**Stephen P. King** (*stephenk1@home.com*)

*Fri, 23 Jul 1999 15:36:36 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 474] Re: [time 469] Parallel transport, etc.... Part 2"**Previous message:**Stephen P. King: "[time 472] Re: [time 471] Noncomputability = not by TM"**In reply to:**Matti Pitkanen: "[time 471] Noncomputability"

Dear Matti,

I believe that we have ideas that are very very similar, it is just

that we are using complementary ways of talking about them! I am very

grateful for the patience that you show to me! I am sure that I am very

aggravating and difficult! ;-)

I cut this responce in half as it is long and my browser software can't

contain all of it simultaneously.

Matti Pitkanen wrote:

*> > [MP]
*

*> > > Parallel transport and connections emerge both at the level
*

*> > > of spacetime geometry and configuration space geometry.
*

*> >
*

*> > > a) At spacetime level all geometric structures are induced
*

*> > > from those of imbedding space. Although imbedding space
*

*> > > geometry is nondynamical, spacetime geometry is dynamical.
*

*> > > This is metaphorically dynamics of shadows: object is u
*

*> > > nchanged but shadow varies when object moves.
*

[SPK]

*> > This "parallel transport" notion is what Weyl made a careful analysis
*

*> > of in his work and why he reasoned that Riemannian geometry needed to be
*

*> > generalized! But, Weyl did not consider the possibility that multiple
*

*> > space-times are needed to model multiple observers. He assumed, as do
*

*> > most, that there is only one M^4 and its related fields/connections for
*

*> > all...
*

*>
*

*> Parallel transport is extremely general concept: 'connection' in fiber
*

*> bundle with structure group G. Very abstractly. Metric (Riemann)
*

*> connection special case: in this case inner product defined by Riemann
*

*> metric is conserved in parallel transport. For Weyl connection only
*

*> angles between vectors are conserved. In gauge theories one just
*

*> postulates some structure group G (say standard model group SU3 times U2)
*

*> for connection.
*

Could we discuss the notion of connections separately? To me it is a

key notion that distinguishes Hitoshi's LS theory from other models. My

ideas have developed independently from Hitoshi until I read his paper

and found a wonderful mathematical expression of my thoughts.

A key question: Could we construct at least two almost disjoint

4-dimensional Riemannian manifolds from selected "pieces" of a

n-dinensional manifold with Weyl geometry?

*> > Parallel transport is the conceptual tool to model motions of the
*

*> > "shadows", but fact is that that which is projecting the shadows is not
*

*> > a "ONE" in the ontological sense, it is the "MANY" possible finite
*

*> > subsets of U. They project onto each other...
*

*>
*

*> Is there slight misformulation here.
*

*> In case of 'shadows' it is the induction of parallel transport which
*

*> occurs. Parallel transport in imbedding space is projected to spacetime.
*

*> Induction and parallel transport are two different things. Parallel
*

*> transport is the great construction principle of GRT and gauge theories
*

*> and in fact all recent QFT:s. Induction is purely TGD:eish addition
*

*> to the conceptual arsenal used.
*

Ok, I see the difference; but, I would like to better understand your

notion of "induction of parallel transport".

*> > This is a very important point that becomes obvious in a discussion
*

*> > about the difference between "actual" and "potential" infinities... What
*

*> > is ontologically a priori is the Universe, which is an "Actual"
*

*> > infinity, thus it is ONE. The dynamics of the shadows are "potential"
*

*> > infinities, thus are "MANY", thus the uncertainty formalism that Hitoshi
*

*> > has discovered and discussed in his papers connects the time of the LS
*

*> > to its measure of uncertainty.
*

*> > The idea that the Universe, as a "static, pre-given entity" is
*

*> > non-dynamical is part of my thinking and that of Hitoshi and,
*

*> > appearently yours.
*

[MP]

