Tycho and Kepler

by Kitty Ferguson

  KEPLER’S MARRIAGE to Susanna began only a brief respite from personal problems. In December 1615, news arrived from Württemberg from his sister Margarethe, who was now Margarethe Binder: Their elderly mother had been accused of witchcraft.14

  Katharina Kepler’s reputation as an unpleasant, meddlesome woman and her expertise in herbs and folk medicine had set her up as a target for the sort of grudges and gossip that in the sixteenth and seventeenth centuries in southern Germany could easily degenerate into a witch trial. Frau Kepler was probably an intelligent woman, but she was not a wise one, and she had no social skills. Those people with whom she associated, or who were willing to associate with her, were the dregs of society.

  The crisis had begun when she had sided with her son, Kepler’s brother Christoph, in a minor business dispute with one of her friends, Ursula Reinbold. Frau Reinbold, whom Kepler later dubbed “the crazy,” had been imprisoned for a time for prostitution. One of the disadvantages of that profession was that she often had to abort illicit pregnancies, sometimes with the dubious help of her brother, a barber-surgeon, and at least once in the past with the help of a herbal mixture Katharina Kepler had provided. The present difficulty had erupted when Frau Reinbold, ill after a botched abortion that had nothing to do with Katharina, chose to believe that the potion Katharina had given her three and a half years earlier had been a “witch’s drink” and was causing her present distress. She demanded that Katharina produce a “witch’s antidote.” Even though Frau Reinbold’s brother held his sword at her throat, Katharina refused. To produce the potion would be admitting she practiced witchcraft.

  After that frightening episode, in August 1615 Katharina, on the advice of Christoph and Margarethe’s husband, a village pastor, took the wisest step available, though by no means a good one. She brought a libel suit against Ursula Reinbold.

  In late December, when Kepler finally received Margarethe’s letter informing him of these events, his “heart almost burst.” He immediately wrote to the town senate of Leonberg, choosing his words skillfully to remind them they were dealing with a powerful and influential man and demanding they send him copies of all legal proceedings involving his mother. Several years before, he had revised his fanciful student essay about the Moon, using a plot device in which he described the narrator’s mother as an old woman skilled in folk magic with the power to summon a demon. He agonized over the possibility that news of his essay, or even a copy, might have reached Württemberg or Leonberg.

  As it happened, events in Leonberg were delayed for a time. The bailiff there, one Lutherus Einhorn, had been present when Frau Reinbold’s brother held the sword to Katharina’s throat. Not wanting to reveal his part in this affair, he managed to postpone the libel case until the following October.

  Six days before the proceedings were finally to begin, Katharina was walking along a narrow path and met a group of girls who were carrying bricks to a kiln. The girls, knowing the old woman’s reputation as a witch, stepped aside as much as they could to avoid any physical contact. Katharina’s version of what followed was that she gave them a dirty look and wide berth but, because the path was so narrow, brushed their clothing and walked on. The girls’ version was that one of them (whose mother owed money to Frau Reinbold) had been hit on the arm and that the pain in that arm had increased until she could no longer feel or move her hand. Katharina’s enemies, including the girl’s family, contrived to have Katharina brought before the bailiff, still Lutherus Einhorn. He called in a medical consultant, none other than Frau Reinbold’s brother, who had earlier held his sword to Katharina’s throat. Einhorn’s verdict was, “It is a witch’s grip; it has even got the right impression.”

  At this point, Katharina Kepler made a disastrous move. She attempted to bribe Einhorn with a silver goblet if he would proceed with her libel action and forget the arm incident. This was a windfall for Einhorn, still fearful that his part in the lawsuit would come to light. He suspended the libel case and sent charges of “witch’s drink” and “witch’s grip,” as well as attempted bribery, to the High Council in Stuttgart. Christoph Kepler, Margarethe, and Margarethe’s husband made a quick decision. Though there was a risk of implying that she had fled because of a bad conscience, they bundled Katharina off to Margarethe’s house in Heumaden and from there to Kepler in Linz, just in time, for the council issued an immediate order for Katharina’s arrest and “strenuous examination” about these matters and her theological beliefs. A witch trial had begun.

