[time 461] Re: Generalizing Manifolds and ideas

Stephen P. King (stephenk1@home.com)
Tue, 20 Jul 1999 19:40:58 -0400

Dear Matti,

Matti Pitkanen wrote:
> Dear Matti,
respond allowance of quantum superpositions of W:s in LS framework.
> Matti Pitkanen wrote:
> >
> > On Sat, 17 Jul 1999, Stephen P. King wrote:
> > [MP]
> > Of course! You have general relativity
> > with Riemann geometry replaced by Weyl geometry.
> Close... The local dynamics of GR are given by the local
> compositions
> of LS projections into W. I am considering GR to be a model of the
> "glocal" structure of extremal geodesics, but as I see it, we move from
> the assumption of a single Riemannian manifold X to a supermanifold W
> that has as submanifolds almost disjoint X_i. Each has a slightly
> different inner product, maybe? This is an attempt to model how each
> observer perceives itself to be in the center of a finite universe that
> has a Robertson-Walker like metric.
> [MP]
> Here you have the problem of defining X as a union of almost
> disjoint X_i precisely. This requires probably modification
> of manifold concept. In TGD framework almost disjointness is
> realized in terms of sub-manifold concept: two spacetime sheets
> connected by tiny wormhole are almost disjoint. The effective
> p-adic topologies can be different for two sheets joined by
> wormhole contacts.

        This has to do with the concept of neighborhood of a point, that
Hausdorfness property. Your "almost-disjointness" is "pictorially" the
same as my notion! The problem I have is with the idea that "spaces"
exist a priori to observation. We do not have a good concept of a
statistical operator for space and time! Schommers offers such! But I
have a problem with some interpretation notions he uses...
        I think of a space-time as a construct, as a subjective perception. It
is no less "real" It is just not assumed to have properties independent
of the particular subjective state. Thus, if there exist an infinity of
observations, there would also co-exist an infinity of space-time
framings. This is, to me the essence of the subject-object dichotomy.
> Isn't the basic property of RW metric that each point is
> center of the universe? All points are metrically equivalent
> for given value of cosmic time.

        Ah, but it is assuming that there is a subjective independent cosmic
time! This is the problem! We can use the RW metric with the
understanding that each observer, having their own time, has its own
perseption of a Hubble expansion.
> [SPK]
> The notions of positions is a relative notion in my thinking. It is
> perhaps good to think of a graph were the centers-of-mass of other LSs
> are the nodes and the edges are the relative overlaps in W. In this way
> we define the space aspects of the observation in terms of extensions
> and the time aspects in terms of durations, given the particular
> internal behavior of the LS propagator.
> Thus, if the LS is in a bound state, it has not time associated and all
> extensions are null, e.g. LSs that are at internal equilibrium have no
> space or time associated. The consequences of this when considering how
> other LSs, in interaction with such, is interesting! It looks like the
> situation where a worm hole, connecting separated space-time regions in
> the classical GR picture, is pinched closed.
> [MP] I did not understand why bound states have no space or time.
> Does it mean that LS is mapped to single point? And that there are
> no relative positions and no relative times?

        Yes. If the LS is in a bound state, it is a closed system in a single
state, incapable of interacting with other LSs. It's internal propagator
generates no clocking action and thus only maps to a single point of W.
In a scattering state, thus has a multiplicity of states that can map to
different points which are considered as the outsides of other LSs. So
in a sense the LS theory identifies the exteriors of LSs with points in
some type of manifold that under very general conditions models a
classical world, but this is only half of the picture! :-)
        There is more involved but I need to have Hitoshi's input and he is
very busy now.
> [MP]
> > This looks like fiber bundle structure: different LS:s as regions
> > of fiber bundle related by transition functions. One could not
> > define uniquely single LS but would have some minimum number of
> > LS:s, patches of the bundle. OK? But the mapping of LS to
> > several points of W breaks this picture.
> The key notion is how the "connections" are defined! LS have no a
> priori connections between them, this allows connections, which define
> the forces between LS, to be dependent on the local histories of the
> LSs, e.g. the information content of the LS's quantum history constrains
> the mapping. The fiber thus look more like a tree, N to 1 map, than a
> string, 1 to 1 map.
> [MP] I think I understand this. By the way, in the hierarchy of
> selves selves form an infinite hierarchy describable
> as infinite tree: branches in given node
> are selves summing up to higher level self identified as branch
> coming to that node.

