Scale

Geoffrey West

I am quite a fan of patterns. It is difficult to look around and not believe that there is some grand order in the scheme of things. But it becomes even more difficult when one does not have the luxury of faith. And thus it is a pleasure when science points to a possible unifying theory that brings some amount of order to what could be mistaken for randomness. Scale begins with showing how ‘there are scaling relationships that quantitatively describe how almost any measurable characteristic of animals, plants, ecosystems, cities and companies scales with size.‘ We are talking of things as varied as metabolic rate, patents, and companies’ income and assets! The simplicity underlying the complexity is what this book is about.

This also raises another set of interesting set of questions. For instance, why don’t we grow forever and be immortal? And why do different animals have different lifespans and yet have the same number of heartbeats in a lifetime? Why do cities seem to scale indefinitely while companies more often than not collapse after a while?

And through the answers, scaling laws emerge. The 3/4 power scaling law is where we begin. For example, even though elephants have 10000 (10^4) more cells than rats, its metabolic rate is only 1000 (10^3) times. This, known as Kleiber’s Law, is valid across all cellular, plant and animal groups. Interestingly, when a city’s population doubles, socioeconomic qualities like patents, wages, wealth, crime, educational institutions increases by 15% beyond doubling. The former is sublinear, the latter is superlinear. What that means, the network dynamics in biology constrains the pace of life systematically with size increases as per the 3/4 scaling law. But the pace of life in cities increase systematically as per the 15% rule. A new dynamic courtesy our species.

We begin with the history of people who first thought of these things. Galileo and his argument on how areas (^2) and volumes (^3) scale differently with the change in one dimension. The implications of this are not only in the real world (e.g. importance of the cross section of supporting structures as opposed to length), but also deflates the strength of Superman and the size of Godzilla! Isambard Kingdom Brunel , considered by many as the greatest engineer of the twentieth century, whose ship design became the prototype for all modern ships. William Froude and the beginning of modeling theory.

The importance of 4 in the design of things is fascinating. In addition to the 3/4 law, there is also 1/4th, which applies for a bunch of things from cross sectional areas of aortas and genomes to rates of evolution. Also fascinating is the intersection of physics and biology. The scaling laws in biology is deeply rooted in the universal mathematical, dynamic and organisational properties of the networks that distribute energy, materials and information in organisms.

Thus, it was possible to develop a set of network properties that possibly emerged from natural selection and gave rise to these laws. I found the “invariance of terminal units” among the three properties most fascinating. This is the reason why despite the size difference, the capillaries (end units in the circulatory system) of mice, humans and elephants are all the same size! The other two properties are space filling (the network has to reach the ends of the system it serves) and optimisation (minimise energy used for maintenance, maximise energy for reproduction and raising the offspring, just like the principle of minimised action in physics). At some point, we reach a stage (around 20 years!) where the energy we take in is just about sufficient to maintain the grown body. From then on, it’s a battle.

Another interesting concept is that of fractals that have an implication on many things from the length of coastlines to stock market behaviour! It also means that though our lungs are only the size of a football, the total surface area of the alveoli (terminal units of the respiratory system) is the size of a tennis field.
These concepts are then discussed in various contexts – humans and our growth, ageing and death, and the cities and companies we create. I, for one, am glad to understand how and why the pace of our lives has quickened. Along the way, we come across more interesting laws – Zipf law, the more familiar Dunbar’s number. Companies, interestingly, are more similar to organisms than cities, though their ‘metabolic rate’ is exactly linear.

The last part of the book has consequences, predictions, and raises some important points on the sustainability of the growth of our species. The final bit also highlights the need for a grand unified theory of sustainability so that we understand better the nuances of man’s interactions with the environment and how we can achieve long-term sustainable growth.

This is a fascinating book in many respects – the underlying laws, their impact on practically everything around us, and the predictability it makes possible. Despite the absolutely complexity of the subject(s), Geoffrey West makes it accessible and interesting.