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  Rudolf surely suffered a tremor of foreboding when, not long after Kelley's demise, he found himself confronted by yet another outlandish foreigner with a prosthesis. Big blond Tycho of the flowing moustache and metal nose must have seemed a very Viking to the pyknik Emperor. All the more remarkable then that Brahe should have been received at the imperial court with such warmth and generosity. Of course, the Dane had a Europe-wide reputation as an astronomer, but Kelley had been vouched for by Doctor Dee who in turn had been favoured by Elizabeth I.28 Nevertheless, Rudolf was as good as his promise of patronage, and offered to settle Tycho and his extended family in the house of the former pro-chancellor Jacob Kurtz - Kurtz was dead - which Tycho described as 'a splendid and magnificent palace (which [Kurtz] had built in the Italian style, with beautiful private grounds, at a cost of more than 20,000 dalers).' The house stood on the brow of hill to the west of the palace; it is no longer there, but gigantic statues of Tycho and Kepler have been erected on the site, near the Cernin Palace. Secretary Barwitz showed the Dane over the property, but Tycho was not satisfied, noting that the tower attached to the house would not be large enough to accommodate even one of the astronomical instruments he had brought with him from Hven. Barwitz, no doubt accustomed to the lordly caprices of Rudolf's clients, suggested that perhaps Herr Brahe would prefer to have one of the outlying imperial castles. The choice seems to have been between the Emperor's favourite hunting lodge, Brandys, and a property perched on a hill some forty kilometres or a six-hour carriage ride from the city. Benatky Castle stood in beautiful surroundings above the floodplain of the river Jizera, and was known as 'Bohemian Venice' because when the river was in spate the country round about was under water. Tycho was delighted. At the landlocked heart of Europe, here was another Hven. Before the end of August, the Brahes had moved into Benatky, and Tycho had set up his first instrument.29

  At once, Tycho embarked on a lavish rebuilding programme at the Emperor's expense. Within weeks the administrator of the estate, Caspar von Miihlstein, was sending urgent warnings to Bar­witz about the mounting cost of the Dane's renovations. It was the beginning of a series of wranglings with imperial officials that would continue to Tycho's death and beyond. To complicate matters, a month after Tycho's move to Benatky there was yet another outbreak of plague in the city and the Emperor had fled the Hradcany for the safety of the countryside. Inevitably the plague reached Benatky, and when the death toll in the area had reached 2,000 Tycho himself - urged, as he loftily pointed out, by his womenfolk, who were frightened he temporarily abandoned the nascent new Ur­aniborg and retreated thirty kilometers down­river to a castle at Girsitz. He was still there when, at the beginning of 1600, Johannes Kepler arrived in Prague, and thus there was a delay to one of the most momentous meetings in the history of science.

  It would be hard to imagine two more dissimilar figures than Kepler and Tycho Brahe. Kepler, the younger of the two by twenty-five years, was born in 1571 - at 2.30 pm on December 27th of that year, to be precise, which Kepler liked to be - on the northern fringes of the Black Forest, in the town of Weilderstadt, a 'free city' within the duchy of Wurttemberg. The family were a mixed lot; Grandfather Sebald was for a time Biirghermeister of Weilderstadt, while his son Sebaldus was, in Johannes Kepler's laconic description of him, 'an astrologer, a Jesuit, acquired a wife, caught the French sickness, was vicious.' Kepler's father, a professional mercenary, was a braggart and a bully who cruelly mistreated his wife and children, eventually abandoning them altogether to go off to the Low Countries to fight with the Duke of Alba's marauders. The mother, Katarina, was quick-witted but cold; like her son, she was fascinated by the natural world, although her interest in herbs and homemade medicines would eventually lead to her being tried on a charge of witchcraft. Johannes was a sickly child, made sicklier by being sent out to work as a farm labourer at the age of eight. Eventually he was put back to school, and received an excellent education thanks to the enlightened policies of the Duke of Wurttemberg. At seventeen he entered the University of Tubin­gen, where he was taught by the famous Michael Mastlin, a mathematician and astronomer admired even by the great Tycho Brahe.

