Tycho and Kepler

by Kitty Ferguson

  She announced5 one should do with her what one would. Should one pull one vein after another out of her body, she knew that she had nothing to say. She fell to her knees, uttered the Lord’s Prayer, and declared that God should make a sign if she were a witch or a demon or ever had anything to do with sorcery. Should she be killed, God would see that the truth came to light and reveal after her death that injustice and violence had been done to her, for she knew that He would not take His Holy Spirit from her but would stand by her.

  The charges were dismissed, and Katharina was set free. The Reinbolds were fined ten florins for having begun the proceedings, and Christoph Kepler was ordered to pay thirty florins for the expense of transferring the trial to Güglingen. Despite the power of her self-defense, Kepler’s mother was a broken woman, and she died the following April.

  As soon as he knew his mother was acquitted, Kepler set off on the journey back to Linz. There were two young children in his family now, for Susanna had given birth to a daughter, Cordula, the previous January, and Sebald was nearly three. But Linz, in the autumn of 1621, was a different city from the one they had left in secret a year earlier. Not long after his departure, the Bohemian rebel army had been defeated at the Battle of White Mountain. The Protestant revolution in Bohemia was over, but the Bavarian army still occupied Linz. In Prague, Ferdinand II, the same man who had been responsible for the Counter-Reformation edicts that had forced Kepler out of Graz years before, was now emperor of the Holy Roman Empire and was overseeing the brutal execution of Protestant leaders. Jesensky (who had aided Kepler in his early unhappy negotiations with Tycho, had delivered the eulogy at Tycho’s funeral, and had been Kepler’s powerful friend during the years in Prague) was one of them. Jesensky’s tongue was cut out before he was quartered. His gory head, along with others, was stuck on a pike on the bridge tower, where they were left to decompose for ten years and finally fell off, one by one, onto the bridge or into the river.

  A seventeenth-century drawing showing the heads of executed Protestant leaders impaled on the bridge in Prague.

  There was fortunately less savage treatment of Protestants in Linz. Kepler remained unscathed, despite speculation in the city that he had fled because Ferdinand had put a price on his head, an odd suspicion since everyone knew the Lutherans had excluded Kepler from Communion. Though Kepler entertained some doubts that it would happen, Ferdinand reconfirmed his appointment as imperial mathematician. The next year, 1622, when all Protestants in Linz were required to convert to Catholicism or leave the city, Kepler was allowed to stay, although his library was sealed6 for a time and he agonized over the requirement that to have it unsealed he must choose which of his beloved books to surrender to the censors. His children were forced to attend Catholic church services. But he was allowed to keep Protestant Planck, his printer, with him along with as many skilled assistants as Planck required. All the turmoil had not completely halted Kepler’s work on the Rudolfine Tables, nor had the death of yet another of his children, four-year-old Sebald, in the early summer of 1623.

  The production of the Tables had been a matter of the highest priority when Tycho died, and during his years in Prague Kepler had filled hundreds of sheets with calculations7 in preparation for eventually completing them. Kepler’s discovery of his planetary laws were a huge step toward this end, but those discoveries also presented new challenges.

  Kepler had derived his first two laws from the Mars observations. In order to complete the Tables, he had to show that the same laws applied to the other planets. Much of this work had been accomplished in connection with the writing of Epitome and Harmonice Mundi, but it was not finished. Kepler explained in the preface to the Tables that the reason for the long delay in their appearance was “the novelty of my discoveries8 and the unexpected transfer of the whole of astronomy from fictitious circles to natural causes.” No one, he pointed out, had ever attempted anything of the kind before.

  In 1617, while at work on Harmonice Mundi, Kepler had come across a book by John Napier9 on logarithms. A year later he realized how much this new invention would simplify the computations that took so much of his time. In the winter of 1621–22 he wrote his own book on logarithms, and he proceeded to use them to solve some of the problems involved in composing the Tables.

