That year of 1617, however, was another terrible year. His daughter Margareta Regina, the little one, had already died on September 8, of consumption and epilepsy, before Kepler arrived home. And his stepdaughter, Regina, the little girl that Barbara had brought into the marriage, a girl whom Kepler had raised as if she were his own flesh, a woman now fully grown with a husband and children of her own, died in Walderbach, near Regensburg. She and her husband, Philip Ehem, a son of a prominent Augsburg family, had just moved there with their children. Ehem had a good job too, as Friedrich V’s representative from the Palatinate to the imperial court. Suddenly, Regina took sick, and then all too quickly died. Ehem was lost in his grief for his wife and fear for his children. He begged Kepler to send his eldest daughter, fifteen-year-old Susanna, to help care for the children. Kepler agreed, but new worries had piled on top of the old.
He was still suffering from the news of Regina’s death when he received the terrible letter from his sister, Margaretha, the wife of Pastor Binder, about the strange and terrifying accusations of witchcraft against their mother. So Kepler began his journey from Linz, up the Danube to Regensburg, passing through Walderbach, on the way to Leonberg, to see Philip and to leave his daughter Susanna with him. Along the way, he read a little book on harmony in music by Vincenzo Galilei, the father of Galileo Galilei, called Dialogo della musica antica e moderne, A Dialogue on Ancient and Modern Music. Kepler’s Latin was strong enough that he could pick his way through Galilei’s Italian. In this book, Vincenzo had returned to the original theory of harmony based on Pythagorean mathematics, an idea that piqued Kepler’s interest because it appealed to his own astronomical, mathematical, and theological ideas. He had long been convinced that the best way to synthesize all three, to get that peek into God’s cosmographic mind, was through the idea of harmony as it applied to the motion of the planets.
Ultimately the trip to Leonberg was a disaster. He was never able to silence the accusations against his mother, nor was he able to reconcile himself with the Lutheran church, no matter how hard he tried. His visit to Hafenreffer in Tübingen had ended in his final excommunication. After a short stop in Walderbach on the way back to Linz, when he returned home, his children started dying. One after another, the world dropped stones on him. Weighed down by all the troubles of his life, he could not return to the grinding calculations of the Rudolphine Tables, and so he started his work on the Harmony. Like Mozart, who would follow him two hundred years later and who would write his sweetest music during the blackest times, Kepler was at his best when things were worst.
So what was this “harmony”? It is a complex word for us, meaning just about anything good depending on the predilections of the hearer. For Kepler, however, the word had a precise mathematical meaning. Each instance of harmony was a regular mathematical pattern that Kepler found in the world, a comparison between two or more things the coming together of which created something beautiful. Harmony was a geometric as well as an arithmetic idea and turned on everything from the complex shapes of snowflakes to the motions of the planets in the heavens. It was not a single abstract experience, like “humankind,” but a complex array of individual harmonies, something more like “people.” The harmonies were arranged in phalanxes of ever more complicated patterns coalescing into a great cosmic symphony, a music so profound that it harrowed the heart and set fire to the soul.
At the core, harmony corralled all that Kepler believed about science as well as all he believed about God, for the two could not be easily separated. Divine harmony was his answer to the troubles of the world, troubles that he was all too well aware of. Over the years, he collected tidbits about the multitude of harmonies from writings in philosophy, theology, astronomy, and mathematics, until he gradually formed a new synthesis. Geometry was at the heart of it, for the secret structure of the universe was geometric, and therefore geometry was the blood of harmony, the marrow of God’s thought. Kepler’s researches led him back to the roots of mathematics.
