Those, however, who lived on the other side of the watershed, who believed in the ageless dream of an a priori deduction of the cosmic order, were enthusiastic and delighted. Most of all, of course, the endearing Maestlin, who wrote to the Tuebingen Senate:
"The subject is new and has never before occurred to anybody. It is most ingenious and deserves in the highest degree to be made known to the world of learning. Who has ever dared before to think, and much less to try to expose and explain a priori and, so to speak, out of the hidden knowledge of the Creator, the number, order, magnitude and motion of the spheres? But Kepler has undertaken and successfully done just this... Henceforth [astronomers] shall be freed from the necessity of exploring the dimensions of the spheres a posteriori, that is by the method of observations (many of which are inexact and not to say doubtful) after the manner of Ptolemy and Copernicus, because now the dimensions have been established a priori... Whereby the computation of the movements will become much more successful..." 11
In a similar vein enthused Limneus in Jena, who congratulated Kepler, all students of astronomy and the whole learned world that "at last the old and venerable [Platonic] method of philosophy had been resurrected". 12
In a word, the book which contained the seeds of the new cosmology was welcomed by the "reactionaries" who did not see its implications, and rejected by the "moderns", who did not see them either. Only one man took a middle course and, while rejecting Kepler's wild speculations, immediately realized his genius: the most outstanding astronomer of the day, Tycho de Brahe.
But Kepler had to wait for three years until he met Tycho, became his assistant, and started on his true lifework. During these three years (1597-99) he at last got down to a serious study of mathematics, of which he had still been shockingly ignorant when he wrote the Mysterium, and undertook a motley variety of scientific and pseudo-scientific researches. It was a kind of limbering up before the great contest.
The first task he set himself was to find direct confirmation of the earth's motion round the sun by proving the existence of stellar parallax, that is, a shift in the apparent position of the fixed stars according to the earth's position on its annual journey. He pestered, in vain, all his correspondents to help him with observations, and at last decided to take a peep for himself; but his "observatory" consisted of a self-made staff suspended on a rope from the ceiling: "it comes from a workshop like the huts of our forebears – hold your laughter, friends, who are admitted to this spectacle." 13 Even so, it would have been sufficiently precise to show the variation of half a degree, which Kepler expected, in the positions of the polar star as seen from extreme points of the earth's path. But there was no variation; the starry sky remained immutable, poker-faced. This meant either that the earth stood still, or that the size of the universe (that is, the radius of the sphere of fixed stars) was much larger than previously assumed. To be precise, its radius must be at least five hundred times the distance of the earth from the sun. This works out at 2,400 million miles, a trifle by our, but not a lot even by Kepler's, standards; only about five times more than he had expected. 14 However, assuming that even much better instruments failed to show a parallax, meaning that the stars are quite inconceivably distant, in the eyes of God the universe would still have a reasonable size, only man's physical stature would shrink. But this would not diminish his moral stature, "otherwise the crocodile or the elephant would be nearer to His heart than man, because they are larger. With the help of this and similar intellectual pills, we shall perhaps be able to digest this monstrous bite." 15 In fact, no pill has been discovered since to digest the lump of infinity.
Other problems which occupied him were his first researches into optics, out of which eventually a new science was to emerge; investigations of the moon's orbit, of magnetism, of meteorology – he started a weather diary which he kept up for twenty or thirty years; of Old Testament chronology, and the like. But dominating all these interests was his search for a mathematical law of the harmony of the spheres – a further development of his ideé fixe.
In the Mysterium, Kepler had tried to build his universe around the five Pythagorean solids. Since the theory did not quite fit the facts, he now tried to build it round the musical harmonies of the Pythagorean scale. The combination of these two ideas led, twenty years later, to his great work Harmonice Mundi, which contains the third of Kepler's laws; but the ground work to it was laid during his last years in Gratz.