*> But what one means by Universe! I do not mean by Universe imbedding space.
*

*> Rather, Universe is one possible spacetime surface classically. Single
*

*> configuration space spinor field quantum mechanically. And Universe
*

*> in latter sense is replaced by a new one in any quantum jump. It can
*

*> quite well occur that the sequence of quantum jump produces almost
*

*> fixed points: at least parts of universe can become almost fixed points:
*

*> this is what self organization by quantum jump produces.
*

*> But basically there is endless evolution: the prime characterizing p-adic
*

*> topology of universe increases all the time.
*

Here is the most dramatic difference in our thinkings. I am saying that

the Universe can not possible be "one possible spacetime surface"

classically or otherwise, this is inconsistent, since the existence of

such requires, at a miminum, that the information content of such to be

knowable by an arbitrary entity. This is why the classicists, such as

Newton and Laplace, relied on Gods or other "supernatural" entities to

observe such and thus make it actual. Existence and actuality are NOT

the same. The Universe in it-self can only exist, it can not be a

"space-time" in-itself. The experiences of finite LSs of it, are given

in terms of space-times, yes, but to identify a space-time with the

Universe is not helpful!

*> > Michael C. Mackey also addresses this notion in his
*

*> > book Time's Arrow with his "God Theorem"... The key notion that we all
*

*> > seem to agree on is that the "parts" can have dynamical behavior (are
*

*> > not at equilibrium) while the "whole" is static. The notion of time is
*

*> > given in the manner that the parts, by interacting among themselves,
*

*> > evolve toward equilibrium, e.g. evolve toward isomorphism with the
*

*> > whole: the "Union with All" of mystics. But the key notion is that this
*

*> > process literally takes forever to accomplish!
*

*> >
*

*> p-Adic evolution indeed never ends. Even God as the self of entire
*

*> universe is evolving all the time!
*

No. There can be no ultimate self associated with the entire universe,

if we are talking about the Totality of Existence. It is static, it does

not evolve, it merely exists. The western concept of a single Divine

entity that exists "in eternity" is at odds with the most basic

requirements of a consious "Self". Only finite entities can be

self-aware. Consiousness without the ability of self-awareness is a mute

notion, it is useful only to model particles. There is no Mind, in the

usual meaning involved, only simple logical entailment.

*> > > b) In accordance with this parallel transport in spacetime surface
*

*> > > reduces to parallel transport in imbedding space. Measuring of
*

*> > > distances reduces to that in imbedding space. Etc...
*

*> > > Especially important induced quantity is CP2 Kahler form
*

*> > > whose projection on spacetime surface defines Maxwell field.
*

*> >
*

*> > The argument about "a priori orderings" that I have been trying to
*

*> > communicate since the beginning of the Time List relates to this! The
*

*> > Oneness aspect of the Universe is forever out of reach since it is
*

*> > Everything simultaneously. It would have at least a multiple connected
*

*> > topology - everything mapping isomorphically to everything else... I am
*

*> > proposing that the subsets of U are simply-connected manifolds, up to
*

*> > isomorphism in the classical limit of hbar = zero.
*

*>
*

*> I understand your point completely. But this is simply all about basic
*

*> philosophy.
*

I am a philosopher after all! :-)

*> I accept three ontological levels. Material existence (spacetime
*

*> surfaces), subjective existence (sequence of quantum jumps as moments of
*

*> cs and objective/informational/whatever existence (single quantum history).
*

*>
*

*> Correct me if I am wrong: You accept only single ontological
*

*> level: experiences/subjective existence and since this subjective
*

*> existence obviously gives very limited information about spacetime
*

*> etc... Thus it is logical that you want replaced the Riemannian geometry
*

*> etc... by more primitive concepts containing not so much information.
*

Umm, I am not getting information flow... I see a Hierarchical ordering

of Levels.

1)The One: At the grundlagen, we have The Universe In-itself. It is

Existence, it included all and is all.

2)The TWO: there we have the essential dichotomy of subject-Object, the

Duality of Self versus Other, of Information versus Matter.

3)The Many: there we have the potential infinity of possible different

aspects of the One, relative to each other.

The idea I have that information is not mere epiphenomena of matter or

matter merely epiphenomena of information. We really need to have a

discussion on Pratt's work to get into the subtleties of this notion.

