Zero - Charles Seife [31]
The new numbers didn’t catch on, even though a tenth-century pope, Sylvester II, was an admirer of them. He probably learned about the numerals during a visit to Spain and brought them back with him when he returned to Italy. But the version he learned did not have a zero—and the system would have been even less popular if it had. Aristotle still had a firm grip on the church, and its finest thinkers still rejected the infinitely large, the infinitely small, and the void. Even as the Crusades drew to a close in the thirteenth century, Saint Thomas Aquinas declared that God could not make something that was infinite any more than he could make a scholarly horse. But that implied that God was not omnipotent—a forbidden thought in Christian theology.
In 1277 the bishop of Paris, Étienne Tempier, called an assembly of scholars to discuss Aristotelianism, or rather, to attack it. Tempier abolished many Aristotelian doctrines that contradicted God’s omnipotence, such as, “God can not move the heavens in a straight line, because that would leave behind a vacuum.” (The rotating spheres caused no problem, because they still occupied the same space. It is only when you move the spheres in a line that you are forced to have a space to move the heavens into, and you are forced to have a space behind them after they move.) God could make a vacuum if he wanted. All of a sudden the void was allowed, because an omnipotent deity doesn’t need to follow Aristotle’s rules if he doesn’t want to.
Tempier’s pronouncements were not the final blow to Aristotelian philosophy, but they certainly signaled that the foundations were crumbling. The church would cling to Aristotle for a few more centuries, but the fall of Aristotle and the rise of the void and the infinite were clearly beginning. It was a propitious time for zero to arrive in the West. In the mid-twelfth century the first adaptations of al-Khowarizmi’s Aljabr were working their way through Spain, England, and the rest of Europe. Zero was on the way, and just as the church was breaking the shackles of Aristotelianism, it arrived.
Zero’s Triumph
…a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it lent to all computations put our arithmetic in the first rank of useful inventions.
—PIERRE-SIMON LAPLACE
Christianity initially rejected zero, but trade would soon demand it. The man who reintroduced zero to the West was Leonardo of Pisa. The son of an Italian trader, he traveled to northern Africa. There the young man—better known as Fibonacci—learned mathematics from the Muslims and soon became a good mathematician in his own right.
Fibonacci is best remembered for a silly little problem he posed in his book, Liber Abaci, which was published in 1202. Imagine that a farmer has a pair of baby rabbits. Babies take two months to reach maturity, and from then on they produce another pair of rabbits at the beginning of every month. As these rabbits mature and reproduce, and those rabbits mature and reproduce, and so on, how many pairs of rabbits do you have during any given month?
Well, during the first month, you have one pair of rabbits, and since they haven’t matured, they can’t reproduce.
During the second month you still have only one pair.
But at the beginning of the third month, the first pair reproduces: you’ve got two pairs.
At the beginning of the fourth month, the first pair reproduces again, but the second pair is not mature enough: three pairs.
The next month the first pair reproduces, the second pair reproduces, since it has reached maturity, but the third pair is too young. That