Fifty years ago this week, on April 8, 1960, a little-known astronomer named Frank Drake sat at the controls of an 85-foot radio telescope at an observatory in Green Bank, W.Va., and began to sweep the skies, looking for a signal from an alien civilization. It was the start of the most ambitious scientific experiment in history.

Barely an hour had passed when the equipment suddenly went wild. A loudspeaker hooked up to the giant antenna began booming and the pen recorder gyrated manically. The radio telescope was pointed at...