Two sequences with the same distribution of individual observations can produce different cumulative excursions because their temporal ordering and dependence differ.

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But great theories are often humbled by mere facts. It was not that simple. Looking up Hearst's papers revealed that his point had not been the size of the variations, but the precise sequence of them. If jumbled up and taken out of their original sequence, his data yielded nothing special at all, a boring bell curve. Now I was hooked. When studying cotton, there had been obvious correlations between past and future prices. I mentioned this at the time, but I could not develop it further. Therefore, I had pushed the precise sequence of prices aside for later study, working as if each had been independent from the last. Hearst's research posed yet another mystery. As a valuable added charm, it was a truly ancient one, as old as the pyramids. How much does the past shape the future? A moral philosopher would phrase it this way. Is it fate that determines our course, or do we choose our paths afresh with each new decision? A mathematician trades in another terminology.

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And Harry's biggest gain was 8 And his worst loss was 3 The range from best to worst score was 11 Now say the game goes on 100 times longer For 10,000 tosses The formula says the range should be about 10 times greater Or 110 Now, the theory suggests Harry's best score might be 67 And his worst, minus 43 So, taking the cue from Harry a hydraulic engineer can make a few simple calculations. Say he wants to replace a 25-year-old dam with a higher one, proof against 100 years of flood. The timescale of the new dam is four times that of the old. So, if conventional math applies, the new dam should be twice as high as the old, tidy and simple, but also wrong. In fact, the dam should be higher than that, Hurst concluded. He found the range from highest Nile flood to lowest widened faster than the coin-tossing rule predicted. The highs were higher, the lows lower. But the problem was not the individual floods. Look at Singley. The bell curve fit the data on each year's flooding reasonably well.