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as an intricate system of nested, transparent spheres, carrying the sun, moon, planets, and stars across the sky in their daily and yearly cycles. It was also the way the great thinker Aristotle imagined the universe in the fourth century B.C. By Aristotle’s time, it was accepted that the Earth itself was spherical; but it was thought to be immobile, fixed at the center of the universe, surrounded by this intricate array of translucent spheres, carrying the five planets—or seven, if we count the sun and moon among these “wanderers.”
    Aristotle also noticed a profound difference between what happened down here on the Earth, and what transpired in the heavens. The terrestrial realm—the “sublunar” world—was marked by continuous change; it was subject to corruption and decay. This stood in stark contrast to the perfection of the sun, moon, and planets, whose movements were as predictable and regular as a well-oiled machine. (The metaphor is less of an anachronism if we think of the cosmic machine as a divine creation rather than something constructed in a blacksmith’s workshop, but either way we have an artifact bearing witness to the talent of its creator.) Here on Earth, everything was thought to be composed of the four elements—earth, air, fire, and water—described by the Greeks even before Aristotle. All that we see around us, from mice to mountains, can be thought of as a particular arrangement of these elements, as they move and combine in different forms. As Christopher Marlowe’s Tamburlaine observes, “Nature that framed us of four elements, / Warring within our breasts for regiment…” ( Tamburlaine the Great, Part 1 2.6.58–59). Even Sir Toby Belch, in Twelfth Night , asks: “Does not our life consist of the four elements?” (2.3.9).
    In a world of hierarchies, it is not surprising that the elements themselves were ranked according to their presumed nobility. Fire was the most worthy; next was air. Water, being heavier, filled the oceans below. Earth, the basest of the elements, lay at the bottom. However quaint such a system may seem today, it basically worked: When flames were observed to rise, it could be seen as an attempt to reach the heavenly spheres, their natural home; the fall of rain to the sea, or a thrown rock to the ground, could be similarly accounted for.
    These elements, confined to the sublunar world, were constantly in flux. But the “superlunar” world—the heavens—showed no such signs of change. To Aristotle, this heavenly realm, with its various spheres, was composed of a kind of quintessence—literally a “fifth element.” Sometimes an additional sphere was added beyond the sphere of the fixed stars; this was the primum mobile (“that which moves first”), which was believed to set the whole system in motion.
    In considering the motion of the heavenly bodies, Aristotle was influenced by Plato, who had in turn been influenced by the followers of Pythagoras, an early Greek thinker who saw the universe as inherently mathematical, its creator a kind of divine geometer. Among the many shapes pondered by the geometers, one was seen as more perfect than any other. This was the circle (or, in three dimensions, the sphere). As a medieval astronomer named Sacrobosco noted, there were three reasons why the heavens must be spherical: First, a sphere has no beginning and no end, and is therefore “eternal.” Second, a sphere encloses a larger volume than any other shape having the same surface area. And third, any other shape would seem to leave “unused” space. The first of these reasons, in particular, permeated Greek mathematical thought. And so Aristotle imagined the planets as moving in perfect circles. This was a little bit tricky, since it was well known that the planets do, in fact, display irregularities in their motion, as seen from Earth. But surely, he reasoned,