Matti Pitkanen (email@example.com)
Thu, 27 May 1999 20:12:23 +0300 (EET DST)
On Thu, 27 May 1999, Stephen P. King wrote:
> Dear Matti,
> Your post makes me smile! :) I have such a hard time trying to
> communicate my mental pictures... but every once in a while... ! ;)
> Matti Pitkanen wrote:
> > On Wed, 26 May 1999, Stephen P. King wrote:
> > > Hi All,
> > >
> > > What is information? Good question! We define it by throwing out what
> > > it is not...
> > > This article is a good start!
> > >
> > > http://www.aip.org/physnews/preview/1997/qinfo/sidebar1.htm
> > Thank you for stimulating me to think about information concept again.
> > I try to collect my older ideas in hope that something new might
> > arise spontaneously.
> > a) Information as selection
> > Basic idea, represented also at the website, is that information
> > involves selection. Your decision to send me email about the the URL
> > reduced my guesses about the possible addresses of
> > URL:s of the web sites containing information about the concept of
> > information. The problem is that the definition involves conscious
> > selection between alternatives, which in my own conceptual framework
> > means quantum jump. It is not clear that this kind of
> > definition of information describes absolute information
> > contained by the physical state.
> :) That makes sense! Information does seem to involve acts of
> selection. I see this as analogous to the "reduction" process used in
> the Copenhagen Interpretation. Taking the analogy further with a
> Darwinian idea, we might ask: what is mutation? Could it be represented
> by the Phi propagator, e.g. the Schroedinger Wave?
> I would like to better understand what "absolute information" means!
> The symbols written between the "." "cause" a mental state for me, but
> how do I know if it is an absolute? By what standard? The term seems to
> imply ("to cause a mental state" !) that all possible observers
> (nonenumerable infinity?) would agree that the physical state X implies
> the meaning A. Then, by symmetry, I could infer with probability 1 that
> if A then X.
> There is something suspicious here! :( The Shannon entropy of such a
> physical state would be 0. Since it is a certainty. I would like to see
> what the Fisher information aspect of this would be...
> This is why I am so exited by Frieden's work...
> > b) Quantum information as information of conscious experience?
> > My original interpretation of negentropy gain in quantum jump
> > is in accordance with the concept of quantum information.
> > The reduction of quantum entanglement is a
> > choice and *negentropy gain= entanglement entropy of the
> > initial state* would thus be a measure for the information gained in
> > conscious experience. Quantum jump would be kind of self-measurement and
> > increase the knowledge of subsystem about itself.
> Is there a function type relation between the entanglement entropy and
> the number of "particles that are entangled"?
[MP] Only the number of entangled states matters.
If N states are entangled then maximum entropy is log(N). This follows
directly from the definition of entanglement entropy. One can diagonilize
density matrix and entropy in this basis is SUM p(n)log(p(n)), just
the Shannon entropy: p(n) are eigevalues of the density matrix. Maximum
entanglement entropy corresponds to p(n)= 1/N.
> > Rather paradoxically, entanglement entropy would represent
> > the potential information gain, and is *indeed a property of the
> > initial state*! This was something which I have not realized
> > earlier. Information would characterize the relationship between
> > subsystem and complement. On the other hand subsystem and complement
> > correspond to measured system and measurer, sender and receiver
> > of information in some sense. Could one define quantum information as
> > quantum entanglement between sender and receiver? Information
> > would be identical with alertness/attentiveness!
> I can see that this function increases with the distance from the
> observer, as in the case
> were more and more particles would have interacted, and thus be
> entangled, the further away one observes phenomena occurring. This would
> also translate to time!
[MP] Entanglement need *not* necessarily decrease with distance: entangled
particles can travel arbitrary far form each other without any change
in entanglement coefficients. This leads to the idea about
telepathy made possible by entanglement.
> The idea is that, given an initial singularity for a given
> observer from which all of the particles that that observer could
> measure "emerge", the particles would have an entanglement entropy that
> depends on the particular relationship R between subject and object or,
> as you say, measured system and measurer. The "time" would related to
> the "potential information gain" given R. If the particles were in a
> distribution that is static there would be no time since there would be
> no "motion", e.g. no change in entropy given the window of observation
> or "attentiveness".
> > In quantum jump this information would be transformed to conscious
> > information and disappear.
