by Carl Sagan
Modern popular astrology runs directly back to Claudius Ptolemaeus, whom we call Ptolemy, although he was unrelated to the kings of the same name. He worked in the Library of Alexandria in the second century. All that arcane business about planets ascendant in this or that solar or lunar “house” or the “Age of Aquarius” comes from Ptolemy, who codified the Babylonian astrological tradition. Here is a typical horoscope from Ptolemy’s time, written in Greek on papyrus, for a little girl born in the year 150: “The birth of Philoe. The 10th year of Antoninus Caesar the lord, Phamenoth 15 to 16, first hour of the night. Sun in Pisces, Jupiter and Mercury in Aries, Saturn in Cancer, Mars in Leo, Venus and the Moon in Aquarius, horoscopus Capricorn.” The method of enumerating the months and the years has changed much more over the intervening centuries than have the astrological niceties. A typical excerpt from Ptolemy’s astrological book, the Tetrabiblos, reads: “Saturn, if he is in the orient, makes his subjects in appearance dark-skinned, robust, black-haired, curly-haired, hairy-chested, with eyes of moderate size, of middling stature, and in temperament having an excess of the moist and cold.” Ptolemy believed not only that behavior patterns were influenced by the planets and the stars but also that questions of stature, complexion, national character and even congenital physical abnormalities were determined by the stars. On this point modern astrologers seem to have adopted a more cautious position.
But modern astrologers have forgotten about the precession of the equinoxes, which Ptolemy understood. They ignore atmospheric refraction, about which Ptolemy wrote. They pay almost no attention to all the moons and planets, asteroids and comets, quasars and pulsars, exploding galaxies, symbiotic stars, cataclysmic variables and X-ray sources that have been discovered since Ptolemy’s time. Astronomy is a science—the study of the universe as it is. Astrology is a pseudoscience—a claim, in the absence of good evidence, that the other planets affect our everyday lives. In Ptolemy’s time the distinction between astronomy and astrology was not clear. Today it is.
As an astronomer, Ptolemy named the stars, listed their brightness, gave good reasons for believing that the Earth is a sphere, set down rules for predicting eclipses and, perhaps most important, tried to understand why planets exhibit that strange, wandering motion against the background of distant constellations. He developed a predictive model to understand planetary motions and decode the message in the skies. The study of the heavens brought Ptolemy a kind of ecstasy. “Mortal as I am,” he wrote, “I know that I am born for a day. But when I follow at my pleasure the serried multitude of the stars in their circular course, my feet no longer touch the Earth …”
Ptolemy believed that the Earth was at the center of the universe; that the Sun, Moon, planets and stars went around the Earth. This is the most natural idea in the world. The Earth seems steady, solid, immobile, while we can see the heavenly bodies rising and setting each day. Every culture has leaped to the geocentric hypothesis. As Johannes Kepler wrote, “It is therefore impossible that reason not previously instructed should imagine anything other than that the Earth is a kind of vast house with the vault of the sky placed on top of it; it is motionless and within it the Sun being so small passes from one region to another, like a bird wandering through the air.” But how do we explain the apparent motion of the planets—Mars, for example, which had been known for thousands of years before Ptolemy’s time? (One of the epithets given Mars by the ancient Egyptians was sekded-ef em khetkhet, which means “who travels backwards,” a clear reference to its retrograde or loop-the-loop apparent motion.)
Ptolemy’s model of planetary motion can be represented by a little machine, like those that, serving a similar purpose, existed in Ptolemy’s time.* The problem was to figure out a “real” motion of the planets, as seen from up there, on the “outside,” which would reproduce with great accuracy the apparent motion of the planets, as seen from down here, on the “inside.”
The planets were imagined to go around the Earth affixed to perfect transparent spheres. But they were not attached directly to the spheres, but indirectly, through a kind of off-center wheel. The sphere turns, the little wheel rotates, and, as seen from the Earth, Mars does its loop-the-loop. This model permitted reasonably accurate predictions of planetary motion, certainly good enough for the precision of measurement available in Ptolemy’s day, and even many centuries later.
