During the thousand years between Charlemagne and Frederick the Great, the world’s population rose on average by 2.5 percent every half-century. With the agricultural revolution of the late eighteenth century, the world’s population rose by 20 percent in fifty years, for the first time in history. During the second half of the twentieth century, the world’s population grew by 140 percent. But that growth rate was always unsustainable—a blip in the statistics, the short lag between the point at which modern prosperity and medicine began to prolong lives and the point at which that improvement
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