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.

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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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HOMOMORPHISM 2)

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A many-to-one mapping of some characteristics of a concrete system onto a model of the same.

An homomorphism is an imperfect, partial or limited isomorphism. K. KRIPPENDORFF writes: "Homomorphisms are important in establishing whether one system is a model of another and which properties of the original of the system the model retains. For each system one can construct a lattice of homomorphic simplifications" (1986, p.36).

G. KLIR explains: "An homomorphic relation between two systems is contingent upon a function from relevant entities of one system (the original) onto the corresponding entities of the other system (the modelling system) under which the relation among entities is preserved. If the function, which is called a homomorphic function, is bijective, the relation is preserved completely (we say that the two systems are isomorphic); otherwise it is preserved only in a simplified form" (1993, p.30).

The last case is by far the most common.

R. VALLÉE, refering himself to the example of "the map, which is not the territory" (KORZYBSKI) states: "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" (1991, p.4).

V. TURCHIN makes the suggestive comment – helpful in placing models in proper perspective – that: "A model is a family of homomorphisms" (1993, p.7).

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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