Stephen P. King (stephenk1@home.com)
Wed, 11 Aug 1999 23:27:31 -0400
Subject: [time 516] Rational mechanics and payoff matrix
Date: Thu, 5 Aug 1999 09:47:12 +0300 (EET DST)
From: Matti Pitkanen <matpitka@pcu.helsinki.fi>
To: "Stephen P. King" <stephenk1@home.com>
CC: time@kitada.com
Dear Matti and Friends,
Please forgive the slowness in my response and the miserable condition
of my grammar. I have not been myself lately! :-(
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?
> > ***********
[SPK]
> One aspect that we must be careful about is that the information as to
> the possible moves of the "other" player are usually subject to
> uncertainty.
[MP]
Certainly in real life: but does not strategy mean a rule which fixes
the move and make thing predictable?
[SPK]
This "fixing" is contextual; it only applies for the particular history
and the available information. I call this "contextual definiteness",
contrasted with the "contrafactual definiteness" of classical logic. It
is easy to forget, and slip back into the classical mode of thinking. We
must constantly be on guard against this, for it clouds our
understanding. For example, when we say that a "rule is fixed", is it
necessary that this "fixing" be such for "all time"? The grue paradox
shows the serious problem that this creates!
http://bayes.phil.uiuc.edu/417/grue.html
[SPK]
>We see in Peter's work how interactions change the systems
> and thus change the "best" strategies 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 consider 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 Schroedinger
> > 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.
>[SPK]
> 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!
[MP]
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(;-).
**
But, you would admit that somehow Nature is doing this! The reality
that is represented by an n-body Lagrangian is computed by Nature
somehow, else the orbits of planets would instantly dissolve! Then we
think of time passing for a system, be it of planets or dust or a living
organism, we must consider how it is that each event that could be
measured of such by another system is selected. You speak of q-jumps an
their initial -> final aspects, with this I concur, but I am saying that
we are missing something. The logical implication or entailment
relations that can be drawn from the information encoded in the events
plays a strong role. It is insufficient to claim that event A physically
causes event B without considering that the information state of B
(represented by B*) be necessarily implied or entailed by the
information state of A (represented by A*). Thus we say that A causes B
iff B* entails or implies A*, thus time is dual to logic, they "flow" in
opposite directions. What makes the difference in this line of thinking
versus that of the traditional thinking is that it takes into
consideration the information content of a given configuration of
matter, the latter classical model only considers matter, its
information content, and thus a mind, is a meaningless epiphenomena at
best.
[MP]
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.
**
Exactly why do we do perturbation? Because we do not know how to solve
n-body problems using infinitesimal calculus! This fact is forced upon
us because the n-body problem has strongly non-integrable situations!
Why do we continue to "kick against the prick"? I admit that the
integration problem may not be easy to deal with, I am not a
mathematician so do not have a solution for such, but I have read of
formalisms such as "interior set theory" that may help us in this
endeavor.
http://link.springer-ny.com/link/service/journals/00153/bibs/5034004/50340269.htm
http://atheism.org/library/modern/graham_oppy/t_finite.html#fn4
http://www.friesian.com/calculus.htm
And Prigogine's Brussel's school is making bold attempts in this
direction!
[MP]
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.
**
Sure, but this Demon can not violate the second law in the meantime!
The problem that I see, and I could be seriously wrong, is that pleading
symmetry arguments is equivalent to postulating a priori synthetics. If
we assume that particular values are given a priori (synthetics) then we
are saying that these values are somehow calculated for free by the
Universe! If we postulate the existence of an Oracle, such as a Platonic
Form, (the quintessential a priori synthetic!), then we are required to
explain how we communicate with such. Either way we are required to
generate entropy (loose free energy) to gain knowledge.
Please look at my link to Maxwell's demon:
http://members.home.net/stephenk1/Outlaw/maxdemon.html
[MP]
I have the feeling that integration over non-zero modes could be done
explicitly. 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.]
**
The serious lack of integrability in n-body systems makes this a
serious problem! Have you ever read Poincare's discussion of the n-body
problem? Or read Prigogine's The End of Certainty : Time, Chaos, and the
New Laws of Nature?
[MP]
> > 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!
[SPK]
> 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.
[MP]
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.
**
I am talking about space-time as being a "precondition of experience",
to quote Von Weizacker! A perception is an act of selection from an
equivalence class (if we can use that notion) and we cannot assume that
the particular properties are given prior to the perception, this is a
clear case of the Einstein-Bohr disagreement. The fact that perceptions
are prone to errors is the proof that objects do not have particular
properties in-themselves, it is the subject-object interaction that
defines the properties, and since we include dynamic behaviors in the
class of properties, we are saying, with Erieden, that the observation
defines the physics!
