Here it is!
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The whole thing: Mercury, Venus, Earth, Mars, Jupiter, Saturn |
The inner grail: Mercury, Venus, Earth, and Mars |
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Kepler’s blackboard drawing was somewhat less elaborate:
Happily Kepler did not know about Uranus, Neptune, or Pluto, but unhappily he did know that the orbits of the planets do not lie on spheres. (The First Law). He managed anyway, in the manner one solves odd-numbered exercises since times immemorial: ’Day and night I spent with calculations to see whether the proposition that I had formulated tallied with the Copernican orbits…Within a few days everything fell into its place. I saw one symmetrical solid after the other fit so precisely between the appropriate orbits, that if a peasant were to ask you on what kind of hook the havens are fastened so that they don’t fall down, it will be easy for thee to answer him. Farewell!’ Kepler’s mysterium calculatum finally came out like this.
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The whole bunch: Mercury, Venus, Earth,
Mars, Jupiter, Saturn |
The inner planets: Mercury, Venus, Earth,
Mars, |
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‘Credo spatioso numen in orbe’
intones Kepler to end his Mysterium Cosmographicum.
Jocus numinis
”I
saw one symmetrical solid after the other…”
Postscript. Mathematicians now see the five perfect solids as platonic images of finite subgroups of SU(2), the simplest of all simple Lie groups. (Sorry). Physicists now prefer SU(3), the Nobel vehicle of the The Eightfold Way, and even more so U(1) x SU(2) x SU(3), the tricyclic Model T advertised as Standard (reviewed in Nobel Lectures, 1979 issue).
The pictures of the grail are reproductions from the
Mysterium Cosmographicum. The picture
of Kepler’s calculated mysterium is a
spread sheet display of the data given there. Photograph courtesy of NASA and Sistine Chapel. WR
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