As you can imagine, the conversations that take place in the lab are difficult. Picture yourself sitting down with someone who has a strong opinion on abortion, one that is opposed to yours, and then trying to discuss the issue and reach consensus on a statement that will be publically shared with others.

It might not surprise you to learn that many of these conversations get hostile and need to be ended early, before the study is complete. Like the session described above, they become deeply personal and historical. But what might surprise you is that they do not all go terribly bad. They do not all escalate, get locked in, and remain stuck. For example, here’s another brief excerpt from a different session, this time from a European American man and an Asian American woman who are also discussing affirmative action.

Session 2

M: “So, what’s your take on affirmative action?

W: “My take on affirmative action? Um, overall, or specifically on these questions?”

M: “Overall.”

W: “Overall? The first thing that comes to mind when you ask the question is . . . an idea to fix a wrong that may not be the right fix . . . that’s my take, generally.”

M: “And when you say may be wrong do you mean that you may be more for or against it?”

W: “The reason that I say I think it’s wrong . . . I think it may be ineffective as a solution to the issue we are talking about . . . because I think it might be a setup for students who are involved in these programs. It might be setups for failure. So it actually makes things worse for them. That’s how I feel about it.”

M: “Do you think it’s ineffective or something you disagree with? I’m just trying to understand.”

W: “I think it’s ineffective . . .”

W: “If I was to see someone else of color that scored much lower than I did and got into the program choice that I wanted to get into, and I was denied that, I would be very upset about it, I would think it was unjust.”

As in the first session, the man and woman in this discussion were paired because of their contrasting views on affirmative action. And as before, the participants quickly discovered they held opposing views on the subject and that their stances on the issue came from their personal history—how they had been raised and taught and where they had been brought up, in this case, Minnesota and New York City.

But something different took place in this second session. Although emotional, even sometimes caustic, the dialogue was less constrained and more emotionally expansive. Both conversations involved negative emotions, attributions, and even some verbal attacks, but they diverged dramatically in the degree to which session 1 had become stuck in a narrow well of negativity and polarization. The participants in session 1 had become engulfed by the conflict.

Session 2 participants did not suffer the same fate. When we asked the participants from both sessions how it went for them, it was clear that those from session 2 felt significantly better about the discussion, their relations with the other person, whether they would want to work with them again on something, and even with the statement they generated. Even though both dyads in the study were discussing the same difficult, politically polarizing issues on which they held strong, morally opposing views, one dyad had discussions that got mired in negativity and the other, although not absent of negativity, was able to speak to the issues in ways that, even though hard, remained constructive.

These same differences in the patterns of more constructive versus more destructive moral conversations—differences in the expansiveness of how the participants thought, felt, and behaved—were found again and again in the various sessions in our research. It was as if the more destructive dyads got mired in a place that became more and more constraining.

Like being caught in quicksand, the more they struggled the more stuck and exhausted they became. The constructive dyads were somehow able to avoid this trap.

What was particularly interesting to us was that, underneath it all, the main thing that distinguished the session 1–type discussions (destructive) from the session 2–type discussions (constructive) was the difference in their degrees of complexity. That difference could be seen in the dramatic contrast between the lower-complexity patterns of the thoughts, feelings, and behaviors of dyads in the destructive encounters and the higher- complexity patterns of the dyads in the constructive conversations. Above, for instance, is what the emotions of the two different dyads looked like during their twenty-minute sessions.

Without paying too much attention to the specifics of the graphs above, just notice the differences in the gray dots and lines from sessions 1 and 2. In session 1, the dots are all tightly organized along two lines, meaning that the people in this discussion felt mostly neutral to negative emotions as they discussed affirmative action.

In session 2, the dots and lines are all over the place. This shows that the emotions of the participants moved back and forth, from positive to negative, as the discussion unfolded. And as we looked further, we found similar differences in simple versus complex patterns in the data between the two sessions, for thought and behavior as well. In other words, the more constructive dyads thought about the issues in more complex, nuanced, and flexible ways. They felt many different types of emotions, both positive and negative, over the course of the discussions. And they behaved in more varied ways that demonstrated a greater degree of openness, flexibility, and curiosity in addition to a strong advocacy for their positions than did the session-1 types.

The findings from this study were particularly striking to us because they flew in the face of conventional wisdom, which argues that the simplest approaches to complicated problems are always the best. In our research, more complex approaches, in terms of how the participants thought about the issues, felt, and behaved, were in fact better. To explain why, it’s necessary to back up and address the psychology of complexity.

