Chances Are

by Michael Kaplan

  Why is this? Because almost everything to do with weather contains the germ of non-linearity. Ice, for instance, reflects sunlight, so Arctic seas stay cold. When the ice melts, the dark sea absorbs more heat, and so more ice melts—and we’re off. A system that in “normal” times maintains its equilibrium need only edge beyond a critical value in one variable for its governing equations to send it spinning off to the other wing of its strange attractor. One effect of warmer water will be more evaporation—which, since moisture is the vital mechanism of energy transfer in the atmosphere, means more fuel for storms—yet, at the same time, the increased cloud cover might reflect back some of the incoming radiation. In this respect, at least, change may damp down rather than amplify. No one can be sure.

  Being sure is the fundamental problem. As meteorology became a science, it automatically took on the scientific ideal of permanent principles and transient phenomena. Humboldt’s assumption of the unity of nature extended to a belief that the planet had the ability to regulate itself—and, a child of the Enlightenment, he assumed that this regulation would be for the best; that is, toward the mean. It is only recently that we have realized these shifts might be sudden and catastrophic: not dimming but switching off the light; not turning up the thermostat but burning down the house.

  All the intrinsic problems of weather—the accuracy of models, the non-linearity of systems, the possibility of significant forces below the scale of observation—are now issues of real social import. Should there be a carbon tax? Should we build more nuclear power plants? Should you buy a house in southern Florida, when it might be a marine park by the time your children retire? Given the form of the science, given that we live under the skies of Bjerknes, Richardson, and Lorenz, none of these questions can have a determined, certain answer.

  Disappointed, you might conclude that expecting certainty from science is little different from a child’s assumption that grown-ups know everything. But to deride science for its uncertainty, confusing this with unsoundness, is to fall into the cynical relativism of adolescence: “It’s all a con; they can’t even predict the weather for next week, for God’s sake.”

  Is there a third view? Well, where uncertainty is unavoidable, probability ought to hold sway. There are signs of this happening: the Intergovernmental Panel on Climate Change, for instance, is switching over to probabilistic, ensemble forecasting from its previous consensus model. Its next report will provide weighted ranges of change, at least giving our fears a shape. Yet problems remain, the greatest of which is scaling up subjective reasoning to encompass all humanity. When applied to questions of utility or value, probability is a matter of human expectation. In its calculations the one thing that doesn’t vary is the expecter: it’s assumed that the same person—you—is taking the risk and looking forward to the return. When it comes to action about climate, though, these two roles are sharply distinct in time, place, and number.

  Would you give up your car on a probability that your grandchildren might live better than otherwise? Forbear to slash a homestead out of the Brazilian rain forest on a probability that Africans might suffer less drought? Plow your company’s capital into expensive energy technology on a probability of a marginal improvement in the lot of humankind? Doing so presumes that utility for you, now, is transferable to everyone and to the future—that, as a species, we are flipping one cosmic coin with Saint Petersburg’s lunatic billionaire.

  A recent study attempted to analyze this game, applying to the planet the same kind of risk/return calculations that govern raisin farming. The problem, though, is that any measurable global return from current action is unlikely to appear in less than a hundred years; and standard economic practice is to discount the value of future gains or losses by between 3 percent and 6 percent a year. This means that hardly any benefit so far in the future is worth paying for now. Both the costs and the benefits are enormous—but, like most enormous numbers, they are sensitive to many assumptions.

  Will we pay to join the game? The wager can be made compelling in purely arithmetic terms, but it still demands a great stretch from human nature (and human nature’s disreputable cousin, political expedience). Fated to conceive children in pleasure, bear them in pain and raise them in debt, we do not easily link current sacrifice with future benefit. Instead, we are more likely to proceed in a Bayesian way, adjusting our assumptions of what is normal as we change the world around us—and suffer the consequences. Homo sapiens hunted in the Sahara when it was a jungle. Greenland once lived up to its name. Our first hint of the possibility of changing sea levels was the discovery by Lyell in 1828 that the pillar tops of the so-called temple of Serapis at Pozzuoli were pitted by marine creatures, meaning that it had been built, covered by the sea, and then revealed again. Like those ancient Neapolitans, we habitually put ourselves in fate’s way, preferring to adapt rather than anticipate.

