Essay — From the June 2017 issue

Safety in Numbers

The mathematics of predicting war

Download Pdf
Read Online
( 3 of 5 )

Lewis Richardson was thirty-two and had a plum job as the superintendent of a government meteorological observatory in Scotland when the First World War broke out. As he later wrote, he was

torn between an intense curiosity to see war at close quarters, an intense objection to killing people, both mixed with ideas of public duty, and doubt as to whether I could endure danger.

But he hit upon a way to satisfy these competing urges. In 1916, after Britain denied his request to serve as a battlefield ambulance driver, he joined the Friends’ Ambulance Unit, which transported wounded French soldiers.

Even at the front, Richardson continued to observe the weather carefully, playing with the equations he thought could capture the way conditions evolved. He used published observations of the weather in Central Europe at seven in the morning on May 20, 1910, to test out his formulas. After six weeks spent hunched in his off-duty hours over a hay-bale desk, he came up with a forecast for one o’clock that afternoon. The barometric pressure would rise sharply over Bavaria, he predicted, and the winds would shift suddenly and blow hard over the entire area. According to the records, however, the day had remained calm, and the barometer had barely budged.

Richardson fiddled some more with his formulas, figuring out, among other things, how to measure wind eddies, but by the time his book came out, he had decided it wasn’t yet possible. Truly forecasting the weather would have to wait for “some day in the dim future [when] it will be possible to advance the computations faster than the weather advances.” He became a professor of physics and a college administrator. In 1940, he began to turn his attention to the other phenomenon he’d witnessed in France: war.

Richardson’s twin fascinations were not as far-flung as they may seem. “What has happened often is likely to happen again,” Richardson wrote, “whether we wish it or not.” War visits us frequently and usually against our wishes, and thus, like bad weather, might also be guided by laws that mathematics could reveal. Given the right models, he thought, people could recognize the storms of war as they gathered and head them off before they broke.

Although several people were using math to aid military strategists, few if any were attempting to forecast the actual outbreak of war. Richardson was, in a way, starting from scratch — from the very definition of war, in fact. Historians, subject to “national sentiment and personal prejudice,” were no help. “One can find cases of homicide which one large group of people condemned as murder, while another large group condoned or praised them as legitimate war,” he complained. “The concept of a war as a discrete thing does not quite fit all the facts. Thinginess fails.” War, he ultimately decided, was only a species of deadly quarrel, and, like a storm, its advent was best understood with numbers — specifically the number of deaths in any conflict. He fashioned a scale of the magnitude of deadly quarrels that, like the Richter scale, was logarithmic: each one-point increase corresponded to a tenfold increase in deaths. A single murder rated a 0, a war in which a thousand people died was a 3, and a magnitude-7 war was one in which upwards of 10 million people died.

Richardson gathered statistics on deadly quarrels ranging from barroom murders to world wars but decided to focus on the 315 conflicts occurring between 1820 and 1952 that reached magnitude 2.5 (317 deaths) or greater. Using sociologists’ accounts, he isolated sixty-five factors (“languages different,” “similar degree of personal liberty,” “membership in United Nations”) as potential causes of war. He gave each variable a code letter and ordered the conflicts, first according to their magnitude, and then in matrices charting, for all wars of that magnitude, the interaction among the variables.

The Statistics of Deadly Quarrels, the book in which Richardson compiled his results, was not published until 1960, seven years after he died. Its equations and tables and foldout charts encompass wars ranging from the magnitude-2.65 conflict between the Bolivian government and the Movimiento Nacionalista Revolucionario in 1952 through the magnitude-5.4 Russo?Turkish War of 1877?78 to the two world wars of the twentieth century, the only magnitude-7 conflicts on record. (He notes that 20 million people might have been killed during the Taiping Rebellion of 1851?64, but the data was not reliable enough to rate the war above a 6.3.)

“This book could not be designed to be read by everyone,” Richardson says at the outset. It’s a fair warning to a reader who will encounter, for instance, his clarification that a particular hypothesis is consistent with “the fact that, in the octantal plan, n*(3,1) > n*(2,2),” but “fails utterly to explain why wars of 1 versus 1 are the commonest type.” On the other hand, he also draws conclusions in plain English — for example, that “humanity in general is not like the Irishman who is said to have asked: ‘Is this a private fight, or may anyone join?’ ”

Much of what Richardson’s calculations demonstrated was already apparent: The longer a war wears on, the more people it kills, for instance, and the probability of being murdered is greater than the probability of dying in a war. Some of the numbers were a little surprising, if not exactly revelatory: The two magnitude-7 quarrels accounted for 60 percent of the quarrel-related deaths in the 130-year period Richardson studied, and the next-largest category was the magnitude-0 quarrels; the nearly 10 million people killed one or two or three at a time may not have the same hold on our moral sensibilities as the fallen soldiers at the Somme, but taken together, their quarrels are no less deadly. Other findings are discouraging to contemporary ears, like his observation that there have been “more wars between Christians and Moslems than would be expected from their populations, if religious differences had not tended to instigate quarrels between them.” And he overlooks at least one glaring implication: that so many deadly quarrels have passed almost unnoticed into history, such as the thirty-five-year war between the Acehnese and the Dutch, which, by the time it ended in 1908, had killed nearly 300,000 people.