  Katharina lived with Kepler and his wife in Linz for almost a year, until the following September, 1617. She was not a congenial presence. Kepler’s description of her much earlier had not been flattering, but now that she was such an elderly woman—she was sixty-eight—he was ready to attribute her “trifling, nosiness, fury, and obstinate complaining” to old age. The household that year included himself and his wife Susanna, his two surviving children by Barbara—Susanna and Ludwig—and one-and-a-half-year-old Margarethe Regina. In late spring there was a new baby, christened Katharina after her grandmother.

  During that year, Kepler put his mind and efforts to refuting the charges against his mother and preserving his own safety and reputation. He hired lawyers for Katharina in Leonberg and for himself in Tübingen and Stuttgart, for there were rumors that he himself dabbled in the “forbidden arts.” He wrote to the vice chancellor of the duke of Württemberg, informing him of Einhorn’s bias in the case.

  In September 1617, double tragedy struck the Kepler family. Two-year-old Margarethe Regina died, and the same month the news arrived of the death of her twenty-seven-year-old namesake, Kepler’s stepdaughter Regina, the dearly loved child who had accompanied him and Barbara into exile and whom he had watched grow to womanhood during the happier years in Prague. Regina’s husband Philip Ehem pleaded with Kepler to send his eldest daughter, fifteen-year-old Susanna, to Regensburg to care for the three motherless grandchildren.

  Kepler and Katharina traveled with Susanna up the Danube from Linz to Regensburg, and then, after seeing Susanna settled there, journeyed to Württemberg. The interest in Katharina seemed to have abated. Kepler hoped he might get her libel suit back in motion, but that was a fruitless effort, as was a visit to Tübingen to try to reconcile himself with those who still thought him a closet Calvinist. He visited the very elderly Mästlin, and they discussed the forthcoming Rudolfine Tables at length.

  It seemed safe enough to leave Katharina in Leonberg, so Kepler returned to Linz. He arrived home just before Christmas to discover that the six-month-old baby Katharina was ill. She died on February 9, 1618. Kepler’s new wife was suddenly childless, and Kepler had lost three daughters within six months.

  22

  AN UNLIKELY HARMONY

  1618–1627

  KEPLER WAS TOO distracted with grief to concentrate on the tedious calculations required for the Rudolfine Tables. “Since the Tables require peace,”1 he wrote, “I have abandoned them and turned my mind to developing the Harmony.” The Harmony was a continuation of the book he had begun in Graz during the time when he and Barbara had mourned the death of his first infant Susanna. Now, in another profoundly heavy period, when the decimation of his family gave scant evidence of a rational, loving deity, he nevertheless returned to this attempt to reveal what he believed was the wondrous wisdom and rationality of God in nature. His research followed up on his conviction that mathematical harmonies among the planetary orbits, speeds, and distances from the Sun must be linked on a deep level with music. In 1607 Kepler had acquired a Greek manuscript by Ptolemy, also entitled Harmony, that had preempted his own ideas by about fifteen hundred years. He was both stunned and inspired by the similarity.

  During Kepler’s lifetime, evolving musical theory had added to the list of musical intervals that the ancient Greeks had declared pleasant to the human ear. There were now seven ratios that were accepted as the basis for what was called the “just” scale. Kepler had listened to these intervals and found he agreed w
ith the additions. With his usual brand of curiosity, he wondered why God had chosen these numbers to produce musical consonance. Why leave out the number 7, for example? Some divisions of a harp string produce harmony, while an infinite number of others do not, and that reminded him of his insight that an infinite number of polygons could produce only five polyhedrons. He began to look for a similar way that the ratios of musical consonance had been singled out. He thought the “knowability” of the polygons might provide the answer.

  Kepler began by dividing the polygons into levels of “knowability.” The triangle, square, pentagon, hexagon, and octagon could all be constructed with ruler and compass, the classical Euclidean tools. Kepler dubbed them “knowable.” Since the heptagon (seven-sided) couldn’t be constructed with ruler and compass, he dubbed it “unknowable.” Likewise nine- and eleven-sided polygons.

