Things Fall Apart*

OK, I always wanted a post with a title stolen from Yeats "The Second Coming" but the punchline here is that when they do, they fall apart into roughly cubical shapes (on average).  Such, at any rate, is the claim of a geologist and a mathematician.  The core insight comes from pure mathematics.  If you slice any large scale object up with random plane slices, you tend to wind up with pieces with six faces and eight vertices. Oddly enough, this result seems to have been anticipated by Plato in his dialogue Timaeus, where he assigned each of his essences (earth, air, water, fire, and a fifth, cosmic essence) to one of the Platonic solids.  Earth got cubes.  So far as I know, there is no cosmic link with the dodecahedron.

Some details here:


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