Williams, 26, knew that forcing compressed air through a hole in the middle of a pipe causes hot and cold air to flow from opposite ends, a phenomenon known as the Ranque-Hilsch vortex-tube effect. No one is quite sure how the separation works, but feed the cold air into a container, he reasoned, and you would have an icemaker and a freezer, which would have zero operating costs and would be environmentally friendly, since it wouldn’t require chemicals and the jet of air could be generated via a compressor powered by wind, water, man or animal.

At least that was the idea. Tinkering with heat-transfer equations, Williams tried to determine how much energy it would take to yield a block of ice. “It had been a while since I’d done real math problems. I had to break out the old textbook,” says Williams, a product-development consultant with his own firm, Dissigno, in San Francisco. After eons of number crunching, he hit on the right formula and built a prototype. It isn’t very efficient; his device uses 35 times as much energy as an electric fridge to make 1 kg of ice. But its simplicity could yield a killer app in Third World villages, where Williams hopes aid groups will distribute his icemaker as an economic-development tool. He aims to field-test it in Haiti later this year.