The Theory of Heliocentrism

The great irony behind Galileo Galilei’s skirmishes with the Catholic establishment was that the whole debate was predicated on outdated information. One thing that both Galileo and the Church could agree upon was that to be a heliocentrist was to be an adherent of Nicolaus Copernicus’s On the Revolutions of the Heavenly Spheres — a book which was, as we’ve seen at some length by now, riven with infelicities. Johannes Kepler had corrected almost all of the flaws in that book in his own book The New Astronomy before Galileo ever looked through a telescope for the first time. Yet the Italians remained blissfully ignorant of his innovations. This made it much easier for conservative Church figures like Robert Bellarmine to argue against heliocentrism than it might have been if they had all had Kepler’s latest proposals to hand.

A vaguely similar dynamic applied to the telescope, the horse which Galileo had ridden to his sudden international fame. Galileo never really understood why his telescopes worked on a theoretical level, only how to build better ones than his competitors. Kepler, by contrast, grasped what was going on inside the magical tubes as soon as he learned how they were put together. Not much of a mechanical tinkerer himself, he was well-equipped to explain the science behind the telescope to the world. In early 1611, while he was still waiting in vain for further correspondence from Galileo, he published a short book called Dioptrice, a sequel to his earlier book on optics that explained in careful detail how a convex and a concave lens, placed one behind the other, were capable of producing such astounding effects by refracting the light which passed through them. We can only speculate about how much these two complementary minds might have been able to accomplish together, if they had only found a way to bridge the divide of culture and language that lay between them.

As it was, Dioptrice would prove the last important piece of writing to leave Kepler’s pen while he was in Prague. Even as it was going to the printing press, tribulations of an all too terrestrial nature were coming to fill his days there, as he once again found himself at the mercy of political and religious upheavals that were out of his control.

Emperor Rudolf II’s lethargy and eccentricity had endeared him to few since the turn of the seventeenth century. His own Habsburg clan watched in dismay as their status in Europe diminished in tandem with the erosion of the Holy Roman Empire as an institution — an erosion which Rudolf was allowing to proceed unchecked. In April of 1606, most of the rest of the adult Habsburgs signed their names to a formal rebuke of their most powerful relation, strongly implying in the process that he was in active communication with the Devil.

His Majesty is interested only in wizards, alchemists, Kabbulists, and the like, sparing no expense to find all kinds of treasures, learn secrets, and use scandalous ways of harming his enemies. He has a whole library of magic books. He strives all the time to eliminate God completely so that he may in future serve a different master.

The rest of the family elevated Rudolf’s younger brother Matthias, who was reasonably charismatic and full of all of the worldly ambitions that seemed to have deserted his older sibling, to the position of their official patriarch. Two years later, Matthias marched on Prague from his home base of Vienna with an army of 20,000 men. Rudolf averted military defeat and deposition from his throne only by ceding to Mathias day-to-day control over most of the empire, retaining more than ceremonial authority over only a relatively small circle of territory around Prague itself. Mathias had good reason to believe that even this territory would come to him sooner rather than later, given that Rudolf looked more wasted than ever, a pale wraith haunting the corridors of his palace. Being a man who seemed to have left the desires of the flesh behind sometime in the last century, he had no wife and no children to stand in the way of Mathias’s succession to his throne once he finally passed away.

Just as Graz had once been, Prague was a religiously mixed city at this time, with an allegedly Catholic but actually agnostic ruler in Rudolf. In addition to traditional Catholics, its streets were full of the only nominally Catholic Hussite sect, with harder-line adherents to the teachings of Martin Luther, and with a substantial Jewish minority as well. Yet Prague was far from anyone’s modern liberal idea of a harmonious multicultural melting pot. All of the factions were constantly jockeying for advantage against one another; only the balance of power between them preserved the peace. In the wake of Rudolf’s humbling, the Lutherans disrupted that balance, by threatening the emperor with violent revolt if he didn’t allow them free rein to open as many churches and schools as they wished and to advertise for their co-religionists from all over Europe to join them here in the heart of Bohemia. Rudolf signed the agreement they set before him, but he was seething with resentment at this latest humiliation even as he was doing so. He may have been helpless to do much about his brother’s depredations, but it might be a different story when it came to these insolent citizens of his own city. The Lutherans were about to learn the dangers of overplaying one’s hand — about to learn that even weak and sickly emperors are provoked at one’s peril.

