Stephen P. King (email@example.com)
Fri, 04 Jun 1999 15:06:36 -0400
Matti Pitkanen wrote:
> On Tue, 1 Jun 1999, Stephen P. King wrote:
> > 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
> 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!
> > [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
> 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"?
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! :)
Entropy Optimization Principles With Applications by J. N. Kapur, H. K.
KesavanAcademic Press, 1992 ASIN: 0123976707
> > [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! :(
> > 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
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.
> > 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
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!
> > [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. 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
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?
> > 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"! 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!
> > [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
> 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
are equivalent is undecidable.
- Cris Moore, Santa Fe Institute
-- As I stepped out upon the landing my heart was already down the stairs... --- Elvis Costello ----------------------------------------------------------------------------- Cris Moore Santa Fe Institute firstname.lastname@example.org 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...
[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... > 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). ;) > > > 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"!
[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. 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... > 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? > 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? > There would be kind of holy trinity of all three nondeterminisms.
Could you elaborate? :) More later,
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