But a century is made up of a hundred years, not fifty. The second half of the 20th century saw a historically unprecedented avoidance of war between the great powers which the historian John Gaddis has called the Long Peace, followed by the equally astonishing fizzling out of the Cold War. How can we make sense of the multiple personalities of this twisted century? And what can we conclude about the prospects for war and peace in the present one?

The 20th century would seem to be an insult to the very suggestion that violence has declined over the course of history. Commonly labeled the most violent century in history, its first half saw a cascade of world wars, civil wars, and genocides that Matthew White has called the Hemoclysm, the blood-flood. The Hemoclysm was not just an unfathomable tragedy in its human toll but an upheaval in humanity's understanding of its historical movement. The Enlightenment hope for progress led by science and reason gave way to a sheaf of grim diagnoses: the recrudescence of a death instinct, the trial of modernity, an indictment of Western civilization, man's Faustian bargain with science and technology.

The competing predictions of Toynbee the historian and Richardson the physicist represent complementary ways of understanding the flow of events in time. Traditional history is a narrative of the past. But if we are to heed George Santayana's advisory to remember the past so as not to repeat it, we need to discern patterns in the past, so we can know what to generalize to the predicaments of the present. Inducing generalizable patterns from a finite set of observations is the stock in trade of the scientist, and some of the lessons of pattern extraction in science may be applied to the data of history.

Suppose, for the sake of argument, that World War II was the most destructive event in history. (Or if you prefer, suppose that the entire Hemoclysm deserves that designation, if you consider the two world wars and their associated genocides to be a single protracted historical episode.) What does that tell us about long-term trends in war and peace?

The answer is: nothing. The most destructive event in history had to take place in some century, and it could be embedded in any of a large number of very different long-term trends. Toynbee assumed that World War II was a step in an escalating staircase, as in the left panel in figure 5-1. Almost as gloomy is the common suggestion that epochs of war are cyclical, as in the right panel of figure 5-1. Like many depressing prospects, both models have spawned some black humor. I am often asked if I've heard the one about the man who fell off the roof of an office building and shouted to the workers on each floor, "So far so good!" I have also been told (several times) about the turkey who, on the eve of Thanksgiving, remarked on the extraordinary 364-day era of peace between farmers and turkeys he is lucky enough to be living in.

The left panel depicts the radical possibility that World War II was a statistical fluke -- that it was neither a step in an escalating series nor a harbinger of things to come, and not part of a trend at all. At first the suggestion seems preposterous. How could a random unfolding of events in time result in so many catastrophes being bunched together in just a decade: the brutal invasions by Hitler, Mussolini, Stalin, and Imperial Japan; the Holocaust; Stalin's purge; the Gulag; and two atomic explosions (to say nothing of World War I and the wars and genocides of the preceding two decades)? Also, the usual wars we find in history books tend to have death tolls in the tens or hundreds of thousands or, very rarely, in the millions. If wars really broke out at random, shouldn't a war that led to the deaths of 55 million people be astronomically improbable? Richardson showed that both these intuitions are cognitive illusions. When the iron dice begin to roll (as the German chancellor Theobald von Bethmann-Hollweg put it on the eve of World War I), the unlucky outcomes can be far worse than our primitive imaginations foresee.

But are the processes of history really as deterministic as the law of gravity or the cycling of the planet? Mathematicians tells us that an infinite number of curves can be drawn through any finite set of points. Figure 5-2 shows two other curves which situate the same episode in very different narratives.

FIGURE 5-1: Two pessimistic possibilities for historical trends in war

FIGURE 5-2: Two less pessimistic possibilities for historical trends in war

The right-hand panel in figure 5-2 places the war in a narrative that is so unpessimistic that it's almost optimistic. Could World War II be an isolated peak in a declining sawtooth -- the last gasp in a long slide of major war into historical obsolescence? Again, we will see that this possibility is not as dreamy as it sounds.

The long-term trajectory of war, in reality, is likely to be a superimposition of several trends. We all know that patterns in other complex sequences, such as the weather, are a composite of several curves: the cyclical rhythm of the seasons, the randomness of daily fluctuations, the long-term trend of global warming. The goal of this chapter is to identify the components of the long-term trends in wars between states. I will try to persuade you that they are as follows:

• A big dose of randomness.

• No cycles.

• An escalation, recently reversed, in the destructiveness of war.

• Declines in every other dimension of war, and thus in interstate war as a whole.

The 20th century, then, was not a permanent plunge into depravity. On the contrary, the enduring moral trend of the century was a violence-averse humanism that originated in the Enlightenment, became overshadowed by counter-Enlightenment ideologies wedded to agents of growing destructive power, and regained momentum in the wake of World War II.

To reach these conclusions, I will blend the two ways of understanding the trajectory of war: the statistics of Richardson and his heirs, and the narratives of traditional historians and political scientists. The statistical approach is necessary to avoid Toynbee's fallacy: the all-too-human tendency to hallucinate grand patterns in complex statistical phenomena and confidently extrapolate them into the future. But if narratives without statistics are blind, statistics without narratives are empty. History is not a screen saver with pretty curves generated by equations; the curves are abstractions over real events involving the decisions of people and the effects of their weapons. So we also need to explain how the various staircases, ramps, and sawtooths we see in the graphs emerge from the behavior of leaders, soldiers, bayonets, and bombs. In the course of the chapter, the ingredients of the blend will shift from the statistical to the narrative, but neither is dispensable in understanding something as complex as the long-term trajectory of war.