Jack

“Finally, power-law distributions have “thick tails,” meaning that they have a nonnegligible number of extreme values. You will never meet a 20-foot man, or see a car driving down the freeway at 500 miles per hour. But you could conceivably come across a city of 14 million, or a book that was on the bestseller list for 10 years, or a moon crater big enough to see from the earth with the naked eye—or a war that killed 55 million people.”
― Steven Pinker, The Better Angels of Our Nature: Why Violence Has Declined

“In theory, Mars could oscillate, causing a war on 3 percent of his throws, then shifting to causing a war on 6 percent, and then going back again. In practice, it isn’t easy to distinguish cycles in a nonstationary Poisson process from illusory clusters in a stationary one. A few clusters could fool the eye into thinking that the whole system waxes and wanes (as in the so-called business cycle, which is really a sequence of unpredictable lurches in economic activity rather than a genuine cycle with a constant period).”
― Steven Pinker, The Better Angels of Our Nature: Why Violence Has Declined

“Suppose you live in a place that has a constant chance of being struck by lightning at any time throughout the year. Suppose that the strikes are random: every day the chance of a strike is the same, and the rate works out to one strike a month. Your house is hit by lightning today, Monday. What is the most likely day for the next bolt to strike your house? The answer is “tomorrow,” Tuesday. That probability, to be sure, is not very high; let’s approximate it at 0.03 (about once a month). Now think about the chance that the next strike will be the day after tomorrow, Wednesday. For that to happen, two things have to take place. First lightning has to strike on Wednesday, a probability of 0.03. Second, lightning can’t have struck on Tuesday, or else Tuesday would have been the day of the next strike, not Wednesday. To calculate that probability, you have to multiply the chance that lightning will not strike on Tuesday (0.97, or 1 minus 0.03) by the chance that lightning will strike on Wednesday (0.03), which is 0.0291, a bit lower than Tuesday’s chances. What about Thursday? For that to be the day, lightning can’t have struck on Tuesday (0.97) or on Wednesday either (0.97 again) but it must strike on Thursday, so the chances are 0.97 × 0.97 × 0.03, which is 0.0282. What about Friday? It’s 0.97 × 0.97 × 0.97 × 0.03, or 0.274. With each day, the odds go down (0.0300 . . . 0.0291 . . . 0.0282 . . . 0.0274), because for a given day to be the next day that lightning strikes, all the previous days have to have been strike-free, and the more of these days there are, the lower the chances are that the streak will continue. To be exact, the probability goes down exponentially, accelerating at an accelerating rate. The chance that the next strike will be thirty days from today is 0.9729 × 0.03, barely more than 1 percent.”
― Steven Pinker, The Better Angels of Our Nature: Why Violence Has Declined

“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.”
― Steven Pinker, The Better Angels of Our Nature: Why Violence Has Declined