Zero - Charles Seife [10]
Worst of all, if you wantonly divide by zero, you can destroy the entire foundation of logic and mathematics. Dividing by zero once—just one time—allows you to prove, mathematically, anything at all in the universe. You can prove that 1 + 1 = 42, and from there you can prove that J. Edgar Hoover was a space alien, that William Shakespeare came from Uzbekistan, or even that the sky is polka-dotted. (See appendix A for a proof that Winston Churchill was a carrot.)
Multiplying by zero collapses the number line. But dividing by zero destroys the entire framework of mathematics.
There is a lot of power in this simple number. It was to become the most important tool in mathematics. But thanks to the odd mathematical and philosophical properties of zero, it would clash with the fundamental philosophy of the West.
Chapter 2
Nothing Comes of Nothing
[ THE WEST REJECTS ZERO ]
Nothing can be created from nothing.
—LUCRETIUS, DE RERUM NATURA
Zero clashed with one of the central tenets of Western philosophy, a dictum whose roots were in the number-philosophy of Pythagoras and whose importance came from the paradoxes of Zeno. The whole Greek universe rested upon this pillar: there is no void.
The Greek universe, created by Pythagoras, Aristotle, and Ptolemy, survived long after the collapse of Greek civilization. In that universe there is no such thing as nothing. There is no zero. Because of this, the West could not accept zero for nearly two millennia. The consequences were dire. Zero’s absence would stunt the growth of mathematics, stifle innovation in science, and, incidentally, make a mess of the calendar. Before they could accept zero, philosophers in the West would have to destroy their universe.
The Origin of Greek Number-Philosophy
In the beginning, there was the ratio, and the ratio was with God, and the ratio was God.*
—JOHN 1:1
The Egyptians, who had invented geometry, thought little about mathematics. For them it was a tool to reckon the passage of the days and to maintain plots of land. The Greeks had a very different attitude. To them, numbers and philosophy were inseparable, and they took both very seriously. Indeed, the Greeks went overboard when it came to numbers. Literally.
Hippasus of Metapontum stood on the deck, preparing to die. Around him stood the members of a cult, a secret brotherhood that he had betrayed. Hippasus had revealed a secret that was deadly to the Greek way of thinking, a secret that threatened to undermine the entire philosophy that the brotherhood had struggled to build. For revealing that secret, the great Pythagoras himself sentenced Hippasus to death by drowning. To protect their number-philosophy, the cult would kill. Yet as deadly as the secret that Hippasus revealed was, it was small compared to the dangers of zero.
The leader of the cult was Pythagoras, an ancient radical. According to most accounts, he was born in the sixth century BC on Samos, a Greek island off the coast of Turkey famed for a temple to Hera and for really good wine. Even by the standards of the superstitious ancient Greeks, Pythagoras’s beliefs were eccentric. He was firmly convinced that he was the reincarnated soul of Euphorbus, a Trojan hero. This helped convince Pythagoras that all souls—including those of animals—transmigrated to other bodies after death. Because of this, he was a strict vegetarian. Beans, however, were taboo, as they generate flatulence and are like the genitalia.
Pythagoras may have been an ancient New Age thinker, but he was a powerful orator, a renowned scholar, and a charismatic teacher. He was said to have written the constitution for Greeks living in Italy. Students flocked to him, and he soon acquired a retinue of followers who wanted to learn from the master.
The Pythagoreans lived according to the dicta of their leader. Among other things they believed that it is best to make love to women in the winter, but not in the summer;