Stephen P. King (stephenk1@home.com)
Sat, 29 May 1999 18:11:16 -0400
Dear Matti,
Sorry about the length of this response... :) I put some quotes on my
web site and have links here to them.
Matti Pitkanen wrote:
>
> Hi,
>
> I think that there is some basic misunderstanding on my side.
> I got the impression in the beginning of discussion that you
> believe on some kind of absolute information independent of
> representations. Actually much of my arguments have been against
> this concept. It however seems that I have been fighting against
> windmills. But this occurs for me often...
That is ok, I am often guilty of making meaningless noise! :)
> Below some comments.
>
> On Fri, 28 May 1999, Stephen P. King wrote:
> > I need to get a better handle on this math. I am reading my information
> > theory and statistics books... :) Umm, are the terms modified for
> > situations were choices are not independent of ordering as in the case
> > of a series of observations of non-commutative measurements?
> >
>
> Density matrix is totally determined by the state of universe.
> It characterizes subsystem.
>
> a) Suppose that the state of entire system
> is given as
>
> Psi = SUM(mM) C_mM |m>|M>
>
> where m and M refer to subsystem and complement.
Is there an inverse to this such that what was the subsystem in one
framing is the complement in the other and the same for the complement?
What do we mean by "the state of the universe"? Is this an infinite
matrix with its entries elements of the set of REAL numbers?
> b) Density matrix of subsystem is defined by summing over the degrees
> of freedom of complement:
>
> rho_mn = SUM (M) C_mM C^*_nM.
What is the complement had only a finite number of components? How do
we distinguish between subsystems?
> c) It can be diagonalized as a Hermitian matrix and reads as
>
> rho_mn= p(m) delta (m,n) (Kronecker delta)
>
> p(m) is entanglement probability.
>
> d) In quantum jump one of the eigenstates of rho is selected if one
> assumes that density matrix is universal observable.
What are the implications/meaning of "universal observability"?
> e) Final state of quantum jump is an entangled state |m>|M> , where m
> and N refer to states of diagonalizes representation. This is *pure*
> state. Subsystem in pure state behaves in this state like its own
> subuniverse and can be described by state vector.
This looks like Hitoshi's definition of an LS! ;)
snip
[SPK]
> > The entangledness of particles, to me, seems to be what composes them
> > into a "subwhole" that is a Local System, and the notions of distance
> > and speed to not apply in the usual sense. I was talking in the section
> > above about the "outside" of the LS, e.g. "what is observed" by an LS.
> > LSs may have have "parts" that are identical to those of another
> > adjoint (?) LS and so we could say that they are causally entangled. I
> > need to discuss this idea more with Hitoshi, as it is his area.
> >
> [MP]
> You are right.
How is this notion symbolically rendered? ;)
> > snip
> > > [MP] Information concept is paradoxical and allows several
> > > interpretations.
> > >
> > > a) One could say that entanglement entropy measures
> > > amount of illusions, the uncertainy of subsystem about its own state:
> > > entanglement entropy would measure disinformation.
> > > In quantum jump subsystem is enlightened and goes to entropy zero state.
> > >
> > > b) On the other hand, one could associate to subsystem information as
> > > *entanglement negentropy gain*= entanglement entropy in quantum jump and
> > > with this interpretation entanglement entropy becomes information.
> > > In order to get enlightned one muust first generate illusions,
> > > the more illusions one has managed to generate, the better are changes
> > > for enlightment!
> > >
> > > Hopeless!!
> >
> > Don't give up yet! :) It could be that you just need to go a bit
> > further! What is finite knowledge but "illusion" given that Absolute
> > knowledge is impossible?! But with a large repertoire of "illusions"
> > bounded truths can be communicated! More detail:
> > We can quantify the measure of "the uncertainly of subsystem about its
> > own state" as an intrinsic error e and show that it can be reduced
> > proportional to the number of simulations that can be performed by the
> > system to "check for error". In the limit, and only there, does the
> > error e-> 0 and the number N of trials go to infinity. This follow the
> > notion that only if we look at all possible predictions of a theory can
> > be be absolutely sure that it is an Absolute truth.
> > It seems that the usual probability theory assumes that the infinite
> > number of trials is available "in finite time" or it is just assumed to
> > exist a priori to construct the ensemble or infinite length time series.
> > This is a pure idealization that must be looked at with caution.
Did my notion make any sense? I do need to be able to communicate this
strange notion of mine... ;)
> > > [As a matter fact, 'englightened' S=0 subsystems can perform
> > > passive quantum jumps]
> >
> > Ok, but this is independent of communications/interactions between such
> > subsystems, is it not?
>
> Yes. These would be classical measurements in which only mathematical
> state but not physical one changes. Passive quantum jump would provide
> 'reason why' for the mysterious phase redundancy of QM: phase redudancy
> would not have physical significance but would be crucial in making
> possible sensory perception as quantum jump not changing physical state.
How do we think of "mathematical states" as aspects of the Universe?
They do exist, but how are they categorized? This question speaks to the
nature of Platonic Ideas/Forms!
