The recent Nova documentary, “The Great Math Mystery,” addresses the question, is math a feature of the universe as an artifact of a brain trying to make sense of the universe. Rather than address that question, as interesting as it is, this essay addresses a different one. That is, what is the quality of mathematics that pertains to policy and its related fields of history, economics, and social science.
The first observation regards phenomena in which math applies well: well-specified physics, such as planetary motion, and experiments in which the number of interacting features is small and the time-scale is constrained. Given these constraints, then mathematical laws can provide almost perfect predictions. One need only think of Copernicus, Galileo, and Newton and their predictions to understand the confidence and promise of the explanatory capabilities of mathematics, a concept that was captured by a 1960 paper entitled, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”
However, mathematics has not been as universally applicable as it once might have seemed, especially in the social sciences. Even in the natural sciences, the three body problem and Chaos, the subject of a 1988 book that provided insights into random and unpredictable behavior with the development of powerful computers, revealed that there were limits to mathematics and science. That doesn’t mean that mathematics and science aren’t applicable to the social and policy sciences, but it does mean that they won’t provide the certainty or exactness of other phenomena and that they need to be reconceptualized.
The Nova documentary explicitly compares the theoretical mathematics of physics with the more applied mathematics of electrical engineering and that, for these messy and inexact or complex domains, the applied mathematics of engineering is a better fit because it only needs to be good enough to get the job done. Naturally, there is a corresponding paper that addresses, “The Reasonable Ineffectiveness of Mathematics,” that addresses this challenge. This in itself is an exciting insight as applied problems often drive theoretical innovations. Current policy problems are increasingly complex and creating a demand for new and innovative ways to think about them, which creates an opportunity for those who can help to make what is currently confusing, understandable.