**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Mon, 7 Jun 1999 08:10:16 +0300 (EET DST)*

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On Fri, 4 Jun 1999, Stephen P. King wrote:

*> Hi Matti,
*

*>
*

*> Matti Pitkanen wrote:
*

*> >
*

*> > On Tue, 1 Jun 1999, Stephen P. King wrote:
*

*> snip
*

*>
*

*> > > Is this why you say that p-adic "universe" is non-deterministic?
*

*> >
*

*> > Purely p-adic universe obeying some field equations. Yes.
*

*> >
*

*> > The situation TGD framework situation seems to be the
*

*> > following.
*

*> > a) Real spacetime and also other geometric objects (imbedding
*

*> > space, configuration space, configuration space spinor fields,...) are
*

*> > mapped to their p-adic counterparts.
*

*> > b) The mapping is unique from General Coordinate Invariance and is the
*

*> > phase preserving canonical identification which I told about in earlier
*

*> > posting (recall Pythagorean phases, parallel with quantum measurement
*

*> > theory, etc...) but the direct image is not continuous p-adic surface.
*

*> >
*

*> > c) One must replace the direct image with its minimal pinary cutoff
*

*> > and continue this to p-adically smooth surface satisfying p-adic
*

*> > counterparts of field equations. This completion is possible only because
*

*> > of p-adic nondeterminism.
*

*> >
*

*> > Consider c) more precisely:
*

*> >
*

*> > a) The mapping of imbedding space to its p-adic counterpart is fundamental
*

*> > and defined by phase preserving canonical identification. It induces the
*

*> > map of spacetime to its p-adic counterpart somehow.
*

*> > b) The p-adic counterparts of field equations determining spacetime
*

*> > surface must be satisfied satisfied.
*

*> > c) Canonical image must coincide with p-adic spacetime surface in
*

*> > *maximal resolution* allowed by p-adic field equations.
*

*> >
*

*> > c) means that *minimal pinary cutoff of the canonical image of the real
*

*> > spacetime surface* (the preferred imbedding space coordinates h^k of
*

*> > spacetime points are replaced with their pinary cutoffs) consisting of
*

*> > discrete set of points coincides with the the pinary cutoff of p-adic
*

*> > spacetime surface satisfying the p-adic field equations.
*

*> >
*

*> > **This is made possible by p-adic nondeterminism!**
*

*> >
*

*> > Phase preserving canonical identification map plus continuation of
*

*> > minimal pinary cutoff of p-adic image to smooth p-adic object is general
*

*> > recipe in the construction of p-adic counterparts of all real objects
*

*> > (configuration spinor field basis, kernel of time development operator
*

*> > satisfying Schrodinger type equation,..).
*

*> >
*

*> >
*

*> > **Important: one must distinguish p-adic nondeterminism from the
*

*> > classical nondeterminism of Kaehler action present also in real context:
*

*> > also this feature forces 'coinductive' philosophy. One cannot predict
*

*> > or retrodict everything from initial values for some snapshot.**
*

*> >
*

*> > Thus it would seem that classical nondeterminism of Kaehler action
*

*> > absolute crucial for cognition and possibility to have conscious
*

*> > experience with contents localized in time, forces also
*

*> > 'coinductive' approach!
*

*>
*

*> snip
*

*> > > [SPK]
*

*> > > > > I would qualify the "either or" operation as to imply that it is only
*

*> > > > > meaningful in a finite context with non-zero error terms.
*

*> > > [MP]
*

*> > > > I think that this would be choice of philosophy with accuracy of epsilon.
*

*> > > > I am not very enthusiastic about philosophy with accuracy of epsilon(;-).
*

*> > >
*

*> > > I understand, but it "works"! We can appeal to Platonic Ideals that are
*

*> > > Absolute truths, but we both understand that these are unknowable from a
*

