December 27 marks the birthday of Johannes Kepler, one of the most important figures in the history of physics and astronomy. (Evidently late December is a good time for birthing physics geniuses: Isaac Newton was a December 25 baby).

Kepler is of course best known for Kepler's Laws of planetary motion, which he derived by rigorous mathematical analysis of observational data collected by Tycho Brahe. The laws are:

1. Planets orbit the Sun in elliptical paths.

2. Planetary speed varies such that a radius from the Sun to the planet sweeps out equal areas in equal times.

3. The square of the length of a planet's year is proportional to the cube of its distance from the Sun.

But the Three Laws were just an intriguing digression as far as Kepler himself was concerned. His primary interest was in what he grandly called the Secret of the Cosmos, which he explained in the book *Mysterium Cosmographicum.* Put simply, the Secret of the Cosmos is that the orbits of the planets can be described as a set of near-spheres inscribed within a nested series of Platonic solids.

The Platonic solids are the three-dimensional shapes whose sides are all matching regular polygons. Dungeons and Dragons players know them as the polyhedral dice: there's the 4-sided tetrahedron, the 6-sided cube, the 8-sided octahedron, the 12-sided dodecahedron, and the 20-sided icosahedron. Kepler found a way to match the orbits of the planets to the Platonic solids. He thought this was the most important discovery of his life.

Nobody else cared. At one point in college I tried to find any astronomer of Kepler's era who even mentioned his cool Platonic-solids theory. I couldn't. As far as I can tell, the universal reaction to the Secret of the Cosmos was a round of embarassed throat-clearing and a quick change of subject.

This is not an uncommon situation with scientists: the things that make their reputations aren't always the things they are most interested in. Isaac Newton wrote more on alchemy and Biblical chronology than on physics and mathematics. In our own time, Linus Pauling turned from his important discoveries about proteins to quackish medical theories about Vitamin C. Francis Crick, the co-discoverer of DNA, teetered on the edge of crackpot-hood with his insistent advocacy of panspermia as the origin of life on Earth.

For the rest of us, watching a first-class mind go off into a dodgy digression is frustrating, because it's such a waste. The time and effort Kepler frittered away messing with model polyhedrons could have been used to anticipate Galileo -- or even Newton. He might have derived the inverse-square law, for instance. As for Newton himself, he might have anticipated half the mathematical and physical discoveries of the 18th Century, especially if he wasn't damaging his brain with mercury fumes trying to create the Philosopher's Stone.

And yet sometimes these dodgy digressions turn out to be important stuff. John Von Neumann was a great mathematician, but as a result of his wartime Manhattan Project work he got interested in mechanical computing. The result was the ENIAC computer, an ancestor of the machine you're using to read this Web log. Luis Alvarez followed his career as a physicist by getting interested in some crackpot idea about the extinction of the dinosaurs and wound up helping discover the cause of the K-T event -- which in turn has made catastrophism much more respectable in modern geology and planetary science.

Unfortunately there's no way to tell in advance if something is going to turn out to be important or a dead end. If Newton's alchemy research had paid off, leading to widespread availability of Philosopher's Stones capable of bestowing immortality, we'd all be grousing about the time he "wasted" on mathematics. So perhaps it is for the best that scientists feel free to go exploring in odd byways off the beaten track.

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