Enter the modeling relation. It turns out that there is a nice, formal theory to talk about all of this. It was done by a systems biologist named Robert Rosen. He called this theory ‘the modeling relation’.
Rosen’s Modeling Relation What the modeling relation portrays is as follows: on the left (#1) we have a natural system of some kind (things happen in the natural system and causality is involved). On the right (#3) we have a formal system. (Formal systems might be math, logic statements, computer simulations, etc.) We can run many experiences, thought experiences, predictions, in the formal system to see what that implies about what a corresponding action should mean in the natural system. Rosen claimed that if we have a means of going between the two—the encoding (#2 or how to represent in the formal system a potential action occurring in the natural system) and the decoding (#4 or how to carry out in the natural system a prediction made in the formal system ) —then we have a model. If one can’t make all of the four elements work as shown, one doesn’t have a model, but rather merely a representation. Rosen’s work was about distinguishing between the existence of modeling relations and representations that people were mislabeling as models. The key to a model, in Rosen’s world, is the ability to use the model to make predictions, to have implications that are then observable in the natural system. If the model can do that, it is a model; if it cannot, then it is merely a representation.