On the assumption that one’s enemy’s enemy ought to be one’s friend, Rudolf reached out to his nephew Leopold. By no means a natural ally of the current emperor under any other circumstances, Leopold was something of a loose cannon of a bishop in Bavaria, being so strident a Catholic as to make his cousin Archduke Ferdinand, who had made life so miserable for Kepler in Graz, seem like a moderate by comparison. He raised a private army of mercenaries and led them to Prague in February of 1611 on the strength of a promise that they would permitted to loot all of the Protestant gold that they could carry home with them. Chaos ensued. Incensed at the incursion, the Lutherans joined with the Hussites, the Jews, and even some of the Catholics of Prague to put up an unexpectedly stiff resistance. The streets were wracked with fighting for days.

For Kepler, huddling inside his house like most of the city’s non-combatants while citizens and mercenaries fought and pillaged and raped and died just outside his front door, the invasion was not even the worst of his problems. A mark on the front door showed that his home had become a dreaded sick-house, to be avoided at all costs; such a mark was better protection for the people inside than an entire battalion of musketeers would have been. In the last weeks before Leopold’s arrival, smallpox had torn through Kepler’s family, laying low his wife Barbara and the three children they had had since moving to Prague a decade before. (Kepler’s stepdaughter Regina had by now married and left Prague for Germany with her husband.) The youngest child, a boy named Friedrich, died on February 19, when the fighting outside the door was at its peak. He had been his mother’s favorite; Kepler wrote in his diary that the bond between them was not “merely love,” but something “deeper, more lavish.” (Was he regretting that he and Barbara had never enjoyed a similar bond?) After Friedrich was gone, Barbara Kepler remained in her bed, her spirit broken, slipping toward her own inevitable passing.

Meanwhile the chaos in the city at large ended in as demeaning a fashion as was imaginable for Emperor Rudolf. For a second time, his brother Mathias marched on Prague with an army. A staunch Catholic he may have been, but he wasn’t willing to watch the imperial capital be burnt to the ground — the direction in which the unrest was fast trending — in the name of his faith. Not wanting to go to battle against his headstrong nephew Leopold either, Matthias simply paid the latter’s mercenaries to go back where they had come from, thereby restoring order in the streets. In one last act of diplomacy or mercy, he allowed Rudolf to continue living in his palace and to retain his title of Holy Roman Emperor, even though he had now stripped him of the last of his worldly authority. All signs were that Rudolf wasn’t long for this world anyway.

So, Rudolf was permitted to haunt his Cabinet of Curiosities for a little while more, eating almost nothing, ingesting strange elixirs instead that he believed could replace food, could restore him to robust health, might even make him immortal. Legend has it that he raised a window and shouted a curse down upon the city on one of his last days on Earth.

Prague, ungrateful Prague, I have made you famous, but now you are driving me, your benefactor, out! Let revenge come upon you and damnation befall you and all the Czechs!

Then, on January 20, 1612, he fell over and died. Coincidentally or not, his old capital would indeed have a pretty hard time of it in the decades to come.

Mathias’s first act upon assuming Rudolf’s old throne was just the beginning of Prague’s troubles: he moved the imperial capital back to Vienna, where it had been prior to his older brother’s ascension (and where it would now stay until the Holy Roman Empire was formally abolished in 1806). But Johannes Kepler and the other Lutherans of Prague soon had something far worse to fret over than this diminution in status: Kepler’s old nemesis Archduke Ferdinand was declared king of Bohemia, taking up residence right there in Rudolf’s former palace. Ferdinand agreed before taking over to display a measure of toleration for the Hussites, Protestants, and Jews of Prague, but his earlier deeds sounded louder in many ears than his current promises. “Non-Catholics consider me unfeeling in my prohibition of heresy,” he had once said. “I do not hate them but love them. Unless I loved them free from any other concern, I would leave them in their error.” The non-Catholic citizens of Prague might be forgiven for concluding that this was a kind of love that was unlikely to do much for their well-being.

