Wilczek, Frank

Frank is a Nobel Laureate in Physics (2004). He is Professor of Physics in the MIT Center for Theoretical Physics, where his research includes pure particle physics; behavior of matter; and applications of particle physics to cosmology. He contributes regularly to Physics Today and to Nature. His popular books are Longing for the Harmonies: Themes and Variations in Modern Physics (with Betsy, Devine, his wife) and Fantastic Realities: 49 Mind Journeys And a Trip to Stockholm. Here is how Frank treats the claim that there is something miraculous in the success of mathematics in natural science. Eugene Wigner, famously, claimed that it is, speaking of “the Unreasonable Effectiveness of Mathematics.” Writing in Physics Today, Frank conjures up a “Devil’s Advocate:” “’It’s no miracle,’ she begins, ‘that clear thinking can clarify things. Nobody, I think, would call the success of mathematics in say, accounting, unreasonable, much less miraculous. It’s just clear thinking, applied to money. It’s useful and important, of course, but there’s nothing surprising about its success. What seems unreasonable, and can even appear miraculous, is that sometimes mathematics is highly leveraged. When a discovery or innovation can be conveyed in a few bits of information, but its purely mathematical elaboration comes to describe an every widening circle of phenomena, it appears that magic is at work. Natural science provides many examples. Isaac Newton’s laws of motion and gravity can be written in a few lines, but they allow us to track the planets, precess the equinoxes, discover Neptune, plan space voyages, and more. Heisenberg’s commutation relation can be written in a small portion of one line, but it allows us to master subatomic worlds. It’s as if great trees could sprout from tiny seeds, or beautiful minds from tiny eggs. We’re tempted to proclaim such occurrences to be miracles. But of course great trees do sprout from tiny seeds, and beautiful minds do grow from tiny eggs. And biologists are explaining how these things happen, step by step, without invoking miracles. Before ascribing special, miraculous status to the leverage of mathematics, we should consider whether it is unique. Can nonmathematical ideas have enormous scientific leverage? Indeed they can. For example: Charles Darwin’s theory of evolution by natural selection is not a mathematical theory. The Origin of Species contains not a single equation. Yet its hypotheses, which can be stated in a few lines of prose, explains a multitude of surprising facts. The atomic theory of Democritus, John Dalton, and Dmitri Mendeleev used no math beyond simple arithmetic, but gave brilliant guidance to chemistry. And while it is not an idea in the conventional sense, the information that differentiates the genomes of homo habilis and modern humans is a few bits (well, maybe a few megabytes) of information. Yet that information is leveraged, by natural biological and historical process that in no way resemble calculation, into the difference between extinct semi-monkeys and readers of Physics Today. The Advocate continues playing to the jury: ‘Not only can nonmathematics have lots of scientific leverage; often mathematics has little. There’s a scene I love in Indiana Jones and the Temple of Doom. Maybe you’ll remember it. Before an impending showdown, a sword-wielding dervish confronts Indiana Jones with a fearsome display of his prowess. In response, Indiana coolly pulls out a pistol and shoots the guy. Virtuoso displays of mathematical gymnastics that are outdone by straightforward calculations remind me of that showdown.’”