*> > > local stance and thus we are left with the reality of non-zero epsilons
*

*> > > in our wfft's statements. This is, explicitly, the message of fuzzy
*

*> > > logic and, implicitly, the message of probability theory. I prefer to
*

*> > > have the "uncertainty" out in the open, where I can keep track of it.
*

*> > >
*

*> > This is similar to dissipative world of standard physics, which we
*

*> > discussed in qmind recently. Basic physics
*

*> > (definining quantum histories) is reversible but observed physics is
*

*> > irreversible. The reason for dissipation is that quantum jumps between
*

*> > histories change the history all the time. Dissipative effective history
*

*> > replaces the sequence of quantum jumps between quantum histories
*

*> > with *single dissipative history*. This definitely wrong
*

*> > and mathematically ugly picture provides however practical effective
*

*> > description.
*

*>
*

*>
*

*> > By the way, macroscopic irreversibelity can be regarded
*

*> > as a direct signature for quantum jumps between quantum histories
*

*> > and is visible to everyone since the only (as I believe)
*

*> > to understand dissipation and reversibelity simultaneously at fundamental
*

*> > level is based on this concept.
*

*> >
*

*> > Growing old must be one of the basic irreversible processes. Even things
*

*> > like chairs and desks grow old and must be performing quantum jumps,
*

*> > perhaps also macroscopic ones now and then, and hence must have moments of
*

*> > consciousness. Hydrodynamic flow dissipates rapidly and must involve
*

*> > moments of consciousness (what it is to be a water flow
*

*> > growing old and losing kinetic energy gradually but unavoidably?(;-))
*

*>
*

*> I highly recommend Michael C Mackey's book: Time's Arrow: The Origins
*

*> of Thermodynamic Behavior. Springer-Verlag, 1992. Prof. Mackey has
*

*> proven that invertible physics can not describe worlds with time! Are
*

*> you talking about "dissipative structures"?
*

*> See:
*

*> http://behavenet.com/capsules/treatments/famsys/flctstrctre.htm
*

*> http://pespmc1.vub.ac.be/:/ASC/DISSIP_STRUC.html
*

Yes. Or rather, first principle explanation for emergence of dissipative

structures. Dissipative dynamics is only a phenomenological description:

Hamiltonian is made non-hermitian in QM, in classical mechanics

various dissipative forces are introduced. Sequence of

quantum jumps between non-dissipative histories is replaced

with single dissipative history.

*>
*

*> I remember an old hypothesis of mine that the dissipation of structure
*

*> -like have you mention above- is a function of error increasing (as
*

*> compared to some global standard) in a toy world in which all motions
*

*> were point to point teleportations... I never figured out how to
*

*> formalize it. :(
*

*>
*

*> > > snip
*

*> > >
*

*> > > I would like to discuss this notion separately! I am reading an
*

*> > > Information Theory book that covers the Real version and your writting
*

*> > > here helps be gain a better intuition of your thinking! :)
*

*> > >
*

*> >
*

*> > OK
*

*>
*

*> Entropy Optimization Principles With Applications by J. N. Kapur, H. K.
*

*> KesavanAcademic Press, 1992 ASIN: 0123976707
*

*>
*

*> snip
*

*> > > [SPK]
*

*> > > > > This would be the case for single observers? The basis of the phase may
*

*> > > > > be different for another observer! This is like having more than one
*

*> > > > > convex vector space (subsets of Universe) in which to embed the "overall
*

*> > > > > phase".
*

*> > > >
*

*> > > > In TGD there is only single huge state space describing the states of
*

*> > > > universe. Strong form of NMP selects subsystem-complement pair as
*

*> > > > decomposiotion of state space to two tensor product factors.
*

*> > > > In p-adic context situation becomes more practical since NMP applies
*

*> > > > separately to subsystems with vanishing entanglement entropy.
*

*> > >
*

*> > > That "single huge state space" looks just like Hitoshi's \phi in, for
*

*> > > instance: http://www.kitada.com/time_III.html:
*

*> > >
*

*> > > "Our axiom 1 which asserts that the total universe, which will be
*

*> > > denoted \phi, is stationary means in its mathematical formulation that
*

*> > > it is an eigenstate of a total Hamiltonian H. This means that the
*

*> > > universe \phi is an eternal truth, which cannot be explained in terms of
*

*> > > duration or time.
*

*> >
*

*> > Yes. This is the standard physics with single objective reality.
*

*> > In TGD \phi changes from quantum jump to quantum jump. Otherwise
*

*> > pictures are identical.
*

*>
*

*> I looks to me that your jumps are "seeing" only the local picture. :) I
*

*> have long thought that there are more than one \phi, in fact an
*

*> "undecidable" infinity of them! They make up all the "proper subsets" of
*

*> the Universe, which is ALL.
*

*> But, are you are using a different mechanism than Hitoshi to quantify
*

*> Becoming? I think it is your Kaehler action. I have not been able to
*

*> understand what it is! :(
*

Good old Maxwell action with Maxwell field expressed in terms of CP_2

coordinate which are the primary dynamical variables.

