Zero - Charles Seife [34]
Figure 18: The vanishing point
It is no coincidence that zero and infinity are linked in the vanishing point. Just as multiplying by zero causes the number line to collapse into a point, the vanishing point has caused most of the universe to sit in a tiny dot. This is a singularity, a concept that became very important later in the history of science—but at this early stage, mathematicians knew little more than the artists about the properties of zero. In fact, in the fifteenth century, artists were amateur mathematicians. Leonardo da Vinci wrote a guide to drawing in perspective. Another of his books, about painting, warns, “Let no one who is not a mathematician read my works.” These mathematician-artists perfected the technique of perspective and could soon depict arbitrary objects in three dimensions. No longer would artists be restricted to flat likenesses. Zero had transformed the art world.
Zero was, quite literally, at the center of Brunelleschi’s painting. The church, too, dabbled with zero and the infinite, though church doctrine was still dependent on Aristotelian ideas. A contemporary of Brunelleschi, a German cardinal named Nicholas of Cusa, looked at infinity and promptly declared, “Terra non est centra mundi”: the earth is not the center of the universe. The church didn’t yet realize how dangerous, how revolutionary, that idea was.
One of the old declarations of the medieval Aristotelian doctrine—as strong as the ban on the vacuum—was the statement that Earth was unique. It was at the universe’s very center. Earth’s special position at the center of the universe made it the only world capable of containing life, as Aristotle held that all objects sought out their proper place. Heavy objects, like rocks or people, belonged on the ground; light objects, like air, belonged in the heavens. Not only did this imply that the planets—in the heavens—were made of light, airy stuff, but it also meant that any people in the heavens would naturally fall to Earth. Thus creatures could only inhabit the nutmeat in the center of the nutshell cosmos. Having other planets with life on them was as silly as having a sphere with two centers.
When Tempier declared that the omnipotent God could create a vacuum if he so desired, Tempier insisted that God could break any Aristotelian law. God could create life on other worlds if he wished. There could be thousands of other Earths, each teeming with creatures; it was certainly within God’s power, whether Aristotle agrees or not.
Nicholas of Cusa was bold enough to say that God must have done so. “The regions of the other stars are similar to this,” he said, “for we believe that none of them is deprived of inhabitants.” The sky was littered with an infinite number of stars. The planets glowed in the heavens; the moon and the sun each glowed with light. Why couldn’t the stars in the sky be planets or moons or suns on their own? Maybe Earth glows brightly in their heavens, just as they glow in ours. Nicholas was sure that God had, indeed, created an infinite number of other worlds. Earth was no longer at the center of the universe. Yet Nicholas was not declared a heretic, and the church didn’t react to the new idea.
In the meantime another Nicholas turned Cusa’s philosophy into a scientific theory. Nicolaus Copernicus showed that Earth is not the center of the universe. It revolves around the sun.
A Polish monk and a physician, Copernicus learned mathematics so he could cast astrological tables, the better to cure his patients with. Along the way, Copernicus’s dabblings with the planets and stars showed him how complicated the old Greek system of tracking the planets was. Ptolemy’s clockwork heavens—with Earth at the center—were extremely accurate. However, they were terribly complex. Planets course around the sky throughout the year, but every so often they stop, move backward, and then shoot ahead once more. To account for the planets’ bizarre behavior, Ptolemy added epicycles to his planetary clockwork: little circles