Johannes Kepler

At this time, it was usual for all students at a university to attend courses on "mathematics". In principle this

Johannes Kepler



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nvolved 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.


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.


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

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