Kepler's Witch Read online

  But all things for Aristotle were stacked into hierarchies. There were perfect flowers and imperfect flowers—the rose was at the top, the queen of all flowers. The diamond was the most perfect of gems. The circle was the most perfect of shapes. How could it be otherwise? The circle was simple, uncomplicated, and elegant. Therefore, since the perfect shape was the circle, the motions of the heavens had to be circular. For two thousand years, people believed this—they believed it the way we believe in democracy. There was a moral as well as a geometrical elegance to it. The vision passed from Aristotle to Ptolemy, who, being an observant fellow, realized that, although the philosopher’s perfect circles were elegant, they never fit exact observation, and he set about making Aristotle’s vision connect to the appearances.

  One observation that had to be explained was that there were two types of planetary motions: the lower and the upper. The lower planets—Mercury and Venus—moved in an uncomplicated way. The upper planets, however—Mars, Jupiter, and Saturn—were more mysterious and more complex. Every day, Mars advanced along the plane of the ecliptic from west to east until in a period of about 780 days it completed one revolution. So far so good, but as each of these upper planets neared its position most opposite to the sun, where it could be seen at its highest point in the sky at midnight, it seemed to stop. It would hold that position for a short while and then, curiouser and curiouser, begin to move backward. After a while, it would halt again and roll forward once more. No one quite knew what to make of this. They called these meandering stars “planets,” that is, wanderers, misfits who were out of step with the divine march of the heavens. The planets were oddly halfway between the perfect regularity of the stellar sphere and the frightening oddity of the comets, which appeared out of nowhere and flashed across the sky for a few months, only to vanish once again, predicting famines, floods, and the deaths of kings. Ptolemy’s answer to this strangeness was the invention of epicycles, circles that turned on the larger circles of the planetary orbits, circles upon circles, perfect circles upon perfect circles.

  Copernicus simplified this elegant mess by showing that the epicycles were an artifact of the motion of the earth. We need epicycles only to explain these odd motions of the planets if the earth is stationary, but if the earth moves, and if the earth moves at a faster clip relative to the upper planets, then there will come a time in each year when the earth will lap the higher planets, making them look as if they were standing still for a time, then running backward. But this only happens along a certain range of the arc of earth’s orbit, when the planet is in opposition, meaning that the planet is in nearly a direct line with the earth and the sun, with the earth in between. As the earth passes each of the upper planets, the relative motion becomes less apparent, and the backward motion of the planets will cease.

  But Copernicus believed, as did everyone else, in the perfect circularity of the motions of the planets. Although his brilliant simplification solved the problem of the planets’ erratic motions, it didn’t solve the other problem, the little one that kept hanging out in the shadows. Over the centuries, people noticed that the periods were not equal, that is, that the times between two oppositions were different, slightly different, but measurably so. But then, if the motions of the planets were in fact perfect circles, as Aristotle had presupposed, and if the centers for all the circles were the same point, that is, the earth, then the periods of the planets should have been uniform. But, as it was, the planetary orbits were not, well, perfect. How is it that the period would shift from year to year? Here, the vision warred with experience; what was seemingly right warred with what was seen. Observation of the planets over centuries had shown this.

  The answer that Ptolemy gave was to offset the earth, as the center of the universe, from the orbit of the planet. This would make the orbit appear irregular. He called this offset the planet’s eccentricity. Therefore, the planet still orbited in perfect circles, but the imperfection came about when the perfect circle was moved over slightly, like a hoola hoop. We, having been raised in a universe of gravitational forces, look for the mechanism that would make this possible, but astronomy in Ptolemy’s day, even in Copernicus’s day, did not take physics into account, because that science described the state of affairs on the earth, not in the heavens. All that mattered for the astronomer was to account for the appearances. Copernicus accepted this idea, except that he placed the sun at the center and tried to solve some of the problems by inventing a system of two overlapping circles. Tycho, who still held on to an earth-centered universe, accepted it as well. But mathematically the assumption became more and more untenable. The eccentricity of the orbit, the geometrical measure of its irregularity, was meant to explain how the orbit was irregular, but not why.