        Yes, the LSs can be composed of LSs themselves. I originally asked
Hitoshi if ultra-metrics could be used to think about the hierarchical
relationships of the components of LSs... I see the tree like aspect of
the fiber as defining the ordering of the LS. The history is encoded in
the connections of the branches, in the phylogeny of the LS...
(http://phylogeny.arizona.edu/tree/home.pages/whatisphylogeny.html) This
internal structure defines, for me, the means by which the subjective
view is projected. It constitutes the subject or "self" as a whole.
Subsets of it are separate "selfs"...
> [MP]
> > Generalized fiber spaces with projection mapping fiber to
> > several points? Could the number in image depend on base point and
> > could one allow the image be empty set? In this manner one
> > would avoid the counter argument about fiber space
> > realization of LS. When image is empty there is no LS.
> Yes to all! :-) Also, we can reason that an empty LS maps to the
> whole W, as the null or empty set. A singleton LS, e.g. an LS having a
> single quantum particle maps to all singleton points of W.
> [MP]
> > More or less but quite not as I realized just now.
> > I try to explain.
> >
> > a) The decomposition of spacetime surface
> > to cognitive spacetime sheets having *finite time duration* (I stress
> > this since this is crucial) and material spacetime sheets has turned
> out
> > instrumental for the model for self and binding.
> Umm... I still have trouble with this wording, but I can see how
> you use it, I think. I see "cognitive space-time sheets" and "material
> space-time sheets" as Stone-Birkhoff duals of each other, as Pratt
> defines the latter.

> [MP] Without knowing what Stone-Birkohoff means,
> I somehow feel that this identification is not correct.
> Cognitive spacetime sheets provide non-faithful representations
> for material spacetime sheets: they mimick some aspects of their
> behaviour.

        Pratt defines it in his papers... I will try to write up a post about
this soon.
> I have myself talked about geometric matter mind duality: the
> phrase is misleading. One should only talk about geometric
> matter-mind decomposition of spacetime.
> Visualize in terms of the size and shape and topological sum.
> Material spacetime sheet has infinite duration since conservation
> laws does not allow it to cease in time direction. Then you take
> cognitive spacetime sheet, initially vacuum, and glue it to
> material sheet by topological sum. You can use several wormhole contacts.
> The net result is that some energy and some momentum and other stuff
> flows to cognitive spacetime sheet from material sheet and of course
> also back to material sheet because otherwise conservation laws would
> fail. This is a model of self. Quantum jump by quantum jump these
> cognitive spacetime sheets drift gradually to the future and self
> finds time running. Since self dissipates, self also finds that
> self is getting old.

        Is it necessary to consider "cognitive" behaviors as space-times? The
Chu space concept seems more fundamental as it gets to the relationships
of the primitives that make up space-times themselves, e.g. the groups
that define the Lorentz and Poincare transformations can easily be
defined in Chu space terms. It is not necessary to consider the
actuality of space-times prior to the act of observation.
        I think that we should seriously consider that the act of observing is
the act of generation a space-time framing, e.g. when we observe
something, we automatically are aware of such only in the context of a
given poset of extensions and durations. These "extensions" and
"durations" are Local System-specific in the sense that the LS's
propagator determines them.
        I wish I has a better grasp of the mathematics that Hitoshi uses. I can
only point to his papers. I have been under a lot stress lately and am
not thinking very clearly at all. :-(

> Could it be possible to extend the notion of local system to
> something akin to a pair of material and cognitive spacetime sheets.
> This would bring in matter-mind decomposition.
> I know that this goes outside the standard physics and hence one should
> have good motivations for doing this.

