[time 516] Re: [time 515] Re: [time 513] Rational mechanics and payoff matrix

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Thu, 5 Aug 1999 09:47:12 +0300 (EET DST)

On Wed, 4 Aug 1999, Stephen P. King wrote:

> Dear Matti,
> Matti Pitkanen wrote:
> >
> > Dear Stephen,
> >
> > Thank You for the posting. I think I understand now something
> > about the basic ideas of Pratt's theory. Some critical comments
> > below.
> >
> > I read also the posting about pay-off matrix.
> > Did I understood correctly: payoff matrix tells how much
> > either participant wins in the game in which the 'initial
> > states' of the players are M and N and both
> > players have selected their strategies so that
> > the end result of the game is predictable.
> > Perhaps the interpretation of M and N is not correct.
> > What kind of game is basically in question and what is the
> > interpretation of the indices of the payoff matrix?
> > ***********
> One aspect that we must be carefull about is that the information as to
> the possible moves of the "other" player are usually subject to
> uncertainty.

Certainly in real life: but does not strategy mean a rule which fixes
the move and make thing predictable?

>We see in Peter's work how interactions change the systems
> and thus change the "best" stratergies as the games are played. Remember
> that this is not deterministic in the sense that all information is
> given a priori, information is what the game produces! This is the basic
> idea of Frieden's work and why I advocate it.
> I think that it would help to use Peter's notions to consiter the
> "initiality" notion! We are dealing with "windows" not absolute
> pre-givens, we see this in the way that person to person interactions
> work. We are dealing with the situation where what is a game in one
> framing is a player in another! This follows along the same lines as the
> subject-object situation.
> (a note added in editing) It seems that the "size" of the "window" is a
> measure-like term, it relates to the sample from which the relative
> frequency terms are calculated. It looks like the \epsilon term that I
> had mentioned earlier on that you think is related to the prime... Umm,
> I am thinking hard about this!
> > [SPK]
> > Dear Friends,
> >
> > I have been talking a lot about the work of Vaughan Pratt on the Time
> > List and it has become evident that I need to write a post on his work
> > and how it is relevant to our work here. This post is only a rough
> > sketch that I hope is polished by the interactive discussions to follow.
> > I will start with a quote from Richard Feynman speaking about the
> > Principle of Least Action:
> >
> > "We have lost the idea of causality that the particle feels the pull
> > and moves in accordance with it. Instead of that, in some grand fashion
> > it smells all the curves, all possibilities, and decides which one to
> > take (by choosing that for which our quantity is least)."
> > [Richard P. Feynman, The Character of Physical Law, The M.I.T. Press,
> > Cambridge, 1965.]
> >
> > [MP]
> > I am objecting from the very beginning! The summation over histories
> > is mere formal representation. One can quite well do without it!
> > The calculation of all these histories would involve huge amount
> > of computational work since even in case of single point like
> > particle the space of paths is infinite-dimensional and one must
> > allow also nondifferentiable paths. Using simple Schrodinger
> > equation one avoids all this huge computational activity!
> > The fact is also that whereas Wiener integrals are well defined
> > objects (measures), path integrals do not simply allow rigorous
> > mathematical formulation as measures.
> Matti! Are not the formal representations of Heisenberg's matrix
> mechanics and Schrodinger's Waves and Feynman's path summations
> mathematically
> equivalent? Your point that "calculation of all these histories would
> involve huge amount of computational work" holds for all of these
> methods and is exactly why I am making a big fuss about computational
> issues! Your point here is an example of my reasoning!

What I am saying that only the sum over amplitudes is actually
calculated. This would be like weighing a kilogram of matter by
measuring the energy of every quark, electron and neutrino, separately
and summing up the results. Something like 10^27 protons for instance.
It is easier to put the matter in ordinary scale, takes five minutes,
no need for building particle detectors and atomic smashers(;-).

It is true that path integral in practice reduces to standard
perturbation based on Gaussian integrals: but in this case it is only a
formal and very elegant trick to derive the standard perturbation
expansions. For instance, gauge invariant systems can be treated
in very elegant manner unlike in Hamiltonian formalism: for instance,
the calculation of infinite dimensional Jacobians reduces to perturbative
calculations of diagrams involving fictive particles called Faddeev-Popov
ghosts. The connection of infinite-dimensional integral with particle
physics language is fascinating. But not even
attempt is calculate path integral as a real integral defined by
measure in this practical approach.

