[time 501] Re: [time 491]Forms, Entailment structures, intersections, etc.

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Wed, 28 Jul 1999 14:13:30 +0300 (EET DST)

On Mon, 26 Jul 1999, Stephen P. King wrote:

> Dear Matti,
> Matti Pitkanen wrote:
> snip
> [MP]
> > > LOGOS= COSMOS is what I indeed assume.
> [SPK]
> > Yes, I agree, it is just that I see LOGOS as only asymptotically
> > infinite. The phylogenetic hierachy represents the process of the LOGOS.
> > Remember LOGOS is an action, "the verb" in greek, literally!
> MP]
> > I see LOGOS as wisdom existing there, objective realities.
> > You mean by LOGOS the cognitive
> > process (cascades generating selfs and essentially phenomenon of
> > subjective reality).
> So, do you see the LOGOS as an a priori Platonic FORM? I understand it
> as such, but say that, to think of LOGOS as a FORM is to automatically
> make it unknowable, e.g. we are framing it as an aspect of the ONE. I am
> considering the finite implementation of the LOGOS with in the MANY. The
> duality (TWO) of aspects of the MANY are united in the ONE. So we have a
> trinity. Umm, I think that category theory has formal ways to thinking
> of this situation!
> snip
> [MP]
> > OK. I define qualities as red, green, etc.., as properties
> > of experiences, not properties of the world. You
> > obviously see them properties of the world. More generally,
> > Hume's law says that values are not in the world
> > since one cannot measure values. I agree, values relate to quantum jumps,
> > subjective reality not physical realities. What about values
> > in your approach?
> Values are given only within finite contexts. I am thinking as Mach
> did. We will discuss this more when we get into the Schommers
> material...
> snip
> [MP]
> > > These isomorphisms between local systems are replaced in my approach
> > > by mappings of real geometric structure to their p-adic counterparts:
> > > there is ineed 'reality' (realities) and this reality is mapped
> > > to p-adicity of particular self. There is no direct mapping
> > > between selves.
> [SPK]
> > YES! This is what Pratt is saying in ratmech.ps! "Bodies can not
> > interact directly..."
> [MP]
> > > You could counterargue that there is no communciation between selves
> > > in my approach: communciation is contained in quantum jump:
> > > Psi_i--> UPsi_i --Psi_f
> > >
> > > U is the informational time development giving rise to informational
> > > currents modelling the communication. Selves can hence
> > > communicate by forming cognitive representations about other
> > > selves as subselves. This is only mimicry but it is enough!
> [SPK]
> > That is all I say that interactions are! You and I are respectively
> > "real" to each other only within the "window" of our computer inteface.
> > Tis is what Peter's work talks about. Each Observer (LS) can only
> > "interact" with others "through" the surface that is modeled as a common
> > surface. (Here we think of LSs as being like the insides of bubbles that
> > share a surface.)
> >
> [MP] This common surface is the 'real' reality behind p-adic realities
> > in TGD.
> But, do you insist that this common surface is a priori to the
> experience of such. I do not think so as I see that observational
> properties are only probabilities prior to actual observation. Thus I
> say that the actualization of the local properties of the common
> surfaces are given by the end result of the quantum jump, it is not a
> "'real' reality" a priori!

No. There is no objective reality. Objective
reality is replaced by a new one in each quantum jump.
Quantum jumps for the subjective reality and each self in
quantum jumps expeirences its own subjective p-adicity
determined by initial and final the objective p-adicitities.

