The Mathematics of Marriage: Dynamic Nonlinear Models

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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.
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Editorial Reviews

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

  • ISBN-13: 9780262072267
  • Publisher: MIT Press
  • Publication date: 2/2/2000
  • Series: Bradford Books Series
  • Edition description: New Edition
  • Pages: 500
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.75 (d)

Meet the Author

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.

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Table of Contents

1 What do we mean by theory? 1
2 What phenomena are we modeling? 5
3 Nonlinear dynamic modeling 35
4 Calculus - the mathematics of change 41
5 Introduction to dynamic modeling 65
6 Modeling catastrophic change 81
7 Intuitive discussion of phase space plots 99
8 Interacting dyadic systems 111
9 Writing the equations of marriage 127
10 Initial results of our modeling 151
11 Who needs all this math? 165
12 Applying the model to newlyweds 173
13 Repair and damping 189
14 Extending the marriage model 233
15 The core triad of balance 251
16 The marriage experiments 291
17 How to prepare data for modeling 337
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