“Galileo also wanted to avoid the error of his colleague Johannes Kepler (1571–1630). For all his brilliant work, Kepler had insisted on making the five Platonic solids the basis for his model of the solar system, rendering it useless for further empirical research. It was a bizarre example of carrying the faith in the perfection of mathematics too far.35 By contrast, Galileo understood that even a divinely ordered cosmos could not be perfect. There were craters on the moon and spots on the sun. Kepler himself had shown that the planetary orbits were not perfect circles as Aristotle and even Copernicus had assumed, but ellipses.”