Those who know me also know that Kepler, the brilliant 17th-century German astronomer, is my scientific hero, a real source of inspiration. And since today is my birthday, I am giving myself a small gift and writing about him. In my mind, no other character in the history of science, not even Galileo and his embattlement with the Inquisition, represents so clearly the archetype of the lone visionary fighting to vindicate his world vision while his life is torn to pieces by personal tragedy and religious persecution. I even wrote a historical novel about his life, which was published in Portuguese and hopefully one day will be published in English. (I'm working on revisions now...)
Kepler is popularly known for his discovery of the three laws of planetary motion: orbits are elliptical; the planets trace equal areas in equal times as they go around the Sun; and his harmonic law, a mathematical relation between the time it takes for a planet to orbit the Sun and its distance from it. These were the first quantitative laws of astronomy, found in Kepler's book New Astronomy, published in 1609, the year Galileo pointed his telescope to the sky. What people don't learn in school is who Kepler was, what motivated his thinking. (Or Galileo's, or Copernicus's, or Newton's, a real lack in a too-rigid and pragmatic scientific education. But that's for another day.)
Kepler was a true Pythagorean, a believer in the notion that the cosmos is ultimately rational, constructed by God according to geometric rules which men, through their creativity and utter devotion to natural philosophy, could understand. In this, Kepler is perhaps the best example of the "mind of God" metaphor, that there is an underlying order to Nature that we can uncover through the diligent application of the scientific method. In this, Kepler was a man with a foot in Plato's Academy and another in the future: he believed that Nature could be understood a priori, through mind alone, although he also believed that any theory had to be confronted with data and discarded if not proven correct. If only he had lived up to his own philosophy...
In 1595, Kepler had a vision while lecturing a handful of sleepy students at a Lutheran school in Graz, Austria. He realized that the distance between Jupiter and the Sun is half that of Saturn and the Sun (approximately). Of course he knew that, but somehow it hit him anew that day, with deeper meaning. Could it be a coincidence? Never! In a cosmos designed by a rational God there were no coincidences. So, he spent a few days trying to come up with a geometric formulation of the then-known solar system (only up to Saturn). First, he wanted to understand why there were only six planets; second, how their distances from the Sun were fixed. In an explosive flash of intuition, Kepler realized that he could nest the five Platonic solids (pyramid, cube, octahedron, dodecahedron, icosahedron) one inside another like Russian dolls, interspersing shells between them. The shells marked the planetary orbits, while the ordering of the solids, fixed by geometry, determined the distances between the shells and thus between the planets and the central Sun. With five solids, there could be only 6 interspersed spheres, one for each planet. Voila!
Kepler rejoiced when he found an arrangement precise to about 5%, quite an amazing feat. There it was, a rational explanation for the cosmos, based on geometry! The cathartic impact of this revelation never left him, even after he used Tycho Brahe's data to find his laws of elliptical orbits; surely, he reasoned, the shells have some thickness and Tycho's data, albeit great, is not perfect. If it were, he believed, we would see that his geometrical model was correct.
Kepler would have been quite shocked to find out that there are more than six planets in the solar system, and that his scheme simply doesn't make any sense. He died in blissful ignorance, as Uranus was only discovered in 1781. Still, his laws remain valid and are key in the study of astronomy.
His mistake was to believe irrationally on his rational vision of the cosmos, giving it a finality it (or any other a priori scientific theory) didn't deserve. We may do well to learn from Kepler's mistake, especially when we start to take our models and theories well beyond the level of empirical validation. Although there are many such notions around, none of course is more an heir to this sort of Platonic rationalism as current versions of superstring theories. (A recent post by co-blogger Adam Frank addresses some of these issues.) To rely on human reason to uncover "eternal truths" is a danger that is too easy to succumb to. I counter that we must look at physical reality with our eyes wide open, acknowledging our fallibility with the humility that Nature deserves.