Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life, in Organisms, Cities, Economies, and Companies

by Geoffrey West

For instance, most heating, cooling, and lighting is proportional to the corresponding surface areas of the heaters, air conditioners, and windows. Their effectiveness therefore increases much more slowly than the volume of living space needed to be heated, cooled, or lit, so these need to be disproportionately increased in size when a building is scaled up. Similarly, for large animals, the need to dissipate heat generated by their metabolism and physical activity can become problematic because the surface area through which it is dissipated is proportionately much smaller relative to their volume than for smaller ones. Elephants, for example, have solved this challenge by evolving disproportionately large ears to significantly increase their surface area so as to dissipate more heat.

That’s why builders, architects, and engineers involved in construction classify wood by its cross-sectional dimensions, and why lumber yards at Home Depot and Lowe’s display them as “two-by-twos, two-by-fours, four-by-fours,” and so on.

relative strength becomes progressively weaker as size increases. Or, as Galileo so graphically put it: “the smaller the body the greater its relative strength. Thus a small dog could probably carry on his back two or three dogs of his own size; but I believe that a horse could not carry even one of his own size.”

The calculation of how big a dosage should be used on Tusko was based on the implicit assumption that effective and safe dosages scale linearly with body weight so that the dosage per kilogram of body weight was presumed to be the same for all mammals.

the sum of the cross-sectional areas of the daughter tubes leaving the branch point is the same as the cross-sectional area of the parent tube coming into it.

You probably thought that this was for lubrication purposes but in fact it’s actually for matching impedances. Without the gel, the impedance mismatch in ultrasound detection would result in almost all of the energy being reflected back from the skin, leaving very little to go into the body to be reflected back from the organ or fetus under investigation.

The effect of this energy loss is to progressively dampen the wave on its way down through the network hierarchy until it eventually loses its pulsatile character and turns into a steady flow. In other words, the nature of the flow makes a transition from being pulsatile in the larger vessels to being steady in the smaller ones. That’s why you feel a pulse only in your main arteries—there’s almost no vestige of it in your smaller vessels.

But what’s really surprising is that blood pressures are also predicted to be the same across all mammals, regardless of their size.

Simply put, fractals are objects that look approximately the same at all scales or at any level of magnification. A classic example is a cauliflower or a head of broccoli shown opposite.

The critical take-home message from this section is that sublinear scaling and the associated economies of scale arising from optimizing network performance lead to bounded growth and the systematic slowing of the pace of life.