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The Misconception of Doubling Effects

A fable tells the story of when the inventor of chess showed his new game to the Emperor of India. The Emperor is so impressed he exclaims, “name your reward!” The inventor says, “my needs are few, Oh Emperor!  Simply give me one grain of wheat for the first square and double it for the remaining 64 squares of the chessboard.” The Emperor quickly agrees, surprised that the man would ask for so little.

But the Emperor is not a systems thinker and does not understand the exponential effects of simple doubling.  The first square has 1 grain, 2 grains in the second square, then 4, 8, 16, etc. But, on the entire chessboard there would be 2^64 − 1 = 18,446,744,073,709,551,615 grains of wheat! This wheat would weigh 1,199,000,000,000 metric tons or 1,645 times the global production of wheat (780.8 million tons in 2019).