Text: http://www.cco.caltech.edu/~winter/unilab/module1650/kepler/harm.html In the sixteenth century, learning in general, and science in particular, were very different enterprises from today. Not only did people approach problems in markedly different ways, but they also studied fields that are for us nonexistent. For example, in Kepler's time fields such as alchemy, astrology, and harmonics were considered important subjects. Harmonics in particular is nowadays a mere sub-topic to fields such as physics and music. In Kepler's day, however, harmonics meant much more. It was considered one of the major mathematical sciences. The principles of harmonics were important to, and were applied in, music, architecture, and even astronomy. In Kepler's eyes, the theory of harmony was essential to astronomy. As an astronomer, he felt himself responsible for supporting one of three competing theories dealing with the motions of the planets. There was the Hellenistic Ptolemaic system, in which all bodies moved around a stationary earth. There was the Coperican system, which was (almost) heliocentric and involved all of the six planets moving around the sun. And there was a third system, invented by Tycho Brahe (and, probably independently, by a number of others), which had the sun moving around a stationary earth but the other planets moving around the sun. Today, one could decide which of these systems sounds the most reasonable in a second. In the sixteenth century it was less clear which to choose. All three could be made mathematically equivalent, and it was in any case unclear why an astronomer should be held to any one commitment. One of the most important factors in each decision, for Kepler, was harmony. Harmony was a concept of beauty and grace combined with simplicity. Kepler believed that these were attributes of God - a God whose mind was essentially disposed to geometrical archetypes. So he chose the system which he found most aesthetic pleasure, and justified his choice with complex theories of harmony. This is how and why he chose to support the Copernican system. Kepler's theories of harmony are therefore both fascinating and important. He adopted the ancient view that geometry was the basis of all mathematics. This was a view which the great philosopher Plato had supported. Kepler further claimed that God himself - in Christian terms, the Creator - thought in geometry terms. This idea had serious implications, since man was supposedly created in God's image. It was this belief that led Kepler to create his model of the universe around the five perfect solids. Moreover, the laws governing the angular velocity of each planet in its elliptical path derived from musical harmonies, which he in turn derived from two-dimensional plane geometry. Kepler therefore claimed that the structure of the universe revealed the interaction of two-dimensional and three-dimensional geometry. In doing so, it captured the very essence of harmony, and reflected the archetypes of God's own mind. Kepler claimed to have revealed the ultimate interaction of these two types of geometry in this model of the heavens.

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