*>
*

*> > > In fact, the eigenstate in itself contains no
*

*> > > reference to time, as may be seen from its definition: H\phi=\lambda\phi
*

*> > > for some real number \lambda. The reader might think that this
*

*> > > definition just states that the entire universe \phi is frozen at an
*

*> > > instant which lasts forever without a beginning or end.
*

*> >
*

*> > In TGD \phi would be completely determined by its values of ligthcone
*

*> > boundary in strictly causal theory and one could say that everything
*

*> > reduces to lightcone boundary: no psychological time. Classical
*

*> > nondeterminism of Kaehler action changes the situation. In order to
*

*> > specify nondeterminism one must introduce moments of multifurcations for
*

*> > spacetime surfaces, and data like this and these parameters correspond
*

*> > closely to time values around which contents of cs experience is
*

*> > concentrated.
*

*>
*

*> I think that your \phi and Hitoshi's \phi are very different! Hitoshi's
*

*> LSs has no lightcone structure internal, all spacetimes and their
*

*> defining lightcone structures are constructed from interactions between
*

*> Local Systems. This is why I say that your work is coming from the
*

*> opposite direction from Hitoshi's.
*

*>
*

Certainly the mathematical structures are different.

*> > > However, as we
*

*> > > will see, the total universe \phi has
*

*> > > infinite degrees of freedom inside itself, as internal motion of finite
*

*> > > and local systems, and never freezes. Therefore, as an existence itself,
*

*> > > the universe \phi does not change, however, at the same time, it is not
*

*> > > frozen internally. These two seemingly contradictory aspects of the
*

*> > > universe \phi are possible by virtue of the quantum mechanical nature of
*

*> > > the definition of eigenstates."
*

*> > >
*

*> > I think that I understand this. System can have vanishing momentum even
*

*> > when component systems have nonvanishing momenta.
*

*> > If phi does not change it seems that universe has zero energy.
*

*> > If one applies naively the idea that energy is additive one would
*

*> > conclude that negative energies must be present. Gravitational binding
*

*> > energy?
*

*>
*

*> Yes, if we use your formalism. In the level of the whole, all
*

*> properties (energy included) sum to zero at U! This is not the quantum
*

*> vacuum, such is an inference construction given observations as we can
*

*> not ever observe a vacuum!
*

*>
*

*> > By the way, also in TGD zero energies might be possible if spacetime
*

*> > surface is allowed to have time orientation opposite to that of
*

*> > imbedding space. I do not really know whether to allow this or not.
*

*> > The energy densities of various spacetime sheets could sum up to zero!
*

*> > Everything would be created from emptiness!
*

*>
*

*> The embedding space is CP^2? "Creation from emptiness"? Sort of, but,
*

*> again, this is an inference not an observation!
*

Imbedding space M^4_+xCP_2 is nondynamical given. Spacetime surface would

be created from emptiness in this kind of scenario in the sense that

classical total energy would vanish.

*>
*

*> > > [SPK]
*

*> > > The role of Diff^4 is localized in LS theory such that it is not
*

*> > > assumed to cover \phi at the totality level! We only have Diff^4 over
*

*> > > the set of simultaneous observables (time-like hypersuface?) of
*

*> > > individual observers. Thus it is not a single Diff^4 group for all
*

*> > > observers, but one Diff^4 for each observer, and thus a uniquie
*

*> > > space-time for each observer. Of course, when we generalize this notion,
*

*> > > as you have done by using p-adics, we get the "many sheeted" spacetimes
*

*> > > and can have overlapping and underlapping of the sheets...
*

*>
*

*> I am not sure that Hitoshi agrees with this take of LS theory... But,
*

*> we will see were it takes us... :)
*

*>
*

*> > So you don't assume that different LS:s integrate to single spacetime
*

*> > surface. In fact, manysheeted spacetime makes sense also in real
*

*> > context: point is that different spacetime sheets allow effective p-adic
*

*> > topology which is very useful in the construction of QFT limit:
*

*> > in excellent approximation one can construct QFT in single region
*

*> > of this kind forgetting what happens on boundaries.
*

*>
*

*> Yes, the very idea of integration is changed since we do not have a
*

*> single metric or gauge or norm, etc. ("a priori synthetics"), for all
*

*> possible observers! Classical physics is blind to this idea because of
*

*> its assumption of a Universal Observer (GOD) fixing the a priori
*

*> synthetics for all.
*

On the other hand, one could say that basic structure, where integration

takes place place represents all possible Universal Observers (I would

call them objective realities).

