He had nobody to talk to, nobody even to quarrel with.
This last need, however, was fulfilled after a while by the local parson, one Daniel Hitzler. He also came from Wuerttemberg, and knew all about Kepler's scandalous crypto-Calvinist deviations. On the first occasion when Kepler came for Communion, they had an argument. Kepler denied, as he had always done, the Lutheran doctrine of the ubiquity – the omnipresence in the world, not only of the spirit, but of the body of Christ; while Hitzler insisted on a written statement of conformity to the doctrine (which, later on, was dropped by Lutheran theology). Kepler refused, whereupon Hitzler refused him Communion. Kepler complained in a fervent petition to the Church Council in Wuerttemberg; the Council answered in a long, patient and paternally chiding letter that Kepler should stick to mathematics and leave theology to the theologians. Kepler was forced to go for Communion to a parish outside Linz, whose parson was apparently more broadminded; the Church Council, while backing Pastor Hitzler, did nothing to prevent his colleague from giving Communion to the errant sheep. Kepler kept protesting against the curtailment of his freedom of conscience, and complaining that gossips called him an atheist and a double-dealer, who was trying to curry favour with the Catholics and flirting with the Calvinists. Yet this repeated falling between three stools seemed to agree with his innermost nature:
"It hurts my heart that the three factions have miserably torn the truth to pieces between them, that I must collect the bits wherever I can find them, and put them together again... I labour to reconcile the parties with each other whenever it can be done with sincerity, so that I should be able to side with all of them... Behold, I am attracted either by all three parties, or at least by two of them against the third, setting my hopes on agreement; but my opponents are only attracted by one party, imagining that there must be irreconcileable division and strife. My attitude, so help me God, is a Christian one; theirs, I do not know what." 7
It was the language of Erasmus and Tiedemann Giese, of the Golden Age of tolerance – but entirely out of place and out of date in Germany on the eve of the Thirty Years War.
Engulfed in that European disaster, Kepler had to endure an additional ordeal: a kind of ghastly private epicycle turning on the greater wheel. His old mother had been accused of witchcraft and was threatened with being burnt alive. The proceedings lasted for six years, from 1615 to 1621; compared with this, the quasi- or semi-excommunication of Kepler himself was only a minor nuisance.
4. The Witch Trial
The witch-hunting mania, which had grown in furore throughout the sixteenth century, reached its peak in the first half of the seventeenth, both in the Catholic and Protestant parts of Germany. In Weil der Stadt, Kepler's idyllic birthplace, with a population of two hundred families, thirty-eight witches were burnt between 1615 and 1629. In the neighbouring Leonberg, where Kepler's mother now lived, a place equally small, six witches were burnt in the winter of 1615 alone. It was one of the hurricanes of madness which strikes the world from time to time, and seems to be part of man's condition.
Kepler's mother was now a hideous little old woman, whose meddlesomeness and evil tongue, together with her suspect background, predestined her as a victim. She was, we remember, an inn-keeper's daughter, brought up by an aunt who was said to have perished at the stake; and her husband had been a mercenary who vanished after barely escaping the gallows. In that same year, 1615, when Leonberg was seized with witch-hysteria, Katherine had a quarrel with another old hag, her former best friend, the wife of the glazier Jacob Reinhold. This was to be her undoing. The glazier's wife accused Katherine of having given her a witches' potion which had produced a chronic illness (in fact, her ailment was caused by an abortion). It was now remembered that various burghers of Leonberg had been taken ill at various times after being offered a drink from a tin jug which Katherine always kept hospitably prepared for her visitors. The wife of Bastian Meyer had died of it, and the schoolmaster Beutelspacher was permanently paralysed. It was remembered that once upon a time Katherine had asked the sexton for the skull of her father, which she wanted to have cast in silver as a drinking goblet for her son – that court astrologer, himself an adept of the black art. She had cast an evil eye on the children of the tailor Daniel Schmidt, who had promptly died; she was known to have entered houses through locked doors, and to have ridden to death a calf, of which she offered a cutlet to her other son, Heinrich the vagrant.
