Around that time, a Santa Fe Institute computer scientist named Aaron Clauset was applying the same approach to what seemed like a distinctly different problem. Rather than looking at specific guerrilla movements, Clauset was examining total deaths caused by global terrorist attacks since 1968. When he plotted nearly 30,000 incidents on a graph, they formed a curve to the power of –2.38. (The power number is negative because it reflects a decrease rather than an increase in the number of events as death tolls rise.) With its characteristic downward slope, the curve was eerily similar to those generated by Johnson and Spagat for Colombia and Iraq.
To rule out coincidence, Johnson, Spagat, and University of Oxford physicist Sean Gourley gathered data on nine other insurgencies. One after another, the curves clicked into place: Peru’s Shining Path guerrilla movement: a curve with a power of –2.4. The Indonesian campaign against rebels in East Timor from 1996 to 2001: –2.5. The Palestinian second intifada: –2.55. Fighting against Afghanistan’s Taliban from 2001 to 2005: –2.44. By contrast, traditional conflicts in which two armies squared off against each other (such as the Spanish and American civil wars) yielded graphs that looked a lot more like bell curves than power curves. Although the politics, religion, funding, motives, and strategies of the insurgencies varied, the power trends did not.
In an age of biological weapons and dirty nukes, the implications are chilling. Although truly massive power-law events—like the Great Depression or killer storms—are drastically less common than smaller disruptions, they still occur. In the normal distribution of a bell curve, you never get such extremes, but the pattern underlying the power curve enables a few rare events of extraordinary magnitude. One might use the math to argue that the 9/11 attack that killed more than 2,700 people in New York City was bound to happen. And there is ample reason to believe that an even bigger one is on the way, sooner or later.
For Johnson, a Cambridge- and Harvard-educated physicist who has studied stock markets and other apparently unpredictable systems, the power law was familiar territory. Whether in New York, Tokyo, or London, markets tend to follow the same boom-bust cycles, with little daily upticks and downticks punctuated every few decades by a big crash or boom. “Markets move every day, but some days they move a lot,” Johnson says. “There are different people, different stocks, but that just seems to be the way people get together and trade.”
If physics-based models can predict the behavior of stock markets, Johnson reasoned, why couldn’t they foresee the behavior of insurgents so that attacks could be prevented? “Prediction is the holy grail everyone is in pursuit of,” says Brian Tivnan, a modeling expert at a U.S. Department of Defense–funded think tank called the Mitre Corp. Tivnan brought Johnson’s work to the attention of Pentagon officials. “We were very encouraged to see physicists and mathematicians looking at the data from an apolitical, analytic perspective,” he says.
But if they were going to develop a predictive model, Johnson and his team would have to figure out what it was about the behavior of insurgents and terrorists that made their bloody fingerprints so similar all around the world. They started by tossing the traditional take on insurgencies out the window.
Conventional counterinsurgency thinking tries to get into the heads of rebels by understanding their motivations and methods. Political scientists and sociologists studying the conflicts in Iraq and Afghanistan have emphasized tribal affiliations, nationalism, religion, social networks, and other cultural concerns. Using lessons learned (or perhaps mislearned?) in Vietnam, meanwhile, Pentagon planners approached these conflicts as if they were facing smaller armies with worse equipment, hoping that if they could knock out the enemy’s leadership they would decapitate and demoralize the insurgency.
But these assumptions were off. Guerrilla fighters in Vietnam, like U.S. troops, answered to a central command; insurgents in Iraq did not. And from a physics point of view, getting inside an insurgent’s head was irrelevant. “In political science literature, human rationality is primary. They assume groups are rational actors, have access to all the information, and make the right decisions,” Clauset says. “A physicist’s natural approach is to assume people are like particles, and their behavior the result of constraints beyond their control.”
Basing their computer models on programs written to predict all sorts of fluctuating phenomena, from traffic flow to stock prices, Johnson’s team tried to create equations that reflected the behavior of the individual insurgents seen in the data. The equations that came closest “involved a soup of conflict groups of varying strengths, in a constant process of coalescing and dissolving,” Spagat says.
Johnson likens the insurgent groups in his computer model to a pane of glass that shatters into smaller and smaller splinters with each hit. The bigger shards are capable of delivering the deepest, nastiest cuts, but they are also the easiest to target. The smallest slivers of glass, on the other hand, might deliver the casualty equivalent of a pinprick, but there are so many of them, and they are so hard to spot, that the total amount of damage they cause stays high.
If the model is correct, then insurgents conduct “asymmetrical warfare,” battling a larger and better-equipped enemy with a loose network of fighters lacking central command. However obvious this seems today, it was a concept that escaped American military planners when the fighting in Iraq and Afghanistan began nearly a decade ago. “The insurgents kept the most powerful military the world has ever seen at bay for four years,” says John Robb, a former Special Operations pilot and author of Brave New War: The Next Stage of Terrorism and the End of Globalization. “You’re not going to defeat them by killing groups or killing people. You have to change the entire dynamic. It’s a tough lesson for a lot of military folks to absorb.” Indeed, the harder the U.S. forces hit, the more the insurgency shattered into near-invisible shards. By the time Johnson’s paper was published in Nature last year, the military had learned, through bitter experience, the futility of fighting insurgents with traditional tactics. (The military has never published on the issue, but Johnson says that strategists have recently heard about his ideas.)
The splintered, disorganized nature of insurgencies became still clearer when Johnson and his colleagues looked at the timing of attacks. The numbers in Iraq, Colombia, Peru, and Afghanistan followed similar patterns, with “sudden bursts of activity, then quiet periods,” Spagat says. “If it were random, you would have far fewer busy days and far fewer quiet days than are captured in the data.” Without a centralized command to issue orders, there must be something else behind the clustered timing of attacks.