We were able to derive a set of nonlinear difference equations for marital interaction as well as physiology and perception. These equations provided parameters, that allowed us to predict, with over 90 percent accuracy, what was going to happen to a relationship over a three-year period. The main advantage of the math modeling was that using these parameters, we are not only be able to predict, but now understand what people are doing when they affected one another. And through the equations we were now really able to build theory. That theory allows us to understand how to intervene and how to change things. And how to know what it is we're affecting, and why the interventions are effective. This is the mathematics of love.
MATHEMATICS OF LOVE [4.14.04]
Psychologist John Gottman's goal is "to be like the guy who invented Velcro. Nobody remembers his name, but everybody uses Velcro". He is a psychologist who looks at relationships and focus on the interaction, the "fleeting architectural fluid form that people are creating as they talk to each other, as they smile, as they move."
At Gottman's "Love Lab" he conducts empirical research projects that study human nature scientifically. He follows up his empirical research of interviews, physiological measurements, observations, and creates mathematical models that provide theoretical understanding of all these processes.
Gottman, trained as a mathematician, has been influenced by the field of psycho-physiology, which is concerned with "the study of the body and the face and voice and emotion in relationships, and just try to understand the naturalistic development of relationships. How do people respond emotionally to one another?" He's made his own contribution to this field of emotion with his concept of "met-emotion," or "how people feel about feelings, what their history is with specific emotions like pride, respect or disrespect, love, fear, anger, sadness".
He is looking for nothing less than the universality in relationships. We are as social as bees, he points out, and "Von Frisch discovered the language of bees by going right to the hive and watching them dance. So we will discover the human dance."
So far, his surmise is that "respect and affection are essential to all relationships working and contempt destroys them. It may differ from culture to culture how to communicate respect, and how to communicate affection, and how not to do it, but I think we'll find that those are universal things".
JOHN GOTTMAN, emeritus professor of psychology at the University of Washington, and co-founder of The Gottman Institute, is world renowned for his work on marital stability and divorce prediction, involving the study of emotions, physiology, and communication. He is the author of numerous books including (with Nan Silver) The Seven Principles for Making Marriage Work.
THE MATHEMATICS OF LOVE
(JOHN GOTTMAN:) I look at relationships. What's different about what I do, compared with most psychologists, is that for me the relationship is the unit, rather than the person. What I focus on is a very ephemeral thing, which is what happens between people when they interact. It's not either person, it's something that happens when they're together. It is like a structure that they're building by the way they interact. And I think of it that way, almost like a fleeting architectural fluid form that people are creating as they talk to each other, as they smile, as they move.
I've been working on a couple of puzzles right now. One is trying to understand couple violence, and how violence occurs between two people who supposedly love each other, and have a contract to nurture and protect one another, and to support one another's dreams in a real and meaningful way. Violence occurs so frequently in relationships in this country. Estimates by Leonard are that 36 percent of newlyweds in the United States have had a violent fight before they get married. How does violence happen in an ordinary relationship? And is all violence the same? At one point can you do something about it; is there a point of no return, where you can't do anything about it? And it must be very ordinary, and so there must be a pattern to it that's understandable.
It's a very hard thing to look at.
We've reconstructed it from what we have learned by talking to people about it, and it does seem that there are two very distinct forms of violence. One form is where the conflict escalates, and people somehow lose control. They get to a point where the trigger seems to be feeling disrespected and there's a loss to their dignity. They feel driven to defend that dignity, and start doing things like posturing and threatening while in a state of high and diffuse physiological arousal, and they increasingly have a loss of control. The violence tends to be symmetrical, and there is not a clear victim and perpetrator.
Another kind of violence, which is very different, is where one person in the relationship is using violence to control and intimidate the other person and is very much not physiologically aroused, very much in control and trying to do something to the other person that alters their idea of reality. There is a perpetrator and a victim here, The late Neil Jacobsen and I have called this kind of mind control "gaslighting," after the movie with Ingrid Bergman. I'd like to understand those two kinds of violence. I think the first one is treatable, particularly early, by looking at the couple relationship and changing the relationship. It may be even treatable later on, by slowing things down enough and physiological arousal has a place in it. The second type of violence is more elusive at the moment, although some initial experiments that I and Julia Babcock and her students have designed show promising proximal, that is, short term effects with these perpetrators.
