Coming of Age in the Milky Way - Timothy Ferris (2003)



There is no new thing under the sun.


Amazed, and as if astonished and stupefied, I stood still, gazing for a certain length of time with my eyes fixed intently upon it…. When I had satisfied myself that no star of that kind had ever shone forth before, I was led into such perplexity by the unbelievability of the thing that I began to doubt the faith of my own eyes.

—Tycho, on the supernova of 1572

           Mikolai Kopernik, though rightly esteemed as a great astronomer, was never much of a stargazer. He did some observing in his student days, assisting his astronomy professor at Bologna, Domenico Maria de Novara, in watching an occultation of the star Aldebaran by the moon, and he later took numerous sightings of the sun, using an instrument of his own devising that reflected the solar disk onto a series of graph lines etched into a wall outside his study. But these excursions served mainly to confirm what Kopernik and everybody else already knew, that the Ptolemaic system was inaccurate, making predictions that often proved to be wrong by hours or even days.

Kopernik drew inspiration less from stars than from books. In this he was very much a man of his time. The printing press—invented just thirty years before he was born—had touched off a communications revolution comparable in its impact to the changes wrought in the latter half of the twentieth century by the electronic computer. To be sure, Greek and Roman classics had been making their way from the Islamic world to Europe for centuries, and with enlightening effect—the first universities had been founded principally to house the books and study their contents—but the books themselves, each laboriously copied out by hand, were rare and expensive, and frequently were marred by transcription errors. All this changed with the advent of cheap, high-quality paper (a gift of Chinese technology) and the press. Now a single competent edition of Plato or Aristotle or Archimedes or Ptolemy could be reproduced in considerable quantities; every library could have one, and so could many individual scholars and more than a few farmers and housewives and tradespeople. As books spread so did literacy, and as the number of literate people increased, so did the market for books. By the time Kopernik was thirty years old (and printing itself but sixty years old), some six to nine million printed copies of more than thirty-five thousand titles had been published, and the print shops were working overtime trying to satisfy the demand for more.

Kopernik was as voracious a reader as any, at home in law, literature, and medicine as well as natural philosophy. Born in 1473 in northern Poland, he had come under the sponsorship of his powerful and calculating uncle Lucas Waczenrode, later bishop of Warmia, who gave him books and sent him to the best schools. He attended the University of Cracow, then ventured south into the Renaissance heartland to study at the universities of Bologna and Padua. He read Aristotle, Plato, Plutarch, Ovid, Virgil, Euclid, Archimedes, and Cicero, the restorer of Archimedes’ grave. Steeped in the literature and science of the ancients, he returned home with a Latinized name, as Nicolaus Copernicus.

Like Aristotle, Copernicus collected books; unlike Aristotle, he did not have to be wealthy to do so. Thanks to the printing press, a scholar who was only moderately well off could afford to read widely, at home, without having to beg admission to distant institutions of learning where the books were kept chained to the reading desks. Copernicus was one of the first scholars to study printed books in his own library, and he studied none more closely than Ptolemy’s Almagest. Great was his admiration for Ptolemy, whom he admired as a thoroughly professional astronomer, mathematically sophisticated and dedicated to fitting his cosmological model to the observed phenomena. Indeed, Copernicus’s De Revolutionibus (On the Revolutions), the book that would set the earth into motion around the sun and bring about Ptolemy’s downfall, otherwise reads like nothing so much as a sustained imitation of Ptolemy’s Almagest.

It is widely assumed that Copernicus proposed his heliocentric theory in order to repair the inaccuracies of the Ptolemaic model. Certainly it must have become evident to him, in his adulthood if not in his student days, that the Ptolemaic system did not work very well: “The mathematicians are so unsure of the movements of the sun and moon,” notes the preface to De Revolutionibus, “that they cannot even explain or observe the constant length of the seasonal year.”1 Prior to the advent of the printing press, the failings of Ptolemy’s Almagest could be attributed to errors in transcription or translation, but once reasonably accurate printed editions of the book had been published, this excuse began to evaporate. Copernicus owned at least two editions of Almagest, and had read others in libraries, and the more clearly he came to understand Ptolemy’s model, the more readily he could see that its deficiencies were inherent, not incidental, to the theory. So considerations of accuracy may indeed have helped convince him that a new approach was required.

But by “new,” Copernicus the Renaissance man most often meant the rediscovery of something old. Renaissance, after all, means “re-birth,” and Renaissance art and science in general sprang more from classical tradition than from innovation. The young Michelangelo’s first accomplished piece of sculpture—executed in the classical style—was made marketable by rubbing dirt into it and palming it off, in Paris, as a Greek relic. Petrarch, called the founder of the Renaissance, dreamed not of the future but of the day when “our grandsons will be able to walk back into the pure radiance of the past”2 (emphasis added); when Petrarch was found dead, at the age of seventy, slumped at his desk after an all-night study session, his head was resting not on a contemporary volume but on a Latin edition of his favorite poet, Virgil, who had lived fourteen centuries earlier. Copernicus similarly worked in awe of the ancients, and his efforts, like so much of natural philosophy then and since, can be read as a continuation of the academic dialogues of Plato and Aristotle.

