"Thus God himself / was too kind to remain idle / and began to play the game of signatures / signing his likeness unto the world: therefore I chance to think / that all nature and the graceful sky are / symbolised in the art of Geometria... / Now, as God the maker play'd / he taught the game to Nature / whom he created in his image: / taught her the selfsame game / which he played to her..." 25
Here at last was the jubilant refutation of Plato's cave. The living world no longer is a dim shadow of reality but Nature's dance to which God sets the tune. Man's glory lies in his understanding of the harmony and rhythm of the dance, an understanding made possible through his divine gift of thinking in numbers:
"... these figures pleased me because they are quantities, that is, something which existed before the skies. For quantities were created at the beginning, together with substance; but the sky was only created on the second day... 26 The ideas of quantities have been and are in God from eternity, they are God himself; they are therefore also present as archetypes in all minds created in God's likeness. On this point both the pagan philosophers and the teachers of the Church agree." 26a
By the time Kepler wrote down this credo, the first stage in the young pilgrim's progress was completed. His religious doubts and anxieties had been transformed into the mystic's mature innocence – the Holy Trinity into a universal symbol, his craving for the gift of prophecy into the search for ultimate causes. The sufferings of a mange-eaten, chaotic childhood had left a sober thirst for universal law and harmony; memories of a brutal father may have influenced his vision of an abstract God, without human features, bound by mathematical rules which admitted of no arbitrary acts.
His physical appearance had undergone an equally radical change: the adolescent with the bloated face and spindly limbs had grown into a sparse, dark, wiry figure, charged with nervous energy, with chiselled features and a somewhat Mephistophelian profile, belied by the melancholia of the soft, short-sighted eyes. The restless student who had never been able to finish what he began, had changed into a scholar with a prodigious capacity for work, for physical and mental endurance, and a fanatical patience unequalled in the annals of science.
In the Freudian universe, Kepler's youth is the story of a successful cure of neurosis by sublimation, in Adler's, of a successfully compensated inferiority complex, in Marx's, History's response to the need of improved navigational tables, in the geneticist's, of a freak combination of genes. But if that were the whole story, every stammerer would grow into a Demosthenes, and sadistic parents ought to be at a premium. Perhaps Mercury in conjunction with Mars, taken with a few cosmic grains of salt, is as good an explanation as any other.
III GROWING PAINS
1. The Cosmic Cup
THE inspiration about the five perfect solids had come to Kepler when he was twenty-four, in July 1595. During the next six months he had worked feverishly on the Mysterium. He reported on every stage of his progress to Maestlin in Tuebingen, pouring out his ideas in long letters and asking for his former teacher's help, which Maestlin gave in a grumbling but generous manner.
Michael Maestlin was a kind of inverted Rheticus to Kepler. He was twenty years Kepler's senior, yet was to outlive him. A contemporary engraving shows him as a bearded worthy with a jovial and somewhat vacant face. He had held the chair of mathematics and astronomy at Heidelberg, then at his native Tuebingen, and was a competent teacher with a solid academic reputation. He had published a textbook of astronomy of the conventional type, based on the Ptolemaic system, although in his lectures he spoke with admiration of Copernicus, and thus ignited the spark in young Kepler's inflammable mind. After the manner of good-natured mediocrities who know and accept their own limitations, he had a naive admiration for the genius of his former pupil and went to considerable trouble to help him, though with an occasional growl at Kepler's unceasing demands. When the book was finished and the Senate of Tuebingen asked for Maestlin's expert opinion, he enthusiastically recommended that it should be published; and when permission was granted, he supervised the printing himself. This, in those days, was practically a full-time job; as a result Maestlin was reprimanded by the University Senate for neglecting his own work. He complained about this to Kepler in understandably peeved tones; Kepler replied, among his usual effusions of gratitude, that Maestlin shouldn't worry about the reprimand since, by seeing the Mysterium through print, Maestlin had acquired immortal fame.
