Chances Are (39 page)

“People aren't used to thinking about a range of possible events that could happen normally—they tend to divide things between the unimportant and the catastrophic. They have to think more probabilistically about risk management. In finance, you don't make a point forecast for exchange rates six months ahead: instead, you talk about a
range
of movement with a
percentage
of likelihood. If you can think this way about all kinds of risk, it makes the world as a whole a less risky place, because you accept that the unusual is within the range of probability. Otherwise you're committing to a guess—and the one sure thing about a guess is that it will be erroneous.”

Schauble has no use for forecasting (“We had a forecaster for a while: he was neither consistently right nor consistently wrong—either of which would have been preferable”) because he deals in smoothing out variation. Long series of recorded data provide all he needs to know about volatility, and his clients are prepared to pay a little from the surplus of good years to reduce the loss in bad. For some enterprises, though, accurate prediction of this year's weather could be essential to business decisions.

California's southern San Joaquin valley is a one-crop district—something you might guess if you drove through the town of Raisin on a September afternoon. Out in the vineyards, paper trays laid out between the rows hold the year's harvest: more than $400 million worth—99 percent of the state's crop—by far the largest single collection of raisins in the world. It takes three weeks of sunshine to dry out a Thompson's Seedless; if you fear that rain is on the way during that crucial period, you could decide to sell your grapes off the vine for juice. The profit would be smaller, but certain. What should you do?

This decision links to the broader question of how to calculate risk and advantage from random events. Its treatment dates back to the solution proposed in 1738 by Daniel Bernoulli to the Saint Petersburg Paradox, a problem first described by his cousin Nicholas in 1718. The paradox is easily stated: A lunatic billionaire proposes a coin-flipping game in which tails pays you nothing, but the first head to come up will pay you 2
ⁿ
ducats—where
n
is the number of the flip on which heads first appeared. How much should you pay to join the game? Your expectation should be the chance of the payout times the amount of the payoff. In this case, the first flip has probability 1/2 and a payment of 2 ducats, so your expectation for it is 1 ducat; the second has a probability of 1/4, a payout of 4, an expectation of 1 ducat; and so on. Your expectation of the game as a whole, therefore, is 1 + 1 + 1 + 1 + ... in fact, it's infinite. Should you therefore pay an infinite number of ducats to make the bet even? You would have to be even more deranged than your opponent.

Daniel Bernoulli's solution was to propose that money, although it adds up like the counting numbers, does not grow linearly in
meaning
as its sum increases. If the billionaire proposed either to pay you one dollar or to flip a coin double or quits, you (and most people) would take your chance on winning two dollars. If instead the billionaire proposed to pay you one
million
or give you a 1-in-2 chance at two million, you, like most people, would swallow hard, probably thinking of what they would say at home if you came back empty-handed. Money's value in calculations of probability is based on what you could do with it—its
utility
, to use the term favored by economists. When the financier John Jacob Astor comforted a friend after the Panic of 1837 by saying, “A man who has a million dollars is as well off as if he were rich,” he was making a subtle point: the
marginal utility
of wealth over that sum was small. So if you assume that there is some term that expresses the diminishing marginal utility of money as it increases, then you should multiply your expectation from each of the games in the Saint Petersburg series by that term: the result is a finite stake for the game.

Information also has marginal utility for all transactions that depend on uncertainty. If you are a raisin farmer, the accuracy of the weather forecast can have enormous marginal utility, because it moves your decision—whether to sell now for grape juice or go for the full shrivel—out of the realm of coin flipping and into sensible risk management. You could even take the probability figure for rain and use it to calculate which proportion of the harvest to bank as juice and thus cover the extra costs of protecting the remainder from rain on its journey to raisinhood. The problem is that the marginal utility of information is also a function of how many people have it. Fresno County, home to some 70 percent of the crop, is not a big place: every vineyard is subject to the same weather. Demand, whether for raisins or grape juice, is not fathomless. So in fact, the market price of juice or raisins depends in part on at least a few growers' having bet the wrong way on the weather. If
all
raisin growers had access to a perfect three-week forecast and thus made the “right” decision every time, supplies would rise, prices would fall, and the industry as a whole be out of pocket.

Fate, it seems, justifies a premium for business dependent on the weather—and for some this premium, in turn, justifies a stubborn insistence on letting fate do its worst. No French
appellation contrôlée
allows the farmer to irrigate in times of drought. Most forbid using black plastic mulches to keep down weeds and warm the soil. Rules closely circumscribe rootstocks, fungicides, and winemaking techniques—all in the name of
terroir,
the mystical union of microclimate and geology that makes a Chablis
grand cru
distinguishable from a Catawba super-Chard. Such a self-denying regime may indeed be essential to assure the subtle evocation of time and place that French wine achieves at its best; but there is also the argument that only by allowing the weather to wash out the Cabernet in '97 and frizzle the Merlot in '03 can the industry justify the prices it asks when everything miraculously comes out right. Nothing in this business—not pricing, not information, not the weather itself—has a normal distribution. Things do not settle to the average; the system remains resolutely non-linear.

 

Ed Lorenz said that the upper bound for dependable forecasting is ten days. Of course, our biggest worry now is about dependable forecasting for the next hundred years. The old meteorological saw says, “Climate is what you expect; weather is what you get”—but even climatic expectation is shot through with uncertainty.

Back in 1939,
Time
magazine breezily mentioned that “gaffers who claim that winters were harder when they were boys are quite right . . . Weathermen have no doubt that the world at least for the time being is growing warmer.” This improving climate seemed another of fate's gifts to America, favorite among nations. Life was becoming daily richer and more convenient—why not the weather? Who wouldn't welcome the idea of palm trees in Maine? So why are we worried now? Because we begin to have an inkling of the dynamics of climatic change—just enough to see how little positive control we have over it.

Climate is a human invention: an “average” of a system that does not tend to averages. Like rippling water in a stream, climate moves in reaction to many superimposed forces. Recurring ice ages seem related to wobbles in our orbit. The Sun itself varies in its radiant energy. Populations of living things, like the phytoplankton at the base of the ocean's food chain, go through their own chaotic trajectories of growth and collapse. The Southern Oscillator, source of El Niño events, knocks the regularity of tropical weather off center every four or five years. Volcanoes periodically call off every meteorological bet: one in New Guinea in the sixth century blotted out the sun for months, drawing a final line under the Roman Empire; Tambora in Indonesia canceled summer in 1816; and the great magma chamber under Yellowstone will one day blow its lid and make all human worries seem comparatively trivial. Each of these independent forces pulses at a different rate, enforcing or retarding the effects of the others on our climate. And then there's us, burning our coal and oil, reversing, in a couple of centuries, millions of years of carbon absorption by ancient plants.

Time
was right: things are getting warmer. Global average temperatures have gone up about 0.6°C over the twentieth century; mean sea level has risen around seven inches as the warmer water expands and as melting glaciers and ice caps add their long-hoarded substance to the liquid ocean. The mean, though, is a fiction; things are warming up much faster in the high subarctic latitudes while areas of the North Pacific are actually cooling. We also know that change, when it happens, happens fast: ice cores, tree rings, lake sediments all reveal past major climate shifts occurring within a geological blink.

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.