        I do not think is it possible as a Local System (LS) is purely quantum
mechanical internally, all space-time associations are done "from the
outside" point of view. This makes the subject quantum mechanical and
the object classical in the context of the subject-object dichotomy of
        This is the one aspect of your work that troubles me. :-( I do not
understand how you deal with the information content of a "cognitive
space-time sheet", I can think of such only as having the group
theoretical properties of space-time sheets, but the idea that they are
a priori objects "I can't eat." Umm, this causes an impasse between us
that I do not like at all! :-( I hope to be able to send the Schommers
paper to you soon, (my finances are very bad!) Perhaps we can just look
at his ideas and forge ahead.
> [SPK]
> I see the ideas implicit in the concept of a
> "space-time" as applicable to both information and matter, each has
> extentional and durational attributes. The identification between the
> two is modeled by the "informorphism": material event A causes material
> event B if and only if the information content of B implies the
> information content of A, thus A -> B iff A* <= B*; "<-" is material
> causation and "<=" is logical entailment or implication.
> [MP]
> I understand this. In TGD cognitive spacetime sheets represent
> unconscious mind geometrically. Events involve reductions of
> matter-mind entanglement. The related experience could be 'I cause that
> happen'.
> This is not the only possibility: volition could be related solely with
> the localization in zero modes characterizing various
> degenerate absolute minima of Kahler action: classical nondeterminism
> of Kahler action would make possible volition: this looks very nice to me.
> I must be able to decide what is the truth(:-)!

        We do need to be able to falsify this idea. I think that your notions
are more falsifiable than mine, this does bother me! How can I test the
notion that each observer has its own space-time and that the common
world is merely the overlap? This is my fundamental notion... I see the
"interference patterns" in the famous two-slit experiment as evidence
that I am right, but ...
> [SPK]
> Other key differences are in the way the "physics" of the two
> work. Material "bodies" are incompressible and rotatable, information
> "minds" are compressible and irrotatable. Bart Kosko explains the latter
> properties in his book Fuzzy Engineering...
> [MP]
> For me the basic difference between mind and matter is
> *finite time duration* of cognitive spacetime sheets: more generally,
> cognitive spacetime sheets are *bounded* but possibly infinite (recall
> the possibility of infinite primes).

        Umm, I think that there is much more to this! One aspect that we have
failed to discuss is the computational issue. Perhaps Karl Svozil's
paper will help: http://tph.tuwien.ac.at/~svozil/publ/maryland.ps .
I still have serious problems, I do not think I understand your concepts
of "cognitive space-time sheets". For instance, what mechanism defines
the finite time duration? LSs have a propagator that defines its clock.
> > b) In quantum jumps only the entanglement between cognitive and
> > material spacetime sheets can be reduced. This generalizes von Neumann's
> > intuitions.
> This idea, to me, speaks to a generalization of Pratt's notions.
> The transition or quantum jump from event A to event B is a process of
> selecting the particular points of W that are dual to the information
> content of the LS. Umm, I have been trying to work out an idea where the
> points on the surface bounding an LS encode a n-ary bit of information,
> but this is still very crude. I am using the ideas of Wheeler about the
> information content of a Black-Hole's event horizon.
> > c) Selves are pairs of material-cognitive
> > spacetime sheets unentangled with the other
> > selves and containing as nested subsystems lower level selfs:
> > Russian dolls inside Russian dolls. Self is
> > synonymous to observer.
> I agree with this. I believe that the notion of a homunculus
> existing inside our head with a mini-humunculus inside of its head, etc.
> is generated by this p-adic hierarchy of LS selves! :-)
> [MP]
> There is indeed certain analogy with homunculus idea. But also important
> difference. The smaller the homunculus the higher it
> is at cognitive hierarchy according to the traditional homunculus
> idea.