Aristotle, the first of the Greeks to have been rediscovered in the West, was so widely revered that he was routinely referred to as “the philosopher,” much as lovers of Shakespeare were to call him “the poet.” Much of his philosophy had been incorporated into the world view of the Roman Catholic Church. (Most notably by Thomas Aquinas—at least until the morning of December 6, 1273, when, while saying mass in Naples, Thomas became enlightened and declared that “I can do no more; such things have been revealed to me that all I have written seems as straw, and I now await the end of my life.”) From Aristotle, Copernicus acquired an enthusiasm for the universe of crystalline spheres—although, like Aristotle, Copernicus never could decide whether the spheres actually existed or were but a useful abstraction.

Copernicus also read Plato, as well as many of the Neoplatonic philosophers whose work ornaments and obfuscates medieval thought, and from them absorbed the Platonic conviction that there must be a simple underlying structure to the universe. It was just this unitary beauty that the Ptolemaic cosmology lacked. “A system of this sort seemed neither sufficiently absolute nor sufficiently pleasing to the mind,” Copernicus wrote.3 He was after a grasp of the more central truth. He called it “the principal thing—namely the shape of the universe and the unchangeable symmetry of its parts.”4

Rather early on, perhaps during his student days in sunny Italy, Copernicus decided that the “principal thing” was to place the sun at the center of the universe. He may have drawn encouragement from reading, in Plutarch’s Morals, that Aristarchus of Samos “supposed that the heavens remained immobile and that the earth moved through an oblique circle, at the same time turning about its own axis.”5 (He mentions Aristarchus in De Revolutionibus, though not in this context.) Possibly he encountered more recent speculations about the motion of the earth, as in Nicole Oresme, the fourteenth-century Parisian scholar who pointed out that

if a man in the heavens, moved and carried along by their daily motion, could see the earth distinctly and its mountains, valleys, rivers, cities, and castles, it would appear to him that the earth was moving in daily motion, just as to us on earth it seems as though the heavens are moving…. One could then believe that the earth moves and not the heavens.6

Copernicus was influenced by Neoplatonic sun worship as well. This was a popular view at the time—even Christ was being modeled by Renaissance painters on busts of Apollo the sun god—and decades later, back in the rainy north, Copernicus remained effusive on the subject of the sun.* In De Revolutionibus he invokes the authority of none other than Hermes Trismegistus, “the thrice-great Hermes,” a fantastical figure in astrology and alchemy who had become the patron saint of the new sun-worshipers: “Trismegistus calls [the sun] a ‘visible god,’ Sophocles’ Electra, ‘that which gazes upon all things.’”7 He quotes the Neoplatonist mystic Marsilio Ficino’s declaration that “the sun can signify God himself to you, and who shall dare to say the sun is false?”8 Finally, Copernicus tries his hand at a solar paean of his own:

In this most beautiful temple, who would place this lamp in another or better position than that from which it can light up everything at the same time? For the sun is not inappropriately called by some people the lantern of the universe, its mind by others, and its ruler by still others.9

Trouble arose not in the incentive for the Copernican cosmology, but in its execution. (The devil, like God, is in the details.) When Copernicus, after considerable toil, managed to complete a fully realized model of the universe based upon the heliocentric hypothesis—the model set forth, eventually, in De Revolutionibus—he found that it worked little better than the Ptolemaic model. One difficulty was that Copernicus, like Aristotle and Eudoxus before him, was enthralled by the Platonic beauty of the sphere—“The sphere,” he wrote, echoing Plato, “is the most perfect… the most capacious of figures … wherein neither beginning nor end can be found”10—and he assumed, accordingly, that the planets move in circular orbits at constant velocities. Actually, as Kepler would establish, the orbits of the planets are elliptical, and planets move more rapidly when close to the sun than when distant from it. Nor was the Copernican universe less intricate than Ptolemy’s: Copernicus found it necessary to introduce Ptolemaic epicycles into his model and to move the center of the universe to a point a little away from the sun. Nor did it make consistently more accurate predictions, even in its wretchedly compromised form; for many applications it was less useful.

Copernicus’s model of the solar system is generally portrayed in simplified form, as in this illustration based upon one in his De Revolutionibus. In its details, however, it was as complex as Ptolemy’s geocentric model.

