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.



The problem, first considered by H. POINCARÉ (In "Méthodes nouvelles de la Mécanique Céleste", 1892-99) is to compute exactly the future or past position at some instant of three celestial bodies whose initial positions and velocities are known and which are submitted to Newtonian reciprocal attraction.

POINCARÉ showed that such a prediction was not possible by using anyone of the usual functions: linear, trigonometric, exponential and their combinations. Moreover he demonstrated that a three bodies system may well be unstable.

This has been confirmed during the 1960's by KOLMOGOROV, ARNOL'D and MOSER (The so-called KAM theorem), who showed that for some values of the initial conditions, the trajectories are quasi periodic, as if they were integrable, but for other initial conditions, arbitrarily close, instabilities zones do appear (chaotic zones), where dynamics are quitemore intricated.

This has been confirmed by computing comets and asteroids orbits, which result chaotic in the long run, i.e. subject to significant discontinuous changes. Very generally the classical newtonian two-bodies problem is an arbitrary simplification, obtained by elimination of secondary perturbations. Thus chaotic dynamics is also a feature of celestial mechanics and, conversely, it appears that Newtonian mechanics may imply non absolutely deterministic consequences.

As explained by R. ROSEN, the three bodies problem has wide implications in relation to the interactions of elements within any system or for groups of interacting systems: "Yet we might argue that we could study such a threebody system by decomposing it into subsystems; a two-body system and a one-body system, both of which are solvable in closed form. This does not help us, because the very act of decomposing the original system in that fashion will irreversibly destroy the dynamical laws of the original system; in other words, the properties of the subsystems prepared in that fashion will have nothing whatever to do with the properties of the system we are interested in. The properties of the subsystems will be artifacts. Stated another way, a three-body system is simply not the algebraic sum of a two-body and a one-body system"…

"Now biological systems are typically organized in a manner like that of the three-body system; they resist physical decomposition into subsystems which would possess the same dynamical properties in isolation that they did when connected into the system" (1974, p. 172).

As expressed by J. CASTI: "The essence of the three bodies problem resides somehow in the linkages between all three bodies" (1994, p. 41 – emphasis ours). Simultaneities of causes and effects, when complex, cannot be perfectly modelized, and still less so at long term.

This is possibly the clearest indictment of reductionism applied to complex systems.


  • 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]

We thank the following partners for making the open access of this volume possible: