Kepler's Platonic model of the solar system
Geometria una et aeterna est in mente Dei refulgens: cuius consortium hominibus tributum inter causas est, cur homo sit imago Dei.
-Kepler [*]
Geometria una et aeterna est in mente Dei refulgens: cuius consortium hominibus tributum inter causas est, cur homo sit imago Dei.
-Kepler [*]
The Earth’s sphere is the measure of all other orbits. Circumscribe a dodecahedron around it. The sphere surrounding it will be that of Mars. Circumscribe a tetrahedron around Mars. The sphere surrounding it will be that of Jupiter. Circumscribe a cube around Jupiter. The surrounding sphere will be that of Saturn. Now, inscribe an icosahedron inside the orbit of Earth. The sphere inscribed in it will be that of Venus. Inscribe an octahedron inside Venus. The sphere inscribed in it will be that of Mercury. There you have the basis for the number of the planets.
- Mysterium Cosmographicum
Kepler's mixture of science/math/numerology/mysticism/platonism places Earth between the Dodecahedron and Icosahedron since those solids embody (via the pentagon) the Divine Proportion, or Golden Ratio, which according to him is also the basis for all human proportion.
Five Platonic solids, or Perfect solids (nice java demo at Wolfram.com)
I've modified the demo, and put planet positions in, to make Kepler scheme clear:
Inner Planets: mercury, venus, earth, mars
All planets: mercury, venus, earth, mars, jupiter, saturn
Placing the 6 planetary spheres between the 5 perfect solids actually leads to spacings for the planets which match the data. (note: to this day there is really no satisfactory theory for why the planets are spaced the way they are; it is often presumed to be due to chance.)
But it ignores new data, e.g., Uranus, Neptune and Pluto
Geometry, which before the origin of things was coeternal with the divine mind and is God himself (for what could there be in God which would not be God himself?), supplied God with patterns for the creation of the world, and passed over to Man along with the image of God.
- Harmonices Mundi
Welcome the 16th-century re-incarnation of Pythagoras' Music of the Spheres...
What would this Music_of_Spheres.MP3 sound like?
Kepler's 3rd Law, the Harmonic Law p2 = a3, in his words:
Modern Music still pays homage to Geometry:
Check out the sounds of PI.mp3 by Steve Coleman and the Five Elements
Biological Addendum: These Platonic forms also manifest microscopically in nature. c.f., Plates from Ernst Haeckel's Kunstformen der Natur (Artforms of nature) (1904)
Document URL: http://www.uh.edu/~jclarage/astr3131/lectures/3/kepler/kepler.html
