“Taking temporarily high rates of annual exponential growth as indicators of future long-term developments is a fundamental mistake.”

Vaclav Smil, writing in Growth: From Microorganisms to Megacities:

Taking temporarily high rates of annual exponential growth as indicators of future long-term developments is a fundamental mistake — but also an enduring habit that is especially favored by uncritical promoters of new devices, designs, or practices: they take early-stage growth rates, often impressively exponential, and use them to forecast an imminent dominance of emerging phenomena.

Many recent examples can illustrate this error, and I have chosen the capacity growth of Vestas wind turbines, machines leading the shift toward the de-carbonization of global electricity generation. This Danish maker began its sales with a 55 kW machine in 1981; by 1989 it had a turbine capable of 225 kW; a 600 kW machine was introduced in 1995; and a 2 MW unit followed in 1999. The best-fit curve for this rapid growth trajectory of the last two decades of the 20th century (five-parameter logistic fit with R2 of 0.978) would have predicted designs with capacity of nearly 10 MW in 2005 and in excess of 100 MW by 2015. But in 2018 the largest Vestas unit available for onshore installations was 4.2 MW and the largest unit suitable for offshore wind farms was 8 MW that could be upgraded to 9 MW (Vestas 2017a), and it is most unlikely that a 100 MW machine will be ever built.

This example of a sobering contrast between early rapid advances of a technical innovation followed by inevitable formation of sigmoid curves should be recalled whenever you see news reports about all cars becoming electric by 2025 or new batteries having impressively higher energy densities by 2030.

But the final, inescapable power of this reality may seem inapplicable in those cases where exponential growth has been underway for an extended period of time and when it keeps setting new record levels. More than a few normally rational people have been able to convince themselves — by repeating the mantra “this time it is different” — that performances will keep on multiplying for a long time to come.


October 28, 2020
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