Kepler's Witch Read online

  The Stiftschule, the Lutheran seminary school that had hired Kepler, was part of the landslide. It had been founded to compete with the new Jesuit college that the old Archduke Charles had set up in 1574. The Lutheran school therefore played a central role in the Lutheran resistance and was the principal meeting ground for the Lutheran party. When Kepler arrived, the rector of the school, Johann Papius, quickly befriended him, but Papius would last only a few more months before he left to teach medicine at Tübingen. His replacement, Johannes Regius, would not be so pleasant. At the time, there were twelve to fourteen teachers in charge of two levels, an upper and a lower, with four preachers above them keeping one eye on the archduke and the other on the teachers. The school inspectors included Pastor Wilhelm Zimmerman, the father of one of Kepler’s schoolmates, the one who had been asked to leave Tübingen for lack of academic progress. He was also a friend of Mästlin. The good pastor quickly put Kepler on the spot and asked him why his son had been expelled from the university, and Kepler, typically, blurted out that it was because his son was spoiled by his mother and didn’t know how to apply himself. Pastor Zimmerman, understandably, was not pleased. Kepler did his best to smooth things over, and all indications are that Zimmerman was big enough to accept his apology.

  The school paid Kepler 150 gulden annually, 50 gulden less than his predecessor. Also, the administration felt a bit uncertain about the young man, so they decided to give him a probationary period of two or three months to see if he would work out. They assigned him to teach mathematics in the philosophical component of the upper level of the school, part of the second tier among the students; the first tier was for preachers and theologians, the second for those studying law. Part of that section included advanced mathematics, including astronomy, which had been important in Melanchthon’s vision of education. The problem for Kepler was that not many students wanted to study mathematics—it was too hard and not very practical, except for astrology. The first year he had only a few students, and the second year he had none. No one blamed Kepler, because they knew that mathematics had never been popular, so the school administration assigned him to teach basic arithmetic, history, ethics, the poetry of Virgil, and even rhetoric as a substitute.

  Kepler and the new rector, Regius, quickly found that they did not get along. “The Rector is hostile to me, and toward the end of the year, this became dangerous.”7 Regius got his nose twisted by the feeling that Kepler, that young, untried fellow from Württemberg, did not give him enough respect. The boy was brash, plain-spoken, even blunt, and would not listen to his instructions. For all this, Kepler got high marks from the school inspectors, who said that he had distinguished himself first as a speaker, then as a teacher, and finally as a debater. That second year was a year of good and bad omens. Kepler wrote that the stars indicated some future problems with his mother and her bad standing in the community and the suppression of her inheritance.

  The other part of his assignment, the part that did not involve students, was as district mathematician for Graz and the surrounding region, which meant that the authorities expected Kepler to write a series of calendars, astrological forecasts giving them all a heads-up on the weather, the political situation, the crops, and any other possible disasters that might befall them. Kepler took to this, because there was extra money in it.

  Personally, he was lukewarm about astrology. He referred to it often enough to make sense of the strange turns in his life, the character of each of his family members, and even some general things about the future of the nation, but he constantly worried that he might be “nourishing the superstition of fatheads.”8 Still, he practiced it, as did every other astronomer of the day. Tycho Brahe wrote horoscopes. So did Galileo, though he had an even worse opinion of astrology than Kepler did. This is what kings and emperors wanted from stargazers, to cast some light into the future effects of their royal actions. Taking a middle position on the subject, Kepler thought that astrology could cast some light into the world, but that light was diffuse, vague, and full of shadows.

  In 1595, partly from his calculations and partly from his commonsense reading of the times, Kepler made three predictions: one, a terrible winter, with bitter cold weather that would damage fruit trees and cause hardship all around; two, an attack by the Turks from the south; and three, a peasant uprising. All three came true. That winter was so bad, they said, that anytime a shepherd in the mountains blew his nose, it would pop off.9 The Turks did attack, which wasn’t all that surprising, and there was a peasant revolt, again, not all that surprising. Suddenly, Kepler was a celebrity. “On October 27, we had a visit from a baron from Tschernembl, who was sent from the Stände (body of representatives) in Austria ‘above the Enns’ [north of the River Enns], to call for help against the farmers. The same called upon me and started out by mentioning the correctness of the predictions of my astrological calendar in the matter of these revolts.”10

  Another peasant revolt had broken out north of the River Enns, and the local lord, Baron Georg Erasmus von Tschernembl, later a major Protestant leader in Bohemian revolt against the Habsburgs, came by. He also mentioned that the ruler of the territories south of the Enns wanted Kepler to draw a map of his territory. Excited about the idea, Kepler agreed and, with the permission of his superiors at the school, constructed his first scientific instrument, a wooden double right-angled triangle with movable parts. It was about ten feet in length and five in height with a crossed base so that it could stand perpendicular. Soon, between the map and his calendars, Kepler had developed a second career, moving him deeper into the world of numbers, measurements, and all things mathematical.