Kepler’s title of Imperial Mathematician was not stripped from him after the passing of Rudolf, but it was momentarily forgotten by a new emperor with less intrinsic interest in such things. For his part, Kepler certainly wasn’t inclined to stick his Protestant head up and raise the issue. Having seen how one other takeover of a city by Archduke Ferdinand ended for him already, he was instead frantically writing letters, looking for a new position somewhere — anywhere — else. The difficulty he had finding one showed how thoroughly his revolutionary book The New Astronomy had failed to break through. Not for the first time, his alma mater the University of Tübingen turned down his request for a job. Intriguingly, he also corresponded briefly with the University of Padua, about the possibility of filling Galileo’s now-vacant post; if this had come to pass, he and Galileo might have been forced by simple proximity to reckon with one another’s ideas more carefully, possibly to the enormous benefit of astronomy as a whole. But it did not come to pass. In the end, Kepler had to settle for a modest teaching post in the northern Austrian town of Linz, where Archduke Ferdinand’s pogroms against Protestants had not yet penetrated before he was called out to Prague. Kepler stayed in the former imperial capital just long enough to give Barbara time to die. Then he set out for Linz with his two surviving children. From the heights of the Holy Roman Emperor’s personal mathematician, he was reduced to his previous state of a humble teacher. His life had become a proverb.

Linz was a tidy enough town, but it was no Prague. This was no city of magic and wonders, just a quietly prosperous community of Germanic burghers plying their various trades. But then again, Kepler himself had never been all that well-suited to cosmopolitan company. For a while, Linz looked like it might provide a congenial home for him. Being still possessed of the title of Imperial Mathematician, Kepler gradually rebuilt his links with the court of Emperor Mathias in Vienna, which lay only about 100 miles (160 kilometers) away. And despite being, as he put it, “a philosopher who has passed and is nearing the end of his prime, who has muted passions, who is soft of body and dried up by nature,” the 42-year-old Kepler married a 24-year-old woman named Susanna, who had “won me over with love, humble loyalty, economy of household, and the love she gave her [future] stepchildren. I also liked her loneliness, and the fact that she was an orphan.” It may not have been the most passionate of relationships, but Susanna gave Johannes the domestic tranquility that had eluded him with Barbara.

As matters transpired, he would have need of both the measure of protection provided by his links to Vienna and the comfort provided by Susanna. For his stubborn determination to say what he believed and not say what he didn’t soon planted him squarely in the middle of yet another religious conflict — one that, absent his highfalutin title, might have threatened his livelihood and possibly even his life. This time, the conflict was with his fellow Protestants rather than any Catholic authority.

Setting all of his achievements in astronomy and other fields of science and mathematics aside for a moment, one of the most amazing aspects of Johannes Kepler was his attitude toward religious faith, which reads as breathtakingly modern today. He thought that religion was a matter for every individual’s personal conscience, one which ought to have little to no bearing on the prospects of his public-facing life and career. That Kepler could hold such a point of view while remaining deeply religious himself only makes him that much more amazing. He embraced wholeheartedly Jesus Christ’s maxim of rendering unto Caesar that which was Caesar’s, rendering unto God that which was God’s. Further, he refused to condemn anyone else for his or her religious beliefs. Whether one was a Catholic, an adherent to any of the fast-multiplying sects of Protestantism, or even a Jew or a Muslim, one deserved respect, and along with it the freedom to practice one’s faith as one saw fit. Kepler perceived a commonality in all of the “Peoples of the Book” who believed in the Bible in whole or even just in part, a shared heritage that he thought ought to be sufficient to bridge any differences separating them. Unfortunately for him, this was no more the prevailing attitude among the Protestants of the seventeenth century than it was among the Catholics. Anyone who might have once thought that Martin Luther’s history as a conscientious objector to the ironclad Catholic dogma of his day would lead either him or those who followed him to adopt a more flexible posture toward the practicing of Christianity had long since had to live through a very rude awakening.