> SPK]
> > To interact is to mimic each other's internal behaviour. This is what
> > is defined as "bisimulation"; your mind, with its actions, simulates the
> > actions of my body and my mind, with its actions, simulates the actions
> > of your body. If our respective simulations are identical, our knowledge
> > of each other is total! We would be one and the same person. The fact
> > that our framings of the world differ is an indication of the difference
> > that occurs in our bisimulations of each other.
> > The beforementioned notion of almost dijointness is relevant here!
> >
> > [MP] Selves within us provide these simulations. Selves for
> > all kinds of objects we perceive either outside or inside our
> > body.
> Yes! :-)
> snip
> [MP]
> > > Objective existence has nothing to with meaning, would I say.
> > > Qualities and meaning are involved with quantum jump between objective
> > > existences. Matter does not give meaning: it is change
> > > of material configuration which contains the meaning.
> [SPK]
> > Yes! Information content gives matter meaning, but only in the
> > bisimulational sense. Remember how information is defined in terms of
> > mutual agreements of associations. Thus if the material symbol "tree"
> > implies a green, leafy, fruitbearing, shadow-creating, etc. object for
> > you and for me, then we transfer information using such symbols. Howard
> > Pattee's papers are an excellent discussion of this notion:
> > http://ssie.binghamton.edu/~pattee/
> [MP]
> > Mutual agreemens of associations would results in my framework
> > from the formation of abstractions: self containing unentangled
> > subselves experiences what it is to be average subself.
> > Quantum statistical determinism implies that these averages
> > tend to be more or less same: you 'tree' =about my 'tree'.
> >
> > Question: who I am? Am I self or abstraction of subselves
> > of a larger self? What is Earth: is it really individual
> > Earth or abstraction about planets circling some average
> > star we call Sun?(;-)

> Your self (in each moment) are the weighted sum of the subselves that
> have entailments greater than or equal to the pinary cut off for that
> moment's entailment structure. This is dual to the light-cone structure
> that delineates the material causality of that event.
> The Earth, and any other object for that matter, follows the same
> definition, the key is the dual light-cone\logical entailment structure.
> This picture is a bit deceptive since it is a static picture, like the
> notion of the instantaneous movement in the calculus. It is really a
> process and the static picture is merely a way of thinking of it...
Identity crisis happily over! I already explained my stupid
interpretational blunder (building of interpretations is
extremely risky business). Self X experiences its subselves
as collection of separate selves: no averaging. Self
at next level of hierarchy contaning X experiences the
selves of X as average self, typical representative of
its class. This is the quantum mechanism for forming

> [MP]
> > > And also change of informational configuration: in quantum
> > > jumps conscious information gain is the difference
> > > between initial and final informations. Selves are eaters
> > > of information and U generates it in every quantum jump: we
> > > live in an information-prosperous world.
> [SPK]
> > Yes, the construction of a self dissipates information, in the
> > sense that observing a given event or configuration alters it such that
> > its information content vanishes. This is the information equivalent to
> > the consumption of free energy or the generation of thermodynamic entropy!
> > The "U", I see as the construction of a new menu of choices from which
> > the observation is made. This united free will with the idea of local
> > determinism, e.g. each LS determines its reality, but only to the degree
> > that it can predict its behaviour.
> [MP] You identify nondeterminism and nonpredictability. I regard
> > nondeterminism as real phenonenon having nothing to do with
> > predictability. Even very young childs can differentiate between living
> > creatures and nonliving objects: they certainly cannot predict the
> > behaviour of nonliving objects. This supports
> > that nonpredictability not= nondeterminism.
> This deserves a separate discussion! My thinking is that determinism
> (causality) follows Peter's use of hypersets and not the usual classical
> notion!