  At last, in 1624, Kepler finished the Rudolfine Tables in the new logarithmic form. Tables like these did not give daily positions of the planets; rather, they were far more generally useful, making it possible to figure out any planet’s position for any time thousands of years into the future or the past. In the case of the Rudolfine Tables, Kepler’s instructions about their use, with examples, took up about half the volume of the work. Kepler included logarithm tables, Tycho’s catalog of a thousand stars, and latitudes and longitudes of many cities.

  Once again, having completed a major work, Kepler’s difficulties with it were far from over. Financing publication was a serious problem. A trip to Vienna, where the imperial court was now situated, won him promises that payment would be forthcoming via various cities that would turn imperial funds over to Kepler, but after ten months of traveling among these cities, he came back with virtually nothing to show for the effort. He had taken the opportunity to order four bales of paper from the cities of Memmingen and Kempten and had them sent directly to Ulm, where he expected to print the book. Eventually he would have to pay for the publication himself, with Tycho’s heirs all the while trying to claim a share of the profits and censorship rights. Nevertheless, it was the Rudolfine Tables, more than any of Kepler’s other works, that led to the widest recognition of what he had achieved.

  A manuscript such as this, with 120 pages of text and 119 pages of complicated tables, was a printing challenge beyond anything Planck had attempted so far, and he, in any case, was eager to leave Linz and its religious turmoil. Ulm seemed to Kepler the best place to print the book, where there were other skilled printers and no war going on, but Emperor Ferdinand rebelled at the notion of having the work done outside Austria.

  As this was debated, the Thirty Years War, which had not ended with the quashing of the Bohemian rebellion, came perilously close again. A peasant uprising in the summer of 1626 almost succeeded in driving the Bavarian troops and Ferdinand’s forces out of Linz and Upper Austria. Kepler’s house, situated on the city wall, had to be opened for soldiers guarding the wall, while peasant bands, burning and looting, threatened the capital. During this two-month siege, Kepler almost lost the Rudolfine Tables. On June 30, a fire started by peasant rebels spread and consumed Planck’s press but somehow spared the handwritten manuscript.

  The loss of the press and the near destruction of his manuscript were the last straw for Kepler. He had lived in Linz for fourteen years, longer than he had in Prague. He was exhausted by the confusion and disorder and wanted nothing so much as to complete the publication of the Rudolfine Tables in relative peace. When the siege was finally lifted in August, he wrote to request again the emperor’s permission to depart, and this time it was granted. In mid-November 1626, the Kepler family took a boat up the Danube in the direction of Ulm. By this time, there were two more young children, Fridmar, three years old, and Hildebert, one. Their elder sister Cordula was five. Beyond Regensburg the river was completely frozen, so Kepler left his wife and children there and went on alone overland toward Ulm “on a wagon10 laden with plates of my figures and Table work.” When he arrived, on December 10, 1626, he found lodgings across the street from the printing shop of Jonas Saur, who finally printed the Tables.

  Kepler oversaw every aspect of the printing and worked almost daily with the typesetters. He had brought with him his own set of numerical type (which had not been destroyed when the press burned) and the astronomical type that he had had custom-made for the Tables. As the pages came off the press, he proofread each one. Kepler saw this book as the crowning achievement of two lifetimes, Tycho Brahe’s and his own. Even though he had written it himself, discovered the new laws that made it c
orrect, and done all the calculations, he put Tycho’s name first on the title page as the primary author.

  Kepler decided that the Rudolfine Tables should have an elegant frontispiece. He had an idea in mind and asked a friend from Tübingen, Wilhelm Schickard, to prepare a sketch of it. The frontispiece summed up Kepler’s concept of the world of astronomy, including its history, and was at the same time a masterpiece of whimsy. It shows a pavilion with twelve columns. Those at the back are hewn logs, and a Babylonian astronomer stands there using only his fingers to make an observation. Babylon was where astronomy had its roots. Nearer the front, Hipparchus on the left and Ptolemy on the right stand by columns built of brick. Closer in the foreground sits Copernicus by an Ionic column on whose pedestal he has propped his famous book, and Tycho stands by a Corinthian column with some of his celebrated instruments hung on it. He and Copernicus are deep in discussion, presumably about the Tychonic and Copernican systems, for Tycho points at the ceiling of the temple, where there is a drawing of his system. Kepler cunningly has him not telling Copernicus that it is correct, but asking, “Quid si sic?” (How about that?)

