Second half of the chessboard
In technology strategy, the “second half of the chessboard” is a phrase, coined by Ray Kurzweil, in reference to the point where an exponentially growing factor begins to have a significant economic impact on an organization’s overall business strategy. While the number of grains on the first half of the chessboard is large, the amount on the second half is vastly (232 > 4 billion times) larger.
The number of grains of wheat on the first half of the chessboard is 1 + 2 + 4 + 8 + … + 2,147,483,648, for a total of 4,294,967,295 (232 − 1) grains, or about 279 tonnes of wheat (assuming 65 mg as the mass of one grain of wheat).
The number of grains of wheat on the second half of the chessboard is 232 + 233 + 234 + … + 263, for a total of 264 − 232 grains. This is equal to the square of the number of grains on the first half of the board, plus itself. The first square of the second half alone contains more grains than the entire first half. On the 64th square of the chessboard alone there would be 263 = 9,223,372,036,854,775,808 grains, more than two billion times as many as on the first half of the chessboard.
On the entire chessboard there would be 264 − 1 = 18,446,744,073,709,551,615 grains of wheat, weighing about 1,199,000,000,000 metric tons. This is about 1,645 times the global production of wheat in 2014 (729,000,000 metric tons).
Carl Sagan titled the second chapter of his final book The Persian Chessboard and wrote that when referring to bacteria, “Exponentials can’t go on forever, because they will gobble up everything.” Similarly, The Limits to Growth uses the story to present suggested consequences of exponential growth: “Exponential growth never can go on very long in a finite space with finite resources.”
According to Nassim Taleb, in 2009, the banking sector lost in 18 months all the profits it ever made since the beginning of banking. Is this true?
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