[time 462] Re: Generalizing Manifolds and ideas

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Wed, 21 Jul 1999 14:49:00 +0300 (EET DST)

On Tue, 20 Jul 1999, Stephen P. King wrote:

> 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:
> snip
> > > [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...

In connected sum the almost disjointness corresponds also to
existence of kind of horizons at which metric
changes to metric of wormhole having Euclidian signature.

> 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.

You might be right. Here our views differ. I would see this kind
of spacetime as a model for the infinite collection of perceived
spacetimes, each self would have its own perceived p-adic spacetime.

Actual spacetime contra perceived spacetimes.

> > 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.

OK. I see.

> snip

> > [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.
> snip
> > [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.
> [SPK]
> > 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"...

I being to realize that this hierarchical structure of selves
is crucial for understanding what thinking and language is.
I thought to make a small digression about this but found
that text became so long that it is better to send it as
a separate posting.

> > [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.
> [SPK]
> > 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.
> snip
> > [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.
> [SPK]
> > 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.

Well, here we believe differently. I preach for geometrization
and topologization of cognition. Explanation for the arrow of
psychological time I see as real victory of the approach.
Could one see Chu spaces as
possible tools for modeling general structure of conscious
experience, say conscious thought?

> 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. :-(
> [MP]
> > 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
> consciousness.

This classical-qm/subject-object dichotomy is deep. In TGD it relates
to decomposition of infinite-dimensional configuration
space to fiber (quantum fluctuating degrees of freedom) and
base (zero modes). Clsasicality in zero modes results
from the localization in zero modes occurring in
each quantum jump.

> 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.

The earlier work with information contents of conscious experience
relates to this. Information content of cs experience
is difference of information contents for UPsi_i and Psi_f.
Pinary cutoff makes it possible to define infinite number
of different information measures for different types of
information. In particular, it is possible to assign this
kind of information measures to cognitive spacetime sheets.

The crux of matter is that the unique pinary cutoff for a
value of physical quantity means that finite number
N of pinary digits characterizes the value.
Information content is N_R log(p)/log(2)
bits where N_R is the image of p-adic integer N
under canonical identification SUM x_np^n-->SUM X_n p^(-n).

I do not see our different philosophies as an impasse! Why not just
compare: comparison generates ideas and helps to see things
from different angle.

> > [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 ...

The subjective experiencing own body as separate from rest of
the world supports the views of both of us but does not differentiate
between them.

> > [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.

Finite time duration is possible because there need not be
any classical conserved quantum numbers: some of energy can
flow from material spacetime sheet to cognitive one when it begins
and back to material when it ceases ('begin' and 'cease' refer
to geometric time now).

The properties of Kahler action
make cognitive spacetime sheets possible: huge *vacuum degeneracy*
is the crux of matter (or rather mind!). One can take this
kind of vacuum solution with finite temporal and spatial size
and glue it to material spacetime sheet and deform the resulting
spacetime surface until absolute mininum of Kahler action is
obtained (this of course need not happen always but I believe
that it actually does: the number of vacua is simply so huge).

Think of small disk glued by topological sum contacts to infinite t-x
plane. Disk is now cognitive spacetime sheet. Plane is now material
spacetime sheet.

> > > b) In quantum jumps only the entanglement between cognitive and
> > > material spacetime sheets can be reduced. This generalizes von Neumann's
> > > intuitions.
> [SPK]
> > 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.
> [SPK]
> > 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.

Yes, I see Your philosophical point of view. I find myself
between Leibnitz and Newton. Spacetime concepts is behind
observations. Spacetime is however not given but dynamical,
even quantum dynamical: only its macroscopic aspects
are fixed in quantum jump by localization to zero modes so
that one can speak of single spacetime in good
approximation and QFT makes sense.

I see the basic problem understanding of how conscious experience
can form representations of underlying spacetime reality.

In one aspect I am Newtonian: imbedding space is really God given and
non-dynamical and this for purely mathematical reasons: quantum
TGD does not exist mathematicall otherwise. String modelists
have same dream.