To put this in perspective from my side: the path integral is formal
construct. In TGD it would mean summation of all paths in the space of
configuration space spinors to calculate S-matrix elements and would
be useless construct.

In TGD however configuration
space integral over 3-surfaces appears. It is integral in a sense
of actual integration measure and involves
delicate cancellations of standard infinites and nonlocality of
Kahler function with respect to surface to avoid divergences. Using the
language of Feynmann, the task of the demon calculating this
integral would be to sniff the value of absolute minimum of Kaehler
action for each 3 surface Y^3 on lightcone boundary. I believe that it is
possible to sniff the value by symmetry arguments: infinite-dimensional
group of isometries for configuration space.

I have the feeling that integration over non-zero modes could be done
explicitely. There is 'theorem' stating that any path/functional
integral can be reduced to a Gaussian integral around classical
saddle points/maxima of exponential of action. The 'theorem' of course
fails in reality but works for completely integrable systems. I have the
feeling that 'theorem' might work in p-adic context. Integration would
reduce configuration space integral to sum of integrals around
maxima of Kahler function for given values of zero modes. Note that one
needs to consider only fixed values of zero modes since quantum jump
involves localization in zero modes.
[For the actual theorem see: Duistermaat, J., J. and Heckmann, G., J.
(1982), Inv. Math. 69, 259.]

> > Path integral is the only manner to get connection with classical
> > theory but my belief is that it is just here were standard
> > QFT fails. Classical world (spacetime) is much more than stationary phase
> > approximation of mathematically non-existing path integral!
> The "classical world" is a mental construction. It is NOT "out there",
> it is in our head! So we are faced with the question: How does the self
> "calculate" the path that minimizes the action? We know that the q-jump
> is just such a computation; now we need to look more carefully how the
> "measures" (Wiener integrals, etc.) are defined by the "way" that the
> observation is made.

Our philosophies are different.

I believe that our mental constructions are much more than
constructions, they are sensory perceptions, subject to all kinds
of mis-interpretations and errors, but perceptions in any case.

Q-jump is computation but not in the classical sense. I must
be able to mimick quantum jump in order to calculate somthing from
my theory that is simulate what Universe is doing withouth slightest
computational efforts. Computation begins when universe
begins to simulate itself.

But we can forget our different philosophies. We have a common problem!
You are talking about the path minimizing the action.
I would be happy if I could calculate the absolute minimum of Kaehler
action for given Y^3 exactly to simulate the universe.

