Johannes Kepler

Kepler's first book, the Mysterium Cosmographicum of 1596, argued that the spacing of the six known planets was fixed by the five regular solids nested between their spheres. The scheme is wrong. The conviction behind it he never abandoned: that the heavens are ordered by exact ratios, and that the ratios can be found.

The work that made him was done on Tycho Brahe's observations of Mars, the most accurate then in existence. He spent years trying to fit them to circles and failed by an amount, eight minutes of arc, small enough that almost any other astronomer would have set it aside. He did not, and the Astronomia Nova of 1609 states the result: a planet moves on an ellipse with the sun at one focus, and the line from sun to planet sweeps equal areas in equal times. The second of those broke the assumption of uniform circular motion that astronomy had held since antiquity.

The Harmonices Mundi of 1619 is where the search for ratios pays twice. It contains the third law, relating a planet's period to its distance, set inside a book largely concerned with musical consonance, polyhedra and the harmonies he believed the planetary motions sound. He then compiled the Rudolphine Tables, published in 1627 on Tycho's data and his own theory, which made the new astronomy usable for prediction and settled the practical argument in its favour long before the physical one was won.

Kepler cast horoscopes for a living, most famously for Wallenstein, and thought most of what other astrologers did indefensible. His position is set out in De Fundamentis Astrologiae Certioribus of 1602 and in the Tertius Interveniens of 1610, which warns theologians and physicians that in throwing out astrology they may be throwing out something worth keeping along with it.

What he wanted kept was narrow. He rejected the twelve houses, distrusted the signs of the zodiac as arbitrary divisions of a continuous circle, and would not accept that planets carry characters or govern parts of the body. What he thought defensible was the aspects, the angular relations between planets, because an angle is a real geometrical fact and because the ratios that make a musical interval consonant are the same ratios. On that reasoning he added aspects the tradition did not have, dividing the circle by five and by eight as well as by three, four and six: the quintile at seventy two degrees, the biquintile, the semi-square and the sesquiquadrate. Western astrology took them up and uses them still, usually without knowing where they came from.

He also held that the soul responds to these geometrical relations at the moment of birth, which is how he could hold both halves of his position at once. His mother Katharina was accused of witchcraft and stood trial between 1615 and 1621. He conducted much of her defence himself, and she was released.