> This would translate, for me, to the zero time situation above and
> could be considered as the measure of a "moment of consciousness".
[MP] Information concept is paradoxical and allows several
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
[As a matter fact, 'englightened' S=0 subsystems can perform
passive quantum jumps]
> > On the other hand, it is very natural to interpret the reduction of
> > entanglement entropy as a measure for the 'catchiness' of the conscious
> > experience. But is 'catchiness' equivalent
> > with information content? Does a catchy commercial really contain
> > *information*? I would rather say that commercial just catches my
> > attention? But perhaps these commercials have some deeper meaning which
> > I have not grasped(;-)!
> This is an idea similar to something that I have been thinking about.
> :) I call "catchyness" "resonance" in the sense that the more catchy a
> set of information is the more resonant it is with my thinking. This
> does, of course, make it a subjective quantity... Umm, I should
> elaborate more... "more resonant it is with my thinking" means that I
> can relate the set of information (and its order is important!) to a
> larger number of "situations" than another set of information. I think
> that Peter's "expressiveness" captures this idea. Have you ever heard of
> "memes"? http://www.ed.cqu.edu.au/~bigumc/Meme/meme_definition.html,
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.
> > c) Sensory perception as a quantum measurement?
> > The interpretation of quantum jump as quantum measurement
> > suggests that the information content of conscious
> > experience is represented by the values of quantum numbers
> > for the selected state. Information gain would correspond to the
> > reduction of ignorance about quantum numbers.
> Is this "reduction of ignorance" balance by a consumption of free
> energy? The Maxwell Demon stuff comes to mind...
[MP] Entanglement entropy characterizes single
subsystem. Thermal entropy is statistical quantity: perhaps average
of entanglement entropy for a large number of identical subsystems
(I have been too lazy to really clear this to myself).
Concepts of free energy and thermal entropy involve assumptions
and statistical modelling of system. Entanglement entropy involves
no such assumption and is more fundamental quantity.
> > I have proposed a rather speculative model of color vision
> > inspired by a model of quantum model of honeybee dance
> > and by the identification of information as quantum numbers.
> I recommend our friend Robert Fung's essay on color at:
> > i) The original motivation for the term 'color group' was that
> > the Lie-algebra of the 'color group' SU(3) codes the algebra of
> > color vision. Various values of color quantum numbers (isospin and
> > hypercharge) would correspond to different colors (all colors can be
> > formed by mixing two basic colours in suitable proportions) and the
> > intensity of color would correspond to color Casimir operator, which is
> > counterpart of angular momentum squared. Black is obtained, when
> > Casimir goes to zero (no color rotation).
> Could you elaborate on this "Casimir operator"?
It is generalization of angular momentum squared. Angular momentum
squared is J.J, where J is angular momentum vector understood
as operator whose components are infinitesimal generators of rotations
around various axis. Eigenvalues are J(J+1), J=0,1,2,....
In case of color Casimir operator you have 8 component 'angular
momentum'. Eigenvalues are also now discrete, I do not remember
the precise formula. Color Casimir operator
corresponds to Laplacian for CP_2 just like J^2 corresponds to Laplacian
for CP_1= S^2. The simplest Hamiltonian for rotation rigid body is
J^2 and same is true in case of color rotations.
> > Of course, in QCD framework no one in his right mind would go to
> > suggest that QCD color could have anything to do with color vision but
> > in TGD situation is different!
> > ii) In TGD macroscopic objects correspond to spacetime sheets,
> > which behave like rigid bodies in CP_2 degrees of freedom
> > and can color rotate and color rotation gives them
> > color quantum numbers. Rods and cones (both) in retina could be in
> > various color rotating states and the distribution of these states would
> > be determined by the incoming light.
> 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.
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.
[Synchronous firing of neurons, syncronous assemly and disassembly of
microtubules, perhaps also coordinated biochemical reactions
could all be understood as consequence of strong NMP
requiring simultaneous quantum jumps to maximize negentropy gain.]
> > iii) Classical gauge electromagnetic fields are accompanied by
> > classical color fields and visual perception is known to generate
> > electric field in retina. Therefore observed color experience
> > would be the collective experience resulting from the simultaneous
> > measurement of color rotational states of rods and cones.
> > This picture seems to encourage the identification of information
> > content of sensory experience as measured quantum numbers (but perhaps
> > this is wishful thinking on my side(;-)).
