Anthropocentric Invariants in Measurement: A Formal Taxonomy, Cross‑Ratio Analysis, and Quantitative Bias Assessment

In the paper's words

Conventional measurement units embed human‑specific cognitive choices—decimal numeracy, body‑scale references, and water‑based mass standards—creating anthropocentric invariants that obscure observer‑independent physics. Existing work has not formalized how such conventions transform under changes of radix, physiology, or chemistry, nor quantified the bias they introduce for non‑human observers. We define a taxonomy of measurement conventions as functions of three cognitive parameters (radix r, body‑scale factor s, chemical‑basis factor c) and prove that only dimensionless constants remain invariant under the induced “cognitive transformations”, by analogy with projective cross‑ratio invariance.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. A cognitive diversity framework for radar target classification demonstrates that varying sensor perspectives ($\Delta \theta$) improves performance, with a median of three perspectives yielding an 85 % detection rate at $\Delta \theta$ = 5° [5].

   from 2. Background and Related Work

2. Quantitative analysis of the SI catalog confirms that over 90 % of the features are anthropocentric, and a concrete alien observer example illustrates the magnitude of unit bias.

   from 8. Conclusion

3. Using the SI catalog of anthropocentric features [9] and the cross‑ratio theorem [11], we compute (i) the proportion of anthropocentric features ($P=0.90323$), (ii) a concrete length‑unit scaling factor ($\lambda_{L}=5.31\times10^{-3}$) and mass‑unit scaling factor ($\lambda_{M}=2.10$) for a hypothetical alien observer with octal radix, insect body scale, and silicon‑based chemistry, and (iii) the radix‑economy overhead for representing the inverse fine‑structure constant in base 10 versus the optimal radix (overhead factor $2.24$).

   from Abstract

4. A proof that only dimensionless ratios are invariant under cognitive transformations, using projective cross‑ratio invariance [11] (Section 3).

   from 1. Introduction

5. A radix‑economy analysis quantifying the overhead of decimal representation for the inverse fine‑structure constant, showing an overhead factor of $2.24$ relative to the optimal radix (Section 4.3).

   from 1. Introduction

6. The bound $\beta_{\operatorname{sep}}(S(n,m))\leq4n^{2}\log_{2}(n)+12n^{2}-4n$ demonstrates that invariance can be quantified even in high‑dimensional algebraic settings, motivating our formal treatment of measurement invariance.

   from 2. Background and Related Work

How it is done

1. We define a taxonomy of measurement conventions as functions of three cognitive parameters (radix $r$, body‑scale factor $s$, chemical‑basis factor $c$) and prove that only dimensionless constants remain invariant under the induced “cognitive transformations”, by analogy with projective cross‑ratio invariance.

   from Abstract

2. A proof that only dimensionless ratios are invariant under cognitive transformations, using projective cross‑ratio invariance [11] (Section 3).

   from 1. Introduction

3. The theory of invariants for matrix actions provides algorithmic tools to decide orbit‑closure intersections and to bound the degree of separating invariants [1].

   from 2. Background and Related Work

4. We model a measurement convention $U$ as a mapping $$ U = f(r, s, c), $$ where $r\in\{8,10,12,16\}$ denotes the radix, $s\in\{\text{insect},\text{human},\text{elephant}\}$ the characteristic body scale, and $c\in\{\text{water},\text{silicon},\text{carbon}\}$ the dominant chemical basis.

   from 3.1 Taxonomy of Measurement Conventions

What would falsify it

1. If an empirical measurement performed by a non‑human observer (e.g., a robotic probe with silicon‑based mass standards and octal processing) yields a value for a traditionally dimensional quantity (e.g., the speed of light) that cannot be reconciled with any scalar transformation of the human SI value, then the claim that all conventional units are purely scalar‑transformable would be falsified.

   from 6.2 Falsification Criterion

2. The variability illustrates how internal states (here, physiological parameters) can bias observable outputs, analogous to how human physiology biases unit definitions.

   from 2. Background and Related Work

3. Compare the derived value of $\alpha$ with the known human value; a discrepancy beyond $10^{-6}$ would refute the invariance claim.

   from 7. Practical Implications and Engineering Pathways

Where the claim stops

1. The body‑scale factor assumes a single characteristic length per species; real organisms exhibit a distribution of sizes.

   from 6.1 Limitations

2. The invariance proof relies on multiplicative scaling; if an alien observer adopts a fundamentally different dimensional analysis (e.g., non‑multiplicative units), the proof does not apply.

   from 6.1 Limitations

3. The SI base units, however, encode human‑specific cognitive features—decimal numeracy, body‑scale references, Earth‑centric geometry, and water‑based mass standards—as documented in a systematic catalog of “anthropometric fossils” [9].

   from 1. Introduction

Where to read

1. Abstract204 words · 1 min
2. 1. Introduction246 words · 1 min
3. 2. Background and Related Work445 words · 2 min
4. 3. Methods323 words · 1 min
5. 4. Analysis228 words · 1 min
6. 5. Results82 words · 1 min
7. 6. Discussion224 words · 1 min
8. 7. Practical Implications and Engineering Pathways197 words · 1 min
9. 8. Conclusion98 words · 1 min
10. Provenance and AI Involvement225 words · 1 min
11. Appendix A. Divergence Report202 words · 1 min
12. Appendix B. Claim Attribution161 words · 1 min