> [SPK]
> > If the LS has infinite predictive
> > power, we get the absolute determinism of Newton and Laplace, if the LS
> > has zero predictive power, we get the complete randomness of
> > conventional QM. By allowing the computational (e.g. predictive) power
> > of an LS to range from 0 to 1 by "fuzzifying" the notion of a
> > topological neighborhood of a point, we can think of an LS as having a
> > real valued \epsilon of "self-determination". [WOW, I have not been
> > able to say this idea so well before! It has been a picture in my mind
> > for a very long time.]
> > Anyway, when we apply the pinary mapping formalism that you are
> > expert at, we get a model with a hierarchy of ever more "expressive"
> > [Peter's word] LSs. :-)
> [MP]
> > Objection! QM is NOT completely nondeterministic! Far from that.
> > It would be easy to model QM mechanically if this were the case.
> > Only discrete subset of the states is possible outcome in quantum jump:
> > this is what I think makes hopeless the simulation of QM
> > probabilistically.
> I was talking about how it is assumed that the quantum jumps are purely
> random. I do not think so! I think Peter's conjecture about the role of
> "Secondary Observers" is valid! I disagree with Einstein in the idea of
> local determinism, the quantum jump is "aimed" by non-local interactions
> (the minimization computation). It is easy to forget that there it is
> impossible to isolate any thing! We need to discuss this notion!


> snip
> MP]
> > > I state this somewhat inprecisely. I should have said that
> > > only some components of curvature tensor commute.
> > > This relates to the canonical quantization of metric as quantum field.
> > >
> > > a) The components of 3-metric are commuting physical
> > > quantities. g_ij: 6 alltogether. The remaining
> > > components of metric are nondynamical since general coordinate
> > > invariance (4 coordinates) implies that 4 components of metric
> > > are nondynamical and can be fixed: this gauge condition
> > > fixes the coordinates used. g_00 and g_0i are indeed
> > > good candidates for components of metric tensor fixed by some
> > > coordinate conditions. For instance g_0i could vanish.
> > >
> > > b) In quantization one constructs Hamiltonian formalism and
> > > identifies the canonical momentum densities as
> > > partial derivatives of Lagrangian density (curvature scalar
> > > times sqrt(g) with respect to time derivatives of metric
> > > components g_ij. Canonical momentum densities and g_ij commute
> > > to delta function as operators: this is microlocal causality
> > > stating that gravitons are point like particles.
> > >
> > > This is how it should roughly work. Unfortunately it does not.
> >
> > Yes! I think that the main problem is that "point-like particles"
> > can not encode curvature, it is a non-local notion. Penrose talkes about
> > this in his work on 'twistors" space-time has no curvature, in his
> > model, until an infinite number of "gravitons" are introduced in it! I
> > believe that Frieden's method of constructing Lagrangians from the
> > Fisher information is a strong clue for us, since the information
> > involved in the bisimulation idea is exactly what Fisher information is
> > about! We, hopefully, will get into this in detail soon. I wish Frieden
> > would join our group!
> >
> > [MP] I think that the basic problem is the concept of point like
> > particle: particles are not pointlike: they are small 3-surfaces, would
> > I say. When particle becomes very large it becomes the space in which
> > smaller particles reside (topological sum). This is really
> > big idea: particle and space containing it are only instances
> > of one and the same thing! Getting rid of a concept is always
> > a victory!
> Yes, but is it possible that we need to wean ourselves away from the
> use of the assumption that every observer's world is one and the same.
> All that is really required is an understanding of how observers (LSs)
> communicate (and thus interact) with each other!

Observer's subjective worlds are not same. This we agree.
Concerning communication, the fundamental description would
in TGD be based on informational time development operator U. But this
is description practical in time scale of 10^4 Planck times.
In biosystems relevant time scales could be about 10^40 times larger!
Something more practical is needed.

A reasonable model for the communication is to start
from the notion that communicators are selves as also we are.
Selves have sensory experiences: in neuronal length scales
these experience could correspond to chemical experiences
(neurotransmitters,..). Nerve pulses and chemical
communication could provide a self-self type communication:
talk between individuals.

There is communciation also between selves at different
levels of hierarchy. This communication is perhaps
 communication analogous to mass media and is possible. That
it occurs is suggested by the success of the global workspace
model of Baars and advocatated also by Pinker in 'How the Mind
Works'. There is kind of common blackboard containing
messages readable by a rather large group of 'agents'.
Brain contains a surprisingly large empty volume (as I learned
for some time ago): there is evidence that some gases (say CO_2)
and chemicals could make possible mass media like communication.
Coherent photons, which are TGD:eish prediction could make
possible also mass communication. Various linear structures,
DNA:s, proteins, microtubules,.... could act as receiving and sending
quantum antennas and receive the global workspace messages
and also send them.