That's one puzzle I'm working on — trying to understand violence, and how to help people because it is so common, and it has a huge effect on families, and especially on children, and their development.
puzzle I'm working on is just what happens when a baby enters a relationship.
Our study shows that the majority (67%) of couples have a precipitous
drop in relationship happiness in the first 3 years of their first baby's
life. That's tragic in terms of the climate of inter-parental hostility
and depression that the baby grows up in. That affective climate between
parents is the real cradle that holds the baby. And for the majority
of families that cradle is unsafe for babies.
We are working with lower-income couples to see whether we can do something about when that baby arrives. So far we've found that with middle-class couples, in just two days of the couple's life, ten hours, we can change the drop in relationship satisfaction that happens to two-thirds of couples and not only change the relationship so there's no increasing hostility over time so relationship satisfaction doesn't go down, and we can have a major effect on postpartum depression. We can also really affect that baby's emotional and cognitive development in quite a profound way, with a very brief intervention. And the baby didn't take the workshop. The question is can we do it when there are many other problems present, like addiction, incarceration, violence, racism, and poverty. Can we also have that kind of effect? That's what we're going to see in the next nine years, whether we can change families. We are now engaged with the nonprofit policy group Mathematica in the largest randomized clinical trial ever done with couples anywhere in the world. There will be 10,000 couples in this study.
Once again, like Head Start, it looks like families are changing in a major way, in terms of social class, from the bottom up. And the government is thinking that when these scientifically based programs will teach social skills to lower-income couples, couples on welfare, that they'll learn and they'll be better. They'll learn from what the middle class is doing. But I think the major learning's going to come the other way because many of the couples we have worked with who have been through a history of slavery, forcible breakups of families by slaveholders, bad schooling, racism, poverty, unequal employment opportunities, bad parenting, criminals as their only successful role models, incarceration, drug addiction, and alcoholism, and violence, and some of these couples are still together. Many of these people who have triumphed despite it all are amazingly articulate when my wife talks to them, and helps them to reveal their highly articulate wisdom. We are seeing a new kind of commitment on the part of men, and on the part of women supporting the men, and who are staying with them in spite of incarceration and addiction. It's breathtaking, because it's a real existential change.
The learning is going to come from the bottom up because a lot of the middle-class couples in this country are lost, existentially. They're focusing much more on money and accomplishments and status, and achievement, and having things. We see something different among these so-called "fragile families", a spiritual sense of meaning and purpose that is coming largely from the baby — from the optimism of having this new baby, and saying, it stops here. The violence stops here. The lack of a father stops here. We're ending the heritage of slavery (African-Americans are saying) and it stops with me, right now. Here I am, I am not going anywhere. I am going to be a consistent presence in my baby's life. And I will mentor other fathers to take this same journey with me. It's a breathtaking change. I think with the scientific application of studying people who really triumph through this, compared with the people who have tremendous difficulty and the relationships are breaking up, or there is increased violence and addiction, we can create a major change in this country. What an opportunity.
One thing we know from Peggy Sanday's work on male domination of women and women's power, in her classic study of 186 hunting-gathering cultures is that when men are involved in the care of babies, not just children but babies, that culture doesn't make war. I think that's what we're seeing now. We're seeing the possibility of an end to war, where fathers are going to be saying, "not my kid. My kid's not going to that war. I am not going to let that happen. My kid isn't dying for that cause, no way. I am going to change the values of this country. If I have to, I'm getting out of here, I'm getting out of this country with my kid alive, I refuse to have my kid go to that war and die for nothing." When fathers are involved in the care of babies everything changes. That's what I think we're going to see, so I'm very excited, very optimistic. I want to write a book called "We fathers will now end war." Just a dream, maybe, but, as John Lennon said, I'm not the only one. A scientific approach to helping this happen is really very powerful, because the right information makes a big change.
approach to the study of families and relationships makes a real difference.
