In 1948 Lewis Fry Richardson plotted the casualties from various wars and found that they followed a power law — there were lots and lots of little wars and a few cataclysmic World Wars.
Now Neil Johnson and his team have found another such lethal formula:
Dr Johnson’s proposal rests on a pattern he and his team found in data on insurgent attacks against American forces in Afghanistan and Iraq. After the initial attacks in any given province, subsequent fatal incidents become more and more frequent. The intriguing point is that it is possible, using a formula Dr Johnson has derived, to predict the details of this pattern from the interval between the first two attacks.
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 [left]), 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.