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WD_241/ 2006
(  Satoshi Kinoshita )
| Series: | Works on paper: Drawings 3 | | Medium: | oil pastel on paper | | Size (inches): | 30.1 x 21.3 | | Size (mm): | 765 x 542 | | Catalog #: | WD_0241 | | Description: | Signed, date and copyright in pencil on the reverse.
Johannes Kepler – 1571-1630;
Today, Kepler is mostly remembered for his three laws of planetary motion, first published in 1609. He also did important work in optics from 1604 to 1611. In 1611 He applied the first mathematical treatment of close packing of equal spheres (explaining the shape of honeycomb cells). He gave the first proof of how logarithms work in 1624; and he devised a formula for volume that (from hindsight) contributed to the development of calculus by Isaac Newton and Gottfried von Leibniz. Moreover, he advanced Tycho Brahe’s astronomical tables which did much to confirm heliocentric astronomy.
A large measure of Kepler's correspondence still survives today. Many of his letters were in the form of scientific papers, (there were no scientific journals then) and the various correspondents kept them for their interest-value. Consequently, we know a lot about Kepler and his beliefs, and a few details about his personality.
Kepler was born in the small town of Weil der Stadt in Swabia and moved to nearby Leonberg with his parents in 1576. His father was a mercenary soldier and his mother the daughter of an innkeeper. Johannes was their first child. His father left home to go to battle in the Netherlands when Johannes was five, and it’s believed that he was killed in the war there. As a child, Johannes lived with his mother in his grandfather's inn, where he’d help by serving tables. Customers were often perplexed by the boy’s unusual competence at arithmetic.
Kepler's early education was in a local school, and then at a nearby seminary, from where he went on to enroll at the University of Tübingen, (a fortress of Lutheran orthodoxy).
His opinions:
Throughout his life, Kepler was deeply religious. All his writings contain numerous references to God, and he saw his work as a fulfillment of his Christian duty. In addition, Kepler was convinced that God had made the Universe according to a mathematical plan (a belief found in the works of Plato and Pythagoras).
Since it was generally accepted at the time that mathematics provided a secure method of arriving at truths about the world (Euclid's common concepts and assumptions) Johannes applied it as a strategy for understanding the Universe. Kepler repeatedly thanks God for granting him insights, but the insights are presented as rational ones.
Formal education:
At this time, it was normal for all university students to attend courses in mathematics. In principle this included the four mathematical sciences – arithmetic, geometry, astronomy and music. However, what was taught usually depended on the university. At Tübingen Kepler was taught astronomy by one of the leading astronomers of the day, Michael Maestlin (1550 - 1631). The astronomy of the curriculum was, of course, geocentric astronomy, (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).
This system was more or less in accordance with the current concepts of physics, though there were certain difficulties. One difficulty dealt with the question of considering as 'uniform' (and therefore eternal) a circular motion that was constant around a point other than its own center (called an equant). However, most astronomers were content to continue calculating positions of planets and leave it to philosophers to worry about mathematical models dealing with physical mechanisms. Kepler however, did not take this attitude. His earliest published work (1596) proposed to consider the actual paths of the planets, and not the circles used to describe them.
At Tübingen, Kepler studied not only mathematics but also Greek and Hebrew (both necessary for reading the scriptures in their original languages). Teaching was in Latin. At the end of his first year Kepler got 'A's for everything except mathematics. Probably Maestlin was trying to tell him he could do better, because Kepler was in fact one of the select pupils to whom he chose to teach more advanced astronomy by introducing them to the new, heliocentric cosmological system of Copernicus.
In Kepler's younger days there were indications that his religious beliefs didn’t run parallel with orthodox Lutheranism. Kepler's problems with this Protestant orthodoxy concerned the supposed relation between matter and 'spirit' (a non-material entity) in the church doctrine. He found similar difficulties in explaining how 'force' from the Sun could affect the planets. In his writings, Kepler was always given to frank honesty, and when he applied it to religion his church was less than pleased. This may explain why Kepler was asked to abandon plans for ordination and instead to accept a post teaching mathematics in Graz.
Religious intolerance sharpened in the following years. Kepler was excommunicated in 1612. This caused him much anguish, but despite his (by then) relatively high social standing as Imperial Mathematician, he never succeeded in getting the ban lifted.
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 presents a more elaborate mathematical model than the earlier. The mathematics in this work includes the first systematic treatment of tessellation, a proof that there are only thirteen convex uniform polyhedra (the Archimedean solids) and the first account of two non-convex regular polyhedra. The Harmony of the World also contains what is now known as Kepler's Third Law – 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. Kepler had always sought a rule relating the sizes of the orbits to the orbital periods, but there was no direction 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 of Harmony of the World, it was not actually discovered until the work had gone to 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 on 8th March in the 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 labor 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..."
-www.belmontnc.4dw.net/AstroBio.htm
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