REPLY TO SACKS AND DOYLE, “PROLEGOMENA TO ANY FUTURE QUALITATIVE PHYSICS”

The validity of Sacks and Doyle’s conclusion that standard tools for mathematical analyses of dynamic systems should be the basis for “any future qualitative physics” seems to turn on one’s definition of qualitative physics. Sacks and Doyle embrace a particular view of QP that focuses on qualitative solution of differential equations, a problem that I will call QSODE, for short. The acronym is intentionally an analogy to LSODE, the wellknown numerical solver for differential equations, to emphasize that the objective of QSODE is to qualitatively interpret or solve sets of differential equations. SPQR is one approach to QSODE, and in their paper Sacks and Doyle outline an alternate philosophy for QSODE. Much of the qualitative physics literature deals with QSODE, but the hegemony of this problem does not reflect the scope (or at least the potential scope) of qualitative physics, just as LSODE the numerical simulator does not reflect the full scope of system modeling and simulation problems in the quantitative domain. If one subscribes to the definition of qualitative physics as QSODE, then Sacks and Doyle’s conclusions are quite reasonable; SPQR is not a comprehensive approach to QSODE, and (as the QP community widely recognizes) additional tools and techniques are needed to complete the picture. If the objective is to determine stability, map limit cycles and bifurcation points, etc., then it is undoubtedly useful to employ the mathematical tools cited by Sacks and Doyle instead of approaching these issues indirectly via SPQR. However, Sacks and Doyle’s implication that QP and QSODE are synonymous problems must be seriously examined. The behavior of dynamic systems is important in some applications but not all; to address the range of QP problems that exist in practical reality, a much broader view of qualitative modeling and simulation is required. In the field of chemical engineering, problems require many different types of qualitative models and a like variety of methods of behavioral prediction. The subject systems may be dynamic, steady state, continuous or discrete, or involve combinations of these types. It may be convenient in certain contexts to express system models in the form of rules, confluences, symbolic algebraic equations, fuzzy relations, qualitative differential equations I or causal diagrams, and behavior can be inferred by symbolic algebra, order-of-magnitude reasoning, constraint propagation, interval arithmetic, eigenvalue analysis, or frequency response characteristics. Not all systems can be modeled using the SPQR representation, and not all types of objectives are addressed by it; in a given situation it may be more convenient to use Petri nets, qualitative transfer functions, directed graphs, belief networks, bond graphs, incidence matrices, or other representations. Different problems have different characteristics, and models should be selected to reflect the modeler’s goals. Development of a model without a specific objective leads inevitably to arbitrary decisions on which features of the system to ignore, which to approximate, and which to include in detail in the model. It is always easier to develop a representation to fit a specific problem than to develop a representation for an unspecified problem.