The Law of Accelerating Returns

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t is important to ponder the nature of exponential growth. Toward this end, I am fond of telling the tale of the inventor of chess and his patron, the emperor of China. In response to the emperor's offer of a reward for his new beloved game, the inventor asked for a single grain of rice on the first square, two on the second square, four on the third, and so on. The Emperor quickly granted this seemingly benign and humble request. One version of the story has the emperor going bankrupt as the 63 doublings ultimately totaled 18 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. Another version of the story has the inventor losing his head.

It should be pointed out that as the emperor and the inventor went through the first half of the chess board, things were fairly uneventful. The inventor was given spoonfuls of rice, then bowls of rice, then barrels. By the end of the first half of the chess board, the inventor had accumulated one large field's worth (4 billion grains), and the emperor did start to take notice. It was as they progressed through the second half of the chessboard that the situation quickly deteriorated. Incidentally, with regard to the doublings of computation, that's about where we stand now--there have been slightly more than 32 doublings of performance since the first programmable computers were invented during World War II.

This is the nature of exponential growth. Although technology grows in the exponential domain, we humans live in a linear world. So technological trends are not noticed as small levels of technological power are doubled. Then seemingly out of nowhere, a technology explodes into view. For example, when the Internet went from 20,000 to 80,000 nodes over a two year period during the 1980s, this progress remained hidden from the general public. A decade later, when it went from 20 million to 80 million nodes in the same amount of time, the impact was rather conspicuous.

As exponential growth continues to accelerate into the first half of the twenty-first century, it will appear to explode into infinity, at least from the limited and linear perspective of contemporary humans. The progress will ultimately become so fast that it will rupture our ability to follow it. It will literally get out of our control. The illusion that we have our hand "on the plug," will be dispelled.

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Some prominent dates from this analysis include the following:

• We achieve one Human Brain capability (2 * 10^16 cps) for $1,000 around the year 2023.
• We achieve one Human Brain capability (2 * 10^16 cps) for one cent around the year 2037.
• We achieve one Human Race capability (2 * 10^26 cps) for $1,000 around the year 2049.
• We achieve one Human Race capability (2 * 10^26 cps) for one cent around the year 2059.

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