Essay — From the June 2017 issue

Safety in Numbers

The mathematics of predicting war

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I went to fetch some new chickens the other day. The birds were Rhode Island Reds, homely and reliable, and so meek that it took the breeder and me only a few minutes to get eight of them into the metal crate in the back of my station wagon. They huddled together at the center of the cage, craning their heads like a single many-headed creature scanning the horizon for predators. The jouncing of the car on the rocky driveway broke up the scrum, leaving each hen to fend for herself. Some tried to fly out the top of the cage, others threw themselves against its sides. I switched on the stereo to drown out the noise. But the Neville Brothers did better than that, calming the hens so that they settled onto the floor of the crate.

We wound our way past greening lawns and fields. I leaned my elbow out the open window, let the mild air wash my face, took in the bright white clouds and the azure sky — a May-in-December afternoon almost gorgeous enough to make me glad for global warming, and certainly enough to make me glad for the day, for the road, for the Nevilles and the chickens, and for the absence of traffic at the intersection with the highway I had to cross to get home. Its four lanes were empty, as if Moses had parted the traffic for me. But just as I started across, I heard the urgent bleat of a car horn. Something flickered at the periphery of my vision, behind me and to the left. I thought of a concept I had once taught to undergraduates: inattentional blindness, the failure to see something obvious when you are preoccupied. The term was perhaps most famously illustrated by two Harvard professors who conducted an experiment in which almost half of their test subjects, shown a video of a basketball passing drill and instructed to count the passes of one team, failed to discern a person in a gorilla suit walking through the game. I braced for the crash.

Illustrations by Darrel Rees

Preoccupation was not going to kill me, however, at least not today. Even before my memory had faded, I found myself safely on the other side of the road. I looked in my mirror. The highway was as empty as it had been a moment before. The horn sounded again. It was the rise to the second verse of “Fire and Brimstone.” The title made me laugh.

The mild pleasures of sky and balmy air and locomotion returned in an amped-up form only one stop shy of ecstasy. Terror had stripped away dullness, and, like a whetstone restoring the edge of a knife, rendered life sharp and shiny. I was almost grateful to it.

But only almost. We’re built for terror, as witness the slowing of time, the flooding thoughts, the reflexive mashing of the accelerator, the adrenaline surge. We’re also built to ignore it, which is a good thing considering everything there is to be terrified of. Car wrecks, of course. But also an aneurysm that will wipe you out in the middle of a sentence, the cancer that will take its sweet time to eat you alive, or just the knowledge that somewhere out there is a bullet with your name on it. All the species of terror, most of them variations on one theme: death itself, the dizzying, horrifying, ungraspable prospect of nonbeing. Maybe the din of life has drowned out the tocsin of your impending demise, or thoughts of heaven have turned its music sweeter, or you’ve come to ignore it as you ignore a jackhammer outside your window. In any case, you’ve managed to soldier on. You’ve learned how to keep your eye on the game instead of on the gorilla.

In cultivating this obliviousness we’ve had a lot of help. Evolution has bequeathed us a capacity to ignore the obvious almost as strong as our capacity to apprehend it; culture, meanwhile, lavishes us with distraction. And then there is our long history of triumph over wildness. If there is any justification for thinking that we are marching toward progress, it can be found in the freedom we have attained from everyday terror.

“Nature, Mr. Allnut, is what we are put in this world to rise above,” Rose Sayer informs Charlie in the film adaptation of The African Queen, and if you’ve ever seen a wild animal up close, you know she is not just talking about sex. She means the frenzy in the eyes of the deer after you scare it up from its bed, or the frantic back-and-forth of the squirrel in the road, smart enough to know it’s in trouble, too dumb to know what to do. Animals may not be troubled by thoughts of mortality and extinction, but that’s only because they’re too busy with more immediate threats.

Say what you will about our alienation from nature, it has at least this one virtue: It relieves us of the constant confrontation with death that characterizes daily life for these beasts. We may not have been intended by a creator to rise above nature, and natural selection may not have provided us intellect specifically to moderate our fears, but it has to be counted one of the few nearly unambiguous achievements of the human race that we have used our big brains to free ourselves from panic long and well enough to sing songs, draw on cave walls, invent love.

And it’s not just those fight-or-flight moments that we’ve managed to minimize by building civilization. Hank Morgan, the Connecticut Yankee Mark Twain placed in King Arthur’s court, saves his skin and earns a place at the Round Table by predicting an eclipse, but the power to know when the sun will disappear or rise does not belong only to the wizard who can make the predictions. Knowing when is also knowing that. It is being certain that the sun will return from the eclipse or the night or winter, that it will not simply disappear and leave us in the cold and dark. To know that the heavenly bodies will make their appointed rounds is to know that the future is out there waiting to happen. The resulting confidence accrues to every poor forked radish on earth.

