Hitoshi Kitada (hitoshi@kitada.com)
Sun, 6 Jun 1999 10:56:13 +0900
Dear Stephen,
----- Original Message -----
From: Stephen P. King <stephenk1@home.com>
To: Matti Pitkanen <matpitka@pcu.helsinki.fi>
Cc: <time@kitada.com>
Sent: Saturday, June 05, 1999 4:06 AM
Subject: [time 384] Re: [time 380] Re: [time 376] What are observers
> 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
>
> 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!
>
> > > 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.
>
> > > 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!
>
> > > [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
> 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?
>
> > > 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
> 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
>
> --
> 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...
>
> [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...
If you argue in LS theory, the inner products are of an infinite
number, proper to each Local System. I.e. LS theory considers an
infinite number of Hilbert spaces describing the inner state of each
observer's system. The outside of an observer's system is not
described by Hilbert spaces. Only a part of the outside that is an
object of an observation is described by a Hilbert space structure.
In LS theory, the phenomena arise by the participation of the
observer. In this sense, my standpoint is the same as the Wheeler's
"participatory universe."
The total state \phi of the universe is not considered in a Hilbert
space. It represents just the state of the total universe, which
does not evolve. No inner product is considered regarding \phi.
>
> > > 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.
> >
[MP]
> > 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(:-).
Single \phi does not need any inner product. By materialism, what do
you mean?
In
> > TGD I allow all possible phis, quantum histories. TGD is
nonmaterialistic
> > theory in strong sense.
In the observable world for an observer, all histories are possible.
\phi does not appear in observations. The universe \phi is different
from the observed universe.
>
> Thus I am proposing many \phi! :)
To each obsevation, there corresponds a proper universe. In this
sense, there are many \phi, where \phi is used in different meaning
from the \phi in the above.
>
> > > [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,
>
> Stephen
>
Best wishes,
Hitoshi
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