Spirals and Sprouts
(9-28-03) Featured photograph: In April of this year, in the Chugach Mountains, I was scanning the ground for lichens. Working between patches of snow with my nose several inches from the leaf litter, I saw a snail shell about 4mm in diameter. It had lain among the decaying leaves for a year or more since the death of the snail that had secreted it. The brown outer layer of the shell bore the tooth marks of an insect that had chewed its way into the white interior just as a wolf might gnaw weathered bones found scattered in the tundra. The snail shell and the budding twig ( both deceased in the photo) grow in a spiral.
This particular logarithmic spiral, although common, is famous and is known as the golden spiral because the golden ratio (an irrational number approximately 1.618) is revealed in its construction. Jakob (aka Jacques) Bernoulli (1654-1705), the Swiss mathematician, wrote a treatise entitled Spira Mirabilis in which he extolled not only its mathematical elegance but also its great natural beauty. His wonder at the spiral has been shared by mystics, artists, and mathematicians for thousands of years as ancient art and modern science testify.
Geometry and life intersect in man's understanding of nature in many ways. The orbits of the planets about the sun are elliptical, a bubble in space is spherical, salt crystals are cubic, DNA is a helix, carbon molecules are tetrahedral etc. The spiral has a particular story to tell about organic growth which has not been fully deciphered by biologists. Its repetetion throughout nature from molecules to galaxies is a testament to its importance but it is no more mystical than any other shape. It simply has its own story to tell. A story of rhythm and flow and constancy of form. A form that implies an impossibly small beginning and an infinite trajectory...More on spirals later....