*> One we realize that such an assumption is impossible
*

*> and that observers can only be finite (although hierarchies are the
*

*> rule!) we find that integration is no longer possible in the pragmatic
*

*> sense by using infinitesimal pieces. Thus my complaints about
*

*> infinitesimals and my attempt to discuss Herman Weyl's original gauge
*

*> invariant geometry!
*

*> My main reasoning for thinking that Weyl is correct is that the
*

*> smearing of spectra is not observable since individual LSs can only
*

*> sample discretely each other's behavior and so each have convex
*

*> probability distributions of their own sets of observables. This is
*

*> implicated by the idea that each observer (which is composed of a
*

*> partial ordering of observations, as you show) has a different
*

*> spacetime, given any particular moment. Thus your notion of quantum
*

*> jumps makes sense to me. :)
*

*>
*

*> > > > The power of General Coordinate Invariance is remarkable: it has
*

*> > > > practically fixed the general form of the theory totally. Configuration
*

*> > > > space geometry; quantum jump between quantum histories concept fixing the
*

*> > > > general structure of TGD inspired theory of consciousness; and finally the
*

*> > > > mapping of real spacetime surfaces to their p-adic counterparts
*

*> > > > and p-adicization of entire TGD, which I told in some earlier posting.
*

*> > >
*

*> > > Yes, GCI is powerfull but it is far to restricive in the usual form.
*

*> >
*

*> > Yes! But this might be its power! Only month ago I was ready to consider
*

*> > the possibility of giving up GCI since it seemed that it simply does not
*

*> > allow p-adicization of quantum TGD.
*

*>
*

*> Could you elaborate?
*

*>
*

The problem was caused by the fact that canonical identification mapping

SUM x_np^n --> SUM x_np^(-n) of real imbedding space coordinates

to their p-adic counterparts is not manifestly GCI.

Mapping looks like this only in single coordinate system. One must thus

find physical arguments fixing the coordinate system uniquely. Or if the

coordinate system is not fixed uniquely, one must modifify the form of

canonical identification map such that it commutes with the allowed

coordinate transformations.

This requirement fixes the choice of imbedding

space coordinates and fixes canonical identification (remember the

postings involving Pythagorean angles, etc...)

In case of complex plane modified canonical identification

maps radial coordinate by canonical identification but

rational phase factors exp(iphi) of z-coordinate are identified as such

as p-adic numbers (rather than mapping phi using canonical

identification). Rational phases correspond to Pythagorean triangles,

*> > > It is necessary to say "the laws of physics look the same to all observers"
*

*> > > but this assumes that "all observers" form a convex set (complete graph)
*

*> > > and that there is only one such set.
*

*> >
*

*> > This statement goes outside my mathematical intuitions (convex set,..).
*

*> > Again this dangerous notion of 'observers': what about replacing
*

*> > it with 'observations'?
*

*>
*

*> A convex set here is an all inclusive collection. Observers are defined
*

*> by partial orderings of observations and a partial ordering of physical
*

*> events that encode the information content of the observations. This
*

*> follow from the duality of physical "events", and information states.
*

*> See Pratt's work.
*

*>
*

*> > > I claim that there is not, there an
*

*> > > an unenumerable number of such sets that are "almost convex" in that
*

*> > > they have a fuzzy boundary instead of a crisp binary boundary. This
*

*> > > notion is part of the "window" notion that represents the sampling of
*

*> > > the stream in my discussion of Peter's work.
*

*> > > In sort I say, "all observers that have similar enough perceptions of a
*

*> > > *set of physics* can communicate with non-zero *expressiveness*". Thus
*

*> > > this implies that observers that have different physics can not
*

*> > > communicate anything to each other other than noise! But, given
*

*> > > sufficient "interactive computational" time, ways to decode messages
*

*> > > from the noise become possible.
*

*> > >
*

*> > 'Physics' is cognitive representation for what happens in external world?
*

*>
*

*> Yes! But note that this implies that were is not a single 'physics'
*

*> just as there is not a single observer, and thus there are more than one
*

*> "cognitive representation" and "external world"!
*

Yes. This is certainly true. The ultimate physics/theory of cs must be

such that it also predicts this.

*> The classical mistake
*

*> is the assumption of a single "external world" observable by an
*

*> arbitrary observer (i.e. is an element in at least one of the posets)
*

*> identified with the Totality Universe. This notion is "not even wrong"!
*

*> It is impossible!
*

*>
*

You are right.

