Second Half of the Chessboard
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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.
The term is derived from the fable of an ancient Indian mathematician who according to the fable invented the game of chess. The emperor of India is so pleased with the game that he tells the mathematician he may have anything in his kingdom he wishes. The mathematician replies that he only asks for a meek amount of rice placed on the squares of his chessboard: one grain of rice on the first square, two for the second, et cetera. Each successive square would have grains of rice double the number of the prior square until all 64 squares of the chessboard have had their said amounts.[2]
The total number of grains of rice on the first half of the chessboard is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 ... + 2,147,483,648, for a total of exactly 232 − 1 grains of rice, or about one field of rice. This total amount is considered economically insignificant to the emperor of India.
The total number of grains of rice on the second half of the chessboard is 232 + 233 + 234 ... + 263, for a total of approximately 264 grains of rice (264 − 232 grains of rice to be exact). This is more rice than could be grown on the planet in the lifetime of the emperor.
The 64th sqare of the chessboard there would be exactly 264 − 1, or 18,446,744,073,709,551,615 grains of rice. In total, on the entire chessboard there would be aproximately 36.893.488.147.419.100.000 grains of rice.
[edit] References
- ↑ Raymond Kurzweil (1999). The Age of Spiritual Machines, Viking Adult. ISBN 0-670-88217-8.
