Let there be two polynomials, Pr is a bounded set that defines the delivery rate for the most constrained resource. Then any other polynomial that increases efficiency will result in a new production function Pr * Px; but |Pr|*|Px| > |Pr*Px| So, increasing energy efficiency results in more ways to use energy, but the total amount of energy used cannot exceed the original constraint. The issue came up in Brad's blog:
Rebound Redux: Have we moved past Jevons on efficiency? – The Great Energy Challenge
Getting a bit more wonkish, this applies regardless of the norm about which the calculus is built. So also does a fixed point theorem, meaning regardless of the Norm used, there will always be a Golden Rule, a prime basis set which best represents the underlying manifold. If our norm results in bounded functionals, then we will revert to the prime basis set that best contains a constrained delivery channel, and appears as a sudden mean reversion.
Consider this Slate article
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