* > > [SPK]
*

*> > > > > I would not assume a unique metric (inner product norm) for the
*

*> > > > > integration, such assume that the configuration spaces of observations
*

*> > > > > all have the same size "parts", this is wrong! My comments about using
*

*> > > > > Weyl's geometry speaks to this. We solve the indefinite spectra problem
*

*> > > > > by showing that observers can only sample discrete partitions of the
*

*> > > > > continuous spectra and thus, just as Weyl said, the smearing is
*

*> > > > > unobservable just like "pure" states!
*

*> > > > >
*

*> > > > In TGD approach the 'physics as geometry' philosophy
*

*> > > > fixes the inner product to very high degree. p-Adicization
*

*> > > > seems however necessary. Real valued S-matrix elements simply do not
*

*> > > > exist mathematically. Integration in infinite-dimensional context
*

*> > > > is extremely tricky. Consider only volume of infinite-dimensional sphere:
*

*> > > > it is typically zero or infinite.
*

*>
*

*> Umm, but notice that the number of possible geometries of 4-dimensional
*

*> manifolds is nonenumerable infinity! This there is more that one inner
*

*> product! I am identifying an observer with each manifold. To quote Chris
*

*> Moore:
*

*> ***
*

*> > I vaguely remember that the problem for the next dimension up (4-manifolds)
*

*> > is Turing machine equivalent, so no classification procedure can exist
*

*> > (although this was a long time ago - I'm not sure about that).
*

*>
*

*> This is true; it's because a 4-manifold can have an arbitrary group
*

*> as its fundamental group, and the question of whether two infinite
*

*> groups
*

*> are equivalent is undecidable.
*

*>
*

*> - Cris Moore, Santa Fe Institute
*

In TGD the situation is not quite this.

a) 3-surface is the basic

object: 4-surface is determined by minimization of Kaehler

action and by the requirement that it 'goes through' given 3-surface.

b) 3-surfaces must be also imbeddable to M^4_+xCP_2. This

gives a restriction to the topology of 3-surface. Not

all topologies are imbeddable: various manifold structures

is more refined concept and would probably require even higher

dimension for imbedding space.

*>
*

*> --
*

*> As I stepped out upon the landing my heart was already down the
*

*> stairs...
*

*> --- Elvis
*

*> Costello
*

*> -----------------------------------------------------------------------------
*

*> Cris Moore Santa Fe Institute moore@santafe.edu
*

*> http://www.santafe.edu/~moore
*

*> ***
*

*> I am unfamiliar with the specifics of the S-matrix. :( I have read that
*

*> the volume of an infinite dimensional sphere is "on the surface" of the
*

*> manifold...
*

*>
*

S-matrix codes the predictions of QFT.

S-matrix elements S_mn represent transition amplitudes m-->n

Unitarity means that the rows (columns) of S-matrix are unit vectors

orthogonal to each other. Unit vector property tells that

total probability for transtion m-->some state is one.

Unitarity generalizes probability conservation and makes it much more

stringent condition since orthonormality of rows gives very strong

constraints. Once particle physicists hoped unitarity to fix S-matrix

uniquely.

*> [SPK]
*

*> > > But is this "fixing" necessarily unique for
*

*>all possible observers and
*

*> > > strictly not definable relative to finite subsets of communicating
*

*> > > observers? If it is, then there is a serious problem with my notion. :(
*

*>
*

*> > In TGD the inner product belongs to the Platonic Realm and is
*

*> > observer/observation dependent. The inner
*

*> > product is for the states of entire universe, for phi:s as you call them.
*

*> > Jumps between quantum histories phi_1--> phi_2 pjio_2-->phi_3 ..!
*

*>
*

*> So are you saying that there is only one inner product for the
*

*> Totality? I do not think so...
*

*>
*

In infinite-dimensional context the mere divergence free existence is

extremely strong constraint.

a) Inner product reduces almost completely

to metric of configuration space dV= sqrt(detG) dX^3, G metric of

configuration space. The metric of configuration space is however

unique from requirement of Kaehler structure and existence of Riemann

connection: metric possesses maximal group of symmetries.

Configuration space turns out to be a union of symmetric spaces (CP_2 is

also such) whose all points are equivalent metrically.

Symmetric space property implies that curvature tensor is covariantly

constant and one has Einstein space property R_ab= lambda g_ab.

The requirement that curvature scalar R= g^abR_ab is finite

requires lambda =0. Vacuum Einstein equations are satisfied!

b) Besides this there are constraints from divergence cancellation.