This, in retrospect, was the tragedy of Copernicus’s career— that while the beauty of the heliocentric hypothesis convinced him that the planets ought to move in perfect circles around the sun, the sky was to declare it false. Settled within the stone walls of Frauenburg Cathedral, in a three-story tower that afforded him a view of Frisches Haff and the Gulf of Danzig below and the wide (though frequently cloudy) sky above—“the most remote corner of the earth,”11 he called it—Copernicus carried out his sporadic astronomical observations, and tried, in vain, to perfect the heliocentric theory he had outlined while still a young man. For decades he turned it over in his thoughts, a flawed jewel, luminous and obdurate. It would not yield.

As Darwin would do three centuries later, Copernicus wrote and privately circulated a longhand sketch of his theory. He called it the “ballet of the planets.” It aroused interest among scholars, but Copernicus published none of it. He was an old man before he finally released the manuscript of De Revolutionibus to the printer, and was on his death bed by the time the final page proofs arrived.

One reason for his reluctance to publish was that Copernicus, like Darwin, had reason to fear censure by the religious authorities. The threat of papal disapproval was real enough that the Lutheran theologian Andreas Osiander thought it prudent to oil the waters by writing an unsigned preface to Copernicus’s book, as if composed by the dying Copernicus himself, reassuring its readers that divine revelation was the sole source of truth and that astronomical treatises like this one were intended merely to “save the phenomena.” Nor were the Protestants any more apt to kiss the heliocentric hem. “Who will venture to place the authority of Copernicus above that of the Holy Spirit?” thundered Calvin,12 and Martin Luther complained, in his voluble way, that “this fool wishes to reverse the entire science of astronomy; but sacred Scripture tells us that Joshua commanded the sun to stand still, and not the earth.”13*

The book survived, however, and changed the world, for much the same reason that Darwin’s Origin of Species did—because it was too technically competent for the professionals to ignore it. In addition to presenting astronomers with a comprehensive, original, and quantitatively defensible alternative to Ptolemy, De Revolutionibus was full of observational data, much of it fresh and some of it reliable. Consequently it was consulted regularly by astronomers—even by non-Copernicans like Erasmus Reinhold, who employed it in compiling the widely consulted Prutenic Tables—and thus remained in circulation for generations.

To those who gave it the benefit of the doubt, Copernicanism offered both a taste of the immensity of space and a way to begin measuring it. The minimum radius of the Copernican sphere of stars (given the unchanging brightnesses of the zodiacal stars) was estimated in the sixteenth century to be more than 1.5 million times the radius of the earth. This represented an increase in the volume of the universe of at least 400,000 times over al-Farghani’s Ptolemaic cosmos. The maximum possible size of the Copernican universe was indefinite, and might, Copernicus allowed, be infinite: The stars, he wrote, “are at an immense height away,” and he expressed wonderment at “how exceedingly vast is the godlike work of the Best and Greatest Artist!”14

Interplanetary distances in Ptolemy were arbitrary; scholars who ventured to quantify them did so by assuming that the various orbits and epicycles fit snugly together, like nested Chinese boxes. The Copernican theory, however, precisely stipulated the relative dimensions of the planetary orbits: The maximum apparent separation of the inferior planets Mercury and Venus from the sun yields the relative diameters of their orbits, once we accept that both orbit the sun and not the earth. Since the relative sizes of all the orbits were known, if the actual distance of any one planet could be measured, the distances of all the others would follow. As we will see, this advantage, though purely theoretical in Copernicus’s day, was to be put to splendid use in the eighteenth century, when astronomical technology reached the degree of sophistication required to measure directly the distances of nearby planets.

The immediate survival of Copernicanism was due less to any compelling evidence in its favor than to the waning fortunes of the Ptolemaic, Aristotelian model. And that, as it happened, was prompted in large measure by changes in the sky—by the apparition of comets, and, most of all, by the fortuitous appearance of two brilliant novae, or “new stars,” during the lifetimes of Tycho, Kepler, and Galileo.

Integral to Aristotle’s physics was the hypothesis that the stars never change. Aristotle saw the earth as composed of four elements—earth, water, fire, and air—each of which naturally moves in a vertical direction: The tendency of earth and water is to fall, while that of fire and air is to rise. The stars and planets, however, move neither up nor down, but instead wheel across the sky. Aristotle concluded that since objects in the sky do not partake of the vertical motion characteristic of the four terrestrial elements, they must be made of another element altogether. He called this fifth element “aether,” from the Greek word for “eternal,” and invested it with all his considerable reverence for the heavens. Aether, he argued, never ages or changes: “In the whole range of time past,” he writes, in his treatise On the Heavens, “so far as our inherited records reach, no change appears to have taken place either in the whole scheme of the outermost heaven or in any of its proper parts.”15

Aristotle’s segregation of the universe into two realms—a mutable world below the moon and an eternal, unchanging world above—found a warm welcome among Christian theologians predisposed by Scriptures to think of heaven as incorruptible and the earth as decaying and doomed. The stars, however, having heard neither of Aristotle nor of the Church, persisted in changing, and the more they changed, the worse the cosmology of Aristotle and Ptolemy looked.

