Questions and answers with Steven Strogatz

Steven Strogatz is the Jacob Schurman Professor of Applied Mathematics at Cornell University in Ithaca, New York. He conducts research on dynamical systems in physics, biology, and social science. His 1998 Nature article “Collective dynamics of ‘small-world’ networks ” is considered a seminal contribution to complexity research.

Strogatz is also an active communicator of mathematics and related topics to the public. He frequently appears on public radio and writes for The New Yorker and other publications. A 2015 recipient of the Lewis Thomas Prize for Writing About Science, he has written books that include Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life (Hyperion, 2003) and The Joy of x: A Guided Tour of Math, from One to Infinity (Houghton Mifflin Harcourt, 2012).

Strogatz recently published the second edition of a text he wrote more than two decades ago. The new edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Westview Press, 2015) contains new exercises on such topics as protein dynamics and superconductivity and covers applications in such emerging fields as sociophysics and systems biology. Physics Today reviewed the book in the April issue.

We recently caught up with Strogatz to discuss his new book.

PT: After two decades, what motivated you to write a second edition of Nonlinear Dynamics and Chaos?

Strogatz: I wanted to convey some of the recent applications of nonlinear dynamics to emerging fields like sociophysics, evolutionary game theory, and systems biology. A new edition seemed like a great opportunity to give students and their teachers a taste of these developments.

PT: What are some of the most exciting updates in the field that you cover in the new edition?

Strogatz: The second edition includes about 20 substantial new exercises on diverse topics, including neuroscience (binocular rivalry in visual perception), sociophysics (models of opinion dynamics and tipping points), systems biology (protein dynamics), animal behavior (calling rhythms of Japanese tree frogs), superconductivity (solving for the current–voltage curve of a Josephson junction with quadratic damping), linguistics (modeling the dynamics of language death), prebiotic chemistry (Eigen and Schuster’s hypercycle model), and even psychology and literature (Rinaldi’s model of love dynamics in Gone with the Wind).

In a few cases, these exercises were generously contributed by colleagues around the world—all experts in the associated application area—who’d developed them for their own courses based on the first edition of the book. Each exercise includes a gentle introduction to the relevant scientific issues, as well as citations of the original research.

PT: How important is this topic to undergraduate physics majors?

Strogatz: I’d like to see all physics majors learn the language, ideas, and techniques of nonlinear dynamics. Many of the major unsolved problems in physics today—and, more generally, in all of science—are fundamentally nonlinear. In everything from general relativity and fluid mechanics to economics and climate science, the whole is often more, or less, than the sum of the parts, and the superposition principle fails spectacularly. Familiarity with nonlinear systems and how to analyze them will be absolutely critical to all future generations of physicists.

PT: How have your experiences communicating mathematics to the public informed the way you communicate math and science to students and practitioners, and vice versa?

Strogatz: I’ve come to feel that we need to help people love the questions we’re asking. If our students and the broader public don’t appreciate the questions, our answers won’t move them, no matter how important they are or how clearly we explain them. It’s a matter of empathy: Think of how boring it is to listen to an answer to a question you don’t understand.

PT: As a mathematician, how did you celebrate Pi day this year?

Strogatz: Two days beforehand, I wrote a piece for The New Yorker called “Why pi matters.” And then I made sure to stay off the streets when the big moment came: On 3/14/15 at 9:26:53, pi was approximated to 10 digits, and there was no telling what sort of chaos might ensue.

PT: What books are you currently reading?

Strogatz: Mathematics Without Apologies by Michael Harris (Princeton University Press, 2015). It’s a wry and insightful look at what being a pure mathematician is all about, as seen from the inside