One of Richardson’s conclusions, however, stands out. He calculated how many deadly quarrels of each magnitude had started in each of the first 110 years of his sample. His table for conflicts between 3.5 and 4.5 from 1820 to 1929 looked like this:

NUMBER OF WARS
STARTED (n)
YEARS IN WHICH
n WARS BEGAN
0 65
1 35
2 6
3 4
4 0
>4 0
TOTAL 110

At first glance, this chart seems to say something unremarkable, even obvious: Every time a war breaks out, the likelihood that another war will break out is reduced. So in any given year the chances of three wars starting are about one tenth the chance of one war starting, and one sixteenth the chances of none at all. War, in other words, is a relatively unlikely event, and multiple wars in the same year are even more unlikely. But you can’t draw from this data what would seem to be the commonsense conclusion: that if three wars start by March, you can pretty much count on another one not beginning before January. That would be like thinking that if the airplane ahead of yours crashes, then your plane is less likely to crash than it would be otherwise. Infrequent events occur independently of one another and at random times. If they seem to cluster together or be spaced far apart, that’s only because events that occur randomly will do that; that’s what “random” means.

However, if two wars of magnitude 7 break out within twenty-five years of each other, it’s possible there might be some kind of nonrandom force at work after all, maybe some historical momentum toward increasingly deadly wars. Sorting out the random from the ordered is the work of statisticians, and as it happened, in 1837, Siméon-Denis Poisson, a French mathematician, had developed a formula that could determine whether the intervals between instances of a phenomenon that occurred infrequently were indeed random.

Events will conform to the Poisson distribution of improbable events unless something happens to space them out nonrandomly — the same bad fuel pumped into two airplanes, for example. You can think of the Poisson distribution as the statistic that demonstrates that fate, untroubled by human hands, is at work.

When Richardson ran his magnitude 3.5?4.5 data through the Poisson formula, he came up with this table:

NUMBER OF WARS
STARTED (n)
YEARS IN WHICH
n WARS BEGAN
POISSON
DIST.
0 65 64.3
1 35 34.5
2 6 9.3
3 4 1.7
4 0 0.2
>4 0 0.0
TOTAL 110 110

Across the 110 years Richardson tabulated, the frequency of the onset of war is distributed almost exactly the way that Poisson predicted for infrequent and randomly occurring events — and not only for the years Richardson studied intensively but, as he showed in a different table, for 299 wars occurring over 432 years. He ran a similar analysis of the number of “outbreaks of peace” in each year. Had war alone conformed to the Poisson law, then this might indicate a “persistent background of pugnacity.” But since “the ends of wars have the same distribution as the beginnings,” he could safely, if reluctantly, conclude that what was consistent was the persistent probability of both war and peace — as he put it in an uncharacteristically speculative comment, “The background appears to be composed of a restless desire for change.” The numbers didn’t show Richardson how to know when a war was going to occur. But they did show him something about these repeating events: that, like plane crashes, deadly quarrels just happen.

You are currently viewing this article as a guest. If you are a subscriber, please sign in. If you aren't, please subscribe below and get access to the entire Harper's archive for only $23.99/year.

= Subscribers only.
Sign in here.
Subscribe here.

Download Pdf
Share
is a contributing editor of Harper’s Magazine and the author, most recently, of The Book of Woe: The DSM and the Unmaking of Psychiatry.

More from Gary Greenberg:

Get access to 169 years of
Harper’s for only $23.99

United States Canada

THE CURRENT ISSUE

November 2019

Men at Work

= Subscribers only.
Sign in here.
Subscribe here.

To Serve Is to Rule

= Subscribers only.
Sign in here.
Subscribe here.

The Bird Angle

= Subscribers only.
Sign in here.
Subscribe here.

The K-12 Takeover

= Subscribers only.
Sign in here.
Subscribe here.

The $68,000 Fish

= Subscribers only.
Sign in here.
Subscribe here.

view Table Content

Close

You’ve read your free article from Harper’s Magazine this month.

*Click “Unsubscribe” in the Weekly Review to stop receiving emails from Harper’s Magazine.