*> > Here is a crude sketch of my idea about the applicability of Weyl's
*

*> > geometry:
*

*> > "The necessary and sufficient condition that a Weyl geometry may be
*

*> > reduced to a Riemannian geometry is that a vector keep its original
*

*> > length after transplantation along an arbitrary closed trajectory.
*

*> > Indeed, the condition of such a length preservation is ...
*

*> >
*

*> > (15.40) \surface integral_C of dl/l = \surface integral_C \PHI_\alpha
*

*> > dx^\alpha = 0
*

*> >
*

*> > [forgive my terrible ascii]
*

*> >
*

*> > and it is well known that \PHI_\alpha|\beta - PHI_\beta|\alpha
*

*> > \equivalent 0 is the necessary and sufficient condition for the
*

*> > integrability requirement of (15.41) in simply connected regions."
*

*> > [from Introduction to General Relativity by Adler, Bazin and Schiffer,
*

*> > 1975. pg. 496]
*

*>
*

*> OK. This is obvious.
*

*>
*

*> > These "simply-connected regions" would have properties that are
*

*> > represented by Maxwell field equations. These define the patterns of
*

*> > causal connections that M^4's represent. They have the appearance of
*

*> > being unique from the point of view of an observer O because they are
*

*> > the framing within which an observation by O is possible. If we consider
*

*> > for the sake of illustration the ability to observe this projection
*

*> > process "from a divine point of view" we would see that each O (an LS)
*

*> > has its own M^4 constructed piece by piece by mappings between its
*

*> > internal propagator's (quantum mechanical) dynamic's configuration space
*

*> > and points in the manifold W.
*

Did this make any sense?

*> > What is difficult to grasp is that the "points" that make up W are the
*

*> > possible exteriors as centers of mass ("cm"). In other words, the
*

*> > "exteriors" of LS are ontologically different from the "interiors"! The
*

*> > former are facets of the "MANY" and thus appear "classical" while the
*

*> > latter are finite facets of the "ONE" and are quantum mechanical! The
*

*> > ONE and the MANY are co-inductive aspects of the Universe, they define
*

*> > each other, but the "meaning" of such definition is only possible for CE
*

*> > reasons as being "in time" and since each LS, as a unique facet of U,
*

*> > has its own time and gauge scale, it constructs its own local consistent
*

*> > "reality".
*

*> >
*

*> > > c) This means geometrization of classical
*

*> > > gravitational and classical gauge fields.
*

*> > > Metric, the vector formed by components of spinor connection
*

*> > > of imbedding space, etc are projected to corresponding
*

*> > > tensor quantities defined on spacetime surface.
*

*> > > Note that since shadow is created by projection map,
*

*> > > dynamics of shadows is indeed in question in precise sense!
*

*> >
*

*> > Umm, I fail to see how it is necessary and sufficient to require that
*

*> > spinoral properties be aspects of the ONE.
*

*>
*

*> What is beautiful is that spinor structure is direct concomitant of
*

*> Riemannian geometry. Under very general conditions Riemann geometry
*

*> defines spinor structure uniquely. Spin is thus purely geometric
*

*> property. In case of infinite-dimensional configuration space
*

*> spin is extremely abstract concept and does not have interpretation as
*

*> spin as rotation. Different many particle states are in
*

*> infinite-dimensional context analogous
*

*> to different spin states of ordinary spinor.
*

Yes! This is why I say that spinor structure is a construction, since

it is "direct concomitant of Riemannian geometry". The notion that each

observer "constructs" its local reality or world by interacting with

other such observers is an attempt to model experience. It is impossible

to model any particular sujective experience, why? Because "to

experience it" is equivalent to "to construct it". If two observers were

to construct the very same local reality they would have to be one and

the same observer at that moment! If we generalize and use fuzzy logic,

we can say that two or more observers "have the same local reality" and

thus we can explain the illusion of a single classical space-time, with

its Riemannian geometry and spinor structures, etc.!

The a priori existence of "different spin states of ordinary spinor" is

merely an inference based on local experience, it only exist in our

minds, in the sense that it is knowable. To posit that the Universe

(Level 1) has any particular features is inconsistent. Properties are

Level 3.

