Tycho and Kepler (48 page)

When Kepler began producing calendars again in 1616, Planck printed those too. The production of the calendars was, according to Kepler, “a little more honorable
¹³
than begging.” It was his way of raising money for the next publishing effort he had in mind,
for which there had been many requests, a textbook that would make the discoveries he had written about in
Astronomia Nova
more accessible to nonexpert readers, to “the low schoolbenches,” as he put it. The first three volumes of the seven that would comprise
Epitome Astronomiae Copernicanae
(The Epitome of Copernican Astronomy) were ready for Planck in 1615, but the final pages of the seventh
did not come off the press until 1621. By this time Kepler had added enormously to Copernican astronomy, and there was as much if not more of Kepler in the book than of Copernicus.
Epitome
was an influential book, read all over Europe.

Meanwhile, however, after completing the first three volumes of
Epitome
, Kepler turned to producing an immediate moneymaker, an
Ephemeris
for 1618. An ephemeris
consisted of tables giving the position of each planet for every day of the year, and such a book was an invaluable reference for both navigators and astrologers. Kepler knew that after the Rudolfine Tables were published, anyone who was not lazy would be able to calculate planetary positions without using an ephemeris, and sales on those would drop. If he wanted to profit from the sale of ephemerides
(plural of ephemeris), now was the time. Printers normally did not have enough numbers on hand to print an ephemeris, and Kepler purchased his own set of numerical type for Planck to use. Kepler’s confidence about producing these ephemerides year after year is evidence that he had made substantial progress studying the orbits of the other planets besides Mars and Earth.

K
EPLER’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

A
N
U
NLIKELY
H
ARMONY

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 with 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.