The Better Angels of Our Nature: Why Vio - By Steven Pinker Page 0,125

. . beep . . . beepbeep . . . beepitybeepitybeepbeepbeep.” They didn’t appreciate that that’s what randomness sounds like.

This cognitive illusion was first noted in 1968 by the mathematician William Feller in his classic textbook on probability: “To the untrained eye, randomness appears as regularity or tendency to cluster.”33 Here are a few examples of the cluster illusion.

The London Blitz. Feller recounts that during the Blitz in World War II, Londoners noticed that a few sections of the city were hit by German V-2 rockets many times, while others were not hit at all. They were convinced that the rockets were targeting particular kinds of neighborhoods. But when statisticians divided a map of London into small squares and counted the bomb strikes, they found that the strikes followed the distribution of a Poisson process—the bombs, in other words, were falling at random. The episode is depicted in Thomas Pynchon’s 1973 novel Gravity’s Rainbow, in which statistician Roger Mexico has correctly predicted the distribution of bomb strikes, though not their exact locations. Mexico has to deny that he is a psychic and fend off desperate demands for advice on where to hide.

The gambler’s fallacy. Many high rollers lose their fortunes because of the gambler’s fallacy: the belief that after a run of similar outcomes in a game of chance (red numbers in a roulette wheel, sevens in a game of dice), the next spin or toss is bound to go the other way. Tversky and Kahneman showed that people think that genuine sequences of coin flips (like TTHHTHTTTT) are fixed, because they have more long runs of heads or of tails than their intuitions allow, and they think that sequences that were jiggered to avoid long runs (like HTHTTHTHHT) are fair.34

The birthday paradox. Most people are surprised to learn that if there are at least 23 people in a room, the chances that two of them will share a birthday are better than even. With 57 people, the probability rises to 99 percent. In this case the illusory clusters are in the calendar. There are only so many birthdays to go around (366), so a few of the birthdays scattered throughout the year are bound to fall onto the same day, unless there was some mysterious force trying to separate them.

Constellations. My favorite example was discovered by the biologist Stephen Jay Gould when he toured the famous glowworm caves in Waitomo, New Zealand. 35 The worms’ pinpricks of light on the dark ceiling made the grotto look like a planetarium, but with one difference: there were no constellations. Gould deduced the reason. Glowworms are gluttonous and will eat anything that comes within snatching distance, so each worm gives the others a wide berth when it stakes out a patch of ceiling. As a result, they are more evenly spaced than stars, which from our vantage point are randomly spattered across the sky. Yet it is the stars that seem to fall into shapes, including the ram, bull, twins, and so on, that for millennia have served as portents to pattern-hungry brains. Gould’s colleague, the physicist Ed Purcell, confirmed Gould’s intuition by programming a computer to generate two arrays of random dots. The virtual stars were plonked on the page with no constraints. The virtual worms were given a random tiny patch around them in which no other worm could intrude. They are shown in figure 5–5; you can probably guess which is which. The one on the left, with the clumps, strands, voids, and filaments (and perhaps, depending on your obsessions, animals, nudes, or Virgin Marys) is the array that was plotted at random, like stars. The one on the right, which seems to be haphazard, is the array whose positions were nudged apart, like glowworms.

Richardson’s data. My last example comes from another physicist, our friend Lewis Fry Richardson. These are real data from a naturally occurring phenomenon. The segments in figure 5–6 represent events of various durations, and they are arranged from left to right in time and from bottom to top in magnitude. Richardson showed that the events are governed by a Poisson process: they stop and start at random. Your eye may discern some patterns—for example, a scarcity of segments at the top left, and the two floaters at the top right. But by now you have learned to distrust these apparitions. And indeed Richardson showed that there was no statistically significant trend in the distribution of magnitudes from the beginning of the sequence to the end.