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from the list of those allowed to lecture, and accusing him of sodomy and incest, had him exiled from the province. When Cardano left Milan at the end of 1563, he wrote in his autobiography, he was “reduced once more to rags, my fortune gone, my income ceased, my rents withheld, my books impounded.”20 By that time his mind was going too, and he was given to periods of incoherence. As the final blow, a self-taught mathematician named Niccolò Tartaglia, angry because in Ars magna Cardano had revealed Tartaglia’s secret method of solving certain equations, coaxed Aldo into giving evidence against his father in exchange for an official appointment as public torturer and executioner for the city of Bologna. Cardano was jailed briefly, then quietly lived out his last few years in Rome. The Book on Games of Chance was finally published in 1663, over 100 years after young Cardano had first put the words to paper. By then his methods of analysis had been reproduced and surpassed.

CHAPTER 4

Tracking the Pathways to Success

IF A GAMBLER of Cardano’s day had understood Cardano’s mathematical work on chance, he could have made a tidy profit betting against less sophisticated players. Today, with what he had to offer, Cardano could have achieved both fame and fortune writing books like The Idiot’s Guide to Casting Dice with Suckers. But in his own time, Cardano’s work made no big splash, and his Book on Games of Chance remained unpublished until long after his death. Why did Cardano’s work have so little impact? As we’ve said, one hindrance to those who preceded him was the lack of a good system of algebraic notation. That system in Cardano’s day was improving but was still in its infancy. Another roadblock, however, had yet to be removed: Cardano worked at a time when mystical incantation was more valued than mathematical calculation. If people did not look for the order in nature and did not develop numerical descriptions of events, then a theory of the effect of randomness on those events was bound to go unappreciated. As it turned out, had Cardano lived just a few decades later, both his work and its reception might have been far different, for the decades after his death saw the unfolding of historic changes in European thought and belief, a transformation that has traditionally been dubbed the scientific revolution.

The scientific revolution was a revolt against a way of thinking that was prevalent as Europe emerged from the Middle Ages, an era in which people’s beliefs about the way the world worked were not scrutinized in any systematic manner. Merchants in one town stole the clothes off a hanged man because they believed it would help their sales of beer. Parishioners in another believed illness could be cured by chanting sacrilegious prayers as they marched naked around their church altar.1 One trader even believed that relieving himself in the “wrong” toilet would bring bad fortune. Actually he was a bond trader who confessed his secret to a CNN reporter in 2003.2 Yes, some people still adhere to superstitions today, but at least today, for those who are interested, we have the intellectual tools to prove or disprove the efficacy of such actions. But if Cardano’s contemporaries, say, won at dice, rather than analyzing their experience mathematically, they would say a prayer of thanks or refuse to wash their lucky socks. Cardano himself believed that streaks of losses occur because “fortune is averse” and that one way to improve your results is to give the dice a good hard throw. If a lucky 7 is all in the wrist, why stoop to mathematics?

The moment that is often considered the turning point for the scientific revolution came in 1583, just seven years after Cardano’s death. That is when a young student at the University of Pisa sat in a cathedral and, according to legend, rather than listening to the services, stared at something he found far more intriguing: the swinging of a large hanging lamp. Using his pulse as a timer, Galileo Galilei noticed that the lamp seemed to take the same amount of time to swing through