The Drunkard’s Walk (LEONARD MLODINOW) | Part A’

The Drunkard’s Walk (LEONARD MLODINOW) | Part A’

In 1814, near the height of the great successes of Newtonian physics, Pierre-Simon de Laplace wrote:
If an intelligence, at a given instant, knew all the forces that animate nature and the position of each constituent being; if, moreover, this intelligence were sufficiently great to submit these data to analysis, it could embrace in the same formula the movements of the greatest bodies in the universe and those of the smallest atoms: to this intelligence nothing would be uncertain, and the future, as the past, would be present to its eyes.
Laplace was expressing a view called determinism: the idea that the state of the world at the present determines precisely the manner in which the future will unfold.
In everyday life, determinism implies a world in which our personal qualities and the properties of any given situation or environment lead directly and unequivocally to precise consequences. That is an orderly world, one in which everything can be foreseen, computed, predicted. But for Laplace’s dream to hold true, several conditions must be met. First, the laws of nature must dictate a definite future, and we must know those laws. Second, we must have access to data that completely describe the system of interest, allowing no unforeseen influences. Finally, we must have sufficient intelligence or computing power to be able to decide what, given the data about the present, the laws say the future will hold. In this book we’ve examined many concepts that aid our understanding of random phenomena. Along the way we’ve gained insight into a variety of specific life situations. Yet there remains the big picture, the question of how much randomness contributes to where we are in life and how well we can predict where we are going.
In the study of human affairs from the late Renaissance to the Victorian era, many scholars shared Laplace’s belief in determinism. They felt as Galton did that our path in life is strictly determined by our personal qualities, or like Quételet they believed that the future of society is predictable.
Often they were inspired by the success of Newtonian physics and believed that human behavior could be foretold as reliably as other phenomena in nature. It seemed reasonable to them that the future events of the everyday world should be as rigidly determined by the present state of affairs as are the orbits of the planets.
In the 1960s a meteorologist named Edward Lorenz sought to employ the newest technology of his day—a primitive computer—to carry out Laplace’s program in the limited realm of the weather. That is, if Lorenz supplied his noisy machine with data on the atmospheric conditions of his idealized earth at some given time, it would employ the known laws of meteorology to calculate and print out rows of numbers representing the weather conditions at future times.
One day, Lorenz decided he wanted to extend a particular simulation further into the future. Instead of repeating the entire calculation, he decided to take a shortcut by beginning the calculation midway through. To accomplish that, he employed as initial conditions data printed out in the earlier simulation. He expected the computer to regenerate the remainder of the previous simulation and then carry it further. But instead he noticed something strange: the weather had evolved differently. Rather than duplicating the end of the previous simulation, the new one diverged wildly. He soon recognized why: in the computer’s memory the data were stored to six decimal places, but in the printout they were quoted to only three. As a result, the data he had supplied were a tiny bit off. A number like 0.293416, for example, would have appeared simply as 0.293.
Scientists usually assume that if the initial conditions of a system are altered slightly, the evolution of that system, too, will be altered slightly. After all, the satellites that collect weather data can measure parameters to only two or three decimal places, and so they cannot even track a difference as tiny as that between 0.293416 and 0.293. But Lorenz found that such small differences led to massive changes in the result. The phenomenon was dubbed the butterfly effect, based on the implication that atmospheric changes so small they could have been caused by a butterfly flapping its wings can have a large effect on subsequent global weather patterns. That notion might sound absurd—the equivalent of the extra cup of coffee you sip one morning leading to profound changes in your life. But actually that does happen—for instance, if the extra time you spent caused you to cross paths with your future wife at the train station or to miss being hit by a car that sped through a red light. In fact, Lorenz’s story is itself an example of the butterfly effect, for if he hadn’t taken the minor decision to extend his calculation employing the shortcut, he would not have discovered the butterfly effect, a discovery which sparked a whole new field of mathematics. When we look back in detail on the major events of our lives, it is not uncommon to be able to identify such seemingly inconsequential random events that led to big changes.
