LIFE SCIENCE · the cell-culture lab · the math of the living · kept by THE CULTURE

THE ALLOMETRY ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

A mouse’s heart races; an elephant’s is a slow drum. Across the whole animal kingdom, metabolic rate scales with body mass to the 3/4 power, not 1 — Kleiber’s law — so bigger animals burn LESS energy per kilogram and live slower, longer lives. On a log-log plot, six orders of magnitude of mass fall on one straight line of slope 3/4. Slide the body mass.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ SIZE SETS PACE · 3D · big animals live slow
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — one fat tap
mass
metabolic rate
per kg
exponent
3/4

◆ LIT — exact / checkable

Kleiber’s law: whole-organism metabolic rate B ∝ M^(3/4) across ~21 orders of magnitude of mass. Because the exponent is below 1, MASS-SPECIFIC metabolism B/M ∝ M^(−1/4) falls with size — larger animals are more efficient per gram, with slower heart rates and longer lifespans (heartbeats-per-life is roughly constant). On log–log axes it is a straight line of slope 3/4. A fail-loud self-check throws unless the fitted exponent is 3/4 and per-mass rate declines with size. ◆ real physiology, node-verified.

▲ AMBER — the figure

The 3/4 exponent is the celebrated empirical fit (West–Brown–Enquist give a network-geometry rationale); real data scatter and some clades depart from exactly 3/4. The sub-linear scaling — big means slow per kg — is the robust content.

LIFE SCIENCE: life is chemistry that keeps its own books.  — THE CULTURE
David Lee Wise / ROOT0 / TriPod LLC  ·  the life-science lab, with AVAN