The Better Angels of Our Nature: Why Vio - By Steven Pinker Page 0,130

can see from their lonely perch atop the vertical axis, high above the point where an extrapolation of the line for the wars would hit it, he was pushing his luck when he said that all deadly quarrels fell along a single continuum. Richardson gamely connected the murder point to the war line with a swoopy curve so that he could interpolate the numbers of quarrels with death tolls in the single digits, the tens, and the hundreds, which are missing from the historical record. (These are the skirmishes beneath the military horizon that fall in the crack between criminology and history.) But for now let’s ignore the murders and skirmishes and concentrate on the wars.

FIGURE 5–7. Number of deadly quarrels of different magnitudes, 1820–1952

Source: Graph adapted from Weiss, 1963, p. 103, based on data from Richardson, 1960, p. 149. The range 1820–1952 refers to the year a war ended.

Could Richardson just have been lucky with his sample? Fifty years later the political scientist Lars-Erik Cederman plotted a newer set of numbers in a major dataset of battle deaths from the Correlates of War Project, comprising ninety-seven interstate wars between 1820 and 1997 (figure 5–8).52 They too fall along a straight line in log-log coordinates. (Cederman plotted the data in a slightly different way, but that doesn’t matter for our purposes.)53

Scientists are intrigued by power-law distributions for two reasons.54 One is that the distribution keeps turning up in measurements of things that you would think have nothing in common. One of the first power-law distributions was discovered in the 1930s by the linguist G. K. Zipf when he plotted the frequencies of words in the English language.55 If you count up the instances of each of the words in a large corpus of text, you’ll find around a dozen that occur extremely frequently, that is, in more than 1 percent of all word tokens, including the (7 percent), be (4 percent), of (4 percent), and (3 percent), and a (2 percent).56 Around three thousand occur in the medium-frequency range centered on 1 in 10,000, such as confidence, junior, and afraid. Tens of thousands occur once every million words, including embitter, memorialize, and titular. And hundreds of thousands have frequencies far less than one in a million, like kankedort, apotropaic, and deliquesce.

FIGURE 5–8. Probabilities of wars of different magnitudes, 1820–1997

Source: Graph from Cederman, 2003, p. 136.

Another example of a power-law distribution was discovered in 1906 by the economist Vilfredo Pareto when he looked at the distribution of incomes in Italy: a handful of people were filthy rich, while a much larger number were dirt-poor. Since these discoveries, power-law distributions have also turned up, among other places, in the populations of cities, the commonness of names, the popularity of Web sites, the number of citations of scientific papers, the sales figures of books and musical recordings, the number of species in biological taxa, and the sizes of moon craters.57

The second remarkable thing about power-law distributions is that they look the same over a vast range of values. To understand why this is so striking, let’s compare power-law distributions to a more familiar distribution called the normal, Gaussian, or bell curve. With measurements like the heights of men or the speeds of cars on a freeway, most of the numbers pile up around an average, and they tail off in both directions, falling into a curve that looks like a bell.58 Figure 5–9 shows one for the heights of American males. There are lots of men around 5’10” tall, fewer who are 5’6” or 6’2”, not that many who are 5’0” or 6’8”, and no one who is shorter than 1’11” or taller than 8’11” (the two extremes in The Guinness Book of World Records). The ratio of the tallest man in the world to the shortest man in the world is 4.8, and you can bet that you will never meet a man who is 20 feet tall.

FIGURE 5–9. Heights of males (a normal or bell-curve distribution)

Source: Graph from Newman, 2005, p. 324.

But with other kinds of entities, the measurements don’t heap up around a typical value, don’t fall off symmetrically in both directions, and don’t fit within a cozy range. The sizes of towns and cities is a good example. It’s hard to answer the question “How big is a typical American municipality?” New York has 8 million people; the smallest municipality that counts as a “town,” according to Guinness, is Duffield, Virginia, with only 52. The ratio of the largest