The Protestants who were still tolerated in the officially Catholic town of Linz were of the old-school Lutheran stripe, following the strict line laid down by their titular guiding light, as carefully outlined  in a document known as the Formula of Concord. Daniel Hitzler, the chief Lutheran pastor of Linz, regarded Kepler with suspicion from the first, thanks to his many and ongoing dealings with Catholics; he was, after all, still the Imperial Mathematician, at the beck and call of the Holy Roman Emperor himself. When Kepler dared to tell Hitzler that he disagreed with one point found in the Formula of Concord, Hitzler pounced.

That point involved the ritual of Communion, the reenactment of the Last Supper in which the faithful ingested the body and blood of Jesus Christ in the form of bread and wine. Its exact nature and meaning had been a controversial issue among theologians for almost as long as Christianity had existed. Back in 1054, a dispute over whether the Communion bread should be leavened or unleavened — meaning whether it should be made with yeast or not — had been the proximate cause of the first great schism of Christian history. Western European theologians had pointed to the commandment from God in the Old Testament that his followers eat only unleavened bread on holy days, while their more easterly counterparts had argued that this dictum no longer applied in the wake of the New Covenant between God and his people that had been brought down to Earth by Jesus. Over this dispute, which a secularist might be excused for calling picayune in the extreme, one Christian faith had become two: the Roman Catholic Church and the Eastern Orthodox Church.

Now, after Christianity had been splintered yet further by the rise of Protestantism, Johannes Kepler was gored on the horns of another raging dispute about the nature of Communion. The Lutherans were in agreement with the Catholics that the bread and wine that were served during Communion literally turned into the body and blood of Jesus in the mouth of the believer. But Kepler, bless his heart, was just too much of an empiricist — too much of a scientist — to accept this notion. All of the evidence of his senses told him that no such transubstantiation took place, that the ritual was in reality just a metaphor. To insist that it was happening in the face of the evidence struck him as no different from the insistence by some benighted souls that the sights revealed by the telescope didn’t really exist, were just tricks set up to deceive the mortal gaze. Kepler’s God was not a trickster, and still less a being who would allow the Devil to play such tricks on his beloved flock. He had given humans the ability to perceive and understand his creations for a reason; his universe was not some sort of cosmic practical joke. That said, Kepler wasn’t ready to wage a holy war over the point. Much as most of us might today, he considered the exact physical properties of the Communion bread and wine as they slid down the throat to be a pretty minor point when set against the larger message of the Christian faith that they symbolized.

But if the history of Christianity teaches us anything, it is that it is often the most fine-grained, esoteric disputes that generate the most heat in human affairs. Much to the disadvantage of Kepler in Linz, the doctrine of transubstantiation was also denied by another Protestant sect known as Calvinism, which had sprung up in France while Martin Luther was still alive and was now the biggest rival to Lutheranism. By denying transubstantiation, Kepler set himself up in Daniel Hitzler’s zealous eyes as a closet Calvinist, as bad or worse than a Catholic. Hitzler eventually presented Kepler with a document listing all of the provisions of the Formula of Concord, point by point, including the doctrine of transubstantiation. He must sign his name to a statement at the bottom that he believed all of it, he was told, or he would be ejected from the Lutheran congregation. “Subtly, in any organization,” writes Kepler’s biographer James A. Connor, “solidarity becomes ossification, the faith becomes orthodoxy, and compliance becomes more important than conversion of spirit.” The Lutheran church had reached that juncture with rather astonishing speed.

Anyone of who has followed the story of Kepler’s life to this point can probably guess what happened next: he refused to sign, not angrily or insultingly as he might have done as a younger man, but calmly and firmly.  Hitzler replied, equally firmly but somewhat less calmly, that Kepler was no longer welcome in the pews of Linz’s Protestant churches. This was a less devastating blow than excommunication might have been for a Catholic, for there was no Protestant doctrine that salvation was only possible through certain individuals and community rituals. Nonetheless, it was plenty devastating enough for a deeply religious man who wished only to gather in worship with others of his faith. His attempts to go above Hitzler’s head by writing to higher Lutheran authorities in other cities managed only to embitter his local enemy that much more. “Don’t trust your mind too much, and make sure your faith rests not on human wisdom but on God’s strength,” wrote the authorities back to Kepler. But for Kepler, human wisdom was the ultimate manifestation of God’s strength, proof that he loved and valued his people.

