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An illustration for Triple Modeling Relation and Note

In my understanding, a holistic view to modeling relationship is very important and somewhat neglected, where raising the triple relation of a model with its target (original) and the subject (human or agent) is the first step towards to a holistic view of modeling. Based on his great review of a huge amount of literature for models, Dr. Roland Mueller implied this is an important progress in the last century: “Most scholars in the 20th century had in view only the relation ‘image’.” (from here)

There is a very concise formulation of the triple modeling relation defined by Marx W. Wartofsky (1966, 1979)

M (S, x, y) where S takes x as a model of y

Dr. Mueller called it triple relation “subject-model-original” and provided a more comprehensive illustration which was appeared in Wörterbuch der Kybernetik 1969 (Dictionary of Cybernetics) edited by Georg Klaus. Here is an English version


Figure 1 Triple Modeling Relation (Adopted from Georg Klaus (Ed.): Dictionary of Cybernetics. Frankfurt / Hamburg: Fischer Library, 1969)


It is translated by Google translate engine first, than have a bit revision by me.

  • Organism, Automatic -> Organism, Machine
  • Construction, Use, Aufweisung -> Construction, Use, Demonstration

I asked Markus Kerz and he gives the following recommendations:

  • translate “Abbildung” by “Image” instead of “Figure” in this context.
  • normen: i think both words (standards, norms, rules) will do
  • plan: it’s how it >should< be
  • detection: perhaps recognition is better here

All his recommendations is reflected in the Figure 1. And the understanding may be restricted by that the lack of the context in the book.

In addition, this topic have a great relationship to my idea such as Model as Use and the Three Spaces of entities/models.


About TY

interested in models & modeling, software, information systems, applications & engineering for enterprises



  1. Pingback: General Modeling Relationship | THINK IN MODELS - July 20, 2013

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