  Ringing the rooftop are six goddesses, each a symbol of something that helped Kepler in his discoveries: Magnetica (on the far right); then Stathmica, the goddess of law; Geometria; Logarithmica; and finally a goddess holding a telescope and another with a globe that casts a shadow.

  The frontispiece of the Rudolfine Tables.

  At the very top of the pavilion flies the Hapsburg eagle, with coins dropping from its beak, a symbol that needs no explanation.

  Kepler did not show Tycho’s heirs the panels in the base of the pavilion before publication, though they would have approved the center panel, a map of Hven. To the left is a panel showing Kepler sitting at a table, by candlelight, a few numbers scratched on the tablecloth, his major books listed on a banner above his head, and a model of the roof of the temple on the table before him. Tycho stands above beside the most elaborate column, but it is Kepler who has labored in the basement, at night, and brought about this marvelous achievement, this temple of the goddess of astronomy Urania, the Rudolfine Tables. Very few of the coins are dropping onto Kepler’s desk.

  Detail from the frontispiece of the Rudolfine Tables.

  The Rudolfine Tables lived up admirably to Tycho’s and Kepler’s hopes for them. The planetary positions given by the Tables were much more accurate11 than those given by the Alfonsine or Prutenic Tables or tables that had been composed by Longomontanus and others. Predictions for Mars, for instance, had previously erred up to five degrees. The Rudolfine Tables stayed within plus or minus ten arcminutes of the actual positions.fn1 In 1629, when Kepler was preparing an ephemeris for the year 1631, he realized that because of the dependability of his Rudolfine Tables, he could confidently predict two “transits” that would occur during that year—one of Mercury and another of Venus—across the disk of the Sun.fn2 He published his predictions in a short pamphlet, De Raris Mirisque Anni 1631 Phenomenis (1629). He would not live to see how superbly accurate he had been.

  fn1 This information comes from Owen Gingerich (1973).

  fn2 On November 7, 1631, the astronomer Pierre Gassendi observed the Mercury transit from Paris. The result was a triumph for Kepler’s astronomy. The transit of Venus was not visible in Europe, because it was night there when it occurred.

  23

  MEASURING THE SHADOWS

  1627–1630

  ONCE BEGUN, PRINTING the Tables went quickly. In early September 1627 Kepler took copies to the Frankfurt Book Fair and finally rejoined his family in Regensburg in early December, only to leave them again after Christmas to take a presentation copy1 of the book to Emperor Ferdinand. The court was in Prague, where Ferdinand was installing his son as the king of Bohemia, and everyone was in exceptionally good spirits because the Protestant revolt had finally been completely put down. The most immediate cause for celebration was the defeat of invasions in the north by the Protestant King Christian IV of Denmark, none other than Tycho Brahe’s old nemesis. Christian had been driven from German soil and also from the entire formerly Danish peninsula of Jutland.

  Noticeably absent were all Kepler’s old Protestant friends, including poor Jesensky, whose head was a grisly presence on the bridge tower. But many other old friends were in Prague as well as many admirers, and the emperor was so pleased with the Rudolfine Tables that he granted Kepler four thousand florins, ten times his yearly salary. That brought to twelve thousand florins the amount of money owed him from the treasury, or the equivalent of thirty years’ salary. Kepler knew he would never collect that if he left the emperor’s service. As it was, he was told that all his fears that he had already lost his job because of the emperor’s edicts in Linz were groundless. All he needed to do was convert to Catholicism. Kepler, of course, refused.

  Kepler had been offered a job in England, and he might at this point have made an abrupt decision to forfeit all back salary and go there immediately had it not been for a man with whom Kepler had had a long association by correspondence but not met in person before. Albrecht Wallenstein had commissioned a horoscope from Kepler in 1608 without revealing who he was or anything about himself except the date and time of his birth. Kepler, always good at horoscopes, had produced one that greatly impressed Wallenstein.

