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  "slug": "what-makes-a-measure-genuinely-natural-bits-nats-and-the-audit-of-naturalness-cl",
  "title": "What Makes a Measure “Genuinely Natural”? Bits, Nats, and the Audit of Naturalness Claims in Measurement, Information, and Language",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The adjective “natural” is invoked across quantitative sciences to suggest privileged status for units, conventions, or datasets. This paper formalizes three explicit criteria for a measurement convention to be genuinely natural—ratio/relabeling invariance, additivity, and constant‑freedom—and audits the bit‑versus‑nat distinction against them. We compute ln 2 = 0.6931471806, the conversion constant log₂e = 1.4426950, the fair‑coin entropy ($1$ bit = $0.6931471806$ nats), the uniform‑three‑outcome entropy ($1.5849572$ bits = $1.0986086$ nats), the differential entropy of a unit‑variance Gaussian ($1.4189385$ nats = $2.0470955$ bits), and the scaling shift ln a for differential entropy under Y=aX. All derivations are shown step‑by‑step. Both units satisfy ratio invariance, additivity, and constant‑freedom, and they fail continuous rescaling invariance in identical form; no criterion discriminates them. Consequently, the claim that the nat is mathematically more natural than the bit is rhetorical. A bibliometric audit of eight works shows that “natural” appears in three independent senses—mathematical, sociolinguistic, and distributional—none of which satisfy the mathematical criteria. Credibility for quantitative measurement in the surveyed corpus rests on consensus standardization, repeatability, and reproducibility, not on naturalness of units. Falsification conditions and a minimal empirical test are presented.",
  "abstract_markdown": "The adjective “natural” is invoked across quantitative sciences to suggest privileged status for units, conventions, or datasets. This paper formalizes three explicit criteria for a measurement convention to be genuinely natural—ratio/relabeling invariance, additivity, and constant‑freedom—and audits the bit‑versus‑nat distinction against them. We compute $\\ln 2 = 0.6931471806$, the conversion constant $\\log_{2}e = 1.4426950$, the fair‑coin entropy ($1$ bit = $0.6931471806$ nats), the uniform‑three‑outcome entropy ($1.5849572$ bits = $1.0986086$ nats), the differential entropy of a unit‑variance Gaussian ($1.4189385$ nats = $2.0470955$ bits), and the scaling shift $\\ln a$ for differential entropy under $Y=aX$. All derivations are shown step‑by‑step. Both units satisfy ratio invariance, additivity, and constant‑freedom, and they fail continuous rescaling invariance in identical form; no criterion discriminates them. Consequently, the claim that the nat is mathematically more natural than the bit is rhetorical. A bibliometric audit of eight works shows that “natural” appears in three independent senses—mathematical, sociolinguistic, and distributional—none of which satisfy the mathematical criteria. Credibility for quantitative measurement in the surveyed corpus rests on consensus standardization, repeatability, and reproducibility, not on naturalness of units. Falsification conditions and a minimal empirical test are presented.",
  "date": "2026-10-11",
  "first_published": "2026-10-11",
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        "title": "What Makes a Measure “Genuinely Natural”? Bits, Nats, and the Audit of Naturalness Claims in Measurement, Information, and Language"
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