This book proposes a simple model of marital interaction which takes the form \[ W_{t+1}=I_{HW} (H_t)+r_1W_t+a \]
\[ H_{t+1}=I_{WH} (W_{t +1})+r_2H_t+b \] Here \(W\) stands for wive and \(H\) for husband. \(I_{WH}\) and \(I_{ HW}\) are the so-called influence functions. It is inspired from an experimental setup where the couple has a discussion in a conflict situaton. An important variable (called the Gottman-Levenson variable) is the “positive minus negative behaviors at each turn of speech during the conservation” (p. 127). The states represent the behavior scores of the wife and the husband (Notice that they are not well defined in case both partners speak a the same time which may occur in a conflict situation).
The model is improved (chap. 13) by adding terms for repair and damping in the interaction. Modelling here consists in identifying parameters so that they are chosen to fit data. The core ideas are very well described in chapter five of the second author’s recent book [Mathematical biology. Vol. 1 (1992; Zbl 1006.92001)].
Here, the topic is put in a historical context in chapter two. The psychological school overemphasized the personality aspect increasing unnecessarily the complexity of the interaction. In fact interaction could lead to simplified situations. Issues of observing and interpreting meaningfully data are outlined. On the other hand, the cybernetical approach of human interaction would overemphasize the complexity of messages exchanged (verbal, nonverbal). It has turned out that a behavioural perspective pinpointing at quantities which would be quantified as positive and negative would predict meaningfully the situation. Later dynamics and randomness (including information theoretic methods) were introduced. The positivity and negativity quantities introduced earlier are now subject to dynamics and the results of observations are that (with some mild variation) for a happy couple one has a sequence of the type \((+,+,+,+\dots)\) or \((-,\pm,\pm,\dots)\) positively absorbing) while for a distressed couple, one has a sequence of the type \((-,-,-, -,\dots)\) or \((+,\pm, \pm,\dots)\) (negativity absorbing). A possible mechanism proposed for understanding this is that in a message with two distinct components: verbal negative (factual) and nonverbal positive (contextual), a distressed couple will listen to the factual component while a happy couple will listen to the contextual component (seen as a repair mechanism). So perception of the repair mechanism is the issue. But several more concrete criteria for success or failure were proposed. Psychophysiology contributed also to the topic.
Several chapters (three to eight) introduce basic mathematics relevant to the sequel (nonlinear dynamics, phase portrait in the plane, catastrophe theory, predator-prey system). Chapters nine and ten set the model and its validation.
Chapter eleven is controversial with a criticism of homeostasis and feedback which are seen as metaphors and nonscientific. The authors think that sticking to equations would protect against such approaches. But concerning their mathematical conceptions one can read p. 171: “Our equations are nonlinear because linear equations are generally unstable” (in the same vein one has p. 14-15: “Stochastic models are uniquely designed for thinking in terms of systems rather than individual behavours”). Moreover, feedback is quite mathematically expressed in control theory. Their view of catastrophe theory should be clarified. Is a catastrophe (divorce) due to a bifurcation parameter or to structural coupling in the interaction?
Some extensions are considered (homosexual marriage in chapter fourteen, a refinement of the modelling with three variables. One adds to behaviour, perception and physiology. Nine situations corresponding to pairings of these variables are studied).
Chapter sixteen is an attempt for providing means for marriage rescue. It consists in a feedback loop (although the authors do not say so) which reinforces marital friendship via the creation of shared symbolic meaning is what the authors call a culture of marriage arising from the interaction. Thus a communication oriented layer supersedes the “organic” one and what is called “Gottman’s new theory and marital intervention” reminds ideas which can be found in B. Mallinowski [Sex and Repression in a Savage Society (1927)] where culture is seen as arising from the networking of emotions and feelings of individuals. A further interpretation would see it as a regulatory mechanism. A key step for the authors is to modify love by knowledge transforming it into companionship. This idea is not new too and the reviewer recalls a thought of Alain who stated that the loving couple lives in a miserable state which has to be surmounted by marriage and companionship. Let us mention that the equations the authors were previously so found of cannot be found in this chapter.
Although the modelling idea consists in aggregating various aspects of a complicated interaction in a single variable, one has to ask if this reduction is always meaninful. The authors try to study models with more dimensions in a chapter however. For instance the distinction verbal-nonverbal which is emphasized at a stage might be relevant in the repair mechanism outlined in chapter sixteen. The state is extracted from the verbal part (but nonverbal information will influence the verbal part and conversely) so a distinction might be a difficult task. Of great interest would be a comparison with matriarchal societies and this suggest a further limitation of this study in the sense that the authors confine themselves to the couple as an individual pairing without embedding it in the society in which it evolves. (The reproach of previous studies was that the individual was overemphasized but the same argument would apply to the couple). A couple of foreigners in a given society might have to support more stress than a couple of nationals. The role of religion in marriage is (was) considerable. And one has to ask why it is so. There must have been good reasons why marriage was considered as a sacred act. The dissolution of marriage in modern societies might be characteristics of the “flattening” effect that Heidegger attributed to modernity: the loss of the sacred perspective.