Johannes Kepler

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Johannes Kepler (1571–1630) was a German astronomer and mathematician who established the three laws of planetary motion and, in doing so, replaced the circle that had governed astronomy since antiquity with the ellipse. He was also an astrologer by trade and a convinced Pythagorean by temperament, and the two sides of him were not separable: the discoveries that founded modern celestial mechanics came out of a lifelong search for the hidden harmony he was certain the Creator had written into the structure of the world.

He was born on 27 December 1571 in the free imperial city of Weil der Stadt, in Württemberg, into a declining minor family and a household of strain — a mercenary father who drifted in and out, a herbalist mother who would later stand trial for witchcraft. A scholarship reserved for promising sons of the Lutheran lands carried him through the monastery schools to the University of Tübingen, where he matriculated in 1589 intending the ministry. There the professor of mathematics, Michael Maestlin, taught the official Ptolemaic astronomy in the lecture hall and the forbidden Copernican system to a few trusted students in private. Kepler took the sun-centered cosmos not as a calculating convenience — which is all most sixteenth-century astronomers would grant it — but as a physical and theological truth. The sun stood at the center because it ought to: it was the visible image of the Father, the source of light and of the moving force, and a universe arranged around it was a universe that meant something.

The polyhedral cosmos

The ministry never came. In 1594 a teaching post fell vacant at the Lutheran school in Graz, in Styria, and the faculty at Tübingen sent their young theologian off to it as district mathematician and calendar-maker — the man who would cast the annual prognostications the province expected. It was in Graz, by his own account in the middle of a geometry lesson on 19 July 1595, that the governing idea of his life arrived. Why were there exactly six planets, and why spaced as they were? The answer, he became convinced, lay in the five regular solids of antiquity — the tetrahedron, cube, octahedron, dodecahedron, and icosahedron, the only perfectly symmetrical bodies geometry permits. Nest them one inside another, each circumscribed and inscribed by a sphere, and the five solids generate exactly six spherical shells: a cube between Saturn and Jupiter, a tetrahedron between Jupiter and Mars, a dodecahedron between Mars and Earth, an icosahedron between Earth and Venus, an octahedron between Venus and Mercury. The spacing of the heavens was fixed by the geometry God had used to build it.

The Mysterium Cosmographicum of 1596 laid this scheme out, and Kepler never fully abandoned it; he reissued the book a quarter-century later with corrective notes but with the central vision intact. That the polyhedral fit was only approximate did not break his conviction, because the conviction was not in the first instance about numbers. It was that the cosmos is a thought before it is a thing — that the Platonic solids disclose the archetypes in the divine mind, and that astronomy, done rightly, recovers those archetypes. The book is the first openly Copernican treatise by a professional astronomer, and it announced its author at once. Among those who read it was Tycho Brahe.

Tycho’s data and the war on Mars

In 1600 the Counter-Reformation reached Styria. Protestants were ordered to convert or leave; Kepler was examined on 2 August, refused, and was banished among some sixty others. He went to Prague, where Tycho Brahe — the greatest observational astronomer of the age, holder of two decades of naked-eye measurements of unmatched precision — had settled as imperial mathematician to the Emperor Rudolf II. The collaboration was brief and difficult; Tycho guarded his data, and Kepler chafed. Then Tycho died, in October 1601, and Kepler inherited both the observations and the post. As imperial mathematician he had the most precise record of the planets ever compiled and the assignment, left by Tycho, of reducing it to order.

He chose Mars, the hardest case — the planet whose orbit deviates most visibly from a circle, the one on which any wrong theory would break first. The campaign he later called his bellum Martis, his war on Mars, consumed years and hundreds of folio pages of calculation. The decisive moment came when a circular orbit, fitted as well as it could be fitted, still left an error of eight minutes of arc against Tycho’s figures. A lesser astronomer, or one with a less exact predecessor, would have let it pass. Kepler trusted Tycho’s eight minutes absolutely, and on their authority he abandoned the circle that astronomy had assumed for two thousand years. The result was the Astronomia Nova of 1609, which states the first two laws of planetary motion: a planet moves on an ellipse with the sun at one focus, and the line from sun to planet sweeps out equal areas in equal times. Its full title promised a physica coelestis, a celestial physics — astronomy founded not on geometric convenience but on causes, on a force reaching out from the sun to drive the planets around. The ellipse was not, for Kepler, a retreat from harmony. It was harmony correctly heard.

