Drunkard's Walk - Leonard Mlodinow [25]
Gerolamo’s father was a bit of an operator. A sometime pal of Leonardo da Vinci’s, he was by profession a geometer, never a profession that brought in much cash. Fazio often had trouble making the rent, so he started a consulting business, providing the highborn with advice on law and medicine. That enterprise eventually thrived, aided by Fazio’s claim that he was descended from a brother of a fellow named Goffredo Castiglioni of Milan, better known as Pope Celestine IV. When Gerolamo reached the age of five, his father brought him into the business—in a manner of speaking. That is, he strapped a pannier to his son’s back, stuffed it with heavy legal and medical books, and began dragging the young boy to meetings with his patrons all over town. Gerolamo would later write that “from time to time as we walked the streets my father would command me to stop while he opened a book and, using my head as a table, read some long passage, prodding me the while with his foot to keep still if I wearied of the great weight.”10
In 1516, Gerolamo decided his best opportunity lay in the field of medicine and announced that he wanted to leave his family’s home in Milan and travel back to Pavia to study there. Fazio wanted him to study law, however, because then he would become eligible for an annual stipend of 100 crowns. After a huge family brawl, Fazio relented, but the question remained: without the stipend, how would Gerolamo support himself in Pavia? He began to save the money he earned reading horoscopes and tutoring pupils in geometry, alchemy, and astronomy. Somewhere along the way he noticed he had a talent for gambling, a talent that would bring him cash much faster than any of those other means.
For anyone interested in gambling in Cardano’s day, every city was Las Vegas. On cards, dice, backgammon, even chess, wagers were made everywhere. Cardano classified these games according to two types: those that involved some strategy, or skill, and those that were governed by pure chance. In games like chess, Cardano risked being outplayed by some sixteenth-century Bobby Fischer. But when he bet on the fall of a couple of small cubes, his chances were as good as anyone else’s. And yet in those games he did have an advantage, because he had developed a better understanding of the odds of winning in various situations than any of his opponents. And so for his entrée into the betting world, Cardano played the games of pure chance. Before long he had set aside over 1,000 crowns for his education—more than a decade’s worth of the stipend his father wanted for him. In 1520 he registered as a student in Pavia. Soon after, he began to write down his theory of gambling.
LIVING WHEN HE DID, Cardano had the advantage of understanding many things that had been Greek to the Greeks, and to the Romans, for the Hindus had taken the first large steps toward employing arithmetic as a powerful tool. It was in that milieu that positional notation in base ten developed, and became standard, around A.D. 700.11 The Hindus also made great progress in the arithmetic of fractions—something crucial to the analysis of probabilities, since the chances of something occurring are always less than one. This Hindu knowledge was picked up by the Arabs and eventually brought to Europe. There the first abbreviations, p for “plus” and m for “minus,” were used in the fifteenth century. The symbols + and - were introduced around the same time by the Germans, but only to indicate excess and deficient weights of chests.