For instance, infinite-dimensional determinant det(G) is

poorly defined as infinite dimensional determinant. Problem is solved if

configuration space spinor fields are proportional to exp(K/2), K the

Kaehler function oif configuration space. In perturbative Gaussian

integration the Gaussian determinant coming from K cancels sqrt(G) and

one avoids problems. Thus vacuum state functional exp(K/2), which

is the quintessence of quantum theory, is fixed uniquely!

No postulates about dynamics, only mathematical existence and

one has fixed the basic structure of theory uniquely!

c) Second problem. When one

expands sqrt(detG) in geodesic coordinates one obtains in second order

term which gives in Gaussian integration curvature scalar

of configurations space. As already noticed R is either zero or infinite

and zero only if vacuum Einstein equations are satisfied.

*> > The inner product for configuration space spinor fields reduces to inner
*

*> > product ofm configuration space spinors integrated over entire
*

*> > configuration space of 3-surfaces. Inner product of spinors is just Fock
*

*> > space inner product for fermions (oscillator operators create the state).
*

*> >
*

*> > In your case you have single phi and inner product must be inner product
*

*> > for some subsystem (LS?). Hence situation is different from that
*

*> > in TGD.
*

*>
*

*> I am getting confused. :( We need to ask Hitoshi about these details...
*

*>
*

*> > > snip
*

*> > >
*

*> > > [SPK]
*

*> > > > > Making "'our minds' as outsider" is modeling our minds, it does not
*

*> > > > > give a complete knowledge of the subjective stance, but we can use it as
*

*> > > > > information from which to infer sets of observables and the
*

*> > > > > superselection rules that order them. I call this "contextual
*

*> > > > > definiteness". I can not say with probability 1 what you see, but I can
*

*> > > > > calculate what you might see that I can also see. Does this make sense?
*

*> > > > > It is like figuring out if a distant observer that I can talk to on a
*

*> > > > > radio can observe something similar to what I do. I can not "see" what
*

*> > > > > he sees, but I can say with high certainty (low error) that we observer
*

*> > > > > "the same thing".
*

*> > > [MP]
*

*> > > > Your argument certainly makes sense. What I am however troubled is the
*

*> > > > introduction of observers as fundamental (the concept is of course very
*

*> > > > practical approximation). Introduction of observers at fundamental
*

*> > > > level leads to consistency conditions on the observations if they
*

*> > > > correspond to quantum jumps.
*

*> > >
*

*> > > Neither the "observer" nor the "jumps" are "fundamental", as I see it;
*

*> > > they are complementary. Having one without the other renders them
*

*> > > meaningless! Existence is the grundlagen.
*

*> >
*

*> > I think that I disagree. The use of single phi means materialistic
*

*> > (sorry!(;-)) world view with single objective reality. Materialism leads
*

*> > to problems with inner product besides all these social problems(:-). In
*

*> > TGD I allow all possible phis, quantum histories. TGD is nonmaterialistic
*

*> > theory in strong sense.
*

*>
*

*> Thus I am proposing many \phi! :)
*

*>
*

*> > > [MP]
*

*> > > > Introducing only observations one can avoid this problem.
*

*> > > > The point is that *You and I only rarely do we both participate same
*

*> > > > moment of consciousness*. If we participate the same moment of
*

*> > > > consciousness and have separate experiences (are unentangled) then what
*

*> > > > we see, are not views about the same landscape: no consistency problem.
*

*> > >
*

*> > > I am thinking about how it is that we can "participate [in] the same
*

*> > > moment of consciousness"! :) I think of this as a correlation between
*

*> > > the observation (= "quantum jump"). I am identifying correlations with
*

*> > > co-inductions (and/or bisimulations?) between stream, which are "quantum
*

*> > > histories" to me, just in different clothing. :)
*

*> > >
*

*> >
*

*> >From TGD view point I see co-induction and bisimulation is higher
*

*> > level concepts related to cognitive representations, which correspond in
*

*> > TGD to cognitive spacetime sheets. Quantum jump is lower level concept.
*

*>
*

*> The quantum jump is the "primitive", yes! :)
*

*>
*

*> > Participation in same quantum jump with separate conscious experiences
*

*> > mean experiences about different sub-Universes/tensor product factors of
*

*> > overall state space. Objects of perception are different.
*

*>
*

*> Yes. But, there is an illusion that the "same" object is observed by
*

*> more than one observer. Like this text file, as you read it on your
*

*> computer. The particular representation you read is *not* the one I am
*

*> writing, even though it contains very similar information content as
*

*> what I am presently typing (encoding). ;)
*

*>
*

You are right. This perhaps explains how difficult communication is (this

became as a real shock to me, when I started participating various

discussion groups 4-5 yeares ago!). If understanding occurs it happens in

unexpected manner(;-).