Comets were an old problem for the Aristotelians, since no one could anticipate when they would appear or where they would go once they showed up.* (It was owing to their unpredictability that comets acquired a reputation as heralds of disaster—from the Latin dis-astra, “against the stars.”)* Aristotle swept comets under the rug—or under the moon—by dismissing them as atmospheric phenomena. (He did the same with meteors, which is why the study of the weather is known as “meteorology.”)

But when Tycho Brahe, the greatest observational astronomer of the sixteenth century, studied the bright comet of 1577, he found evidence that Aristotle’s explanation was wrong. He triangulated the comet, by charting its position from night to night and comparing his data with those recorded by astronomers elsewhere in Europe on the same dates. The shift in perspective produced by the differing locations of the observers would have been more than sufficient to show up as a difference in the comet’s position against the background stars, were the comet nearby. Tycho found no such difference. This meant that the comet was well beyond the moon. Yet Aristotle had held that nothing superlunar could change.

The other great empirical challenge to Aristotle’s cosmological hegemony came with the opportune appearance, in the late sixteenth and early seventeenth centuries, of two violently exploding stars—what we today call Supernovae. A star that undergoes such a catastrophic detonation can increase a hundred million times in brightness in a matter of days. Since only a tiny fraction of the stars in the sky are visible without a telescope, Supernovae almost always seem to have appeared out of nowhere, in a region of the sky where no star had previously been charted; hence the name nova, for “new.” Supernovae bright enough to be seen without a telescope are rare; the next one after the seventeenth century did not come until 1987, when a blue giant star exploded in the Large Magellanic Cloud, a neighboring galaxy to the Milky Way, to the delight of astronomers in Australia and the Chilean Andes. The two Supernovae that graced the Renaissance caused quite a stir, inciting not only new sights but new ideas.

Tycho spotted the supernova of 1572 on the evening of November 11, while out taking a walk before dinner, and it literally stopped him in his tracks. As he recalled the moment:

Amazed, and as if astonished and stupefied, I stood still, gazing for a certain length of time with my eyes fixed intently upon it and noticing that same star placed close to the stars which antiquity attributed to Cassiopeia. When I had satisfied myself that no star of that kind had ever shone forth before, I was led into such perplexity by the unbelievability of the thing that I began to doubt the faith of my own eyes.16

The next supernova came only thirty-two years later, in 1604. Kepler observed it for nearly a year before it faded from view, and Galileo lectured on it to packed halls in Padua.

Scrutinized week by week through the pinholes and lensless sighting-tubes of the sixteenth- and seventeenth-century astronomers, the two Supernovae stayed riveted in the same spot in the sky, and none revealed any shift in perspective when triangulated by observers at widely separated locations. Clearly the novae, too, belonged to the starry realm that Aristotle had depicted as inalterable. Wrote Tycho of the 1572 supernova:

That it is neither in the orbit of Saturn … nor in that of Jupiter, nor in that of Mars, nor in that of any one of the other planets, is hence evident, since after the lapse of several months it has not advanced by its own motion a single minute from that place in which I first saw it; which it must have done if it were in some planetary orbit…. Hence this new star is located neither … below the Moon, nor in the orbits of the seven wandering stars but in the eighth sphere, among the other fixed stars.17

The shock dealt to the Aristotelian world view could not have been greater had the stars bent down and whispered in the astronomers’ ears. Clearly there was something new, not only under the sun but beyond it.*

Tycho was no Copernican. It was through Ptolemy that his passion for astronomy had crystallized, when, on August 21, 1560, at the age of thirteen, he watched a partial eclipse of the sun and was amazed that it had been possible for scholars, consulting the Ptolemaic tables, accurately to predict the day (though not the hour) of its occurrence. It struck him, he recalled, as “something divine that men could know the motions of the stars so accurately that they could long before foretell their places and relative positions.”18

But when Tycho began making observations of his own, he soon became impressed by the inaccuracy of Ptolemy’s predictions. He watched a spectacular conjunction of Saturn and Jupiter on August 24, 1563, and found that the time of closest approach—which in this case was so close that the two bright planets appeared almost to merge—was days away from the predictions of the Ptolemaic tables. He emerged from the experience with a lifelong passion for accuracy and exactitude and a devotion to the verdict of the sky.