  Kepler was both a devout Protestant and a follower of Pythagoras - the philosopher of the fifth century BC who taught that the universe is centred not on the Earth but on an eternal, invisible flame - and held to the revolutionary theory of Copernicus, who had set the sun at the focus of planetary motion. These were daring beliefs for a young man to hold in those times of religious upheaval and repression.30 He also read widely in the work of the Neoplatonists, and of the mystic and philosopher Cardinal Nicholas of Cusa, who had anticipated Copernicus by a century by declaring that the Earth does not stand still at the centre of the world. From Tubingen in his third year Kepler was directed by the university authorities to take up the post of schoolteacher in Graz in southern Austria. Kepler was aghast at the prospect of being buried alive in the far-off and backward province of Styria; even to get there he would lose ten days because of the different calendar in use in Graz. Nevertheless he bowed to authority, and took up his post at the seminary school in 1594, at the age of twenty-two. His subjects were advanced mathematics, including astronomy. He was a terrible teacher: in his first year he had a handful of students, in his second, none. He also held the position of District Mathematician, which, despite the high sound of it, meant he would be required chiefly to draw up astrological predictions for the town and district at the beginning of each new year. Kepler maintained an ambivalent attitude to astrology, the 'foolish little daughter' of astronomy, as he called it, yet throughout his life he continued to cast horoscopes for himself and his family, especially his children. He took great care with these star charts, while being not at all averse to massaging the data in order to avoid unfavourable predictions.

  Kepler recorded the moment, on July 19th, 1595, when his life as a scientist may be said truly to have begun. He was in the classroom of the Graz seminary school, conducting a lesson in astronomy. He had drawn on the blackboard a diagram illustrating the progression of the great conjunctions of Jupiter and Saturn, that is, the crossing points at which, approximately every twenty years, the planet Jupiter catches up with and passes Saturn. Because of slight variations in distance between the points on the Zodiac at which the conjunctions occur - pay attention, please, this is really not as complicated as it seems - it is possible to inscribe a series of triangles within the circle of the Zodiac joining the conjunction points, triangles which on their inner sides will, as if by magic, or divine intention, 'draw' another, smaller circle . . . Oh, all right, here is an illustration.

  For years already Kepler the astronomer had been pondering essential questions, such as why there should be six planets - only six were known in his day - and why the distances between their orbits should be set as they are. There must be a plan, a rational design; as Einstein centuries later would insist, God does not play dice with the world.31 To Kepler the Pythagorean, the planetary system was a gigantic musical instrument sounding its vast, silent chord in tune to the geometric laws of harmony. It was a conviction he shared with most astronomers back to antiquity. Kepler's genius, his astonishing originality, lay in the way he tackled the questions that he never stopped asking. Before him, cosmologists had bent their best efforts to describing the disposition of things as they seemed, and predicting accurately how things might be expected to be in the future. Kepler was the first to concentrate not on description, but explanation. He wanted to know not only how things are as they are, but why. A plan, a pattern, there must be.

  That day in the schoolroom in Graz when he stepped back from the blackboard - let us imagine the summer sunlight in the dusty window, the chalk-motes drifting in the luminous air, the bored pupils drooping at their desks, one of them dreamily picking his nose - what Kepler saw was that the inner circle was half the size of the outer one. Saturn and Jupiter were the two outermost planets of the solar system, as it was known to him, and Jupiter's orbit was rough
ly half the size of Saturn's. Was the relationship between them dictated by a triangle, the first figure in geometry? And if so, could the relations between the orbits of the remaining planets also be set according to the dimensions of other geometrical forms? He spent the rest of the summer trying to discover what these forms might be, juggling triangles and squares and pentagons, like Beckett's Molloy shuffling his sucking stones from pocket to pocket. And at last it came to him, when he saw that of course he must move from two to three dimensions. In geometry there are five, and only five, regular or perfect solids, from the cube, with six identical sides, up to the icosahedron, which has twenty sides. It is a characteristic of these shapes that they can be set within a sphere so that all their corners touch the surface of the sphere, and that a sphere can be set inside them so that the surface of the sphere will touch the centre of every side. Perfection. This was it, Kepler believed, God's big secret, the framework of the planetary system, the grid of the great world. This was why there are, as he thought, six planets, because the Lord of the Universe had founded the solar system on the five perfect solids, one set inside each of the planetary orbits, with the sun at the centre.