  One more problem, though. It became clear in Kepler’s calculations that the motion of Mars was not uniform, that it moved quicker at perihelion, where Mars is closer to the sun, and slower at aphelion, where the planet is farther away. How to account for all of this? When Kepler received the problem from Tycho, the development of a proper Mars theory required the calculation of the line of apsides, that is, the line joining the real center of the circle and the offset center, then defining various points on the orbit by extending the line out to intersect with the orbit itself. This was best done at the opposition, where theoretically Mars would be on a straight line corresponding to the line of apsides on one side of the earth with the sun on the other. The problem was that this opposition did not happen in a regular way—sometimes Mars was north of the point where it was supposed to be, and sometimes it was south. This was the problem of the latitudes, which meant that the planet’s orbit did not perfectly coincide with the plane of the ecliptic, the single plane going through the sun upon which the orbits of all the planets are supposed to lie like concentric circles. But they don’t coincide, at least not perfectly. Some are tilted in one direction, some in the another. The other problem was the problem of longitudes, the problem that led Kepler to abandon the circle for the ellipse. Longomontanus had already solved the problem of latitudes, that is, how much the orbit of Mars tilted from the plane of the ecliptic, but he couldn’t solve the problem of longitudes. Sometimes Mars was farther east than it was supposed to be, and sometimes it was farther west, which shouldn’t have happened if the orbit was a circle with uniform motion.

  When Kepler took over the problem of the orbit of Mars from Longomontanus in 1599, he was arrogant enough to believe that he could solve in only eight days the problem of the longitudes that had plagued his predecessor for months. Like Babe Ruth pointing at the home-run bleachers, he told everyone so. He even made a bet on it, a bet he lost. Eight days came and went, and Kepler still hadn’t solved the problem, so he set his paces and ran a little harder. He still couldn’t solve it. Shrugging it off, he pushed on with his calculations, sure that he could solve the problem eventually, but frustrated that he had pushed the reason he took on the problem in the first place, his desire to confirm his harmonic speculations, into the background. Writing to Herwart von Hohenberg, he said: “I would have finished my investigations into world harmony, had not Tycho’s astronomy so fettered me that I almost went insane.”1

  Kepler’s problem throughout was his lack of an integral calculus, which would not be invented for more than a century. His calculations were made with high-school Euclidean geometry and trigonometry. Kepler had to invent a mathematics for himself based on old methods for calculating the perimeter of a circle by using smaller and smaller isosceles triangles, in “imitation of the ancients.” Instead of triangles, however, Kepler used ovals, because he had been forced to drop the Aristotelian assumption that the orbits were circular, and therefore he hypothesized that the orbits could be calculated by taking ever smaller ovals as an approximation, thus arriving at the shape of Mars’s orbit through sweaty calculation. He even complained to the readers in his text, saying that if they thought plowing through his method was boring for them, they should think of poor Kepler, wh
o had to work through the math the old-fashioned way, with over seventy calculations to be made for each step of his long process. The abandonment of Aristotelian circles, then, came in stages, a piece at a time, and through much labor. At the end, however, in 1605, came the reward, the great flash of insight, the peek into the mind of God, where Kepler realized that the sun sat at one of the two foci of an ellipse, and that Mars’s orbit, although awfully close to a circle, deviated from it just enough to be noticeable to the observant mind. When Kepler was done, a portion of perfection faded from the universe, but in doing so the universe got a little bigger.

  When Kepler lived on Karlova Street, in the Old Town, on his way to see the emperor he would have first crossed the Charles Bridge. On the other side of the river, he would have seen the great, hulking castle with the spires of St. Vitus Cathedral trying to touch heaven. Inns and taverns lined the streets and above them all the palaces of wealthy men.

  Once at the Imperial palace, he would all too often stand and wait for his wages and exchange news with other gentlemen who also stood and waited for their wages. There were sorcerers in Prague, alongside scholars, both real and fake. There were alchemists and astrologers, some of whom claimed to know the original language of Adam and could therefore talk to the angels. There were also a few scientists, like Kepler himself and his friend Johannes Jessenius, who performed the first public autopsy in the city. Starting with the abdomen and ending with the brains, Jessenius worked away, surrounded by well-dressed ladies and gentlemen seated in a high gallery, while he made witty comments about how fortunate the cool weather was or the stench would have been far worse.

