Chet Raymo, "On Saying 'I Don't Know'"
All around him Kepler saw beautiful shapes in nature: six-pointed snowflakes, the elliptical orbits of the planets, the hexagonal honeycombs of bees, the twelve-sided shape of pomegranate seeds. Why? he asks. Why does the stuff of the universe arrange itself into five-petaled flowers, spiral galaxies, double-helix DNA, rhomboid crystals, the rainbow’s arc? Why the five-fingered, five-toed, bilaterally symmetric beauty of the newborn child? Why?
Kepler struggles with the problem, and along the way he stumbles onto sphere-packing. Why do pomegranate seeds have twelve flat sides? Because in the growing pomegranate fruit the seeds are squeezed into the smallest possible space. Start with spherical seeds, pack them as efficiently as possible with each sphere touching twelve neighbors. Then squeeze. Voila! And so he goes, convincing us, for example, that the bee’s honeycomb has six sides because that’s the way to make honey cells with the least amount of wax. His book is a tour-de-force of playful mathematics.
In the end, Kepler admits defeat in understanding the snowflake’s six points, but he thinks he knows what’s behind all of the beautiful forms of nature: A universal spirit pervading and shaping everything that exists. He calls it nature’s “formative capacity.” We would be inclined to say that Kepler was just giving a fancy name to something he couldn’t explain. To the modern mind, “formative capacity” sounds like empty words.
Source: http://coyoteprime-runningcauseicantfly.blogspot.com/2019/12/chet-raymo-on-saying-i-dont-know_27.html
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