For some time, he had tried to get his hands on a copy of Claudius Ptolemy’s Harmony in the original Greek, for Ptolemy had tried to identify the qualities found in certain things that made them beautiful. But the book was hard to find, and Kepler failed at every attempt until Herwart von Hohenberg loaned him a copy to read. It amazed Kepler that even with several thousand years of difference between them, he and Ptolemy had contemplated the same ideas. This was reassuring to Kepler, because it intimated that he was onto something divine that lurked in the human mind. “The same idea about the construction of harmony has emerged from the minds of two very different men (and separated by so many centuries), simply because they were two men who had dedicated themselves to the contemplation of nature.”9
As his little girl lay dying of pneumonia, Kepler stood at her bedside, watching as her tiny chest rose and fell with every ragged breath, and prayed almost without hope, while the ideas of harmony he had collected over the years almost imperceptibly jelled in his mind. When little Katharina died, Kepler locked himself away in his library, choked with grief, and as a refuge plodded on with his last great work. The Harmony was his fortress. He could enclose himself there, inside the perfection of mathematics, inside the transcendental beauty of geometry, and bolt the door of his mind to keep the screaming world outside. In those few stolen hours, he transported himself to that place of perfection and beauty, that place where God’s will alone ruled the world.
In the process, while he wrangled with Luther Einhorn over the accusations against his mother, he remembered a sudden time when, in a momentary contemplation of harmony, he had discovered the third of his planet laws:
Eighteen months ago, the first light of dawn hit me; three months ago, the light of morning; and then, only a very few days ago, the complete light of the sun has revealed this remarkable spectacle. Now, nothing holds me back. Indeed, I live in a secret frenzy. I sneer at mortals and defy them by the following public proclamation: I have pillaged the golden bowls of Egypt, to decorate a holy tabernacle for my God, far from the lands of the Egyptians. If you will forgive me, then I am happy. If you are angry with me, I will survive it. Well then, I will throw the dice; I will write a book, if not for the present time, then for posterity. To me, they are one and the same. If the book must wait a hundred years to find its readers, so what. God has waited six thousand years to find a true witness. 10
This third law, his “harmonic law,” set the relationship between the mean distance of a planet from the sun and the period of its orbit. This meant that one could calculate the time each planet would take to travel around the sun by knowing its distance, something that carried Kepler’s first two laws and his application of physics to astronomy one step further. It was a cosmic regularity, one that had deep implications for Newton’s law of gravity, for it showed the relationship between the distance from the sun of a body in orbit and the time it took that body to complete its cycle.
This was, for Kepler, another peek into God’s mind. Kepler’s mysticism orbits around this single idea, for he was no plodding empiricist, no earthbound pragmatist. His joy was in the perfect beauty of mathematics, especially geometry, which he always expressed in mystical terms. He was a mystical rationalist, a man who found transcendence by embracing reason rather than by abandoning it. In this, he was the inverse of Blaise Pascal, the French mathematician from Rouen who was born just a few years after Kepler had died and who experienced mystical insight by breaking through the veil of rationalism to find there a God of the burning bush, of the sacred fire, the God of Abraham, Isaac, and Jacob, the God of revelation. Although Kepler believed in the Bible and accepted its teachings, he saw within the Book of Nature a mysticism equally grand, equally vital, and equally important.
In this simple statement, Kepler also identified himself as a thoroughgoing Platonist, with earthbound harmonies rising and converging into the perfect harmonies of the mind. In doing so, he distinguished between sensual harmonies and perfect harmonies, or the ha
rmonies of mathematics. Music, of course, was the living heart of sensual harmony, for it not only had the power to enrapture the soul, but also to engorge the mind with perfect order. Harmony in music, as in all things, is a matter of comparison. Two things are brought into contact—two tones, two colors, two objects, two ideas, and they either blend together to conjure a greater, higher experience or they do not. In other words, they are harmonious or they are not. This is not first a matter of calculation, but of immediate experience. The eye does not need to calculate to see the harmony of color, nor does the ear need to do sums to hear the harmony of music. The harmony is there in the experience, in the first astonishing encounter, emerging like the sun from the ocean out of the byplay of individual things.
However, harmony is not created by the eyes or by the things themselves, but by the soul, which resonates with the interaction between sounds, colors, things, and ideas and builds a new beauty for itself. It resonates because God has planted even deeper harmonies, and the ability to recognize them, into each human person at birth. The structures of the mind are harmonious themselves, which, like the Ideas of Plato, are implanted inside us, and it is up to us to remember them. It is from the comparing of sensual experience that these deeper harmonies emerge, as the human person lives in the world, feels it, weighs it, and measures it, with each experience opening up to new experiences beyond that.