  Barney Schauble points out that the flip side of this complacency is the irrational desire to do something—anything—in the face of probable loss. Some current proposals to tackle climate change combine this spasmodic instinct with a touch of von Neumann’s heroic weather control: huge parasols between Earth and Sun, a new atmospheric layer of reflective aluminum balloons, and belts of mid-ocean fountains loading the winds with vapor. Even Stalin’s plan to reverse the flow of Siberia’s rivers and irrigate the plains of Kazakhstan has been revived in the name of arresting the decay of the polar ice cap. In America, some voices suggest steering weather by manipulating initial conditions—effectively poaching rainfall from our competitors by the judicious flap of an artificial butterfly. It seems the changing climate is not all we will have to fear in the coming century.

  Our intimate but indirect connection with the workings of our environment mean our attempts to change things resemble, at best, riding a horse rather than driving a car: We are trying to make the aims of a greater strength coincide with our own. At worst, our poor abilities at reasoning in uncertainty—our impulsiveness, our selfishness, our shortsightedness—compound the effects of natural unpredictability, turning a complex system into a complicated one. In such a system, error and virtue are unevenly weighted: the error of one man, Thomas Midgley, gave the world atmospheric lead pollution and the destruction of the ozone layer, but undoing his error has taken the concerted effort of millions.

  We talk about nature being “in balance,” as if it had a true mean state, to which—if not for our interference—it would always return. But this is an illusion born of our own adaptability and short memory. Nature is in motion, violent motion, all the time. Its future course is as impossible to predict with certainty as that of the ragged clouds scudding by the window. We may never be able to change that course for the better, but we can plot its shifting probabilities and their likely significance. Like Senator Ingalls’ visitor to Kansas who, “if he listened to the voice of experience, would not start upon his pilgrimage at any season of the year without an overcoat, a fan, a lightning rod, and an umbrella”—we’ll need to keep our wits about us.

  10

  Fighting

  Now, God be thanked Who has matched us with His hour,

  And caught our youth, and wakened us from sleeping,

  With hand made sure, clear eye, and sharpened power,

  To turn, as swimmers into cleanness leaping,

  Glad from a world grown old and cold and weary,

  Leave the sick hearts that honour could not move,

  And half-men, and their dirty songs and dreary,

  And all the little emptiness of love!

  So wrote Rupert Brooke in 1914, celebrating the start of a war that would soon grow dirty and dreary beyond imagining—and, far from wakening Brooke, would kill him. War, for those who do not have to wage it, is existence purged of uncertainty, the gray shades of politics resolved into the absolutes of friend and foe, life and death. The deeds of war, however mundane, are marked by necessity and danger, which give them a vitality missing from the employments of peace.
As Sloan Wilson, author of The Man in the Gray Flannel Suit, said: After four years soldiering, it seems very hard to return to meetings where you decide whether people would prefer a rubber spider or a tin frog as a prize gift in their breakfast cereal.

  As men age, they become more interested in military history. Many otherwise peaceable souls, lovers of music, painting or good food, can relate the minutest events of Waterloo or Chancellorsville, a strange light kindled in their eyes. Why should this be, when death is always dreadful and war so rarely achieves the aims for which it was fought? The answer stems from that deepest human urge: to protest against randomness. Somewhere within us, we all think that war, like betting, is a test of character. We wager our lives and our countries’ honors in the belief that victory endorses them. So in mastering war, we feel we are commanding chance, binding the uncontrollable. Few peacetime lives offer such definitive proof of meaning: there are no squares named for loving fathers; war leaders seem Destiny’s true executors.

