unlikely that everyone who uncovered one of about 200 quarter-power scalings set out to prop up Kleiber’s rule.

Animal bodies exist in three dimensions—this is the logic of the surface law. So where does nature’s fixation with the number 4 come from? There’s one simple way to produce scaling laws that revolve around the number 4. Although we live in a world with three spatial dimensions, it’s perfectly acceptable to do geometry on a four-dimensional shape. The proportions of such a shape scale in the same way as those of a three-dimensional one. Just as in a three-dimensional solid, dimension two (surface area) is proportional to dimension three (volume or mass) raised to the power of 2/3, in a four-dimensional shape dimension three is proportional to dimension four raised to the power of 3/4—the very number we are looking for. In 1977, Jacob Blum pointed out that, if you considered living things as having four dimensions, a four-dimensional version of the surface law led simply to a scaling exponent of 3/4. Find an extra dimension from somewhere and all your problems are solved. Blum didn’t have any definite ideas about what this fourth dimension might be. Twenty years later, another team of researchers did.