*> > > > When we are entangled we see the same
*

*> > > > thing but our conscious experiences fuse together so that there is only
*

*> > > > single experiencer 'we'! Consistency problem disapppears in all these
*

*> > > > three cases!
*

*>
*

*> > > This situation describes what happens in the infinite limit only! This
*

*> > > is the level of the Grundlagen and there is no duality of subject and
*

*> > > object here, thus you are correct. :)
*

*> >
*

*> > No limit is needed. Entanglement as binding solves the binding problem
*

*> > of neurophysiology (how different components of conscious exoerience
*

*> > fuse to form single experience and what this corresponds physically).
*

*> > This is basic hypothesis of TGD inspired theory of consciousness.
*

*>
*

*> :) Interesting.
*

*>
*

*> > When we are entangled, binding occurs and experience is 'we', moment
*

*> > of successful communication(;-).
*

*>
*

*> This is "error minimized bisimulation"!
*

*>
*

OK

*> [SPK}
*

*> > > We need something to use as a starting point in our model of QGR; thus,
*

*> > > yes, it is am "assumption", but we make it clear what we mean by
*

*> > > "observer": an observer is defined as a poset (partial ordering) of
*

*> > > quantum jumps over an ensemble of quantum histories . This wording is
*

*> > > insufficient for the final version, of course; I am just trying to hone
*

*> > > in on it. :) We need to be able to model concurrency!
*

*> > >
*

*> >
*

*> > Concurrency?
*

*>
*

*> Concurrent: "Existing or running together", "Acting jointly". The idea
*

*> involves many systems existing "simultaneously" yet interactions are
*

*> subject to constraints such that not all interactions can occur
*

*> simultaneously with respect to any single system. An example is the
*

*> construction of a house: all of the workers "exist" simultaneously, yet
*

*> they can not do their work on a single house simultaneously. There is an
*

*> order or schedule in which they can do their jobs. I say that "Time
*

*> exists because everything can not happen at once." in this sense.
*

*>
*

Concurrency seems to be related to synchrony.

*> Here are some links:
*

*> http://tebbit.eng.umd.edu/simulation/1994/94-12.html#94-12-08-14-01.43
*

*> http://www.comlab.ox.ac.uk/oucl/courses/MSC/node7.html
*

*> http://www.cs.helsinki.fi/njc/References/nielsenc1995:221.html
*

*>
*

*> This notion is very important in the reasoning that time is not R^1, it
*

*> is an "unfolding" and that this "unfolding" is irreducible to some
*

*> aspect of a static spacetime model of the Universe. I recommend the
*

*> writings of Henri Bergson about this notion... Thus it is also why I ask
*

*> questions involving computation!
*

*>
*

*> > > [MP]
*

*> > > > > > In a more general framework there is still one question making
*

*> > > > > > sense if state function collapse is identified as moment of
*

*> > > > > > consciousness.
*

*> > > > > > What principle determines which subsystem suffers wave packet
*

*> > > > > > collapse.
*

*> > > > > > Strong NMP answers this question in TGD approach.
*

*> > > [SPK]
*

*> > > > > I think it is a local optimization! Thus TDG seems to be in the
*

*> > > > > right track! :)
*

*> > > [MP]
*

*> > > > Strong NMP as such is formulated for entire universe. It reduces to local
*

*> > > > optimization in p-adic context: this is very important result. One can
*

*> > > > apply it to brain/neuron, etc. forgetting the rest of the universe.
*

*> > > > In real context this does not occur.
*

*> > >
*

*> > > Thus we agree on the necessity of p-adics! :)
*

*> >
*

*> > Yes. p-Adics are also necessary for evolution.
*

*>
*

*> :)
*

*>
*

*> > > > The reason for localization in p-adic context is following.
*

*> > > > If universe decomposes to mutually unentangled sub-Universes (which
*

*> > > > can have even finite size) then also general subsystem participating in
*

*> > > > quantum jump has similar decomposition. The real counterpart of
*

*> > > > entanglement entropy must (I leave it as an exercise why!) be defined as
*

*> > > > sum for the real counterparts of p-adic entropies for unentangled parts
*

*> > > > of subsystem. Hence maximization of negentropy gain effectively reduces
*

