The Science of Shakespeare

by Dan Falk

  PAROLLES

  Why think you so?

  HELENA

  You go so much backward when you fight.

  (1.1.190–200)

  Mars, aside from being the god of war, was also the most perplexing of the planets. The magnitude of its retrograde movement was greater than that of the other planets, making it the most readily visible example of backward motion in the heavens and, at the same time, the object whose movement was most urgently in need of explanation. As the French king points out early in Henry VI, Part 1, “Mars his true moving, even as in the heavens / So in the earth, to this day is not known” (1.2.191–92). As familiar as retrograde motion was, it proved baffling to astronomers, who struggled to tweak their models of the heavens to explain this odd feature of planetary motion.

  THE SPHERES ABOVE

  Imagining the sun, moon, and planets affixed to a giant, transparent sphere was a promising start, but it was not quite enough: At the very least, each planet had to have its own sphere, so that it could move independently of the other wanderers; these nested spheres—think of the layers of an onion—could then rotate at different speeds, with the Earth at rest in the center. The innermost sphere carried the moon, which moved a significant distance from night to night; next was Mercury, then Venus. After that came the sun itself. Beyond the sun lay the spheres of Mars, Jupiter, and Saturn; and finally the sphere containing the stars themselves, sometimes called the “firmament” (as Prince Hamlet referred to it in the passage quoted at the start of the chapter). And so one would not speak of a single giant sphere, but of a system of spheres—a system like that imagined in figure 1.1. Perhaps the spheres were composed of some kind of crystal; they needed to be rigid and yet perfectly transparent.

  Although this model had evolved significantly by the sixteenth century, the ancient picture just described was more or less how ordinary people imagined the universe in the time of Shakespeare’s youth. When Hamlet, after seeing his father’s ghost, says the vision threatens to make his eyes “like stars, start from their spheres” (1.5.22), his audience would have had no trouble catching the metaphor. Similar turns of phrase can be found throughout the canon. In A Midsummer Night’s Dream, Oberon describes a mermaid’s song—music so lovely that “certain stars shot madly from their spheres” in order to hear it better (2.1.153). And if you’ve ever seen a Western in which one character says to another that “this town isn’t big enough for the both of us,” remember that Shakespeare was there first—though entire planets, rather than towns, were at issue. In Henry IV, Part 1, Prince Henry says to his archenemy, Harry Percy, “Two stars keep not their motion in one sphere, / Nor can one England brook a double reign / Of Harry Percy and the Prince of Wales” (5.4.64–66).

  Fig. 1.1 In ancient Greece, the universe was earth-centered, with a system of concentric spheres carrying the stars, sun, and planets— including the sun and moon—across the sky. Only in the terrestrial realm do we find the four elements: earth, water, air, and fire. (In this fanciful 1599 engraving, Atlas carries the whole affair on his back.) This ancient model—with various tweaks—remained the dominant view for nearly 2,000 years. The Granger Collection, New York

  What we’ve described here is, roughly, how ancient civilizations across the Near East imagined the heavens for thousands of years: The cosmos was pictured 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, this was an illusion: Aristotle and his followers were confident that, from the correct perspective, all heavenly motion was indeed perfectly uniform and perfectly circular.

  CIRCLES UPON CIRCLES

  This system of nested crystalline spheres was immensely appealing—but anyone who followed the movements of the planets closely came to realize that it was not quite enough; the motion of the planets was too complex. For example, it was still unclear how the circular movement of those spheres could account for retrograde motion. The best guess was that each planet required two such spheres: a large one, to account for the basic eastward motion; and a smaller one, to account for the “loops” that the planet traces out when moving in retrograde. These smaller circles were known as epicycles (from a Greek term meaning “a cycle displaced from the center”).

  The most detailed account of such a system comes from the Greek mathematician and astronomer Claudius Ptolemy (ca. A.D. 90–168).* Ptolemy’s system was intricate and sophisticated, employing geometrical contrivances that today sound unfamiliar to anyone except for historians of astronomy. We will not wade into Ptolemaic astronomy any more than we
have to, but it is worth looking at its main elements. As in Aristotle’s system, the Earth lies at the center of the universe. Each planet, as mentioned, has two motions: it moves in a small epicycle, with the center of the epicycle revolving around the Earth in a larger circle called a deferent. The deferent, meanwhile, is not centered precisely on the Earth, but on a nearby point called the eccentric. One more aspect of Ptolemy’s astronomy merits our attention: Ptolemy had imagined not only that the heavenly bodies moved in perfect circles, but that they did so at a constant speed. This was problematic, because, as measured from Earth, the speed would not be constant in the system as described. But the speed would be constant relative to an imaginary point on the “other side” of the eccentric, displaced from the center by the same amount as the Earth. That imaginary point was called an equant.