> > ********
> > [SPK]
> > In the papers of Vaughan Pratt we find an interesting way of thinking
> > about how a particle could "smell all the curves". He proposes that the
> > short-lived theory of mind-body dualism of Rene Descartes can be fixed. Pratt finds
> > that the formalism of Chu spaces addresses the shortcomings of the
> > philosophy of mind-body dualism. The causal interaction of mind and body
> > is defined in terms of Chu spaces and residuation. First we need to set
> > up some preliminary concepts.
> >
> > [MP]
> > I understood the idea. The idea of finding model for how
> > particle measures the action for all possible paths
> > is natural in computationalistic framework. But is this
> > really needed? Only the sum over paths appears and one can avoid
> > this representation totally. If the predictions of the theory would
> > involve also quantities defined by single path, the situation
> > would be different.
> > *********
> Yes, it is necessary. The problem is not completely intractable since
> we only need to model finite subsets of the Universe, it is only when
> one tries to create a model for the Totality that the intratibility
> appears! The problem with 'quantities defined by single paths" is that
> one needs a context (albeit finite) for such quantities to be
> meaningful, for instance, for the transporation of a vector along a
> single path, it is al least necessary that there be a basis against
> which the vector could be compared at each point on the path...
> After talking to my friend David Woolsey, it has become evident that we
> need to look at how finite limitations are placed on the "neighbors" of
> points in the spinoral configuration space! This is equivalent to saying
> that a given local system can only observe (interact) with a finite
> number of other local systems. It is my opinion that the requirements of
> bisimulational equivalence are what are involved...
> snip
> [SPK]
> > The concepts of Mind and Body speak to the distinct aspects of the
> > Universe, matter and information. It is proposed that matter (qua
> > material configurations) and information (qua "meaning") are not
> > identical, they are complementary or "dual" aspects of finite subsets of
> > the Universe (which is identified with the totality of existence and is
> > non-dual in-itself (or "self-dual"?) and tenseless).
> >
> > Pratt told me in a e-mail today when I asked him about how to define
> > Mind and Body:
> >
> > "Perhaps "mental" and "physical" would have been better, illustrated by
> > such examples as "predicate" ("is red") vs. "subject" ("the ball"), or
> > "thought" vs. "thing", as instances of mental vs. physical."
> > *********
> >
> >
> > A quote from ratmech.ps:
> >
> >
> > "We interpret interaction as causality. Causality is directional, but
> > the direction depends on whether we have in mind physical or mental
> > causality. We interpret $x$ |= $a$ ambiguously as the time elapsed
> > between the occurrence of the physical a and its impression on the
> > mental state $x$, and as the truth value of $a$ as a proposition. [The
> > reader may be understandably concerned at this identification of
> > physical and ostensible mental propositions. However a Boolean
> > proposition about events A is of type 2^2^A and $each exponentiation$
> > dualizes, whence two of them return us to the physical plane. The truly
> > mental propositions are constituent descriptive clauses of a physical
> > DNF formula, each describing a possible world.]
> >
> > [MP] I am not sure whether I understood: I blame
> > my formal philosophical training(;-).
> > ******

> That is ok, we learn from each other as we go! :-) Could you point to
> a particular statement here that is difficult?

[MP] DNF. Each exponentiation dualizes. We interpret.... proposition.

> > [SPK]
> > The former is physical causality or $impression$, flowing forward in time
> > from events to states. The latter is mental causality or $inference$,
> > flowing backwards
> > in time from the thought of $a$ to the inference of $a$'s occurrence. In
> > this way time flows forward (from the usual point of view) while logic
> > flows backwards. This is the $primary$ interaction, and it occurs only
> > $between$ the mental and the physical planes.
> > ****
> >
> > [MP]
> > I tried to understand this in following manner.
> >
> > a) Physical causality corresponds to the causation
> > physical event--> mental event, impression: Sensory experience.
> No, Physical causality is what traditional "forces" are representing.
> Mental events are the information concerning such.

[MP] Yes this of course also my view an standard view
 but this was my interpretation of 'The former is physical causality or
$impression$, flowing forward in time from events to states'. 'From
events to states'! Events correspond to 'physical plane' and states
correspond to 'mental plane'. This causation would be from mental to
physical or vice-versa rather than mental to mental or physical to

> > b) Mental causality of inference: Thought of a ---> inference of
> > a:s occurrence. I would identify this typically as motor activity.
> > I decide to raise my hand and it raises.
> > But it seems that mental causation and physical causation are understood
> > to be duals of each other.

> Here you are confusing mental and physical causalities.

[MP] Again this was my interpretation of 'The latter is mental causality
or $inference$, flowing backwards in time from the thought of $a$ to
the inference of $a$'s occurrence.' My own view is
of course quite different.

> The neuro-motor
> activity follows physical causality, the particular action that results
> follows from the selection of one particular physical movement out of
> the many possible by the action of mental inference, the mental
> (information) state dual to the neuronal pattern "consults" all possible
> physical events and select the one that closest one to the movement
> required. (We need to frame this in the mathematics of bisumulation, my
> wording here is merely metaphorical!)
[MP] I think this is roughly my view: quantum jump
selects between degenerate braches of multifurcation of
spacetime surface: this is volitional action. And the ordering of
quantum jumps automatically fixes the time ordering.

