IN THEIR BOOK THE DREAM MACHINE: EXPLORING the Computer Age, authors John Palfreman and Doron Swade share a forecast from Howard Aiken, an American mathematician and computer engineer: In 1947, Aiken predicted that "only six electronic computers would be needed to satisfy all the United States' computing needs." Today, with more than 400 million personal computers in the world and a billion anticipated by 2005, Aiken's forecast seems laughable.

In 1944, Aiken and his colleagues from IBM and Harvard University created the Mark I, which many consider the first general—purpose computer. Fifty feet long and eight feet high, it cost $500,000, read data from punch cards, and spit out calculations at the then—astounding rate of about three to five a second. Today, computers no larger than a slim—volumed book can process many thousands of bits of data per second and cost less than a thousand dollars. Compact...