> > I am not too enthusiastic about Fisher information, too specific.
> > This I-J decomposition also leads to nonsensical consequences in TGD
> > framework. Signs do not come correctly.
> I think it would help if we discussed this in detail step by step. It
> would be a terrible thing if we ignore it just because we can't easily
> fit it into our pet models!

I see the problems at basic philosophical level. The idea about each
measurement type defining its own laws of physics simple
does not make sense to me and one cannot restrict the
measurement to just one measurement type.

> > I interpret Kahler action as a measure for the cognitive
> > degeneracy of spacetime surface. This interpretation involves
> > a hypothesis about what this degeneracy is: it is motivated
> > by thermodynamical analogy but I cannot prove this hypothesis.
> Let us discuss this! Tell me the details. :-)

a) Denote by N(Y^3) the number of absolute minima of
Kahler action going through given 3-surface Y^3 on lightcone boundary
times CP_2. Y^3 is like 3-dimensional soap film on lightcone boundary
xCP_2. Nondeterminism of Kahler action implies N(Y^3)>1 in

b) How N(Y^3) depends on Y^3? Since N is determined by the properties
of Kahler action, a good guess is that
N(Y^3) is function of K(Y^3). Guess: N(Y^3) is exponent
of the negative of Kahler function for some critical value
of Kahler coupling strength a_cr appearing in the definition
of Kahler function and analogous to temperature.
This is pure *guess*: one should find good arguments supporting

c) Vacuum functional Omega is exponent of Kahler function and
analogous to thermodynamical partition function and vanishes
when absolute value of Kahler function increases.

i) This implies that when Kahler coupling alfa is smaller than
alpha_cr, N*Omega vanishes exponentially for large
values of Kahler function.

ii) For alfa larger than alfa_cr N*Omega diverges exponentially and theory
very probably does not exist at all.

iii) For alfa_cr= alfa theory does not exist in real context
but exists p-adically. Critical theory is the correct

d) There is direct analogy with thermodynamics of strings.
String thermodynanics does not exist when temparture is larger
than Hagedorn temperature analogous to alfa_cr. Now thermodynamical
state degeneracy behaves as g(E)= about exp(E/T).
Thermodynamical degeneracy of states is analogous to
cognitive degeneracy of states causes by degeneracy of absolute
minima of Kahler action in turn caused by the classical nondeterminism of
Kahler action.

e) Cognitive degeneracy of Kahler action is the basic
prequisite of cognition. This makes possible cognitive spacetime sheets
and selves able to have experiences with contents localized around
definite value of geometric time. N(Y^3) is measure
for the 'intelligence' of Y^3 and its logaritm is entropy
type information measure.

> snip
> [MP]
> > > Some people are promiting the idea that realities are intersections
> > > of higher-dimensional realities. Interesting idea but I do not know how
> > > to realize it.
> >
> > We are discussing it right here and now! LSs are
> > "higher-dimensional realities", their interactions are "intersections"! We
> > just need to genetralize our language to n-dimensions! People are trapped
> > by their ignorance in 2-dimensions. Ever read the work of P. D. Ouspensky?
> > http://www.fourthway.org/
> >
> > [MP] I have not. LS could be also 4-dimensional realities: their
> > intersections would correspond to the elementary particle horizons
> > at which spacetime metric is degenerate: much like
> > blackhole horizons. Always in pairs.
> Could you elaborate on this last point?

The wormhole has Euclidian metric signature and is glued
to the two spacetime sheets with Minkowski signature. Therefore
two horizons at which signature changes, are necessarily present.
Metric determinant vanishes at these horizons.


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