# HEY BABY! I THINK OUR INTERACTION FUNCTIONS WOULD MESH WELL. LET’S DATE

A review of research by Dr. John Gottman at the University of Washington: “A General Systems Theory of Marriage: Nonlinear Different Equation Modeling of Marital Interaction”. J. Gottman, C. Swanson, K. Swanson. Personality and Social Psychology Review: 6(4), 326-340, 2002.

ABSTRACT:
This article describes a new mathematical approach for modeling the prediction of divorce or marital stability from marital interaction using nonlinear difference equations. The approach is quite general for modeling social interaction, and can be applied to any time series data generated over time for two individuals. We pursued a balance model in selecting the dependent variables of this modeling. Both the mathematical methods and the theoretical gains obtained when using this approach are reviewed

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It’s happened to many of us in the relationships we are part of – we make an idle comment to our other halves and five minutes later, an all-out battle is ensuing which threatens all known modes of normality. Of course, we’ve also all seen those cutesy-wutesy couples that wander around holding hands constantly, whispering sweet nothings to each other. And, we can all sigh, wonder at the mystery of relationships, and question why some work out and others just don’t.

Well, you’ll be pleased to know that scientists at the University of Washington have claimed that after watching a couple interact for as little as 30 minutes, they have a 90% chance of predicting whether the relationship will last.

To take all the mystery out of it (or maybe add some of the mystery back in, depending on your perspective), one of the tools that they use are a class of mathematical modes called difference equations. In this case, the difference equations are used to model the effect of one of the partner’s comments on the behaviour of the other. The behaviour, which is a assessed through a combination of physiological signals as well as simple stances and replies, is tracked through the course of a carefully controlled interaction between the couple. This observation leads to the prediction of an “interaction function” for each member of the couple and, through a series of mathematical manipulations, these “interaction functions” can be converted into two nullclines or lines which predict the state at which that individual’s behaviour will not change, assuming that the other partner’s behaviour remains constant.

For example, let’s assume that your mood has some influence on your partner’s (hopefully this is a valid assumption), and that the researchers can somehow control your mood so that it does not change. According to the assumptions of this model, your partner’s mood will reach some state which will be dependent on your mood. If the researcher’s change your mood, your partner’s will too and will reach another steady state. If we look at a continous graph of all your moods and plot your partner’s against that, the line that is formed by joining up all the points will be your nullcline. The same thing can be done the other way around where your partner’s mood can be experimentally manipulated and your final resting mood observed.

Now comes the key point about the models predictability. Where the two nullclines cross is what mathematicians call a steady state. This is a point where if each member of the couple starts on that exact mood predicted by where the nullclines cross, and assuming that there are no external influences, they will stay at that point no matter how long the interaction between them takes place.

There are two types of steady states: stable ones and unstable ones. Think about steady states as the tops of hills or the bottom of valleys: if a ball is placed at the very top of a hill or the very bottom of a valley, it will stay there forever as long as nothing forces it to move. However, the behaviour of the ball, if it is moved slightly will vary drastically depending on whether it is on the hill or in the valley. The same thing applies for the relationship steady states. If a couple’s nullclines cross in such a way that they form a stable steady state, no matter how they get emotionally pushed, they will return to a good interaction and both partners will be happy. However, if they cross in such a way that they have an unstable steady state, things do not look too good and the divorce lawyers might as well be lining up outside the door.

Interestingly, by understanding the factors that make for really happy relationships, researchers are able to teach bad relationships to get a little better, but, unfortunately, this is only a temporary improvement. Long term improvement can only come by changing the couple’s nullclines which, presumably is heavily influenced by the personalities involved and so would take drastic change on the part of the individual.

Of course, with all the current debates raging around much of the western world about what marriage really means, one wonders if a 30 minute session with one of the UW researchers would make any further debate a moot point.

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