The Big Idea

The pattern behind 'random' terrorist attacks

By Kate Julian
Sunday, July 25, 2010

Terrorism's power curve

Random acts of violence are, well, random. It's the unpredictable nature of terrorism, after all, that makes it so terrifying.

But according to "The Mathematics of Terror," an article by Andrew Curry in the latest issue of Discover magazine, acts of terrorism aren't random at all -- not mathematically speaking, anyway. Curry pulls together work by a number of physicists, mathematicians and economists who, in recent years, have analyzed terror attacks the way they analyze more mundane phenomena: by plotting them on a graph.

If deaths due to terrorism were random, Curry explains, they would form a normal distribution, also known as a bell curve, with most casualties coming from medium-size attacks falling in the center of the curve, and a few rare deaths from small and large attacks forming outliers at either end.

Instead, terrorist and guerrilla killings follow an L-shaped power law curve. The smaller the event governed by the curve, the more likely it is to occur -- and the larger it is, the less likely. Any number of natural and man-made phenomena follow power law curves, from earthquakes and hurricanes to income distribution worldwide.

A team led by University of Miami physicist Neil Johnson and University of London economist Mike Spagat found that, in the case of actions by the Revolutionary Armed Forces of Colombia (FARC), an attack causing 10 deaths was 316 times as likely as one killing 100.

Johnson, Spagat and physicist Sean Gourley repeated the exercise with other guerrilla attacks, insurgencies and terrorist movements. The same pattern recurred, from Peru's Shining Path to the Palestinian intifada, from Taliban insurgents in Afghanistan to rebels in East Timor.

"The pattern underlying the power curve enables a few rare events of extraordinary magnitude," Curry writes. "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."

But if the goal of terrorists is to strike by surprise, to cultivate the appearance of randomness, why would there be a terror curve at all?

Johnson and Spagat point out that if attacks in Iraq, Colombia, Peru and Afghanistan were random, then extremely peaceful and extremely violent days should both be rare. The data, however, show sudden bursts of activity and long quiet periods. Even in the absence of a coordinated command, terrorists operating in a given area seem to operate in sync.

Perhaps this is because such individuals are trying to maximize media coverage. "For an insurgent group," Curry notes, "a successful strike is not one that does the most damage, but one that draws the most attention." Terrorists, therefore, may be waiting for relatively calm moments to strike, in an effort to dominate the news. But the more they all try to break away from the pack, the more they can't escape it.

The effect is not so different from many drivers all trying to avoid the same congested roads-- only to cluster together. "Think of traffic jams that come out of nowhere and disappear just as quickly," Curry writes.

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