The harmony of the world

A decade later came the work he regarded as the summit of his life. The Harmonices Mundi of 1619, written across his years in Linz, where he had moved after losing his Prague footing in 1612, is at once a treatise on geometry, on music, on astrology, and on metaphysics, and it contains, almost in passing, the third law of planetary motion: the square of a planet’s period is proportional to the cube of its mean distance from the sun, the law that binds the whole system into a single ratio and that would later let Newton derive an inverse-square force. Kepler had found it, by his own dating, on 15 May 1618. But the third law arrives inside the book as one consonance among many, because the book’s subject is the literal harmony of the spheres rendered as mathematics.

Kepler looked not at the distances of the planets but at their speeds — and not their speeds simply, but their angular velocities as they would appear to an observer stationed on the sun, fastest at perihelion and slowest at aphelion. The ratio of each planet’s extreme speeds, he found, falls close to a musical interval. Each planet thus sings, not a single note, but a range, sliding between its slowest and fastest pitch. Mercury, on its eccentric orbit, runs up and down nearly an octave and a fifth; Venus, almost circular, holds very nearly a single tone. Earth covers a half-step, from mi to fa and back, and Kepler permitted himself the grim pun that one may infer from the syllables that misery (miseria) and famine (fames) hold sway in this our home. Taken together the planets form a six-part polyphony, a chord the whole heavens are perpetually sounding — audible, in the end, to no ear but the sun’s, or God’s, and resolving into perfect concord perhaps only once, at the moment of creation. This was not metaphor decorating the science; for Kepler the harmonies and the laws were one finding. The same geometric archetypes that fixed the consonances fixed the orbits, and to read one was to read the other.

That conviction had a lineage, and Kepler knew it precisely. He held that the human mind can read the cosmos because it shares in the same geometry that shaped it — that the soul carries the figures of the Pythagorean-Platonic harmonics within it as its native furniture. He traced the descent of the idea through Proclus, whose commentary on Euclid he quoted at length, back through Plato’s Timaeus to Pythagoras, and he stood squarely in the current of Neoplatonic and Neopythagorean cosmology that the Renaissance had revived — though he parted company with its more credulous wing, keeping the geometry while discarding the talismans. Astronomy, for him, was a form of worship: he called himself a priest of the book of nature, and the Harmonices closes with a prayer of thanks for being permitted to see the works of the Creator’s hands. The notion of harmonia as the binding ratio of the world, running from antiquity into Renaissance natural philosophy, reaches in Kepler its most rigorously mathematical statement.

The Fludd controversy

That statement at once drew a rival who claimed the same ground. The English physician Robert Fludd, in the great two-volume Utriusque Cosmi Historia (1617–1621), had set out his own cosmic harmony — the universe as a single monochord, a string stretched by the hand of God from earth to the empyrean and graduated by the musical intervals, with interpenetrating pyramids of light and darkness marking the proportion of form to matter at each level of being. Kepler appended to the Harmonices Mundi a comparison of his own harmonics with Fludd’s, and a four-text exchange followed across 1619 to 1622: Fludd’s Veritatis Proscenium (1621), Kepler’s Pro suo Opere Harmonices Mundi Apologia (1622), and Fludd’s Monochordum Mundi Symphoniacum (1622). The dispute is often misread as science against magic. It was nothing so simple. Both men were Platonists who held that mathematics underlies the cosmos; they disagreed about how mathematical ideas touch the observable world. Kepler insisted on ratios drawn from measurable quantities — the actual velocities of the actual planets — and drew a hard line between a demonstration, which constrains and can be checked, and a picture, which merely asserts a likeness. Fludd answered that Kepler had grasped the husk and missed the kernel: his monochord and pyramids encode what quantity cannot, the qualitative descent of being from light into matter, and to demand numbers of them is to mistake the question. Neither party moved, because they disagreed about what would count as an answer. The wider seventeenth century took Kepler’s side, and the Minim friar Marin Mersenne and after him Pierre Gassendi pressed the attack on Fludd home. But the issue between them — why there should be proportion in the world at all — was the issue Kepler had spent his life inside, and he did not regard the demand for it as illegitimate. He regarded Fludd’s answer as untestable.

