...To appreciate the implications of this (or any) geometric trend, it is useful to recall the legend of the inventor of chess and his patron, the emperor of China. The emperor had so fallen in love with his new game that he offered the inventor a reward of anything he wanted in the kingdom
"Just one grain of rice on the first square, Your Majesty."
"Just one grain of rice?"
"Yes, Your Majesty, just one grain of rice on the first square, and two grains of rice on the second square."
"That's it- one and two grains of rice?"
"Well, okay, and four grains of rice on the third square, and so on."
The emperor immediately granted the inventor's seemingly humble request. One version of this story has the emperor going bankrupt because the doubling of grains of rice for each square ultimately equalled eighteen million trillion grains of rice. At ten grains of rice per square inch, this requires rice fields covering twice the surface area of the Earth, oceans included.
The other version of the story has the inventor losing his head. It's not quite clear which outcome we're headed for.
But there is one thing we should note: It was fairly uneventful as the emperor and the inventor went through the first half of the chessboard. After thirty-two squares, the emperor had given the inventor about four 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 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.
So where do we stand now? There have been about thirty-two doublings of speed and capacity since the first operating computers were built in the 1940s. Where we stand right now is that we have finished the first half of the chessboard. And, indeed, people are starting to take notice.
Now, as we head into the next century, we are heading into the second half of the chessboard. And this is where things start to get interesting. -Ray Kurzweil (The Age of Spiritual Machines)