The reason for us getting all these significant effects changing up
to 75 percent of couples, in a very short time period, is because all
we're doing is studying the people who cope well and how they're different
from the people who don't cope well; in this case it's about relationships.
It's not rocket science, it's very simple science, like observing how
stars and planets move. Primitive science. And with that knowledge,
with good information, people just take it and use it and run with it.
So it's a matter of really changing what people know.
Science comes into the study of families and relationships because a scientist always admits to profound ignorance, doesn't presume to know about these things, takes this ignorance and goes to the people and observes them in situations that are vitally important — when people are having dinner, when they meet at the end of the day, when they are in the bedrooms cuddling, when they're having sex, when they're interacting with their babies — in these very important moments, a scientist without preconceptions observes and tries to understand — interviews people, measures their physiology, and tries to get at their inner experience. And then creates mathematical models that provide theoretical understanding of all these processes.
By putting this information together, in a way that is unbiased, with proper controls, so the observers are double-blind and don't know the hypotheses and so on, then you can come up with information that is really useful and helpful to people. It may have to be done over and over again when we do this research with French Creole, black people, married to a Cuban black. Or when we go to Arizona and study Pima Indians or Navahos. It may be different there. And when we do this work across cultures, we will discover, through doing this over and over again, without bias, what the universality is in relationships.
I am sure that universality is there. We are no less social than bees, and Von Frisch discovered the language of bees by going right to the hive and watching them dance. So we will discover the human dance. What's an example of what we may find? So far I believe we're going to find that respect and affection are essential to all relationships working and contempt destroys them. It may differ from culture to culture how to communicate respect, and how to communicate affection, and how not to do it, but I think we'll find that those are universal things.
I started off as a mathematician, and always thought I would be a mathematician. I was going to study math at MIT, and my first year I was randomly paired with a roommate at MIT who was a psychologist, and I got really interested in his books and changed fields, and went to the University of Wisconsin. And at the University of Wisconsin there was a tremendous amount of interest in Pete Lang's work on psychophysiology, Harry Harlow's work on love in mom and baby rhesus monkeys, and Dick McFall's work on social skills, Mavis Hetherington 's work on families, and interaction, and — especially using observational methods and tight quantitative analyses.
what really fascinated me: observing people and trying to see what you
could learn from a much more objective analysis. I've been influenced
tremendously by my friend Paul Ekman's work Looking at Faces,
which started with Charles Darwin's and Sylvan Tomkin's work, looking
at the universality of how emotions get expressed, by Harry Harlow and
John Bowlby's work in how normal dependency is in relationships. These
views presented a new alternative to behaviorism and also to psychoanalysis.
What I have added to this field of emotion is my concept of "met-emotion," or how people feel about feelings, what their history is with specific emotions like pride, respect or disrespect, love, fear, anger, sadness. What their philosophy is about emotions and why they have this philosophy. It's critical to parenting and to couple relationships as well. It determines emotional behavior in families. And with my former students Lynn Katz and Dan Yoshimoto the study of meta-emotion now is providing us with new tools for changing families.
Bob Levenson and I were very surprised when, in 1983, we found that we could actually predict, with over 90 percent accuracy, what was going to happen to a relationship over a three-year period just by examining their physiology and behavior during a conflict discussion, and later just from an interview about how the couple viewed their past. 90% accuracy! Nobody was getting that kind of prediction in psychology. In fact, Walter Michel had just published a book challenging psychology with really terribly low rates of being able to predict human behavior. He said the Emperor has no clothes. But here we were with huge correlations, and getting enormous stability in couples interaction over time (with no intervention). We thought at first that it might be just chance, but we found after doing study after study that very simple patterns replicated in sample after sample. You could tell from just looking at how a couple talked about how their day went, or talked about an area of conflict, what was going to happen to the relationship with a lot of accuracy.
