International Encyclopedia of Systems and Cybernetics

2nd Edition, as published by Charles François 2004 Presented by the Bertalanffy Center for the Study of Systems Science Vienna for public access.


The International Encyclopedia of Systems and Cybernetics was first edited and published by the system scientist Charles François in 1997. The online version that is provided here was based on the 2nd edition in 2004. It was uploaded and gifted to the center by ASC president Michael Lissack in 2019; the BCSSS purchased the rights for the re-publication of this volume in 200?. In 2018, the original editor expressed his wish to pass on the stewardship over the maintenance and further development of the encyclopedia to the Bertalanffy Center. In the future, the BCSSS seeks to further develop the encyclopedia by open collaboration within the systems sciences. Until the center has found and been able to implement an adequate technical solution for this, the static website is made accessible for the benefit of public scholarship and education.



Similar rules of energy use that operate at various levels in a system.

Power laws occur when the average frequency of an event of a given size is inversely proportional to some power of its size. For example, small earthquakes are quite frequent, but much less destructive than the strong ones, which in turn are quite less frequent.

Systems near critical states seem governed by such optimization rules (or power laws) which minimize their expenditures of energy.

As a consequence, according to I. RODRIGUEZ ITURBIDE et all (in P. YAM, 1994, p.17): "Rather than emerging from events happening nearby or taking place immmediately before, critical catastrophes may occur because of a global, long term mechanism. Specifically, the systems may be minimizing the amount of energy they expend in maintaining themselves, thereby optimizing the way in which they develop".

The authors created a mathematical model whose statistical properties are exactly the same as those of a drainage network, in which "the length of the stream channels and the distribution of branches, and of the energy at any point, all obey these (power) laws. It seems also possible that in earthquakes models, tectonic plates may be organizing themselves locally so as to minimize stress for the entire system".

The same model could explain how "trees are optimizing their leaf distribution to take advantage of the light they receive".

YAM adds: "The finding raises the question of whether all self-organized critical systems evolve through some global principle of energy minimization". It also poses interesting question marks about the ways of interactions between particles, elements or agents which are not connected in any known functional way. We obviously need not only a model of global action, but also one of local and possibly non-local action in connection with the global one.

This could lead to a clearer interpretation and understanding of holographic order and, generally, of implicate order in BOHM's terms and even possibly make sense of R. SHELDRAKE's morphic fields.

Power laws seem also related to the fractal character of many systems. They could offer interesting insights in relation to social organization and quiet or violent change.

A connection between power laws and so called "small worlds"is also probable; the many frequent small connecting steps among nearby elements are somehow opposed to unfrequent big leaps between distant hubs in a network.

This can be observed for instance as two different ways of propagation in epidemics

Power laws seem also to explain some typical relations in ecosystems (A. FROOD, 2001, P. 30-33)

It could be said that power laws and fractalization are the two faces of the same coin.

This is also obvious in the case of WEIERSTRASS renormalization group transformation

Self-similarity in the Weirstrass function


  • 1) General information
  • 2) Methodology or model
  • 3) Epistemology, ontology and semantics
  • 4) Human sciences
  • 5) Discipline oriented


Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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