> > [MP]
> > > Yes. I consider quite seriously the possibility that cognitive spacetime
> > > sheets are the memes, living systems at the highler level of cognitive
> > > hierarhcy. Able to replicate and fill the Earth.
> >
> > Umm, since I am distinguishing information from matter as categorically
> > different (dual in Pratt's CHu space sense), I would say that memes are
> > an example of "cognitive spacetime sheets" not the other way around. I
> > am trying to be more general... :)
>
> [MP] Of course! This is what I meant.
:)
> > Could we have a discussion about operators in general? The use of
> > infinitesimals is still problematic since we they are unobservable in
> > principle...
> >
> This would take a lot of room. In quantum theory basic operators
> Hermitian and unitary operators. I recomment some book of quantum
> mechanics.
>
> Hermitian operators represent observables: their eigenvalues are real
> and represent the measured values of the corresponding physical
> observables. Angular momentum, spin, momentum, etc... Also density
> matrix is Hermitian and therefore identifiable as observable.
Umm, I am still not understanding these assumptions of what constitutes
an "observable". :( I have yet to find a definition of "Hermitian" that
makes sense to me. :( I will look at D. Bohm's text that I have on my
book shelf... : See
https://members-central.home.net/stephenk1/Outlaw/Hermite.html
> Unitary operators define the allowed changes of basis. Unitarity means
> that inner products are preserved: kind of general coordinate invariance
> at the level of state space. Time development operator is the most
> important unitary operator and defines unitarity S-matrix. Eigenvalues
> of unitary operators are phase phase factors. Unitarity operators can
> be represented as exponentials of Hermitian operators (U= exp(iH), H
> Hermitian).
Umm, I have been reading Smolin and other's papers were the inner
product is a bit ambiguous as a notion. I am thinking that it too
follows the principle of Subjectivity: For any given Local System there
is a set of "rules" with which it constructs its set of observables.
This includes an inner product and norm, etc.! I also need to discuss
this idea with you all... :)
> > [SPK]
> > > > So would we say that the particular "experienced" colors are selected
> > > > by the "incoming light" or by a selective "game" played by the rods and
> > > > cones against the spectra of the incoming light? See Frieden's
> > > > discussion of "EPI as a game of knowledge acquisition" pg. 79-82, 275 of
> > > > his book.
> > >
> > > [MP] One might perhaps say that incoming light kicks rods and cones
> > > (both?) to color rotational motion and isospin and hypercharge depend
> > > on the wavelength of light. Our color experience would be kind of average
> > > over contributions of all rods and cones.
> >
> > I am trying to see both sides, the "incoming light" and the "rods and
> > cones" as opposing players in the information acquisition game... I
> > believe that it is a mistake to assume that either one is a priori
> > definite in its properties.
>
> [MP] Difficult to say. Here our backgrounds are so different. I do not
> catch the idea of perception as game. One could however see
> subsystems (at least sufficiently intelligent ones) as participants of
> information acquisition game. Strong NMP would tell which subsystem had
> been able to generate the largest
> entanglement entropy: the prize is moment of consciousness,
> moment of free will (and power to change world!).
:) Indeed! This is were Frieden's work is of use! We solve the
"measurement problem" by working out the implications of the
subjectivity of observers! Reading from Jeeva Anandan's paper "Quantum
Measurement Problem and the Gravitational Field" in The Geometric
Universe, edited by S. A. Huggett et al; pg. 359
"The quantum measurement problem is the problem of understanding (2.3)
[see below for equations], which is referred to as the reduction of the
wave packet or collapse of the wave function. For example is (2.3) an
objective dynamical process [i.e. independent of subjectivity!], which
we may take (2.2) to be, or is it a subjective process we make in our
minds due to additional information we obtain from measurements? Or what
determines the _preferred states_ alpha_i into which the reduction takes
place?"
(2.2) Phi\alpha -> SUM c_iPhi_i'\alpha
i
(2.3) SUM c_iPhi'\alpha_i -> Phi_k\alpha_k
i
(see the second part of
https://members-central.home.net/stephenk1/Outlaw/Hermite.html for
longer quote.
I am saying that subjectivity in essence is a unique (for each on the
nonenumerable observers!) subjective process. I think that the idea of
"superselection" rules is applicable!
[MP]
> > > Strong NMP requires maximum negentropy gain in quantum jump and this
> > > favours simultaneous quantum jump for a large number of rods and cones.
> > > They must be quantum entangled mutually of their conscious
> > > experience are to integrate to single conscious experience.
[SPK]
> > Ok, but light has to be emitted by something and that ever the emitter
> > is, it is gaining information itself. The light would be the
> > "information channel".
>
> [MP] One could perhaps say so. I am however a little bit sceptic about
> bringing classical concepts in quantum context.
