Zero - Charles Seife [33]
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.
—WILLIAM SHAKESPEARE, HAMLET
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 our world is four-dimensional, as we shall see in a later chapter.) The clock on your dresser, the cup of coffee you drink in the morning, the book you’re reading right now—all these are three-dimensional objects. Now imagine that a giant hand comes down and squashes the book flat. Instead of being a three-dimensional object, the book is now a flat, floppy rectangle. It has lost a dimension; it has length and width, but no height. It is now two-dimensional. Now imagine that the book, turned sideways, is crushed once again by the giant hand. The book is no longer a rectangle. It is a line. Again, it has lost a dimension; it has neither height nor width, but it has length. It is a one-dimensional object. You can take away even this single dimension. Squashed along its length, the line becomes a point, an infinitesimal nothing with no length, no width, and no height. A point is a zero-dimensional object.
In 1425, Brunelleschi placed just such a point in the center of a drawing of a famous Florentine building, the Baptistery. This zero-dimensional object, the vanishing point, is an infinitesimal dot on the canvas that represents a spot infinitely far away from the viewer (Figure 18). As objects recede into the distance in the painting, they get closer and closer to the vanishing point, getting more compressed as they get farther away from the viewer. Everything sufficiently distant—people, trees, buildings—is squashed into a zero-dimensional point and disappears. The zero in the center of the painting contains an infinity of space.
This apparently contradictory object turned Brunelleschi’s drawing, almost magically, into such a good likeness of the three-dimensional Baptistery building that it was indistinguishable from the real thing. Indeed, when Brunelleschi used a mirror to compare the painting and the building, the reflected image matched the building’s geometry exactly. The vanishing point turned a two-dimensional drawing