Katherine's foremost enemy, the glazier's wife, had a brother, who was court barber to the Duke of Wuerttemberg. In that fateful year, 1615, the Duke's son, Prince Achilles, came to Leonberg to hunt, with the barber in his suite. The barber and the Town Provost got drunk together, and had Ma Kepler brought to the Town Hall. Here the barber put the point of his sword on the old woman's breast and asked her to cure his sister by witches' magic of the ailment she had cast on her. Katherine had the sense to refuse – otherwise she would have convicted herself; and her family now sued for libel to protect her. But the Town Provost blocked the libel suit by starting formal proceedings against Katherine for witchcraft. The incident which provided him with an opportunity to do so involved a girl of twelve, who was carrying bricks to the kiln, and on passing Ma Kepler on the road felt a sudden pain in the arm, which led to a temporary paralysis. These sudden, stabbing pains in shoulder, arm or hip, played a great part in the trial of Katherine and others; to this day, lumbago pains and stiff necks are called in Germany Hexenschuss – witches' shot.
The proceedings were long, ghastly and squalid. At various stages, Kepler's younger brother, Christoph, drillmaster of the militia of Leonberg, and his brother-in-law, the vicar, dissociated themselves from the old woman, squabbled over the cost of defence, and would apparently have been quite glad to see their mother burnt and have done with, except for the reflection it would cast on their own bourgeois respectability. Kepler had always been fated to fight without allies, and for unpopular causes. He started with a counter-attack, accusing his mother's persecutors of being inspired by the devil, and peremptorily advised the Town Council of Leonberg to watch their steps, to remember that he was his Roman Imperial Majesty's Court Mathematicus, and to send him copies of all documents relating to his mother's case. This opening blast had the desired effect of making the Town Provost, the barber and their clique proceed more warily, and to look for more evidence before applying for formal indictment. Ma Kepler obligingly provided it, by offering the Provost a silver goblet as a bribe if he consented to suppress the report on the incident of the little girl with the bricks. After that, her son, daughter and son-in-law decided that the only solution was flight, and bundled Ma Kepler off to Johannes in Linz, where she arrived in December 1616. This done, Christoph and the vicar wrote to the ducal Chancellery that should the Provost's accusations prove justified, they would disown old Katherine, and let justice take its course.
The old woman stayed for nine months in Linz; then she got homesick and returned to live with Margaret and the vicar, stake or no stake. Kepler followed her, reading on the journey The Dialogae on Ancient and Modern Music by Galileo father. He stayed in Wuerttemberg for two months, wrote petitions, and tried to obtain a hearing of the original libel suit – to no avail. He succeeded only in obtaining permission to take his mother back with him to Linz. But the stubborn old woman refused; she did not like Austria. Kepler had to return without her.
There followed a strange lull of two years – the opening years of the Thirty Years War – during which Kepler wrote more petitions and the court collected more evidence, which now filled several volumes. Finally, on the night of 7 August, 1620, Ma Kepler was arrested in her son-in-law's vicarage; to avoid scandal, she was carried out of the house hidden in an oak linenchest, and thus transported to the prison in Leonberg. She was interrogated by the Provost, denied being a witch, and was committed to a second and last interrogation, before being put to the torture.
Margaret sent another S.O.S. to Linz, and Kepler set out once again for Wuerttemberg. Th
e immediate result of his arrival was that the Supreme Court granted Ma Kepler six weeks to prepare her defence. She was lying in chains in a room at the Town Gate, with two full-time guards – whose salary had to be paid by the defence, in addition to the extravagant quantities of firewood which they burnt. Kepler, who had built a new astronomy on a trifle of eight minutes arc, did not neglect such details in his petitions; he pointed out that one guard would be a sufficient security precaution for his chained mother, aged seventy-three, and that the cost of the firewood should be more equitably shared. He was his irrepressible, indefatigable, passionate and precise self. The situation, from the point of view of the authorities, was summed up by a slip in the court scribe's record: "The accused appeared in court, accompanied, alas, by her son, Johannes Kepler, mathematician." 8
The proceedings lasted for another year. The accusation comprised forty-nine points, plus a number of supplementary charges – for instance, that the accused had failed to shed tears when admonished with texts from Holy Scripture (this "weeping test" was important evidence in witch-trials); to which Ma Kepler retorted angrily, she had shed so many tears in her life that she had none left.
