Matti Pitkanen (matpitka@pcu.helsinki.fi)
Thu, 27 May 1999 09:10:10 +0300 (EET DST)
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
>
> Later,
>
> Stephen
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.
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.
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!
In quantum jump this information would be transformed to conscious
information and disappear.
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(;-)!
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.
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) 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).
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.
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(;-)).
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.
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.
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.
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.
But again I find that I might have more natural interpretation
as kind of intelligence quotient. Can one identify intelligence as
information content?
MP
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