All of this left Johannes Kepler, the perpetual outcast, more on the outside than ever. Everyone in Linz seemed to think the worst of him.

I have been denounced as a man without principle, approving everyone, incited not by an honest heart but by a desire to have the friendship of all parties, whatever may happen, today or tomorrow. I have been called a godless scoffer of God’s work and God’s holy Communion, who cares nothing about whether the church accepts him or not, and who, instead of being eager to receive Communion, decides that it should be kept from him. I have been attacked as a skeptic who in his old age has yet to find a foundation for his faith. I have been condemned as unsteady, now siding with this group, now with that group, as each new and unusual thing is brought into the arena.

Against his own will, Kepler had become that rarest of all human creatures in seventeenth-century Europe: a man of no organized faith. At his day job, he had to bear with the cold shoulders of his colleagues and even many of his students, knowing that only a fear of provoking the wrath of Emperor Matthias in Vienna saved him from being dismissed from his teaching post. With nowhere else to turn, Kepler fell back on the original maxims of Jesus, the very ideas that always seem to be forgotten in internecine disputes like this one. His faith was strengthened, not weakened, by his spiritual refugee status. The boy who had once had to have the last word in every argument was approaching a state of grace, brought on by a social if not a physical scourging.

I bind myself to all simple Christians, whatever they call themselves, through the bond of Christian love. I am the enemy of misunderstanding, and I speak kindness wherever I can. My conscience commands me to love an enemy and not harm him, to avoid adding new causes for separation. It tells me that I ought to be an example of moderation and mildness for my enemy. Perhaps through my actions, I might encourage him to do the same, and then at last may God send us the dear desired peace.

In the midst of all these agonies, Kepler’s position in Linz was made still more uncomfortable by a scandal involving his mother.

I have had very little say in these recent chapters about the family Kepler was born into, for the very good reason that they had little bearing on Kepler’s life and work after the eleven-year-old budding astronomer left his birthplace of Weil der Stadt to take the duke of Württemberg’s exam. To be sure, his mother and his three siblings had stayed in touch by post, had even come to visit him occasionally in Graz, Prague, and now Linz. All were pleased to be able to say that their close relation was the Imperial Mathematician, even if they understood not at all and cared even less about his intellectual endeavors. Kepler himself was friendly and when necessary helpful to his relations, as Christian charity dictated he should be, but emotionally he kept them at arm’s length.

In 1608, Kepler’s mother, whose name was Katharina, moved from Weil der Stadt to Leonberg, another village in the Duchy of Württemberg, setting up in a tidy cottage there that appears to have been paid for by Johannes. An amateur physician who had a foul-smelling cream or acrid-tasting potion on hand to cure any ailment, Katharina was a loud, garrulous woman who frequently brought up the achievements of her eldest son as a way of lording it over her neighbors; Kepler himself made note of her “trifling, nosiness, fury, and obstinate complaining.” One of those who took exception to such traits was a woman named Ursula Reinbold, whose own reputation in the village was none too good: she was rumored to have worked as a prostitute and to have had a series of abortions before marrying the local glazier. She was, in other words, just the sort of woman whom Katharina enjoyed looking down upon. But sadly for the latter, a day came when Ursula decided she had had enough of her neighbor’s boasting manner and constant insinuations about her past. In 1615, she went to the village magistrate and told him that Katharina had given her a cursed potion to drink, under the guise of a healing draught that was supposed to help her recover from a sickness that was keeping her in bed. Her body had indeed gotten better almost immediately, but her soul and spirit had been plagued ever since by infernal visions and temptations. The implication was clear: Katharina Kepler was a witch, in league with the Devil.