  The distinction between the two—between the alchemists, astrologers, and the angel whisperers on one side, and the true scientists—was not so clear in Kepler’s day. The clear distinction is a modern one though it was incipient in the culture. Intelligent observers of the time—only a handful—could point to sets of assumptions that divided the two camps. Some believed, as Tycho Brahe and Kepler did, that regular, precise observation of the natural world, scanning for patterns of understanding that might arise out of the observations, was the only way to true knowledge. This is precisely what drives the Astronomia Nova, which makes it a distinctly modern text. Other natural philosophers believed first in the unity of the cosmos, that all things were mystically connected into the whole, so that while the pattern sifters such as Kepler talked of forces, the universalists such as John Dee talked of cosmic sympathies. The latter believed that because the cosmos was a single unified thing, objects within that universe could be transmuted from one form to another. Lead could be transmuted into gold, implying that alchemists, who worked for the wealthy and powerful, could also produce silver and precious stones out of lesser elements. Some believed that they could even distill small flasks of aurum potabile, liquid gold, which, being the most perfect of all metals, would give anyone who drank it eternal youth.

  For all his title and apparent importance as imperial mathematician, Kepler’s position at court was not that different from that of a court astrologer. The common folk of his time called him “the stargazer” and assumed that he was part of the troop of sorcerers and alchemists who marched up the Steep Stair to Rudolf’s palace looking for imperial favor. Those who knew something of science and philosophy often feared Kepler, as if he secretly practiced the dark arts and was, if not a heretic (that would come later), then a suspicious fellow. This was true of Catholics and Protestants alike, for all feared the coming of Copernicus and the changing of the heavens.

  Most astronomers of the time—Tycho and Kepler, Galileo and Mästlin—were astrologers as well. Kepler and Galileo were different from the general pack, however, because they thought that astrology was unreliable, even a bit silly, but they practiced it nevertheless. Astronomers at the time also practiced medicine, since a reading of the stars was essential for compounding cures, and therefore the practice of medicine was implicated in the art of alchemy, blending scientist and sorcerer, physician and alchemist into one strange amalgam.

  At any moment, Kepler, Tycho, or any other scientists, if the politics of the city turned against them, could find themselves branded as a charlatan and trickster, just as Edward Kelley and John Dee had been a few decades before. And because Kepler was a Lutheran, the Catholic faction was always on the lookout for ways to discredit him. The only thing that made his life more stable than those of the practitioners of the occult arts may well have been the presence of the few Jesuits who understood his work and appreciated it.

  The sorting process, wheat from chaff, of the seventeenth century continued on, however. Many natural philosophers had been already begun to question astrology. Kepler himself held such notions, and in 1610 he wrote a small book in response to Philip Feselius, who had roundly condemned astrologers as “absurd dunces, grunters, cyclopses.”2 Kepler too questioned astrology, but he took a middle position, saying that it still had merit. He distinguished between the old Chaldean astrology, which he considered a kind of augury, and astronomy based on physics, which he considered the royal road to knowledge of the heavens. The various rules of astrology were meaningful to the degree that they described the harmonic or disharmonic states. There are no good constellations and no evil constellations. The different aspects of the heavens affect human beings by seduction, rather than control. Their effect is psychical rather than physical, just as the sound of a bagpipe encourages the peasant to dance. He titled the book Tertius Interveniens, das ist Warnung an etliche Theologos, Medicos, und Philosophos, sonderlich D. Philippum Feselium, dass sie bey billicher Verwerffung der Sternguckerischen Aberglauben nicht das Kindt mit dem Badt ausschütten und hiermit ihrer Profession unwissendt zuwider handlen (“A Warning to Certain Theologians, Physicians, and Philosophers, Especially D. Philip Feselius, That by Cheaply Condemning the Superstition of the Stargazer, They Not Throw the Baby Out with the Bath, Thus Acting Against Their Own Profession”).

  The stars did not control life, therefore—they sang to it.

