From C to Shining Sea: Complex Dynamics from Combinatorics to Coastlines

If there’s one thing Williams-Mystic students learn first, it’s that you can’t study a topic as vast as our world’s oceans and coasts from the vantage point of a single discipline. From day one, Williams-Mystic prompts students to draw connections among topics as (seemingly) far afield as literature, policy, science, and history.

In his presentation Friday as part of Williams-Mystic’s Biannual Lecture Series, Williams College professor Steven J. Miller brought another perspective to bear: mathematics, specifically complex dynamics.

Complex dynamics is the study of iterations of maps. From very simple, basic rules, incredibly complex and highly structured behavior emerges, frequently surfacing in wildly different settings at many different scales. Miller’s talk introduced some of the general theory in the complex plane C and explored these connections, starting with binomial coefficients and progressing to the fractal dimension of coastlines and chaos in weather prediction.

The goal: To emphasize how the same ideas and techniques can be fruitfully applied again and again. Mathematical perspectives on complexity might seem abstract. But, Miller stressed, these perspectives can yield unique insights into real-world problems, from how to accurately measure a single island’s coastline to how to predict changing weather patterns the world over.

You can watch Miller’s talk on YouTube, and follow along on the slides posted online.

Steven Miller earned his BS in mathematics and physics from Yale and his PhD in mathematics from Princeton. He has taught at numerous colleges and universities, including Brown, Mount Holyoke, NYU, Ohio State, Princeton, Smith, and Williams, and been supported by multiple NSF grants for both research and expository writing. He is the author of over 100 papers in accounting, computer science, economics, geology, marketing, mathematics, physics, sabermetrics, and statistics, as well as five books. For several years he has recorded all his classes and many talks, which are freely available at .