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

This is an amazing book with a broad perspective on the statistical foundations of how things are born, grow, and die. Beyond just the life of plants and animals it expands its thinking into the life cycles of economies, corporations, and cities (the last of these apparently being the only immortal entity on the list).

Geoffrey West is a theoretical physicist and former president of the Santa Fe Institute in New Mexico. Ten or fifteen years ago he began to wonder whether the mathematics of his discipline could be applied to other sciences. He found a major gap in the study of biology where there was a great deal of information gathering and identification but few attempts to answer questions out of the information gathered using statistics. West wanted to see if there could be insights into some of the fundamental questions of biology. Why do things die? Why can animals only reach certain sizes, and beyond that how did whales become so big?

In biology he found startling comparisons, that the arterial systems of animals compare in design and scale to plants and trees. He found that arterial systems branch out uniformly to the point that blood stops surging but flows through capillary branches. He found the math almost identical to the way limbs and channels branched off in trees until reaching the constant flow in leaves. He learned that animals have nearly identical systems, from the smallest shrew to the whale, and that once you know, say, the size of kidneys in one you can calculate the same in other animals. More importantly, perhaps, he notes that the increased size of animals creates efficiencies so that an animal that is double the size of another needs far less than double the caloric energy.

This efficiency of scale transfers using the same mathematical constants to non-living entities. West found that cities grow at the same uniform scales, so that knowing the population of a city will allow you to make calculations on statistics such as the number of attorneys, the number of restaurants, the number of residential units, etc., with only small variations on some items that will define the unique personality of a city.

West also found comparisons of scale for corporations, with great similarities among all sizes, and identified a life cycle of birth, growth, and death lasting around half a century for those that survived the first five years.

Because the math used in all the different areas is consistent it’s easy to grasp (even for this liberal arts major) and it’s fascinating to watch these ideas redevelop in areas that seem so widely divergent.

West is a personable writer and includes information about how these discoveries were worked out with researchers in the different fields and even occasional talk about his children, such as calculating quantities of medications for his infant son.

There are also enlightening discussions on logarithmic scales and visualizations to help understand what exponential means and the alarming things it could mean for population growth.

The book moves from topic to topic with just enough time spent on each so the reader feels neither cheated nor overwhelmed in each, with every section building on the last. It’s an excellent book for anyone interested in health, public policy, economics, or management.