Measurements Change Dramatically Depending on the Methodo...

Benoit Mandelbrot asked his famous question “How long is the coast of Britain?” long before this symposium was written, but it perfectly captures the sort of puzzle people in this crowd love. The question seems simple. Just look it up in the encyclopedia. But as Mandelbrot observed, the length of the coast of Britain depends on what you use to measure it. If you draw lines on a map to approximate the coastline, you get one length, but if you try to measure the real bumps in every inlet an...

 Geometry Seems Disconnected from Reality

Why is geometry often described as 'cold' and 'dry?' One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line... Nature exhibits not simply a higher degree but an altogether different level of complexity.

 The Earth Self-Heals Better Than Humans Try to Heal It

Ecologically speaking, a spilt tanker load is like sticking a safety pin into an elephant’s foot. The planet barely notices. After the Exxon Valdez accident in Alaska the oil company spent billions tidying up the coastline, but it was a waste of money because the waves were cleaning up faster than Exxon could. Environmentalists can never accept the planet’s ability to self-heal.