Everything Is Obvious

by Duncan J. Watts

  The difficulty that we experience in trying to think about the future in terms of probabilities is the mirror image of our preference for explanations that account for known outcomes at the expense of alternative possibilities. As discussed in the previous chapter, when we look back in time, all we see is a sequence of events that happened. Yesterday it rained, two years ago Barack Obama was elected president of the United States, and so on. At some level, we understand that these events could have played out differently. But no matter how much we might remind ourselves that things might be other than they are, it remains the case that what actually happened, happened. Not 40 percent of the time or 60 percent of the time, but 100 percent of the time. It follows naturally, therefore, that when we think about the future, we care mostly about what will actually happen. To arrive at our prediction, we might contemplate a range of possible alternative futures, and maybe we even go as far as to determine that some of them are more likely than others. But at the end of the day, we know that only one such possible future will actually come to be, and we want to know which one that is.

  The relationship between our view of the past and our view of the future is illustrated in the figure on the facing page, which shows the stock price of a fictitious company over time. Looking back in time from the present, one sees the history of the stock (the solid line), which naturally traces out a unique path. Looking forward, however, all we can say about the stock price is its probability of falling within a particular range. My Yahoo! colleagues David Pennock and Dan Reeves have actually built an application that generates pictures like this one by mining data on the prices of stock options. Because the value of an option depends on the price of the underlying stock, the prices at which various options are being traded now can be interpreted as predictions about the price of the stock on the date when the option is scheduled to mature. More precisely, one can use the option prices to infer various “probability envelopes” like those shown in the figure. For example, the inner envelope shows the range of prices within which the stock is likely to fall with a 20 percent probability, while the outer envelope shows the 60 percent probability range.

  We also know, however, that at some later time, the stock price will have been revealed—as indicated by the dotted “future” trajectory. At that time, we know the hazy cloud of probabilities defined by the envelope will have been replaced by a single, certain price at each time, just like prices that we can currently see in the past. And knowing this, it’s tempting to take the next step of assuming that this future trajectory has in some cosmic sense already been determined, even if it has not yet been revealed to us. But this last step would be a mistake. Until it is actually realized, all we can say about the future stock price is that it has a certain probability of being within a certain range—not because it actually lies somewhere in this range and we’re just not sure where it is, but in the stronger sense that it only exists at all as a range of probabilities. Put another way, there is a difference between being uncertain about the future and the future itself being uncertain. The former is really just a lack of information—something we don’t know—whereas the latter implies that the information is, in principle, unknowable. The former is the orderly universe of Laplace’s demon, where if we just try hard enough, if we’re just smart enough, we can predict the future. The latter is an essentially random world, where the best we can ever hope for is to express our predictions of various outcomes as probabilities.

  Past Versus Future Stock Price

  PREDICTING WHAT TO PREDICT

  The distinction between predicting outcomes and predicting probabilities of outcomes is a fundamental one that should change our view about what kinds of predictions we can make. But there is another problem that also arises from the way we learn from the past, which is if anything even more counterintuitive—namely that we can’t know which outcomes we ought to be making predictions about in the first place. Truth be told, there is an infinitude of predictions that we could make at any given time, just as there is an infinitude of “things that happened” in the past. And just as we don’t care at all about almost all of these past events, we don’t care about almost all such potential predictions. Rather, what we care about is the very small number of predictions that, had we been able to make them correctly, might have changed things in a way that actually mattered. Had U.S. aviation officials predicted that terrorists armed with box cutters would hijack planes with the intention of flying them into the World Trade Center and the Pentagon, they could have taken preventative measures, such as strengthening cockpit doors and clamping down on airport screening, that would have averted such a threat. Likewise, had an investor known in the late 1990s that a small startup company called Google would one day grow into an Internet behemoth, she could have made a fortune investing in it.

  Looking back in history, it seems we ought to have been able to predict events like these. But what we don’t appreciate is that hindsight tells us more than the outcomes of the predictions that we could have made in the past. It also reveals what predictions we should have been making. In November of 1963, how would one have known that it was important to worry about snipers, and not food poisoning, during JFK’s visit to Dallas? How was one to know before 9/11 that the strength of cockpit doors, not the absence of bomb-sniffing dogs, was the key to preventing airplane hijackings? Or that hijacked aircraft, and not dirty bombs or nerve gas in the subway, were the main terrorist threat to the United States? How was one to know that search engines would make money from advertising and not some other business model? Or that one should even be interested in the monetization of search engines rather than content sites or e-commerce sites, or something else entirely?