  Kepler's model of the universe, from Mysteriwn Cosmograpicum

  Kepler was to devote the rest of his life to proving his theory, despite the fact that it was unprovable, because mistaken. Even after he had made the momentous discovery that the planets do not move in perfect circles, but in ellipses, and had devised his three laws of planetary motion which revolutionised astronomy and the science of physics, he still clung to his beautiful idea, resorting to some shameless mathematical sleight of hand in his efforts to smooth out the inconsistencies. In the summer of 1595, however, in the first flush of discovery, his immediate need was for the most accurate planetary observations then available. He thought at once of Tycho Brahe. However, it would be more than four years before he would meet the Dane, and even then it took another year and a half, and Tycho's death, for this 'little house dog', as he liked to describe himself, to get his teeth into the juicy meat of Tycho's planetary charts. By then he was a married man with a stepdaughter - his wife, Barbara, twenty-three when he met her, was already twice a widow - and the author of a book setting out his theory of the heavens, with the catchy title Prodromus dissertationum cosmographicarum, continens mysterium cosmographicum, de admirabili proportione orbium coelestium, deque causis coelorum numeri, mag-nitudinis, motuumque periodicorum genuinis & proprijis, demonstratum, per quinque regularia corpora geometrica, or Mysterium cosmographi-cum for short.

  In the final years of the sixteenth century life had become extremely difficult for Protestants in the province of Styria. The Counter-Reformation was well under way, and the Catholic authorities in Graz were imposing increasingly harsh religious strictures. When in the summer of 1599 the Keplers' baby daughter Susanna died after less than a month of life, Kepler refused a Catholic burial for the infant and was consequently fined. In the autumn, rumours began to fly that soon any Lutheran moving out of the city would have his wealth and possessions confiscated, which, if the rumours were true, would mean that the Keplers would lose Barbara's considerable inheritance. There were sectarian riots in the countryside, and then in the streets of the city itself. The time had come to move on. Kepler turned his increasingly desperate attention in the direction of Prague. Tycho Brahe, the Great Dane in the manger, possessed a wealth of astronomical data. 'Only, like most rich men,' Kepler wrote to his old teacher Mastlin, 'he does not know how to make proper use of his riches. Therefore, one must take pains to wring his treasures from him, to get from him, by begging, the decision to publish all his observations without reservation.' Later, in 1601, Kepler wrote from Prague to the Italian astronomer Antonio Magini of his reasons for coming there: 'What influenced me most was the hope of completing my study of the harmony of the world - something that I have long contemplated and that I would be able to complete only if Tycho were to rebuild astronomy or if I could use his observations.' Despite his double vision, Kepler was never less than clear-eyed.

  At the beginning of 1600 Kepler's chance came. An acquaintance of his, Baron Johann Friedrich Hoffmann, a wealthy, cultured man and a close adviser to the Emperor Rudolf, had been in Graz to attend a convention of the Styrian Diet and was now returning to Prague, and offered him a lift in his entourage. The Baron was of a kindly disposition, and, although a Catholic, had sympathy with Kepler's difficulties as a Lutheran. Also, Hoffmann was an amateur astronomer, and had read and admired Kepler's work. He was acquainted too with Tycho Brahe and had determined that the two men should meet. And Kepler did need a friendly advocate, for he had already blundered into a series of embarrassing and potentially disastrous misunderstandings with the prickly Dane, including seeming to back up the claims of a certain Ni-cholaus Reymers Bar - his punningly Latinised name was Ursus, ursus being Latin for bear who had briefly assisted Tycho on Hven, and had published a system of the world which Tycho vehemently claimed was a plagiarism of his own work; Tycho would have got in first, were it not for his extreme unwillingness to publish, since in his circle and among his family the writing of books was considered no fit occupation for a gentleman and a knight. However, Tycho in his lordly way had forgiven young Kepler his trespasses, and had written graciously to invite him to Prague, assuring him that 'whatever comes to pass, you will find in me not a follower of fortune . . . but your friend who even under untoward circumstances will not fail you with his advice and help, but rather will advance you to everything that is best,' Kepler, however, did not receive this letter, for it crossed with his journey to Prague.