  Kepler uncovered a mysterious link. If the number of sides of the knowable polygons (3, 4, 5, 6, and 8) were used in the ratios between string lengths, harmony resulted. For instance, both the triangle and the square were, by Kepler’s definition, “knowable,” and a ratio of string lengths of 3:4 produced a harmonious musical interval. The triangle and the pentagon were “knowable,” and a ratio of string lengths of 3:5 produced a harmonious interval. On the other hand, a heptagon, with seven sides, was “unknowable.” Sure enough, a ratio with a 7 in it produced dissonance. It seemed logical to Kepler that the numbers of sides in the unknowable polygons would have been avoided by God when designing the universe. Hence 7, 9, 11, and so forth were not part of ratios producing musical consonance. Kepler reasoned that because human beings are fashioned in the image of their Creator, they have an innate ability to enjoy manifestations of consonant ratios, an ability that doesn’t require any knowledge or awareness of the mathematics or geometry involved. Tycho had thought similarly when he designed Uraniborg. A house built on the principles of harmony would be conducive to lofty thoughts and worthwhile study, even for those unaware they were living in such a structure.

  When Kepler had devised his polyhedral theory and compared the results with the available data, he had been content with a margin of discrepancy that his faith in Tycho’s observations had not allowed him to tolerate later when he wrote Astronomia Nova. He decided to revisit the polyhedral theory and investigate what other principles, in addition to the polyhedrons, God might have used in setting up the solar system, principles that could explain the discrepancies Kepler knew he now had to take more seriously. Kepler’s research included acquiring an extensive knowledge of music theory, for he was becoming more and more convinced that the answers he sought were intimately connected with the combinations of musical intervals that human ears find pleasing.

  Kepler examined the planets’ distances from the Sun at perihelion and at aphelion, and their mean distances from the Sun. He could find no helpful harmonious relationships there. He tried looking for relationships between a single planet’s slowest speed (at aphelion) and its fastest speed (at perihelion), and between and among those speeds using more than one planet. Within a few months he did indeed find an arrangement that was true both to the principles of musical harmony and to the planets’ observed distances, speeds, and eccentricities.

  Of more significance, on May 15, 1618, as he was finishing the book, he discovered a third law of planetary motion, his “harmonic law,” the true relationship between the orbital periods of the planets and their distances from the Sun. Kepler was ecstatic, wanting to give way to a “sacred frenzy,”2 as he put it. “I am . . . writing the book,” he rejoiced, “whether for my contemporaries or for posterity, it does not matter. It can await its reader for a hundred years, if God Himself waited six thousand years for His contemplator.” Near the end of the book he included a prayer that vividly reveals this remarkable man:

  O you who by the light3 of nature arouse in us a longing for the light of grace, so that by means of that You can transport us into the light of glory: I give thanks to You, Lord Creator, because You have lured me into the enjoyment of Your work, and I have exulted in the works of Your hands: behold, now I have consummated the work to which I pledged myself, using all the abilities that You gave to me; I have shown the glory of Your works to men, and those demonstrations to readers, so far as the meanness of my mind can capture the infinity of it, for my mind was made for the most perfect philosophizing; if anything unworthy of Your deliberations has been proposed by me, a worm, born and raised in a hog wallow of sin, which You want mankind to know about, inspire me as well to change it; if I have been drawn by the admirable beauty of Your works into indiscretion, or if I have pursued my own glory among men while engaged in a work intended for Your glory, be merciful, be compassionate, and forgive.

  Figure 22.1: Kepler’s third law of planetary motion, the “harmonic law.” Kepler discovered the true relationship between the orbital periods of the planets and their distances from the Sun in 1618, as he was finishing his book Harmonice Mundi. Kepler’s third law of planetary motion states that the ratio of the squares of the orbital periods of two planets is equal to the ratio of the cubes of their average distances from the Sun.