By February 1596, the rough draft of the book was completed and Kepler asked his superiors in Gratz for leave of absence to visit his native Wuerttemberg and make arrangements for its publication. He asked for two months, but stayed away for seven, as he had become involved in a typically Keplerian chimera. He had persuaded Frederick, Duke of Wuerttemberg, to have a model of the universe, incorporating the five perfect solids, made in the shape of a drinking cup. "A childish or fatal craving for the favour of princes," as he later confessed, had driven him to Stuttgart, to Frederick's court, to whom he explained his idea in a letter:
"Since the Almighty granted me last summer a major inventum in astronomy, after lengthy, unsparing toil and diligence; which same inventum I have explained in a special booklet which I am willing to publish any time; which whole work and demonstration thereof can be fittingly and gracefully represented by a drinking cup of an ell in diameter which then would be a true and genuine likeness of the world and model of the creation insofar as human reason may fathom, and the like of which has never before been seen or heard of by any man; therefore I have postponed the preparation of such a model or its showing to any man to the present time of my arrival from Styria, intending to put this true and correct model of the world before the eyes of your Grace, as my natural sovereign, for him to see it as the first man on earth." 1
Kepler went on to suggest that the various parts of the cup should be made by different silversmiths, and then fitted together, to make sure that the cosmic secret would not leak out. The signs of the planets could be cut in precious stones – Saturn in diamond, Jupiter in jacinth, the moon a pearl, and so on. The cup would serve seven different kinds of beverage, conducted by concealed pipes from each planetary sphere to seven taps on its rim. The sun will provide a delicious aqua vita, Mercury brandy, Venus mead, the moon water, Mars a strong Vermouth, Jupiter "a delicious new white wine", and Saturn "a bad old wine or beer", "whereby those ignorant in astronomical matters could be exposed to shame and ridicule." Assuring Frederick that in ordering the cup he would do a favour to the arts and a service to God Almighty, Kepler remained Frederick's obedient servant, hoping for the best.
The Duke wrote on the margin of Kepler's letter: "Let him first make a model of copper and when we see it and decide that it is worth being made in silver, the means shall not want." Kepler's letter was dated 17 February and the Duke's answer was transmitted to him on the next day; Frederick's imagination had obviously caught on. But Kepler had no money to make a copper model, as he resentfully conveyed to the Duke in his next letter; instead, he settled down to the Herculean task of making a paper model of all the planetary orbits and the five perfect solids in between. He laboured day and night for a week; years later he nostalgically remarked that it had been quite a pretty model, made out in paper of different colours, with all the orbits in blue.
When the paper monster was finished, he sent it to the Duke, apologising for its clumsiness and huge dimensions. Again promptly on the next day, the Duke ordered his chancellery to ask for the expert opinion of Professor Maestlin. The good Maestlin wrote to Frederick that Kepler's cup would represent a "glorious work of erudition", and the Duke wrote on the margin: "Since this is so, we are content that the work should be executed."
But apparently it had been easier for God to build the world around the five polyhedra than for the silversmiths to execute a copy of it. Besides, Frederick did not want the cosmic mystery in the form of a drinking cup, but to have it encased in a celestial globe. Kepler made another paper model, left it with the silversmith, and in
September returned to Gratz, having wasted nearly six months at Frederick's court. But the Duke would not drop the project, and it dragged on for several years. In January '98, Kepler wrote to poor Maestlin (who now served as the go-between): "If the Duke agrees, it would be best to break up the whole junk and refund the silver to him... The thing is hardly worth while... I started it too ambitiously." 2 But six months later, he submitted via Maestlin a new project. The cup, which had turned into a globe, was now to turn into a mobile planetarium, driven by a clockwork. The description of it occupied ten printed pages in folio. Kepler informed the Duke that a Frankfurt mathematician, Jacob Cuno, had offered to construct a planetarium which would reproduce the heavenly motions "within an error of one degree for the next six or ten thousand years"; but, Kepler explained, such a machine would be too large and costly, and proposed a more modest one, guaranteed for a century only. "For it is not to be hoped (apart from the Last Judgement) that such a work would remain undisturbed in one place over a hundred years. Too many wars, fires and other changes are wont to occur." 3
The correspondence went on for another two years; then the subject was at last mercifully forgotten. But this quixotic escapade inevitably reminds one of the ill-fated vagabondages of his father, uncle and brother. He worked off his innate restlessness in bold imaginations and plain drudgery; but from time to time some residual poison in his blood would make him break out in a rash and momentarily turn the sage into a clown. This fact is painfully evident in the tragicomedy of Kepler's first marriage.