To compile more accurate records of the positions of the stars and planets required state-of-the-art equipment, and that cost money. Fortunately, Tycho had money. His foster father had saved King Frederick II from drowning, dying of pneumonia as a result, and the grateful king responded with a hefty grant to the young astronomer. With it, Tycho built Uraniburg, a fabulous observatory on an island in the Sund between Elsinor Castle (Hamlet’s haunt) and Copenhagen. He ransacked Europe in search of the finest astronomical instruments, complemented them with improved quadrants and armillaries of his own design, and deployed them atop the turrets of a magnificent castle that he equipped with a chemical laboratory, a printing plant supplied by its own paper mill, an intercom system, flush toilets, quarters for visiting researchers, and a private jail. The grounds sported private game preserves, sixty artificial fishponds, extensive gardens and herbariums, and an arboretum with three hundred species of trees. The centerpiece of the observatory was a gleaming brass celestial globe, five feet in diameter, on which a thousand stars were inscribed, one by one, as Tycho and his colleagues remapped the visible sky.

No dilettante, Tycho drove himself and his assistants in a ceaseless pursuit of the most accurate possible observations, charting the positions of the stars and the courses of the planets night after night for over twenty years. The resulting data were more than twice as accurate as those of the preceding astronomers—precise enough, at last, to unlock the secrets of the solar system.

Tycho, however, was an observer and not a theorist. His chief contribution to theoretical cosmology—a compromise geocentric model in which the planets orbit the sun, which in turn orbits the earth—created as many problems as it solved. Needed was someone with the ingenuity and perservance to compose Tycho’s tables into a single, accurate and simple theory.

Tycho proposed a compromise between the Copernican and Ptolemaic models in which the sun orbited the earth, and was in turn orbited by the other planets. (Not to scale.)

Amazingly, just such a man turned up. He was Johannes Kepler, and on February 4, 1600, he arrived at Benatek Castle near Prague, where Tycho had moved his observatory and retinue after his benefactor King Frederick drank himself to death. Tycho and Kepler made for unlikely collaborators, with each other or anybody else. Tycho was an expansive, despotic giant of a man, who sported a belly of Jovian proportions and a gleaming, metal-alloy nose (the bridge of his original nose having been cut off in a youthful duel). Heroically passionate and wildly eccentric, he dressed like a prince and ruled his domain like a king, tossing scraps to a dwarf named Jepp who huddled beneath the dinner table. Kepler, for his part, was a prototypical outsider. Myopic, sickly, and “doglike” in appearance (his words) he came from the antipodes of nobility. His father was a mercenary soldier and a dipsomaniac wife-beater. His mother had been raised by an aunt who was burned alive as a witch, and she herself narrowly escaped the stake. (Among her other objectionable habits, she enjoyed spiking people’s drinks with psychedelic drugs.)

Neurotic, self-loathing, arrogant, and vociferous, Kepler was drubbed with tiresome regularity by his classmates. He fared little better once out in the world, where he tried but failed to become a Lutheran minister. He sought solicitude in marriage, but his wife, he said with the bleak objectivity of a born observer, was “simple of mind and fat of body … stupid, sulking, lonely, melancholy.”19 Kepler tried to make a living casting horoscopes, but was seldom paid; he spent much of his time trekking from one court to another to plead for his fee, drawing titters from the flunkies when he appeared, in his baggy, food-stained suit, tripping over himself with apologies and explanations, getting nowhere. His lifetime earnings could not have purchased the star-globe in Tycho’s library.

Kepler’s initial scientific endeavors amounted to a comedy of errors and absurdities. He tried to sight the stars using only a wooden staff suspended from a rope: “Hold your laughter, friends, who are admitted to this spectacle,” he wrote of his makeshift observatory.20 His first great theoretical idea—which came to him with the force of revelation, halting him in mid-sentence while he was delivering a soporific lecture on mathematics in a high school in Graz, Austria—was that the intervals between the orbits of the planets describe a nest of concentric Platonic solids. They do not.

Yet this was the man who would discern the architecture of the solar system and discover the phenomenological laws that govern the motions of the planets, thus curing the Copernican cosmology of its pathologies and flinging open the door to the depths of cosmic space. An extraordinarily perspicacious theorist—no less exacting a critic than Immanuel Kant called him “the most acute thinker ever born”21—Kepler was blessed with an ecstatic conviction that the world that had treated him so harshly was, nonetheless, fundamentally beautiful. He never lost either this faith or the clearheaded empiricism with which it was tempered, and the combination eventually rewarded him with some of the most splendid insights into the workings of the universe ever granted a mortal mind.