> > c) One could argue that experiments of Libet about active
> > aspects of consciousness (EEG activity starts before
> > I decide to raise my hand) shows that mental event is later
> > than physical event and mental to physical goes backwards in
> > time. On the other hand: we experience these two kinds of causations
> > as different. How this difference is explained if impression and
> > inference are identified? What in these events make matter
> > or mind active agent?
> > **************
> Umm, this is in accord with the "cognito, ergo erram" (I think,
> therefore I was) aspect of Pratt's notion! The "identification of
> impression and inference" is equivalent to the identification of wave
> and its Fourier transform, they are mathematically dual! Both matter and
> mind are "active"! The notion of invariants and "static" quatities are
> merely the result of synchronizations or, more generally, like the
> situation seem in dissipative structures. WE derive "Being" from
> "Becoming"! :-)
I understand the basic philosophy: interactive dualism might be
the proper classification for Pratt's approach. Matter and Mind
would be connected by kind of Generalized Fourier Transform.
You certainly already know my objections agains this so that I do
not repeat them.

Subjective/conscious Being is Becoming. Here I agree but
on different grounds.

> > [SPK]
> > We thus see that the seat of casual interaction in Cartesian duality is
> > not the pineal gland but the identification of impression and inference.
> > We write $x$ |= $a$ as expressing equally the impression of event $a$ on
> > subsequent state $x$ and the deduction by state $x$ of the prior
> > occurrence of event $a$. The Cartesian dictum $cogito, ergo sum$ is the
> > case of this where $x$ is the thinker's state and $a$ the event of his
> > or her existence." ... "Examined closely, our analysis shows that
> > Descartes' dictum properly tensed becomes $cognito, ergo eram$ (I
> > was)..." ...
> >
> > [MP]
> > I think I have understood the idea. Interaction within each plane is
> > derived from primary interaction between matter and mind
> > by some kind of conscistency requirements.
> > But how matter-mind interaction is defined?
> > *********
> This is the key question! We look at the behaviour of matter and notice
> that its dynamics can be considered as transforming the information
> content encoded in the configuration that are changed, likewise, we can
> look at a database of information and consider how changes in it can be
> used to identify the dynamics of the matter that encodes the
> information.
> I will try an example, I may be very wrong here! Consider the
> configuration space X formed by identifying a material dynamical
> system's events to points and consider a space I where each point
> represents a different description of the system. We can see that when
> we consider the path through X defined by the particular transformation
> of the system, there would also be a "path" defined through I, but how
> is it given? The "connection" that links points in I is one of logical
> entailment, and the connection that links points in X is one of
> "physical" causality.

Does the duality between matter and mind imply that the two spaces
are more or less isomorphic from the requirement that
it presevers some basic structures? Is the mapping matter to mind
one-to-one mapping?

OK. Let's forget this and ask what 'description' really means.
Is it possible to describe system as such? Or are all descriptions
only comparisons as they seem to be in my own approach (contents
of cs depend on initial and final states of qjump).

Is the number of descriptions of the system same as the number of
configurations of system? I think one should ponder this problem first?

> > [SPK]
> > "We pass now to interaction $within$ each plane, whether
> > physical or mental, which we derive as $secondary$ interaction from the
> > primary form with the aid of $residuation$, a pair of operations on
> > binary relations that constitutes dynamic implications forwards and
> > backwards in time: For K = 2, =| as a matrix of 0's and 1's is an
> > ordinary binary relation: the event $a$ either is or is not related to
> > state $x$. This relation is understood ambiguously as a two-valued
> > distance in either time-space (a =| x, physical) or information space
> > (x|= a, mental)." (pg. 8)
> >
> > [MP]
> > I understand time-space but what would information space mean
> > mathematically?
> > Are these spaces isomorphic?
> > *******
> No, they are not isomorphic. Pratt says that the graphs of functions
> and antifunctions are opposites, anti-parallel(?). See page 4 of
> ratmech.ps...
 [MP] I will look. I am wondering whether these spaces have same
dimension. Some concrete example might help.

> > [SPK]
> > Here Pratt discusses how the $direction$ of causality depends on
> > whether one is considering the physical aspects of a subset of the
> > Universe (identified by Hitoshi as a Local System) or the informational
> > aspect of a LS. A LS is considered as a generic model of an observer or
> > measuring system, capable of registering the dynamical behavior of other
> > LSs via the mechanism of $ coinductive bisimulation$ between LSs.
> > Bisimulation is discussed in Peter Wegner & Dana Goldin's paper
> > (http://www.cs.brown.edu/~pw/papers/math1.ps)
> >
> > "Symmetry of equivalence gives rise to the terms bisimularity and
> > bisimulation that captures the if-and-only-iff nature of relations
> > between equivalent objects. Coinductive bisimulation captures mutual
> > two-way behavior simulation of each system by the other." (pg. 16,
> > Mathematical Models of Interactive Computing, By Peter Wegner & Dana
> > Goldin)
> >
> > [MP]
> > I think that simulation is what selves are doing all the time.
> > They must do so. Higher selves can have only abstracted
> > average experiences about the life of subsubselves
> > and cannot catch at all what it is to be subsub...subself.
> Yes, we agree on this. I am saying that the mathematics of bisimulation
> that Peter discusses are the best way to think of this. Peter's
> "expressiveness" captures your thinking about "Higher selves can have
> only abstracted..." :-)
> > This forces selves to build simulations of the subsub...selves
> > on their on spacetime sheets. We are indeed doing busily
> > Monte Carlo calculations on elementary particle physics.
> That does this tell us, that we resort to random samples to model
> particle properties?!
[MP] Yes. We simulate statistical determinism. Probability
distributions for the configurations of outcoming particles.

Also discretized functional integral is evaluated by Monte
Carlo. This is like measuring the are of lake by surrounding
it by square of 10 kilometers times 10 kilometers and bonbarding
it and counting the hits per the total number or bombs
in this area to get the area of the lake. Very simple computationalism!
Very far from construction of infinite-dimensional geometries but those
who have the money can understand what is done and find these activities
rather rational as compared to playing with infinite-dimensional

> > I am pondering concrete mechanisms of how this could
> > be possible. This leads immediately to the question
> > how selves could replicate. DNA replication would be
> > only special case of this and perhaps induced
> > by the replication of cognitive spacetime sheets. A more refined
> > possibility to is to generate messages generating desired cascades
> > of selves of subselves of... on receiver. These
> > self-cascades would be memes/ideas/thoughts. Nerve pulses,
> > written and spoken language, movies, art..., email discussion
> > groups...
> > **********
> The idea that Natural Selection is a Universal Principle is becoming
> more tenable. Lee Smolin and Loius (?) Kauffmann and advancing it in
> their books... Again, we see this reflected also in Peter's model of
> computation; interactive computers "evolve"!

[MP] I found that Pinker (computationalist) was rather near to my
views about Natural Selection, whatever it really means.
He did not agree with those who claim that it reduces to say
self-organization in classical sense (no
quantum jumps so that everything is determined from the initial
values). Or that complex determistic systems automatically generate
something which might be called life. There must be some local principle
leading to selections and selection must be something absolutely real.

I identify the basic principle as p-adic evolution automatically
forcing evolution and implied by localization in zero modes implying
classicality of observed world. Strong NMP is second principle involved.
And self-organization by quantum jumps. Self-organization
could be understood as SELF-organization: selves are indeed generated.
Selves within selves within ...

> > [SPK]
> > The physical configurations of a LS's observations are ordered via
> > physical $implication$ and the information of a LS is ordered via the
> > mechanism of logical $entailment$. Individual physical properties are
> > called $events$ and individual mental or informative properties are
> > called $states$ in Pratt's presentation.
> >
> > [MP]
> > I understand now this better. You have matter and mind and
> > must have two different causations. I am somewhat confused
> > of terminology. Why properties are events/states? I have been
> > accustomed to assign properties with states.
> > ************
> I understand. Pratt uses "events' to represent physical aspects and
> "states" to represent mental, or more generally, informational aspects.
> :-)

