Zero - Charles Seife [19]
There was a problem, though. It is not so easy to reject both infinity and zero. Look back through time. Events have happened throughout history, but if there is no such thing as infinity, there cannot be an infinite number of events. Thus, there must be a first event: creation. But what existed before creation? Void? That was unacceptable to Aristotle. Conversely, if there was not a first event, then the universe must have always existed—and will always exist in the future. You’ve got to have either infinity or zero; a universe without both of them makes no sense.
Aristotle hated the idea of the void so much that he chose the eternal, infinite universe over one that had a vacuum in it; he said that the eternity of time was a “potential” infinity like Zeno’s infinite subdivisions. (It was a stretch, but many scholars bought the argument; some even chose the creation story as further evidence for God. Medieval philosophers and theologians were doomed to battle over this puzzle for several hundred years.)
The Aristotelian view of physics, as wrong as it was, was so influential that for more than a millennium it eclipsed all opposing views, including more realistic ones. Science would never progress until the world discarded Aristotle’s physics—along with Aristotle’s rejection of Zeno’s infinities.
For all his wit, Zeno got himself into serious trouble. Around 435 BC, he conspired to overthrow the tyrant of Elea, Nearchus. He was smuggling arms to support the cause. Unfortunately for Zeno, Nearchus found out about the plot, and Zeno was arrested. Hoping to discover who the coconspirators were, Nearchus had Zeno tortured. Soon Zeno begged the torturers to stop and promised that he would name his colleagues. When Nearchus drew near, Zeno insisted that the tyrant come closer, since it was best to keep the names a secret. Nearchus leaned over, tilting his head toward Zeno. All of a sudden Zeno sank his teeth into Nearchus’s ear. Nearchus screamed, but Zeno refused to let go. The torturers could only force Zeno to let go by stabbing him to death. Thus died the master of the infinite.
Eventually, one ancient Greek surpassed Zeno in matters of the infinite: Archimedes, the eccentric mathematician of Syracuse. He was the only thinker of his day to glimpse the infinite.
Syracuse was the richest city on the island of Sicily, and Archimedes was its most famous resident. Little is known about his youth, but it seems that Archimedes was born around 287 BC in Samos, Pythagoras’s birthplace. He then immigrated to Syracuse, where he solved engineering problems for the king. It was the king of Syracuse who asked Archimedes to determine whether his crown was pure gold or had been mixed with lead, a task beyond the abilities of all the scientists at the time. However, when Archimedes settled into a tub of water, he noticed that the water flowed over the sides, and he suddenly realized that he could measure the density of the crown, and thus its purity, by submerging it in a tub of water and measuring how much water it displaced. Elated by the insight, Archimedes leapt out of the tub and ran through the streets of Syracuse shouting, “Eureka! Eureka!” Of course Archimedes forgot that he was stark naked.
Archimedes’ talents were useful to the Syracusan military as well. In the third century BC the era of Greek hegemony was over. Alexander’s empire had collapsed