breeding. Others, such as fish and molluscs, seem to keep gaining weight throughout their lives, but this rate nevertheless decreases as they age. For all sorts of animals, plotting their size against their age creates an s-shaped curve, which starts shallow, takes a rapid turn upward, and then levels off. An animal’s growth rate seems to be some function of its age. Thompson keenly sought the laws of growth that controlled this trajectory, for he believed they controlled animal form. But in On Growth and Form, he had to admit defeat:

For the main features which appear to be common to all curves of growth we may hope to have, some day, a simple explanation…. The characteristic form of the curve of growth … is a phenomenon which we are at present little able to explain, but which presents us with a definite and attractive problem for future solution.

By the time the second edition came out in 1942, someone had offered that simple explanation.

Born near Vienna in 1901, Ludwig von Bertalanffy got his Ph.D. at that city’s university in 1926, for a study of the work of Gustav Fechner, a nineteenth-century German psychologist and philosopher who studied human vision. Soon after, Bertalanffy concluded that the life sciences had reached an impasse. Knowledge was being churned out faster than ever before, but without theory the babble of unconnected facts drowned out understanding. “Today biology is in its pre-Copernican period. We possess an enormous mass of facts, but we still have only a very incomplete insight into the laws governing them,” he wrote. “Only if the multiplicity of facts is ordered, brought into a system, subordinated to great laws and principles, only then does the heap of data become a science…. The chief task of biology must be to discover the laws of biological systems to which the ingredient parts and processes are subordinate. We regard this as the fundamental problem for modern biology.

Bertalanffy saw the impasse as an opportunity as well as a crisis. He took inspiration from physics, then convulsing as quantum theory replaced the Newtonian worldview. Perhaps an equally radical shift in biological thought could reap similar rewards. He began to ponder the fundamental properties of life. The two he settled on are themes we have already encountered repeatedly: hierarchical organization and the continual exchange of matter and energy with the environment. Just as

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