That was surprising to us. It seemed that people either started in a mean-spirited way, a critical way, started talking about a disagreement, started talking about a problem as just a symptom of their partner's inadequate character, which made their partner defensive and escalated the conflict, and people started getting mean and insulting to one another. That predicted the relationship was going to fall apart. 96% of the time the way the conflict discussion started in the first 3 minutes determined how it would go for the rest of the discussion. And four years later it was like no time had passed, their interaction style was almost identical. Also 69% of the time they were talking about the same issues, which we realized then were "perpetual issues" that they would never solve. These were basic personality differences that never went away. She was more extroverted or she was more of an explorer or he was more punctual or frugal.
Some couples were caught by the web of these perpetual issues and made each other miserable, they were "grid locked" like bumper-to-bumper traffic with these issues, while other couples had similar issues but coped with them and had a "dialogue" that even contained laughter and affection. It seemed that relationships last to the extent that you select someone whose annoying personality traits don't send you into emotional orbit. Once again conventional wisdom was wrong. The big issue wasn't helping couples resolve their conflicts, but moving them from gridlock to dialogue. And the secret of how to do that turned out to be having each person talk about their dream within the conflict and bringing Viktor Frankl's existential logotherapy into the marital boxing ring. Once people talked about what they wished for and hoped for in this gridlock conflict and the narrative of why this was so important to them, in 86% of the cases they would move from gridlock to dialogue. Again a new door opened. Not all marital conflicts are the same. You can't teach people a set of skills and just apply them to every issue. Some issues are deeper, they have more meaning. And then it turned out that the very issues that cause the most pain and alienation can also be the greatest sources of intimacy and connection.
Another surprise: we followed couples for as long as 20 years, and we found that there was another kind of couple that didn't really show up on the radar; they looked fine, they weren't mean, they didn't escalate the conflict — but about 16 to 22 years after the wedding they started divorcing. They were often the pillars of their community. They seemed very calm and in control of their lives, and then suddenly they break up. Everyone is shocked and horrified. But we could look back at our early tapes and see the warning signs we had never seen before. Those people were people who just didn't have very much positive connection. There wasn't very much affection — and also especially humor — between them.
These are the people you see in restaurants who've been married a long time and they're sitting there not talking to each other throughout the whole dinner and they don't look very happy about the vast chasm between them. Those are the couples where you say to your partner "Let's never become like them, okay?" These sorts of emotionally disconnected relationships were another important dimension of failed relationships. We learned through them that the quality of the friendship and intimacy affects the nature of conflict in a very big way. My former student Janice Driver studied this friendship aspect of emotional connection with detailed analyses of our apartment lab tapes, hundreds of hours of people doing ordinary things like reading the paper or having dinner.
Again. Like Leunhook with his microscope, Jani discovered a hidden world in the ordinary everyday moments. These moments were the key to how people build friendship and even sexual intimacy. Foreplay really happens all the time. Eventually in our theory there were three circles having to do with conflict, friendship, and sense of purpose and meaning, that were interlocked here. That became our theory, we called the "sound relationship house theory." It also worked for the gay and lesbian couples that Levenson and I studied for a dozen years.
Over a decade ago I began working with James Murray, an amazingly gifted applied mathematician, who in many ways is the father of a new field called mathematical biology. All that theorizing about chaos actually led to new mathematical developments that could model very complex phenomena in biology with very few parameters because the equations were nonlinear. So James and I and his students collaborated and after 4 year of meeting once a week, we were able to get equations for marital interaction as well as physiology and perception, that allowed us to understand our predictions, of what was going to happen to a relationship over time. Using these parameters, we are not only be able to predict, but now understand what people are doing when they affect one another.
And through the equations we could really build a quantitative theory, and we can understand how to intervene and how to change things. Now the sound relationship house theory had a mathematical basis. That's when physics really moved forward by leaps and bounds, after Newton and Leibnitz invented the math for it, the calculus. And perhaps, who knows, perhaps we could do the same with our math. And how we could know what it is we're affecting, what parameters, and maybe understand why our interventions are effective or why at times they fail. This is the mathematics of love.
For the past eight years I've been really involved, working with my amazingly talented wife, trying to put these ideas together and use our theory so that it that helps couples and babies. And we now know that these interventions really make a big difference. We can turn around 75 percent of distressed couples with a two-day workshop and nine sessions of marital therapy. These are couples that have waited as long as six years to get any kind of help. So it's a considerably deteriorated situation.
