Study: Like Earthquakes & Financial Markets, Terrorist Attacks Follow Laws of Math

By Andrew Moseman | December 17, 2009 1:04 pm

iraq220For soldiers and civilians alike, insurgency wars are not only deadly but also frustrating in their apparently random spikes of violence. In a study in Nature, however, researchers put forth a mathematical model that shows terrorist attacks and insurgencies are not so scattershot as they seem.

The team searched for statistical similarities across nine historic and ongoing insurgencies including those of Iraq, Afghanistan and Northern Ireland [BBC News]. That meant compiling more than 50,000 acts of violence. And despite the fact that these events happened in different countries in different times, Neil Johnson and his team found a relationship between the size of an attack in casualty terms and how often it occurs.

By plotting the distribution of the frequency and size of events, the team found that insurgent wars follow an approximate power law, in which the frequency of attacks decreases with increasing attack size to the power of 2.5. That means that for any insurgent war, an attack with 10 casualties is 316 times more likely to occur than one with 100 casualties (316 is 10 to the power of 2.5) [Nature].

Researchers have used power laws to try to find order in natural phenomena, like a size vs. frequency pattern in earthquakes or avalanches. Johnson and his colleagues argue that the pattern arises because insurgent wars lack a coherent command network and operate more as a “soup of groups”, in which cells form and disband when they sense danger, then reform in different sizes and composition [Nature]. Also, he says, terrorist groups compete for media attention, which could help drive the pattern.

Other researchers doubt the reliability of the model. For one thing, terror cells battle one another and probably aren’t as free to break up and reform as the study suggests, terrorism modeler Roy Lindelauf says. And the number of insurgents in a fight might not stay close to constant, as the model presumes. But the math could have real-world practicality, team member Michael Spagat argues. “We could never say with certainty that there were going to be 10 attacks on one day, for example,” [BBC News] he says, but the model could predict whether a given day carried a lighter or heavier probability for a deadly attack.

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Image: flickr / :.phoenix.:

MORE ABOUT: math, war
  • Brian Too

    Intriguing concept; worth pursuing.

    This wouldn’t likely be very useful to troops on the ground. Can you imagine a “terror forecast” based upon this stuff? ‘Scattered harassment attacks with intermittent IEDs’. It’s too vague with no corrective action suggested.

    This might be useful to higher-ups in the military chain of command. For troop deployments, strength assessments, and the like. However even then, I suspect that commanders really deploy based upon the resources they can get, rather than what some mathematical model says they might need. You defeat the enemy when and how you can, not when an idealized model says might be the best time. Still, at the right time and place, this information might have some value.

    The real problem is that you have a human enemy. Every time you develop a strategy and start achieving some success, they counter that with tactics and strategy of their own. This method too may be vulnerable to changes in approach by the terrorists.

    But you never know until you try. And there is value in the meta-strategy of out-innovating the enemy.

  • YOOO

    Another prime example of academics overthinking a simple situation and attempting to apply nonsensensical explanations to the obvious.

    All they “discovered” is that major attacks occur far less frequently than minor ones. Everybody with a lick of common sense already knows this.

    The fact that they needed to research this is absurd. The fact that they came up with NO usable recommendations based on this “discovery” is to be expected.

    This is typical of acadamia but it is shameful that Discover feels this is worth publishing simply because it deals with the attention grabbing topic of terrorism.

  • no, yoo

    yeah, what (s)he said.

  • Happy Phil

    How about this formula?
    Most terrorist acts are retaliation for real or perceived wrongdoing by those they attack. We would be much better served by addressing and correcting the injustices, rather than attempting to shoot our way to a solution.

  • Paul

    Well, since they are often retaliation for *perceived* wrongdoings, correcting *perceived* but potentially non-existent injustices is not really a great answer, wouldn’t ya say? Sometimes a terrorist really is just a terrorist, and the best cure is an injection of hot lead to any one of many vital organs.


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