RESPONSE TO “PROLEGOMENA TO ANY FUTURE QUALITATIVE PHYSICS” BY ELISHA SACKS AND JON DOYLE

The authors make three claims: (1) that SPQR is a weak method for analyzing the qualitative behavior of physical systems; (2) that advanced mathematics such as dynamical systems theory and numerical simulation techniques, as routinely used by experts, provides a complete qualitative understanding of many systems; and (3) that, in ignoring established and well-proven mathematical concepts and techniques, the qualitative physics researchers are guilty of reinventing the wheel, or, perhaps more aptly, of rejecting the traditional round wheel in favor of the square one they invented. We are in agreement to some extent with all these claims. However, in the present context it seems more appropriate to focus on our qualms. In particular, we want to argue that (1) there are domains for which SPQR is entirely appropriate, effective, and even aesthetically pleasing; (2) the advanced mathematics, so enthusiastically embraced by the authors, are still rather limited; and (3) none of the first-generation QP researchers, at least those we know personally, is opposed to the incorporation of more mathematical concepts into their systems; it just takes time and effort to learn the relevant mathematics. Finally, we want to point out that one reason for the appeal of SPQR is its applicability to commonsense reasoning as well as expert reasoning about system dynamics. Most of the field is now evolving toward the second area of application, as suggested by Sacks and Doyle, but the first is possibly even more challenging. Let us elaborate. In his Ph.D. dissertation (de Kleer 1979), which we consider as one of the most important works in QP and which should be much more widely read, de Kleer studied how engineers analyze and explain electronic circuits. He observed that, to understand the gross behavior of a circuit and explain its function, an accomplished expert rarely resorts to elaborate algebraic manipulation or numerical simulation. Instead, the expert explains and predicts the circuit’s behavior by postulating causal changes in circuit quantities that are consistent with known circuit laws and component models. Furthermore, these changes are describe qualitatively, i.e., whether they are increasing, decreasing, or unchanging. To capture this style of expert reasoning, de Kleer developed a representational scheme (sign arithmetic and qualitative component models) and reasoning techniques (causal analysis and teleological reasoning), which are subsequently incorporated into several SPQR style analysis programs. The simplicity and effectiveness of de Kleer’s approach in generating transient analysis and teleological explanations is unsurpassed. For this level of analysis, it is neither necessary nor desirable to appeal to more advanced mathematical techniques. Of course, if a circuit exhibits more complicated steady-state behaviors such as subharmonic resonances and even chaotic response (and many circuits do), then the expert will fall back on more elaborate techniques. But the point is that simple problems should have simple solutions. Before we begin to turn the large number-crunching crank and plot the multidimensional phase portraits, it is wise to ask if the problem could be solved in a simpler way. De Kleer has shown us that at least in the electronics domain many interesting questions can already be settled by simple, incremental causal analysis.