THE PSYCHOLOGY OF COMPLEXITY, COHERENCE, AND CONFLICT

In 1910, the philosopher Max Wertheimer bought a small toy while away on vacation. This toy ended up turning the field of psychology on its head. On his journey, Wertheimer had been staring out the window of a train, puzzling over the blur of perceptions before him. He got off the train during a station stop and purchased a stroboscope, a spinning drum with viewing slots and pictures on the inside, like a primitive movie machine.

While playing with the toy, Wertheimer was struck by something. He noticed that the pictures in the toy looked like they were moving, but were not. It occurred to him that at times we perceive motion when it is really not there, when there is nothing more than an effect called apparent motion, a rapid sequence of individual sensory events. He realized that we often experience things not part of our simple sensations, that what we see is an effect of the whole event we are perceiving, not just the sum of its parts. He later wrote: “What is given me by the melody does not arise . . . as a secondary process from the sum of the pieces as such. Instead, what takes place in each single part already depends upon what the whole is.”² In other words, while listening to music, only after first hearing the melody do we perceptually divide it up into notes. Similarly with perception, we see the form of the circle first and only later notice that it is made up of lines or dots or stars.

At the time, psychology was interested in the small things. Psychologists studied learning, perception, and cognition by breaking things down into their smaller parts, like sensations, images, and feelings, and then investigating them in their own right. Wertheimer rebelled against this approach, arguing that psychology should take a unified approach to the study of human perception and behavior, and view it as a meaningful whole. That is how we make sense of things. How we feel and behave depends on our broader context of experience and cannot be understood by merely studying the pieces. This idea resembles the Taoist and Aristotelian principles of holism. It was the basis for Gestalt psychology, a radical paradigm shift in the field away from atomistic, micro, and mechanical perspectives toward a more holistic and dynamic view of psychological phenomena.

Enter Kurt Lewin, a bright, gregarious German Jew who studied psychology in Berlin under Wertheimer’s former teacher, Carl Stumpf.^b Lewin was forced to flee Nazi Germany in the 1930s and traveled to the United States. There his work had a major impact on social psychology, in particular the theoretical study of group dynamics, prejudice, authoritarianism, and, most important for us, social conflict.^c

While in the United States, Lewin developed his field-theoretical approach to the study of social conflict, which incorporated much of what he had learned from his Gestalt colleagues, as well as some new ideas coming out of physics (which was undergoing a similar paradigm shift at the time from Newtonian mechanics to field theory). In particular, there were two main principles from Gestalt that influenced his work.

1. All social phenomena should be conceived as occurring in a “field.” This means that in order to best comprehend any social phenomenon such as conflict, we must not prematurely oversimplify it, but be able to see the broad field of forces operating to move it in a positive or negative direction. For example, take a look at the electromagnetic field below.

Before the discovery of such fields in the latter part of the nineteenth century, physicists understood most natural phenomena as the result of forces acting between one body and another in an empty space. But a series of brilliant experiments on electromagnetic phenomena, conducted by Hans Christian Oersted and Michael Faraday, challenged this basic view and profoundly altered scientific conceptions of physical reality. They demonstrated that between two magnetic poles, instead of empty space, there lies a complex field of forces acting to attract or repel the poles.

The impact of these ideas crumbled the foundations of popular philosophical viewpoints at the time and served as a model for new conceptions in the biological and social sciences. The Gestalt conceptualization of psychological perception occurring in a field and Kurt Lewin’s development of a field theory of human motivation and social conflict were two of the more influential models emerging from this view.

The second Gestalt principle was derived originally from psychological research on perception.

2. Psychological processes act to move us toward states of the field that are as simple and orderly as conditions allow. Allow me to illustrate. Turn the page and look at the image. What do you see? Anything?

Source: The Intelligent Eye. R. L. Gregory, Weidenfeld and Nicholson, 1970.

People see all kinds of things in this image. Alligators, fish, trees, ant hills, boats, faces, dogs, even a lady dancing in the upper left-hand corner. So what do you see?

Eventually, most people see a dog, a Dalmatian, in the center of the image, leaning away from the viewer and eating something on the ground. Can you see it?

Now notice what just happened. What did your mind do? Your eyes saw some black blotches on a white background, and then what? Did you see an object right away or did it take a while? Did you see the Dalmatian or something else? If something else, was it hard to then change your perspective to see the Dalmatian? Were you ever able to see the dog?

Research shows that when we are faced with abstract or ill-defined images, we are driven to make sense of them. We feel we have to. It is as though we are hardwired to impose meaning on the world.

