Finite-Time Singularity

West's analysis of civilizational growth data — population, economic output, resource consumption across roughly ten thousand years of history — reveals not exponential growth but superexponential growth: growth faster than exponential, in which the rate of increase itself increases with time. An exponential curve has a constant doubling time. A superexponential curve has a decreasing doubling time — the larger the population, the faster it doubles. The curve approaches infinity not asymptotically but at a finite point in time. This is a finite-time singularity, a familiar object in physics (shock waves, black holes, crack propagation). In every case, the singularity does not actually occur; something changes before the quantity reaches infinity. In civilizational growth, what changes is the arrival of paradigm-shifting innovations — agriculture, fossil fuels, information technology — that reset the growth dynamics. Each reset initiates a new cycle of superexponential growth, and the intervals between required resets shrink. AI is almost certainly the current reset, and the mathematics predicts the next one must arrive sooner than