Can There Be a Mathematics of War?
People do many things without knowing why: buy stuff they didn't think they wanted, vote differently when they're in one setting than they would in another, order a different lunch because of what the person next to them just ordered. As scientists learn more about all this, they should be able to predict, more often and more accurately, what people will do--regardless of what those people think they'll do.
Those predictions will be a scientifically rigorous version of our usual methods for interpreting behavior: explaining people's actions as the result of their feelings, perceptions and thoughts. When Josh Aronson and his colleagues showed they could get women to score better on a math test by telling them gender doesn't affect math scores, they're showing what psychologists can do with better knowledge of that familiar subject, the individual person. It's impressive, but not eerie.
There are other methods of predicting people's behavior, though, that aren't intuitively easy to grasp. They're based on patterns in the actions of very large numbers of people—stock markets, highway systems, cell-phone calls by the billions, and the like. That kind of prediction is harder to grasp, because it contradicts our intuitions about free will. How could my decision next Friday depend on what millions of other people do? The prospect is a little freaky.
Case in point: Today's issue of Nature features a paper by Juan Camilo Bohorquez, Sean Gourley, Alexander R. Dixon, Michael Spagat and Neil F. Johnson, which argues that all insurgencies--wars in which guerrilla-type units are fighting a standing military--share a single, predictable pattern in their violent attacks. In other words, according to their model, the decisions of insurgents--about whether to attack on a Wednesday or a Saturday, about whether to try for an average success or go for a spectacularly bloody result--don't take place in a wildly unpredictable "fog of war.'' Instead, they'll always tend to follow the same rhythm. Regardless of their beliefs, ideologies and motives. Regardless of their immediate tactical concerns. Regardless of what they may think they are doing.
Johnson, Spagat and their colleagues analyzed 54,679 violent events in nine separate insurgencies -- Colombia, Peru, Senegal, Sierra Leone, Northern Ireland, Israel-Palestine, Iraq, Afghanistan and Indonesia -- and plotted the frequency of insurgent attacks against the number of people killed in each one. They found the same relationship between the two in every conflict.
Let's back up to see what that means. (If you prefer video, check out one of the authors describing the work here.) All over nature and in human affairs as well, that kind of a plot (size of a measurement against frequency of occurrence) often reveals a relationship between the two. For human height, for example, the most typical measurements are the most frequent (a lot more human beings measure five foot ten than reach eight feet), so height measurements fall on the familiar "bell curve": small at the extremes, fat in the middle.
The bell curve teaches you to expect that what's typical is frequent, which makes extreme and rare events look unpredictable. But the bell curve isn't the only possible relationship between size and frequency. For any given earthquake zone, for example, there will be a hundred quakes that score 2.0 in the Richter scale for every 4.0 quake. The Richter scale is logarithmic--3 is ten times stronger than 2, and 4 is ten times stronger than 3--so this relationship between strength and frequency isn't anything like a bell-curve plot. It's looks more like Chris Anderson's "long tail,'' where a few rare giants reach the top of the graph and most of the measurements trail after.