ECO-Essays are daily 2.5-minute short programs, each combining music and nature sounds uniquely matched to a spoken essay. They are intended to be aired on public radio stations nationwide at least twice a day, preferably right after "Morning Edition" and "All Things Considered."

[jungle/insect sounds--] "It's a steamy summer day in the Amazon jungle. A blue butterfly perches on an orange orchid, then sees the shadow of a hungry bird. Reacting like a graceful ballerina, the butterfly springs away. So begins the story of a tiny butterfly--dooming a girl and her dog Toto in Kansas."

Welcome to ECO-Essays--encouraging environmental awareness and responsibility.... Math Professor Ed Burger of Williams College in Massachusetts is bringing the abstract idea of "chaos theory" down to earth for his students. In the natural world, our complex weather is a classic example of chaos. Ed continues:

"Flapping her wings, our butterfly changes the course of micrograms of air surrounding her slender body. This minute change has enormous consequences. Air masses move in a pack: tiny differences can result in one mass sliding under or over another--like the edge of a wedge. The butterfly's unpredictable flapping causes a small air mass to rise, instead of fall. This causes bigger air masses to change their courses, sending even larger air masses in other directions. Eventually, two weeks later, Dorothy is knocked unconscious when she's hit in the head by her flying dog, Toto, during a Kansas tornado."

"Somebody might ask, 'Can't that butterfly be found and stopped?' Well, we just don't understand the chaos of weather patterns, where little changes lead to dramatic outcomes. If we did, then a bomb could be set off over the ocean tomorrow, causing drought-ending rains a month later."

"So will accurate long-range weather prediction always remain a fantasy like the land of Oz? Today, no one knows. If only that butterfly had remained still, she would not have changed the course of a few puffs of air. Then the good people of Kansas would have seen a beautiful clear day instead of a devastating tornado raining cats and dogs--in particular, Toto."

Our writer was Williams College Professor Edward Burger, co-author of the forthcoming entertaining book and kit: "The Heart of Mathematics: An invitation to effective thinking" published by Springer-Verlag.