Cosmos (10 page)

In 1589, Kepler left Maulbronn to study for the clergy at the great university in Tübingen and found it a liberation. Confronted by the most vital intellectual currents of the time, his genius was immediately recognized by his teachers—one of whom introduced the young man to the dangerous mysteries of the Copernican hypothesis. A heliocentric universe resonated with Kepler’s religious sense, and he embraced it with fervor. The Sun was a metaphor for God, around Whom all else revolves. Before he was to be ordained, he was made an attractive offer of secular employment, which—perhaps because he felt himself indifferently suited to an ecclesiastical career—he found himself accepting. He was summoned to Graz, in Austria, to teach secondary school mathematics, and began a little later to prepare astronomical and meteorological almanacs and to cast horoscopes. “God provides for every animal his means of sustenance,” he wrote. “For the astronomer, He has provided astrology.”

Kepler was a brilliant thinker and a lucid writer, but he was a disaster as a classroom teacher. He mumbled. He digressed. He was at times utterly incomprehensible. He drew only a handful of students his first year at Graz; the next year there were none. He was distracted by an incessant interior clamor of associations and speculations vying for his attention. And one pleasant summer afternoon, deep in the interstices of one of his interminable lectures, he was visited by a revelation that was to alter radically the future of astronomy. Perhaps he stopped in mid-sentence. His
inattentive students, longing for the end of the day, took little notice, I suspect, of the historic moment.

There were only six planets known in Kepler’s time: Mercury, Venus, Earth, Mars, Jupiter and Saturn. Kepler wondered why only six? Why not twenty, or a hundred? Why did they have the spacing between their orbits that Copernicus had deduced? No one had ever asked such questions before. There were known to be five regular or “platonic” solids, whose sides were regular polygons, as known to the ancient Greek mathematicians after the time of Pythagoras. Kepler thought the two numbers were connected, that the
reason
there were only six planets was because there were only five regular solids, and that these solids, inscribed or nested one within another, would specify the distances of the planets from the Sun. In these perfect forms, he believed he had recognized the invisible supporting structures for the spheres of the six planets. He called his revelation The Cosmic Mystery. The connection between the solids of Pythagoras and the disposition of the planets could admit but one explanation: the Hand of God, Geometer.

The five perfect solids of Pythagoras and Plato. See
Appendix 2
.

Kepler was amazed that he—immersed, so he thought, in sin—should have been divinely chosen to make this great discovery. He submitted a proposal for a research grant to the Duke of Württemberg, offering to supervise the construction of his nested solids as a three-dimensional model so that others could glimpse the beauty of the holy geometry. It might, he added, be contrived of silver and precious stones and serve incidentally as a ducal chalice. The proposal was rejected with the kindly advice that he first construct a less expensive version out of paper, which he promptly attempted to do: “The intense pleasure I have received from this discovery can never be told in words … I shunned no calculation no matter how difficult. Days and nights I spent in mathematical labors, until I could see whether my hypothesis would agree with the orbits of Copernicus or whether my joy was to vanish into
thin air.” But no matter how hard he tried, the solids and the planetary orbits did not agree well. The elegance and grandeur of the theory, however, persuaded him that the observations must be in error, a conclusion drawn when the observations are unobliging by many other theorists in the history of science. There was then only one man in the world who had access to more accurate observations of apparent planetary positions, a self-exiled Danish nobleman who had accepted the post of Imperial Mathematician in the Court of the Holy Roman Emperor, Rudolf II. That man was Tycho Brahe. By chance, at Rudolf’s suggestion, he had just invited Kepler, whose mathematical fame was growing, to join him in Prague.

A provincial schoolteacher of humble origins, unknown to all but a few mathematicians, Kepler was diffident about Tycho’s offer. But the decision was made for him. In 1598, one of the many premonitory tremors of the coming Thirty Years’ War engulfed him. The local Catholic archduke, steadfast in dogmatic certainty, vowed he would rather “make a desert of the country than rule over heretics.”
^*
Protestants were excluded from economic and political power, Kepler’s school was closed, and prayers, books and hymns deemed heretical were forbidden. Finally the townspeople were summoned to individual examinations on the soundness of their private religious convictions, those refusing to profess the Roman Catholic faith being fined a tenth of their income and, upon pain of death, exiled forever from Graz. Kepler chose exile: “Hypocrisy I have never learned. I am in earnest about faith. I do not play with it.”

Leaving Graz, Kepler, his wife and stepdaughter set out on the difficult journey to Prague. Theirs was not a happy marriage. Chronically ill, having recently lost two young children, his wife was described as “stupid, sulking, lonely, melancholy.” She had no understanding of her husband’s work and, having been raised among the minor rural gentry, she despised his impecunious profession. He for his part alternately admonished and ignored her, “for my studies sometimes made me thoughtless; but I learned my lesson, I learned to have patience with her. When I saw that she took my words to heart, I would rather have bitten my own finger than to give her further offense.” But Kepler remained preoccupied with his work.

He envisioned Tycho’s domain as a refuge from the evils of the time, as the place where his Cosmic Mystery would be confirmed. He aspired to become a colleague of the great Tycho Brahe, who for thirty-five years had devoted himself, before the invention of the telescope, to the measurement of a clockwork universe, ordered and precise. Kepler’s expectations were to be unfulfilled. Tycho himself was a flamboyant figure, festooned with a golden nose, the original having been lost in a student duel fought over who was the superior mathematician. Around him was a raucous entourage of assistants, sycophants, distant relatives and assorted hangers-on. Their endless revelry, their innuendoes and intrigues, their cruel mockery of the pious and scholarly country bumpkin depressed and saddened Kepler: “Tycho … is superlatively rich but knows not how to make use of it. Any single instrument of his costs more than my and my whole family’s fortunes put together.”