  Some practitioners, such as Kepler, however—physicians, astronomers, and naturalists—stood in the breach and practiced both schools of natural philosophy without making much of the distinction. Many were fascinated by obscure Egyptian and Alexandrian texts, which they believed were written in far antiquity, but which actually came out of second-century Greek and Egyptian Gnostic cults. Possibly because of this confusion in natural philosophy, there were just as many con artists and swindlers in Prague as there were true practitioners, flimflam artists who often claimed a special knowledge acquired from some arcane text passed down to them by a magus on his deathbed or rescued from his grave. These charlatans sold their wild claims to the highest bidder, and all too often those who bought into them purchased nothing but dreams. But someone, often a member of the nobility, was always willing to buy. Such charlatans would blow into town, make extravagant claims, put on a quick séance, cheat some gullible baron out of a stack of money, and then disappear.

  At first, Rudolf was tolerant of such fakes. Like everyone else, he couldn’t tell the difference between the real and the counterfeit, and although he treasured those who made real contributions to knowledge, men such as Tycho and Kepler, he also wanted to know what alchemists and astrologers, real and fake alike, had to show him. In his own way, he was a universal man who wanted to gather as much knowledge as he could, so he could order it and place it into categories. Knowledge too was an essential part of his Kunstkammer, his museum of marvelous machines, magic stones, and exotic animals. His admirers praised him as the second Hermes Trismegistos, that fabled king of Egypt who once ordered the deep secrets of alchemy to be written on a single sapphire.

  Under the influence of the Spanish Catholic faction at court, who deemed all occult matters as heretical, Rudolf imprisoned a few alchemists who had cheated some noble, but he executed none. Those who had to flee Prague, however, were often not so lucky outside Bohemia. Philip Jakob Güstenhofer, after a famous career in Prague, was
finally hanged in Saxony. Another, Count Marko Bragadino, who had successfully played the part of Greek nobility, and with great theatrical flourish, set Prague atwitter as he strode through the city leading his black hounds. He was finally executed in Munich, stylish to the end, dressed in his best suit, and covered with jewelry made of fake gold. An Italian named Alessandro Scotta, for a time the talk of the city, eventually fell so far out of favor that he ended up in the Old Town Square, where he was reduced to displaying his magical wonders from inside a little wooden booth. Later on, he had a quick tryst with the duchess of Coburg and gave her a child, something she wanted desperately. Since this was not achieved by magic, but by the old-fashioned way, Scotta fled the scene before her relatives could find him and cut his throat.

  What kings and emperors wanted from the likes of Kepler was knowledge that they could turn to power. From his earliest days in Tübingen, Kepler had accumulated a reputation as an astrologer, a reputation he was not really happy about, but one he had nevertheless. Rudolf II was no different. He was, to be sure, a Renaissance man who was enthralled with the natural world, but behind this there was always burning that royal need to know the future, to turn lead to gold, or to read the mystic encryptions of angels. In the early 1580s, John Dee and Edward Kelley arrived in Prague. Dee had already achieved some notoriety invoking spirits through a magic mirror, supposedly from Aztec Mexico, as well as through a crystal ball fashioned from polished smoky quartz, once given to him by the angel Uriel.3 According to legend, he could speak the original language once spoken by Adam, the language that the angels themselves use to speak to one another. He could also understand the language of birds. In England, he achieved notoriety by gathering an astounding occult library full of ancient manuscripts written by long-dead magi, both forgotten and fabled. Because many of these books concerned old Gnostic theologies and philosophies, some in England questioned his Christianity. Eventually, he came to the attention of Queen Elizabeth and advised her on matters both naval and dental, assisting her not only with matters of military deployment, but with her bad teeth. She summoned him to Richmond on several occasions to visit with her and even visited him at his home in Mortlake, in Surrey, on the banks of the Thames. Like Kepler, Dee wanted to plumb the secrets of the universe, and at first he believed that this could be achieved through mathematics. Unhappy with the rhetorical program of a university education, he abandoned his early interest in mathematics, patterns of numbers that give structure to the world, and became interested in their arcane meaning. Soon after, in 1581, he held a séance in his house to call down the angels and to learn their secret wisdom. He believed that with the help of the right translator, or “skryer,” he could seduce the angels to speak to him and could thereby read their language, much of which involved interpreting numerical codes.