The Impressionist painters knew this and used it to engage the public with their art. Of course, we do this all the time as we walk down the street, processing trillions of bits of data coming in through our senses. It is mostly automatic. But it becomes noticeable and most interesting when we cannot make sense of things. When we cannot see anything in the image or, worse yet, when most other people see a Dalmatian but no matter how hard we try, we simply cannot. How does that feel?

It usually feels bad. Most of us do not like not being able to see what others see or make sense of something new. We do not like it when things do not come together and fit together nicely for us. That is why most popular movies have Hollywood endings. The public prefers a tidy finale. And we especially do not like it when things are contradictory, because then it is much harder to reconcile them (this is particularly true for Westerners).³ This sense of confusion triggers in us a feeling of noxious anxiety. It generates tension. So we feel compelled to reduce it, solve it, complete it, reconcile it, make it make sense. And when we do solve these puzzles, there’s relief. It feels good. We really like it when things come together.

What I am describing is a very basic human psychological process, captured by the second Gestalt principle. It is what we call the press for coherence. It has been called many different things in psychology: consonance, need for closure, congruity, harmony, need for meaning, the consistency principle. At its core it is the drive to reduce the tension, disorientation, and dissonance that come from complexity, incoherence, and contradiction.

In the 1930s, Bluma Zeigarnik, a student of Lewin’s in Berlin, designed a famous study to test the impact of this idea of tension and coherence. Lewin had noticed that waiters in his local café seemed to have better recollections of unpaid orders than of those already settled. A lab study was run to examine this phenomenon, and it showed that people tend to remember uncompleted tasks, like half-finished math or word problems, better than completed tasks. This is because the unfinished task triggers a feeling of tension, which gets associated with the task and keeps it lingering in our minds. The completed problems are, well, complete, so we forget them and move on. They later called this the Zeigarnik effect, and it has influenced the study of many things, from advertising campaigns to coping with the suicide of loved ones to dysphoric rumination over past conflicts.

In the United States, Lewin went on to integrate these two basic Gestalt principles of complex force fields and the press for coherence into his field-theoretical approach to the study of human motivation and social conflict. He also borrowed a lot from physics, but was clear that he saw physical systems and psychological or social systems as very different, although he believed that the underlying logic of dynamics might be very similar across different areas of science.

Lewin’s approach to understanding social conflict had five main components.

1. Start with the total situation, then essentialize. Although Lewin found it critical to identify the essence of things, he believed we needed to start with an understanding of the whole, of the many forces operating in a situation, before we focused in on the core. He defined conflict in holistic field theoretical terms as “a situation in which oppositely directed forces of about equal strength play upon a person simultaneously.”⁴

2. Understand the constellation of forces operating now. Lewin believed that the current situation was what mattered most; the past was only important in how it affected people in the present.

3. Do not emphasize things; focus on the relations between things. Psychology in Lewin’s time was focused on things like sensations, instincts, and habits (the classificatory approach) and tended to discount the relations between things (the constructive approach). Lewin flipped this and said it was the relations between things—the social bonds between people, competing goals in groups, communication links—that really mattered. In fact, he came to define the essence of groups as how the members see their goals linked together: are they with, against, or unconnected from one another? This inspired his student Morton Deutsch to define the essence of constructive versus destructive conflict as cooperative versus competitive goal linkages between people and between groups.

4. Remember that people and groups are alive. Unlike the more static views of psychology at the time, Lewin saw humans and groups as living, evolving systems that seek some type of balance with their environment. This view of humans as living systems was a hard sell in psychology, but it has risen in prominence over the last two decades.

5. Do your math homework. Finally, Lewin believed that for psychology to ever really grow up and mature into a rigorous scientific discipline, it would have to come to understand human behavior through the use of formal mathematical models. Note that this requires careful specification of the essence of phenomena, but only after they are understood in their broader context. Unfortunately, mathematics and computers were not sufficiently advanced during Lewin’s time. But that, too, has changed.

Tragically, Lewin died quite young, at age fifty-seven. And although he inspired many and blazed a trail for the study of conflict, he left much unfinished business.

THE BIG IDEA

Nevertheless, Lewin and his Gestalt colleagues brought to light a major idea central to our work on impossible conflicts; namely the relationship among complexity, contradiction, and coherence.

It is critical to recognize that we live in an increasingly complex world—biologically, socially, politically, technologically, you name it—that holds many inherent contradictions. In the middle of this complex world are we humans, who have a natural tendency to seek coherence in what we see, feel, think, and do.

