Zero - Charles Seife [18]
Another philosophy vied with the atomic theory, and instead of posing such bizarre concepts as the infinite vacuum, it turned the universe into a cozy nutshell. There was no infinity, no void—just beautiful spheres that surrounded the earth, which was naturally placed at the very center of the universe. This was the Aristotelian system, which was later refined by the Alexandrian astronomer Ptolemy. It became the dominant philosophy in the Western world. And by rejecting zero and infinity, Aristotle explained away Zeno’s paradoxes.
Aristotle simply declared that mathematicians “do not need the infinite, or use it.” Though “potential” infinities could exist in the minds of mathematicians—like the concept of dividing lines into infinite pieces—nobody could actually do it, so the infinite doesn’t exist in reality. Achilles runs smoothly past the tortoise because the infinite points are simply a figment of Zeno’s imagination, rather than a real-world construct. Aristotle just wished infinity away by stating that it is simply a construct of the human mind.
From that concept comes a startling revelation. Based upon the Pythagorean universe, the Aristotelian cosmos (and its later refinement by the astronomer Ptolemy) had the planets moving in crystalline orbs. However, since there is no infinity, there can’t be an endless number of spheres; there must be a last one. This outermost sphere was a midnight blue globe encrusted with tiny glowing points of light—the stars. There was no such thing as “beyond” the outermost sphere; the universe ended abruptly with that outermost layer. The universe was contained in a nutshell, ensconced comfortably within the sphere of fixed stars; the cosmos was finite in extent, and entirely filled with matter. There was no infinite; there was no void. There was no infinity; there was no zero.
This line of reasoning had another consequence—and this is why Aristotle’s philosophy endured for so many years. His system proved the existence of God.
The heavenly spheres are slowly spinning in their places, making a music that suffuses the cosmos. But something must be causing that motion. The stationary earth cannot be the source of that motive power, so the innermost sphere must be moved by the next sphere out. That sphere, in turn, is moved by its larger neighbor, and on and on. However, there is no infinity; there are a finite number of spheres, and a finite number of things that are moving each other. Something must be the ultimate cause of motion. Something must be moving the sphere of fixed stars. This is the prime mover: God. When Christianity swept through the West, it became closely tied to the Aristotelian view of the universe and the proof of God’s existence. Atomism became associated with atheism. Questioning the Aristotelian doctrine was tantamount to questioning God’s existence.
Aristotle’s system was extremely successful. His most famous student, Alexander the Great, spread the doctrine as far east as India before Alexander’s untimely death in 323 BC. The Aristotelian system would outlast Alexander’s empire; it would survive until Elizabethan times, the sixteenth century. With this long-standing acceptance of Aristotle came a rejection of the infinite—and the void, for Aristotle’s denial of the infinite required a denial of the void, because the void implies the existence of the infinite.