*> >I see them as constructed
*

*> > dynamically in the act of observation in that they are aspect of the
*

*> > framing. Thus I do not see them as a priori givens! Is it not enough to
*

*> > show that the "shadow" is a construction of the mapping between LSs? Do
*

*> > we really have to suppose that the "statue" exists "out there" prior to
*

*> > the sculptor's work?!
*

*>
*

*> This is a good question. Your point of view makes possible to avoid
*

*> dualism: observations contra world out there.
*

Could you elaborate? I don't understand? I thought that I was saying

that there is a duality, Level 2?!

*> But so does also my approach. I see painting and landscape as one and the
*

*> same thing! Painter exists only in the moment of consciousness when
*

*> painting/landscape is replaced with a new one. Painter experiences some
*

*> of the beauty of painting and, by artst's vanity concludes that he did
*

*> it!
*

Sure, Pratt says that Chu spaces are both the player of the Game and

the Game itself. The Duality is in the complementarity! I agree with you

completely here! But notice that the "painting" and the "landscape" are

instances of "information" and "matter" structures! Their relationship

is the infomorphism! The Stone-Birkhoff duality!

(http://www.mcs.newpaltz.edu/faculty/clark.html)

The construction of a material symbol [painting] within is only the

construction of an information carrying structure [beauty] iff a similar

material symbol [print] elsewhere/when could be constructed from a

description of a similar information carrying structure [beauty]. We

must understand that [beauty] is a local notion and is not a priori

given. All properties are given only in relation to a finite subset of

all possible. Plato was wrong!

*> I see as the difficulty of your approach the necessity to provide
*

*> formula for the contents of consciousness: this indeed seems to be the
*

*> case if you identify reality as observations.
*

*> *********
*

Yes. But, a model that gives us a way to predict what will be

experienced under an arbitrary conditional is what a physics is all

about! Thus, my attempt to identify "reality as observations" is a local

only notion, local in the sense that they are constructed within finite

M^4 framings which I am identifying with piece-wise constructed

Riemannian maifolds from the "bricks" that are posets of points in a

W^n.

*> > It "exists" only in the sense of being a
*

*> > possibility! The metric or related properties are given by the act of
*

*> > observation which is determined by the local logical entailment aspect
*

*> > of the informorphism that is the interaction between LSs.
*

*> > To be sure, I need to discuss the "compactness" notion that you
*

*> > mentioned before with regards to the W(r)...
*

*> >
*

*> This leads to the problems in the following sense. Our observations give
*

*> extremely limited information about spacetime. I do not experience
*

*> all the values of the metric tensor or classical gauge fields defined
*

*> on it. Does this mean that one should give up entirely the notion
*

*> of spacetime and what should be left? Some set discrete points perhaps:
*

*> but how can you understand in this kind of context how observes
*

*> invent concepts like moral and freedom and how the idea of infinity
*

*> arises?
*

Good questions! The limitation of the information content involved in

our observations is due to the finiteness of the material configurations

available to encode information within the local "reality" of the

particular observer. We note that this local reality has the form of a

space-time as noted by Kant and other philosophers.

We can not experience all possible values of the metric tensor (or all

of the energy spectra, which range over -/+ R) simultaneously because of

the above restriction!

We only give up the notion of an independently pre-given space-time.

Instead we have the understanding that individual's observations and

measurements are not "absolutes given from above" but are local

constructions that are selected from the set of all possible by an act

of finite and discrete act of interaction.

While the concepts of "morals" and "freedom" are very important, I an

not addressing them directly, I see them as concepts that can be

communicated about within the interactions that are infomorphisms

between local systems. My idea here is very similar to Leibnitz's

monadology, except that I do not require that an external Divine entity

create them ab inition ex nihilo!

*> > > d) Thus everything is classical mathematics: even induction
*

*> > > procedure which is standard mechanism of building new bundles
*

*> > > by mapping manifolds to base spaces of bundles but not noticed
*

*> > > by say string model people.
*

*> >
*

*> > Umm, I an missing something! :-( I say that each LS observes a
*

*> > classical like world, thus can be approximated and modeled by classical
*

*> > math, but we need to consider co-induction, not just classical
*

*> > induction... Perhaps I am misunderstanding you!
*

[MP]