When we experience conflict, this tendency intensifies. Conflict is essentially a contradiction, an incompatibility, oppositely directed forces, and a difference that triggers tension. When we encounter conflict, within the field of forces that constitute it, the natural human tendency is to reduce that tension by seeking coherence through simplification. Research shows that this tendency toward simplification becomes even more intensified when we are under stress, threat, time constraints, fatigue, and various other conditions all absolutely typical of conflict.

So what is the big idea? It is not that coherence is bad and complexity is good. Coherence seeking is simply a necessary and functional process that helps us interpret and respond to our world efficiently and (hopefully) effectively. And complexity in extremes is a nightmare—think of Mogadishu, Somalia, in the 1990s or the financial crisis of 2009 or Times Square during rush hour on a Friday afternoon.

On the other hand, too much coherence can be just as pathological: for example, the collapse of the nuances and contradictions inherent in any conflict situation into simple “us versus them” terms, or a deep commitment to a rigid understanding of conflicts based on past sentiments and obsolete information. Either extreme—overwhelming complexity or oversimplified coherence—is problematic. But in difficult, long-term conflicts, the tide pulls fiercely toward simplification of complex realities. This is what we must contend with.

And if you look around, you see that this basic idea of complexity and coherence is all over the research on well-being: in brain science, physical and mental health, innovation, learning, psychology, and conflict. Here are some examples.

Physical health. In an article published in Science in 1989, researchers summarized a series of research results, stating that “chaos [a highly complex pattern] may provide a healthy flexibility to the heart, brain, and other parts of the body. Conversely, many ailments may be associated with a loss of chaotic flexibility.”⁵ For instance, a healthy heart rate tends to show a highly complex, variable pattern but collapses into a much simpler pattern days and hours before a cardiac arrest.⁶ Similar patterns have been found for healthy versus pathological EEGs of brain behavior associated with seizures.⁷ Health scientists conclude that “individuals with a wide-range of different illnesses are often characterized by periodic and predictable (ordered) dynamics, even though these disease processes themselves are referred to as disorders.”⁸

Psychological well-being. A review of the Diagnostic and Statistical Manual of Mental Disorders shows that most psychopathologies are associated with either too much rigidity in psychosocial functioning or too much complexity, or wide swings between both. Psychologists suggest that psychosocial movement toward complexity that accomplishes some balance of both structure and chaos in mental health is the most stable and adaptive.⁹

Integrative complexity. This refers to the level of complexity of the cognitive rules people use to process and analyze incoming information. Research spanning decades shows that people who have higher levels of integrative complexity tend to be more conciliatory in conflict and also that as conflicts escalate, peoples’ level of cognitive complexity diminishes.¹⁰

Political thinking. Differences in the cognitive structures associated with how people think about political issues have been labeled political thinking. Higher-level, more systematic political thinking is associated with a tendency for cooperation and compromise in political conflict. Lower-level, linear political thinking is associated with a simple, dualistic view of conflict situations and with a more competitive and destructive orientation.¹¹

Need for closure. This is defined as the degree to which people feel a need for closure in life, for order and structure. Research demonstrates that those with a high need for closure tend to escalate conflict more rapidly and dramatically, after reaching a threshold.¹² The need for closure is also tied to black-and-white thinking (you’re either with me or against me, for instance) and can be found in those uncomfortable with enduring ambiguity.¹³

Emotional complexity. People whose emotional experiences have been broad and well differentiated can be distinguished from those whose emotional experiences have been more narrow and homogeneous. This quality is called emotional complexity. People with greater emotional complexity tend to be more open to experience, empathetic, cognitively complex, and have a better ability to adapt to different interpersonal situations.¹⁴ Research on moral conflicts has also found a strong association between high emotional complexity and constructive conflict processes.¹⁵

Behavioral complexity and flexibility. This refers to the ability to engage in a wide array of roles and behaviors to effectively meet multiple and competing needs of groups and organizations. Leaders who display higher levels of behavioral complexity tend to be more effective and successful in achieving their goals.¹⁶ Research on social conflict has also found behavioral complexity to be associated with more constructive and innovated processes.¹⁷

Social identity complexity. This describes the degree to which people see themselves as members of different groups that are aligned and coherent versus groups that are contradictory and do not overlap. A liberal, pro-choice, pro–gay rights, antiwar individual would therefore have much lower social identity complexity (more coherence) than a gay, Republican, antiwar NRA supporter (higher internal contradiction). Research shows that people with higher social identity complexity are more tolerant of out-groups and more open in general. ¹⁸

