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, four for the third 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 = 4294967295 grains of rice, or about 100 000 tons of rice. This total amount is about 1/1000th of total rice production in India per annum (in 2005) and was considered economically viable 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 about 7000 times the entire weight of the Earth biomass.
On the 64th square of the chessboard there would be exactly 263 = 9 223372 036854 775808 grains of rice. In total, on the entire chessboard there would be exactly 264−1 = 18 446744 073709 551615 grains of rice.
[edit] References
- ↑ Raymond Kurzweil (1999). The Age of Spiritual Machines, Viking Adult. ISBN 0-670-88217-8.