I am saying that "classical concepts" are, like "observers", an
illusion, but as Bohr explained, they are useful to communicate ideas...
snip
[SPK]
> > > > Two points: 1) How can we think of copying information in a
> > > > multi-observer quantum world? 2) what are the key differences and
> > > > similarities between "cognitive spacetime sheets" and "material
> > > > spacetime sheets". They look to me to be examples of Pratt's Mind and
> > > > Body as described in http://boole.stanford.edu/chuguide.html#ratmech
> > > > !!!!!! :) with the caveat that they have "reverse" dynamics...
> > > >
> > >
> > > [MP] The copying of classical information could be more or less copying
> > > of cognitive spacetime sheets. It would be counterpart of DNA
> > > replication/cell replication at the level of cognitive spacetime sheets:
> > > DNA replication is indeed geometric replication of 3-surfaces in TGD
> > > framework.
[SPK]
> > That would make sense but it looks like there has to be a separateness
> > between the "material" upon which information can be encoded by means of
> > ink spots, localized magnetizations, neuron connections, etc. There is
> > also the matter of a decoding scheme to transform the material encoding
> > to another form.... so that it can be communicated. I am not saying that
> > information is a substance, like the old theory of heat, but that it has
> > a categorical existence that is different from that of matter... The
> > fact that the "same" information can be encoded and transformed between
> > many different material substances is the evidence that I start with to
> > form this hypothesis. And Descartes' reasoning... :)
[MP]
> Could this independence of representation tell something about us rather
> than information? We know that these different representations are
> representation of same thing because they yield same conscious experience
> (simulation) using some interpreter? A a matter fact, this aspect
> led me to the 'absolute information' misunderstanding.
Well, we could use the mutual or correlation entropy formalism, which I
am interpreting to represent the similarities between systems involved
in the act of communication. But, since we are being a bit philosophical
here (my doing), why not use the term until we find something more
useful... Your idea that "different representations are representation
of same thing because they yield same conscious experience
(simulation) using some interpreter" is what, for me, proves the duality
of information and matter. The key is understanding that there is no
absolute "interpreter"! All observers are interpreters. I will explain
this below.
[MP]
> By the way, I studied Pratt's paper about Chu spaces but found I do not
> have the needed background in mathematical logic, etc... I understood
> however that the basic philosophy is to realize Cartesian dream
> of describing mathematically interaction of mind and matter.
Yes. :) This is a proposed solution to the infamous Mind-Boby problem,
and I believe, as does Pratt, that is resolves the measurement problem
of QM as explained above. :)
[MP]
> > > The first possibility is that replication is driven by purely
> > > classical dynamics. I have tried to understand how the absolute
> > > minimization of Kahler action could somehow lead to replication but in
> > > vain.
> > >
> > > An alternative possibility is that quantum jumps lead to
> > > states containing replicas: this would be quantum self-organization.
> > > The 3-surfacse containing several more or less identical cognitive
> > > spacetime sheets would have especially large negative Kaehler action and
> > > would be favoured by the vacuum functional of the theory: quantum jumps
> > > would sooner or later lead to this kind of situation. Precisely like
> > > spin glass enters at the bottom of especially deep energy valleys.
> > > Note that in hydrodynamical self-organization structures consisting of
> > > identical basic units are created.
[SPK]
> > I think that part of quantum jumping is "replication". I believe that
> > we need to extend our notions. I like that Hitoshi's model gives us the
> > needed extension by relativizing and quantizing individual observers.
> > You see, the original Classical world was one were there is only one
> > observer, God, who can observe *all* of the subsets of the Universe with
> > arbitrary precision without disturbing them in any way. We now know that
> > this is a severe idealization and that we must construct our models such
> > that we are always considering the observables of finite subjects with
> > limited resolvability. This is also why I say that Oracles can not be
> > consulted in finite time to get "True" information...
> >
> [MP] Here I full heartedly agree and my approach is one attempt to
> realize this. But my belief is that one must even give up the idea
> of observer at basic level and keep only the series of observations.
> Observation creates the subjective experience 'I am observer'.
Yes! I agree. I say that "observers" are represented by a partial
ordering (">/=" poset?) of observational acts. The trick is to identify
a given poset with an LS as its observations, where the LS's internal
propagator, as a clock, "ticks" off the observations in the sequence
spanning the poset ("life-time") of the LS. But, again, we use the
non-well-founded "streams" (that Peter discusses in his papers) instead
of the traditional R^1 strings to model this line of thinking. So I am
saying that Time is not R^1 and the posets are more like sampling
windows (DSP notion) than an "objective" a priori.
[SPK]
> Perhaps Descartes made too strong conclusion. Perhaps there are only
> deeds and no doers. Perhaps we are victims of our culture, in which doers
> have become so important. There are languages without subjects.
> I learned in qmind that Navajo Indians can talk for hours using only werbs
> (Dances with the wolfs).
Again we agree. I came to these conclusions from reading Bohm and
Finkelstein's work that all finite subsets of the Universe are actions.
The use of nouns, with their tacit static-ness, in Western cultures has
been obscuring the truth! Only the Universe (and its "proper" infinite
subsets) are in themselves is Static.
Onward to the Unknown,
Stephen
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