*> This induction is not induction in the sense as co-induction defines it.
*

*> Induction in the sense of Faraday! When you have metric in some space
*

*> you have also natural metric for its submanifolds: distances are measured
*

*> using the length units of imbedding space.
*

Since I consider the Universe as having to definite properties in

itself, and the notion of an embedding space, as Level 2, has all

possible "length units", (not an absolute ONE, but MANY) but such are

not given independent of interactions, they are only defined within

particular interactions.

snip

[SPK]

*> > The way that M^4s are constructed "piece-by-piece" is well illustrated
*

*> > in Penrose's discussion of quasi-crystals and it highlighted in by
*

*> > Forbidden Symmetry paper:
*

*> > http://members.home.net/stephenk1/Outlaw/forbiden.html
*

*>
*

*> [MP]
*

*> I agree that this what you are saying applies to how our ideas about
*

*> spacetime evolve.
*

Not quite how I see it, our knowledge (relationships between

information) evolves along with our space-times (relationships between

matter).

snip

*> > [MP]
*

*> > > The mere existence fixes that which exist essentially uniquely
*

*> > > in infinite-dimensional context: this is the basic idea. One cannot
*

*> > > construct dynamics for the metric of infinite-dimensional configuration
*

*> > > space because it is fixed already by the requirement that it
*

*> > > exists! The existence of Cauchy hypersurface poses problems when
*

*> > > one assumes dynamical spacetime and tries to quantize metric.
*

*> > > Now imbedding space is given and these problems disappear.
*

[SPK]

*> > But how do we derive particular actual properties by merely evoking the
*

*> > fact that they exist? Existence is "outside of time", it is tenseless.
*

*> > The dynamics that define sharp properties only occur "in time", in fact,
*

*> > I propose that in a subtle sense, they ARE time, but since each LS has
*

*> > its own unique dynamics (defined by its internal QM propagator), each
*

*> > has their own time and thus their own length scale or gauge. Thus I say
*

*> > that each LS constructs its space-time M^4 framings by interaction with
*

*> > other LSs.
*

[MP]

*> We have articulated rather precisely the differences in our philosophy.
*

*> For you LS:s are all that is. For me LS:s could represent models for
*

*> contents of conscious experiences of selves but besides this
*

*> the realities behind these experiences would exist.
*

No, LS are not "all that is". They are "all that can experience

anything" or "can have a subjective self". The "realities" "behind these

experiences would exist" is given, but as I said before, existence does

not imply experienceability! In order to experience something that

exists it is necessary to construct a finite structure that can encode

the descriptive information about it, this allows for the information to

be communicated. The brain's structure of interconnected neurons is what

allows for the information content of our experiences to be communicated

and to be used to apprehend new information. Thus information requires

matter to be encoded in as symbols and matter requires information to

give it actual meaning. The existence property is mute with regard to

meaning or configurations!

[SPK]

*> > The Cauchy problem holds in the static case since the Uncertainty
*

*> > principle prohibits the a priori definite "sharp" properties!
*

[MP]

*> This is true if one consdier QFT in Minkowski space. One can fix
*

*> only E or B. Similar conclusion holds for the components of
*

*> spacetime metric regarded as small perturbation of Minkowski metric.
*

*> It is nonsensical to speak about entire spacetime metric as given.
*

Yes, this is part of my reasoning!

*> Only some of its components commute at given time =constant section.
*

Can you elaborate on this?

*> But as we know, this approach to quantum gravitation does not work!
*

*> TGD approach is quite different and in complete accordance with
*

*> uncertainty principle. There is no quantization of
*

*> metric or other classical gauge fields.
*

Topological Geometro-Dynamics, to me is a model of how the worlds

(given by the intersection of a finite number of local "realities")

behave. This is well within the preview of Hitoshi's LS theory. He has

worked out how the LS itself can be modeled consistently, but the model

needs to be extended with regard to the way LS observe each other.

Hitoshi's remarks about GR's field equations and the role of connections

is important in comsidering this.

