Math as a Tool to Study Peace: With Equations 'You Can't Fudge'
Did a 19-year-old Serb nationalist named Gavrilo Pricip really detonate the world-shattering conflagration that killed some 80 million people when he assassinated Archduke Franz Ferdinand of Austria-Hungary in June 1914? Some historians and CNN have called him the man who started World War I.
Were the forces that led to the Crimean War set in motion by a squabble over the keys to the front gate of the Church of the Nativity in Bethlehem? Historian Trevor -Roper has argued they were. And in his book The Landscape of History, military historian John Lewis Gaddis says that dispute and its consequences exemplify sensitive dependence on initial conditions. Also known as the “butterfly effect,” this sensitive dependence means that in nonlinear systems, such as international relations, small details of initial conditions can be amplified tremendously and unpredictably.
What makes some conflicts bloody and intractable while others can be resolved? Larry Liebovitch and Peter Coleman belong to a team of leading edge scholars and researchers who are trying to understand peace and conflict by applying principles of complexity science. War and violence have been studied more than peace, and Dr. Liebovitch and Dr. Coleman are among the authors of a research paper focusing on the challenge of identifying variables and interactions that would be needed for sustainable world peace.
Dr. Peter T. Coleman is a professor of psychology and education, a certified mediator, and a scholar who has researched the dynamics of conflict and sustainable peace. He is the director of the Morton Deutsch International Center for Cooperation and Conflict Resolution at Teachers College, Columbia University and Executive Director of Columbia University’s Advanced Consortium on Cooperation, Conflict, and Complexity (AC4).
Dr. Larry S. Liebovitch is an astrophysicist, mathematician and multi-disciplinary scholar who has created mathematical models to explore phenomena large and small—on scales that range from the molecular interactions to the dynamics of international politics. He has studied cooperation and competition in small world networks and the dynamics of two people in conflict trying to reach consensus, in marriage, in therapy, and in randomly assigned pairs.
As Dr. Liebovitch explains, math can provide new ideas to approach conflict. For example, he says, looking at conflict in terms of attractors, you find that people keep trying to do different things but wind up in the same place. Math can also suggest new ideas and paradigms for looking at sudden changes in systems, and the elements that preceded the changes.
In a Columbia radio discussion, Dr. Coleman provided an example of roommates who live together for a while, seem to get along, then suddenly separate in anger. He said research suggests the split may not have been caused by a bad event, but because of something one or both roommates had from the beginning that later emerged as very important. As Dr. Liebovitch puts it, conflict involves people, their past, the way they have interacted before, the environment, the culture, space, time, emotions and rationality. “So this system has many moving pieces. How do we need to think of a system like that, and what are its properties?” he reflects. “What I do is make rigorous mathematical models of how people behave and translate assumptions of how people interact into equations, and then use math to see the consequences.”
Sometimes, he says, the math will show things in the system that were previously imperceptible, and sometimes a metaphor from math can suggest a more precise equation. Not all human behaviors can be quantified, he explained in an interview with Plexus, but it is possible to gain insights from mathematical examination of slices of behaviors—specific actions or feelings and results of those actions or feelings.
“Making anything quantitative forces you to be really clear about what you are stating,” Dr. Liebovitch said. “If you want to operationalize a dyad and examine if one person feels one way, how will the other person feel, and make it quantitative, you have to decide what’s a reasonable function. If you’re writing an equation, you can’t fudge. You can’t write words you don’t understand or effects you’re just intuiting.” Dr. Liebovitch and scientists in many fields say understanding the simplest and most basic dynamics is useful in understanding what happens in pairs, small groups, and networks of people.