  Generals, though, know better: war is a contest not with fate, but with another intelligence. Because the world does not care about us, we can assume it behaves according to the rules of classical probability; but war projects the power of thousands through the decision of a single mind: aware, speculative, devious. The business of a general is to know all that is in that mind—plus at least one thing more. “The enemy has three courses open to him,” said the great Prussian Field Marshal von Moltke, “and of these he will adopt the fourth.”

  Chess was devised, so Indian fables say, as a model for war. We hear of rajahs accepting single combat over the board to spare their armies, but this was rare—perhaps because they suspected that, despite its complexity, chess is still a deterministic system. There is always a best move, regardless of your opponent. If your mind were sufficiently capacious, you would be unbeatable—assuming you played White. Success in war, on the other hand, depends on the combined intentions of the combatants. A battle takes one to win and one to lose, which makes it not only a matter of forces but of mutually affecting choices. It is a new kind of uncertainty with its own, separate laws.

  “There is satiety in all things, in sleep, and love-making, in the loveliness of singing and the innocent dance. In all these things a man will strive sooner to win satisfaction than in war; but in this the Trojans cannot be glutted.” The Iliad is not just a glorious poem—it is a textbook, and was taken as such throughout the history of the ancient world. How should you defend a gate? Like Telamonian Ajax. How should you follow up an attack? Like Hector, “flame-like,” when he drove the Danaans back on their ships. How should you handle your most powerful weapon? Not, presumably, as Agamemnon handled Achilles.

  Homer presents the hero’s view of war, where to act worthily is the first aim, to act successfully the second. The Chinese general Sun Tzu produced the oldest surviving manual of war as a realist’s pursuit, where retreat is as advisable as attack and the greatest prize is to win without fighting: “Hold out baits to entice the enemy . . . If he is in superior strength, evade him. If your opponent is of choleric temper, seek to irritate him. Pretend to be weak, that he may grow arrogant. If he is taking his ease, give him no rest.” Sun Tzu’s The Art of War is much in demand at airport bookstores, perhaps because its antiquity lends the luster of antique heroism to the necessary ruses and evasions of business. It was also a favorite of Mao Zedong’s; but then strategy knows no politics.

  These two works illuminate distinct faces of war, but there are many more; more theories than campaigns, more books than battles. Every successful general eventually moves from the battlefield to the desk, where he reveals for posterity the techniques he had kept secret when in action. Xenophon has his Histories, Caesar his Commentaries, the Maréchal de Saxe his Rêveries, Frederick the Great his Instructions, and Napoleon his Maxims. Even the most prosaic commander feels he has discovered something worth passing on: Field Marshal Montgomery told the world that “there are only three rules of war. Never invade Russia. Never invade China. Never invade Russia or China.”

  War is movement—war is position; war is daring—war is planning; war is genius—war is discipline . . . and war is, as Napoleon pointed out, a study where every law has essential exceptions. Can there be something beyond all these proverbs? Is victory ever a science—something to be learned as a set of principles rather than quotations? The Roman Flavius Vegetius thought so, in part because he realized that it was training and system, rather than any innate superiority, that had allowed his countrymen to conquer the world: “Without these, what chance would the inconsiderable numbers of the Roman armies have had . . . ?” Well aware of the personal strength and bravery of the barbarians, Vegetius took a formal approach to conflict. He felt the gods favor not the hero but the legion—a structure whose collective performance outweighs the individual martial virtues of the enemy. He emphasized the unglamorous: logistics, accounts, forage, drill, entrenching. Yet he also pointed out the necessity of knowing the enemy, anticipating the opponent’s expectations, habits of thought, and choices. No matter how disciplined your legions, no matter how four-square your encampments, war is not deterministic: you choose your strategy in the knowledge that your enemy chooses, too.