Kepler’s chief source of inspiration was the Pythagorean doctrine of celestial harmony, which he had encountered in Plato. “As our eyes are framed for astronomy, so our ears are framed for the movements of harmony,” Plato wrote, “and these two sciences are sisters, as the Pythagoreans say and we agree.”22 In the final book of the Republic, Plato portrays with great beauty a voyage into space, where the motion of each planet is attended to by a Siren singing

one sound, one note, and from all the eight there was a concord of a single harmony. And there were three others who sat round about at equal intervals, each one on her throne, the Fates, daughters of Necessity, clad in white vestments with garlands on their heads, Lachesis, and Clotho, and Atropos, who sang in unison with the music of the Sirens, Lachesis singing the things that were, Clotho the things that are, and Atropos the things that are to be.23

Aristotle found all this a bit much. “The theory that the movement of the stars produces a harmony, i.e., that the sounds they make are concordant, in spite of the grace and originality with which it has been stated, is nevertheless untrue,” he wrote.24 Kepler sided with Plato. The muddy tumult of the world, he felt, was built upon harmonious and symmetrical law; if the motions of the planets seem discordant, that is because we have not yet learned how to hear their song. Kepler wanted to hear it before he died. At this he succeeded, and the sunlight of his success banished the gloom of his many failures.

The doctrine of celestial harmony was, literally, in the air, in the new music and poetry of Kepler’s generation and those that immediately followed it. Milton, who was always ransacking science for promising themes, celebrated it in verses like this one:

Ring out ye Crystall sphears,
Once bless our human ears,
   (If ye have power to touch our senses so)
And let your silver chime
Move in melodious time;
   And let the Base of Heav’ns deep Organ blow,
And with your ninefold harmony
Make up full consort to th’ Angelike symphony.25

Even Shakespeare, who was rather unsympathetic toward astronomy, found room in the Merchant of Venice for a nod to Pythagoras:

Sit, Jessica. Look how the floor of heaven
Is thick inlaid with patens of bright gold.
There’s not the smallest orb which thou behold’st
But in his motion like an angel sings,
Still quiring to the young-eyed cherubims;
Such harmony is in immortal souls,
But whilest this muddy vesture of decay
Doth grossly close it in, we cannot hear it.26

The churches of the day rang with approximations of the music of the spheres. The plainsongs and chants of the medieval cathedrals were being supplanted by polyphony, the music of many voices that would reach an epiphany in the fugues—the word fugue means “flight”—of Johann Sebastian Bach. For Kepler, polyphony in music was a model for the voices sung by the planets as they spun out their Pythagorean harmonies: “The ratio of plainsong or monody … to polyphony,” he wrote,

is the same as the ratio of the consonances which the single planets designate to the consonances of the planets taken together….

… The movements of the heavens are nothing except a certain ever-lasting polyphony (intelligible, not audible)…. Hence it is no longer a surprise that man, the ape of his Creator, should finally have discovered the art of singing polyphonically, which was unknown to the ancients, namely in order that he might play the everlastingness of all created time in some short part of an hour by means of an artistic concord of many voices and that he might to some extent taste the satisfaction of God the Workman with His own works, in that very sweet sense of delight elicited from this music which imitates God.27

Kepler’s interest in astronomy, like Tycho’s, dated from his boyhood, when his mother took him out in the evening to see the great comet of 1577 and, three years later, to behold the sanguine face of the eclipsed moon. He was introduced to heliocentric cosmology at the University of Tübingen, by Michael Mastlin, one of the few Copernican academics of his day. Attracted to it partly out of mystical, Neoplatonic motives like those that had inspired Copernicus himself, Kepler wrote of sunlight in terms that would have brought a smile to the countenance of Marsilio Ficino:

Light in itself is something akin to the soul…. And so it is consonant that the solar body, wherein the light is present as in its source, is endowed with a soul which is the originator, the preserver, and the continuator. And the function of the sun in the world seems to persuade us of nothing else except that just as it has to illuminate all things, so it is possessed of light in its body; and as it has to make all things warm, it is possessed of heat; as it has to make all things live, of a bodily life; and as it has to move all things, it itself is the beginning of the movement; and so it has a soul.28

But Kepler’s penchant for Platonic ecstasy was wedded to an acid skepticism about the validity of all theories, his own included. He mocked no thinker more than himself, tested no ideas more rigorously than his own. If, as he avowed in 1608, he was to “interweave Copernicus into the revised astronomy and physics, so that either both will perish or both be kept alive,” he would need more accurate observational data than were available to Ptolemy or to Copernicus. Tycho had those data. “Tycho possesses the best observations,” Kepler mused. “… He only lacks the architect who would put all this to use according to his own design.”29 Tycho was “superlatively rich, but he knows not how to make proper use of it as is the case with most rich people. Therefore, one must try to wrest his riches from him.”30 Suiting action to intention, Kepler wrote adoring letters to Tycho, who in reply praised his theories as “ingenious” if rather too a priori, and invited him to come and join the staff at Benatek Castle.