Then we are also finding that if we intervene early, and do preventative intervention, our effects are much bigger, and we have an impact not only on the couple, and changing their longitudinal course, in a dramatic way, in not a very long time, but we can also have an impact on the emotional development of their children. We're following those children — we're now studying children whose parents went only to a two-day workshop, and their babies are now turning three years old, and we'll know at the end of this year whether this emotional developmental change continues and the children are in a dramatically different trajectory than kids whose parents didn't take the workshop.
It sounds as if we have a stake in relationships staying together — but we don't. My major stake is in understanding. We have a stake in people not staying together if they don't feel good about their relationship and it's not really going anywhere for them, it's not really helping them build one another's dreams, it's not a relationship that has dignity. But we like to help people understand why it is that it didn't work, so that the next relationship, or next set of relationships, can be better. One of the major things we found is that honoring your partner's dreams is absolutely critical. A lot of times people have incompatible dreams — or they don't want to honor their partner's dreams, or they don't want to yield power, they don't want to share power. So that explains a lot of times why they don't really belong together.
Psycho-physiology is an important part of this research. It's something that Bob Levenson brought to the search initially, and then I got trained in psycho-physiology as well. And the reason we're interested in what was happening in the body is that there's an intimate connection between what's happening to the autonomic nervous system and what happening in the brain, and how well people can take in information — how well they can just process information — for example, just being able to listen to your partner — that is much harder when your heart rate is above the intrinsic rate of the heart, which is around a hundred to a hundred and five beats a minute for most people with a healthy heart.
At that point we know, from Loren Rowling's work, that people start secreting adrenalin, and then they get into a state of diffuse physiological arousal (or DPA) , so their heart is beating faster, it's contracting harder, the arteries start getting constricted, blood is drawn away from the periphery into the trunk, the blood supply shuts down to the gut and the kidney, and all kinds of other things are happening — people are sweating, and things are happening in the brain that create a tunnel vision, one in which they perceive everything as a threat and they react as if they have been put in great danger by this conversation.
All of which are really great conditions for running away from a predator, or fighting aggressively to protect the tribe. And survival. So when you have less blood in the periphery you create what Malcolm Gladwell calls a bloodless armor that lets you strike without really bleeding too much, or run away without hurting yourself too much. But in the context of a discussion with somebody you love clearly this DPA is not very functional. And we found in fact that physiological arousal is one of the best predictors of what happens to that relationship. That's why it predicts.
And men and women are somewhat different, not a lot, but enough, which is another fascinating puzzle, because we find that if the woman is driving the husband's heart rate, that predicts the dissolution of the relationship — and not the other way around. Now why should that be? Why should it be that DPA, the general physiological arousal of men is a worse indicator of the fate of a heterosexual relationship than that of the woman? Unless she's been abused, physically or sexually, when the arousal of both of them is a really good indicator.
Because men are different. Men have a lot of trouble when they reach a state of vigilance, when they think there's real danger, they have a lot of trouble calming down. and there's probably an evolutionary history to that. Because it functioned very well for our hominid ancestors, anthropologists think, for men to stay physiologically aroused and vigilant, in cooperative hunting and protecting the tribe, which was a role that males had very early in our evolutionary history. Whereas women had the opposite sort of role, in terms of survival of the species, those women reproduced more effectively who had the milk-let-down reflex, which only happens when oxytocin is secreted in the brain, it only happens when women — as any woman knows who's been breast-feeding, you have to be able to calm down and relax. But oxytocin is also the hormone of affiliation. So women have developed this sort of social order, caring for one another, helping one another, and affiliating, that also allows them to really calm down and have the milk let-down reflex. And so — it's one of nature's jokes. Women can calm down, men can't; they stay aroused and vigilant.