Out-group perception. This concerns differences in the tendency to view members of out-groups in individualized, complex, and multifaceted ways, as opposed to essentializing out-group members in corresponding stereotypical terms. Research shows that perceptions of out-groups in single-categorical versus multiple-categorical terms have significant implications for understanding and attenuating intergroup discrimination and conflict. ¹⁹

Person-situation fit. There is considerable evidence to support the idea that people prefer situations that fit with their dominant personality characteristics. Extraverts tend to like busy environments, whereas introverts prefer less stimulating places. When a person gets stuck in an antithetical environment for a long period of time (like a prison or university), his or her personality will tend to change over time to better fit the situation. ²⁰

Relational balance. Research also shows that people prefer their relationships with others to be aligned and balanced. In other words, we prefer that all our friends be friendly with each other and that they dislike our enemies. Any imbalances between our friends and enemies results in the motivation to change friends to enemies or enemies to friends.²¹

Creativity and innovation. Classic research in social psychology demonstrates the strong press for uniformity operating in most groups, particularly those that are cohesive, public, or under threat from other groups.²² However, recent research on strategy groups in business shows those who are less constrained and have more emotionally, cognitively, and behaviorally complex processes among their members are more effective and innovative at work.²³

Social network complexity. People with more diversified, complex social networks have been found to be more tolerant of out-groups and more supportive of policies helpful to them. They tend to have more positive out-group experiences, share more interests with people outside their own groups, and learn more about the contributions of out-group members and the problems they face.²⁴

Cultural rule complexity. Research also shows that when cultural groups either have or are given very simple rules for negotiating with others (“When others deceive you, never trust them again”), they tend to have more contentious negotiations and come away less satisfied. But when groups have or are given more complex, nuanced rules for conflict negotiations (“When others deceive you, never trust them unless they were forced to deceive you or were unaware of their actions or generally meant well”), their negotiations tend to go far more successfully.²⁵

Culture and contradiction. Cross-cultural research shows that cultural groups differ in the degree to which they avoid or prefer contradiction. Cultures based on Confucianist philosophy prefer contradiction. This results in a dialogic or compromise approach to conflict resolution that retains basic elements of the opposing interests and perspectives in a conflict. Cultural groups derived from a lay version of Aristotelian logic are less comfortable with contradiction. They tend toward a differentiation model of conflict resolution that polarizes contradictory perspectives in an effort to determine which position is correct.²⁶

Cultural tightness or looseness. Other cross-cultural research finds that cultural groups differ in the relative tightness or looseness of their culture. This is the degree to which groups have constraining social norms actively enforced by their members versus more open, flexible norms that are not readily enforced.²⁷ Tighter cultures have been found to have more consensus and agreement on the meaning of common concepts than looser cultures. For example, cultures that display a tight culture of honor—a concern for the public image of status and toughness—encourage much harsher reactions to provocations than those with looser cultures of honor.²⁸ The specific implications of this for conflict and peace are currently being explored.

Structural and institutional complexity. Anthropological research demonstrates that societies differ in the degree to which they are structured in isolated versus integrated ways. Some societies are organized in nested groups (low complexity), where members of distinct ethnic groups tend to work, play, study, and socialize with members of their own group; they have little collaborative contact with members of other groups. Other societies are organized through crosscutting structures (high complexity), including ethnically integrated business associations, trade unions, professional groups, political parties, and sports clubs. This has been identified as one of the most effective ways of making intergroup conflict manageable and nonviolent.²⁹

Linked conflicts. At the broadest level, research on international conflict shows that when conflicts between state rivals become linked with other conflicts between other nations or groups, the potential for serious conflict and escalation increases significantly. In other words, when multiple bilateral conflicts link together into one interrelated problem, they become exponentially more intractable. In fact, the vast majority of intractable conflicts between nations involved connections with at least one other enduring rivalry. ³⁰

THIS IS A BIG IDEA. And it seems that all of this is essentially the same idea. Whether it is how people tend to think, feel, or behave; how they view their own group identities or members of out-groups; how they approach their relationships and group processes; or how their cultural groups and societies are structured and organized, the degree of complexity and coherence matters. Of course, there are meaningful differences in the various models outlined above, but basically they are all about complexity, contradiction, and coherence.

So although psychology, unlike physics, doesn’t yet offer us any laws of human behavior, it does offer us a few big ideas, and this is one. Which leads us to a rule of thumb for 5 percent conflicts:

THE CRUDE LAW OF COMPLEXITY, COHERENCE, AND CONFLICT (C³) Human beings are driven toward consistency and coherence in their perception, thinking, feeling, behavior, and social relationships. This is natural and functional. Conflict intensifies this drive, which can become dysfunctional during prolonged conflicts. However, developing more complex patterns of thinking, feeling, acting, and social organizing can mitigate this, resulting in more constructive responses to conflict.

