Kepler's Use Of The Platonic Solids To Explain The Relative Distance Of Planets From The Sun
In 1595 Johannes Kepler proposed a deep, elegant and beautiful solution to the problem of determining the distance from the Sun of the six then-known planets. Nesting, as in the case of Russian dolls, each of the five Platonic solids within a sphere, and having those solids arranged in the proper order—octahedron, icosahedron, dodecahedron, tetrahedron, cube- he proposed that the succession of spherical radii would have the same relative ratios as the planetary distances. Of course the deep, elegant and beautiful solution was also wrong but then, as Joe.E.Brown famously said in Some Like it Hot's last line "Nobody's perfect."
Two thousand years earlier, in a notion that would come to be commonly described as Harmony of the Spheres, Pythagoras had already sought a solution by relating those distances to the sites on a string at which it needed to be plucked in order to produce notes pleasing to the ear. And almost two hundred years after Kepler's suggestion, Johann Bode and Johann Titius offered, without an underlying explanation for its existence, a simple numerical formula that supposedly fit the distances in question. So we see that Kepler's explanation was neither the first nor the last attempt to explain the ratios of planetary orbit radii, but in its linking of dynamics to geometry, it remains for me the deepest as well as being the simplest and most elegant.
In a strict sense none of the three proposals is strictly wrong. They are instead solutions to a problem that doesn't exist for we now understand that the location of planets is purely accidental, a byproduct of how the swirling disk of dust that circled our early Sun evolved under the force of gravity into its present configuration. The realization that there was no problem came as our view expanded from one in which our own planetary system was central to a far greater vision in which it was one of an almost limitless number of such systems scattered throughout the vast numbers of galaxies comprising our Universe.
I have been thinking about this because, together with many of my fellow theoretical physicists, I have spent a good part of my career searching for an explanation of the masses of the so-called elementary particles. But perhaps the reason it has eluded us is a proposal that is increasingly gaining credence, namely that our own visible Universe is only a random example of an essentially infinite number of Universes, all of which contain quarks and leptons with masses taking different values. It just happens that in at least one of those Universes, the values allow for there being at least one star and one planet where creatures that worry about such problems have come to life.
In other words a problem that we thought was central may once again have ceased to exist as our conception of the Universe has grown, in this case extended to one of many Universes. If this is indeed true, what grand vistas may lie before us in the future? I only hope that our descendants may have a much deeper understanding of these problems than we do and that they will smile at our attempts at our feeble attempts to provide a deep, elegant and beautiful solution to what they have recognized is a non-existent problem.