Impatient to see Tycho’s astronomical data, Kepler would be thrown only a few scraps at a time: “Tycho gave me no opportunity to share in his experiences. He would only, in the course of a meal and, in between other matters, mention, as if in passing, today the figure of the apogee of one planet, tomorrow the nodes of another … Tycho possesses the best observations … He also has collaborators. He lacks only the architect who would put all this to use.” Tycho was the greatest observational genius of the age, and Kepler the greatest theoretician. Each knew that, alone, he would be unable to achieve the synthesis of an accurate and coherent world system, which they both felt to be imminent. But Tycho was not about to make a gift of his life’s work to a much younger potential rival. Joint authorship of the results, if any, of the collaboration was for some reason unacceptable. The birth of modern science—the offspring of theory and observation—teetered on the precipice of their mutual mistrust. In the remaining eighteen months that Tycho was to live, the two quarreled and were reconciled repeatedly. At a dinner given by the Baron of Rosenberg, Tycho, having robustly drunk much wine, “placed civility ahead of health,” and resisted his body’s urgings to leave, even if briefly, before the baron. The consequent urinary infection worsened when Tycho resolutely rejected advice to temper his eating and drinking. On his deathbed, Tycho bequeathed his observations to Kepler, and “on the last night of his gentle delirium, he repeated over and over again these words, like someone composing a poem: ‘Let me not seem to have lived in vain … Let me not seem to have lived in vain.’ ”

After Tycho’s death, Kepler, now the new Imperial Mathematician, managed to extract the observations from Tycho’s recalcitrant family. His conjecture that the orbits of the planets are circumscribed by the five platonic solids were no more supported by Tycho’s data than by Copernicus’. His “Cosmic Mystery” was disproved entirely by the much later discoveries of the planets Uranus, Neptune and Pluto—there are no additional platonic solids
^*
that would determine their distances from the sun. The nested Pythagorean solids also made no allowance for the existence of the Earth’s moon, and Galileo’s discovery of the four large moons of Jupiter was also discomfiting. But far from becoming morose, Kepler wished to find additional satellites and wondered how many satellites each planet should have. He wrote to Galileo: “I immediately began to think how there could be any addition to the number of the planets without overturning my Mysterium Cosmographicum, according to which Euclid’s five regular solids do not allow more than six planets around the Sun … I am so far from disbelieving the existence of the four circumjovial planets that I long for a telescope, to anticipate you, if possible, in discovering two around Mars, as the proportion seems to require, six or eight round Saturn, and perhaps one each round Mercury and Venus.” Mars does have two small moons, and a major geological feature on the larger of them is today called the Kepler Ridge in honor of this guess. But he was entirely mistaken about Saturn, Mercury and Venus, and Jupiter has many more moons than Galileo discovered. We still do not really know why there are only nine planets, more or less, and why they have the relative distances from the Sun that they do. (See
Chapter 8
.)

Tycho’s observations of the apparent motion of Mars and other planets through the constellations were made over a period of many years. These data, from the last few decades before the telescope was invented, were the most accurate that had yet been obtained. Kepler worked with a passionate intensity to understand them: What real motion of the Earth and Mars about the Sun could explain, to the precision of measurement, the apparent motion of Mars in the sky, including its retrograde loops through the background constellations? Tycho had commended Mars to Kepler because its apparent motion seemed most anomalous, most difficult to reconcile with an orbit made of circles. (To the reader who might be bored by his many calculations, he later wrote: “If you are wearied by this tedious procedure, take pity on me who carried out at least seventy trials.”)

Pythagoras, in the sixth century
B.C.
, Plato, Ptolemy and all the Christian astronomers before Kepler had assumed that the planets moved in circular paths. The circle was thought to be a “perfect” geometrical shape and the planets, placed high in the heavens, away from earthly “corruption,” were also thought to be in some mystical sense “perfect.” Galileo, Tycho and Copernicus were all commited to uniform circular planetary motion, the latter asserting that “the mind shudders” at the alternative, because “it would be unworthy to suppose such a thing in a Creation constituted in the best possible way.” So at first Kepler tried to explain the observations by imagining that the Earth and Mars moved in circular orbits about the Sun.

After three years of calculation, he believed he had found the correct values for a Martian circular orbit, which matched ten of Tycho’s observations within two minutes of arc. Now, there are 60 minutes of arc in an angular degree, and 90 degrees, a right angle, from the horizon to the zenith. So a few minutes of arc is a very small quantity to measure—especially without a telescope. It is one-fifteenth the angular diameter of the full Moon as seen from Earth. But Kepler’s replenishable ecstasy soon crumbled into gloom—because two of Tycho’s further observations were inconsistent with Kepler’s orbit, by as much as eight minutes of arc:

The difference between a circular orbit and the true orbit could be distinguished only by precise measurement and a courageous acceptance of the facts: “The universe is stamped with the adornment of harmonic proportions, but harmonies must accommodate experience.” Kepler was shaken at being compelled to abandon a circular orbit and to question his faith in the Divine Geometer. Having cleared the stable of astronomy of circles and spirals, he was left, he said, with “only a single cartful of dung,” a stretched-out circle something like an oval.