Family Ties

Dominic, age fifteen, and his stepfather, Charlie, age forty-eight, lived together in a small duplex apartment in the Midwest with the boy’s mother and two siblings. Dominic had been raised by his biological parents in a middle-class area of a major city, but after their divorce he was moved by his mother to a small, working-class town where she met the boy’s stepfather. Charlie had been raised on a farm in a small rural town and now worked in a factory.

When this new family first came together, they were very happy. New to the town, Dominic and his younger siblings were thrilled to have a man around to show them the area, fix things up around the home, and in particular help Dominic navigate the perils of being the new kid in a tough working-class neighborhood. Charlie really enjoyed having these young children around because he had become estranged from his now grown-up children from his first marriage.

Shortly after Charlie’s marriage to the boy’s mother, however, the relationship between him and Dominic began to sour. Initially, the arguments were over chores around the house, habits, and household rules. Gradually, they escalated into more serious territorial and power conflicts, with screaming, name-calling, threats, destruction of property, and physical violence. In time, the relations between the two escalated to the point where virtually every interaction they had resulted in hostilities. They began avoiding each other and went for weeks without speaking. The entire family was affected by these relations. Dominic’s siblings, other relatives, friends, and neighbors attempted to intervene. They took sides and then eventually lessened contact with the family. The boy’s mother was consistently put in the middle and told to decide between them. This continued for approximately two years.

Eventually, the family was referred to community mediation by the police. Events had escalated to the degree where severe violence was imminent. The police had been called in on several occasions, and both the boy and stepfather were demanding that the mother decide “who should stay and who should go.” The mother, having suffered a painful divorce from her first husband, was determined to keep her family together.

LIVING IN A NEW TOWN with a new family, Dominic and his siblings were very happy to meet someone who could bring some stability to their lives. Charlie’s guidance and support, even his strict sense of discipline, were a welcome shelter during this disorienting transition. But in time, and particularly when in conflict, Charlie’s rigidity and Dominic’s adolescent rebellion were an explosive cocktail. The dynamics that ensued from their increasingly hostile encounters became more and more widespread in terms of the problems and people they involved. They also became more and more simple. “He” was the problem.

To sum up, coherence is natural and necessary. It can provide people and groups with a sense of stability, predictability, and a platform for decisive action. It simply makes life easier for us to navigate. But when taken to extremes, this natural tendency has its associated pathologies. This is especially true in conflict, where the press for coherence intensifies, and much more so in intractable conflicts, where we see the virtual collapse of contradiction and complexity. Left unchecked, this super coherence can lead to the escalation and spread of conflict, as well as to the development of strong, destructive, ingrained patterns of thinking, feeling, and behaving—in other words, to impossible conflicts.

THE MATHEMATICS OF COMPLEXITY, COHERENCE, AND CONFLICT

Understanding how the psychological dynamics of complexity and coherence lie at the core of intractability in conflicts was a critical step toward grasping how they operate and, ultimately, how they might be resolved. Following Lewin’s guidance, the next step was to move toward a more careful specification of the essence of this phenomenon by working with more formal mathematical concepts and models. Constructing such models requires that you carefully examine your basic assumptions about how complexity and coherence operate in social relations experiencing conflict, which is not a trivial matter. However, if you can identify the critical variables and the nature of how they affect one another over time, these models can provide deep insights into difficult conflict dynamics.

A branch of applied mathematics called complexity science provides us with the basic platform and tools to understand how complex systems can evolve into more simple, coherent structures. Although rooted in mathematics, complexity science is a highly interdisciplinary field that seeks the answers to some fundamental questions about living, adaptation, and change. It teaches us that complex systems have three important characteristics: emergence, unintended consequences, and self-organization.

• Emergence. Emergence is the way complex patterns and coherent structures arise from a series of very simple interactions. The spatial patterns of beehives are not at all predictable from knowledge of each individual bee. The dynamical patterns of market bubbles and crashes are not at all predictable from knowledge of each individual investor. As Wertheimer noticed, the whole is quite different from the sum of its parts.