There the two quarreled constantly. Tycho, justly fearful that the younger and more incisive Kepler would eclipse him, played his cards close to his chest. “Tycho did not give me the chance to share his practical knowledge,” Kepler recalled, “except in conversation during meals, today something about the apogee, tomorrow something about the nodes of another planet.”31 Kepler threw fits and threatened to leave; at one point he had packed his bags and boarded a stage before Tycho finally summoned him back.

Realizing that he would have to give his young colleague something of substance to work on if he wanted to keep him on staff, Tycho devised a scheme redolent with the enmity that Kepler seemed to attract like lightning to a summit pine. “When he saw that I possess a daring mind,” Kepler wrote, “he thought the best way to deal with me would be to give me my head, to let me choose the observations of one single planet, Mars.”32 Mars, as Tycho knew and Kepler did not, presented an almost impossible challenge. As Mars lies near the earth, its position in the sky had been ascertained with great exactitude; for no planet were the inadequacies of both the Ptolemaic and Copernican models rendered more starkly. Kepler, who did not at first appreciate the difficulties involved, brashly prophesied that he would solve the problem of determining the orbit of Mars in eight days. Tycho must have been cheerful at dinner that night. Let the Platonist take on Mars. Kepler was still working on the problem eight years later.

Tycho, though, was out of time. He died on October 24, 1601, as the result of a burst bladder suffered while drinking too much beer at a royal dinner party from which he felt constrained by protocol from excusing himself. “Let me not seem to have died in vain,” he cried repeatedly that night.33

Kepler was to grant his dying wish. Named Tycho’s successor as imperial mathematician (albeit, as befitting his lesser status, at a much reduced stipend), he pressed on in his search for a single, straightforward theory to account for the motion of Mars. If every great achievement calls for the sacrifice of something one loves, Kepler’s sacrifice was the perfect circle. “My first mistake was in having assumed that the orbit on which planets move is a circle,” he recalled. “This mistake showed itself to be all the more baneful in that it had been supported by the authority of all the philosophers, and especially as it was quite acceptable metaphysically.”34 In all, Kepler tested seventy circular orbits against Tycho’s Mars data, all to no avail. At one point, performing a leap of the imagination like Leonardo’s to the moon, he imagined himself on Mars, and sought to reconstruct the path the earth’s motion would trace out across the skies of a Martian observatory; this effort consumed nine hundred pages of calculations, but still failed to solve the major problem. He tried imagining what the motion of Mars would look like from the sun. At last, his calculations yielded up their result: “I have the answer,” Kepler wrote to his friend the astronomer David Fabricius. “… The orbit of the planet is a perfect ellipse.”

Now everything worked. Kepler had arrived at a fully realized Copernican system, focused on the sun and unencumbered by epicycles or crystalline spheres. (In retrospect one could see that Ptolemy’s eccentrics had been but attempts to make circles behave like ellipses.)

Fabricius replied that he found Kepler’s theory “absurd,” in that it abandoned the circles whose symmetry alone seemed worthy of the heavens. Kepler was unperturbed; he had found a still deeper and subtler symmetry, in the motions of the planets. “I discovered among the celestial movements the full nature of harmony,” he exclaimed, in his book The Harmonies of the World, published eighteen years after Tycho’s death.

I am free to give myself up to the sacred madness, I am free to taunt mortals with the frank confession that I am stealing the golden vessels of the Egyptians, in order to build of them a temple for my God, far from the territory of Egypt. If you pardon me, I shall rejoice; if you are enraged, I shall bear up. The die is cast.35

And so on. The cause of his celebration was his discovery of what are known today as Kepler’s laws. The first contained the news he had communicated to Fabricius—that each planet orbits the sun in an ellipse with the sun at one of its two foci. The second law revealed something even more astonishing, a Bach fugue in the sky. Kepler found that while a planet’s velocity changes during its year, so that it moves more rapidly when close to the sun and more slowly when distant from the sun, its motion obeys a simple mathematical rule: Each planet sweeps out equal areas in equal times. The third law came ten years later. It stated that the cube of the mean distance of each planet from the sun is proportional to the square of the time it takes to complete one orbit. Archimedes would have liked that one. Newton was to employ it in formulating his law of universal gravitation.

Kepler’s first law: The orbit of each planet describes an ellipse, with the sun at one of its foci.

Kepler’s second law: If time AB = time CD, area ABSun = area CDSun.

Kepler’s third law: The cube of the distance of each planet from the sun is proportional to the square of its orbital period.