  Arriving in the city in the bitterly cold dawn of a new century - it was January, 1600 - Kepler, no doubt exhausted after the ten-day journey, was alarmed to find that Brahe, like Old Possum's cat Macavity, was not there. He was not even at Benatky, for he was still sheltering from the plague at Girsitz. Kepler, who had left Barbara and her seven-year-old daughter Regina in Graz, lodged with the hospitable Baron Hoffmann at his house on the in a street behind the royal gardens that would one day be called Tychonova, named after you know who. What an adventure Prague must have been for this poor son of Weilderstadt. The transfer of the imperial court from Vienna had made Prague the first city of the empire, and for the thirty years of Rudolf's rule there it was the centre of Europe not only geographically but in terms of wealth and power. Like every capital city it acted as a magnet, drawing to it people from all over the continent, ambassadors and foreign diplomats, scholars, artists, scores of alchemists and sorcerers and, inevitably, as we have seen, countless mountebanks and swindlers. To Kepler the city must have been a dazzling spectacle, a very image of the 'gold rooms and spontaneous applause, the attention of magnificent people'32 that he had anticipated. There were magnificent Gothic palaces and Romanesque churches,33 while the Castle itself, brooding on its hill, must have seemed a city within a city. Kepler will have cast a speculative eye toward the Hradcany, Rudolf's keep, for he knew of the Emperor's enthusiasm for new science and old magic, in the first of which Kepler was an adept, and the second of which he was prepared to practise, if horoscopes and numerology should prove the route into imperial favour.

  At the end of January, when the cold had killed off the last of the pestilence, Tycho returned to Benatky, and wrote another letter to Kepler. This one got delivered. In it, Tycho was promisingly cordial, inviting Kepler to the Bohemian Venice, the new Uraniborg. 'You will come,' the Dane wrote, 'not so much as guest but as a very welcome friend and highly desirable participant and companion in our observations of the heavens.' In a further show of favour he sent his son, Tycho the younger, accompanied by Franz Tengnagel, an elegant young Westphalian noble and one of the astronomer's assistants, to Prague to fetch the newcomer. When Kepler and his two escorts reached Benatky, Tycho received him warmly, offering to reimburse his travel expenses and enquiring after his family and what plans he had for his wife and stepdaughter to join him. Kepler could scarcely contain his excitement and jo
y. The world's greatest, or at least its most renowned, astronomer - Kepler had no doubt who the really great one was - the legendary lord of Hven, magus of Uraniborg, and now Imperial Mathematician to His Majesty Rudolf II, was shaking his hand and inviting him to join with him in work to solve the mysterium cosmogra-phicum.

  Within a day or two, however, Kepler's hopes had turned to ashes. He had not yet learned the ways of the aristocracy, and had mistaken Tycho's automatically courtly greeting for a pledge of comradeship. When the niceties were done with, Tycho promptly turned and swept away to his own concerns, which were many and burdensome. Benatky was still a building site, with workmen traipsing everywhere, hammering and whistling. Four of Brahe's most precious instruments were still on Hven, while others were in transit somewhere in the German lands. And Kepler was not the only one being disappointed in the matter of patronage: the Emperor's pledges of financial support for Tycho and his plans had not been made good, while Mlihlstein, the increasingly alarmed administrator of Benatky, was refusing to countenance further expenditure on renovations to the castle without direct authorisation from the Emperor.