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 Chinese mathematician that did a great deed for the emperor of China. In return the emperor tells the mathematician he may have anything in his kingdom he wishes. The mathematician replies that each day he would like a certain amount of rice placed on a square of his chessboard: one grain of rice on the first square and each successive square would have double the prior square until all 64 squares of the chessboard have had their said amount of rice.

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 China.

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.

In total, on the entire chessboard there would be exactly 2⁶⁴ − 1, or 18,446,744,073,709,551,615 grains of rice.

References

1. Raymond Kurzweil (1999). The Age of Spiritual Machines, Viking Adult. ISBN 0-670-88217-8.

See also

• Moore's law
• Exponential growth
• Technology strategy

Technology strategy