The moment this new idea had occurred to him, his letters resounded with jubilant Eurekas: "Fill the skies with air, and they will produce true and real music." But as he began to compute the details of his cosmic musical box, he ran into increasing difficulties. He was never short of an excuse for ascribing to any pair of planets the musical interval which approximately happened to fit it; when things became sticky, he asked the shadow of Pythagoras for help – "unless the soul of Pythagoras has migrated into mine." He managed to construct a system of sorts, but its inadequacies were obvious to himself. The principal trouble was that a planet does not move at uniform speed, but faster when it is close to the sun, slower when away from it. Accordingly, it does not "hum" on a steady pitch, but alternates between a lower and a higher note. The interval between the two notes depends on the lopsidedness or "eccentricity" of the planet's orbit. But the eccentricities were only inaccurately known. It was the same difficulty he had come up against when he had tried to define the thickness of the spherical shells between his perfect solids, which also depended on the eccentricities. How could you build a series of crystals, or a musical instrument, without knowing the measurements? There was only one man alive in the world who possessed the exact data which Kepler needed: Tycho de Brahe. All his hopes became now focused on Tycho, and his observatory at Uraniburg, the new wonder of the world:
"Let all keep silence and hark to Tycho, who has devoted thirty-five years to his observations... For Tycho alone do I wait; he shall explain to me the order and arrangement of the orbits... Then I hope I shall one day, if God keeps me alive, erect a wonderful edifice." 16
Thus he knew that the building of that edifice still lay in the distant future, though in his euphoric moments he claimed to have it already completed. During his manic periods, the discrepancies between theory and fact appeared to him as contemptible details, which could be smoothed over by a little cheating; yet the other half of his divided self humbly acknowledged the duty of pedantic accuracy and patient observation. With one eye he was reading the thoughts of God; the other squinted enviously at Tycho's shining armillary spheres.
But Tycho refused to publish his observations until he had completed his own theory. He jealously guarded his treasure, volumes of figures, the result of a lifetime of work.
"Any single instrument of his," young Kepler wrote bitterly, "cost more than my and my whole family's fortune put together... My opinion of Tycho is this: he is superlatively rich, but he knows not how to make proper use of it as is the case with most rich people. Therefore, one must try to wrest his riches from him." 17
In this outcry, Kepler had revealed his intentions towards Tycho de Brahe a year before they met for the first time.
4. Waiting for Tycho
Had Kepler not succeeded in getting hold of Tycho's treasure, he could never have discovered his planetary laws. Now Newton was born only twelve years after Kepler's death, and without the planetary laws he could not have arrived at his synthesis. No doubt somebody else would have done so, but it is at least possible that the scientific revolution would have carried different metaphysical undertones if it had been fathered not by an English empiricist, but, say, a Frenchman with Thomist inclinations, or a German mystic.
The point of such idle speculation is merely to insert a question mark here and there against the supposed logical inevitability and cast-iron determinism of the evolution of scientific thought. The shape of Cleopatra's nose influences not only wars, but ideologies. The mathematics of the Newtonian universe would have been the same
whoever worked them out, but its metaphysical climate might have been quite different. 18
Yet it was touch and go whether Kepler's laws would be ready for Newton. 19 They could only be discovered with Tycho's help; and by the time Kepler met him, Tycho had only eighteen months left to live. If it was divine providence which timed their meeting, it chose a rather perverse method: Kepler was hounded out of Gratz and into the arms of Tycho, by religious persecution. Though he always endeavoured to read the thoughts of God, he never offered his thanks for this Machiavellian stratagem.
That last year in Gratz – the last of the century – was indeed not easy to endure. The young Archduke Ferdinand of Hapsburg (later Emperor Ferdinand II) was determined to cleanse the Austrian provinces of the Lutheran heresy. In the summer of 1598, Kepler's school was closed down, and in September all Lutheran preachers and schoolmasters were ordered to leave the Province within eight days or forfeit their lives. Only one among them received permission to return, and that was Kepler. His exile, the first, lasted less than a month.
The reasons why an exception was made with him are rather interesting. He himself says 20 that the Archduke was "pleased with my discoveries" and that this was the reason for his favour at his court; besides, as a mathematicus he occupied a "neutral position" which set him apart from the other teachers. But it was not as simple as that. Kepler had a powerful ally behind the scenes: the Jesuit order.