• Unintended consequences. These are simply surprises, good and bad, that result from how our actions operate in complex systems. We try to reduce the cost of gasoline, and thereby the cost of living, by substituting corn ethanol for gasoline. But all this does is raise the price of food, which depends so heavily on corn products. As Wallace White said, “When you pick up one piece of this planet, you find that, one way or another, it’s attached to everything else—if you jiggle over here, something is going to wiggle over there.”

• Self-organization. The self-directed actions of individuals alone can lead to organization of a whole group of people. According to Richard Feynman, the actions of a single despotic leader are not needed to organize a curved line of humans, all brushing their teeth once a day just after sunrise, that circles the globe.

Mathematics has helped us understand how emergence, unintended consequences, and self-organization arise from the interaction of individual elements. Mathematics gives us a way to compute how low-level individual actions, like simple rules for behavior, lead to higher-level global properties, like the V-formation of flocks of birds, synchronized patterns in schools of fish, or common adolescent dating rituals.

It’s a great game. You make up any rules you want for the players, and the mathematics then describes for you the plays, strategies, and who wins. There are lots of different possible rules and lots of different mathematical methods that can be used to compute their consequences. Thus, there are many different mathematical flowers in the garden of complexity—self-organized critical systems, small-world networks, artificial neural networks, differential equations—each with its own shape, color, and fragrance. Used as a metaphor, each of these mathematical approaches gives us its own unique insight into conflicts. In work on enduring conflicts, conflict specialists rely mostly on insights provided by the mathematical method called ordinary differential equations, or ODEs.

Ordinary differential equations predict how the values of variables in a model change over time. Usually, there are only a few different things being measured in any one model; for instance, conflict intensity, relative power, cooperation, or emotion. Yet ODEs can have fascinating properties. Sometimes, the deterministic rules you put into the equations produce values that vary as if they were random. This is called chaos. Even stranger, although you know all the rules, you typically cannot predict all the future values. Sometimes, you change one thing just a little, and then all the current and future values change quite a lot. This is called a bifurcation. This type of equation has been useful in understanding turbulence and the motion of air in the atmosphere, the rattling of mechanical gears, dripping faucets, and teams of people working together in an organization.

One way to think about ODEs is of them representing the journey of variables across an artificial landscape. The variables are simply the things we can measure about a conflict; for example, the different types of emotions of the people involved or their intensity. We can watch the trail of these variables as they move through the valleys, hills, and mountain passes of the landscape.

Just like a real landscape, it is a lot easier to walk downhill than uphill. So we watch the trail most often settle into the depths of the nearest valley. These valleys are called attractors because they are what the conflict settles into. The peaks are called repellers because the conflict never stays there; it rapidly falls downhill into someplace else. The mountain passes are called saddles. Like the saddle on a horse, it’s easy to go downhill along the direction that curves off the side of the horse and hard to go uphill along the direction toward the horse’s head or tail. In a conflict, emotions can drive a situation into a positive or negative attraction.

A Conflict Landscape

ATTRACTORS

The ideas from mathematics are being used here as a metaphor, as an illustration of the way social science uses concepts as ways of thinking, categorizing, and recognizing phenomena. The deep valleys in the landscape are the attractors, the somewhat stable patterns or tendencies in systems that draw us in and that resist change. For instance, when we go to a funeral in the Western world there is a strong tendency to wear dark colors, sit quietly and respectfully, and look sad. Even if we did not know the deceased, we tend to do this. We are pulled into it. Alternatively, when we are at a football game, even if we are not big fans of the team, we are likely to begin to jump around a little and cheer and talk trash with the opponent’s fans. It is hard not to.

The behavior patterns that attractors pull us toward are influenced by many, many different things, from the smell of a funereal bouquet to the sound of a marching band. But it is not any one thing that creates an attractor. It is how the many pieces come together that matters. It is how they fit together or not. It is their degree of coherence.

Weaker attractors will have many pieces moving against or away from each other; many mixed signals and low coherence. This results in less clarity about what the situation requires of us and less of a pull toward conformity. In other words, this looks more like a flat landscape where movement in any direction is equally possible. With stronger attractors the pieces all come together. They fit into a coherent picture that draws us all into fairly uniform patterns of thinking, feeling, and behaving. These create deep valleys (attractors) and high peaks (repellers) in the landscape, which make it much more likely that we will journey into the valley of the attractor and be forced to act in ways consistent with it.

Research reveals that conflict can take place within a variety of attractor landscapes. They tend to have current attractors (how people are responding to a conflict right now) and latent attractors (hidden tendencies to think, feel, and act in very different ways in the conflict). They can have positive attractors, drawing people into more constructive and satisfying conflict interactions, and negative attractors, encouraging the opposite. These may be weak attractors (faint impulses to respond in a certain way) or strong attractors (extraordinary determinants of our experiences of and reactions to conflicts). Together, the current and latent, the positive and negative, the weak and strong attractors make up what we call landscapes for conflict.