> snip
> > 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.

In principle can and do. In each quantum jump sheet
is replaced with new one: besides moving in time direction
it can also grow or get reduced in size and also change its

Almost vacuum property means that cognitive
spacetime sheets in general form cognitive representations
by taking very small 'samples' of fields
from material spacetime sheets. Oscillations, etc. are
transferred from matter to very small oscillations of cognitive
spacetime sheet involving very small energies.
Cognitive spacetime sheet is measuring instrument taking
sample about small 4-volume. The presence of cogntive
spacetime sheet does not usually perturb matter much.
Of course, volitional actions are different thing.

> > 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?

In-itself: or rather In-themselves: quantum jumps occur to
superpositions of classically identical spacetime surfaces.
Imbedding space in-itself. Subjective has a priori nothing
to do with geometric time and psychological time and its
arrow emerge as prediction of the theory.

> 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
> durations.

This is interesting point.
a) 'Our' cognitive spacetime sheets are dynamical and duration
might actually vary. There is entire hierarchy of
cognitive spacetime sheets with various durations.

b) The distribution of information content of conscious experience
about spacetime in principle gives information about duration.

c) For instance, sensory experiences seem to be sharply time localized.
This could mean sensory cognitive sheets have duration of say
one second and are located in a region of larger cognitive
spacetime sheet having small time duration.

d) If memories correspond re-experiences
occurring in geometric past together with component now,
then cognitive spacetime sheets with duration of order
lifetime might be present. If Stan Grof's and other's
reports on transpersonal and prenatal experiences
are what I believe them to be then also cognitive spacetime
sheets with much longer duration than lifetime can
be present occasionally (remember the posibility to
get entangled)

e) It is actually difficult to say, whether nonsensory component
of conscious experience contains time-localized information
or not.

> > [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!

Yes. I agree.

> "Self" is a subsystem separate from what?
> I do not think of
> consciousness as an object at all;

I agree completely! Consciousness is between two worlds
in quantum jump between them. Cognitive representations
provided by cognitive spacetime sheets are however objects. As such not

Self is subsystem which is able to remain unentangled under U:
sub-Universe effectively behaving like entire universe.
Matter and Mind like spacetime sheets such that related quantum
systems can generate entanglement reduced in quantum jumps.
Our cognitive acts are like tree with root at body length scale
and highest branches at DNA length scale.

>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.

This is true. Informational time evolution U lasting infinite
lightcone proper time (having nothing to do with
experienced time!), although it leaves self unentangled,
can generate temporal entanglement and hence give
rise to information transfer between self and external world.

>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!

Calculus is dangerous. For instance, Newtonian notion of
absolute time is implicitely contained in Hamiltonian formalism
and although it has led to deep crisis in quantization attempts
of GRT, people desperately try to use it rather than
trying to find genuinely new, relativistically invariant
approach to quantum physics.

> 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?

[MP] When two subselves entangle, they disappear. This
is what falling in sleep is!

The larger self containing
two subselves plus possibly some other selves however existed
already before the entanglement and exists also after that.
This is what binding of experiences is. Immediate consequence
is that there is infinite hierarchy of selves with Universe at
top. Self integrates the experiences of its subselves to kind of
abstracted summary experience.

If all my all subselves sleep and I am making quantum jumps
reducing entanglement between material and cognitive
spacetime sheets, I am in the state of 'whole-body-consciousness':
see the separate posting about selves.

When I think and cognize, I generate hierarchical sequences of subselves.
Selves can represented various modular structures of experiences:
sentences, worlds, phonomenes, etc of language. Objects in
visual experience, etc...

I have described the model of self in earlier posting and
I send separate posting about model of thinking. It is
very 'computational'; hierarchical structures in which
program modules correspond to subselves gradually
waking-up during the cognitive act.

I think, I will stop here. The message becomes too long to read
by ordinary humane selves.


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