When will the next terrorist strike? It may not be as unpredictable as you think.

Whether building a boat or developing experimental surgery techniques — people working in groups on a complex challenge get better with practice. And that learning tends to follow a predictable mathematical pattern of improvement called a power-law progress curve.

Now new research shows that — grimly — this is also true of terrorists.

In a recent edition of the journal Science, Brian Tivnan, a researcher affiliated with the University of Vermont, working with Neil Johnson of the University of Miami in Florida, and colleagues, presents data showing that seemingly random violence perpetrated by insurgents and terrorists against military operations actually follows a pattern.

Their finding may prove useful to military leaders in understanding and predicting how and when terrorists might next strike—and, therefore, let planners do a better job of allocating resources and protecting soldiers.

Their study, “Patterns in Escalations in Insurgent and Terrorist Activity,” relied on a decade-long record of publically available data about combat fatalities in both Afghanistan and Iraq. Sifting through these records on a piece of open-access software, the team found that the interval between the first fatality in a particular region or combat zone and the second provided an interval that would be strongly predictive of the accelerating pace of future attacks.

On the curve

For example, if the second attack were 100 days after the first, the third attack would be likely about two months later, the fourth about seven weeks, the fifth less than that — all fitting nicely on the graph of a power curve.

To test this idea, the researchers took the equation they had developed and applied it to information about deadly attacks by terrorists around the world, suicide bombings by militants in Lebanon and Pakistan, and IED attacks on soldiers in both Iraq and Afghanistan.

They all fit the curve. In other words, the increasing rate of actual killings by the terrorists — regardless of location, and, obviously, without the terrorists communicating with each other — fit the mathematical model.

“That pattern is very robust both within a country, say in differing regions of Afghanistan, as well as using the same equation, with different parameters, to look at the pattern of attack behavior in Iraq or other places,” says Tivnan, “ it can let planners forecast out when the next effective attack would happen.”

And, therefore, address practical questions like, “how many boots on ground are likely to be needed, where, when?” Tivnan and Johnson ask.

“This work may help to answer that difficult question," says Tivnan, a graduate of UVM’s engineering program and former Marine — who now serves as the chief engineer in Modeling & Simulation for the MITRE Corporation, a nonprofit organization that works on many federally funded research projects, including for the U.S. Department of Defense. He researches and teaches at UVM in a cooperative venture with UVM’s Complex Systems Center.

Not surprisingly, the technique described in his new paper does not pinpoint a day and street corner for the next suicide bombing. “If I’m in the Helmand Province of Afghanistan and I want to know the calendar date when the eleventh fatal event may occur — that might not be possible,” Tivnan says. “There may be noise in my forecast.”

“But if you ask, ‘Can we characterize the arrival time of fatal events two through fifty and what trajectory they will follow?’” he says. “Our method will show that very, very clearly."

Degrees of freedom

How can this be? Does this study suggest that free will and learning are illusions? “Not at all,” says Tivnan. In fact, their findings demonstrates the power of learning.

The team has generalized an idea from evolutionary biology called the Red Queen hypothesis. Named after the strange race in Alice in Wonderland — where Alice and the Red Queen find themselves in the same place they began, and the queen says, "It takes all the running you can do, to keep in the same place,” — the hypothesis explains how predators and prey, and parasites and their hosts, are continuously adapting to each other’s more effective competitive behaviors.

“There’s no surrender of free will,” Tivnan says, “but the predictable pattern is explained by that fact that these two forces — the Red Queen (for the terrorists) and Blue King (for the counterterrorists) — are coupled in this competitive game, dynamically adapting to each other.”

And these two competing sides are “imposing so many external constraints on their opponent that their opportunity for freedom of choice — their options, their alternatives — are very limited,” says Tivnan.

Since the pattern of terrorist attacks appears independently in so many places, times, and populations, it’s probably “not explained by sociological, economical, religious or environmental conditions,” the researchers suggest. Indeed the researchers aren’t accounting for any specific development by either side, say a new weapon on one side followed by more sophisticated armor on the other.

Instead, they are noting a complex pattern that appears when almost any two groups of people are both adapting and counteradapting at the same time — like cyberhackers versus computer security experts or many other forms of group learning between adversaries.

“What we may be describing are the boundary conditions of that constrained environment,” says Tivnan, “not the behaviors themselves happening inside it.”

Still, how can cagey terrorists and their equally determined and clever opponents be so predictable? Consider the average traffic jam, Tivnan suggests.

“A traffic jam is this large-scale, highly predictable, macro event. Intelligent commuters themselves know the traffic jam is coming,” he says. “Yet the same commuter will get stuck in the same traffic jam over and over, not because they couldn’t make another choice, but because of external constraints and limited alternatives — you live here, the kids are in school here, and the grocery store is here.”

Of course, resetting of the rules can happen — as more radical expressions of free will are exercised. A lot of workers start to telecommute instead of drive or the military makes a huge surge in the number of soldiers in an area — but then a new, and equally predictable, pattern begins, Tivnan says.

“Primarily we’re responding to those that couldn’t make sense of the attack patterns that they were seeing or anyone who might speculate and say ‘Well, it’s just random,’” Tivnan says. “We have dispelled that and found structure in the pattern.”