  His career as an astronomer, however, began in that same year, on July 19, 1595. He says in his journal from February 27, 1596: “The Almighty revealed a central discovery in astronomy to me last summer, after long, exhaustive work and diligence. I explained this in a special treatise which I want to publish soon. The whole work and its demonstration could, with the utmost sophistication, fit nicely into a serving cup with the diameter of a Werkschuh.11 This would be a true reflection of the design of creation, as far as human reason may reach, and at the same time, no man had either seen or heard the like.”12

  The idea hit him in the middle of a lecture on the great conjunctions of Jupiter and Saturn. One can almost imagine him in the middle of a sentence, stopping, staring into the air above his students’ heads for a long, excruciating moment, then stepping aside to write a furious note to himself. In spite of what the inspectors had said about him, Kepler had a reputation as a muddled lecturer, his mind hopping from one idea to the next, faster than the students could follow. For all his students could see, his mind had just made one more leap. For Kepler, however, the moment was decisive. He had put together the pieces, seen that the orbits of Jupiter and Saturn, within the Copernican system, could be drawn on the inside and then on the outside of an equilateral triangle, with Jupiter on the inside and Saturn on the outside. An equilateral triangle is the first regular polygon, one of the simplest archetypes of geometry. What if he could find similar relations between the other planets? Wouldn’t this be an indication of a geometric regularity in the cosmos? For Kepler, this regularity was chock-full of meaning. It was a peek into the mind of God, into the cosmic template used to create the universe.

  The problem was that it didn’t quite work. He tried to draw a square inside the circle of Jupiter, and then another circle inside this square to indicate the orbit of Mars, and then another regular polygon inside the circle of Mars, and then on through the rest of the planets, but the circles he inscribed inside the polygons didn’t quite match up with the known distances to the other planets. The regularity that he found in the orbits of Jupiter and Saturn couldn’t be extended to the other planets, so it wasn’t a universal principle. Besides, it didn’t really explain why there were only six planets and not seven, or twelve, or sixteen. With the discovery of Uranus, Neptune, and Pluto (though there is some doubt about Pluto), we have
since learned that there are indeed more than six planets, and that Kepler’s scruples about the number was unnecessary, if in fact his system had explained anything.

  But Kepler didn’t stop there. He reasoned that two-dimensional figures were by nature inappropriate for explaining a three-dimensional universe with three-dimensional planets, so he looked into ways of nesting three-dimensional figures into each other to explain the distances between the planets, and that led him to the five Platonic solids. Since the time of the Greeks, the Platonic solids had been a mystery in mathematics bordering on mysticism.

  There are only five such solids—the tetrahedron, with four triangular faces, four vertices, and six edges; the cube, with six square faces, eight vertices, and twelve edges; the octahedron, with eight triangular faces, six vertices, and twelve edges; the dodecahedron, with twelve five-sided faces, twenty vertices, and thirty edges; and the icosahedron, with twenty triangular faces, twelve vertices, and thirty edges. There are only five, and there can never be more than five. Plato connected these with the atoms of nature, the building blocks of everything. In this, he followed the earlier philosopher Empedocles: fire for the tetrahedron, earth for the cube, air for the octahedron, and water for the icosahedron. The dodecahedron he connected to the element cosmos, the stuff from which the stars and planets are made.13 Following Plato, Kepler thought that he had found another place where these solids appeared, and since nothing that God fashions is created without a plan, he believed that he had found a way to calculate the distances between the planets in an a priori manner, that is, before any observation takes place. The planets were at these distances not because they happened to be there; they were there because God meant them to be there.

  On August 2, 1595, Kepler wrote to Mästlin in Tübingen, remarking how he had discovered a way of calculating the planetary orbits a priori. He wrote again on September 14, outlined his polyhedral hypothesis, and then went on to explain why the planets moved as they did. The polyhedral hypothesis constructed an account of the number, order, and distances of the planets, but not why they moved. In his letter, Kepler suggested that an anima movens, a spirit of movement, existed in the sun and that its power, a vigor movens, weakened as one moved farther away from the sun. In this one short comment, he set the stage for his own discovery of the area law and the elliptical shape of the planetary orbits. He also set the stage for Newton’s law of gravitation, including the idea that the effect of the moving action decreased with distance. Later in his life, Kepler changed the idea of a moving spirit to a mechanical movement, a force, leaving Newton with the task of defining this mechanism, this action at a distance, in terms of postulates, theorems, and universal laws.