The Kashmiri Landscape

A largely frozen and uninhabitable mountainous region that lies at the border between India and Pakistan, Kashmir has sparked three wars between those two countries since 1947. An average of twenty-five hundred violent incidents occur there every year. Official Indian estimates have seventy thousand people killed in fighting in Kashmir since 1989. Some claim the number is twice that. Two hundred thousand people have fled the valley. Half a million Indian security forces occupy the area, which today is the most highly militarized zone in the world. This is Kashmir.

Largely Hindu India and predominantly Muslim Pakistan became independent of the British Empire in 1947 and quickly went to war over Kashmir, a Himalayan territory that had been a princely state with a Hindu maharajah and mostly Muslim populace. The war ended with India controlling two-thirds and Pakistan one-third of the state. In 1989, Kashmiri independence rebels began a separatist struggle against India and were soon joined by Pakistani militants. India reacted by flooding Kashmir with soldiers and paramilitary troops. Conventional and guerrilla war ensued. In recent years, the conflict has attracted a growing number of Islamic fundamentalists who define the conflict as a jihad, or holy war.

In 2001, Atal Bihari Vajpayee, the prime minister of India, ended India’s six-month cease-fire in Kashmir, calling it a sham. The next day, Mr. Vajpayee officially invited Pakistan’s military ruler, General Pervez Musharraf, to India for peace talks. On a violent day in Kashmir, when fourteen people were killed, Mr. Vajpayee’s letter read: “Our common enemy is poverty. For the welfare of our peoples, there is no other recourse but a pursuit of the path of reconciliation.”³¹ In response, Pakistan’s foreign minister accused India of “state terrorism,” “repression,” and the massacre of seventy-five thousand Kashmiris, while announcing that his nation would accept India’s invitation for talks “in a positive spirit.”³²

Today, there is an ongoing ethnopolitical struggle between India, Pakistan, and Kashmiri independence rebels over Kashmir. It is a story that combines the increasingly common elements of terrorism, religious militancy, human rights abuses, movements for local independence, and nuclear threat.

Politicians on both sides have used Kashmir as a rallying point for so long that compromise is viewed as political suicide. Even the most liberal, optimistic Indians and Pakistanis tend to turn conservative and belligerent when discussing Kashmir. It is as if it is impossible not to. The potential use of nuclear weapons by both sides is a persistent reality.

And still, every evening at sunset, an extraordinary spectacle occurs. Pakistani and Indian troops, stationed a stone’s throw across from one another at a checkpoint, meet. Dressed in full military regalia, these armed units march ceremoniously in formation directly toward one another to within a few feet, swing and slam closed their respective border gates in unison, then turn their backs abruptly to one another and march away. This too is Kashmir.

IN KASHMIR, the landscape is both treacherous and hopeful. The misery, volatility, and danger of the situation there are painfully obvious. The destructive attractor reigns. But there are also hints of other possibilities. Slight glimpses of what might one day be. The mixed messages of the leaders. The peculiar, almost intimate rituals of the soldiers. The desire for peace of the people. They point to another way of being that is perhaps latent in Kashmir, and in India and Pakistan, waiting for its moment.

THE ATTRACTION OF THE 5 PERCENT PROBLEM

What is important to understand now is that the 5 percent problem represents a special kind of attractor landscape for conflict. Picture being trapped on the icy face of K2, the second-highest mountain on earth.^d In addition to the treacherous terrain of the mountain slope, you find yourself plagued by mounting physical ailments and exhaustion, as well as impaired decision making, hallucinations, and a rising sense of hopelessness. These are perilous conflict landscapes, with very strong, coherent current attractors for destructive interactions pulling you down, and relatively weaker latent attractors for other, more constructive types of interactions just over the next ridge. This means that even a random thought we may have about the “other,” not to mention an actual encounter with them, will tend to pull us down into the negative responses of the destructive attractor valley—no matter what the other person does and whether or not we really want to act that way. It is so much easier and makes much more sense to go down the slope!

The power of this negative attraction is bolstered by many different things—memories, social norms, beliefs about the “other,” strong feelings, the other’s current behaviors—but our experience of it is simple. They are bad and we are good. At this point, our sense of our options in this situation is extremely limited. And the ways we do respond will tend to build an even stronger attractor for destructive conflict between us and them. It all works very well together.