all interact with one another. The demand for nutrients, and the rate at which the body processes and gets rid of them, depends on metabolic activity. The heart rate needs to match the rate at which the cells burn oxygen. In combination the scaling laws display a kind of unity. For example, because metabolic rate for each cell decreases as the −1/4 power of body size, but life span increases as the 1/4 power, each cell burns approximately the same amount of energy in its life, regardless of the animal it lives in. What was harder to explain was why scaling laws should all revolve around the number 4.

By the mid-1960s, most biologists believed that Kleiber’s rule was an accurate reflection of the relationship between mass and metabolism. We know this because they voted on the question. At an international symposium on energy metabolism held in the Scottish town of Troon in May 1964, Kleiber argued that 0.75 should be adopted as the standard for calculating metabolic rate from body weight. Despite the objections of those who pointed out that metabolic rate varied greatly within species, between species, and at different times in an animal’s life, the conference adopted Kleiber’s motion by 29 votes to nil. Kleiber’s victory reversed a defeat 30 years earlier, when the same conference had voted in favor of Brody’s suggested 0.73. This seems like an odd way for scientists to settle their issues—you would hope that evidence, rather than majority opinion, would be the arbiter. Some of the arguments about Kleiber’s rule have a strong whiff of numerology—Kleiber and Brody had fierce arguments about what the third decimal place of the scaling factor should be, even though there was no way of measuring this number precisely.

Agricultural researchers such as Kleiber and Brody needed to know how metabolic rate changed with size, but they weren’t much interested in explaining why. Kleiber’s rule, and other allometries, gave good predictions, and highlighted exceptions, without any theoretical underpinning, so most biologists probably saw little use for one. A serious mathematical attack on the problem would require someone with a different background, and a fresh angle, to the nutritionists and physiologists who until then had dominated the study of metabolism. This person arrived in the early 1970s.

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