Math – from statistics to game theory – has long been applied to understanding why and how people kill each other in coordinated ways.

Now, Neil Johnson, a statistician at the University of Miami, and others are seeking to show that the “power law” developed in the 1940s to describe the frequency of wars can be extended to attacks by terrorists and insurgents. A new paper currently under review at Science outlines a method for forecasting the evolution of conflicts. The Economist explains:

The formula in question (Tn = T1n-b) is one of a familiar type, known as a progress curve, that describes how productivity improves in a range of human activities from manufacturing to cancer surgery. Tn is the number of days between the nth attack and its successor. (T1 is therefore the number of days between the first and second attacks.) The other element of the equation, b, turns out to be directly related to T1. It is calculated from the relationship between the logarithms of the attack number, n, and the attack interval, Tn. The upshot is that knowing T1 should be enough to predict the future course of a local insurgency. Conversely, changing b would change both T1 and Tn, and thus change that future course.

Though the fit between the data and the prediction is not perfect (an example is illustrated right), the match is close enough that Dr Johnson thinks he is onto something. Progress curves are a consequence of people adapting to circumstances and learning to do things better. And warfare is just as capable of productivity improvements as any other activity.

The twist in warfare is that two antagonistic groups of people are doing the adapting. Borrowing a term used by evolutionary biologists (who, in turn, stole it from Lewis Carroll’s book, “Through the Looking-Glass”), Dr Johnson likens what is going on to the mad dash made by Alice and the Red Queen, after which they find themselves exactly where they started.

In biology, the Red Queen hypothesis is that predators and prey (or, more often, parasites and hosts) are in a constant competition that leads to stasis, as each adaptation by one is countered by an adaptation by the other. In the case Dr Johnson is examining the co-evolution is between the insurgents and the occupiers, each constantly adjusting to each other’s tactics. The data come from 23 different provinces, each of which is, in effect, a separate theatre of war. In each case, the gap between fatal attacks shrinks, more or less according to Dr Johnson’s model. Eventually, an equilibrium is reached, and the intervals become fairly regular.

The equation doesn’t yet help explain how to stop wars, but perhaps it will get more soldiers and insurgents interested in math.

See also this Wired piece on war math, and Sean Gourley’s TED talk on “the mathematics of war”: