Math Matters: IMA Public Lectures

The IMA public lecture series raises awareness of the impact of mathematical research on everyday life. The two winter lectures in the 2004-2005 IMA public lecture series Math Matters demonstrated the versatility of mathematics, presenting innovative applications of mathematical models to marriage and movies.

Mathematician James Murray and psychologist John Gottman use the most rational of sciences to analyse one of the least rational of human activities—arguing with a spouse. In his lecture The Marriage Equation: A Practical Theory for Predicting Divorce and a Scientifically-Based Marital Therapy, November 18, 2004, Murray described a novel, simple, and yet impressively powerful dynamical systems analysis of the dynamics of an emotionally charged discussion between spouses. Murray's lively, down-to-earth presentation helped win his audience over to the unsettling notion that the evolution of something as subtle, complex, and seemingly unique as a marriage could be predicted by a planar phase portrait. The bad news: most couples really do keep having essentially the same argument over and over again, with personality differences and marital history influencing the progression of the interaction as much as, or more than, the actual subject of disagreement. The good news: this predictability can be used to estimate the stability of a marriage with an accuracy of 94%, and to design marital therapies for high-risk couples. Using their model, Murray (University of Oxford and University of Washington) and Gottman (University of Washington) have developed a marital interaction theory that distinguishes several types of stable couples whose marriages are likely to last from two types of unstable couples and guides the formulation of strategies for modifying destructive patterns of interaction.

On February 9, 2005, David Baraff, of Pixar Animation Studios, spoke to a large and enthusiastic audience on Math Behind the Curtains: Dynamic Simulation at Pixar. Dr. Baraff provided glimpses of an animator's virtual universe, complete with carefully tailored costumes, lights, cameras, and—of course—action. He gave an introduction to dynamic simulation, a state-of-the-art animation technique that uses sophisticated mechanics-based mathematical models to efficiently simulate complex objects, including water, fabrics, and hair, at levels of detail and realism unattainable in traditional hand-drawn animation. Cadres of video game developers nodded sagely and murmured approval when some of Pixar's preferred rendering techniques were disclosed, while IMA visitors intently followed the description of the many-body simulations used to model breaking waves and foam. Clips and out-takes from Pixar's award-winning animated features, including Monsters Inc. , Finding Nemo, and The Incredibles, illustrated the creative interplay between science and art in computer animation. The unexpected outcomes of human animators' improvised fixes and the computer's faithful implementation of the logical consequences of those improvisations gave the audience insight into the appeal, and frustration, of all of mathematics—even in a universe in which you write all the rules, strict enforcement of those rules can yield surprising results.

The final talk in the 2004-2005 Math Matters public lecture series will be Computers and the Future of Mathematical Proof, given by Professor Thomas C. Hales , of the University of Pittsburgh, on March 30.