On the face of it, this accusation was rich coming from a woman of Ursula’s reputation, but it was fraught with peril for Katharina nonetheless. European witch hunts were at a feverish peak in 1615. “Witches were the terrorists of the seventeenth century,” writes James A. Connor: “unseen, moving about society disguised as ordinary citizens, with malevolent wills hidden behind smiling faces. This was not superstition, as some Enlightenment writers would claim — it was a worldview.” Catholics and Protestants subscribed to said worldview with equal enthusiasm; Martin Luther had been infamously inclined to look for a witch behind every tree he passed. In villages like Leonberg, accusations of witchcraft were the great social leveler, used to punish women who failed to understand their place, who evinced unacceptable sexual mores, or who just annoyed their neighbors, as Katharina did. The accusers were most commonly other women — often women like Ursula Reinbold, who might themselves be at risk of condemnation and sought to head it off by engaging in a kind of distracting preemptive strike.

Ursula found an ally in the village magistrate, a grasping man named Luther Einhorn who had designs on confiscating for himself Katharina’s comfortable house. Needless to say, Katharina’s blood relation to a figure who was himself embroiled in conflict with the Lutheran establishment did her cause no favors — and vice versa for Johannes in Linz. The evidence for witchcraft was so tenuous that it was difficult for Einhorn to bring the matter to court even in these hysterical times, but the case hung over Katharina like a Sword of Damocles, especially when a second accuser emerged, a young girl whose family was, probably not coincidentally, in debt to that of Ursula Reinbold. This girl said that Katharina had used her magic to hit her so hard one time when she was walking by the presumably frail old widow’s house that her arm ached for days afterward there where the blow had landed.

Katharina may not have shared her son’s intellectual interests, but she proved like him another respect: she refused to flee the Duchy of Württemberg or to compromise with her persecutors there. This left Johannes in the unwonted position of being the voice of pragmatism, urging her to sell her house to whoever would buy it for whatever they would pay and join him in Linz. (Not that this would have looked very good for him…) But the old woman was determined to stay put. At some level, Johannes must have understood and appreciated her stubborn commitment to the truth of the matter.

Through it all, Kepler found solace in his research and writing, which had long been, alongside his intensely personal version of Christianity, his primary hedge against the lonely isolation from his peers that was his perpetual lot in life. He became fixated for a while on, of all things, methods for calculating the volume of wine casks of different shapes and sizes; Linz did a lively trade in the fruity beverage. Despite the prosaic topic, some of the ideas and formulas included in his 1615 pamphlet A New Stereometry of Wine Casks, like some of those found in his far more grandiose The New Astronomy, pointed the way toward calculus. And speaking of the latter book: Kepler also produced during this period a more concise, conventional volume describing the insights he had elucidated in such a rambling way in The New Astronomy. Consciously crafted to be useful as a teaching text, it created no more of a stir than had its predecessor. When Kepler voiced trivial disagreements about Christian practices of worship, it brought a firestorm of disapprobation down on his head; when he drew a revolutionary new picture of the cosmos, all he heard was crickets.

Franz Tengnagel von Camp, another of Kepler’s collection of past and present nemeses, had moved with the new Emperor Matthias to Vienna, but he had lost influence as his long-mooted published edition of Tycho Brahe’s observational data still failed to materialize. Thus Kepler was finally able to pry the so-called Rudolphine Tables out of Tengnagel’s grasp and embark himself upon the huge project of turning them into a comprehensive reference to the night sky. But the prize which he had striven after for the last decade and a half proved a decidedly mixed blessing now that it was on his desk. In his mid-forties, Kepler was by no means elderly even by the standards of his time, but his health had never been robust, and he was now weighed down by both his exile from the comforts of worship and his mother’s travails. To all of this was added yet another source of grief, the death of his and Susanna’s first daughter from pneumonia. He couldn’t seem to focus on the drudging clerical labor of preparing Tycho’s data for publication, no matter how important he told himself that it was at long to last deliver his irascible mentor’s greatest achievement into the hands of anyone and everyone who could make use of it. At an impasse with himself, he set the project aside for the time being. “Since the Tables require peace,” he wrote in a letter, “I have abandoned them and turned my mind to developing the Harmony.”

