Johann Kepler Imperial Mathematician

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One of the most extraordinary things about Galileo's life and work is his relationship with his greatest colleague, a man seven years his junior, whom he nevermet andonlyveryrarelycorrespondedwith. TheGermanProtestant Kepler had the keys that Galileo needed. They were moreover simply and strikingly formulated "in the language of mathematics".

Johann Kepler had been born in the small town of Weil on the Rhine, where the river forms the border between modern Germany and Switzerland. He became a teacher at a Protestant grammar school at Graz in Steiermark, in the south of what is now Austria, and where in 1596, at the age of twenty-five, he published a great work The Cosmographical Mystery, a sober description of the Copernican system, mixed with large doses of religiously influenced numerology

Kepler assumed that the planets - including the Earth - revolved around the Sun. At that time there were six of them (the discovery of Uranus, Neptune and Pluto was awaiting the telescope). In the five spaces between the planets' orbits Kepler believed he could prove - with the help of a good deal of guesswork - that the five so-called perfect bodies,consistingofregular polyhedrons, were found.

Using this astute construction, he turned the religious argument against Copernicus on its head. He declared simply that God's ingenious plan for creation was not refuted by the Copernican system, but on the contrary, it was demonstrated in its full perfection: "Now you see how, through my endeavours, God also allows himself to be acclaimed in astronomy," he wrote to his teacher Mastlin. More sceptical colleagues were impressed, but not convinced.

Galileo also got a copy of The Cosmographical Mystery, and Kepler asked for his comments on it, but they never materialised, only a non-committal letter of thanks in which Galileo acknowledges that he shares the conviction that Copernicus was correct - but does not want to state the fact publicly.

Prague was the seat of the ruling Holy Roman Emperor, Rudolf II. As the power struggles raged around him, the Emperor retreated into studies of art and science. Rudolf saw to it that Tycho Brahe, who had virtually fled Denmark after complaints that he mistreated his tenants, was summoned to Prague as Imperial Mathematician.

Tycho Brahe recognised that Kepler was a genius and asked him to come to Prague, to cease his speculations and concentrate on empirical observations, the area in which Brahe himself was a passed master. Kepler did go - but not before the fateful year of 1600, and then only because he, as a Protestant, had literally been driven out of the predominantly Catholic Steiermark.

Kepler was a mystical and speculative theoretician. Brahe's strength lay in minute observation in which every assumption was checked. In his heyday in Denmark he had dispatched an expedition to Frombork merely to check that Copernicus had got precisely the correct latitude for his observations. Kepler and Brahe did not get on well personally, but their work changed astronomy for ever. Their first meeting took place on 4 February 1600, a date which may well be called the dawn of a new age.

Kepler, shy and sensitive, soon discovered that the rather blustering Danish aristocrat was not easy to work with. In addition, he did not much like the work he had been given - writing a pamphlet attacking one of Brahe's opponents! But their direct collaboration did not last long, because in October 1601 Brahe died suddenly and unexpectedly. The story has always been that it was court etiquette that killed him - his bladder is said to have burst because he could not rise from the Emperor's table before the Emperor himself. But in all probability he died of lead or mercury poisoning, perhaps as a result of many years' experimenting with chemicals.

Emperor Rudolf II of the Holy Roman Empire had no scruples about appointing yet another Protestant - Kepler - to the post of Imperial Mathematician after Brahe. In this role Kepler was given the task of putting Brahe's posthumous effects in order. And this would have given him access to something Brahe had guarded as a treasure: incomparably accurate observations of the course of Mars across the sky.

The orbit of Mars was the key to the description of the heavens. It was irregular and capricious, impossible to fit into any astronomical system. Brahe's heirs certainly did not intend to allow Kepler free access to this painstaking work. But Mars' orbit was something he just had to find out about - so he simply stole the notes.

Using Brahe's decades of observations, Johann Kepler correctly described the solar system based on Copernicanism. With pen and paper he calculated, using a series of observations, the movements of a planet - Mars - that had a certain orbit. These observations were not, of course, made from a "fixed point" - that was what made them difficult - but from another mobile planet, the Earth, that was moving on an entirely different orbit. He had to do this without knowing the exact shape of the orbits in advance, far less their circumferences.

He published his calculations in the book The New Astronomy, which came out in 1609. In it he demonstrated that the orbit of Mars with its seemingly unexpected capers across the sky could be explained simply and correctly from two fundamental assumptions. One was Copernican: that the Sun stood still and was orbited by Mars and the Earth.

The other assumption was, in a way, a yet more radical break with the entirety of Aristotelian thought. For no one - and certainly not Copernicus -had been able to conceive that the planets' orbits would be anything but circular. The circle was the perfect shape, the classical symbol of perfection, where every point was equidistant from the centre.

But Kepler did his calculations. And he discovered that the planetary orbits were not divinely perfect circles, but earthly, bulging ellipses, figures that do not even have a centre, just two "foci", of which the Sun was one. He also demonstrated a peculiar proportionality, "Kepler's Second Law", that should have gladdened Galileo's heart: the area an imaginary line from the Sun to a planet "sweeps across", is always proportional to the planet's periodic time, regardless of how the distance between that planet and the Sun varies.

This was serious stuff from Kepler. He was not talking about mathematical models, but giving a factual description of cosmological reality, a description that also had the merit of providing correct calculations.