*> > > > to that occurring separately in each unentangled sub-universe and one
*

*> > > > obtains the desired localization.
*

*> > >
*

*> > > Hitoshi is proposing that Local Systems are "mutually unentangled
*

*> > > sub-Universes" composed of a finite number of parts which he calls
*

*> > > "quantum particles". They become LSs themselves when we shift to a frame
*

*> > > of observation that "focusses" on them. I believe that the hierarchical
*

*> > > nesting that this manifests is a clear example of p-adic orderings! Thus
*

*> > > my interest in your thinking. :)
*

*> >
*

*> > p-Adic ultrametricy leads naturally to hierarchical structures. Trees
*

*> > in which each node has p branches. Second hierarchical structure are
*

*> > p-adic spacetime sheets with various values of p glued on each other.
*

*>
*

*> Hitoshi's model, as I understand it does not model how "histories" are
*

*> generated; histories in the sense of ordering of physical events that
*

*> follow what is considered to be causal ordering.
*

*>
*

*> > > We do not have a clear definition of entropy in Hitoshi's papers, in
*

*> > > my opinion, so I am very interested in your reasoning here. :) I see
*

*> > > this "maximization of negentropy gain" as an example of Frieden's "EPI"!
*

*> > > It is local to individual LSs (as "unentangled sub-universe[s]") and
*

*> > > thus your conclusion follows. :)
*

*> >
*

*> > There is strong similarity. But strong NMP is not like ordinary
*

*> > variational principles. It does not imply deterministic time development
*

*> > since each quantum jump/quantum measurement has several possible
*

*> > outcomes. It only selects quantum jump. One cannot predict the future
*

*> > using this variational principle since one ends up to a garden
*

*> > of branching paths.
*

*>
*

*> So strong NMP gives us a model of how selection occurs? I would ask if
*

*> it is analogous to how environmental pressures select organisms by
*

*> culling the unfit...
*

*>
*

This is natural looking interpretation: moment of consciousness means

free will and power.

*> > The interpretation of absolute minimization of Kaehler action as
*

*> > maximation of classical nondeterminism<--> cognitive resources
*

*> > is much nearer to Frieden's ideas. Note however that also now
*

*> > nondetermninsm is involved!
*

*>
*

*> :)
*

*>
*

*> > There are strong reasons to believe that the most
*

*> > interesting quantum jumps select between branches of classical
*

*> > multifurcations: particle states being entangled with the branches
*

*> > of multifurcation. Classical and quantum nondeterminism would be
*

*> > very closely related!
*

*>
*

*> Is nondeterminism modelable mathematically by "one to many" and "many
*

*> to one" mappings?
*

*>
*

I believe that only statistical aspects of quantum nondeterminism are

modellable mathematically.

*> > Finally, principle what I call 'ontogeny repeats phylogeny'
*

*> > states that nondeterminism time development at spacetime level
*

*> > mimicks time development by quantum jumps at the level
*

*> > of configuration space. This could perhaps mean that
*

*> > p-adic nondetermism mimicks/simulates quantum nondetermism.
*

*>
*

*> I might say that the two are dual in a relative sense, relative to the
*

*> p?
*

I see quantum nondeterminism as fundamental.

*>
*

*> > There would be kind of holy trinity of all three nondeterminisms.
*

*>
*

*> Could you elaborate? :)
*

The idea is that these three nondeterminisms are closely related.

Classical---Quantum---p-Adic.

Classical---Quantum

Classical nondeterminsm is crucial for cognition and my volitional

acts (quantum nondeterminism) select between branches of

multifurcations of nondetermnistic classical spacetime developments.

Classical---p-Adic

When I assing p-adic spacetime surface to real spacetime surface,

p-adic nondeterminism is necessary in order to represent

classical nondeterminism of real spacetime surface.

I was very enthusiastic about this idea but it is not so precise idea

as I first believed. In any case, these 3 nondeterminisms are

very closely entangled in the structure of quantum TGD.

*>
*

*> More later,
*

*>
*

*> Stephen
*

*>
*

**Next message:**Matti Pitkanen: "[time 388] Re: [time 384] Re: [time 380] Re: [time 376] What are observers"**Previous message:**Stephen P. King: "[time 386] Re: [time 385] The Universe, \Phi and Inner Products"**In reply to:**Matti Pitkanen: "[time 380] Re: [time 376] What are observers"**Next in thread:**Hitoshi Kitada: "[time 385] Re: [time 384] Re: [time 380] Re: [time 376] What are observers"

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