> I see no conflicts so far. ;) But, again, such :identifications" are
> intrinsic to particular finite "relationships between subsystem and
> complement" and are thus not "absolute". I think this due to the very
> nature of "knowability", e.g. it is not possible to "know" an infinite
> amount of information...
Here our beliefs differ. I am sceptic about the concept of absolute
information. I believe that information is thoroughly 'relativistic
concept' because it is related to communication/measurement. I would
like to see information in the relationship between teacher and
student. If there is alertness, there is information in the
relationship and strong NMP might allow the transformation of this
information to conscious information in quantum jump. Information as
alertness/as catchiness of potential conscious experience.
> > d) Passive quantum jumps and sensory experiene
> > The counter argument against sensory perception as a choice
> > is that the experience of red does not involve a conscious
> > choice (unless the direction of attention to the object of
> > perception is this choice). Also the objectivity of sensory
> > experience seems to require that physical state does not change
> > in the sensory perception. Sensory perception would be like
> > classical measurements giving classical information.
> Well, the observer must not be blind to red to start with! :) So the
> fact that the observer has to have the ability to recognize red, or to
> put this is more physics terms, the apparatus must be able to have a
> physical change occur due to the impact of the frequency the corresponds
> to "red". Umm, this to me connects to my earlier thought of resonance...
> > This led to the hypothesis that also quantum jumps in which the state of
> > subsystem changes only by a phase factor, are possible. Physical
> > state does not change in these quantum jumps and
> > strong form of Negentropy Maximization Principle allows these quantum
> > jumps for the unentangled subsystem resulting
> > in quantum jump. Thus state function reduction would
> > be followed by a sequence of passive quantum jumps giving
> > rise to the sensory experience of say red. In previous
> > example passive seing would correspond to situation in which
> > rods and cones remain in their color rotational eigenstates
> > during some number of subsequent quantum jumps.
> Umm, this "sequence of passive quantum jumps", what determines the
> number? This is "persistence"?
The subsequent quantum jumps performed by other subsystems are bound to
lead to a situation in which entanglement is generated between subsystem
and complement. Then the perception of red no more continues.
One could characterize persistence or duration of conscious experience by
this number of quantum jumps.
> > e) Classical information
> > I find the concept of classical information (information
> > that can be copied) somewhat problematic from the point of view of
> > quantum theory. In TGD framework classical nondeterminism of
> > Kaehler action leads to a model of cognition based
> > on cognitive spacetime sheets glued on material spacetime
> > sheets and providing simulations of the material spacetime sheet.
> 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
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
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.
Cognitive spacetime sheets are almost vacuums, probably very few particles
of ordinary matter. Cognitive spacetime sheets have finite TIME
duration: this means that a little amount of energy flows to cognitive
spacetime sheet from material spacetime sheet when it 'starts'. When
cognitive spacetime sheet ends this energy flows back to the material
spacetime sheet. This is like putting adding measurement instrument
to electronic circuit: some current flows through circuit and provides
'cognitive representation' of circuit.
> > As I mentioned in earlier posting the number
> > of cognitive spacetime sheets glued to given region
> > of material spacetime sheets would give a possible upper for
> > classical information. I = log(N*M), where N is the number of
> > cognitive spacetime sheets and M is the the number of different
> > states of single cognitive spacetime sheet.
> Interesting, I am starting to understand what you mean by this pair of
> spacetime sheets. What mathematical relation exists between them? If
> they are Stone-Birkhoff dual then Pratt's ideas apply!
If you want to grasp spacetime sheet concept instantaneously, I
*strongly* (yes!) recommend the two-dimensional illustrations on my
homepage. I have again and again found in various discussions that all
my attempts to explain it verbally lead only
to wrong associations. Still one stubborn attempt: You have certainly
seen the Einstein-Rosen bridges in General Relativity books. Now you taken
finite piece of plane (say disk) and glue it to larger disk by this kind
of bridge. You can repeat this procedure. Same in higher dimensions.
> > But again I find that I might have more natural interpretation
> > as kind of intelligence quotient. Can one identify intelligence as
> > information content?
> Umm, perhaps intelligence is a measure of the range of different
> meaningful questions that can be asked... or the number of different
> simulations that can be performed given the observer's knowledge, this
> would correspond to your suggestion...
You are right: number of cognitive spacetime sheets describes the ability
to simulate classically.
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