  In effect, this problem is the flip side of Danto’s argument about history in the previous chapter—that what is relevant cannot be known until later. The kinds of predictions we most want to make, that is, require us to first determine which of all the things that might happen in the future will turn out to be relevant, in order that we can start paying attention to them now. It seems we ought to be able to do this, in the same way that it seems Danto’s Ideal Chronicler ought to be able to say what is going on. But if we tried to state our predictions for everything that might conceivably happen, we would immediately drown in the possibilities. Should we worry about what time the garbage truck will show up tonight? Probably not. On the other hand, if our dog gets off the leash and runs out on the street at exactly that time, we will have wished we’d known before we went for a walk. Should we attempt to predict whether our flight will be canceled? Again, probably not. But if we get bumped onto another flight that subsequently crashes, or we sit next to the person we will one day marry, that event will seem tremendously significant.

  This relevance problem is fundamental, and can’t be eliminated simply by having more information or a smarter algorithm. For example, in his book about prediction the political scientist and “predictioneer” Bruce Bueno de Mesquita extols the power of game theory to predict the outcomes of complex political negotiations.14 Given the intrinsic unpredictability of complex systems, it seems unlikely that his computer models can in fact predict what he says they can. But leaving that aside for the moment, let’s look at the larger question of what they could predict even if they worked perfectly. Take for example his claim to have successfully predicted the outcome of the 1993 Oslo Accords between Israel and the then Palestine Liberation Organization. At the time, that would have seemed like an impressive feat. But what the algorithm didn’t predict was that the Oslo Accords were, in effect, a mirage, a temporary flicker of hope that was quickly extinguished by subsequent events. From what we now know about what happened afterward, in other words, it is clear that the outcome of the Oslo negotiations wasn’t the most important outcome to have predicted in the first place.

  Of course, Bueno de Mesquita might reasonably point out that his models aren’t designed to make that sort of prediction. But that’s precisely the point: Making the right pred
iction is just as important as getting the prediction right. When we look back to the past, we do not wish that we had predicted what the search market share for Google would be in 1999, or how many days it would take for US soldiers to reach Baghdad during the second Gulf war. Those are certainly valid predictions that we might have thought to make. But at some point we would have realized that it didn’t really matter whether they were right or wrong—because they just weren’t that important. Instead we would end up wishing we’d been able to predict on the day of Google’s IPO that within a few years its stock price would peak above $500, because then we could have invested in it and become rich. We wish we’d been able to foresee the carnage that would follow the toppling of Saddam Hussein and the dismantling of his security forces, because then we could have adopted a different strategy or even avoided the whole mess in the first place.

  Even when we are dealing with more mundane types of predictions—like how consumers will respond to such and such a color or design, or whether doctors would spend more time on preventative care if they were compensated on the basis of patients’ health outcomes rather than the number and expense of their prescribed procedures—we have the same problem. These sorts of predictions seem less problematic than predictions about the next great company or the next war. But as soon as we think about why we care about these predictions, we are forced immediately to make other predictions—about the effects of the predictions we’re making now. For example, we are concerned about how customers will react to the color not because we care about the reaction per se, but because we want the product to be a success, and we think the color will matter. Likewise, we care about the reaction of doctors to incentives because we wish to control healthcare costs and ultimately design a system that provides affordable healthcare to everyone without bankrupting the country. If our prediction does not somehow help to bring about larger results, then it is of little interest or value to us. Once again, we care about things that matter, yet it is precisely these larger, more significant predictions about the future that pose the greatest difficulties.

  BLACK SWANS AND OTHER “EVENTS”

  Nowhere is this problem of predicting the things that matter more acute than for what former derivatives trader and gadfly of the financial industry Nassim Taleb calls black swans, meaning events that—like the invention of the printing press, the storming of the Bastille, and the attacks on the World Trade Center—happen rarely but carry great import when they do.15 But what makes an event a black swan? This is where matters get confusing. We tend to speak about events as if they are separate and distinct, and can be assigned a level of importance in the way that we describe natural events such as earthquakes, avalanches, and storms by their magnitude or size. As it turns out, many of these natural events are characterized not by “normal” distributions, but instead by heavily skewed distributions that range over many orders of magnitude. Heights of people, for example, are roughly normally distributed: the typical U.S. male is 5 feet 9 inches, and we essentially never see adults who are 2 feet tall or 12 feet tall. Earthquakes, by contrast, along with avalanches, storms, and forest fires, display “heavy-tailed” distributions, meaning that most are relatively small and draw little attention, whereas a small number can be extremely large.