  Wallenstein was a favorite of the emperor and was, in fact, the general largely responsible for the defeat of Christian IV of Denmark. He let it be known that he believed the different faiths must coexist peacefully, and he allowed the practice of Protestantism in his Silesian duchy of Sagan. By moving there, Kepler would be able to maintain his faith while remaining in imperial service. As the agreement finally was worked out the following February 1628, Kepler was promised a house, a printing press, and a generous stipend of a thousand florins a year.

  Kepler made a final trip to Linz in the early summer, where the beleaguered city surprised him with a payment of two hundred florins for their presentation copy of the Rudolfine Tables. Kepler moved his family to Sagan in July. He was fifty-six years old.

  Kepler was unhappy in Sagan2. No one knew him, and he knew no one. There was little intellectual stimulation, and the local dialect was so different from the German Kepler spoke that he had difficulty understanding it or making himself understood. He was suffering, as usual in his later years, from eczema and abscesses. Most discouraging of all, he had hardly arrived when the Counter-Reformation followed him. Once again he was exempted from enforced conversion and the banishment of those who refused to convert, but it was a bitter experience to see it all happening for a third time.

  In the winter and spring of 1630, Kepler’s mood lifted a little. The long-promised printing press and a printer to work at it finally materialized, saving Kepler the trouble of setting his own type by hand and taking it to a nearby town for printing. In March Susanna, Kepler’s daughter by Barbara, married Jacob Bartsch, a student of mathematics and medicine in Strasbourg who had worked for Kepler as an assistant. Kepler decided that the wedding should take place in Strasbourg, though that was too far away for him to attend, given his age and the fact that his own wife would be eight months pregnant by the time of the festivities.

  Matthias Bernegger, a longtime friend and correspondent living in Strasbourg, had recommended Bartsch as a suitor and brought the young couple together. Bernegger gave Kepler a detailed and glowing account of the celebration in a letter. On March 12, the bridegroom received his medical degree in the morning, and later in the day the couple were wed. Kepler’s brother Christoph, his sister Margarethe, and his son Ludwig were part of a wedding procession that included Strasbourg’s most prominent citizens, and huge crowds lined the streets as they passed. “It was meant3, especially, to honor you,” Bernegger told Kepler.

  A month later Kepler’s youngest child, Anna Maria, was born. Now he had two grown children by Barbara and four younger ones by Susanna, although two of those would not live to adulthood. There had been five others who had d
ied in infancy or early childhood. There had been Friedrich, the shining boy who had died in Prague, and Kepler’s beloved stepdaughter Regina, who had died as a young married woman.

  In the days just after Anna Maria’s birth, when Kepler could not leave his wife’s side long enough to oversee the printing of his next series of ephemerides, he told his printer to work instead on a book that he had begun as an essay when he was a student in Tübingen. During the Prague years he had expanded the essay into a short story, much to the delight of his friends, for he laced it with puns and allusions that they could appreciate. This was, in fact, the piece that he had feared might jeopardize his mother’s case in the witch trial, and with the trial long past he felt vindicated in publishing it, with some notes pointing out how it might have been used out of context. Somnium4 (The Dream) consists of a twenty-eight-page story and fifty pages of notes and diagrams and is widely regarded as the first work of science fiction. The hero and narrator, in the course of his travels, visits Uraniborg, where he finds Tycho and many assistants all speaking languages he does not understand until he learns sufficient Danish. Most of the story takes place on the Moon and is about the way the heavens and Earth appear to inhabitants there.

  The notes concerned much more than the possible misuse of the story in the witch trial. It was here that Kepler showed that he understood the concept of gravity better than he is often given credit for. He described clearly the point between Earth and Moon where their separate gravitational attractions exactly cancel out.

  The printing of Somnium proceeded sporadically between printing runs for the ephemerides. It was not finished when Kepler set out from Sagan in October to try, once again, to recover some of his back salary. This time it seemed there was hope. After being put off again and again, Kepler had been promised that if he appeared in Linz on November 11, he would be paid some interest on investments there. He also planned to attend a meeting taking place near that time in Regensburg at which the future of his patron Wallenstein, now fallen from grace, hung in the balance.