> In TGD the situation is exactly the opposite. Primitive experiences of
> small homunculi sum up to those of larger. All these expriences of course
> exist separately in each moment of conscious experience as its separate
> parts. The hierarchy also stops at elementary particle level or already
> earlier, not all subsystems are able to remain unentangled under U. It
> migh well be that elementary particles are not even accompanied by
> cognitive spacetime sheets and thus are not able to form 'homunculi'.
        I agree. That is what I meant. But, the space-time sheet is still, for
me, something that is an aspect of the framing of an observation. Umm,
are you familiar with the discussion between Newton and Leibnitz
concerning the nature of space and time? Newton considered them to be
quantities separate from the objects and did not consider any role at
all to the subjective. Leibnitz proposed that space and time to be
merely the extensional and durational relations between objects and thus
have no meaning independent of observations. I am trying to extend
Leibnitz' notion to deal with the strange world that QM shows us.
> Umm, I am skeptical of the notion of the literal transmigration of
> souls, since it assumes that the awareness of self is continuous a
> priori and the idea that the self is a "rigid object" that "move in
> space-time".
> [MP] These are exactly the reasons why also I was sceptic about self.
> The notion of self as subsystem able to remain unentangled under action
> of U however mildens dramatically these conditions. Cognitive
> spacetime sheet would be geometrical counterpart of a soul attached
> to matter. It can born. It cand disappear. It can change its
> shape and size. It is very much like material but has finite
> time duration and is almost vacuum.

        Can its topological properties vary? I don't understand the "almost
vacuum" property.
> Without quantum jump cognitive spacetime sheet certainly cannot move in
> spacetime since it is part of spacetime
> itself. The *notion of quantum jump saves the situation*.
> In each quantum jump the spacetimes in superposition of macroscopically
> equivalent spacetimes changes as also change the precisely defined
> temporal positions of cognitive spacetime sheets.

> Since the future of given point of future lightcone contains much more
> room than its past, cognitive spacetime sheet is bound to diffuse
> or even drift to future. Some average amount of geometric
> time passes per quantum jump: most naturally 10(-39) seconds
> ('CP_2 time'): this is arrow of psychological time.
> Psychological time is quantized with this average size
> of quantum. Geometrical time is continuous.

        Again, do you consider space-time as something that has properties
"in-itself" or is it merely a way of communicating about the world?
Personally, the question of the "objective nature of space-time" is
something that I really would like to talk about!
> [SPK]
> This contradicts the basic notion of quantum jumps. I am
> claiming that the notion of rigid bodies is at best an illusion!
> [MP] No, it does not! See above. The crux of matter is
> finite time duration of cognitive spacetime sheet and
> the fact that its temporal position changes in quantum jump.

        Ok, I can accept that. I agree, but that I have a hard time
understanding is how this "duration" is given. How is it measured? It
seems to me to be something purely subjective and this is why I would
like to explore the possibility that the subjective sense involves a
single instance given a Universe that allows for all possible such
> [SPK]
> The unity of "flow of consciousness" is given by the unitary evolution
> of entanglements of the material particles that make up a mortal body.
> When a body dies, the entanglements decohere and so does the unity of
> consciousness that is associated. This idea looks very bleak, I know!
> [MP]
> This picture however leads to the basic difficulties of models
> describing self as continuous stream of consciousness. Self
> as subsystem remaining unentangled between subsequent quantum
> jumps does not introduce continuous stream of cs.
> Just as an example I send a short piece of text about what happens
> in wake-up and fall-asleep experiences.

