In 1494 Luca Pacioli, in a fat Venetian book of arithmetic for merchants, gave a rule for how long money takes to double: divide 72 by the rate of interest. At six percent, twelve years. He did not say why it worked, which is usually taken to mean it was already old. Nobody could have said why. The reason sits in the natural logarithm of 2, and logarithms were not published until 1614, a hundred and twenty years after the book. The honest number is nearer 69, but 69 divides by almost nothing, and 72 splits cleanly by 2, 3, 4, 6, 8, 9 and 12, and at the sort of rates merchants actually charged it happens to land closer to the truth anyway. So the rule was picked for being easy to do in your head, and turned out more accurate because of who would be using it. It worked for more than a century before anyone could explain it, and it has never needed the explanation to keep working.