However accurately our forebears calculated planetary motion, they were left with one area of vast uncertainty: the sensible weather. Centuries after we learned to extract fuel from the ground, to recognize the microbes that were killing us and to kill them first, to send airplanes and rockets into the sky, to map the earth, to send instantaneous messages around it, to annihilate it with nuclear weapons: Long after all these achievements, farmers and sailors and city dwellers alike were still dependent on red-sky-at-night augury complemented by barometric observations and telegraphed accounts of what was going on upwind. Until very recently — yesterday relative to recorded history — it was hard to know whether a blackening sky foreshadowed a dangerous storm or a passing shower. But because it could be just about anything, terror was that much harder to keep at bay.

Not that no one had an idea of how to accurately forecast the weather. By 1922, a British mathematician named Lewis Fry Richardson thought he had figured out how to use atmospheric physics, direct observations, and differential equations to calculate the probability of the next day’s weather. His method, described in a book called Weather Prediction by Numerical Process, depended on brute calculation at a scale possible, at the time, only in Richardson’s imagination. He pictured an enormous indoor arena, arranged in tiers and rows like one of our sports stadiums. “The walls are painted to form a map of the globe,” he wrote. “The ceiling represents the north polar regions, England is in the gallery, the tropics in the upper circle, Australia on the dress circle, and the Antarctic in the pit.” In the seats were 64,000 computers “at work upon the weather of the part of the map where each sits.” Each computer — these were people who computed, not machines — would receive data from his district, run it through his assigned equation, and then pass the solution along to a regional boss, who would compile his section’s findings and pass them up the chain of command, which culminated in a man at a podium atop a pillar in the center of the hall, “like the conductor of an orchestra in which the instruments are slide-rules and calculating machines.” The man’s clerks would aggregate the information into forecasts and send them to the “quiet room,” where other clerks would relay them to the radiomen who would broadcast them to the world.

It would be nearly thirty years before an actual computer was built that could do the work of those 64,000 people. It took the Electronic Numerical Integrator and Computer (ENIAC) twenty-four hours to spit out a (mostly accurate) twenty-four-hour forecast, but it proved Richardson’s point: mathematics could be used to predict the weather. Since then, satellites and supercomputers have improved the process such that we can now consult hour-by-hour forecasts of comparatively astonishing accuracy. Fearsome as they were, Katrina and Sandy were not total surprises. There was enough time to muster camera crews and correspondents. If you weren’t in the teeth of the storm, you could watch it whirl up the weather map, just another spectacle among spectacles.

Not that AccuWeather has entirely tamed the skies. The weather can still be pretty scary, even when you know what is coming. Indeed, it may be a good thing that, satellites and supercomputers notwithstanding, the weather is not yet fully domesticated. We still can’t know a hurricane will strike until just a few days before, and when it arrives, there is nothing to do but buy the milk and bread and ride it out. Whatever forecasting prowess we have achieved, we still have extensive practice at enduring the weather. It reminds us of its inescapability every time we step outside, the more so now that we are fully in the grip of climate change. The globe isn’t the only thing heating up around us. But our carefully cultivated inattentional blindness is going to come in handy.

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.

In 1898, the Marxist economist Ladislaus Bortkiewicz published The Law of Small Numbers, a treatise that featured statistical analysis of the 196 times between 1875 and 1894 that Prussian soldiers were kicked to death by their horses. He concluded that the deaths followed the Poisson distribution. The pattern did not indicate that, for instance, the cavalrymen (or their mounts) needed better training. Rather, the numbers reflected the background of probability: If you put enough soldiers around enough horses for enough time, someone is going to get killed. Richardson cited Bortkiewicz’s work as a good illustration of a Poisson distribution. He also mentioned research proving that radioactive substances emit alpha particles at random rates; spend enough time around uranium and you are bound to get a dangerous dose.

But you have to wonder why he used these examples and not the one that had inspired the inquiry in the first place: the weather. You can understand the physics of tornadoes all you want, but that will not tell you exactly when those forces will converge. You can only know that deadly storms of a certain magnitude will arise with a certain frequency over a period of time. The Poisson formula and a little bit of weather history make possible what amounts to a parlor trick: Tell me how big the tornado was and I can tell you more or less how many of those storms occurred in any single year; tell me how many storms of a particular magnitude blew through and I can tell you what that magnitude was. I can even tell you how many cyclones there may be over the next century. But I cannot tell you what you probably most want to know: when the next twister will emerge, how bad it will be, and where it will wreak havoc.

