A First-Principles Theory of the Human Body: Volume Matters

Body mass index (BMI) relates body mass to squared height and therefore uses an area-type normalization for a three-dimensional body. This paper examines the dimensional limitation of this representation and the projection-induced merging that occurs when different transverse body configurations are mapped to the same planar scale. A minimal cylindrical model separates the longitudinal scale h from an independent transverse scale r, giving the volume proxy r²h. In the empirical implementation, measured waist circumference w represents the transverse scale, and the integral density measure is defined as k = m/(w²h). The model is tested using unweighted NHANES 2017–2023 anthropometric data with 20,699 observations. Body mass is compared with the height-squared parameter h² and with the circumference-based volume proxy w²h. The coefficient of determination increases from R² ≈ 0.58 for h² to R² ≈ 0.92 for w²h. The corresponding Pearson correlation between body mass and w²h is approximately 0.96. Histogram-based shape analysis shows that, compared with BMI, k has lower relative dispersion, lower skewness, negative excess kurtosis, a lower Jarque–Bera statistic, and a larger proportion of observations within one standard deviation of the mean. These results do not define a medical norm and do not assign biomedical meaning to individual values of k. They show that a circumference-based volume proxy provides a dimensionally consistent population-level coordinate for relating body mass to body geometry and provides a basis for later testing of local features of the population distribution. This work is part of the research series A First-Principles Theory of the Human Body. Series repository: Open Science Framework, DOI: https://doi.org/10.17605/OSF.IO/ENAUQ.