Double an animal’s mass and its metabolic rate does not double. It rises by a factor closer to 1.68 — mass raised to the three-quarter power. This relationship, Kleiber’s law, holds from bacteria to blue whales, some twenty-one orders of magnitude. A pattern that stubborn is not a coincidence; it is a clue about mechanism.
The leading explanation is geometric. Organisms are fed by branching networks — circulatory, respiratory — that must service a volume while constrained to a surface-like delivery system. Optimise such a network for minimal energy loss and the three-quarter exponent falls out of the mathematics. The body plan is downstream of a transport problem.
The methodological lesson: the most powerful biological facts are often not about any one organism but about the constraints every organism shares. Find the invariant and you have found something closer to a law than a description.