Determinism in human affairs fails to meet the requirements for predictability alluded to by Laplace for several reasons. First, as far as we know, society is not governed by definite and fundamental laws in the way physics is. Instead, people’s behavior is not only unpredictable, but as Kahneman and Tversky repeatedly showed, also often irrational (in the sense that we act against our best interests). Second, even if we could uncover the laws of human affairs, as Quételet attempted to do, it is impossible to precisely know or control the circumstances of life. That is, like Lorenz, we cannot obtain the precise data necessary for making predictions. And third, human affairs are so complex that it is doubtful we could carry out the necessary calculations even if we understood the laws and possessed the data. As a result, determinism is a poor model for the human experience. Or as the Nobel laureate Max Born wrote, “Chance is a more fundamental conception than causality.”
In the scientific study of random processes the drunkard’s walk is the archetype. In our lives it also provides an apt model, for like the granules of pollen floating in the Brownian fluid, we’re continually nudged in this direction and then that one by random events. As a result, although statistical regularities can be found in social data, the future of particular individuals is impossible to predict, and for our particular achievements, our jobs, our friends, our finances, we all owe more to chance than many people realize. On the following pages, I shall argue, furthermore, that in all except the simplest real-life endeavors unforeseeable or unpredictable forces cannot be avoided, and moreover those random forces and our reactions to them account for much of what constitutes our particular path in life. I will begin my argument by exploring an apparent contradiction to that idea: if the future is really chaotic and unpredictable, why, after events have occurred, does it often seem as if we should have been able to foresee them?
In any complex string of events in which each event unfolds with some element of uncertainty, there is a fundamental asymmetry between past and future. This asymmetry has been the subject of scientific study ever since Boltzmann made his statistical analysis of the molecular processes responsible for the properties of fluids. Imagine, for example, a dye molecule floating in a glass of water. The molecule will, like one of Brown’s granules, follow a drunkard’s walk. But even that aimless movement makes progress in some direction. If you wait three hours, for example, the molecule will typically have traveled about an inch from where it started. Suppose that at some point the molecule moves to a position of significance and so finally attracts our attention. As many did after Pearl Harbor, we might look for the reason why that unexpected event occurred.
Now suppose we dig into the molecule’s past. Suppose, in fact, we trace the record of all its collisions. We will indeed discover how first this bump from a water molecule and then that one propelled the dye molecule on its zigzag path from there to here. In hindsight, in other words, we can clearly explain why the past of the dye molecule developed as it did. But the water contains many other water molecules that could have been the ones that interacted with the dye molecule. To predict the dye molecule’s path beforehand would have therefore required us to calculate the paths and mutual interactions of all those potentially important water molecules. That would have involved an almost unimaginable number of mathematical calculations, far greater in scope and difficulty than the list of collisions needed to understand the past. In other words, the movement of the dye molecule was virtually impossible to predict before the fact even though it was relatively easy to understand afterward.
That fundamental asymmetry is why in day-to-day life the past often seems obvious even when we could not have predicted it. It’s why weather forecasters can tell you the reasons why three days ago the cold front moved like this and yesterday the warm front moved like that, causing it to rain on your romantic garden wedding, but the same forecasters are much less successful at knowing how the fronts will behave three days hence and at providing the warning you would have needed to get that big tent ready. Or consider a game of chess. Unlike card games, chess involves no explicit random element. And yet there is uncertainty because neither player knows for sure what his or her opponent will do next. If the players are expert, at most points in the game it may be possible to see a few moves into the future; if you look out any further, the uncertainty will compound, and no one will be able to say with any confidence exactly how the game will turn out. On the other hand, looking back, it is usually easy to say why each player made the moves he or she made. This again is a probabilistic process whose future is difficult to predict but whose past is easy to understand.

 

The Drunkard’s Walk
LEONARD MLODINOW



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