*> > It is for
*

*> > this reason that Einstein was very opposed to QM! His statement "GOD
*

*> > does not play with dice" [to determine the properties of the world]
*

*> > speaks directly to this!
*

*>
*

*> Einstein's argument relied on spacetime concept he had invented: the
*

*> idea about quantum jump occurring at definite value of time is in violent
*

*> conflict with space-time democracy. It breaks general coordinate
*

*> invariance and it breaks the hypothesis about deterministic
*

*> field equations. Quantum jump between quantum histories concept was
*

*> originally forced by the requirement of General Coordinate Invariance and
*

*> the avoidance of determism-nondeterminism paradox.
*

OK. Could you discuss your thoughts on the "determism-nondeterminism

paradox" sometime soon?

[MP]

*> > > The point is that I do *not* identify observations as points of
*

*> > > spacetime or configuration space. They are not active 'events'.
*

*> > > Quantum jumps between quantum states= quantum histories are events and one
*

*> > > cannot localize them to anywhere (one can of course, identify
*

*> > > these events as pairs of possible initial and final quantum histories
*

*> > > so that one can speak about the space of all possible experiences).
*

[SPK]

*> > I say that observations are co-inductively related posets of points (as
*

*> > an abstraction since true infinitesimal points can not be distiguised
*

*> > from each other as they can not encode any information!!!), not
*

*> > individual points per say.
*

[MP]

*> I undestand that you great idea is identify observations with geometrical
*

*> structures, 'posets of points of space'. I also parametrize
*

*> the set of all possible observations: not as posets but as
*

*> allowed quantum history pairs: but this parametrization tells
*

*> anything about content of observation: it is just labelling: the only
*

*> thing that matters that this naming scheme is one-to-one. I believe
*

*> that the content of observation/cs experience cannot be expressed by any
*

*> mathematical formula.
*

Sure, but when we construct intricate geometrical model we are doing

just that! We are attempting to express the content of observations/cs

experience with a mathemathical formula! SO long as we understand that

the "model" is not the "thing" we are ok.

*> > To call them "space-time framings" speaks to
*

*> > the fact that we always make observations in terms of a M^4 frame... The
*

*> > quantum jumps are more epiphenomena that objective, but the restriction
*

*> > that observers can only communicate effectively about M^4 framings that
*

*> > do not logically contradict each other follows from CE! The
*

*> > schizophrenic is an example of an observer that is attempting to
*

*> > communicate about a M^4 framing that is logically inconsistent with
*

*> > another's!
*

*> >
*

*> But there is the notion of observer. You take it as granted. I take
*

*> observation fundamental.
*

No! I, like you, take observation as fundamental! I just am being

explicit about the fact that what each observer has a framing of their

observations is not an a priori given, it is a construction! Thus, with

Pratt I say "cognito, ergo eram", I think therefore I was....

*> > > I see no problems with Heisenberg's uncertainty relations: informational
*

*> > > time development operator U reduces at QM limit to Schrodinger equation.
*

*> > > Metric, etc.. classical gauge fields are *not* quantized in TGD.
*

*> > > Neither spacetime coordinates are quantized. There is
*

*> > > absolutely no quantization, only classical geometry of
*

*> > > infinite-dimensional configuration space and classical spinor fields of
*

*> > > configuration space. Oscillator operator algebras etc are geometrized in
*

*> > > this approach.
*

*> >
*

*> > I see the evolution of information in terms of the evolution of the LSs
*

*> > as they interact. Thus the act of the Universe 'experiencing itself' is
*

*> > an ongoing process. It is what "concurrent computation" is all about is
*

*> > a fundamental sense! Again, this is why I find Peter's work so useful!
*

*> > :-)
*

*> >
*

*>
*

*> Here here agree completely. But 'universe=experience about universe'
*

*> is where I cannot follow you. This is simply too strong assumption and
*

*> leads to the hopeless attempt of writing formula for the contents
*

*> of cs experience.
*

The Universe is not experience about the Universe! I apologize if I did

not express this well. The Universe is mere Existence of All that

exists, everything simultaneously. Experiences are \epsilon-consistent

information structures (Complete Atomic Boolean Algebras are examples)

that require finite material structure to be actualized. An observation

is an actualization, it is the "enbodiment" of the information.