  From this point on in his life, Kepler began to search for this divine plan with grand hopes and grand visions. His life as a scientist was as theological as it was scientific. He wanted to find out what God really intended, God’s final cause of the universe. He wanted to find out what was in God’s mind, actually, really. To do this, he had to break with the astronomical tradition, since Ptolemy, that astronomers used mathematics to create plausible accounts of the appearances in the sky. Like Copernicus, Brahe, and Galileo, he believed that his theories represented the structure of the universe as it really is, accurately and completely. If observation didn’t support his theories, and it eventually did not, he was willing to cast them aside and go on looking. The next seven months after his discovery, he set his ideas into a book he ponderously titled Prodomus Dissertationum Cosmographicarum, Continens Mysterium Cosmographicum, the Forerunner of the Cosmological Essays, Which Contains the Secret of the Universe. The subtitle was On the Marvelous Proportion of the Celestial Spheres, and on the True and Particular Causes of the Number, Size, and Periodic Motions of the Heavens, Established by Means of the Five Regular Geometric Solids.14 Arguably, no book title in the history of Western civilization has ever claimed more for itself than this one. Cosmologists talk like this from time to time, however. Books on “the theory of everything” are part of a long-standing tradition. Ultimately, Kepler’s theory was largely speculative, and he never could get it to fit the data. Today, it has been disproven, and in spite of what Kepler thought about it, it does not generally stand among his greater achievements.

  What Kepler believed was that he had found the map to the shape of the universe, and that his “little book,” as he called it, was a book of cosmography, a picture of that map. The truth of the universe, he maintained, can be found in the mysteries of geometry and not in the properties of pure numbers. Three centuries later, Einstein returned to this idea when developing his general theory of relativity, setting geometry once again at the head of the math class. Kepler considered the properties of pure numbers to be accidental, with the sole exception of the Trinity, the number of God, because God is of course the exception to everything. In saying this, he abandoned numerology. The numbers one, two, four, sixteen, the twelve tribes of Israel, forty days and forty nights had no significance in themselves, but gained significance only when they were used to calculate geometrical relations, which were grounded in nature, which measured real things, land, cities, stars and planets, and were not mere abstractions. Following Nicholas of Cusa, Kepler said that the most fundamental and most important distinction in geometry was between the straight and the curved, the curved representing God and the straight humans. There was no strict line, no impassable wall, between Kepler’s astronomy and his theology. Such walls and divisions developed in later years, possibly by the tidal shifts in Western culture initiated by the Thirty Years’ War, the war that caused Kepler himself so much grief.

  Kepler’s search of the heavens was a search for God. It was, he believed, God’s will. God wanted us to find the plan of creation for ourselves and thereby share in the divine thoughts. The world did not come out as it had for no reason; distinctions like the curved and the straight were inherent in the universe from the beginning. The world as God intended it had to be the best and most beautiful possible, with perfect divine order underlying all the seeming chaos of sinful humans. On April 9, 1597, he wrote to Mästlin and argued, as Plato had done in the Timaeus, that just as the eye is apt to seeing light and the ear to hearing sound, so the intellect is apt to the knowledge of quantity.

  Kepler finished the Mysterium Cosmographicum in 1596 and set about looking for a publisher. He wrote to Mästlin about this, sent him a copy of the manuscript, and asked for his opinion. Mästlin was deeply impressed with the book and offered to help get it published. He had only one criticism, that Kepler had not taken the epicycles into account, which led to problems about the thickness of the spheres, but Kepler pointed to Tycho Brahe’s work on the comet of 1577, in which he showed that the spheres were not real at all, but mathematical fictions.

  To get a book published, even a book on astronomy, perhaps especially a book on astronomy, it had to pass muster with the theologians, the guardians of tradition and orthodoxy. Just as Galileo would have trouble with the Inquisition a few decades later, Kepler would have trouble with the faculty at Tübingen, and for many of the same reasons. As a believing man, Kepler wrote a chapter in the book that tried to show that the Copernican universe was not in disagreement with Scripture, as Galileo would later do in his Letter to Grand Duchess Cristina. Hafenreffer and others gave Kepler the same advice that would be given to Galileo—keep this theory, conjecture, hypothesis, not reality. Don’t try to make overreaching claims for your ideas. Otherwise, you could get in trouble.

  LETTER FROM KEPLER TO MICHAEL MÄSTLIN

  FEBRUARY 10, 1597

  No mortal, I believe, is alive whose destiny is farther from foresight than mine. Already, I was hoping for happiness and believed in its enjoyment, when it got away from me. Contrarily, when I feared the worst and saw it coming, the good appeared. And the more my destiny is in my favor, the more I fear it will once more turn against me, as it is not constant, that it may stay that way for a long time. In the year 1596, I chose a wife and didn’t think o
f anything else for a half year, since letters from exceedingly serious men encouraged me. Happily, I returned to Steiermark [Styria]. When no one congratulated me upon my arrival, I was taken aside and told that I had lost my bride. Since the hope for marriage had taken root over a half year, it took another half year to get over it and to convince myself entirely that it is nothing and embark on a new path of life. After all hope was gone and the outcome already reported to the authorities, another change occurred. The people [the bride, Barbara, and her father] were moved by the governing authority and by ridicule whenever they showed themselves. Then one [of my supporters] worked harder than the next for the disposition of the widow and her father; they were successful and thus prepared another marriage for me. Because of this turmoil, all my decisions for a change of path were canceled. That is how little control each man has over his future.