Wednesday, September 02, 2009

The divine proportion


The July 27 New Yorker had an article on Thomas Campbell, the new director of the Metropolitan Museum of Art in New York. The writer asked him what was his favorite object in the museum's collections. After some hesitation, Campbell mentioned a particular fondness for "The Harvesters" by Pieter Bruegel the Elder, painted in 1565 (click to enlarge). "It's a timeless image, an affectionate but critical eye on humanity," he is quoted as saying.

As I read this, I remembered Tom's visit to the Met several years ago and his confession of his own particular fondness for "The Harvesters" -- which prompted a post you can read here. As I said in that post, my own fondness for the painting derives from having had pretty much the same experience harvesting hay and oats when I first summered in this part of Ireland 30 years ago. Saving the hay successfully in those days required a period of dry weather, something in short supply this summer.

But never mind. No one here cuts and dries hay by hand any more. In Lizzie's fields below, where I used to ply the rake and pike, tractors in short order cut the grass, gather it into rolls, and wrap it in black plastic, all mechanically. The musty, dusty hay sheds have given way to mountainous outdoor stacks of what look like gigantic black beach balls. This method of making fodder apparently works rain or shine.

But back to Bruegel. Part of the charm of the painting may be due to the vertical tree that divides the panel into approximately the Golden Ratio. (The Golden Ratio is such that the whole is to the larger part as the larger part is to the smaller part. That is: (a+b)/a = a/b. A little algebra and the quadratic formula yields the ratio a/b = (see below).) Euclid was apparently the first to give a mathematical expression to the ratio. In 1509, Luca Pacioli described the aesthetic significance of the ratio in a work called De Divina Proportione. Whether Bruegel the Elder consciously employed the ratio in this painting, I don't know, but that it represents a pleasing proportion to artists, architects and viewers alike is well documented.

Science too. Kepler thought the Creator of the universe -- artist that he was -- would surely have used the ratio in the creation, and his long struggle with mathematical aesthetics led eventually to the laws of planetary motion. (Kepler's teacher Michael Maestlin was the first to give the Golden Ratio a decimal expression.) The Golden Ratio shows up in many places in nature, from flowers to shells. For all of the millions of words that have been written about it, no one knows why the human mind finds pleasure and delight in that marvelous irrational number 1.6180339887498948482...