So it's a real challenge, now that relationships, in the last couple of centuries, have started becoming important in terms of affection and nurturance and support — and we're having fathers come back into the equation in a big way in baby's life. Physiology becomes really critical in this whole thing. A provocative finding from Alyson Shapiro's recent dissertation is that if we take a look at how a couple argues when the woman is in the sixth month of pregnancy, we can predict over half the variation in the baby, the three-month-old baby's vagal tone, which is the ability of the vagus nerve, the major nerve of the parasympathetic branch of the autonomic nervous system, which is responsible for establishing calm and focusing attention. That vagus nerve in the baby is eventually going to be working well if the parents, during pregnancy, are fighting with each other constructively. That takes us into fetal development, a whole new realm of inquiry.
And if they're not, if they're fighting destructively, that fetus, that baby is on a different longitudinal course — its neurological development is already handicapped — from the time it's born. The fetal development is really affecting the function of this vagus nerve, the tenth cranial nerve. Now this destructive process that happens to two thirds of all couples can be reversed, just in a 10-hour workshop the parents take in the last trimester of pregnancy. One of the things that's very interesting is that with psychological interventions you can change neurological growth and development, and emotional growth and development in the baby. This makes for more empathetic children — and more empathetic infants as well. Daniel Siegel is beginning to help us understand how this happens, how to integrate attachment theory, relationship science and brain neurophysiology and growth. It's a rich and exciting new field, what Jaak Panksepp calls this "affective neuroscience."
We find that there are differences between men and women and the way you to study these differences is independent of sexual orientation. You have to study gay and Lesbian couples who are committed to each other as well as heterosexual couples who are committed to each other, and try and match things as much as you can, like how long they've been together, and the quality of their relationship. And we've done that, and we find that there are two gender differences that really hold up.
that if a man presents an issue, to either a man he's in love with or
a woman he's in love with, the man is angrier presenting the issue.
And we find that when a woman receives an issue, either from a woman
she loves or a man she loves, she is much more sad than a man would
be receiving that same issue. It's about anger and sadness. Why? Remember,
Bowlby taught us that attachment and loss and grief are part of the
same system. So women are finely tuned to attaching and connecting and
to sadness and loss and grief, while men are attuned to defend, stay
vigilant, attack, to anger. My friend Levenson did an acoustic startle
study (that's where you shoot of a blank pistol behind someone's head
when they least expect it). Men had a bigger heart rate reactivity and
took longer to recover, which we would expect, but what even more interesting
is that when you asked people what they were feeling, women were scared
and men were angry.
So there are all these small but reliable differences, and I think they have big implications for what you do in relationships. Now it's women who matter here, because we find that 80 percent of the time women are the ones in our culture who raise issues, and they raise them harshly in an unhappy relationship and more gently in a happy relationship.
But does that mean that women are to blame in some way for relationships going bad? The poor men get so physiologically aroused they can't think straight and the women are calmer, so it's no wonder, we might think, that men withdraw or aggress. Not so at all. Levenson and I did a study where we had couples talk about how their day went before they talked about their big conflict area, and it turned out that the women who raised the issue harshly — and by the way, the men who raised the issue harshly as well, 20 percent of the time it's guys who raise the issue — had partners who weren't very interested in how their day went. They'd look at their watch, or, you know, they were bored, or they were — they were kind of insulting when the person started talking about their day. Like one guy said to his wife, "Why don't you go first? It won't take you very long." Really a putdown, just in their talking about how their day went. Those people had partners who started harshly. So it's really a circle. Friendship and emotional connection and the management of conflict.
We've now gotten to the point where not only can we predict what's going to happen to the relationship, and not only can we intervene to prevent decay of relationships for people who really want to stay together, not only can we help people who really are continually unhappy with one another, to find out why their relationship isn't working, but we're really starting to understand the whole equation of this process, of having close relationships.
enormous predictability. But there's nothing random or hard to understand
about it. The principles are very simple. And they're easy to learn,
and it makes a difference if you have the right ways to think about
this, compared to the wrong ways of thinking about it. There's a lot
of stuff that makes sort of logical sense, that seems like it would
be right, and turns out to be a complete myth about relationships. We're
at the point where we're starting to understand how to have an impact
on a societal level, not just on individual cases, but really to change
families in our whole culture.
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