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Using dynamic nonlinear mathematical models to explain patterns of marital interaction and the failure of marital therapy.

Article Excerpt
The Mathematics of Marriage: Dynamic Nonlinear Models. By John M. Gottman, James D. Murray, Catherine C. Swanson, Rebecca Tyson, and Kristin R. Swanson. Cambridge, MA: The MIT Press, 2002, 403 pages. Hardcover, $42.95.

This book shows how dynamic nonlinear modeling can be used to describe intimate relationship interaction in a variety of situations. The idea of using differential equations to model dyadic interaction is not new--Broderick and Smith (1979) developed the concept many years ago--but Gottman and his colleagues have taken it to a new depth in The Mathematics of Marriage. The complexity of this book limits the ability of any reviewer to do an adequate job of responding; our first review was three times as long as permitted! Here we greatly abbreviate our summary of the book to focus on its limitations.

Gottman and his colleagues begin by arguing that we have learned little about what makes marriages work and that the benefits, if any, of marital therapy are usually short-lived. They argue that the "field of marriage research is in desperate need of theory" (p. xi). Their answer is the use of mathematical models inspired by recent works from Murray (1989) and others. They believe that their work "represents the missing step necessary to complete the seminal thinking that the family general systems theorists started in the 1950s" (p. xiii). However, recent reviews have indicated moderate effect sizes for treatment (Denton, Burleson, Clark, Rodriquez, & Hobbs, 2000; Dunn & Schwebel, 1995). A primary contribution of this book, though, is more specific identification of how interventions could be targeted to improve relationship processes.

Chapter 2 is a solid review of the literature on marital interaction (also see Gottman & Notarius, 2000, 2002). Chapters 3 through 9 explain the development and application of dynamic nonlinear models. On page 37 the authors state, "The amount of mathematics needed is relatively minimal." However, even though I (Schumm) had six semesters of calculus in college, I was on the verge of being lost after chapter 7. Chapter 4 does include a basic review of calculus and differential equations. Chapter 5 concludes with an illustration of how a hyperbolic tangent function could be used...