WHEN WILL A MODELING RELATION COMMUTE?
D. C. Mikulecky
Professor of Physiology
Medical College of Virginia Commonwealth University
In his discussion of the modeling relation in Life Itself (pp53-54), Rosen makes the following observation: "We should note parenthetically here that the word model is overworked and has been used in a whole host of different, sometimes unrelated, and even contradictory senses. There is, for example, a well-developed Theory of Models, employed mainly to study the consistency of axiom systems in foundational Studies in mathematics. The use of the term 'model' in this context is not quite the same as mine; in fact, it is more closely akin to what I have called "realization". However, since I will never use the word "model" in any other sense than the one I have specified, there will be no danger of internal confusion."
Rosen was very aware of the confusion around this term. What is a model in his context? A commuting modeling relation. Notice that this can be a relation linking a natural system to a formal system or formal systems to each other. The important point is that the modeling relation is not a model unless it commutes.
The commutation of a modeling relation is something Rosen never defines. This is probably because it could entail volumes. Let us try to at least outline what it means. If we accept the idea that the mind relates percepts in various ways, there can be a structure to those relations. This structure is as much a product of the mind as it is the percepts themselves, and the situation has already become extremely complicated. The mind imputes this structure on the natural world by finding relations between percepts.
Let us try to characterize that structure. The percepts that are important to us in science are observables.
The relations between them are linkages. The process by which observables are measured and linked is extremely detailed and is the crux of the scientific method. The observables are abstractions represented by symbols and, most of the time, to which numbers are assigned. The common term for collections of these is data. The linkages are often dealt with using statistics or other mathematical data processing tools.
Those observables and the linkages are then made sense of by encoding them into some formal system. That formal system has symbols and propositions, algorithms, and theorems that deal with the relations represented by the linkages.
There is one other consideration in this admittedly superficial account. When we make observations we are interested in changes. We watch things happen. We make more than one measurement. We attribute this all to causality. After encoding the natural system into a formal system, we then manipulate the formal system to try to achieve the equivalent of the linkages we made/observed between observables. Finally, there has to be some way of comparing these "implications" with the natural system.
Here is where we must determine whether the modeling relation works or not. We borrow a term from math and ask if the diagram "commutes" or not. In his latest, unpublished works, Rosen uses the metaphor of "surrogate" for this. It is a good term because it answers many potential questions about how well the match must be for we acknowledge the commutative. The other thing Rosen does is to use formal systems as natural systems and model them with other formal systems as examples. In this way, he show us that the modeling relation works for all the activities of out minds, not just a select, rigidly circumscribed few. Thus, as are the encoding and decoding, the determination of commutative, really the acceptance or rejection of a model, is a very subjective enterprise. This is true in spite of the many elaborate and sophisticated methods of model identification and verification that have been developed and which now fill many shelves in the appropriate sections of our libraries. Rosen has added other measures of model veracity which are unrecognized in the Newtonian Paradigm. These involve the causal relations between percepts and become extremely valuable when dealing with issues like computer simulation, metaphors, analog models and related concepts.
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