Descartes was incorrect in his dualism, because he assumed that mind and

matter were invariant substances, I, with Pratt, propose that they are

"acts", and acts can only be actual *in time*. Existence has no time

associated, thus it does not generate local experience; it is the local

actualities of LSs that do that. :-)

snip

[MP]

*> > > I just saw a paper in which it was shown that divergence problem is
*

*> > > not solved by noncommutatitivy of the spacetime coordinates. There is also
*

*> > > problem with the loss of general coordinate invariance. One must assume
*

*> > > special coordinates and very high symmetries if one wants
*

*> > > special coordinates.
*

*> >
*

*> > Could you give me the reference of this paper? I can order a copy from
*

*> > the library! :-)
*

*>
*

*> It was paper by my 'boss' Masud-Chaichian and Peter Presnajder and third
*

*> theoretician. They constructed noncommutative QFT in two-dimensional case.
*

*> For cylinder it worked but for more general case they found infinities.
*

*> They also suggested generalization of results to higher dimensional case.
*

*> I do not have the paper here but I could ask for bibliodata.
*

Thanks! ;-)

snip

*> > [MP]
*

*> > > God of Singularity concept is based on traditional concept of
*

*> > > psychological time. Also the question why everything has not already
*

*> > > happened is created by the same concept of psychological time.
*

*> >
*

*> > Yes, but here the error is in the tacit (subconscious) assumption that
*

*> > the psychological time of one person is one and the same of that of
*

*> > another! The clocking by the QM propagator of the LS defines the
*

*> > individual time of the LS, thus representing psychological time very
*

*> > well!
*

*>
*

*> Also that. But the real blunder is the identification
*

*> is the assumption that *contents of cs experience correspond to
*

*> time=constant snapshot*.
*

*> Neurophysiologists tell us that this is not the case. Consdier music
*

*> as example. We are able to experience frequencies, which
*

*> is nonlocal concept with respect to time.
*

Yes, that is why I use an M^4 to frame an observation, there are both

spatial and temporal non-localities involved. This is also why we can

use a RW metric to model how the space-time configurations of a single

observation are distributed! This speaks to concurrence, we are not able

to experience points, we experience hyper-surfaces! So, we agree here!

:-)

*> > The "everything has not already happened" notion is indeed related to
*

*> > psychological time, but in the sense stated above. "Everything" much
*

*> > included all possible "actual" experiences, and obviously, these involve
*

*> > NP-complete computational issues! This later notion is at the heart of
*

*> > my argument.
*

*> >
*

*> > > I regard this concept as badly wrong. In TGD framework subjective time
*

*> > > corresponds to quantum jumps and there can be *no first quantum jump*.
*

*> >
*

*> > I am not communicating my notion since your are not aware of the
*

*> > NP-completeness problem! Karl Svozil's papers point the way! We agree
*

*> > that "there can be *no first quantum jump*"! The ideas of co-induction
*

*> > and related issues involved are in Peter's papers...
*

*>
*

*> I have studied Peter's papers (rather technical!). My view is that cannot
*

*> start from so technical concept like NP-completeness in building model
*

*> for universe: the reason is that I do not believe that universe computes
*

*> itself into existence: it just exists! Even more, it is able to replace
*

*> itself with a new one again and again and do also some computation
*

*> besides that!
*

Matti, NP-Completeness is not merely a technical concept! It is a

fundamental problem! How does the Universe calculate the minimum energy

configuration of a protein molecule? How does the Universe figure out

the most stable orbits in a stellar system? How is it that soap bubbles

always cover the most volume with the least surface? How is it that a

quasi-crystal can grow at all? How is it that Lagrangians are calculated

by the Universe? All of these questions are aspects of the

NP-Completteness problem!

What is interesting is that it has been proven that if there exists a

finite computational scheme that can compute a given example of an

NP-complete problem, this scheme or algorithm can be transformed in

polynomial time into a scheme to compute any other NP-Complete problem.

But this, I think, only works for situations that can be modeled (or

"simulated") by Turing Machines. Peter's work shows us that most of the

computations that occur are not TM simulatable and thus we need to look

at this more closely.