  Vegetius wrote in the last century of Rome’s glory, and the violent era that followed destroyed many of the assumptions behind his rational view of warfare; particularly the belief that the purpose of war is to secure peace. If you were a Frankish knight in the tenth century, your view would be very different. Here in your tiny domain, master of a hut marginally bigger than your neighbors’, you are the only one not required to work the land; your business is the protection of those who do. Better fed, better trained, and better armed than any peasant, you lend your invulnerability to the village in return for deference and your keep; it is as if, in you, they owned a tank. Your only hope of improving your position is through seizing the cattle or harvest of the neighboring village—but it too owns a knight. But then, if it didn’t, your villagers would not be threatened and would not need to feed you—your most dangerous enemy is also the essential justification for your existence.

  Murderous struggle, pitiless, omnipresent, and perpetual—where all gain is another’s loss—was the natural state. It was only when the Crusades offered the prospect of booty beyond the neighbor’s barns that war became organized again. With that organization, and its assumption that by cooperation all could gain more than they had before, came a new concept of knightliness: the code of chivalry, adding to valor the ideals of obedience, loyalty, discipline, and self-restraint.

  To be fair, it would make little difference to a Saracen or a Slav whether the mail-encased figure hurtling toward him were inspired by mere lust for slaughter or by devotion to Christ, admiration for Lancelot or service to the Lady Odile—but within Europe, the willingness of armed men to find value in intangibles was a vital first step on the journey back to civilization. It moved violence away from the center of existence, creating that essential division between fighting and things worth fighting for. Leaders of armies, applying force for a purpose beyond plunder, became gradually more professional. By the sixteenth century, the military once more studied and aspired to the ideals of Vegetius: the “disciplines of the wars” so revered by Fluellen in Shakespeare’s Henry V. Once more, armies fought in order of battle, arranged by arms and responding to orders from a single commander. Once more, war became a matter of thought: the opposed strategies of careful minds.

  War, love, and cards—why do the three seem so related? Because they are all games: that is, they are taken as if seriously, with rules confining the scope of action, where each step depends on the wishes of someone else, and where a broad gulf gapes between success and failure. What they do not resemble, though, are the games of chance studied by Cardano, Fermat, Pascal, and Jakob Bernoulli. In these, both players put themselves at the mercy of randomness: the contest is against the gods, not each other; and the calculations determine hope and fairness, not strategy a
nd second-guessing. The early probabilists were not blind to this difference: Leibniz, correspondent of them all, said in 1710 that games combining chance with strategy “give the best representation of human life, particularly of military affairs.” He hoped that it might be possible to create a complete mathematical theory of them, but for this, as for his idea of simulating naval combat on a tabletop, he would have to wait a long time.

  Only one figure in the early history of probability tackled a problem involving strategy: the first Earl Waldegrave, who described in 1713 a card game, “Le Her,” in which two players draw cards from a shuffled deck and the higher wins. Here, one player—Pierre—deals a card to Paul and then one to himself. If Paul is unhappy with his card, he can force Pierre to exchange with him (unless Pierre holds a king, the winning card); and if Pierre is unhappy with the exchange (or with his original card), he can draw a new card from the deck—but if he draws a king, he must put it back and accept what he holds. They then turn over their cards; if there is a tie, Pierre, as dealer, wins.

  As in blackjack, there are some straightforward rules of thumb: Paul should exchange all cards lower than 7 and hold all higher; Pierre should change all cards lower than 8 and hold all higher. But what about those exact values—7 and 8? Here, the will of the opponent makes a difference: if Paul always exchanges when he draws a 7, Pierre should exchange when he holds an 8. But if Pierre always exchanges when he holds an 8, Paul gains an advantage if he never exchanges his 7. Here’s the dilemma: one player gains if the two strategies are the same, the other if they are different. How can either plan to win?

  Waldegrave realized that the problem is not in the probabilities of the draw but in the wishes of the players. Each wants the highest probability of winning regardless of the opponent; each wants to gain a certain amount, well knowing that anything better would be at the mercy of the man across the table. Waldegrave proposed, therefore, that Pierre should hold his 8 five-eighths of the time and change it three-eighths; Paul should hold his 7 three-eighths of the time and change five-eighths: a probability not of the cards but of the rules.