  It’s tempting to think that historical events also follow a heavy-tailed distribution, where Taleb’s black swans lie far out in the tail of the distribution. But as the sociologist William Sewell explains, historical events are not merely “bigger” than others in the sense that some hurricanes are bigger than others. Rather, “events” in the historical sense acquire their significance via the transformations they trigger in wider social arrangements. To illustrate, Sewell revisits the storming of the Bastille on July 14, 1789, an event that certainly seems to satisfy Taleb’s definition of a black swan. Yet as Sewell points out, the event was not just the series of actions that happened in Paris on July 14, but rather encompassed the whole period between July 14 and July 23, during which Louis XVI struggled to control the insurrection in Paris, while the National Assembly at Versailles debated whether to condemn the violence or to embrace it as an expression of the people’s will. It was only after the king withdrew his troops from the outskirts of the city and traveled to Paris in contrition that the Assembly managed to assert itself, and the Bastille became an “event” in the historical sense. It’s hard to stop even there, in fact, because of course the only reason we care about the Bastille at all is because of what came next—the French Revolution, and its transformation of the notion of sovereignty from the divine right of a king, handed down by birth, to a power inherent in the people themselves. And that event included not only the days up until July 23, but also the subsequent repercussions, like the bizarre mass panic, often called the Great Fear, that gripped the provinces over the next week, and the famous legislative session that lasted the entire night of August 4, during which the entire social and political order of the old regime was dismantled.16

  The more you want to explain about a black swan event like the storming of the Bastille, in other words, the broader you have to draw the boundaries around what you consider to be the event itself. This is true not only for political events but also for “technological black swans,” like the computer, the Internet, and the laser. For example, it might be true that the Internet was a black swan, but what does that mean? Does it mean that the invention of packet-switched networks was a black swan? Or was the black swan the growth of this original network into something much larger, eventually forming what would at first be called the ARPANET and then this thing called the Internet? Was it solely the development of the physical infrastructure on which other technological innovations, such as the Web and voice-over IP, were built? Or was it that these technologies, in turn, led to new business models and modes of social interaction? Or that these developments ultimately changed the way that we discover information, share opinions, and express our identities? Presumably it is all these developments together that give the Internet its black swan status. But then the Internet isn’t really a thing at all. Rather, it’s shorthand for an entire period of history, and all the interlocking technological, economic, and social changes that happened therein.

  Much the same is true even of natural events that acquire black swan status. Hurricane Katrina, for example, was a huge storm, but it wasn’t the biggest storm we’ve ever witnessed, or even the biggest that summer. What made it a black swan, therefore, had less to do with the storm itself than it did with what happened subsequently: the failure of the levees; the flooding of large portions of the city; the slow and ineffective emergency response; the thousands of residents who were subjected to unnecessary suffering and humiliation; the more than 1,800 people who died; the hundreds of thousands more who were evacuated; the decision of many of these evacuees not to return; the economic effect on the city of New Orleans of losing a large chunk of its population; and the impression left in the public mind of a monstrous debacle, shot through with latent racial and class discrimination, administrative incompetence, and the indifference of the powerful and privileged to the weak and vulnerable. When we talk about Hurricane Katrina as a black swan, in other words, we are not speaking primarily about the storm itself, but rather about the whole complex of events that unfolded around it, along with an equally complicated series of social, cultural, and political consequences—consequences that are still playing out.

  Predicting black swans is therefore fundamentally different than predicting events like plane crashes or changes in the rate of unemployment. The latter kind of event may be impossible to predict with certainty—and hence we may have to make do with predicting probabilities of outcomes rather than the outcomes themselves—but it is at least possible to say in advance what it is that we are trying to predict. Black swans, by contrast, can only be identified in retrospect because only then can we synthesize all the various elements of history under a neat label. Predicting black swans, in other words, requires us not onl
y to see the future outcome about which we’re making a prediction but also to see the future beyond that outcome, because only then will its importance be known. As with Danto’s example from the previous chapter about Bob describing his prizewinning roses before they’ve actually won any prizes, this kind of prediction is not really prediction at all, but prophecy—the ability to foresee not only what will happen, but also what its meaning will be.17

  Nevertheless, once we know about black swans, we can’t help wishing that we had been able to predict them. And just as commonsense explanations of the past confuse stories with theories—the topic of the last chapter—so too does commonsense intuition about the future tend to conflate predictions with prophecies. When we look to the past, we see only the things that happened—not all the things that might have happened but didn’t—and as a result, our commonsense explanations often mistake for cause and effect what is really just a sequence of events. Correspondingly, when we think about the future, we imagine it to be a unique thread of events that simply hasn’t been revealed to us yet. In reality no such thread exists—rather, the future is more like a bundle of possible threads, each of which is assigned some probability of being drawn, where the best we can manage is to estimate the probabilities of the different threads. But because we know that at some point in the future, all these probabilities will have collapsed onto a single thread, we naturally want to focus on the one thread that will actually matter.