Two years previously the Catholic Chancellor of Bavaria, Herwart von Hohenburg, amateur philosopher and patron of the arts, had asked Kepler – among other astronomers, for his opinion on certain chronological problems. It was the beginning of a life-long correspondence and friendship between the two men. Herwart tactfully advertized his protective interest in the Protestant mathematicus by sending his letters to Kepler via the Bavarian envoy at the Emperor's court in Prague, who forwarded them to a Capuchin father at Ferdinand's court in Gratz; and he instructed Kepler to use the same channels. In his first letter to Herwart, 21 Kepler wrote delightedly: "Your letter so impressed some men in our Government that nothing more favourable to my reputation could have happened."
It was all done with great subtlety; yet on later occasions Catholic and especially Jesuit influences were more openly active on behalf of Kepler's welfare. There seem to have been three reasons for this benevolent cabal. Firstly, a scholar was still, to some extent, regarded as a sacred cow amidst the turmoil of religious controversy – one remembers how Rheticus was fêted in Catholic Ermland at the time of Bishop Dantiscus' edicts against the Lutheran heresy. Secondly, the Jesuits, following in the steps of the Dominicans and Franciscans, were beginning to play a leading part in science and specially in astronomy – quite apart from the fact that it enabled their missionaries in distant countries to make a great impression by predicting eclipses and other celestial events. And lastly, Kepler himself disagreed with certain points of Lutheran doctrine, which made his Catholic friends hope – though in vain – that he might become a convert. He was repelled by the clerics of both warring churches who, from their pulpits, screamed at each other like fishwives – or like his parents and kin in old Sebaldus' house. His attitude was the same as the gentle Bishop Giese's: "I refuse the battle"; and he also did a certain amount of fence-straddling. Yet he refused to change sides, even when he was excommunicated by his own Church, as we shall hear; and when he suspected that Herwart was counting on his conversion, Kepler wrote to him:
"I am a Christian, the Lutheran creed was taught me by my parents, I took it unto myself with repeated searchings of its foundations, with daily questionings, and I hold fast to it. Hypocrisy I have never learnt. I am in earnest about Faith and I do not play with it." 22
It was the outburst of a man of basic integrity, forced to swim in the troubled waters of his time. He was as sincere in matters of religion as circumstances permitted him to be; at any fate, his deviations from the straight path were perhaps not greater than those of his orbits from God's five perfect solids.
Kepler was, then, made an exception and permitted to return from exile in October 1599. Since his school had been closed down he could devote most of his time to his speculations on the harmony of the spheres; yet he knew that the reprieve was only a temporary one, and that his days in Gratz were numbered. He sank into a profound depression, deepened by the death of his second child; in a despairing letter he asked Maestlin, in August 1599, for his help in finding a job at home in Protestant Wuerttemberg.
"The hour could not have been more propitious; but God has offered this fruit, too, only to take it away again. The child died of a cerebral meningitis (exactly as its brother a year ago) after thirty-five days... If its father should follow soon, his fate would not be unexpected. For everywhere in Hungary bloody crosses have appeared on the bodies of men and similar bloody signs on the gates of houses, on benches and walls, which history shows to be a sign of a general pestilence. I am, as far as I know, the first person in our town to see a small cross on my left foot, the colour of which passes from bloody red to yellow. The spot is on the foot, where the back of the foot curves into the instep, half-way between the toes and the end of the shin-bone. I believe it is just the spot where the nail was hammered into the foot of Christ. Some carry, I am told, marks in the shape of drops of blood in the hollow of the hand. But so far this form has not appeared on me...
The ravages of dysentry kill people of all ages here, but particularly children. The trees stand with dry leaves on their crowns as if a scorching wind had passed over them. Yet it was not the heat that so disfigured them, but worms..." 23
He had the worst fears. There was talk of torture for heretics, even of burnings. He was fined ten dalers for burying his child according to Lutheran rites: "half of it was remitted at my request, but the other half I had to pay before I was allowed to carry my little daughter to her grave." If Maestlin cannot get him a job at once, would he at least let him know about the present cost of living in Wuerttemberg: "How much wine costs and how much wheat, and how things stand regarding the supply of delicatessen (for my wife is not in the habit of living on beans)."
