BCSSS

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.

About

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.

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DIFFERENTIAL EQUATION: limits to its uses 2)3)

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These very significant limits are thus stated by A. RAPOPORT: "Both the strength and the limitations of the mechanical outlook reside in the mathematical methods used in the construction of mechanistic theories. The fundamental tool of this method is the differential equation which is essentially a precise statement about how certain quantities and their rates of change are related" (1966, p.3).

After reminding the role of second derivatives (the rates of change of the rates of change), he notes that: "If several bodies are involved… their motions would then be described by a system of differential equations in which the relations between the positions and the accelerations are all interwoven by a network of interdependencies. Now if the differential equations comprising a system are linear, i. e., if the variables and their rates of changes appear at most in the first degree, the same general methods of solution apply regardless of how many equations are involved" (Ibid).

This unfortunately, is a very special case, to which most complex phenomena cannot be reduced, lest the model would eliminate the very nature of the modelized system.

In celestial mechanics, for example, perturbations calculus can be superposed on a basically dual system (The sun and the earth for example – a two-body system), but with three or more bodies of comparable mass, the differential equations cannot be solved anymore (POINCARE) and we enter the realm of deterministic chaos.

Categories

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

Publisher

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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