[MP]
Q-jump is computation but not in the classical sense. I must
be able to mimick quantum jump in order to calculate something from
my theory that is simulate what Universe is doing without slightest
computational efforts. Computation begins when universe
begins to simulate itself.
**
Yes, that is what I am saying! But, the act of the Universe simulating
itself has a thermodynamic price! To be sure, the Universe, qua the
totality of existence, does not "simulate itself", it merely "is"
itself. It is the acts of mutual simulation among the subsets of the
Universe that is the subsets evolving toward equilibrium relative to
each other. This equilibration, from the physical aspect, gives us
thermodynamics and this translates over to a sense of flow, an arrow of
time. The duality picture then explains how, for each subset of the
Universe (an LS), the particular configurations that are taken along the
way are selected by the logical entailment requirements of the mutual
simulations of the LSs.
The bi-simulations occur between the subsets of the Universe, and it is
they that constitute all interactions, and thus the act of observation
is complementary to the maximization of thermodynamic entropy.
We must look carefully at what we mean by "classical computation"! If
we are speaking of Turing Machines, we can easily prove that any
classical differential equation can be matched to an equivalence class
of TMs (differentiated by language) and so we can see that the Newtonian
"clockwork" can be well-represented by a TM. Peter's discussion of the
differences between well-founded and non-well-founded sets points out
the essence of this argument. TM's are defined within precise initial
(or final) Cauchy boundary conditions and are invertible. (On a side
note, the halting problem of TMs seems to represent classical chaos! It
is deterministic, but its simulation time is irreducible!)
[MP]
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.
********
Ok, (Y^3 is the light cone surface? I forget)… if so then we indeed
have a common problem, but I am wondering if your requirements of
"absolute minimum" and "exactly" are too strong! Where is the \epsilon
of error fit in? I see a situation were the finite bound on the ability
("expressiveness") of a Local System allows for local minima and
approximations, not absolute (global) minima and exact bi-simulations.
Pratt's example of the strict binary involution of a Chu spaces give us
a model that satisfies your strong requirements, but it is obvious (from
the fact that error and irreversibility are experienced) that exact
simulations are not realistic! We should say that it is the errors in
the bi-simulations among the LSs (as subsets of the Universe) that given
us time, for if exact bisimulations could occur, there would be no time
or motion at all. Every action that could occur would occur in an
arbitrarily small duration and such a situation converses to 1/
\infinity or zero. Thus I say that time exists because everything can
not happen at once. And this discussion does not get into the subtleties
of non-commutativity and concurrency.
> > [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.
> > *********
[SPK]
> 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 intractability
> 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 transportation 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(;-).
> > ******
[SPK]
> 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.
Ok, I will try! :-) Pratt gave me this definition in response to my
query: "DNF is disjunctive normal form. A logical formula is in DNF
when it is a disjunction of conjunctions of literals. (A literal is a
propositional atom or its negation.)"
The notion that "each exponentiation dualizes" relates to how
residuation works, thus if we take the power of a SET we get an
anti-Set, and if we that the power of it in turn, we get back a Set.
His definition of "truly mental propositions" seems to relate to the
use of Complete Atomic Boolean Algebras (CABAs) which completely
describe the logical relations of a closed system, I think. :-)
It is best to read and re-read ratmech.ps, Pratt's paper to understand
his subtle notion. This is a paradigm shift, and a big one! We can not
understand Pratt (or Wegner) when we use the old paradigm…
> > [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.
[SPK]
> 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
physical.
Yes, that is the whole point of the Pratt's duality. Look at the first
paragraph of section 2, pg. 3. "A physical event a in the body A
impresses its occurrence on a mental state x of the mind X" and "dually,
in a state x the mind [X] infers the prior occurrence of [an] event a".
After thinking more about your point here, I see what you are saying and
I can only conclude that your reading of ratmech is incomplete!
Pratt clearly says in the abstract: "We apply Cartesian logic to reject
…an assumption that Descartes somehow himself neglected to reject, that
causal interaction *within* these planes is an easier problem than
between." I would agree with the criticism that Pratt is not a good
philosopher when it comes to arguing his idea to death, like most
professional philosophers, but I can forgive that and "read between the
lines" and grasp the implications of his words, couched as they are in
the jargon of computer science.
It is when we try to model the physical interactions (Body <-> Body) or
model the mental interaction (Mind <-> Mind) that we must use the
algebra (if it could be called that) of residuation. The mechanics" of
bisimulation make this point obvious! Common sense aside, my physical
body does not interact directly with your my body. The choice of my
body's next event that would appear to the material monist as a
"reaction" by considering all possible mental states that would be
entailed by such a change, the one state that best encodes the logical
entailment has a dual event, which is the one that is chosen as the next
event of my body.
