The two men in the coach were twenty-eight years old, born within a few months of each other in 1571. Johannes was German and Frederik was Danish, and for different reasons these two strangers now found themselves jostled together, in early June 1600, travelling from Prague to Vienna.
Frederik had been deeply shaken by events in Denmark that had sentenced him into exile and his twenty-year-old lover to be walled up for life in a room in her father’s moated castle. Whirling through Johannes’s head was the mathematics that he was convinced would prove there could only ever be six planets orbiting the sun. Unknown to either Frederik or Johannes, a man in London was working on a text that would make the name of one of them famous. The other’s hopes would be dashed, though he would also become famous—more famous, indeed, than his travelling companion—but for reasons that would surprise him.
What had brought both of them to Prague was the arrival there the year previously of Frederik’s third cousin, Tycho, a fifty-four-year-old bear of a man with an artificial nose made of gold and silver—his fleshly one had been sliced off in a duel. At the age of thirty, in 1576, Tycho had established the most advanced astronomical observatory in the world, Uraniborg, on the island of Hveen, of which he was lord.
Both Tycho and Frederik had for different reasons aroused the considerable anger of their new king, Christian IV. Following his coronation in 1596, Christian refused to continue the generous pension his father had granted Tycho—a sum amounting to 1 percent of the treasury of Denmark. After an exchange of angry letters, Tycho abandoned his homeland and wandered through Europe for twelve months with his household in a procession of two dozen carriages, looking for a new location for his observatory. Finally, after Emperor Rudolf II offered him the position of Imperial Astronomer, he settled his household in Prague.
Frederik’s troubles were more earthy: although already betrothed to one young woman, Christence, he had fallen in love with another, Rigborg, a lady-in-waiting at Christian’s court, and she had become pregnant. Because of the prior betrothal, and because the affair had happened within the royal palace, King Christian sentenced Frederik under the laws of promiscuity and seduction to have two fingers amputated and his nobility revoked. Rigborg’s punishment was several times harsher: her child was taken away from her and she was walled up in a room at Egeskov, her father’s castle at Kvaendrup. A small opening was left to admit food and remove wastes.
For some reason—perhaps the intervention of Tycho—Frederik’s sentence was softened: he was allowed to retain his fingers and his nobility but was compelled instead to enlist in the Austrian campaign against the Turks, who were poised to seize Vienna. On his way from Copenhagen to the front, Frederik stopped off in Prague to visit cousin Tycho and procure a letter of introduction to Archduke Matthias, the emperor’s brother and commander of the Austrian defences.
Frederik’s coachmate Johannes had been teaching at a seminary in Graz when he was struck by what seemed to him a divine revelation about the structure of the universe. Under the still-prevailing Ptolemaic system, Earth was understood to be immobile in the centre of the universe, surrounded by the fixed stars and seven planets (the sun and the moon were also considered to be planets). Johannes, however, was inclined to put his faith in the revolutionary cosmology proposed by Copernicus in 1543, which placed the sun in the centre, demoting Earth to planet status and the moon to a satellite of Earth. At that time—telescopes had not yet been invented—only the five naked-eye planets were known to exist: Mercury, Venus, Mars, Jupiter, and Saturn. Adding Earth to their company brought the total to six. But why, Johannes wondered, had God made only six planets? And why had He arranged their orbits in the particular proportions that He had? There must be an answer: God would not make an unintelligible universe.
The revelation, which occurred to him on July 19, 1595, in the middle of teaching a class on planetary alignment, involved the curious geometric properties of Platonic solids. These are three-dimensional polygons, every face of which is identical: a cube is a Platonic solid. So is a tetrahedron (a pyramid whose three faces and one base are all equilateral triangles). It had been understood since antiquity—and much discussed by Plato, hence the name—that there can only be five such polygons: the laws of geometry forbid any others. In addition to the tetrahedron and cube, which have respectively four and six faces, there are the octagon (eight), dodecahedron (twelve), and icosahedron (twenty). It became blindingly obvious to Johannes that God must have interleaved invisible Platonic solids between the orbits of the planets, such that spheres based on the radius of each orbit were contained and in turn contained by each polygon, like a series of nested Russian dolls. Since there were only five Platonic solids there could only be six planetary spheres: qed.