The Act of Accusation, read in September, was answered a few weeks later by an Act of Contestation by Kepler and counsel; this was refuted by an Act of Acceptation by the prosecution in December; in May, next year, the defence submitted an Act of Exception and Defence; in August, the prosecution answered with an Act of Deduction and Confutation. The last word was the Act of Conclusion by the defence, a hundred and twentyeight pages long, and written mostly in Kepler's own hand. After that the case was sent, by order of the Duke, to the Faculty of Law at Tuebingen – Kepler's university. The Faculty found that Katherine ought to be questioned under torture, but recommended that the procedure should be halted at the stage of territio, or questioning under threat of torture.
According to the procedure laid down in such cases, the old woman was led into the torture chamber, confronted with the executioner, the instruments were shown to her, and their action on the body described in detail; then she was given a last chance to confess her guilt. The terror of the place was such that a great number of victims broke down and confessed at this stage. 9 The reactions of Ma Kepler were described in the Provost's report to the Duke as follows:
"Having, in the presence of three members of the Court and of the town scribe, tried friendly persuasion on the accused, and having met with contradiction and denial, I led her to the usual place of torture and showed her the executioner and his instruments, and reminded her earnestly of the necessity of telling the truth, and of the great dolour and pain awaiting her. Regardless, however, of all earnest admonitions and reminders, she refused to admit and confess to witchcraft as charged, indicating that one should do with her as one liked, and that even if one artery after another were to be torn from her body, she would have nothing to confess; whereafter she fell on her knees and said a pater noster, and demanded that God should make a sign if she were a witch or a monster or had ever anything to do with witchcraft. She was willing to die, she said, God would reveal the truth after her death, and the injustice and violence done to her; she would leave it all to God, who would not withdraw the Holy Ghost from her, but be her support... Having persisted in her contradiction and denial regarding witchcraft, and having remained steadfast in this position, I led her back to her place of custody." 10
A week later, Ma Kepler was released, after fourteen months of imprisonment. She could not return to Leonberg, though, because the populace threatened to lynch her. Six months later, she died.
It was against this background that Kepler wrote the Harmony of the World, 11 in which the third planetary law was given to his engaging contemporaries.
5. Harmonice Mundi
The work was completed in 1618, three months after the death of his daughter Katherine, and three days after the defenestration of Prague. No irony was intended by the title. Irony he only permitted himself in a footnote (to the sixth chapter of the Fifth Book), where the sounds emitted by the various planets as they hum along their orbits are discussed: "The Earth sings Mi-Fa-Mi, so we can gather even from this that Misery and Famine reign on our habitat."
The Harmony of the World is a mathematician's Song of Songs "to the chief harmonist of creation"; it is Job's daydream of a perfect universe. If one reads the book concurrently with his letters about the witch-trial, his excommunication, the war, and the death of his child, one has the impression of being abruptly transported from one play by his Stratford contemporary to a different one. The letters seem to echo the monologue of King Lear – "Blow winds and crack your cheeks! Rage! Blow! – You cataracts and hurricanes spout – Till you have drenched our steeples, drowned the cocks – And thou all-shaking thunder – Strike flat the thick rotundity of the world." But the book's motto could be: "Here we will sit and let the sounds of music creep in our ears – Soft stillness and the night become the touch of sweet harmony. – There's not the smallest orb which thou behold'st – But in his motion like an angel sings... – Such harmony is in immortal souls."
The Harmony of the World is the continuation of the Cosmic Mystery, and the climax of his lifelong obsession. What Kepler attempted here is, simply, to bare the ultimate secret of the universe in an all-embracing synthesis of geometry, music, astrology, astronomy and epistemology. It was the first attempt of this kind since Plato, and it is the last to our day. After Kepler, fragmentation of experience sets in again, science is divorced from religion, religion from art, substance from form, matter from mind.
