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.



A possible general representation of 3-dimensional phenomena produced by field dynamics (Adapted from D. Mc NEIL).

Helical dynamics are the result of interactions between fields, as in vortexes. In abstract, a torus should be a specific topological attractor for this kind of movements. However, in many complex systems, the imbricated character of their internal organization needs be represented by more complex forms, including toroids containing toroids.

Mc NEIL generalizes the topological torus, using fully its dynamic character, that results from the complementary opposition of two types of displacements.

And: "… toroidal contours represent dynamic, connected volutions rather than the separate, rigid structures or the hermetically encapsulated nuggets found in so many conventional worldviews" (1993 a, p.15).

Or: "Toroids map the conceptual space into comprehensible orders without resorting to artificial linear dichotomies or rigid arrays of pigeon holes" (1993 b, p.14).

Mc NEIL states: "Natural as well as artificial toroids can be generated in many ways other than by the rotation of a plane figure… Toroidal forms can be traced by continuous spirals of helical dynamics" (1993 b, p.9).

As to the toroidal dynamics: "In the context of a simple toroidal whole, the center is the region closest to equilibrium in the sense that the meridial as well as the annular fluxes are most concentrated there, much as a whirlpool captures and holds what would otherwise drift along in a stream. The periphery of the toroid is farthest from equilibrium, with relatively diffuse currents and cross-currents over relatively broad surfaces" (1993 b, p.16).

Mc NEIL offers the tree, as a general graphical and dynamic representation of a toroid. This is at the same time a good homomorphic model of real trees and a metaphorical model of any system which obtains inputs from an environment, metabolizes them and produces outputs. This tree model is widely different from the classical tree model of hierarchical organizations, or a computer program: It is not merely the representation of a structure, but altogether one of the ongoing process or processes.

Any living system seems to be basically a toroid, and this model also fits stellar systems, hurricanes and possibly ecosystems and social systems.

It should be taken into account that toroids become easily unstable.

The now rediscovered toroidal model seems to have been first introduced by C.L. WEYHER as early as 1887! (as quoted by C. LAVILLE, 1950, p.54).



  • 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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