Zero by Charles Seife

numerals were not so easily dispensed with; Italian merchants continued to use them, and even used them to send encrypted messages—which is how the word cipher came to mean “secret code.”
    In the end the governments had to relent in the face of commercial pressure. The Arabic notation was allowed into Italy and soon spread throughout Europe. Zero had arrived—as had the void. The Aristotelian wall was crumbling, thanks to the influence of the Muslims and the Hindus, and by the 1400s even the staunchest European supporters of Aristotelianism had their doubts. Thomas Bradwardine, who was to become archbishop of Canterbury, tried to disprove atomism, Aristotle’s old nemesis. At the same time, he wondered whether his own logic was faulty, since he based his arguments on geometry, whose infinitely divisible lines automatically reject atomism. However, the battle against Aristotle was far from over. If Aristotle were to fall, the proof of God—a bulwark of the church—was no longer valid. A new proof was needed.
    Worse yet, if the universe were infinite, then there could be no center. How could Earth, then, be the center of the universe? The answer was found in zero.

Chapter 4
The Infinite God of Nothing
    [ THE THEOLOGY OF ZERO ]
    And new philosophy calls all in doubt,
    The element of fire is quite put out;
    The sun is lost, and th’ earth, and no man’s wit
    Can well direct him where to look for it….’
    Tis all in pieces, all coherence gone;
    All just supply, and all relation:
    Prince, subject, Father, Son, are things forgot.
    â€”J OHN D ONNE , “A N A NATOMY OF THE W ORLD ”
    Z ero and infinity were at the very center of the Renaissance. As Europe slowly awakened from the Dark Ages, the void and the infinite—nothing and everything—would destroy the Aristotelian foundation of the church and open the way to the scientific revolution.
    At first the papacy was blind to the danger. High-ranking clergymen experimented with the dangerous ideas of the void and the infinite, even though the ideas struck at the core of the ancient Greek philosophy that the church cherished so much. Zero appeared in the middle of every Renaissance painting, and a cardinal declared that the universe was infinite—boundless. However, the brief love affair with zero and infinity was not to last.
    When the church was threatened, it retreated into its old philosophy, turning back toward the Aristotelian doctrine that had supported it for so many years. It was too late. Zero had taken hold in the West, and despite the papacy’s objections, it was too strong to be exiled once more. Aristotle fell to the infinite and to the void, and so did the proof of God’s existence.
    Only one option remained for the church: accept zero and infinity. Indeed, to the devout, God could be found, hidden within the void and the infinite.
    The Nutshell Cracked
    O God, I could be bounded in a nutshell and count myself a king of infinite space, were it not that I have bad dreams.
    â€”W ILLIAM S HAKESPEARE , H AMLET
    At the beginning of the Renaissance, it was not obvious that zero would pose a threat to the church. It was an artistic tool, an infinite nothing that ushered in the great Renaissance in the visual arts.
    Before the fifteenth century, paintings and drawings were largely flat and lifeless. The images in them were distorted and two-dimensional; gigantic, flat knights peered out of tiny, misshapen castles (Figure 17). Even the best artists could not draw a realistic scene. They did not know how to use the power of zero.

    Figure 17: Flat knights and misshapen castles
    It was an Italian architect, Filippo Brunelleschi, who first demonstrated the power of an infinite zero: he created a realistic painting by using a vanishing point.
    By definition, a point is a zero—thanks to the concept of dimension. In everyday life you deal with three-dimensional objects. (Actually, Einstein revealed that