# The Mathematics of Marriage

## Overview

Divorce rates are at an all-time high. But without a theoretical understanding of the processes related to marital stability and dissolution, it is difficult to design and evaluate new marriage interventions. *The Mathematics of Marriage* provides the foundation for a scientific theory of marital relations. The book does not rely on metaphors, but develops and applies a mathematical model using difference equations. The work is the fulfillment of the goal to build a mathematical framework for the general system theory of families first suggested by Ludwig Von Bertalanffy in the 1960s.

The book also presents a complete introduction to the mathematics involved in theory building and testing, and details the development of experiments and models. In one "marriage experiment," for example, the authors explored the effects of lowering or raising a couple's heart rates. Armed with their mathematical model, they were able to do real experiments to determine which processes were affected by their interventions.

Applying ideas such as phase space, null clines, influence functions, inertia, and uninfluenced and influenced stable steady states (attractors), the authors show how other researchers can use the methods to weigh their own data with positive and negative weights. While the focus is on modeling marriage, the techniques can be applied to other types of psychological phenomena as well.

## About the Authors

John M. Gottman is Professor of Psychology at the University of Washington.

James D. Murray is Professor Emeritus of Applied Mathematics at the University of Washington.

Catherine Swanson is a software engineer at the University of Washington.

Rebecca Tyson is Research Scientist at the University of Arizona.

Kristin R. Swanson is Senior Fellow in Pathology and Applied Mathematics at the University of Washington.

## Reviews

"... neatly presents marriage as a process both mathematical and unpredictable, both stable and prone to catastrophe." , Jordan Ellenberg, Slate

## Endorsements

"*The Mathematics of Marriage* is a splendid, important, and extremely useful book. Gottman and colleagues set a new standard for psychological explanation with their exquisite conversation among theory, models, data, and clinical intervention. They also provide the most clear and accessible introduction to the mathematics I have seen. This work is compelling evidence of the power of nonlinear dynamic models for understanding complex psychological phenomena. It will also change forever the way you look at marriage."

—Esther Thelen, Department of Psychology, Indiana University, Co-editor of *A Dynamic Systems Approach to the Development of Cognition and Action*

"Dynamic systems theory is infiltrating psychology in a variety of ways, increasing the sensitivity, realism, and scope of psychological models and methods. But I know of no other application that covers so much ground, from theory-building and modeling to methodology and measurement, and finally to clinical interventions that actually work. Gottman's determination to heal marriages fuels a rigorous scientific enterprise, based on a sophisticated understanding of complex systems and the mathematics for decoding them."

—Marc D. Lewis, Professor, University of Toronto, Co-editor of *Emotion, Development, and Self-Organization: Dynamic Systems Approaches to Emotional Development*