Population-scaled adaptive improvement hits the same sub-linear (logarithmic / power-law) brake across evolution, idea-production, and neural scaling

Three fields reach, independently, for the same two-part structure: scaling the generating population accelerates improvement, and then a sub-linear ceiling bites.

• Accelerator. The count of individuals is the supply of variation. Kremer (1993) makes idea output proportional to population via the nonrivalry of ideas; the post-agricultural population boom in Hawks et al. (2007) supplies more mutations for selection. Same engine, different raw material — inventors vs. mutations.
• Brake. Each field also found that scaling that population yields sub-linear returns. Desai, Fisher & Murray (2007): the speed of evolution rises only logarithmically in population and mutation rate, because beneficial mutations interfere. Bloom et al. (2020): research productivity is falling sharply — Moore's-Law progress now needs >18× the researchers. And neural scaling laws (Kaplan 2020) are commonly described as power laws — exponentially more compute per proportional capability gain.

The satisfying part is not that "more agents → faster progress" recurs; it is that all three independently discovered the same functional brake. Kremer is the accelerator; clonal interference and "ideas harder to find" are the same friction in different lab coats.

The honest shape of the bridge. This note deliberately corrects the seed that spawned it rather than confirming it. The seed paired the ~280× AI inference-cost collapse with the Hawks acceleration as if the two numbers connected. They do not: a point-to-point price ratio is a different object than a rate relative to baseline. The real structure sits one level up — and the inference-cost figure is the weakest instance of it, because its drivers (hardware, software, competition) live in the Moore's-Law domain where Bloom et al. document the idea-engine sputtering. The AI leg here (scaling laws) is also the softest-sourced: its exponents were confirmed only by WebSearch, so the "same law" claim stays seedling and [unverified-quant] pending question-verify-neural-scaling-law-exponents-kaplan-hoffmann.

This is a fourth-and-fifth cousin of the vault's other scaling-law threads: sublinear scaling in a regulatory corpus (Santa Fe universal-scaling program) and Wright's Law (cost per cumulative-production doubling). Each is a different object obeying a sub-linear scaling relation.

The AI leg's hinge. Rich Sutton's "Bitter Lesson" (2019) names the pattern that the 1988 Denker hand-designed-kernel → 1989 LeCun learned-kernel transition instantiates — hand-engineered human knowledge loses, long-run, to general methods that leverage computation — and cites vision (hand-designed edges/SIFT vs. learned convolution) as one of four historical cases. But Sutton's essay claims such methods "scale arbitrarily" and never addresses rate; the Kaplan et al. (2020) exponents recorded above (α≈0.05–0.095) are the missing rate, and they say the scaling Sutton celebrates is governed by exactly this note's brake. See 2026-07-27-hop-bitter-lesson-scaling-brake for the full chain. That capture is promoted (2026-07-28) as two atomic notes: claim-sutton-2019-bitter-lesson-names-pattern-silent-on-rate (the essay's claim) and claim-kaplan-2020-scaling-law-exponents-are-small-diminishing-returns (the exponents, α_N≈0.076, α_D≈0.095, α_C_min≈0.050, Tier 1, quoted directly).