Every Unhappy Family Has Its Own Bilinear Influence Function explains some unusual work applying nonlinear equations to psychology:
In The Mathematics of Marriage: Dynamic Nonlinear Models (MIT Press), which he wrote in collaboration with four mathematicians, Mr. Gottman uses the tools of calculus to describe the interactions of couples like Angie and Dave. The models presented in the book, he says, offer insights into the heaven and hell of couplehood that he would never have found by sifting through his data with standard linear statistical tools.
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The germ of The Mathematics of Marriage was a remarkable piece of luck. Around the time of the heart-to-heart conversation with his wife, Mr. Gottman forgot to send in a reply card to a scientific book-of-the-month club, and therefore received a book he’d never heard of: Mathematical Biology (Springer-Verlag, 1989), by James D. Murray, a professor of mathematics at the University of Oxford. The book explains how to use nonlinear equations to illuminate the mechanics of complex dynamic systems, such as the growth of brain tumors.“The book was so different from all the other books I’d been reading in applied mathematics,” Mr. Gottman says. “Finally, concepts like catastrophe theory were very clear. I understood what it all meant.” Mr. Gottman sent a letter to Mr. Murray in Oxford — but the reply came from just five blocks away. Mr. Murray had retired early from Oxford and moved to Seattle; he was teaching at Mr. Gottman’s own university.
The two men met for lunch. “I thought John Gottman’s ideas about having mathematics involved [in his marriage studies] were ridiculous, and I told him that,” recalls Mr. Murray. “But by the end of the lunch, when I saw what he had in mind, I was totally hooked.”