On the other hand, anyone can build a storm cellar, buy a dosimeter and a hazmat suit, or dream up a combination of leghold devices and other gear that would protect even the rashest horseman from the unruliest steed. You can read about the efforts, some of them brilliant and most of them noble, to clean up after hurricanes, to put out fires, to evacuate the wounded from battlefields. But what remains unimaginable, and probably impossible, is eliminating the radiation, the horse’s impulse to kick, the killer storm. Human agency may be better suited to avoiding disaster or mopping up afterward than to erasing its possibility; we may always be a step behind the catastrophes of nature, and war may be more like a natural disaster than we would like to think.

Perhaps Richardson omitted, or even failed to grasp, the obvious comparison because it was so disheartening. After he had put in more than a decade of hard work, his numbers indicated only that war, like killer storms, always lurks in the background. Both can be counted on to occur, but neither can be seen coming until it’s too late to do much but take shelter and count the bodies afterward. Deadly quarrels perhaps turned out to be much more like the weather than Richardson had bargained on, too much to even see.

If that’s the case, you can’t blame Richardson for his inattentional blindness. Underlying his calculations was a deep faith in our ability to use reason to rise above the mess of nature, and a concomitant faith that behind chaos lies mathematical order. He did not abandon his enthusiasm for Esperanto when his data indicated that linguistic differences were not much of a factor in causing or preventing war. Nor did the seemingly eternal penchant of politicians for “bold rhetoric” dissuade him from believing that they could be persuaded to adopt the dispassion of the mathematical mind. “Engineers customarily learn the science of dynamics as a guide to the art of machine design,” he reasoned. “Unless statesmen have studied international dynamics, how can they expect their plans for peace to succeed?” Once they could distinguish “the more fated [from] the less freely choosable forms of international behavior,” he believed, those statesmen would finally be able to make the right choices. Or at least they would have no excuse not to.

“I did not know quite what to condemn, until I found out what was mechanical,” Richardson wrote. We can’t be held accountable for nature’s disasters, he reasoned, only for the ones we bring about. Power-plant executives may be condemned for the Fukushima meltdown, but no one will be judged for the earthquake that set it off. As we extend our reach into the natural world, the distinction between the mechanical and the human may be collapsing along with the Antarctic ice shelf. But what if it never really existed in the first place? What if it was a conceit arising from the same source as Rose Sayer’s prudishness, and as mismatched to reality as her white dress to that filthy boat? What if we are more like those Rhode Island Reds than we care to imagine, pecking and clucking under an azure sky, certain of our freedom and oblivious to the approaching big-brained ape?

It’s hard to say where the war on terror falls on the Richardson scale. As its originator would be the first to point out, much depends on definitions. Are the 9/11 attacks (3.5) their own event? Should the 3,660 people killed by American drones (3.6) be taken as casualties of one war, or separated into their Yemeni and Pakistani components (2.9, 3.5), or combined with the ground wars in Afghanistan and Iraq (5, 5.3), and should those figures include only deaths of soldiers or, now that the battlefield has moved to the cities, should they include civilians? Should all the deaths since 9/11 be considered casualties of a single prolonged war? Thinginess fails.

This hasn’t stopped some latter-day Richardsons from crunching their own numbers. Neil F. Johnson, for instance, a physicist at the University of Miami, claims he and his international team of “complexity scientists” have unearthed the “dynamics of insurgent-group formation and attacks, which neatly explains the universal patterns in all modern wars and terrorism.” Johnson’s team used the number of casualties in individual events (rather than in entire wars) as their standard, and tracked how many events of each magnitude occurred in a given war. It turned out that no matter the conflict — the civil unrest in Peru, the drug wars in Colombia, the Israel?Palestine conflict, Iraq, Afghanistan — if you graph the number of casualties against the number of events resulting in that many casualties, the result falls “neatly on a straight line” — a line whose slope, as it happens, equals ?2.5. Large events are not only more infrequent than small, they are less frequent in proportion to their size. Their distribution is governed by a power-law, according to which the number of events of a given magnitude is equal to the number of people killed, raised to the power of –2.5. Johnson and his team also found a power-law at work in the timing of terrorist attacks. Studying insurgent events in Afghanistan, they discovered that knowing the interval between the first two attacks in a series allowed them to forecast the timing and intensity of subsequent attacks.

“You take all of the conflict, all of the chaos, all of the noise” of war, Johnson’s colleague Sean Gourley said during a 2009 TED talk, “and out of that comes this precise mathematical distribution of the way attacks are ordered.” The math has apparently caught the laws of war at work. Johnson claims that today’s wars and terrorism have

less to do with the geography or ideology, and more to do with the day-to-day mechanics of human insurgency — in other words, it is simply the way in which insurgent groups of human beings fight when faced with a much stronger, but more rigid opponent.