2. Marriage
Before his journey to Wuerttemberg, Kepler's friends in Gratz had found a prospective bride for the young mathematicus in the daughter of a rich mill-owner, twice widowed at the age of twenty-three. Barbara Muehleck had been married at sixteen, against her wish, to a middle-aged cabinet-maker who had died after two years; then to an elderly, widowed pay-clerk who brought into the marriage a bunch of mis-shapen children, chronic illness, and, after his timely demise, was found to have defrauded money in his trust. Barbara, described by Kepler as "simple of mind and fat of body", now lived with her parents, who could not have very high expectations of her future. Yet when Kepler presented his suit through two respectable middle-men (a school inspector and a deacon) the proud miller refused on the grounds that he could not entrust Barbara and her dowry to a man of such lowly standing and miserable pay. This was the beginning of long and sordid negotiations conducted by Kepler's friends with the family.
When he left for Stuttgart nothing was settled, but in the spring his friends wrote to him that his suit had been accepted, advised him to hurry home, and to bring with him from Ulm "some truly good silk cloth, or at least of the best double taffeta, sufficient for complete robes for thyself and the bride". But Kepler was too busy with his cosmic silver cup, delayed his return, and by the time he got back to Gratz, Frau Barbara's father had changed his mind again. Kepler seems not to have been unduly perturbed, but the indefatigable friends continued their efforts; the Dean of the school and even the Church authorities joined in – "and so they vied with one another to assault the minds now of the widow, now of her father, took them by storm and arranged for me a new date for the nuptials. Thus, with one blow, all my plans for beginning another life collapsed." 4
The marriage took place on 27 April, 1597, "under a calamitous sky", as the horoscope indicated. He was somewhat comforted by the arrival of the first printed copies of the Mysterium Cosmographicum, but not even that event was all joy; he had to buy two hundred copies of the book for cash to compensate the printer for the risk; and the author's name in the catalogue of the Frankfurt Book Fair was transformed, by misprint, from Keplerus into Repleus.
Kepler's attitude to marriage in general, and to his own wife in particular, is expressed in several letters with shocking frankness. The first is addressed to Maestlin and dated a week before the wedding. It occupies nearly six pages in folio, of which only the last speaks of the impending great event:
"I ask you only one favour, that you should be close to me in your prayers on my wedding day. My financial situation is such that should I die within the next year hardly anybody could leave a worse situation after him. I am obliged to spend a big sum of my own, for it is the custom here to celebrate marriages splendidly. If, however, God prolongs my life, I shall be bound and constricted to this place... For my bride possesses here estates, friends and a prosperous father; it seems that after a few years I would not need my salary any longer... Thus I shall be unable to leave this province except if a public or a private misfortune intervened. A public misfortune it would be if the country ceased to be safe for Lutherans, or if the Turks, who have already massed six hundred thousand men, invaded it. A private misfortune it would be if my wife died." 5
Not a word is said about the person of his betrothed or his feelings for her. But in another letter written two years later, he blames her horoscope for her "rather sad and unlucky fate... In all dealings she is confused and inhibited. Also she gives birth with difficulty. Everything else is in the same vein." 6
After her death, he described her in even more depressing terms. She had known how to make a favourable impression on strangers, but at home she had been different. She resented her husband's lowly position as a stargazer and understood nothing of his work. She read nothing, not even stories, only her prayer book which she devoured day and night. She had "a stupid, sulking, lonely, melancholy complexion". She was always ailing and weighed down with melancholia. When his salary was withheld, she refused to let him touch her dowry, even to pawn a cup or to put her hand into her private purse.
