Zero - Charles Seife [36]
Despite the church’s Counter-Reformation, the new philosophy wasn’t easily destroyed. It got stronger as time went on, thanks to the investigations of Copernicus’s successors. In the beginning of the seventeenth century, another astrologer-monk, Johannes Kepler, refined Copernicus’s theory, making it even more accurate than the Ptolemaic system. Instead of moving in circles, the planets, including Earth, moved in ellipses around the sun. This explained the motion of the planets in the heavens with incredible accuracy; no longer could astronomers object that the heliocentric system was inferior to the geocentric one. Kepler’s model was simpler than Ptolemy’s, and it was more accurate. Despite the church’s objections, Kepler’s heliocentric system would prevail eventually, because Kepler was right and Aristotle was wrong.
The church attempted to patch the holes in the old way of thought, but Aristotle, the geocentric world, and the feudal way of life were all mortally wounded. Everything that philosophers had taken for granted for millennia was called into doubt. The Aristotelian system could not be trusted, and at the same time it could not be rejected. What, then, could be taken for granted? Literally nothing.
Zero and the Void
I am in a sense something intermediate between God and nought.
—RENÉ DESCARTES, DISCOURSE ON METHOD
Zero and the infinite were at the very center of the philosophical war taking place during the sixteenth and seventeenth centuries. The void had weakened Aristotle’s philosophy, and the idea of an infinitely large cosmos helped shatter the nutshell universe. The earth could not be at the center of God’s creation. As the papacy lost its hold on its flock, the Catholic Church tried to reject zero and the void more strongly than ever, yet zero had already taken root. Even the most devout intellectuals—the Jesuits—were torn between the old, Aristotelian ways and the new philosophies that included zero and the void, infinity and the infinite.
René Descartes was trained as a Jesuit, and he, too, was torn between the old and the new. He rejected the void but put it at the center of his world. Born in 1596 in the middle of France, Descartes would bring zero to the center of the number line, and he would seek a proof of God in the void and the infinite. Yet Descartes could not reject Aristotle entirely; he was so afraid of the void that he denied its existence.
Like Pythagoras, Descartes was a mathematician-philosopher; perhaps his most lasting legacy was a mathematical invention—what we now call Cartesian coordinates. Anyone who has taken geometry in high school has seen them: they are the sets of numbers in parentheses that represent a point in space. For instance, the symbol (4, 2) represents a point four units to the right and two units upward. But to the right and upward of what? The Origin. Zero (Figure 20).
Descartes realized that he could not start his two reference lines, or axes, with the number 1. That would lead to an error like the one Bede encountered when revamping the calendar. However, unlike Bede, he lived in a Europe where Arabic numerals were common, so he started counting with zero. At the very center of the coordinate system—where the two axes cross—sits a zero. The origin, the point (0, 0), is the foundation of the Cartesian system of coordinates. (Descartes’s notation was slightly different from what we use today. For one thing, he didn’t extend his coordinate system to the negative numbers, though his colleagues would soon do that for him.)
Figure 20: Cartesian coordinates
Descartes quickly realized how powerful his coordinate system was. He used it to turn figures and shapes into equations and numbers; with Cartesian coordinates every geometric object—squares, triangles, wavy lines—could be represented by an equation, a mathematical relationship. For example, a circle at the origin can be represented by the set of all points where x2 + y2 – 1 = 0. A parabola