We've been hearing about Moore's Law for so long that we're all but inured to its impact. Sure, computer capability doubles every 18 months, just as Gordon E. Moore described in 1965.

Whatever. Old news.

Not so, say Erik Brynjolfsson and Andrew McAfee of MIT's Center for Digital Business. Their terrific recent book, Race Against the Machine, beautifully explains that when it comes to the ways computers transform business competition, we ain't seen nothing yet. One reason: We still don't get what Moore's Law's adds up to.

In an MIT Sloan Management Review article based on their book, Brynjolfsson and McAfee relate a parable to help us understand recent computing advances.

"It comes from an ancient story about math made relevant to the present by the innovator and futurist Ray Kurzweil. In one version of the story, the inventor of the game of chess shows his creation to his country's ruler. The emperor is so delighted by the game that he allows the inventor to name his own reward. The clever man asks for a quantity of rice, to be determined as follows: one grain of rice is placed on the first square of the chessboard, two grains on the second, four on the third, and so on, with each square receiving twice as many grains as the previous square.

"The emperor agrees, thinking that this reward is too small. He soon sees, however, that the constant doubling results in tremendously large numbers. The inventor winds up with 264-1 grains of rice, or a pile bigger than Mount Everest. In some versions of the story, the emperor is so displeased at being outsmarted that he beheads the inventor."

That tale is bracing enough, but there's a kicker: The most profound effects of the doubling phenomenon aren't felt until you reach the second half of the chessboard. When Kurzweil tells the story in The Age of Spiritual Machines: When Computers Exceed Human Intelligence, he notes that "after 32 squares, the emperor had given the inventor about 4 billion grains of rice. That's a reasonable quantity--about one large field's worth--and the emperor did start to take notice.

"But the emperor could still remain an emperor. And the inventor could still retain his head. It was as they headed into the second half of the chessboard that at least one of them got into trouble."

Question is, Where are we now on the computing-evolution chessboard? The answer, according to Brynjolfsson and McAfee, who do some math to figure it out: We're 32 "doublings" in.

Which is to say, we're only now reaching the board's exponentially impactful second half.