  Kepler dedicated the five-volume work Harmonice Mundi (Harmony of the World) to King James I of England, expressing the hope that these examples of the glorious harmony with which God had endowed his creation might strengthen James in attempts to bring harmony and peace among the tragically divided churches and other polities. However, only four days before Kepler completed his book and penned that dedication, Protestant Bohemia, where he had spent the ten best years of his life, exploded in a revolution that began the Thirty Years War.4

  For Kepler there was soon to be trouble closer to home. In the summer of 1618, an ominous letter came from an old classmate (possibly acting as Kepler’s lawyer) on the law faculty at the University of Tübingen, warning of a strategy that the Reinbolds and Einhorn might be planning. In autumn 1619 the warning proved correct. A counter civil suit was filed against Katharina Kepler for damages for poisoning Frau Reinbold with the “witch’s drink.” By that time Katharina’s enemies had collected a forty-nine-count indictment against her, including a plethora of local gossip and fancy that recalled unnatural, eerie behavior. The charges included riding a calf to death, muttering fatal “blessings” over infant children, causing pain without touching people, the unnatural death of animals, and trying to entice a young girl to become a witch. One accusation was true. Katharina, having heard in a sermon about an archaic custom of fashioning goblets from the skulls of dead relatives, had asked the gravedigger for her father’s skull so that she could have it set in silver for her son Johannes, the imperial mathematician.

  With Einhorn still acting as bailiff, testimony began in November 1619. The following July the Reinbolds succeeded in getting the duke of Württemberg to turn their complaint into a criminal case. A few days later, on August 7, the seventy-four-year-old Katharina was awakened from her sleep in the dead of night, bundled into a large chest, carried out of her daughter’s house, and put in prison in chains. At this point her son Christoph managed to have the trial, with all the spectacle and scandal attached to it, transferred to Güglingen, but he and Margarethe’s husband, Georg Binder, were inclined to abandon Katharina and scramble to salvage whatever they could of their own dwindling reputations. The faithful Margarethe was of a different mind. Once again she wrote to her brother in Linz. Kepler applied to the duke of Württemberg for a delay in the trial until he could arrive, for he planned to defend Katharina himself.

  Kepler chose to take his family with him when he left Linz that September of 1620. He and Susanna now had a young son, Sebald, who had been born in January 1619, and Susanna was pregnant again. They crept away like thieves in the night, without even telling Kepler’s assistant Gringalletus where they were headed. The reason for the trip was too shocking to have it spread abroad in the town. Kepler left his family in Regensburg, where his daughter Susanna may still have been living with Regina’s family, and
proceeded alone on his grim journey to Württemberg. The mystified people of Linz thought their mathematician had fled for good.

  Kepler found his mother in prison in chains with two guards and required to pay these guards herself, as well as for her food and upkeep. The Reinbolds complained that so much of her money was being used up in this manner that there would be little left for them when the trial was over.

  Kepler had been advised that having the defense case written down would help the outcome, and he insisted that all the defense lawyer’s arguments be put in writing. Christoph lamented the greater cost for what he thought was already a lost cause. The proceedings dragged on, with more lawyers, more witnesses, and more written arguments. Kepler traveled to Stuttgart to consult his lawyer in person, and they put together a 126-page legal brief, much of it in Kepler’s handwriting, that rebutted the charges one by one. The trial ended in August, and all the proceedings were sent, as was the custom, to the law faculty of the University of Tübingen. It was they who would make the decision. Kepler’s friend Christoph Besold was on that faculty. Nevertheless, even the force of Kepler’s presence throughout the trial, his skill in devising the defense, and his powerful friend could not bring about an acquittal. The court declared itself uncertain and ordered that Frau Kepler be examined once more under the lightest form of torture, verbal terror while being shown the instruments of torture.

  On September 28, 1621, Katharina was dragged to the torture chamber, accompanied by three representatives of the court, a scribe, and a bailiff (not Einhorn this time). The torturer himself showed her his instruments, described their use, and with the greatest possible sternness and melodrama commanded her to tell the truth. Contrary to all expectation, Katharina Kepler gathered her aging wits about her, summoned the eloquence she had bequeathed to her son, and saved herself. As the report reads: