Rules of engagement
Jul 21st 2005
From The Economist print edition
Scientists find surprising regularities in war and terrorism
ON JULY 19th, IraqBodyCount, a group of academics who are attempting to monitor the casualties of the conflict in that country, published a report suggesting that almost 25,000 civilians have been killed in it so far. In other words, 34 a day. But that is an average. On some days the total is lower, and on some higher—occasionally much higher.
It is this variation around the mean that interests Neil Johnson of the University of Oxford and Michael Spagat of Royal Holloway College, London. They think it is possible to trace and model the development of wars from the patterns of casualties they throw up. In particular, by analysing IraqBodyCount’s data and comparing them with equivalent numbers from the conflict in Colombia, they have concluded that, from very different beginnings, these conflicts are evolving into something rather similar to one another.
The groundwork for this sort of study was laid by Lewis Fry Richardson, a British physicist, with a paper on the mathematics of war that was published in 1948. Using data from conflicts that took place between 1820 and 1945, Fry Richardson made a graph displaying the number of wars that had death tolls in various ranges. The outcome was startling: rather than varying wildly or chaotically, the probability of individual wars having particular numbers of casualties followed a mathematical relationship known as a power law.
Power-law relationships crop up in many fields of science and are often a characteristic of complex and highly interacting systems (which war certainly is). Earthquake frequencies and stockmarket fluctuations are both described by power laws, for example. Power laws also have properties that make them different from statistical distributions such as the normal curve (or bell curve, as it is familiarly known). Unlike a bell curve, a power-law distribution has only one tail and no peak. Small tremors occur frequently, but over a few decades enormously large earthquakes will also occur with reasonable frequency. As will deadly wars and attacks.
In May, Aaron Clauset and Maxwell Young, of the University of New Mexico, modified Fry Richardson’s method to look at terrorist attacks. Instead of total casualties in a conflict, they plotted the deaths from individual incidents. Again, they got a power law. Actually, they got two. Power-law relationships are characterised by a number called an index. For each ten-fold increase in the death toll, the probability of such an event occurring decreases by a factor of ten raised to the power of this index, which is how the distributions get their name. Terrorist attacks within G7 countries could be distinguished from those inside non-G7 countries by their different indices. G7 countries were more likely to suffer large attacks. Indeed, in an article published earlier this year by Britain’s Institute of Physics, Mr Clauset and Mr Maxwell said that “if we assume that the scaling relationship and the frequency of events do not change in the future, we can expect to see another attack at least as severe as September 11th within the next seven years.”
Dr Johnson and Dr Spagat took the method a couple of steps further. They extended Mr Clauset’s and Mr Maxwell’s idea of looking at the sizes of individual incidents within a campaign to other sorts of conflict, and also looked at how those conflicts have changed over time. As they report in a paper published recently in arXiv, an online archive, they found, yet again, that the data follow power laws. And for both of the wars they studied, the indices of those power laws have been approaching the value Mr Clauset and Mr Maxwell found for non-G7 terrorism, though from different directions. In other words, for the war in Iraq, the data indicate a transition from an index characteristic of more lethal, conventional war between armies to one closer to terrorism. No real surprise there, perhaps, though it is interesting to see perceptions on the ground reflected in the maths. For the Colombian conflict, though, the data show the opposite, a transition from a war characterised by smaller, less cohesive forces to a more unified rebel front—something that ought to worry Colombia’s government.
Dr Johnson and Dr Spagat put forward as an explanation a mathematical model they have developed. It consists of a group of self-contained “attack units”, each of a particular strength. Such units can join together or fragment into smaller pieces. Over time, an equilibrium of joining and breaking is reached, but where that equilibrium lies depends on the strength of any central organisation. The model explains the power-law behaviour seen in both conventional wars and terrorist attacks. Different rates of fragmentation lead to different indices—conventional war is fought with robust armies that are unlikely to fragment, while terrorists are more likely to have shifting alliances.
Dr Spagat points out that, if their model is correct, it makes casualty data useful in a situation where intelligence about the enemy is hard to come by—as seems to be the case in Iraq at the moment. For instance, it should be possible to distinguish an insurgency with a rigid command structure from a group of smaller, randomly linked units. Learning about the distribution of earthquakes may not prevent the Big One, but for war and terrorism, power-law statistics may teach governments something about how to defeat the enemy, and make war less deadly.