There was nothing he could do to solve the parallax problem. That aside, he had, if not proved, at least shown it to be overwhelmingly likely that Copernicus was right. It must be stated, though, that this was not the main point for Kepler. It was the great astronomical revelations of a religious, metaphysical nature that he really wanted to find and describe.

The educated world reacted with dismay, wonder - and temporary silence. Galileo said nothing on this occasion either.

The following year, in March 1610, one of the Emperor's most senior counsellors arrived at Kepler's house in his carriage, he was excited and bore extraordinary tidings. There were rumours at court that a mathematician in Padua had looked at the sky through a telescope and seen four new planets!

Kepler waited expectantly for further details. There was little point in looking himself as the telescopes available in Prague could barely be used to make out large and undetailed characteristics on the surface of the Moon. But he did not need to wait long. A few days later he had post from Galileo, the first contact between them for thirteen years. It was The Starry Message.

Even before he received the book, Kepler realised that what the Italian had seen must be satellites. He was not slow in working out that this was a weighty argument in favour of Copernicus. Strictly speaking, the existence of Jupiter's satellites proved nothing about what sort of centre the planets revolved around. But it was a serious warning that one of the basic assumptions of Aristotle and Ptolemy was crumbling. Satellites orbiting Jupiter would demonstrate that the Earth was not the centre of all cosmic motion.

According to Kepler's logic, the circumstantial Copernican evidence was proof enough that the satellites existed. In considerable haste he sat down and wrote a glowing defence of Galileo and the heavenly bodies he himself had never seen. The work was full of digressions, some brilliantly incisive, others comparatively speculative. Amongst the latter mustbe included abrief account of the kind of building styles hypothetical Moon-dwellers might employ. He sent his work by the first courier to Italy, but retained a copy that he polished up a little more and had printed.

He was able to send the printed piece to Magini, when the professor wrote from Bologna trying to mobilise Kepler against Galileo. His covering letter was dry and formal:

"Accept this and excuse me. Both of us [Galileo and himself] are Coperni-

Enthusiastic support from Kepler, the Imperial Mathematician and Astronomer, was just what Galileo needed. Perhaps it was meant more as a lifeline to Copernicanism rather than to Galileo personally, but it arrived at precisely the right moment. Grand Duke Cosimo could now be certain that the Medicean stars really were up there around Jupiter to the eternal glory of his family.

Galileo never returned the favour. He did not even reply to Kepler's letter or thank him for the favourable wind generated by the printed pamphlet. In August he received yet another letter in which Kepler said he had received several other applications from Italy, where the satellites were still in doubt. Kepler distanced himself vehemently from Martin Horky's libel, but added that Galileo must get independent verification of his observations as soon as possible.

Now Galileo had to answer and quickly, too. Kepler's support was too vital to be hazarded. It was an amiable, but empty letter in which Galileo carefully avoided promising to send Kepler a telescope - although that summer he sent telescopes to prominent people all over Europe via the Medici's Ambassadorial network. (It was one of these that Kepler finally managed to borrow.)

We do not know for certain whether Galileo had read The New Astronomy, but even before 1612 at latest, he was well acquainted with the insights it contained. He never used them, however. Perhaps it was Kepler's bombastic style, full of digressions and odd assertions, that scared him. Galileo's The Starry Message is as different from Kepler's writings as it is possible to get; a concise, crystal clear elucidation, in fact the beginnings of the modern scientific style.

Or perhaps it was pure envy.

When Emperor Rudolf died in 1612, Johann Kepler wisely retired from the uneasy court at Prague where the whole of Europe's national and religious disparities were clashing. He settled in the provincial town of Linz. When his mother was implicated in a witch trial, he had to begin a legal and theological battle to save her. But he still found time to work. His last great book World Harmony (1619), was full of mystical speculations, but also contained his "third law": the square of a planet's periodic time is proportional to the cube of its orbit's greatest radius.

However, Kepler did not regard this law as a fundamental key to understanding the mechanics of planet movement - Newton, over fifty years later, was the first to do that. Instead, Kepler believed he had here found a proof for his planet mysticism, the divine harmony that must suffuse the world.

This work made no impression on Galileo either. The Grand Duke's Mathematician in Tuscany never allowed himself to be persuaded by the Imperial one in Austria. (Kepler kept his title for the remainder of his life.)

It is a strange historical paradox that it was the superstitious Kepler, with at least one foot in the mysticism of the Middle Ages, who proved the correctness of the Copernican system. The sober Galileo carried on the self-assured Tuscan tradition of sceptical, independent thought. A good century before, Leonardo da Vinci had announced that astrology was an untenable science whose main function was to get money out of fools. It might just as well have been said by Galileo (which did not prevent him from occasionally casting horoscopes in the course of his duties or for the sake of amusement).

Galileo was in many ways a modern rationalist. Even so, he did not manage to prove that Copernicus was right - and worse still, he repudiated or ignored Kepler's proofs. If, despite all this, he was impressed and influenced by his colleague's deep insights, he never admitted it to anyone. Perhaps the proud Tuscan viewed Kepler not as a brilliant astronomer, a collaborator in the work of gaining new knowledge, but as his major rival in being the principal harbinger of the Copernican truths in Europe.

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