If Johnson and Gourley have found what eluded Richardson — a nonrandom pattern — that may be because they are concerned with the conduct rather than the origins or the outcomes of war. But even if Richardson had focused there, he would not have found the same power-law; they looked at wars from the era Richardson studied and determined that it does not apply. What they’ve found is that the concatenation of forces that gives rise to terrorism generates certain dynamics, not unlike the way a natural ecosystem does, and that these dynamics determine how the armed forces fight. “Just like a fungus will thrive in a forest, or a cancer tumour will thrive in a host, these armed groups are fed by a rich source of nutrients which allows them to self-organize into a robust structure.” Identifying and eliminating those nutrients, Johnson and Gourley hope, can change those dynamics and make the structure less robust. The fact that modern warfare conforms to a power-law does not mean we can do nothing to change it; rather, they say, it points us to what we can do, such as targeting small terrorist groups before they have the chance to grow.

Still, the fact that terrorist attacks follow the laws of physics leaves us with a disturbing possibility: that terrorists and those who would stop them are particles that interact according to quantum rules; the war between them, as Johnson puts it, is “driven by this ecology of agents.” Physicists know that in a system guided by such laws, it is “hard to distinguish between exogenous (i.e., outside) and endogenous (i.e., internal, self-generated) effects.” The system, in other words, has a life of its own, independent of the intentions of any of its constituents. We may think that Osama bin Laden or SEAL Team 6 is the apotheosis of human agency, when in reality they are more like the occupants of what Johnson calls “a multi-species ecological setting,” soldiers in armies of ants that cross paths and engage according to rules of which they have no innate knowledge, with consequences they can’t possibly predict or control. Or, for that matter, more like weather fronts, juiced by greenhouse gases, colliding over the Midwest and unleashing an unprecedented flood.

Take a view from far enough away — Mars, let’s say — and our deadly quarrels cohere into something as smooth and beautiful as an equation, but only at the cost of human agency. Using reason to map chaos only reminds us of how paltry reason is. The mathematics of war, even if undertaken to help us find our way out of terror, only make it more terrifying. They place us into the hands of the probability gods, to whom sin and salvation are only the conceits of the innumerate. The view from Mars may turn our travails into trivial dramas set against a quantum backdrop, but only by turning us into particles helplessly hurling ourselves against the bars of our cages, dying to be calmed.

Of course, it’s not the mathematicians we turn to for reassurance. It is the politicians and the generals and their patrons in high finance and industry, who can be counted on to comfort us with promises that if we surrender this freedom or that dignity or the other pleasure, if we consent to this drone attack or those boots on the ground, if we let our president build that wall or ban those Muslims, we will once again feel safe. Here some math would be useful — not the math of Poisson distributions but the much simpler math of the Richardson scale, on which the ninety-one people killed by jihadis in the United States since 2001 register a 2, with the fifty-six deaths at the hands of domestic (mostly Christian) terrorists close behind at 1.75, and the 400,000 Americans killed by guns or the half million of us dying in vehicle accidents in that period register around a 5.6, and the millions dying around the world from poverty easily reach a magnitude of at least 7.

We might have to take another lesson from Richardson, although not the one he intended. We might have to learn to live with deadly conflicts as we have learned to live with the weather. Perhaps it is part of our ecological setting, inextricable from the world we have built, its dynamics as invisible to us as they remained to Richardson. Lightning doesn’t care whom it strikes, nor cancer whom it kills, nor the rising sea whom it drowns. So why should deadly quarrels?

It is possible that in creating civilization, we have not risen above nature but rather done its bidding. Perhaps we have only given our inattentional blindness more opportunities to miss the gorilla. The basketball game is, after all, so much more beautiful, its dangers so much more contained, its outcome, to the extent that someone will win or lose, so much more certain. Maybe that’s what human agency has been for all along — to help us feel safe by distracting us from what is real.

Still, despite everything the mathematicians say, we are even less likely to surrender our conviction that our lives matter than we are to eliminate war. Freedom, dignity, the search for justice and the struggle for meaning, the sheer pleasure of driving down the road with the warm wind in your face — none of this will be relinquished. Nor should it be, even if the numbers say we do not matter as much as we would like to think. Not because we do, and not because we will finally triumph over nature or ourselves, but because, confronted with a world that spins out hurricanes and wars, it takes courage even to try. It is brave of us to build our shelters and our cities, to tell our stories, to hope. The stubborn fitful effort to fashion a world in our best image lights up this dark corner of the universe, and from this we should take heart.

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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.

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