Here at last was “the principal thing” of which Copernicus had dreamed, the naked kinematics of the sun and its planets. “I contemplate its beauty with incredible and ravishing delight,” Kepler wrote.36 Scientists have been contemplating it ever since, and Kepler’s laws today are utilized in studying everything from binary star systems to the orbits of galaxies across clusters of galaxies. The intricate etchings of Saturn’s rings, photographed by the Twin Voyager spacecraft in 1980 and 1981, offer a gaudy display of Keplerian harmonies, and the Voyager phonograph record, carried aboard the spacecraft as an artifact of human civilization, includes a set of computer-generated tones representing the relative velocities of the planets—the music of the spheres made audible at last.

But the sun of learning is paired with a dark star, and Kepler’s life remained as vexed with tumult as his thoughts were suffused with harmony. His friend David Fabricius was murdered. Smallpox carried by soldiers fighting the Thirty Years’ War killed his favorite son, Friedrich, at age six. Kepler’s wife grew despondent —“numbed,” he said, “by the horrors committed by the soldiers”—and died soon thereafter, of typhus.37 His mother was threatened with torture and was barely acquitted of witchcraft (due, the court records noted, to the “unfortunate” intervention of her son the imperial mathematician as attorney for the defense) and died six months after her release from prison. “Let us despise the barbaric neighings which echo through these noble lands,” Kepler wrote, “and awaken our understanding and longing for the harmonies.”38

He moved his dwindling family to Sagan, an outback. “I am a guest and a stranger here. … I feel confined by loneliness,” he wrote.39 There he annotated his Somnium, a dream of a trip to the moon. In it he describes looking back from the moon to discern the continent of Africa, which, he thought, resembled a severed head, and Europe, which looked like a girl bending down to kiss that head. The moon itself was divided between bright days and cold dark nights, like Earth a world half darkness and half light.

Dismissed from his last official post, as astrologer to Duke Albrecht von Wallenstein, Kepler left Sagan, alone, on horseback, searching for funds to feed his children. The roads were full of wandering prophets declaring that the end of the world was at hand. Kepler arrived in Ratisbon, hoping to collect some fraction of the twelve thousand florins owed him by the emperor. There he fell ill with a fever and died, on November IS, 1630, at the age of forty-eight. On his deathbed, it was reported, he “did not talk, but pointed his index finger now at his head, now at the sky above him.”40 His epitaph was of his own composition:

Mensus eram coelos, nunc terrae metior umbras
Mens coelestis erat, corporis umbra iacet.

I measured the skies, now I measure the shadows
Skybound was the mind, the body rests in the earth.

The grave has vanished, trampled under in the war.

*One could write a plausible intellectual history in which the decline of sun worship, the religion abandoned by the Roman emperor Constantine when he converted to Christianity, was said to have produced the Dark Ages, while its subsequent resurrection gave rise to the Renaissance.

*Modern myth to the contrary, little of the ecclesiastical opposition to Copernicanism appears to have derived from fear that the theory would “dethrone” humanity from a privileged position at the center of the universe. The center of the universe in Christian cosmology was hell, and few mortals would have felt dis-accommodated at being informed that they did not live there. Heaven was the place of distinction, for Christian and pagan thinkers alike. As Aristotle put it, “The superior glory of … nature is proportional to its distance from this world of ours.” When Leonardo da Vinci suggested that the earth “is not in the center of the universe,” he intended no slander of Earth, but was suggesting that our planet is due the same dignity—noblesse—as are the stars.

*Comets are chunks of ice and dirt that fall in from the outer solar system, sprouting long, glowing “tails” of vapor and dust blown off by the sun’s heat and by solar wind. The appearance of new comets cannot be predicted even today; they appear to originate in a cloud that lies near the outer reaches of the solar system, about which little is understood. Their orbits, altered by encounters with the planets and by the kick of their own vapor jets, remain difficult to predict as well.

*The cometary stigma persisted into the early twentieth century, when millions bought patent medicines to protect themselves from the evil effects of comet Halley during its 1910 visitation. Several fatalities were reported, among them a man who died of pneumonia after jumping into a frozen creek to escape the ethereal vapors. A deputation of sheriffs intervened to prevent the sacrifice of a virgin, in Oklahoma, by a sect called the Sacred Followers who were out to appease the comet god.

* Twentieth-century radio astronomers using Renaissance star charts have located the wreckage of both Tycho’s supernova, now designated 3C 10 in the Cambridge catalog of radio sources, and of Kepler’s, known as 3C 358. Also located is the remnant of the Vela supernova, which blazed forth in the southern skies some six to eight thousand years ago, casting long shadows across the plains of Eden. (The word Eden is Sumerian for “flatland,” and is thought to refer to the fertile, rock-free plains of the Tigris-Euphrates.) The Sumerians identified that supernova with the god Ea (in Egypt, Seshat), whom they credited with the invention of writing and agriculture. The Ea myth thus suggests that the creation of agriculture and the written word were attributed by the ancients to the incentive provided by the sight of an exploding star.