> > Huh, how do you conclude that?
> >
> > [MP] Well, I don't know! Somehow I interpreted the idea about
> > several almost non-intersecting spacetimes as geometric counterpart
> > for giving up the notion of single objective reality, which
> > is quantum concept.
>
> 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!
>
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 qjump.
> snip
>
> > [MP]
> > > I think that a lot of confusion is created by different views about
> > > imbedding space. I do not regard its points as reprsentations of events:
> > > it is quite too simple thing for that.
> >
> > Indeed! But, it is helpful as a concept to start out with...
> >
> > [MP]
> > OK. It is certainly what Einstein believed. Classical geometric
> > structures in spacetime would characterize entire physics.
>
> Sure! Invariance structures are defined by geometry, so a physics = a
> geometry.
>
> Next I would like to better understand the problem you have with
> Frieden's work...
I told in earlier postings about the interpretational problems.
Unfortunately I do not remember the dates of these postings.
Best,
MP
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