[MP]

*> > > This requirement plus p-adic evolution
*

*> > > as gradual statistical increase of p-adic prime of the universe
*

*> > > immediately leads to the requirement that
*

*> > > also infinite p-adic primes are possible and that recent universe
*

*> > > must correspond to infinite prime. Every moment of consciousness
*

*> > > decomposes to infinite number of subexperiences with values of
*

*> > > psychological time ranging from zero to infinity. What we really 'know' is
*

*> > > that local arrow of psychological
*

*> > > time exists: if one is satisfied with this then paradoxes disappear.
*

*> > > Universe becomes *4-dimensional* living being getting conscious
*

*> > > information about its entire 4-dimensional body in every quantum jump.
*

*> > > Cognitive spacetime sheets are the sensory organs of this infinitely
*

*> > > large 4-dimensional living system.
*

[SPK]

*> > The notion of "gradual statistical increase of p-adic prime of the
*

*> > universe" is given in my thinking in the sense that the overall
*

*> > concurrent interactions of LSs are modelable in this way. It would be a
*

*> > representation of the accumulated "experience of the Universe", but with
*

*> > the caveat that it is information that can not be gotten in finite time
*

*> > or finite energy with arbitrary accuracy. The operator formalisms that
*

*> > Schommers talks about, I believe, is useful to us in thinking about
*

*> > this!
*

*> >
*

*>
*

*> Yes: I have grasped the universe computes itself into existence philosophy
*

*> but....
*

Umm, I do not say that "the universe computes itself into existence"! I

say that the individual experiences of Local Systems (using Hitoshi's

definition of LSs) are given in terms of space-times framings. This

follow from the distinction that I make between "existence" (qua CE) and

"actuality" which is a "local notion" that represents the subjective

experiences (observations, measurements, etc.) of an LS given any

particular moment of their local time. Thus I say that the Universe

experiences itself by the acts of observation of the finite LSs, which

are considered computations of NP-complete problems.

The key argument is that nothing can "happen" unless a price is paid.

Existence in-itself does not require the generation of equilibria. It

*is* at equilibria with respect to itself, that is why it merely exists.

It does not change, it has no duration or extension or any other

properties other that mere existence. It is the grundlagen! I do not

associate any space or time properties to it, those are the properties

of the observations of Local Systems, not the Universe itself.

*> > > > > [SPK]
*

*> > > > > This notion is very different from Hitoshi's idea, but perhaps the
*

*> > > > > difference is due to the different ways that time is treated.
*

*> > > > > I still see these as complementary! You see space-times as a priori
*

*> > > > > surfaces, subsets of the totality U that are connected by quantum jumps
*

*> > > > > "in time", Hitoshi, as I understand, sees space-times as the "clocked"
*

*> > > > > poset of observations of LS, which are a priori quantum mechanical
*

*> > > > > systems existing tenselessly as subsets of the totality U.
*

*> > > > > Thus you are proposing space-times as a priori and Hitoshi
*

*> > > > > proposes quantum local systems as a priori, this is a chicken-egg
*

*> > > > > complementarity! We need to see that this is just a matter of
*

*> > > > > perspective!
*

*> > [MP]
*

*> > > I have the feeling that this is not a matter of perspective. Our
*

*> > > basic philosophies are different.
*

*> >
*

*> > In a way, yes. You are a Platonist, and I something different. I think
*

*> > that Plato's Idea Reality *is* the Universe in-itself, but as Kant
*

*> > argued well, is not knowable in-itself. I see it as Existence itself!
*

*> > All experiences, measurements, observations, qualia or what ever, are
*

*> > not given directly by their mere existence (as all exist in the
*

*> > ontological sense), but have finite properties given by the interactions
*

*> > between the finite subsets or "facets" or LSs of the Universe. We can
*

*> > only observe shadow, consciousness is not capable of knowling the
*

*> > "in-itself"!
*

*>
*

*> Funny thing, reading this I find that I agree completely. But somewhere
*

*> the differences emerge: computationalism is one of the division lines.
*

And this is exactly why we must discuss the notions we have about

computation!

I will continue my responce in a bit...

Kind regards,

Stephen

**Next message:**Stephen P. King: "[time 474] Re: [time 469] Parallel transport, etc.... Part 2"**Previous message:**Stephen P. King: "[time 472] Re: [time 471] Noncomputability = not by TM"**In reply to:**Matti Pitkanen: "[time 471] Noncomputability"

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