Within a year, Johannes had published this theory in a book, Mysterium Cosmographicum, which he sent to every astronomer and mathematician he could think of, including Galileo and Tycho. As with many new theories, the numbers did not exactly agree with the reality, but there was enough of a promising match to give Johannes hope that if he got hold of the best observational data, everything would click into place. And at that time, in the late sixteenth century, there was no better astronomical data than Tycho’s.
Johannes considered it providential that just after the publication of Mysterium, Tycho was on the move, eventually settling in Prague, only three hundred miles north of Graz. Johannes wrote to Tycho offering his services, and Tycho—who had been impressed by the mathematical mind behind Mysterium—agreed. It took some time for everything to line up, but in the spring of 1600 Johannes was in Prague negotiating his salary, preparing to return to his family and uproot them from Graz. A deal was eventually struck, but to save money, Tycho arranged for Johannes to ride the first leg of the journey with his cousin Frederik, who was heading down to Vienna anyway.
Did Johannes share some of the secrets of Platonic solids with Frederik? Did Frederik tell Johannes about the tragic fate of Rigborg, walled up in her room in Egeskov castle? Did they bemoan the eccentricities of Tycho and the threat of the Turks? All is possible, but there is no surviving record of what they said, only that they travelled together for three days, parting forever upon arriving in Vienna.
Had history turned out differently, we would know hardly any of these details. A young man with a dubious idea about invisible Platonic solids hovering in space, anxious to prove that there could only ever be six planets; and another young man, the disgraced father of an illegitimate son, on his way to battle the Turks. The litter of history could easily have blurred the outlines of their lives.
But within a year, Tycho was dead and Johannes had inherited the role of Imperial Mathematician, finally gaining complete access to all of Tycho’s books. The astronomical data within was so precise, and Johannes so respectful of its precision, that it enabled him to write four monumental treatises based on this data and in the process discover the three foundational laws of modern astronomy: the elliptical nature of planetary orbits; the precise variance of planetary speed; and the exponential relationship between planetary speed and distance from the sun. Three laws upon which Newton built his theory of universal gravitation, laws known to posterity by Johannes’s surname: Kepler. When Newton spoke about standing on the shoulders of giants, it was Johannes Kepler, along with Tycho, Galileo, and Descartes, who he had in mind.
Johannes gradually and reluctantly abandoned his fever-dream of invisible Platonic solids, which did not sit well with Tycho’s data and eventually sank below the horizon of history. As did Frederik: he was killed in Moravia in 1602 attempting to separate two duelling comrades-in-arms. Oblivion seemed imminent.
But in London, in that same year, a new play was being performed about a Danish prince. The playwright had needed names for two treacherous Danes, and he recalled a high-profile diplomatic mission from the King of Denmark to the Queen of England in 1592. Two young courtiers on that mission, both of them relatives of Tycho Brahe, had made fools of themselves in the taverns and fleshpots of London, and the unintended consequence of their carousing was immortality, though of a dubious kind: Frederik Rosenkrantz and his nineteen-year-old friend Knud Axelsen Gyldenstierne attracted the critical notice of twenty-eight-year-old William Shakespeare, and yielded up their surnames to posterity as bywords for bantering fecklessness and sycophantic treachery.
What personal qualities Frederik Rosenkrantz actually revealed to Johannes Kepler on their three-day coach ride to Vienna, however, may be worth pondering. Among other things, he might have let it slip that his fiancée, Christence, the girl whom he and Rigborg betrayed, was the half-sister of his friend Gyldenstierne.
As for Rigborg Brockenhuus, she survived them all. She languished in her cell until 1608, four years after the death of her implacable father, when she was allowed out once a week to attend services at her local parish church. Upon the death of her mother in 1625, she finally gained her liberty and, with King Christian’s assent, moved closer to Copenhagen. She was reunited with her son, Holger, in 1626 and died fifteen years later at the age of sixty-two. Her body was interred at the Kvaendrup parish church, a few miles from the site of her imprisonment at Egeskov. The monogram FR decorates a book on genealogy that she wrote during her years of freedom.
Walter Murch is a film editor, sound designer, director, translator, and amateur astronomer. His pioneering sound and picture editing work on films include The Conversation, The Godfather, Julia, Apocalypse Now, The English Patient, and Cold Mountain. He is author of In the Blink of an Eye, a book about the craft of film editing, and is the subject of The Conversations by Michael Ondaatje. His latest film work is Philip Kaufman’s Hemingway & Gellhorn, currently in post-production.