This is not a matter of bare imagination, however. The mind does not make things happen. The colors, sounds, and objects exist in the exterior world and will not disappear if the observing human person walks away. If a tree falls in the forest, it makes a sound, but whatever sound it makes cannot form a harmony without someone to hear it. Thus, “harmony” is a primary category of existence.
Discovering harmonies is essential to discovering the world. In discovering harmonies, one makes comparisons between the two things that exist in the world—two sounds, two colors, two chairs, two people—in order to produce a harmony, and then goes on to compare that harmony and the internal prototype that exists inside the mind. This grand procession of harmonies has one ultimate function: “to reveal, to understand, and to bring to light the resemblance of the proportion in matters of sense with that exact prototype of a true harmony, that prototype which abides inside the mind.”11 Such prototypes are the perfect harmonies, the Platonic ideas. These perfect harmonies are what the soul recognizes, and in that recognition are aroused the feelings of beauty and joy. I recognize them as I recognize the land of my birth, my neighborhood, my home. I am like an Alzheimer’s patient who has been given a wonder drug and suddenly remembers everything. All education is a matter of remembrance, of bringing the harmonies to light. Mathematics is therefore the ultimate education, for it raises into the conscious mind those innate harmonies that we see projected into the world, in color, light, and joyful sound. And because these harmonies are innate, even the simplest people—the poor, the peasants, the barbarians, the uneducated—can recognize them, though they may do so unconsciously, for they emerge in the very act of perception.
Kepler rejects the idea that the human mind is an empty slate, a tabula rasa, and instead embraces Plato’s notion that the harmonies are born in us, along with a secret storehouse of knowledge that is best expressed in mathematics. Our entire flesh, our bones, our eyes and ears are built for the discovery of this knowledge. The senses that we possess do not exist by themselves, but exist to serve the mind. The mind is not a sifting device, not a computer calculating numbers. The mind is the human soul listening to the universe and finding there a resonance with the mind of God: “If the mind had never benefited from an eye, then it would, in order to understand the world outside itself, demand an eye and invent its own laws for its creation.”12
All of this for Kepler the mathematician, as it did in its own way for Einstein, comes down to geometry. “Geometry, being part of the Divine mind from time beyond memory, from before the origin of things, has provided God with the models for creating the world, models that have been implanted in human beings, together with the image of God. Geometry did not arrive in the soul through the eyes.”
Kepler’s reasoning, therefore, begins with the circle, which he accepts as fixed in the mind. One can inscribe a vast array of polygons inside a circle. Those polygons, which can be constructed with a straight edge and compass, like triangles, squares, and octagons, Kepler says are entities and he considers them to actually exist. Those polygons that cannot be inscribed in a circle—those with seven, eleven, or thirteen sides—Kepler says are nonentities, for they do not exist at all. They do not exist in the mind except as words, for they cannot even be imagined. One could draw a seven-sided polygon, of course, but such a figure could not be inscribed inside a circle. For Kepler, therefore, the world is ordered between those things that are possible and those that are not.
All of this has metaphysical importance. His thinking here becomes more medieval than modern, for his geometric speculations take on emblematic significance within an Aristotelian hierarchy of perfection. If the circle is the perfect two-dimensional shape and a symbol of infinity, then the sphere is the perfect three-dimensional shape and is therefore the symbol of the most complete form of infinity. Kepler instantly identifies it with the Trinity. He places God the Father at the center of the sphere, for the Father is the center of all that lives and moves and has being. God the Son is the surface of the sphere—as the round, dimensionless center point explodes outward into space, so too the Son is the presence of the Father expanding out into the world. The Holy Spirit is the radii from the center to the surface, joining the center with the surface, Father to Son, Son to Father, and remaining constant at each point of the sphere. This is a strange bit of speculation to the modern mind, which does not work like this at all, but it made perfect sense to the intellectuals of the seventeenth century.13
Kepler further identifies the created mind of the human being with the two-dimensional circle, which expresses a two-dimensional level of infinity and projects onto a flat surface some of the very qualities of the sphere. Therefore the polygons that could be inscribed inside a circle Kepler said actually existed in the mind. The human mind is an image of God’s divinity projected into bodily flesh.
