A Brief Review of Gottman and Murray’s book, The Mathematics of Marriage:  Dynamic Nonlinear Models

by Fonya Lord Helm, Ph.D.,ABPP

actractor3Mathematical models confirm the importance of positive interactions in love and marriage.  This powerful perspective describes marriage as a dynamic system, characterized by steady states and periods of chaos followed by abrupt reorganizations.   Divorce would be an example of such a reorganization, and I will focus on the differences between marriages that are stable and those that proceed toward divorce.  These researchers have found some important predictors.  The math that they are using includes strange attractors and null clines, and can be followed by those readers interested in mathematics.

Happy marriages have one very important factor that separates them from unhappy and unstable marriages.  It is the husband’s “set point,” his tendency to communicate more negative than positive affect.  It is a strong predictor of divorce.  The set point or starting point–in terms of positive or negative bias–of each person is different, and the members of the couple bring their set points to the interactions that take place between them.  These set points have to be included in the mathematical model to get an accurate prediction.   The wife’s set point did not emerge as a predictor—a curious phenomenon that needs to be understood.

Marriages in trouble eventually showed that couples were involved in Fritz Heider’s “fundamental attribution error:”  each partner was blamed by the other for the problems of the marriage, and small negative events were seen as being caused by fundamental defects in the partner’s character.  At the same time, people were quite forgiving toward themselves.  Nye in 1988 found that unhappily married couples endorsed almost every negative trait as characteristic of their spouses (the negative halo effect), while happily married spouses endorsed almost every positive trait as characteristic of their spouses (the positive halo effect).

I also want to describe some findings in terms that are not mathematical.  In stable marriages, the couples created FIVE positive communications for every negative communication.  In marriages headed for divorce, the couple had slightly fewer positive communications than negative communications (.8 to 1).  Positive communications include humor, caring and thoughtfulness.

Negative communications include criticism, defensiveness, contempt and stonewalling.  Anger and sadness were not necessarily negative communications—only if they were combined with criticism and contempt and enactments like stonewalling.

Gottman and Silver (2015) discussed videotapes of three kinds of stable couples:  (1) the volatile or bickering couple, (2) the conflict-avoiding couple, and (3) the validating or harmonious couple.  All these couples had FIVE positive communications for each negative communication.  Couples headed for divorce had .8—not even one–positive communication for each negative communication.   Women criticized more and men withdrew by stonewalling more–the “demand-withdraw pattern.”  In fact, the demand-withdraw pattern is characteristic of most marriages, with the wife bringing up problems and the husband withdrawing, but in unhappy marriages, this pattern increases.  Evidence exists that the withdrawal of the husband is due to greater physiological arousal, something that is biologically based.    Escalation of negative affect is very common in unhappy marriages and is an indication of the rejection of being influenced by the partner, indicating a strong need for power and control.

In a happy marriage, if someone does something negative, like being irritable, the partner thinks the cause is situational:  “he’s over-tired and over-worked” or “he’s mourning the loss of his mother.”  In unhappy marriage, the irritability is attributed to an enduring trait:  “that’s just the way he is—grumpy and self-absorbed.”   In a happy marriage, if someone does something positive, like helping out with some chores, the partner thinks:  “he is a kind and considerate person.  That’s the way he is.”  In an unhappy marriage, helping out with the chores is viewed differently:  “he must want something or feel guilty about something and he’s trying to make up for it.”  The positive response is viewed as situation and unlikely to be enduring.

Happy marriages have other things besides the five positive communications for every negative, though, since the researchers also found that unhappy yet stable marriages also included five positive communications for every negative.   What else is different?

Rausch et al. (1974) found that in discussions of problems, distressed couples responded differently from non-distressed couples.  The way they handled the problem description statements as they began the discussion was the critical issue—not the number of problems.  After a statement of the problem, the partner in the non-distressed couple followed with a positive statement repeatedly. In distressed couples, the partner followed with a negative statement repeatedly.  Negativity became an absorbing state for distressed couples, but not for the non-distressed couples.  Soon, non-distressed couples begin to escape from negativity when it occurs, but the distressed couples do not seem to be able to escape. These researchers define negativity as devaluation, fighting back and “yes-butting.”

Attempts at repairing the interaction are often delivered with negative feelings.  For example, “stop interrupting,” or “we’re getting off the topic” may be accompanied by irritation, tension, sadness or another type of distress.  Repair attempts often have 2 components—both negative feeling and content that tries to repair the interaction.  Dissatisfied couples pay more attention to the negative feeling and satisfied ones pay more attention to the content.  The conclusion is that repair processes do not work well in distressed marriages.

Satisfied couples avoid or extricate themselves quickly from the negative by using content (metacommunication), probing the other person for feelings, exchange of information, humor, areas of common ground, gossip and appeals to the basic philosophy and expectations in the marriage.

For example, let’s look at two ways of responding to the same communication:  “stop interrupting me.”  In a happy marriage, the partner might say, “Sorry, what were you saying?”  In an unhappy marriage, the partner might say, “I wouldn’t have to interrupt if I could get a word in edgewise.”

Also, the interaction of happy couples is more random than the interaction of unhappy couples, who have a strong tendency to get stuck in negative interactions.

Two major mysteries remain:  the relapse effect, the finding that initial gains in marital therapy relapse after one to two years, and the delay effect, the finding that couples wait six years after the problems begin to consult someone.