Prominent features: In the Brownian chart, most changes—in fact, about 68 percent—are small. They are within one standard deviation of the average index change, zero. Mathematicians use the Greek letter sigma, σ, for standard deviation. About 95 percent of the changes are within 2σ, 98 percent within 3σ, and very, very few values are any larger. Next look at the Dow variations. The spikes are huge. Some are 10σ; one, in 1987, is 22σ. The odds of that are something less than one in 1050—so minute that the standard Gaussian tables do not even contemplate it. In other words, virtually impossible.
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