Matti Pitkanen (email@example.com)
Sun, 30 May 1999 09:05:29 +0300 (EET DST)
On Sat, 29 May 1999, Stephen P. King wrote:
> 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?
Subsystem and complement are in completely symmetric position as far
density matrix is considered: one could consider also the density matrix
of complement, which is identical with that of subsystem in eigen state
> > 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?
I am not quite sure what you mean. It can quite well occur and occurs
that density matrix in eigenstate basis reduces to NxN matrix. N states
of subsystem are entangled with N states of complement. The number
M of states for subsystem gives upper bound for entangleent entropy
as log(M), which means that too simple systems seem to be losers in the
race about moments of consciousness (situation is however not so simple
Subsystems correspond to tensor product factors algebraically unless one
poses some additional conditions.
> > 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"?
In ordinary quantum measurement theory mysterious 'measurement
interaction' is introduced. Now nothing like this is introduced. Any
interaction serves as measurement interaction if it is able to generate
the needed amount of entanglement making quantum jump possible (NMP).
Any quantum measurement should basically reduce to a measurement of
density matrix. Density matrix representing quantum measumerent of ome
observable O should be expressible in terms of O and observables
commuting with it.
> > 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! ;)
Yes. This reduction to sub-universe has very important consequences. As
long as subsystem X remains in pure state, NMP applies to it
indepenently and in every quantum jump somne subsystem Y of X having X-Y
effectively as its complement makes quantum jump. And so on... This
implies that quantum jumps are top-down cascades of quantum jumps.
One could understand neuron firing (quantum jumps at neuronal level)
as consequence of quantum jumps at higher level (our
consciousness). Neuronal quantum jumps should in turn be followed by
quantum jumps in shorter length scales: syncrhonically occuring
biochemical reactions would be perhaps the lowest level.
> > > 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? ;)
> > > 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.
This last lines I agree: it is the basic idea behind quantum jumps between
quantum histories concepts. Consciousness is what makes possible to
study all possible predictions (quantum histories) of theory and one
can avoid the problem of initial values.
> > > 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... ;)
I did not catch your idea. In any case, in 'real' (as opposed to
p-adic) TGD consciousness is either or property. System is either
conscious or unconscious. System cannot be *consciously* uncertain about
its own state: if system is conscious, it is in pure state with infinite
This holds true in *real TGD*. I have been speaking in 'real mode'
all the time: in p-adic context entanglement with vanishing entanglement
entropy is possible and situation changes. System can make phase changing
quantum jumps while in entangled state with vanishing entanglement
entropy: is this what happens when we 'hesitate'?(;-)
> > > > [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!
I make the following sequence of identifications physical
states<--> quantum histories configuration spinor fields<-->
objective realities<--> Ideas/Forms.
One can multiply idea by overall phase (this must sound nonsensical
without this sequence of identifications!) without changing its physical
aspects. The function of overall phase is to make possible sensory
perception as classical measurement.
> > > 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
Any book on QM gives these basic definitions and short representation of
basic properties of Hermitian operators. In particular, the reality of
eigen values. In matrix representation of operators Hermiticity means O_mn
=(O_nm)^*. In diagonal representation this just means that elements
(eigenvalues) are real.
> > 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... :)
[MP] I have not said nothing about technical delicacies. Just the
physically motivated basic properties. The attempts to quantize
General Relativity nonperturbatively are guess work.
The basic unsatisfactory feature of standard QM based approach is related
to 'quantization'. There are operator ordering
problems related to the definition of observables, in particular
Hamiltonian, in the transition from classical to quantum,
Hamiltonian formalism is basically nonrelativistic since it is based on
In TGD framework the basic idea is 'Do not Quantize: Geometrize!
Quantum theory as theory of configuration space spinor fields representing
the quantum states. The Lie algebras of infinite dimensional symmetries
provide the algebra of observables and there are no normal ordering
Of course, there are still problems. The integration over
infinite-dimensional configuration space is the basic
problem: how to define it so that it exists mathematically and is also
practically calculable. Here lies one motivation for p-adic numbers.
> > > 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?
This question is fundamental but I do not regard it as general enough
since it takes 'our minds' as outsider. I would rather ask: what does
'our mind' mean? TGD answer is that 'our mind'/moment of consciousness
is the quantum measurement.
>Or what determines the _preferred states_ alpha_i into which the
>reduction takes place?"
Density matrix as fundamental observable answers this question in TGD
> (2.2) Phi\alpha -> SUM c_iPhi_i'\alpha
> (2.3) SUM c_iPhi'\alpha_i -> Phi_k\alpha_k
> (see the second part of
> https://members-central.home.net/stephenk1/Outlaw/Hermite.html for
> longer quote.
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.
> 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!
If you assume that there are infinite number of
observables giving rise to state function collapses, you could have
consistency problems: if the state function collapses associated with
different observers occur simultaneously, they might not be consistent
with each other.
Strong NMP solves this kind of consistency problems
automatically. There are only observations. Given quantum jump decomposes
in general into subquantum jumps with separate conscious experiences
defining a set of conscious observers conscious associated with that
> > > > 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.
> > > 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...
Yes. But dangerous unless one makes clear their limits of applicability
> > 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.
Agree with this: observation is interpretation.
But wants to modify information matter duality to identity: quantum
histories=objective realities ('matter') = Platonic Ideas
('information'). I do not know whether I am willing to
identify Platonic Ideas with information, which sounds so mundane(;-).
By the way, one could consider the formulation of the idea about
representation independence also in TGD context.
Quantum entanglement is characterized by the
properties of density matrix (the eigenvalues of density matrix).
The hypothesis would be that entanglement coefficients
and the final state of quantum jump would completely determine the
contents of conscious experience. This would mean that all kinds of
quantum subsystems would give rise to same conscious experience
since everything would reduce to the level of abstract Hilbert space.
I do not believe on this kind of representation independence.
In my own approach I would loose the proposed identifications of
quantum correlates of sensory qualia in terms of order parameters of
macroscopic quantum phases.
> > 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. :)
Might be! In any case, our philosophies differ here in decisive
manner. What troubles me in Cartesian approach is how one can make the
division into matter and mind. What distinguishes mind from matter? Does
matter-information duality mean that matter and mind can be permuted? Why
one could not call both matter and mind like parts of this structure
just matter like parts if deterministic model of world is in question?
I studied the article about Chu spaces and QM.
a) Complementarity (duality) was taken as fundamental feature of QM.
Completementary was also taken as fundamental aspect of QM in Copenhagen
interpretation and double slit experiment was explained in terms of
Uncertainty Principle. It is now clear that Bohr's explanation was wrong.
Quantum entanglement and state function reduction implying reduction of qe
explains the results of experiments. I told about this in some earlier
posting (article in some issue of New Scientist in the beginning of the
b) What troubles me that state function collapse was hardly mentioned
at all in the article (this was my impression at least). I think that this
IS the key problem: here the theory fails and here one should start the
attempts to generalize.
> > [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.
OK. Here we similar picture. I say that subjective time is not R^1 but
only a sequence of qjumps. But that geometric time is also present
(quantum histories are histories with respect to geometric time). I
see that geometric time is present in Hitoshi's approach. Have you
pondered the problem how geometric time is related to subjective time
in your approach?
> > 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.
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