Here it is!


The whole thing:

Mercury, Venus, Earth, Mars, Jupiter, Saturn

The inner grail:

Mercury, Venus, Earth, and Mars




Kepler’s blackboard drawing was somewhat less elaborate:

Eureka!  The inner circle and the outer circle of a regular triangle are proportional to the orbits of Jupiter and Saturn!  (Well, almost.)  Hence stack the five perfect solids in space, inner sphere on outer sphere, and the resulting six spheres for the six planets will ‘put this true and correct model of the world before the eyes. 

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.

The whole bunch:

Mercury, Venus, Earth, Mars, Jupiter, Saturn

The inner planets:

Mercury, Venus, Earth, Mars,

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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