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Infinitesimals 16325/17/2023 ![]() At the end of his first year Kepler got 'A's for everything except mathematics. His earliest published work (1596) proposes to consider the actual paths of the planets, not the circles used to construct them.Īt Tübingen, Kepler studied not only mathematics but also Greek and Hebrew (both necessary for reading the scriptures in their original languages ). However, it seems that on the whole astronomers (who saw themselves as 'mathematicians' ) were content to carry on calculating positions of planets and leave it to natural philosophers to worry about whether the mathematical models corresponded to physical mechanisms. This system was more or less in accord with current (Aristotelian ) notions of physics, though there were certain difficulties, such as whether one might consider as 'uniform' (and therefore acceptable as obviously eternal ) a circular motion that was not uniform about its own centre but about another point (called an 'equant' ). The astronomy of the curriculum was, of course, geocentric astronomy, that is the current version of the Ptolemaic system, in which all seven planets - Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn - moved round the Earth, their positions against the fixed stars being calculated by combining circular motions. At Tübingen Kepler was taught astronomy by one of the leading astronomers of the day, Michael Mästlin (1550 - 1631). It seems, however, that what was taught depended on the particular university. In principle this included the four mathematical sciences: arithmetic, geometry, astronomy and music. Kepler does indeed repeatedly thank God for granting him insights, but the insights are presented as rational.Īt this time, it was usual for all students at a university to attend courses on "mathematics". Since some authors have given Kepler a name for irrationality, it is worth noting that this rather hopeful epistemology is very far indeed from the mystic's conviction that things can only be understood in an imprecise way that relies upon insights that are not subject to reason. Since it was generally accepted at the time that mathematics provided a secure method of arriving at truths about the world ( Euclid's common notions and postulates being regarded as actually true ), we have here a strategy for understanding the Universe. Moreover, Kepler was convinced that God had made the Universe according to a mathematical plan (a belief found in the works of Plato and associated with Pythagoras ). Man being, as Kepler believed, made in the image of God, was clearly capable of understanding the Universe that He had created. All his writings contain numerous references to God, and he saw his work as a fulfilment of his Christian duty to understand the works of God. Throughout his life, Kepler was a profoundly religious man. Kepler's early education was in a local school and then at a nearby seminary, from which, intending to be ordained, he went on to enrol at the University of Tübingen, then (as now ) a bastion of Lutheran orthodoxy. One imagines customers were sometimes bemused by the child's unusual competence at arithmetic. He tells us that he used to help by serving in the inn. As a child, Kepler lived with his mother in his grandfather's inn. His father left home for the last time when Johannes was five, and is believed to have died in the war in the Netherlands. His father was a mercenary soldier and his mother the daughter of an innkeeper. Kepler was born in the small town of Weil der Stadt in Swabia and moved to nearby Leonberg with his parents in 1576. It is partly because of this that Kepler has had something of a career as a more or less fictional character (see historiographic note below ). In consequence, we know rather a lot about Kepler's life, and indeed about his character. Many of his letters are almost the equivalent of a scientific paper (there were as yet no scientific journals ), and correspondents seem to have kept them because they were interesting. Moreover, he calculated the most exact astronomical tables hitherto known, whose continued accuracy did much to establish the truth of heliocentric astronomy ( Rudolphine Tables, Ulm, 1627).Ī large quantity of Kepler's correspondence survives. He also did important work in optics (1604, 1611), discovered two new regular polyhedra (1619), gave the first mathematical treatment of close packing of equal spheres (leading to an explanation of the shape of the cells of a honeycomb, 1611), gave the first proof of how logarithms worked (1624), and devised a method of finding the volumes of solids of revolution that (with hindsight! ) can be seen as contributing to the development of calculus (1615, 1616). ![]() Biography Johannes Kepler is now chiefly remembered for discovering the three laws of planetary motion that bear his name published in 16). ![]()
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