Kepler's Most Beautiful Idea

Johannes Kepler, the 17th-century astronomer credited with discovering that the planets’ paths around the sun are ellipses, was teaching geometry to a bunch of bored kids in Graz, Austria, when he was suddenly struck by the most beautiful idea he would ever have.
Six planets were known at the time --Mercury, Venus, Earth, Mars, Jupiter, and Saturn. Their orbits, which Kepler still believed were circles, placed them at certain distances from the sun. Why six planets? Why those particular distances? Kepler wondered. In the true spirit of modern science, he was confident that the distances of the planets were governed by some sort of mathematical law.
It is a well known geometrical fact that if you wish to construct solid, three-dimensional bodies whose sides are regular polygons (polygons whose sides are all the same length), try as you might, you will end up with no more than five such bodies. This result is a geometrical theorem --in 3D space there exist five and only five regular, or “Pythagorean,” solids. It has nothing to do with the state of our mathematical knowledge or our technological prowess. Like the statement that parallel lines meet at infinity, the existence of no more than five regular solids is an inescapable property of three-dimensional flat space.
Kepler’s idea was this: there are only six planets because there are only five regular solids and if we put these solids one inside the other in a nested pattern, the spheres defining the boundaries where an inner solid touches the next one out have radii which are in the same proportion as the distances of the planets. Kepler called this hypothesis the Mysterium Cosmographicum . It was beautiful in its geometrical simplicity and awe-inspiring in its depth of implication (the existence of god the mathematician). It rang true. But it was not.
Kepler tried hard to make the nested regular solids match the distances of the planets, but to no avail. He had based his calculations on figures obtained by Copernicus seventy years earlier. Perhaps more accurate measurements of the distances might show them to fit his elegant scheme?
The greatest observational astronomer of the age, Tycho Brahe, had performed such measurements. When Kepler got hold of the data after Tycho’s death he was disappointed. In the end --and in view of Galileo’s subsequent discovery of Jupiter’s four large moons, which the Mysterium could not possibly accomodate-- Kepler reluctantly abandoned his pet theory. It took courage, but Kepler was imbued with “the will to find out” as opposed to “the will to believe”. He was skeptical even of his own ideas.
Skepticism is essential in science. It prevents us from foisting our emotions on the universe, and thus helps us to study verifiable facts with a cool head. Gullibility readily accepts claims that may seem satisfying on grounds of personal taste or convenience, but that all too often are simply not true. The Argentinean philosopher of science Mario Bunge wrote:
Scientific knowledge is sometimes unpleasant. It often contradicts the classics; occasionally tortures common sense and humiliates intuition. Lastly, it may prove convenient for some, but not for others. The hallmark of scientific knowledge is that it is verifiable.
Personal taste, appeals to authority, and even democracy (like in deciding by popular vote which one of several contending hypotheses is true) have no place in science. Science is about discovering objective facts whose truth does not depend on who champions or opposes them. As the French mathematician Henri Poincaré said: “The sole source of truth is experiment. Only it can teach us something new; only it can give us certainty.”