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Equation 7 · Part 6 · The Metabolism of Civilization: Energy to 2100

superscript

LR=1−2−bLR = 1 - 2^{-b}
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

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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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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