        The difficulty that I see in the usual discussion of "stream of
consciousness" is that a mistake is made by not realizing that the
subjective aspect can not be objectified, or as you say modeled. The
studies of how an illusion of continuity is observed in a movie is a
good indication. All we need to do is have a model that *allows* for the
possibility of an illusion of continuity as given from a subjective
point of view. The classical model of the world does *not* allow for a
subjective point of view at all!
        "Self" is a subsystem separate from what? I do not think of
consciousness as an object at all; I see it as an active relation
between an LS (a poset of quantum jumps or, in Hitoshi's terms, the
propagation of a unitary operator of a discrete quantum system) and at
least one other LS. I think that the very notion of a self is impossible
if there is not distinguishability between self and not-self. I think
that it is imperative that we discard the Newtonian notions involved in
The Calculus when trying to deal with this question since they contain
implicitly the vary notions that I am questioning!
        Your paper about waking and falling asleep is very interesting!
> [SPK]
> But I found another mechanism that models most paranormal phenomena as
> well as the notion of transmigration. We need to consider that quantum
> entanglements "connect" subsets of LSs that can have very different
> space-times associated, thus we can are resonances in the information
> content. Carl Jung's discussion of "synchronisities" is relevant!
> [MP]
> I agree that entanglement is the royal road to enlighment and explains
> synchronicity. I have written about this even a chapter to
> my book. There are however *two* bindings involved. Entanglement
> binds experience*r*s: summation of sub-experiences of self binds
> experiences and makes possible abstractions!
        Could you elaborate on this last point?
> How is the metric generalize to our tree-like fibers? The "leaves"
> of the tree-fibers are LSs and the truck roots into a non-zero region of
> W, I think... The subtleties involved is that we can invert the picture so
> that the leaves are points in W and the root is an LS... The difference
> in these views is the difference between the subjective and the
> objective. Umm, I am confused! :-) Maybe we say that the tree is a
> fibration of LS_i x X^3_j -> W_ij ? I need to think about how to put my
> picture into words better...
> [MP] I think that we talk about different fiber
> spaces! I am talking about the fiber space structure of
> the space of the infinite-dimensional space of 3-surfaces. You are
> talking about finite dimensional space having W as base: this space
> corresponds to M^4_+xCP_2 in my framework.

        Yes. Can we talk about the "connections" involved? Particularly, I
would like to understand how "parallel transport" is modeled in your
> [MP]
> OK. I think that we were indeed thinking about different things.
> Configuration space is the space in question: it presumably does not
> have any counterpart in LS framework because X^4/W is purely classical
> so that one does not have superpositions of parallel W:s.
> Configuration space in LS context would be the space of all possible W:s.

        The postulation of a configuration space seems to presuppose an
ordering and a basis for observations prior to the act of the particular
observation itself. This is very similar to the Minkowskian notion that
there exists a single space-time manifold that just "exists". The
serious problem that I have with this notion is that it presupposes that
their exists a Cauchy hypersurface of positions and momenta with
definite a priori status. This is completely contradicted by the
Heisenberg's Uncertainty relation. The interpretation of this aspect of
QM is the most troublesome for physicists! What I see is that the very
notion of a configuration space has serious problems! If we are going to
insist on using them then we much at least make their status
statistical, so we talk about statistical distributions of properties
given such and such conditions. This idea seems to be the best aspect of
the Multiple World interpretation of QM.
        My problem is that I see an unanswered question being swept under the
proverbial rug: What makes the world run? We can't just postulate that a
God or Singularity "started" the world! Why do we experience time in the
first place? Why has everything not already happened?

> [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]
> Hitoshi assumes fixed spacetime which is classical
> and satisfies field equations of GRT and puts the quantum dynamics
> to the fiber R^6. In TGD the quantum state is superposition of classical
> spacetimes since spacetime is made quantum dynamical. Localization in
> zero modes however effectively makes dynamics by quantum jumps to hopping
> in zero modes: like Brownian motion.

        Umm, I did not get this thought from reading Hitoshi's papers! He
points out that GRT field equations problematic and outlines a way out.
His theory is incomplete in this sense, again as I see it. I do not
suppose that a fixed space-time is necessary for LS theory, it gives us
a way to model an alternative.
        I would like to discuss the basic notion that observations are the way
that the Universe realizes the existence of consciousness and that
partial orderings of observations can, allowing for the group theoretic
properties, generate space-time framings (subjective views) that can
overlap (have configurations that are similar) such that the appearance
of a single finite universe results.
        Can we put the details of p-adics aside and just talk about
space-time's ontological status? Is it necessary and sufficient to
assume that a single unique space-time exists? If so, how?
Kindest regards,


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