"And because, due to her constant illness, she was deprived of her memory, I made her angry with my reminders and admonitions for she would have no master and yet often was unable to cope herself. Often I was even more helpless than she, but in my ignorance persisted in the quarrel. In short she was of an angry nature, and uttered all her wishes in an angry voice; this incited me to provoke her, I regret it, for my studies sometimes made me thoughtless; but I learnt my lesson, I learnt to have patience with her. When I saw that she took my words to heart, I would rather have bitten my own finger than to give her further offence..." 7
Her avarice made her neglect her appearance; but she lavished everything on the children because she was a woman "entirely imprisoned by maternal love"; as for her husband "not much love came my way". She nagged not only him but also the servant wenches and "could never keep a wench". When he was working she would interrupt him to discuss her household problems. "I may have been impatient when she failed to understand and went on asking me questions, but I never called her a fool, though it may have been her understanding that I considered her a fool, for she was very touchy." 8 There is not much left to be added to this portrait of the perennial Xanthippe.
Nine months after the wedding their first child was born, a little boy, with his genitals so deformed that "their composition looked like a boiled turtle in its shell" 9 – which, Kepler explains, was due to turtles being his wife's favourite dish. After two months the child died of cerebral meningitis, and the next, a little girl, died after a month of the same disease. Frau Barbara bore three more children, of which one boy and one girl survived.
Altogether, their marriage lasted fourteen years; Barbara died at the age of thirty-seven, with a distraught mind. The marriage horoscope had shown a coelo calamitoso, and in predicting disaster Kepler's horoscopes were nearly always right.
3. Limbering Up
When in the spring of 1597, the Mysterium at last appeared in print, the proud young author sent copies to all leading scholars he could think of, including Galileo and Tycho de Brahe. There existed as yet no scientific journals nor, happy days, book reviewers; on the other hand, there was an intensive exchange of letters among scholars and a luxuriant international academic grapevine. By these means the unknown young man's book created a certain stir; though not the earthquake which its author expected, yet remarkable enough if we consider that the avera
ge number of scientific (and pseudo-scientific) books published in Germany in a single year was well over a thousand. 10
But the response was not surprising. Astronomy, from Ptolemy to Kepler, had been a purely descriptive geography of the sky. Its task was to provide maps of the fixed stars, timetables of the motions of sun, moon and planets, and of such special events as eclipses, oppositions, conjunctions, solstices, equinoxes, and the rest. The physical causes of the motions, the forces of nature behind them, were not the astronomer's concern. Whenever necessary, a few epicycles were added to the existing machinery of wheels – which did not matter much since they were fictional anyway, and nobody believed in their physical reality. The hierarchy of cherubim and seraphim who were supposed to keep the wheels turning was, since the end of the Middle Ages, regarded as another polite, poetic fiction. Thus the physics of the sky had become a complete blank. There were events but no causes, motions but no moving forces. The astronomer's task was to observe, describe and predict, not to search for causes – "theirs not to reason why". Aristotelian physics, which made any rational and causal approach to the heavenly phenomena unthinkable, was on the wane, but it had left only a vacuum behind it. Ears were still ringing with the vanished song of the star-spinning angels, but all was silence. In that fertile silence the unformed, stammering voice of the young theologian-turned-astronomer obtained an immediate hearing.
Opinions were divided, according to the philosophy of the scholars. The modern and empirically minded, such as Galileo in Padua and Praetorius in Altdorf, rejected Kepler's mystical a priori speculations and with them the whole book, without realizing the explosive new ideas hidden among the chaff. Galileo, especially, seems to have been prejudiced from the beginning against Kepler, of which we shall hear more later on.