Date: Wed 26 May 2004 - 06:13:46 CEST
Dear colleagues,
In a more abstract formulation one can model a time-space event in a
four-dimensional hyperspace. A four-dimensional probability distribution
allows us to compute with a four-dimensional probablistic entropy:
H = - Sum(ijkl) p(ijkl) log (p(ijkl)
A variation can be modeled as a vector or a one-dimensional probability
distribution. A selection adds structure and one needs a matrix or a
two-dimensional probability distribution for the representation of
variation and selection. A matrix at each moment in time allows us to
model a trajectory (stabilization) or more generally a geometrical
representation (a cube of information). A four-dimensional probability
distribution a hyper-space of time and space, that is, globalization.
As Leibniz noted, the calculus frees us from working with the
imagination. Cellular automata can represent the more complex phenomena
using a graphical interface of (that is, a window on) the complex
dynamics in the array of four dimensions that is used for the computing
in the background. The entropy measures enable us to evaluate the
results algorithmically and also to decompose them.
With kind regards,
Loet
_____
Loet Leydesdorff
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam
Tel.: +31-20- 525 6598; fax: +31-20- 525 3681
<mailto:loet@leydesdorff.net> loet@leydesdorff.net ;
<http://www.leydesdorff.net/> http://www.leydesdorff.net/
<http://www.upublish.com/books/leydesdorff-sci.htm> The Challenge of
Scientometrics ; <http://www.upublish.com/books/leydesdorff.htm> The
Self-Organization of the Knowledge-Based Society
-----Original Message-----
From: fis-bounces@listas.unizar.es [mailto:fis-bounces@listas.unizar.es]
On Behalf Of Viktoras Didziulis
Sent: Wednesday, May 26, 2004 10:20 AM
To: <fis@listas.unizar.es>
Subject: Re: [Fis] Information and communication
Guy, colleagues
indeed Cellular Automation approach can provide many hints solving
structure/information/communication/order related issues.
The CA principle (just without titling it CA) was discussed long long
ago by Conrad Zuse in his "Calculating space" (1969, C. Zuse. Rechnender
Raum. Schriften zur Datenverarbeitung, vol. 1, Freidr. Vieweg & Sohn,
Braunschweig, 1969, 74 pp.) Very similar ideas are exploited by many
digital physicists recently.
CA based deterministic models are not limited to "boring" uniform or
symmetric structures, they can go as far as modeling chaotic or random
things, but the most interesting feature of some of the CA's is their
ability to work on "the edge of chaos" resulting in structures very
similar to those that we observe in our "real world".
My personal programming experience with CA is related with modeling of
exposure to wave action in a lake where waves emerge as a result of
"communicating" dots in space (water volume) under influence of an
external force (wind). Which in principle corresponds to the reality as
it is simply described by a set of "communicating dots".
And my speculative reply to Guy's question on "where is the
communication?" in books, paintings, etc would be that communication may
be delayed and structure (printed text in book or forms and shapes in
painting) is a signal communicated along the time axis. Targets here
are multiple receivers "located" within a past-present-future timeline
(relatively to an occasional receiver) or present-future (relatively to
a communicator). It is also interesting (though at first look this may
look quite a trivial fact) to notice that in the real world
communication between two points in space is inevitably done through a
temporal dimension (energy-waves), while communication between two
points in time necessarily involves spatial dimension (structures). So
the book, painting, and similar cases should represent the later.
Best regards
Viktoras
-------Original Message-------
From: hoelzer@unr.edu
Date: 2004 m. gegu�� 25 d. 11:20:34
To: fis@listas.unizar.es
Subject: Re: [Fis] Information and communication
Viktoras and colleagues,
I applaud the beautiful argument presented below concerning the central
roles of time an communication in all processes resulting in pattern
construction. I have recently perceived an increasing use of the term
"order for free", which I think was originally coined by Stuart
Kauffman, but I think there is some confusion over the scope of this
idea. I personally think it is an appropriate description of the
behavior of a cellular automaton model when a simple set of updating
rules for individual cells results in surprising macroscopic patterns
(e.g., the formation of "gliders" in the game of life). However, the
macroscopic patterns in this case are not actually a "result" in the
sense of physical causation. In fact, the rules implied the
macroscopic patterns at the outset. They were only surprising because
we did not recognize the implications of the rules until we ran the CA
simulation. The notion of "order for free" is sometimes applied to
physical, self-organizing systems, which I think is misguided. The
construction of physical pattern must always require time and
communication, as Viktoras argued, and always requires the doing of
work. It is never "order for free" because the cost of work must
always be paid.
It is interesting (at least to me) to consider the phenomenon of
construction done by an individual human, as in the writing of a book
or the creation of a painting. These are certainly modes of pattern
generation, and they require both time and work; but one could ask
"where is the communication?" given that there is only one individual
involved. My answer would be that these processes depend on internal
communication among agents of cognition inside the head of the
creators. I think we are all familiar with, and rather skilled at
orchestrating this internal dialogue.
Best Wishes,
Guy Hoelzer
On May 20, 2004, at 7:06 AM, Viktoras Didziulis wrote:
>
> if we seriously consider all the 4 dimensions of our space-time
> continuum (or maybe discontinuum) as proved by Einstein and others,
> then all the existing systems are realized as spatio-temporal
> structures and existence of a purely non-dynamical structure has no
> sense in the real world as it would not exist in time. Next, - if we
> consider the time just as "one more axis" in the 4 dimensional space,
> it starts to make no fundamental difference whether communication
> happens in space or in time. In fact, no system emerge "finally and at
> once" - just as "flash-and-done" and remains static without no
> function, but, instead, structure of every natural or
> artificial system emerges step-by-step as a result of a communication
> processes in time. I.e. all structures/systems either grow, evolve or
> are constructed over a period of time - all they are communication
> re-projected from temporal to spatial dimensions. Thus the order can
> be explained in frames of communication theory as a successful or
> meaningful communication either in time or in space - axis makes
> no difference. Any real-world structure of a system as communication
> in space, is always supplemented by its functioning - communication in
> time. A good example would be ergodic systems - one can replace the
> time average (of some property) by an average taken over all members
> of the ensemble frozen at a particular time and still see "the same
> thing".
>
> Let's take a text as an example system. Printed text is nothing more
> then a "frozen" communication, and it takes time to emerge (be
> written) as a result of thoughts or communication among people which
> happens in time. In order to be understood - the printed text has to
> be "unfrozen" i.e. re-projected back to communication in time by
> reading it. Text in books is a spatial structure, but reading of a
> book "takes" time. What is the order then ? Now imagine the book of
> more than 500 pages with random words :) Nobody will read it as it has
> no meaning, purpose, function, sense... It will no have context
> - value in the "surrounding world". Book written with grammatical
> errors would be something in between sense and nonsense. More time has
> to be spent to read and understand correctly what is
> communicated through it. The same is true for the DNR in systems made
> of living cells.
>
> This approach would also make a big difference between a living cow
> and the dead one, or between a clock and a smashed clock :) or just
> any other functioning vs. broken system.
>
> The example with the book seems to nicely explain
> order/meaning/function/communication relations. So I would
> complete referencing to Einstein's thoughts again:
> "We are like a little child entering a huge library. The walls are
> covered to the ceiling with books in many different tongues. The child
> knows that someone must have written these books. It does not know who
> or how. It does not understand the languages in which they are
> written. But the child notes a definite plan in the arrangement of the
> books; a mysterious order it does not comprehend, but only dimly
> suspects..."
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