Astrology, the dream, and the witch trial

Kepler practiced astrology and defended it, while pruning it hard. He cast nativities for patrons, for the emperor, and famously for the general Wallenstein, and he depended on the fees; the prognostications were, he said wryly, the foolish little daughter who supported the wise mother, astronomy. Yet he rejected most of the inherited apparatus as superstition and kept only what he thought physically defensible — chiefly the aspects, the angular relations between planets, which he believed acted on the soul through a real geometric resonance, a harmony the embryo imprints at birth. His reforming tracts, De Fundamentis Astrologiae Certioribus (1602) and Tertius Interveniens (1610), argue this middle position against both the credulous and the dismissive. The same impulse to imagine the heavens from within produced the Somnium, a dream-narrative of a voyage to the moon and of the cosmos as it would look from a lunar vantage, worked up from notes he had begun as a student and published only after his death, in 1634, by his son Ludwig. It is frequently called the first true work of science fiction, and its lunar daemon and its hostile, learned moon-dwellers carry a sting: the marginal notes that explain the fiction also, in places, explain Kepler.

Between 1615 and 1621 the imagined dangers gave way to a real one. His mother, Katharina, an aging herb-woman in Leonberg, was caught up in a local witch-panic and charged; the accusations swelled to dozens of counts. Kepler, at the height of his powers and in the middle of the Harmonices, turned aside to manage her defense — assembling the legal brief, rebutting each charge, intervening with the authorities at Tübingen and Württemberg. In August 1620 she was imprisoned and at the last was confronted with the instruments of torture, the formal territio that was meant to break her. She did not confess. In October 1621 the Duke of Württemberg ordered her release, the very refusal to confess taken as evidence she had nothing to confess. She died a few months later, free.

Research and texts

The standard biography remains Max Caspar’s Kepler (1948; English translation by C. Doris Hellman, 1959), the foundation of all modern study and the work that set the chronology used above (WorldCat). The critical edition of the writings is the Gesammelte Werke, begun by Walther von Dyck and Caspar in 1937 and continued for the Bavarian Academy of Sciences, the basis for serious textual work. On the polyhedral and harmonic cosmology the indispensable study is Judith V. Field’s Kepler’s Geometrical Cosmology (1988), which traces the Mysterium and Harmonices schemes with full attention to their Platonic sources. For the harmonic astronomy and the Fludd quarrel, Peter Pesic’s “Earthly Music and Cosmic Harmony: Johannes Kepler’s Interest in Practical Music” (Journal of Seventeenth-Century Music 11, 2005) is openly available and reads Kepler’s strenuous insistence that harmonies be physically tractable as the very thing that separated him from Fludd (sscm-jscm.org). The early printed works are themselves public domain and widely digitized: the Harmonices Mundi Libri V (Linz, 1619) survives in numerous scans, among them the copy held by the Smithsonian Libraries (library.si.edu), and the Epitome Astronomiae Copernicanae (1618–1621) — his fullest systematic exposition, which carried the new astronomy onto the Index of Prohibited Books — is likewise freely available. Wolfgang Pauli’s 1952 essay on the archetypal ideas in Kepler, written with C. G. Jung, reframed the Fludd exchange as a confrontation of quantitative and symbolic ways of knowing; it is a tendentious but enduring reading, and remains under copyright. The broader Renaissance setting — the Neoplatonism, Hermetism, and infinite-universe speculation of figures from Nicholas of Cusa to Giordano Bruno — is the soil from which Kepler’s mathematized harmony grew, even as he disciplined it.

Historians of science have long debated how to hold the two Keplers together — whether the mysticism was scaffolding the laws outgrew, or the engine that produced them. The stronger reading is that the mathematical results and the religious vision were one undertaking; Kepler never saw a seam between them. He died in Regensburg on 15 November 1630, far from home, having ridden there to press the imperial treasury for years of unpaid salary, and was buried in a churchyard that the wars soon obliterated, the grave lost. Among the last things he finished were the Rudolphine Tables, printed at Ulm in 1627 and dedicated to the Emperor Ferdinand II — the most accurate astronomical tables ever compiled, built on Tycho’s observations and Kepler’s own laws, and accurate enough that when Mercury crossed the face of the sun in 1631, a year after his death, it arrived where his tables said it would. The harmony he had sought all his life he never heard. He had, in the end, computed it.

→ Related: Pythagoras · Neopythagoreanism · Neoplatonism · Marin Mersenne · Robert Fludd · Harmonia · Pythagorean Platonic Harmonics · Proclus · Plato · Astrology · Giordano Bruno · Nicholas Of Cusa · Renaissance Natural Philosophy · Renaissance Neoplatonism