Wednesday, January 4, 2017

News Flash: Nature is a Geometer

A geometer, for those of us who live most of our lives without encountering the word, is a mathematician particularly skilled in geometry, which is what Oswald Veblen was. Because of his generosity and devotion to mathematics, every three years a geometer receives the Veblen Prize from the American Mathematical Society "for notable research in geometry or topology." And because of the Veblens' generosity and love of nature, people in Princeton and from far and wide get to take a walk in Herrontown Woods. A couple days ago, we were out there discussing trail work when a couple came by with a beautiful miniature collie. They were on their way from Boston to D.C. and had chosen Herrontown Woods as a midway rest stop for walking their dog because they were able to find our map online. Stories like that make us feel like the Friends of Herrontown Woods is on the right track.

But this post is about recent backyard research, where a cold night frequently leaves finely crafted geometric renderings in a 35 gallon black tub that catches rainwater from the roof.

Polygons, triangles and squares, oh my. How water molecules can climb up to make these ridges I haven't a clue, but the answer when it comes will only deepen our sense of wonder at nature's creative powers. Nor is it clear why the water in the black tub is more talented than other backyard miniponds. Maybe the shape of the tub affects how the water freezes, or minerals from the roof play a role in how the crystals form. In any case, it's like having a child genius who brings home a brilliant piece of artwork from pre-school every day.

The forms in the lower right of this photo have the shape of beautifully cut precious stones. Here's a wish: May we keep the earth cool enough that this wondrous geometer can play, day after winter's day, far, far into the future.

UPDATE: Writing this post brought back memories of a visit to the Exploratorium in San Francisco a long time ago, and an exhibit in which a sheet of cooled water froze in a flash. The speed with which crystals spread was surprising, though it makes sense, given how fast chemical reactions flash through our bodies to form thoughts and actions. I called the Exploratorium to ask for a video of the phenomenon, and they quickly responded. The exhibit is called Watch Water Freeze, and the inventor demonstrates the secret of the flashfreeze--supercooled water--at 7:35 in this video. Nature's combination of craftsmanship and speed is deceptive. The crystals in the photos above appear finely wrought, but it's possible they, too, were crafted in an instant.

And might our creative process work the same way, that the mind becomes super-saturated with thoughts and experience, until some catalyzing moment arrives when all crystalizes in a flash of insight?

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