Monday, January 25, 2010

Facultas formatrix

Snowflake Bentley is in the news. The BBC website reports that ten of Bentley's more than 5,000 snowflake microphotographs are going on sale at an auction in New York. You may know of Wilson "Snowflake" Bentley as the Vermont farmer who a century ago dedicated his life to recording the exquisite beauty of snowflakes with a microscope and a bellows camera, standing in the cold for hours at a time. Just before he died of pneumonia he published a handsome volume of hundreds of images, no two alike. I've long owned the Dover edition of that book, still in print.

Page after page of snowflakes. Each one an utterly symetrical six-pointed jewel. Ephemeral! Beauty that forms in the air on a core of dust -- a microscopic mineral heart -- and melts away in a flash. But not before Bentley captured an image on film.

There are two stories here that have always intriqued me, and I have written about them before. First, of course, is the human story -- a story of a passionate curiosity, a farmer obsessed by beauty. This is the story told in Jacqueline Briggs Martin and Mary Azarian lovely children's book. The second story is why. Why the symmetry?

The basic hexagonal form of a water crystal is easy enough; that has to do with the shape of a water molecule, an atom of oxygen with two hydrogen atoms hanging off at just the angle that causes them to link up in a hexagonal fashion. (Think of you and a bunch of your friends standing with your arms stretched out with an angle of 120 degrees between them. Now you link up by holding hands. Six of you will naturally fall into a hexagon.) The angle between the arms of the water molecule is explained by quantum physics.

But what about the perfect six-fold symmetry of a snowflake? As a snowflake grows, adding water molecules essentially at random, how does one point know what is going on at another point? On the scale of molecules, the faces of the growing crystal are light-years apart. That is to say, how does a water molecule attaching itself to a flake at the tip of one point, know what's happening 10 million molecules away -- by my rough calculation -- on the other side of the flake? If you go to the internet you will find theories to explain the symmetry -- forced "tiling", sensitive vibrations, that sort of thing -- but I've yet to see anything that is convincing.

Snowflakes aren't the only place in nature where we find symmetry that staggers the imagination. Think of the hexagonal cells of a honeycomb. Or the arms of a starfish. Or the perfect little fingers and toes of a developing human foetus. Why does the stuff of the universe arrange itself into spiral galaxies, planetary ellipses, double-helix DNA, five-petaled flowers, the rainbow's arc? Why?

Why does nature love mathematics?

Standing at the door of his barn with his bulky apparatus, Wilson Bentley was engaged in philosophy of the most profound sort.