Things and Models

This section introduces the concept of the Rosen Modeling Relation as a key concept for understanding systems. This model can be seen as an example of applied Category Theory.

See 1993, Rosen on Models and Modeling for more information. This model uses the term "Congruence" rather than "Functor" as the mapping as the mapping to a natural system may not be easy to make mathematically correct; however, a Formal System Model can be considered as a System Category and can take advantage of Category Theory.

The modeling relation allows us to talk about Reality on the left side and Models of Reality on the right hand side. Some key points are shown in the next diagram:

• Things, objects or Entities are Things in Reality; on the right hand side we see Models of Reality.

• How well the model has been constructed (encoding from reality) to reflect the Things in Reality (physical or conceptual)

• There can be many models on the right for the same thing, object or entity as these models are socially constructed.

• Remembering that the "map is not the territory" or the "model is not the thing".

The next model is a model that shows the relationship of reality with Models of Reality is through congruences: that map the formal model to the thing, object or entity and return.

NOTE: Any model may work for a selected system-of-interest in this representation. Congruences can be weak (analogy or mapping) or formal through Functors when comparing two categories.

The next diagram introduces the way a formal system model is derived for a thing, object or entity. Here are highlights:

The formal system model must be isomorphic to the General System Model to claim that model of a thing is a Formal System Model.

The General System Model can be improved based upon observations of the Formal System Models. System Classification or Typology is an important aspect of the General System Model to promote naming and reuse of models.

The final diagram in this series shows the mathematical foundations for the General System Model and ensures that the General System Model can be improved or aligned with these mathematical foundations. The General System Model, the System Classifications and the Mathematical Foundations form key elements of the General Systems Theory.

The following formal model also highlights the relationships.