Steve Harmon and Wayne Dennison

26.1 Introduction

Bob Dylan famously wrote that the times were a-changing back in 1963. Today he might write that they have already changed, and will probably do so again in the time it takes to read this chapter. The pace of change in modern society is staggering and continually increases. Nagy et al. (2013) show that the pace of technological change tends to be exponential. We have a difficult time seeing this in the short term and an even more difficult time understanding it in the long term, as exponential growth is not an intuitive concept for most people. An ancient fable about the invention of chess may be used to help understand this concept. According to the legend, when the inventor of chess presented the game to the emperor, the emperor was so impressed that he told the inventor to name his own reward for creating the game. The inventor replied that he simply wanted grains of rice, one for the first square of the chessboard, two for the second, four for the third, and so on for every square on the board. The emperor was surprised that the inventor was asking for such a paltry reward and quickly agreed to pay him. The first half of the chessboard led to some fairly large numbers of grains of rice. But the second half of the chessboard led to numbers beyond easy comprehension. What the emperor did not understand was that the exponential growth in the number of grains of rice for each square meant that to fulfill the payment ...

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