But Maestlin knew that his university would never give a job to the unruly Kepler, and he was getting thoroughly fed up with Kepler's unceasing demands and badgerings; the more so, as Kepler had followed up his S.O.S. with the foolish remark:
"Of course, nobody would expel me; the most intelligent among the members of the Diet are the most fond of me, and my conversation at meals is much sought after." 24
No wonder that Maestlin underestimated the urgency of the situation, and delayed for five months before he answered with an evasive and grumpy epistle: "If only you had sought the advice of men wiser and more experienced in politics than I, who am, I confess, as unexperienced in such matters as a child." 25
Only one hope remained: Tycho. The previous year, Tycho, in a letter, had expressed the hope that Kepler would "some day" visit him. Though he was panting and pining for "Tycho's treasure", the invitation was couched in too general terms, and the journey too long and costly. Now, however, it was no longer a matter of scientific curiosity for Kepler, but of the urgent necessity of finding a new home and a livelihood.
Tycho, in the meantime, had been appointed Imperial Mathematicus by Rudolph II, and had taken up residence near Prague. Kepler's long-awaited opportunity came when a certain Baron Hoffmann, Councillor to the Emperor, had to return from Gratz to Prague, and agreed to take him along in his suite. The date of Kepler's departure for the meeting with Tycho is, by the courtesy of History, easy to remember: it was 1 January, anno domini 1600.
IV TYCHO DE BRAHE
1. The Quest for Precision
JOHANNES KEPLER was a pauper who came from a family of misfits; Tycho de Brahe was a grand seigneur from the Hamlet country, the scion of truculent and quixotic noblemen of pure Danish stock. His father had been Governor of Helsingborg Castle, which faces Elsinor across the Sund; his Uncle Joergen, a country squire and vice-admiral.
T
his Uncle Joergen, being childless, had extracted a promise from his brother, the Governor, that if he had a son, Joergen could adopt him and bring him up as his own. Nature seemed to sanction this arrangement, for, in 1546, the Governor's wife bore him twin sons; but unfortunately one of them was still-born, and the father went back on his promise. Joergen, a true, headstrong Brahe, waited until another son was born to his brother, then kidnapped the firstborn, Tyge – Tycho. The Governor, also in true Brahe fashion, threatened murder, but quickly cooled off and generously consented to the fait accompli, knowing that the child would be well looked after and inherit some of Joergen's fortune. This came indeed to pass and sooner than expected, for while Tyge was still a student, his foster-father met an untimely and glorious end. He had just returned from a naval battle against the Swedes, and was riding in the suite of his King over the bridge joining Copenhagen to the royal castle, when the good King, Ferdinand II, fell into the water. Joergen, the vice-admiral, jumped after him, saved his King and died of pneumonia.
Whether Tyge suffered a traumatic shock by being kidnapped from his cradle we cannot know; but the blood of the Brahes and his education by the irascible vice-admiral must have sufficed to turn him into an eccentric in the grand style. This was visible at first glance, even in his physical appearance: for if Tycho was born with a silver spoon in his mouth, he later acquired a nose of silver and gold. As a student, he fought a duel with another noble Danish youth in the course of which part of Tyge's nose was sliced off. According to a contemporary account, 1 the quarrel originated in a dispute as to which of the two noble Danes was the better mathematician. The lost piece, which seems to have been the bridge of the nose, was replaced by a gold and silver alloy, and Tycho is said to have always carried a kind of snuffbox "containing some ointment or glutinous composition which he frequently rubbed on his nose". 2 In his portraits, the nose appears as a too rectilinear, cubistic feature among the curves of a large, bald, egg-shaped head, set between the cold, haughty eyes and the aggressively twirled handlebar moustache.