“To appreciate the nature and significance of the coming ‘singularity,’ it is important to ponder the nature of exponential growth. Toward this end, I am fond of telling the tale of the inventor of chess and his patron, the emperor of China. In response to the emperor’s offer of a reward for his new beloved game, the inventor asked for a single grain of rice on the first square, two on the second square, four on the third, and so on. The emperor quickly granted this seemingly benign and humble request. “One version of the story has the emperor going bankrupt as the sixty-three doublings
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