Thursday, 31 March 2011

Economist: Cry havoc! And let slip the maths of war

Warfare seems to obey mathematical rules. Whether soldiers can make use of that fact remains to be seen

The Economist today has an interesting article for those of us with a mathematical bent....
In 1948 Lewis Fry Richardson, a British scientist, published what was probably the first rigorous analysis of the statistics of war. Richardson had spent seven years gathering data on the wars waged in the century or so prior to his study. There were almost 300 of them. The list runs from conflicts that claimed a thousand or so lives to the devastation of the two world wars. But when he plotted his results, he found that these diverse events fell into a regular pattern. It was as if the chaos of war seemed to comply with some hitherto unknown law of nature.

At first glance the pattern seems obvious. Richardson found that wars with low death tolls far outnumber high-fatality conflicts. But that obvious observation conceals a precise mathematical description: the link between the severity and frequency of conflicts follows a smooth curve, known as a power law. One consequence is that extreme events such as the world wars do not appear to be anomalies. They are simply what should be expected to occur occasionally, given the frequency with which conflicts take place.

The results have fascinated mathematicians and military strategists ever since. They have also been replicated many times. But they have not had much impact on the conduct of actual wars. As a result, there is a certain “so what” quality to Richardson’s results. It is one thing to show that a pattern exists, another to do something useful with it.

In a paper currently under review at Science, however, Neil Johnson of the University of Miami in Coral Gables, Florida, and his colleagues hint at what that something useful might be. Dr Johnson’s team is one of several groups who, in previous papers, have shown that Richardson’s power law also applies to attacks by terrorists and insurgents. They and others have broadened Richardson’s scope of inquiry to include the timing of attacks, as well as the severity. This prepared the ground for the new paper, which outlines a method for forecasting the evolution of conflicts.
The article goes on to outline the theoretical basis for this approach and—although the practical application is not yet fully worked out—it nonetheless makes very interesting reading and raises some thought-provoking questions. How does this fit into the Realist / Liberal interpretations of conflict and human nature, for example?

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