Kepler finds three essential expressions of harmony in the world—in geometry, music, and astronomy. Geometry is the greatest of them, because it is the bridge between those harmonies found in the senses and those found innate in the soul. It is in music, however, that those perfect harmonies best touch the senses. Here we feel them, see them, listen to them. In astronomy, finally, these harmonies express themselves in the structure of the universe. The motion of the stars is an expression of them, so that the human mind, which touches the shapes of circles, triangles, and the like, can also caress the universe itself. It is here that reason reaches its peak, for it is here that human beings shake hands with the Creator God. It is mathematics at its most profound, its most mystical. But like all mysticism, it requires a struggle, a dark night of the soul, a tramp through twisted jungles that clears the mind and prepares for those explosions of insight. In those moments when a person has wrestled with Reason itself, “then he awakens to the true light; he is taken by an astonishing rapture, and, rejoicing, he inspects the whole world and all its different parts, as though from a high tower.”14
KEPLER RETURNED HOME soon after his mother’s trial had ended, in November 1621, but by then Linz had become a conquered city. Old Katharina had recently died, a broken woman, after all of Kepler’s attempts to save her. And then he returned home to the flotsam of war. The Catholic League’s success at White Mountain had crushed the Protestant revolt in eastern Europe and had left occupying armies all over the territory of the rebellious Estates. Bavarian troops still marched through the city as Kepler’s river barge landed, a bit more than a year after the battle. As with all occupying armies, the Bavarians had made it clear who was in charge of the city, and Ferdinand, now firmly in power, had made sure that his rebellious
subjects could see which way the religious world was turning. For a few years he waited, consolidating his power, but everyone knew that he intended to reestablish his program of Catholicization, begun in Graz twenty years before, that would sooner or later choke the Protestant schools and churches until they died. Pastor Hitzler, Kepler’s old antagonist, was one of the first men thrown into prison.
Little happened for the next two or three years after Kepler returned to Linz. The city, like Kepler himself, was depressed. The Battle of White Mountain had solved the problem of open rebellion by Protestants with a great iron boot, but from that time on all of Upper Austria held its collective breath. The Protestant Estates had participated in the rebellion, and some of their most prominent leaders, even a few friends and supporters of Kepler’s, had been executed. Some were continuing the fight, but the fight was not going well. And so the presence of Bavarian troops was a running sore for the people of Linz, for these men were Germans, not Austrians, an occupying army intended by the emperor to send the people a message—the time of the “new doctrines” was coming to an end.
Still, the battle raged on in other parts of Germany. Friedrich V of the Palatinate began holding mock court in the Netherlands, but Christian von Braunschweig and Ernst von Mansfield, both followers of the former king of Bohemia, had swallowed their shame at Friedrich’s cowardice and taken to the field to continue the fight. The emperor, who had eradicated all the new doctrines in Prague and in the rest of Bohemia, would soon turn his eye toward Upper Austria. Just as in Graz, Lutherans found it harder and harder to attend services. Protestant leaders, even some of the most prominent of the nobility, either converted or were exiled. Protestant ministers were either jailed like Pastor Hitzler or sent out of the region.
Generally, the people ground their teeth at the emperor’s new restrictions, but what could they do? There were troops in the city. Foreign troops. Catholic troops. But surprisingly, nothing happened—no explosions, no outbursts, no demonstrations, no sudden reign of terror. In those two or three years, nothing much happened at all, except for subtle things. There were new restrictions on marriage and on burial, the old Graz story all over again, only this time it was unfolding more slowly. The gloom gathering over the city darkened bit by bit every day. The Lutherans waited for the terrible punch line, for the Counter-Reformation to arrive in force. They knew how it would begin: one edict, then another, coming faster and faster, until the Protestants would be surrounded by them. Then one day the emperor would simply tell them to convert or leave.
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