> > [SPK]
> > Pratt says:
> > "When we unravel the primitive causal links contributing to secondary
> > causal interaction we find that two events, or two states, communicate
> > with each other by interrogating $all$ entities of the opposite type.
> > Thus event $a$ deduces that it precedes event $b$ not by broaching the
> > matter with $b$ directly, but instead by consulting the record of every
> > state to see if there is any state volunteering a counterexample. When
> > none is found, the precedence is established. Conversely, when a Chu
> > space is in state $x$ and desires to pass to state $y$, it inquires as
> > to whether this would undo any event that has already occurred. If not
> > then the transition is allowed." (pg. 9, ibid.)
> >
> > [MP]
> > I already protested about the idea of doing the huge calculational
> > work involved in calculating the action of every path in
> > Feynmann integral.
> >
> > Classical nondeterminism of Kahler action however leads to
> > discrete version of Wiener integral in
> > the calculation configuration
> > space integral. In this case the representation
> > is *not* formal and real calculation of the contributions
> > of various spacetime surfaces with degenerate
> > Kahler action is needed. This seems to require the
> > calculation of all possible spacetime surfaces consistent
> > with the initial data.
> > ********
> To be honest, I looked at the first chapter of your (on-line) book and
> I wonder how phenomena can be calculated easily with it! I am looking at
> the philosophical aspect of Quantum gravity, I firmly believe that
> Nature is performing computations that make our miserable machines look
> like stone age tools! :-) I believe that physics is really about
> figuring how Nature works so that we can aim the cause-effect in a
> direction more friendly to our human needs.

The point is that computations are not involved.
Symmetry principles dictate almost everything. What can be done
at this stage is to derive theorems (actually 'theorems'): numerical
calculations are completely out of question at the level
of infinite-dimensional configuration space.

For instance, particle mass squared spectrum is fixed completely from
Super Virasoro invariance. The masses of light particles can be
calculated from p-adic thermodynamics: symmetry
dictates again almost everything. The calculations are
extremely simple since perturbation theory in powers of 1/p
converges extremely rapidly. Predictions are excellent, which
made me to take p-adics deadly seriously.

My strong belief is that physics at this level cannot be done
by computing but using symmetry arguments to guess the result and
then proving it. Calculation of S-matrix elements (have not even tried
that although I know from symmetry arguments that string model
type formalism results) should
also reduce to symmetry principles.

I already mentioned the p-adic version of Duistermaat-Heckmann theorem
could make it possible to calculate the functional integrals involved
analytically: the 'theorem' of real context would be theorem in
in p-adic context.

> > [SPK]
> > Here we are getting closer to our opening remark by Feynman! We must
> > note that in the preceding quote from Pratt, idealistic conditions are
> > considered. In the situation of Local Systems, as modeled By Hitoshi, it
> > is assumed that only a finite number of states (events) can be
> > "consulted" in a finite amount of time and that the "record" is subject
> > to falsification unintentionally by noise or intentionally by secondary
> > "eavesdropping" observers.
> >
> > Going back to Feynman's notion, we must ask
> > how it that the curve that minimizes the action is selected? We are
> > considering the transition of events $x$ to $y$ and dually, of states
> > $a$ to $b$, to be defined by such minimized curves.
> > Now, in traditional physical thinking we have a clear notion of that
> > the curves connecting physical events, they are called $geodesics$ and
> > are considered to be the paths that rays of light take in space-time.
> > The question of whether space-time is defined by the rays or has a
> > priori ontological status will not be addressed here. I merely say that
> > it seems to be enough to consider that a space-time is defined by the
> > Diff^4 group of a set of light-rays.
> > We must note that traditional physics also assumes that a single
> > space-time exists and thus only a single unique set of geodesics, as a
> > light-cone structure, need to be considered. But as we have seen in
> > situations that consider the quantum mechanical properties, it is
> > impossible to define a single unique light-cone structure for all
> > subsets of the Universe since the definition of such implies that a
> > single $anti-set$ of curves exists connecting the information states
> > entailed by the single set of physical events and that this anti-set
> > exists a priori as a "pre-computed" Boolean lattice of logical
> > inference.
> >
> > [MP]
> > Anti-set corresponds to information space and set to space?
> > There is somekind of one-one correspondence.
> > ********
> Of sorts, but we are taking category theory, so we have equivalence
> classes of each. Infomorphisms (or residuations, same thing) are
> identifications between subsets of the the two equivalence classes. So
> we match a particular mind with a particular body by considering the
> duality: what mind best describes the body that best implements the
> mind. So the notion of MNP is very close to my thinking! :-)

Amusing coincidence. I am just pondering the following problem. How
on Earth do I know that the the me of to day is the me of yesterday if my
self has slept over night (not existed). How do I even know
that the me of yesterday existed subjectively: perhaps I was
born when I woke up?(;-)

I think that the solution relies on two kinds of memories:
'memory' with respect to *geometric time* and memory
with respect to subjective time (memories about
previous quantum jumps).

