Saturday, September 06, 2008

Nature loves to hide


A rainbow. Pretty to look at. But what do you see? The arc of a perfect circle. Pure geometry.

Think about how seldom we see pure geometric forms in nature. Rivers never run straight and true. Nature draws straight lines reluctantly. Circles? The sun and moon. I look out my window at a broad panorama or earth, sea and sky, and I see not a single shape or line that might be found in a geometry book.

In the Timaeus, Plato suggested that behind the manifestly ungeometrical higgledy-piggledy of nature there lay a hidden world of geometrical atoms. It was a prescient insight, but led nowhere at the time. Kepler hoped to explain the spacing of the planets with nested Platonic solids -- spheres, cubes, tetrahedra, etc. -- but it turned out to be a bit of a wild goose chase. When Galileo rolled balls downed inclined planes and measured distances and times, a parabola winked in his data. Plato was right! It wasn't long before mathematical regularities started showing up everywhere. The book of nature really is written in the language of mathematics.

But how closely nature hides that secret. I look out the window and I don't see a hint of it. Then -- the rainbow appears in the sky...