  If you’re thinking that all of this is frighteningly complex, you’re not alone. In the thirteenth century, the king of León, Alfonso X, commissioned a new set of astronomical tables to be drawn up; the calculations were carried out using the Ptolemaic system, which still reigned supreme in celestial matters. When one of his aides explained the system to him, the king is said to have remarked, “If the Lord Almighty had consulted me before embarking upon the creation, I should have recommended something simpler.”

  Three centuries later, this apparent complexity would trouble the poet John Milton. In Paradise Lost, Adam inquires about the structure of the heavens; the angel Raphael replies that God must surely be laughing at man’s desperate efforts to explain the cosmos:

  … when they come to model heav’n

  And calculate the stars, how they will wield

  The mighty frame, how build, unbuild, contrive

  To save appearances, how gird the Sphere

  With centric and eccentric scibbled o’er,

  Cycle and epicycle, Orb in Orb …

  (8.79–84)

  Remarkably, as complicated as the Ptolemaic system sounds, it worked: It allowed astronomers (and astrologers) to predict the positions of the planets with reasonable accuracy, allowing them to “save the appearances” of the wandering lights in the night sky. (That phrase, derived from a Greek expression, had long been in common use when Milton borrowed it for use in his poem.) And it worked in spite of a fairly serious glitch. It’s not just that Ptolemy had placed the Earth, rather than the sun, at the center; that, by itself, would not affect the predicted positions, as the two schemes are mathematically equivalent. But his estimates of the sizes of the spheres were all quite far off. They were based on the “best guess” at the distance between the Earth and the sun—which, it turns out, Ptolemy had underestimated by a factor of twenty; this, in turn, threw off all of the other estimates of distance.

  Ptolemy’s vision was laid out in his hefty book, which, thankfully, is no longer known by its Greek title (translated roughly as “Mathematical Systematic Treatise”) but by the name it took on centuries later, the Almagest—derived from an Arabic phrase meaning “the majestic” or “the great.” The Almagest is divided into thirteen sections, or “books,” each crammed full of diagrams, charts, and equations. (And remember, for the first thirteen hundred years of its existence, it could be copied only by hand.) Far more thorough and authoritative than any previous astronomical text, it would dominate cosmological thinking and teaching for the next fourteen centuries.

  In medieval Europe, Christian theology adopted some aspects (though not all) of the ancient Greek description of the cosmos. What endured, both in Catholic nations and in the newly Protestant lands, was a kind of “Christianized Aristotelianism.” It was a worldview that embraced the structure of the heavens and the Earth as described by Aristotle, and the basic elements of the various celestial movements as described by Ptolemy, with all of those deferents, eccentrics, and epicycles. It was an ingenious synthesis—and a remarkably cohesive picture of the world.

  MICROCOSM AND MACROCOSM

  What this discussion of the motion of the heavenly spheres leaves out is just how intimate the medieval universe was—at least, the version of the universe that emerged once Christianity and Greek philosophy had completed their merger. It was not a complete unification, however. Some of the key ideas of Greek thought—those seen to be compatible with the Christian faith—were embraced by the early Church; others were discarded. (For example, the idea of the primum mobile was absorbed rather easily; for Christians, this realm could simply be associated with God himself, who could act as a “first cause,” giving the spheres their initial motion.)

  The picture that emerged was one of profound unity: A sublime order was seen to underlie the arrangement of the natural world, from the lowest rocks to the loftiest stars—with man occupying a unique position in the middle, noble in reason but frail in body. Everything, and every person, had its place in this grand cosmic hierarchy, sometimes called the “Great Chain of Being.” Kings ruled over men; men ruled over their households. It was an interconnected web, with a just and omnipotent God supervising from above. With this hierarchy in mind, we can see why cosmology had a political dimension—or, if you prefer, why politics had a cosmic dimension. The king was next to God, and God ruled the heavens.

