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Statistics of Deadly Quarrels

Brian Hayes

Wars and Peaces

Richardson was born in 1881 to a prosperous Quaker family in the north of England. He studied physics with J. J. Thomson at Cambridge, where he developed expertise in the numerical solution of differential equations. Such approximate methods are a major mathematical industry today, but at that time they were not a popular subject or a shrewd career choice. After a series of short-term appointments—well off the tenure track—Richardson found a professional home in weather research, making notable contributions to the theory of atmospheric turbulence. Then, in 1916, he resigned his post to serve in France as a driver with the Friends' Ambulance Unit. Between tours of duty at the front, he did most of the calculations for his trial weather forecast. (The forecast was not a success, but the basic idea was sound, and all modern weather prediction relies on similar methods.)

After the war, Richardson gradually shifted his attention from meteorology to questions of war and international relations. He found some of the same mathematical tools still useful. In particular, he modeled arms races with differential equations. The death spiral of escalation—where one country's arsenal provokes another to increase its own armament, whereupon the first nation responds by adding still more weapons—has a ready representation in a pair of linked differential equations. Richardson showed that an arms race can be stabilized only if the "fatigue and expense" of preparing for war are greater than the perceived threats from enemies. This result is hardly profound or surprising, and yet Richardson's analysis nonetheless attracted much comment (mainly skeptical), because the equations offered the prospect of a quantitative measure of war risks. If Richardson's equations could be trusted, then observers would merely need to track expenditures on armaments to produce a war forecast analogous to a weather forecast.

Mathematical models of arms races have been further refined since Richardson's era, and they had a place in policy deliberations during the "mutually assured destruction" phase of the Cold War. But Richardson's own investigations turned in a somewhat different direction. A focus on armaments presupposes that the accumulation of weaponry is a major cause of war, or at least has a strong correlation with it. Other theories of the origin of war would emphasize different factors—the economic status of nations, say, or differences of culture and language, or the effectiveness of diplomacy and mediation. There is no shortage of such theories; the problem is choosing among them. Richardson argued that theories of war could and should be evaluated on a scientific basis, by testing them against data on actual wars. So he set out to collect such data.

Others had the same idea at roughly the same time. The Russian-born sociologist Pitirim A. Sorokin published a long list of wars in 1937, and Quincy Wright of the University of Chicago issued another compilation in 1942. Richardson began his own collection in about 1940 and continued work on it until his death in 1953. Of the three contemporaneous lists, Richardson's covers the narrowest interval of time but seems to be best adapted to the needs of statistical analysis.

Richardson published some of his writings on war in journal articles and pamphlets, but his ideas became widely known only after two posthumous volumes appeared in 1960. The work on arms races is collected in Arms and Insecurity; the statistical studies are in Statistics of Deadly Quarrels. In addition, a two-volume Collected Papers was published in 1993. Most of what follows in this article comes from Statistics of Deadly Quarrels. I have also leaned heavily on a 1980 study by David Wilkinson of the University of California, Los Angeles, which presents Richardson's data in a rationalized and more readable format.

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