Emeritus Professor, the University of  Paris-Nord
President of the WOSC

Robert VALLÉE


 "The Observation Operator"

06.12.2008


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The "Kybernetes Journal"

Volume 32, N°4, 2003

© MCB UP Ltd, p 449-453 .

 

"Professor Robert Vallée is a cybernetician, who considers mathematics to be of his main interest. He believes that mathematics helps us “to know what can be understood in the Universe” and so is deeply connected with epistemology.

He is a prolific writer and researcher and his first publication of 1951 introduced the “opérateur d’observation” (observation operator), in a series of notes to the French "Académie des Sciences" under the aegis of Louis de Broglie. He introduced the notion of an “observation operator” as a "mathematical operator" describing how a macroscopic physical entity is perceived by one of a conscious being's sense or, metaphorically, by an instrument performing a measure, that in the broadest meaning of the word. The simplest case is given by linear observation operators, which reduce to Volterra composition, convolution and mere multiplication of functions, within matrix formalism in the most general case, and introduce algebra of macroscopic observation involving informational concepts. Connected with this kind of consideration is the problem of a possible minimal distance between two physical points seen as the smallest of the eigen-values of an adapted distance operator (1973).

When the observed entity is the state of a macroscopic dynamical system, the use of an observation operator, acting necessarily on the past and present history of the state, introduces naturally the concepts of “episternological indiscernibility” of two possible evolutions of the system and of “epistemological inverse transfers” of structures inherent to the system itself into its subjective perceptions (1974). Similar conceptions have been proposed, from 1978 on, by R. Rosen.

 He continued to develop this research and in his later publications showed that: "The uncertainty about the true initial state of a dynamical system , in the macroscopic case of the imperfection of an observation operator, induces to consequences on forecasting its future state. When the initial uncertainty may be described by a probability distribution, informational considerations, in the sense of C.E. Shannon, can be developed, particularly in the linear case giving rather simple results (1979, 1982)". Analogous results have been presented by G. Jumarie in 1991. The same problem may be solved in informational terms (1968), at least asymptotically, in the case of the wave function of an electron,

The formalism of multidimensional linear dynamical systems, he believes, gives a frame for a modeling of perception and memorization of the results of perception. It involves, he writes: 

a “matrix factor of attention", a “matrix factor of memorization” and a “generalized Laplace transform with matrix argument” (1977, 1982, 1995). In the scalar case, this formalism opens a way to an understanding of the perception cf duration and sa of time itself (1980, 1986, 1995). We obtained similar results by the introduction of an “internal time” intrinsic to a dynamical system (1996, 2001). The “internal time” as opposed to the external ‘reference time”, does not elapse when the state of the system does not change. More precisely, it is supposed to elapse, at each instant, proportionally to the square cf the modulus of the speed cf evolution of the state of the system at this instant. So, when considering certain “explosive-implosive” scalar systems evolving on a reference rime interval [0, T]  the “internal time” interval becomes [-, +] providing physiological and cosmological interpretations.

The consideration of a dynamical system able to perceive, decide and act, even in a metaphorical sense, involves an “observation operator” followed by a decision operator or, more briefly, their product which we call “pragmatic operator”. All that which may be said about observation operators can be transposed to pragmatic operators introducing “pragmatical indiscernibility” as well as “pragmatical inverse transfer” (1975) and giving rise to an “epistemo-praxiology” (1984, 1990 1995, 1998).

In his further considerations, Norbert Wiener’s generalized harmonic analysis suggested to him the definition of an “epsilon-distribution” giving interesting properties and applications, as in a way the antithesis of Dirac’s delta  (1992-1993).

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  © Robert VALLÉE - r.vallee@afscet.asso.fr

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