You see, we adapt to our expectation or prediction of each other's
behavior, not the actual behavior, since "actuality" is not "out there"
in some unique absolute space-time, it is contextual, tensed, contingent
and local. This is obvious since we can not perceive each other
directly, we can only perceive our own subjective version of each other.
This follows from the notion that knowledge of the In-itself is not
obtainable, be it the Universe or any of its subsets. All we can do is
to choose a "next" event and state that best fit the context. Exactly
what the mechanism is still a mystery, but there is evidence that
somehow consciousness influences the probability distributions of
"random" events, http://www.fourmilab.ch/rpkp/pk-rad.html , and it need
not be that of a human!
[MP]
> > 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.
>
[SPK]
> 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.
**
OK.
[SPK]
> 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 bisimulation, my
> wording here is merely metaphorical!)
>
[MP] I think this is roughly my view: quantum jump
selects between degenerate branches of multifurcation of
spacetime surface: this is volitional action. And the ordering of
quantum jumps automatically fixes the time ordering.
Sure, but the total ordering of the q-jumps is NOT a priori given, it
simply can not be as such a notion would directly contradict the
experimental evidence of QM, such as interference of electrons "fired"
one at a time through a two slitted barrier and particularly, "quantum
eraser" experiments.
[MP]
> > 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?
> > **************
[SPK]
> 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"! :-)
[MP]
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.
**
Ok.
> > [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?
> > *********
[SPK]
> 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.
[MP]
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?
***
Let me address the first question: "Does the duality between matter
and mind imply that the two spaces are more or less isomorphic from the
requirement that it preservers some basic structures?"
To be honest I fail to see the connection between the isomorphism
(which they are not, they are "complementary" like a directed graph and
another graph with the directions reversed) and the "requirement that it
preserves some basic structure". What structure? There is no "inherent"
structure in a so called "objective" sense! We only have all possible
events and all possible states as the constituents of the Universe. The
distinction between the two is only a subjective one, dependent on the
relational structure that the LS, as a subjective observer, imposes due
to its history of bisimulations with other LSs. Thus the duality only
holds between the LS as their relational structures, there can be no
particular relation outside of these.
Your second question: "Is the mapping matter to mind one-to-one
mapping?" When it has that property, in the sense that the residuation
generates a greatest fixed point under the Chu transform, an example of
which is the exponentiation operation, between the set of possible
events of a LS as a body, and the anti-Set (or Set^op) of possible
states of the LS as a mind.
Your third question relates to the nature of a description. What is a
description? Could be say that a description of a system is an internal
relational structure that "represents" for the observing system. This is
what is happening when a perception occurs! When we generate a poset of
symbols that is a physical implementation of the information inferred
from the bisimulational observation. Let's say that the poset in
question is a book. When another observer "reads" this book, what is
going on? First, the producer and the reader of the book must share
sufficient similarities in their posets of observations such that a
third observer could bisimulate both of them within a single maximally
self-consistent observation.
Your fourth question: "…are all descriptions only comparisons, as they
seem to be in my own approach (contents of cs depend on initial and
final states of q-jump)." Well, your model seems to say that minds are
given as "cognitive space-time surfaces", so if the residuation
formalism, when applied to your model works, then we are only differing
in semantics. :-)
Your final question is interesting: "Is the number of descriptions of
the system same as the number of configurations of system?" Well, it
appears that there is a connection between these two since each distinct
(disjoint?) description has to be implemented or encoded in a distinct
configuration of the system. Thus, when we consider a "quantum
computation" with its superposition of state vectors, we are superposing
the information content thereof also, if we think of state vectors as
being physical. If we think of quantum state vectors as "information",
then we expect a complementary superposition of the physical events
entailed by such. I see Penrose's "one graviton criterion" notion as an
example of this! Umm, this does smell like TGD!
> > [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?
> > *******
[SPK]
> 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.
I don't know the answer, but I am very interested! Perhaps we will find
out as our discussion on the List continue. :-)
> > [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.
[SPK]
> 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..." :-)
[MP]
> > 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.
[SPK]
> 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 bombarding
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
spaces!
I wonder why this is so? :-) Are we using a method that Nature uses to
"compute" what "locally happens next"? I think so! I see something
similar in the way that the Hausdorff dimension of a fractal is
calculated… Umm, I would like to hear more about the Monte Carlo method,
as you see it. :-)
[MP]
> > 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...
> > **********
[SPK]
> 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.
