WHEN WILL A MODELING RELATION COMMUTE?

D. C. Mikulecky

Professor of Physiology

Medical College of Virginia Commonwealth University

http://views.vcu.edu/~mikuleck/

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.

Go back to the Modeling Relation