The work is divided into five books. The first two deal with the concept of harmony in mathematics; the following three with the applications of this concept to music, astrology and astronomy, in that order.
What exactly does he mean by "harmony"? Certain geometrical proportions which he finds reflected everywhere, the archetypes of universal order, from which the planetary laws, the harmonies of music, the drift of the weather, and the fortunes of man are derived. These geometrical ratios are the pure harmonies which guided God in the work of Creation; the sensory harmony which we perceive by listening to musical consonances is merely an echo of it. But that inborn instinct in man which makes his soul resonate to music, provides him with a clue to the nature of the mathematical harmonies which are at its source. The Pythagoreans had discovered that the octave originates in the ratio 1:2 between the length of the two vibrating strings, the fifth in the ratio of 2:3, the fourth in 3:4, and so on. But they went wrong, says Kepler, when they sought for an explanation of this marvellous fact in occult number-lore. The explanation why the ratio 3:5, for instance, gives a concord, but 3:7 a discord, must be sought not in arithmetical, but in geometrical considerations. Let us imagine the string, whose vibrations produce the sound, bent into a circle with its ends joined together. Now a circle can be most gratifyingly divided by inscribing into it symmetrical figures with varying numbers of sides. Thus the side of an inscribed Pentagon will divide the circumference into parts which are to the whole circle as 1/5 and 4/5 respectively – both consonant chords.
But a septagon will produce ratios of 1/7 and 6/7 – both discords. Why? The answer, according to Kepler, is: because the pentagon can be constructed by compass and ruler, but the septagon not. Compass and ruler are the only permissible tools in classical geometry. But geometry is the only language which enables man to understand the working of the divine mind. Therefore figures which cannot be constructed by compass and ruler – such as the septagon, the 11, 13 or 17-sided polygons – are somehow unclean, because they defy the intellect. They are inscibilis, unknowable, 12 inefabilis, unspeakable, non-entia, non-existences. "Therein lies the reason," Kepler explains, "why God did not employ the septagon and the other figures of this species to embellish the world."
Thus the pure archetypal harmonies, and their echoes, the musical consonances, are generated by dividing the circle by means of construable, regular polygons; whereas the "unspeakable" polygons pro
duce discordant sounds, and are useless in the scheme of the universe. To the obsession with the five perfect solids was now added the twin obsession with the perfect polygons. The former are three-dimensional bodies inscribed into the sphere, the latter are two-dimensional shapes inscribed into the circle. There is an intimate, mystical connection between the two: the sphere, it will be remembered, is for Kepler the symbol of the Holy Trinity; the two-dimensional plane symbolizes the material world; the intersection of sphere and plane, the circle, pertains to both, and symbolizes the dual nature of man as body and spirit.
But again the facts did not tally with the scheme, and had to be explained away by ingenious reasoning. The 15-sided polygon, for instance, is construable, but does not produce a musical consonance. Moreover, the number of construable polygons is infinite, but Kepler only needed seven harmonic relations for his scale (octave, major and minor sixth, fifth, fourth, major and minor third). Also, the harmonies had to be arranged into a hierarchy of varying degrees of "knowability", or perfection. Kepler devoted as much labour to this fantastic enterprise as to the determination of the orbit of Mars. In the end he succeeded, to his own satisfaction, in deriving all his seven harmonies, by certain complicated rules of the game, from his perfect polygons. He had traced back the laws of music to the Supreme Geometer's mind.
In the sections which follow, Kepler applies his harmonic ratios to every subject under the sun: metaphysics and epistemology; politics, psychology and physiognomics; architecture and poetry, meteorology and astrology. Then, in the fifth and last book, he returns to cosmology, to complete his vertiginous edifice. The universe he had built in his youth around the five perfect solids had not quite tallied with the observed facts. He now brought the two-dimensional shadow army of polygons to the rescue of the beleaguered solids. The harmonic ratios must somehow be dovetailed in between the solids to fill the gaps and to account for the irregularities.