**
Sure, I agree. I see this happening in Hitoshi's LS model, but I am not
sure what you mean by: "absolutely real". Do you mean that selection is
not "subjective"? If so, that we would seem to not understand each
others definition of "subjective"! For me "subjective" refers to the
observations that can be had by actual LSs. This is equivalent to saying
that "as I write these words on this keyboard, I have the subjective
experience of being in a room, with children making a racket in an
adjoining room, with a TV showing some SciFi show, etc.". This is an
experience that I am perceiving and I expect that another observer, that
I can communicate meaningfully with, would have a similar subjective
experience. When someone writes or says "absolutely real", I wonder: "to
whom?" How is it "absolutely real"? How could it be otherwise, e.g. what
would falsify such a statement? Against what "standard" would I compare
it to? The funny thing is that "absolute standards" involve by their
very nature infinite regress!
[MP]
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 ...
**
So are you saying that the ordering of primes decides in an a priori
way the phylogenic order of organisms? I can see that this would follow
from a Platonic philosophy of mathematics, but does not the fact that
many distinct and mutually exclusive geometries and number systems and
be shown to be consistent makes us wonder if maybe we are taking our
ability to imagine a bit too seriously? The anthropic principle is one
example of this!
> > [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.
> > ************
[SPK]
> 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.
[MP]
> > 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.
> > ********
[SPK]
> 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.
[MP]
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.
**
Umm, I don't have a good argument to write here now about using
"symmetry principles" to argue "why things are as we perceive them", but
I think that we must be very cautious about doing that! For example
circular orbits are more symmetrical that any other shape of orbit, and
this example was used to defend the Ptolemic model of the cosmos! Just
because our model has beautiful epicycles does not necessitate its
"actuality". In fact, all physics is about the intellectual pursuit of
the means by which to predict and control Nature. We must NEVER forget
that our models, no matter how esthetically pleasing, are just models,
and not IT!
[MP]
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.
**
You do not understand what I mean by "compute"! :-) Computation, to me,
is the process by which, given a situation representing a question, lack
of knowledge etc., a system undergoes a selective act that desides the
answer, solution, etc. What a IBM microcomputer or Gateway 2000 system
does is an example of this. I am claiming that each time a q-jump
occurs, it involves a computational act. Please understand that my
definition here of "computation" is not a theorem, it is just a
definition that came to mind as I considered your staements… :-)
> > [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.
> > ********
[SPK]
> 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! :-)
[MP]
Amusing coincidence. I am just pondering the following problem. How
on Earth do I know that the me of today 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?(;-)
Umm, it could even be said that you came into existence five minutes
ago, with a full set of memories (encoded in your brain's neural
topology), and that all that you can infer subjectively is just what can
be entailed from this. We can dismiss this conundrum, by understanding
the computational power required to generate the poset of information
involved in the subjective experience far exceeds what is available in
the brain of the individual at the moment of the earliest memory.
William Poundstone's discussion in Labyrinths of Reason; Paradox,
Puzzles, and the Frailty of Knowledge (January 1990, Anchor; ISBN:
0385242719) is excellent.
[MP]
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).
**
Matti! How can "temporal intentionally, plans, beliefs, expectations"
have any meaning whatsoever independent of an actual observer? Do we
have to repeat the Einstein-Bohr debate? What does the Heisenberg
Uncertainty imply to you? To me it implies that subsets of the Universe
have no properties what so ever in an objective sense. Only when a
subjective act of observation occurs, be it "directly" with eyes or
"indirectly" with a computer controlled sensor, can we say that X has
properties A and none other. And, its even more complicated, since
"fact" that X has the properties A, only holds during the brief interval
of time that is involved. When we stop looking at the moon, we can only
infer that it is still there, to state that it "exists" with such a
brightness and size, etc. independent of the observation is a serious
mistake! The tree falling in the woods, does not make a sound! We can
infer from our memory that it most probably would, but that is not an
"absolute reality". There is no such thing!
[MP]
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!
**
I see this situation of "geometric memory" as the "mental state" of the
environment that is acting as an observer itself of your body's events.
The world observes me when I observe it, we define each other as we
bisimulate each other..
[MP]
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?
**
The subjective "stance" or viewpoint of another mind can not be had by
a mind other than that "having" it. This follow from the tacit
assumptions involved in the definition of "subjectivity", thus I agree;
the specifics of a particular mental action are not modelable, in the
sense that it is not possible to "copy" the quantum state (using the
usual meaning of the word state), but we can simulate "what it might be
like to experience some act". Umm, I am missing your point here! :-)
What do you mean by "irreducible mental acts"?
> > [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.
[SPK]
> 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.
[MP]
OK. I was thinking quite different thing. The terminology confuses
me.
**
That can happen easily in this discussion! :-) It is difficult to keep
track of the meanings and subtleties…
> > [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!
Best,
MP
Onward,
Stephen
This archive was generated by hypermail 2.0b3 on Sat Oct 16 1999 - 00:36:29 JST