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Leaving Prague for Linz
Kepler's years in Prague were relatively peaceful, and scientifically extremely productive. In fact, even when things went badly, he seems never to have allowed external circumstances to prevent him from getting on with his work. Things began to go very badly in late 1611. First, his seven year old son died. Kepler wrote to a friend that this death was particularly hard to bear because the child reminded him so much of himself at that age. Then Kepler's wife died. Then the Emperor Rudolf, whose health was failing, was forced to abdicate in favour of his brother Matthias, who, like Rudolf, was a Catholic but (unlike Rudolf) did not believe in tolerance of Protestants. Kepler had to leave Prague. Before he departed he had his wife's body moved into the son's grave, and wrote a Latin epitaph for them. He and his remaining children moved to Linz (now in Austria).
Marriage and wine barrels
Kepler seems to have married his first wife, Barbara, for love (though the marriage was arranged through a broker). The second marriage, in 1613, was a matter of practical necessity; he needed someone to look after the children. Kepler's new wife, Susanna, had a crash course in Kepler's character: the dedicatory letter to the resultant book explains that at the wedding celebrations he noticed that the volumes of wine barrels were estimated by means of a rod slipped in diagonally through the bung-hole, and he began to wonder how that could work. The result was a study of the volumes of solids of revolution (New Stereometry of wine barrels ..., Nova stereometria doliorum ..., Linz, 1615) in which Kepler, basing himself on the work of Archimedes, used a resolution into 'indivisibles'. This method was later developed by Bonaventura Cavalieri (c. 1598 - 1547) and is part of the ancestry of the infinitesimal calculus.
The Harmony of the World
Kepler's main task as Imperial Mathematician was to write astronomical tables, based on Tycho's observations, but what he really wanted to do was write The Harmony of the World, planned since 1599 as a development of his Mystery of the Cosmos. This second work on cosmology (Harmonices mundi libri V, Linz, 1619) presents a more elaborate mathematical model than the earlier one, though the polyhedra are still there. The mathematics in this work includes the first systematic treatment of tessellations, a proof that there are only thirteen convex uniform polyhedra (the Archimedean solids) and the first account of two non-convex regular polyhedra (all in Book 2). The Harmony of the World also contains what is now known as 'Kepler's Third Law', that for any two planets the ratio of the squares of their periods will be the same as the ratio of the cubes of the mean radii of their orbits. From the first, Kepler had sought a rule relating the sizes of the orbits to the periods, but there was no slow series of steps towards this law as there had been towards the other two. In fact, although the Third Law plays an important part in some of the final sections of the printed version of the Harmony of the World, it was not actually discovered until the work was in press. Kepler made last-minute revisions. He himself tells the story of the eventual success:
...and if you want the exact moment in time, it was conceived mentally on 8th March in this year one thousand six hundred and eighteen, but submitted to calculation in an unlucky way, and therefore rejected as false, and finally returning on the 15th of May and adopting a new line of attack, stormed the darkness of my mind. So strong was the support from the combination of my labour of seventeen years on the observations of Brahe and the present study, which conspired together, that at first I believed I was dreaming, and assuming my conclusion among my basic premises. But it is absolutely certain and exact that "the proportion between the periodic times of any two planets is precisely the sesquialterate proportion of their mean distances ..."
(Harmonice mundi Book 5, Chapter 3, trans. Aiton, Duncan and Field, p. 411).
Witchcraft trial
While Kepler was working on his Harmony of the World, his mother was charged with witchcraft. He enlisted the help of the legal faculty at Tübingen. Katharina Kepler was eventually released, at least partly as a result of technical objections arising from the authorities' failure to follow the correct legal procedures in the use of torture. The surviving documents are chilling. However, Kepler continued to work. In the coach, on his journey to Württemberg to defend his mother, he read a work on music theory by Vincenzo Galilei (c.1520 - 1591, Galileo's father), to which there are numerous references in The Harmony of the World.
Astronomical Tables
Calculating tables, the normal business for an astronomer, always involved heavy arithmetic. Kepler was accordingly delighted when in 1616 he came across Napier's work on logarithms (published in 1614). However, Maestlin promptly told him first that it was unseemly for a serious mathematician to rejoice over a mere aid to calculation and second that it was unwise to trust logarithms because no-one understood how they worked. (Similar comments were made about computers in the early 1960s.) Kepler's answer to the second objection was to publish a proof of how logarithms worked, based on an impeccably respectable source: Euclid's Elements Book 5. Kepler calculated tables of eight-figure logarithms, which were published with the Rudolphine Tables (Ulm, 1628). The astronomical tables used not only Tycho's observations, but also Kepler's first two laws. All astronomical tables that made use of new observations were accurate for the first few years after publication. What was remarkable about the Rudolphine Tables was that they proved to be accurate over decades. And as the years mounted up, the continued accuracy of the tables was, naturally, seen as an argument for the correctness of Kepler's laws, and thus for the correctness of the heliocentric astronomy. Kepler's fulfilment of his dull official task as Imperial Mathematician led to the fulfilment of his dearest wish, to help establish Copernicanism.
Wallenstein
By the time the Rudolphine Tables were published Kepler was, in fact, no longer working for the Emperor (he had left Linz in 1626), but for Albrecht von Wallenstein (1583 - 1632), one of the few successful military leaders in the Thirty Years' War (1618 - 1648).
Wallenstein, like the emperor Rudolf, expected Kepler to give him advice based on astrology. Kepler naturally had to obey, but repeatedly points out that he does not believe precise predictions can be made. Like most people of the time, Kepler accepted the principle of astrology, that heavenly bodies could influence what happened on Earth (the clearest examples being the Sun causing the seasons and the Moon the tides) but as a Copernican he did not believe in the physical reality of the constellations. His astrology was based only on the angles between the positions of heavenly bodies ('astrological aspects'). He expresses utter contempt for the complicated systems of conventional astrology.
Death
Kepler died in Regensburg, after a short illness. He was staying in the city on his way to collect some money owing to him in connection with the Rudolphine Tables. He was buried in the local church, but this was destroyed in the course of the Thirty Years' War and nothing remains of the tomb.
Historiographic note
Much has sometimes been made of supposedly non-rational elements in Kepler's scientific activity. Believing astrologers frequently claim his work provides a scientifically respectable antecedent to their own. In his influential Sleepwalkers the late Arthur Koestler made Kepler's battle with Mars into an argument for the inherent irrationality of modern science. There have been many tacit followers of these two persuasions. Both are, however, based on very partial reading of Kepler's work. In particular, Koestler seems not to have had the mathematical expertise to understand Kepler's procedures. Closer study shows Koestler was simply mistaken in his assessment.
The truly important non-rational element in Kepler's work is his Christianity. Kepler's extensive and successful use of mathematics makes his work look 'modern', but we are in fact dealing with a Christian Natural Philosopher, for whom understanding the nature of the Universe included understanding the nature of its Creator.
J. V. Field, London
Список литературы
Для подготовки данной работы были использованы материалы с сайта http://www-history.mcs.st-andrews.ac.uk/
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