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

This study compares the cross-sectional age patterns of body mass index (BMI) and the integral body-density measure k = m/(w²h), where m is body mass, w is waist circumference, and h is height. The analysis used unweighted individual-level data from the National Health and Nutrition Examination Survey covering 2017–March 2020 and August 2021–August 2023. The working samples contained 21,608 valid observations for BMI and 20,699 for k. Mean, median, KDE peak, coefficient of variation, skewness, and excess kurtosis were compared across age bins from 0–4 through 80 years and older. For the complete individual-level k sample, the descriptive linear relation was k = 62.43 − 0.247 × Age, with R² = 0.434. Among the adult age bins from 20–24 through 80+, the means and medians formed strictly descending sequences. Their fitted slopes were −0.1877 and −0.1923, with R² values of 0.9688 and 0.9624. The KDE-peak sequence retained the same overall descending direction but showed greater local departures from monotonicity; its fitted slope was −0.2246, with R² = 0.8373. BMI followed a non-monotonic sequence: its values rose from childhood, remained high through middle age, and declined in the oldest age bins. Its adult linear fits produced a slightly negative slope for the mean (−0.0036) and positive slopes for the median (+0.0168) and KDE peak (+0.0555), with low R² values. The adult BMI descriptors therefore did not share one linear direction. The coefficient of variation and skewness were lower for k than for BMI in every displayed age bin. The cross-sectional results show that the adult mean and median positions are represented by close descending linear relations along the k axis, whereas BMI retains a non-monotonic age form. These relations describe differences among independently sampled age groups rather than longitudinal change within individuals. 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.