Whatever else it may have been, The Harmony of the World (Harmonice Mundi) was first and foremost an attempt by Johannes Kepler to find in the mysteries of nature the sense of order, balance, and justice that so cruelly eluded him in his daily life. Having shattered so recklessly so much of the ancient wisdom about the stars in The New Astronomy, he now went back to one of the oldest of all astronomical ideas: Pythagoras’s music of the spheres, that divine dance of harmony and proportion. Taking up the themes he had played with more than twenty years earlier in his Mysterium Cosmographicum, he looked for the fingerprints of God in geometry, teasing out all sorts of occult meanings from shapes and ratios, drawing heavily from the mystical insights of the ancient Egyptian demigod Hermes Trismegistus. Only the last fifth of the book dealt directly with astronomy. Here he tried his darnedest to show that his seemingly unbalanced and disorderly elliptical universe was actually more perfect and necessary than Pythagoras’s tidy geocentric cosmos had been.

It’s all too easy for the skeptical modern to dismiss all of this, to write it off as a regression to the mean — as one of the boldest empirical thinkers in history losing his nerve and reverting to pseudo-scientific claptrap. But in light of all Kepler had achieved in The New Astronomy, surely we can find it in ourselves to be generous and side with Goethe when he says that “a man’s shortcoming are taken from his epoch; his virtues and greatness belong to himself.” And then, too, not even the most secular-minded scoffers can dismiss The Harmony of the World completely. For in the midst of its straining to justify an untidy cosmos it introduced the last of Kepler’s major original contributions to the theory and practice of astronomy, the third of what we have come to know as his Three Laws of Planetary Motion.

We have met the other two laws before. The first is the simple fact that the planets’ orbits around the Sun form ellipses rather than perfect circles. The second states that each planet sweeps out equal areas in relation to the Sun in the course of its orbit — or, put more plainly, that the planets increase their speed as their elliptical paths carry them closer to the Sun, decrease their speed as they move away from it. The third law, whose acquaintance we are now making for the first time, states that the square of the time of one revolution of a planet around the Sun is proportional to the cube of its mean distance from the Sun. It is important because it gives us a way of calculating how far away from the Sun any given planet must be on average if we only know how long it takes to complete one full orbit, a period of time that can be discerned from astronomical observations such as those found in the Rudolphine Tables. The distance is expressed in what modern astronomers know as astronomical units, one of which corresponds to the distance of the Earth from the Sun.

A concrete example is worth a thousand abstractions here. Let us take the case of Mars, which orbits the Sun once every 1.88 Earth years. Squaring this figure, we get 3.53. And taking the cube root of 3.53, we end up with 1.52. Thus we know that the mean distance of Mars from the Sun is 1.52 times that of Earth, or 1.52 astronomical units. We can use the same method to calculate the distance from the Sun of any other planet in proportion to that of the Earth, just by knowing how long it takes to complete one orbit. This really is  an incredibly handy little formula. It can tell us how far away the moons of any of the other planets of our solar system are in proportion to one another, and it can even tell us the same thing about planets and their moons that belong to entirely different stars from our own. Maybe Kepler’s mystical ideas weren’t as far-fetched as they seem. Whereas Pythagoras sought harmony in the physical layout of the universe, Kepler sought it at a deeper level, in the laws and ratios that govern its workings. Who is to say that he was wrong to detect a divine hand here?

Kepler discovered the Third Law of Planetary Motion in May of 1618, just as he was finishing up his latest book. He completed the writing in a state of spiritual ecstasy, absolutely convinced that he had glimpsed the face of God and brought the divine wisdom back down from the metaphorical mountaintop.

Now, just a few days since the dazzling sunlight of my most wonderful contemplation shined forth, nothing can restrain me. I want to give in to the sacred frenzy. I want to taunt mortal men with my candid confession: I have stolen the golden vessels of the Egyptians to construct a tabernacle for my God far from the boundaries of Egypt. If you forgive me, I will rejoice. If you are incensed, I will endure. I am throwing the dice and writing the book, whether for my contemporaries or for posterity, it does not matter. It can await its reader for 100 years, if God himself waited 6000 years for his contemplator.

Kepler’s very real truths about the nature of the cosmos would indeed have to wait until after his life was through to be widely understood for the paradigm-smashing revelations that they were. In the meantime, he would face more tests of faith and courage before he could go to his well-earned rest.

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