Equation 22 · Who Builds 2100? The Demographic Engine of Technological Evolution
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The two right-hand boxes both depend on the Aghion-Jones-Jones mechanism actually materializing at the scale their formal model allows for, which Section 5 was careful to label a named, live argument rather than a documented fact. If it does materialize, the difference between the top-right and bottom-right boxes — whether population is also growing or is instead the IHME-scale decline — matters much less than in the human-bound cases, because a large enough term dominates the sum in the numerator of the growth relation regardless of what is doing. That is precisely Aghion, Jones, and Jones’s point about their own model: sufficiently complete automation of the idea-production…
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The two right-hand boxes both depend on the Aghion-Jones-Jones mechanism actually materializing at the scale their formal model allows for, which Section 5 was careful to label a named, live argument rather than a documented fact. If it does materialize, the difference between the top-right and bottom-right boxes — whether population is also growing or is instead the IHME-scale decline — matters much less than in the human-bound cases, because a large enough term dominates the sum in the numerator of the growth relation regardless of what is doing. That is precisely Aghion, Jones, and Jones’s point about their own model: sufficiently complete automation of the idea-production function decouples the growth rate of ideas from the growth rate of the human population searching for them, which is the specific, named mechanism by which a smaller, older 2100 population could still preside over accelerating rather than decelerating invention [ 6 ] .
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