Ptolemy’s aetherial spheres, imagined in medieval times to be made of crystal, are why we still talk about the music of the spheres and a seventh heaven (there was a “heaven,” or sphere for the Moon, Mercury, Venus, the Sun, Mars, Jupiter and Saturn, and one more for the stars). With the Earth the center of the Universe, with creation pivoted about terrestrial events, with the heavens imagined constructed on utterly unearthly principles, there was little motivation for astronomical observations. Supported by the Church through the Dark Ages, Ptolemy’s model helped prevent the advance of astronomy for a millennium. Finally, in 1543, a quite different hypothesis to explain the apparent motion of the planets was published by a Polish Catholic cleric named Nicholas Copernicus. Its most daring feature was the proposition that the Sun, not the Earth, was at the center of the universe. The Earth was demoted to just one of the planets, third from the Sun, moving in a perfect circular orbit. (Ptolemy had considered such a heliocentric model but rejected it immediately; from the physics of Aristotle, the implied violent rotation of the Earth seemed contrary to observation.)
In Ptolemy’s Earth-centered system, the little sphere called the epicycle containing the planet turns while attached to a larger rotating sphere, producing retrograde apparent motion against the background of distant stars.
In Copernicus’ system, the Earth and other planets move in circular orbits about the Sun. As the Earth overtakes Mars, the latter exhibits its retrograde apparent motion against the background of distant stars
It worked at least as well as Ptolemy’s spheres in explaining the apparent motion of the planets. But it annoyed many people. In 1616 the Catholic Church placed Copernicus’ work on its list of forbidden books “until corrected” by local ecclesiastical censors, where it remained until 1835.* Martin Luther described him as “an upstart astrologer … 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.” Even some of Copernicus’ admirers argued that he had not really believed in a Sun-centered universe but had merely proposed it as a convenience for calculating the motions of the planets.
The epochal confrontation between the two views of the Cosmos—Earth-centered and Sun-centered—reached a climax in the sixteenth and seventeenth centuries in the person of a man who was, like Ptolemy, both astrologer and astronomer. He lived in a time when the human spirit was fettered and the mind chained; when the ecclesiastical pronouncements of a millennium or two earlier on scientific matters were considered more reliable than contemporary findings made with techniques unavailable to the ancients; when deviations, even on arcane theological matters, from the prevailing doxological preferences, Catholic or Protestant, were punished by humiliation, taxation, exile, torture or death. The heavens were inhabited by angels, demons and the Hand of God, turning the planetary crystal spheres. Science was barren of the idea that underlying the phenomena of Nature might be the laws of physics. But the brave and lonely struggle of this man was to ignite the modern scientific revolution.
Johannes Kepler was born in Germany in 1571 and sent as a boy to the Protestant seminary school in the provincial town of Maulbronn to be educated for the clergy. It was a kind of boot camp, training young minds in the use of theological weaponry against the fortress of Roman Catholicism. Kepler, stubborn, intelligent and fiercely independent, suffered two friendless years in bleak Maulbronn, becoming isolated and withdrawn, his thoughts devoted to his imagined unworthiness in the eyes of God. He repented a thousand sins no more wicked than another’s and despaired of ever attaining salvation.
But God became for h
im more than a divine wrath craving propitiation. Kepler’s God was the creative power of the Cosmos. The boy’s curiosity conquered his fear. He wished to learn the eschatology of the world; he dared to contemplate the Mind of God. These dangerous visions, at first insubstantial as a memory, became a lifelong obsession. The hubristic longings of a child seminarian were to carry Europe out of the cloister of medieval thought.
The sciences of classical antiquity had been silenced more than a thousand years before, but in the late Middle Ages some faint echoes of those voices, preserved by Arab scholars, began to insinuate themselves into the European educational curriculum. In Maulbronn, Kepler heard their reverberations, studying, besides theology, Greek and Latin, music and mathematics. In the geometry of Euclid he thought he glimpsed an image of perfection and cosmic glory. He was later to write: “Geometry existed before the Creation. It is co-eternal with the mind of God … Geometry provided God with a model for the Creation … Geometry is God Himself.”
In the midst of Kepler’s mathematical raptures, and despite his sequestered life, the imperfections of the outside world must also have molded his character. Superstition was a widely available nostrum for people powerless against the miseries of famine, pestilence and deadly doctrinal conflict. For many, the only certainty was the stars, and the ancient astrological conceit prospered in the courtyards and taverns of fear-haunted Europe. Kepler, whose attitude toward astrology remained ambiguous all his life, wondered whether there might be hidden patterns underlying the apparent chaos of daily life. If the world was crafted by God, should it not be examined closely? Was not all of creation an expression of the harmonies in the mind of God? The book of Nature had waited more than a millennium for a reader.
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 superlativ
ely 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.’ ”