Geometric 'memory' is made possible by
the temporal duration of cognitive spacetime sheet represeting
me: might be of order lifetime.
Geometric memory can be also about geometric future and is more
like temporal intentionality, plans, beliefs, expectations about
what happens if there were no selves around making quantum jumps
and replacing spacetime with a new one and spoiling everything.

Second memory is subjective memory: self experiences all
the quantum jumps it has made after wake up
as single whole and is thus an extended objected in
subjective time (measured by quantum jumps).

This is new feature in theory: earlier I was forced to believe
that single quantum jump determines competely the contents of
cs and that genuine memory about previous moments of cs
is not possible and results only from simulation of past.
The notion of self allows however to give up this
assumption: subjective memory about earlier conscious experiences
after wake-up is possible.

Subjective memory forms kind of a heap of
geometric 'memories'= expectations of future and this entire
heap is experienced. For instance, comparison of subjective
history (what actually occurred) with geometric
histories (expectations) should be primitive mental act not
modellable in any manner. Perhaps all comparison reduce
to this fundamental act of comparison.

OK. After this lengthy introduction I go to the
possible solution of problem. Although I have no subjective
memories about yesterday's me, I have the geometric memory about
my body existing yesterday and I deduce that this body
must have been conscious since this body resembles
my recent, very conscious body. So I indeed identify my yesterday
me as the best fit to my recent body!

BTW, what might be the fundamental irreducible mental
acts performed by conscious mind (self) and not modellable?
Also computationalist should answer this question.
Comparison could be one such act. What other irreducible
mental acts one could imagine?

> > [SPK]
> > The a priori existence of such a Boolean lattice must be
> > considered
> > carefully! If such exists in the same sense that the Universe exists, we
> > are faced with the question as to how this "object", which would have
> > the status of a Platonic Form, would be $knowable$ by the infinity of
> > finite subsets of the Universe or LSs. It is obvious that there is a
> > deep difference between the existence of something and the ability to
> > have useful knowledge of it. The ability to gain useful information
> > about something takes into a discussion of thermodynamics and I wish to
> > reserve that topic to a latter date.
> >
> > It might be asked why am I proposing a dualistic model of interactions
> > instead of a monistic one; to answer this I shall again quote Pratt:
> > "If one truly believed that the [subsets of the] universe proceeded via
> > state transitions, this might seem a rather roundabout and inefficient
> > way of implementing those transitions. However it seems to us ... that
> > the more likely possibility is that the [subsets of the] universe only
> > $seems$ to proceed via state transitions, due perhaps to our ancestors
> > having ill-advisedly chosen monism as the natural world view, perhaps
> > millennia before the rise of Cartesianism, perhaps only some years after
> > its decline. What we conjecture actually happens is that events signal
> > states forward in time, or equivalently that states infer events
> > backwards in time, and the world we imagine we live in is simply what
> > that process looks like to its inhabitants when interpreted
> > monistically.
> >
> > [MP] I did not quite understand what state transitions meant in this
> > context.
> Each physical event (including a space-time framing!) has a particular
> state associated; when we consider the evolution of physical systems by
> transitions of events, for example: E_1 -> E_2 -> E_3, there is a
> corresponding evolution of the associated states, for example: S_3 ->
> S_2 -> s_1.

OK. I was thinking quite different thing. The terminology confuses

> > [SPK]
> > Why this theory as opposed to any other? Well, certainly no other
> > theory has satisfactorily explained this causal interaction of real
> > mental and physical planes as conceived by Descartes."
> >
> > [MP] Certainly monism is not enough. But is even dualism enough? There
> > is also the possibility of tripartism. Matter as geometric form,
> > ideas and subjective existence.
> This is a very good question. I think that you are right, but we do
> need to synchronize our thinking/wording further... I see "subjective
> existence" as the dynamic union of the duality, so the self reflects a
> finite image of the Universe. And this tends to infinity in the limit of
> eternity!



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