IMA best overall commentary (2018)

5th Link of Kepler's Cosmigraphicum (In the Wild)

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"I am an amateur astrophotographer so hopefully you’ll forgive the quality once I explain the maths, I can confirm it is Jupiter, the 5th link in Kepler’s theory of the solar system, the mysterium cosmographicum. To understand what that is, we need to discuss the platonic solids, a platonic solid is a polyhedra built from regular polygons as faces and the same number of faces meet at all its vertices. (Full explanation to many words) following these rules allows only 5 platonic solids to exist in 3D, the tetrahedron, octahedron, icosahedron, cube and dodecahedron, Plato thought of these polyhedra as the elements. Kepler argued that the solar system was heliocentric and that these polyhedra could “prove” it. He thought if you drew a sphere inside an octahedron, circumscribed a sphere around that and placed it inside an icosahedron, circumscribed that icosahedron with another sphere and placed THAT inside a dodecahedron, inside another circle and surrounded it with a tetrahedron and then put that in a sphere and put that in a cube with a sphere around it, you would have 6 spheres, there where only 6 known planets then. Kepler hypothesised that the ratios between each spheres radii matched the ratios between the radii of the planetary orbits. Modern measurements show he was slightly off but he was still able to, at the time, give a logical reason why god would create a heliocentric universe that was beautiful and perfect and was therefore able to encourage science to properly begin."

— Ross J. Macgregor (S6)