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

# Math and Science Book Review

Scale is an impressive body of work authored by one of America’s top scientists, Geoffrey West. Dr. West recently headed up the Santa Fe Institute which is a think tank in the true sense of the term. This is a bunch of scientists with the goal of advancing science unencumbered by some partisan political stance. They bring in a ton of different scientists from many different disciplines and try to tackle the tough problems of the age. One of their big targets has always been complex systems and building on an overall complexity theory. In his book Scale, West takes on the big question of what happens to things when they grow. He draws parallels between biological systems, cities and companies using a scientific approach backed with a good amount of layman’s math and illustration.

This is a wonderful book but it does require a pretty high level of concentration to get through all of the concepts. While you don’t need a mathematical background to enjoy it, having a bit of that background makes the first read through a little easier and I would guess a little more enjoyable. I found that as he dove into scaling and power laws I was able to draw a bunch of parallels to other scientific adventures I had taken in school or independent study.

He does a craftsman’s job of explaining what nonlinear growth means – “nonlinear behavior can simply be thought of as meaning that measurable characteristics of a system generally do not simply double when its size is doubled.” He gives some solid definitions for what sublinear and superlinear growth mean and then starts hitting you with examples. One of the most important example to understand is what happens to a structure when it grows. If you are building a rudimentary square shed that is 10′ X 10′ X10′ and you decide to increase the length of each side by a factor of 10, the area and strength to support that area increases by a factor of 100. So your 100′ X100′ shed now has an area of 10,000 instead of the original 100. The volume increase and the strength to support it is even worse, you go from a volume of 1,000 to a volume of 1,000,000 which is a massive increase required in the strength to support the structure. Another example is the Richter scale for earthquakes which is a logarithmic (exponential) scale. So an earthquake that registers as a 6 on the Richter is 10 times more powerful than one that registers as a 5 and 100 times more powerful than one that registers as a 4.

This concept of Scale and it’s nonlinear growth make up the central questions answered by the book. His first exploration of scale is through biology where we learn why larger animals live longer than smaller animals on average. “Because larger animals metabolize at higher rates following the 3/4 power scaling law, they suffer greater production of entropy and therefore greater overall damage, so you might have thought that this would imply that larger animals would have shorter life spans in obvious contradiction to observations. However…on a cellular or per unit mass of tissues basis metabolic rate and therefore the rate which damage is occurring at the cellular an intracellular levels decreases systematically with increasing size of the animal-another expression of economy of scale.” The main takeaway then being, “So at the critical cellular level cells suffer systematically less damage at a slower rate the larger the animal, and this results in a correspondingly longer life span.”

He dives deep into the scaling of cities and finally the scaling of companies but through all three of these systems he comes up with a universal theory of how we scale ‘allometrically’: “the generic geometric and dynamical properties of biological networks that underlie quarter power allometric scaling are: (1) they are space filling (so every cell of an organism, for instance must be serviced by the network); (2) the terminal units, such as capillaries or cells, are invariant within a given design (so, for instance, our cells and capillaries are approximately the same as those of mice and whales); and (3) the networks have evolved to be approximately optimal (so, for instance, the energy our hearts have to use to circulate blood and support our cells is minimized in order to maximize the energy available for reproduction and the rearing of offspring).”

He then ties this directly to cities and companies. In a city, our road and transportation networks must fill space to service every region as do all of the utilities that must service homes and buildings. This is also true of social networks, we collectively fill the socioeconomic space available to us. As far as the terminal units go, he uses the plug as a great example. A plug is the same standard size regardless of what you plug into it. Finally, we will always try to optimize these systems for both biological and economic reasons.

One other point that I found fascinating and is worth highlighting in this review is around what happens when we get too big. “In this scenario demand gets progressively larger and larger, eventually becoming infinite within a finite period of time. It is simply not possible to supply an infinite amount of energy, resources, and food in a finite time. So if nothing else changes, this inextricably leads to stagnation and collapse,” The key here is ‘so if nothing else changes’ because this is where innovation comes into play. He addresses innovation with, “A major innovation effectively resets the clock by changing the conditions under which the system has been operating and growth occurring. Thus, to avoid collapse a new innovation must be initiated that resets the clock, allowing growth to continue and the impending singularity to be avoided.” Sounds good right? If we just keep innovating we’ll be fine. Not so fast. “There’s yet another major catch, and it’s a big one. The theory dictates that to sustain continuous growth the time between successive innovations has to get shorter and shorter. Thus paradigm-shifting discoveries, adaptations, and innovations must occur at an increasingly accelerated pace.” So, to keep growing we have to innovate faster and faster but it seems inevitable that we will eventually hit this limit and stagnate. Scary stuff.

There are many more beautiful nuggets of wisdom within these 500+ pages but it does tend to get dry at times. Stick with it because it is a brilliant, innovative way to look at what happens when things get bigger.