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Equation 8 · The Metabolism of Civilization: Energy to 2100

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where the experience exponent b sets the learning rate LR = 1 - 2^{-b} , the fractional cost drop for every doubling of z . Way et al.'s working version of the same relationship is stated as a stochastic first-difference equation in log-cost against log-experience, with an estimated autocorrelation parameter of 0.19 held fixed across all fifty-plus technologies studied, chosen because fitting it separately for each technology’s comparatively short historical record degraded genuine out-of-sample forecasting accuracy [ 1 ] . The mathematics is unremarkable; what matters for this argument is what it implies about heritability and compounding. A technology with a high, stable learning rate…
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where the experience exponent b sets the learning rate LR = 1 - 2^{-b} , the fractional cost drop for every doubling of z . Way et al.'s working version of the same relationship is stated as a stochastic first-difference equation in log-cost against log-experience, with an estimated autocorrelation parameter of 0.19 held fixed across all fifty-plus technologies studied, chosen because fitting it separately for each technology’s comparatively short historical record degraded genuine out-of-sample forecasting accuracy [ 1 ] . The mathematics is unremarkable; what matters for this argument is what it implies about heritability and compounding. A technology with a high, stable learning rate converts every unit of deployment — every subsidy dollar, every early adopter, every demonstration project — into a durable, non-reversing reduction in future cost, the economic analogue of a trait that increases fitness in every generation it is expressed. A technology without that property, no matter how much capital or attention it receives, does not compound in the same way; its next generation starts from roughly the same cost position as the last one did.

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