Concerning Some Concepts of Systems Theory

IFSR Newsletter 1991 No. 1 (27)
Robert Vallee
Universite Paris-Nord
2, tue de Vouille, 75015 Paris, France
In this article some concepts commonly employed in systems theory will be discussed. I will try to show, sometimes in a critical way, why they are interesting and suggest how they can be misleading when too radically defined.
System and Environment
The very idea of the system is unfortunately not perfectly clear. The danger of too broad a definition is that systems theory could come to be identified with science itself and its specificity thereby forgotten: it is obviously not acceptable to say that “all is system”. Bertalanffy’s definition (Bertalanffy, 1968), even if it implies unprecise terms and is “nore or less controversial, can be used as a guideline: a system is a set of elements in interaction (obviously interacting between themselves, but with the environment too). It is through the interactions of its elements that a system obtains its cohesion, and if a system is more than the sum of its parts (parts with only one element being considered too), this is mainly due to the presupposition that “sum” means juxtaposition without interactions being taken into account. But the allusion to the environment in the definition raises a question: there is something, called the environment, with which the elements of the system can also interact. How then can the system be separated from this environment which is, perhaps, another system also constituted by elements? l feel that it is not possible to really distinguish a system from its environment with the exception of the whole universe which, by definition, has no environment. Logically the distinction between a system and its environment can only be arbitrary. It implies the acceptance of a border defined in space-time. This border can be complicated, even fuzzy, but logically the observer of the system has to choose it according to his observational possibilities and the use he intends to make of it. But obviously some choices are better than others when a specific purpose and some means for its fulfillment are given.
Subiectivity, Relativism and Complexity
The introduction of the observer (it can be the system itself) leads us to recognize the importance of the power of resolution of a perception process. As do many other concepts, this one also depends upon the observer. This is not surprising if we recognize that the “reference frame” of the observer plays its part, as does more generally his vision of the world, his subjectivity, to which we associate what we call the “observation operator” (Vallee, 1951, 1973). The notion of level of organization, of hierarchy between levels, is obviously important for particles, atoms, molecules, cells, organs, living beings, families, societies, planets, stellar systems, galaxies … But the perception of the levels depends upon observation, hence there is here again some kind of relativism, Even the important idea of complexity, which in fact can arise in systems very simply defined, can be considered partly subjective. Instead of defining an absolute complexity it seems safer to consider a relative or perceived complexity. Complexity is thereby converted into a relation between the observing and the observed systems (Vallee, 1990).
Locality, Globality and Teleonomy
The concepts of locality and globality are not independent of the idea of teleonomy. A dynamic system can be called teleonomic if it evolves as if it had a purpose. This is the case for cybernetic systems whose states tend, under the influence of negative feedback, to come closer to prescribed ones or to approach prescribed trajectories, notwithstanding external influences. In classical mechanics the movement of a material element is such that an integral, the action, is minimal. In the same way a light ray (curved in the case of a non-homogeneous medium) corresponds to a minimal time of propagation (Fermat’s principle). These two rather simple systems are teleonomic; they evolve in such a way that they minimize the value of global entity whose value is known only at the end of the evolution. There is no paradox here because the global criterion is, in each case, equivalent to a local one: to the differential equation of mechanics in the first example and to Descartes’ law of refraction (considered in a differential way at each point of the trajectory) in the second. Here we have an equivalence between differential determinism and integral finalism, between the local and the global. But of course finalism or teleonomy can be involved (in the sense of their strong meanings) if we consider systems to be endowed with some kind of freewill.
Order, Noise and Structure
Another familiar theme of systems theory is order and noise and, more particularly, “order from noise”. The idea that order can be generated from noise is very attractive; it is reminiscent of the birth of the world from chaos. We must, however, not forget that when noise generates order it is due to the fact that this noise has been introduced into a structure which contains some order:the shaking of a box containing magnets, more simply a kernel of corn climbing up a sleeve under the influence of small, erratic movements. In the case of the magnets, order is already present in the very structured interactions between the magnets, in the case of the kernel of corn it is involved in its very dissymmetrical structure. Noise does not create order but it is structure-revealing. It causes very little interference when it is structureless (white noise), but it nevertheless has a triggering influence very important in the emergence of order in the case of the self-organization or autopoiesis of a system.
Isomorphism, Homomorphism and Modelling
Systems theory is considered pluridisciplinary. This comes from one of its fundamental ambitions, which is to reveal, in the most favourable case, structural isomorphisms between systems (or representations of systems) belonging to different disciplines. Demonstrating these isomorphisms, or, more frequently, homomorphisms, was one of the aims of cybernetics. This can be seen from the title of Norbert Wiener’s most famous book(Wiener, 1948). The search for isomorphisms, or at least homomorphisms, leads to the concept of the model which represents a system of a given kind. But the ideal of an isomorphic representation is, in a certain sense,
misleading. The map is not the territory, according to Korzybski. This is due to the limitations of our capacity for representation, but it also has a positive effect; the map is not supposed to provide useless details. Homomorphism is enough, and the degree of accuracy of a representation
ought to be adapted to the purpose for which it has been
chosen: cognition, action or any other end.

  • Bertalanffy L. von, 1968, General System Theory, George Braziller, New York.
  • Vallee R., 1951, Sur deux classes d’ “operateurs d’ observation”, Comptes Rendus de l’ Academie des Sciences, 233, pp. 1350 – 1351.
  • Vallee R., 1973, Sur la formalisation mathematique en theorie de l’observation, in Actes du Time Gongres lnternational de Cybernetique, pp. 225-232, Association lnternationale de Cybernetique, Namur.
  • Vallee R., 1990, Sur la complexite d’un systeme relativement i un observateur, Revue lnternationale de Systemique, vol. 4, n.2.
  • Wiener N., 1948, Cybernetics or Control and Communication in the Animal and the Machine, Hermann et Cie, Paris.
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