  It was a small step to imagine a connection between the monarch and the heavens themselves—an idea illustrated rather vividly on the frontispiece of Sphaera Civitatis (The Sphere of State), a commentary on Aristotle’s Politics by the writer John Case, published in 1588 (see figure 1.2). As a queen without an heir, Elizabeth could be forgiven for fearing disorder above all. But the engraving goes beyond simply equating the sovereign with divine order; it places her in the realm of the heavens themselves. The diagram is solidly Ptolemaic, with the Earth lying as the center. But as Jonathan Bate points out, it wouldn’t be all that disruptive had it been presented as Copernican, with the sun, symbolizing the monarch, placed at the center; either way, the queen “presides over the whole scheme [with] implacable authority.” (Much later, in the second half of the seventeenth century, Louis XIV of France would push the metaphor as far as one might reasonably expect to, declaring himself the “sun king.”) Royalty need not be compared to the sun; a star might suffice. In one of Ben Jonson’s masques, a prince declares,

  I, thy Arthur, am

  Translated to a star; and of that frame

  Or constellation that was called of me

  So long before, as showing what I should be,

  Arcturus, once thy king, and now thy star.

  Elizabeth couldn’t be compared to Arcturus, since she was a woman; instead, as Alastair Fowler points out, she was often compared to Astraea, the “star maiden” of Greek mythology. Astraea was associated with justice as well as innocence and purity. Born a human, she was repulsed by the wickedness of mankind and ascended to the sky to become the constellation Virgo (the Virgin)—rather appropriate for the Virgin Queen.

  Fig. 1.2 With the monarch imagined to have divine properties, it was reasonable to depict her in the heavens, preserving the very order of the cosmos—an idea illustrated vividly in the frontispiece of a 1588 book of political commentary. (Note that Queen Elizabeth presides over an Aristotelian, earth-centered universe.) The Granger Collection, New York

  With great power, of course, comes great responsibility, and so kings and princes must be held to a higher moral standard than the common man. As Imogen notes in Cymbeline, “… falsehood / Is worse in kings than beggars” (3.6.13–14). Few would have doubted a profound connection between social and celestial order, the inherent unity of microcosm and macrocosm—a way of thinking encapsulated in Calpurnia’s famous warning: “When beggars die, there are no comets seen; / The heavens themselves blaze forth the death of princes” (Julius Caesar 2.2.30–31).* In Troilus and Cressida, Ulysses takes the analogy much further. In a remarkable speech, he describes an intricate parallel between social order and cosmic order:

  The heavens themselves, the planets and this centre

  Observe degree, priority and place,

  In
sisture, course, proportion, season, form,

  Office and custom, in all the line of order.

  And therefore is the glorious planet Sol

  In noble eminence enthroned and sphered

  Amidst the other …

  (1.3.85–91)

  As we’ve seen, this passage can be taken as either Ptolemaic or Copernican, depending on one’s interpretation.† Either way, everything and everyone had their place and their purpose. Not surprisingly, there was little hope for improving one’s lot in life; to attempt to do so was like putting a wrench in the divine machinery of the cosmos, and was likely to bring divine retribution. It was, above all, an interconnected world; its every corner, as historian Lawrence Principe says, was “filled with purpose and rich with meaning.”

  The ancient writings were taken seriously. By Shakespeare’s time, Plato and Aristotle had been dead for nineteen centuries, yet were deemed more authoritative than any living thinker. For the natural sciences in particular, Aristotle was the authority. But it was Plato who spoke of the link between man and the cosmos—between microcosm and macrocosm (“little ordered world” and “large ordered world”). As we struggled to understand our lives here on Earth, we could look to the heavens for guidance: Their orderly structure was a model, a blueprint, for living a rational, meaningful life. Every branch of learning, from astrology to medicine, flowed from this simple assertion. We can see why natural philosophy, though roughly equivalent to what we now call “science,” was broader in scope: It encompassed not only the observational sciences, but also theology and metaphysics. And we can understand why as late a figure as Sir Isaac Newton, in the latter part of the seventeenth century, was able to carry out scientific experiments one day, dabble in alchemy the next, and study obscure biblical passages the day after that.

  To study nature was to study God’s creation. That sentiment was commonplace in Renaissance Europe, but its most compact and eloquent expression is found in Psalm 19: “The heavens declare the glory of God; and the firmament sheweth his handywork.” (On this point, Protestants and Catholics were in full agreement. As Calvin writes, “The skillful ordering of the universe is for us a sort of mirror in which we can contemplate God, who is otherwise invisible.”) To see God’s handiwork is one thing; to comprehend it is another. The Creator worked in mysterious ways, and no mere mortal could grasp his plan for humankind in its entirety—but one could glimpse a small part of it, perhaps, by studying God’s creation. One could come to know God through either of the “two books”—the book of nature or the book of scripture. His Word or his Work.