All models are wrong... some more than others

The chapter discusses Robert Rosen's critique of mathematical modeling of complex (biological) systems. With an appreciation of the uncertainty involved in modeling complex natural systems, he demonstrated that not all models are equally good. Robert Rosen argued that mathematical modeling in the Newtonian realm of physics-the world of mechanisms-is inadequate to describe biological systems (organisms). The basis for his argument is a distinction between two approaches for mathematical modeling of cellular systems: synthetic versus analytic modeling. He introduced a class of metaphorical, relational paradigms for cellular activity called (M,R)-systems. Using concepts from category theory, he demonstrated the minimal requirements that would have to be in place for a cell to be "alive." Rosen defines a natural system as a "simple system" or mechanism if all of its models are simulable. The synthetic approach of mathematical modeling is tightly associated with the direct sum, while the notion of an analytical model is tied to the notion of a direct product. In the context of category theory, these two concepts are dual, and only in special circumstances can the two be equivalent.