Are cities and companies biological structures?

Geoffrey West

The book Scale: The universal laws of life and death in organisms, cities and companies, by Geoffrey West, from the Santa Fe Institute, which I discussed in the previous post, asserts that cities and companies are subject to laws very similar to those that apply to living beings. They are general laws, applicable to all entities of these types, regardless of their origin. West explains it this way:

Remarkably, analyses of such data show that, as a function of population size, city infrastructure—such as the length of roads, electrical cables, water pipes, and the number of gas stations—scales in the same way whether in the United States, China, Japan, Europe, or Latin America. As in biology, these quantities scale sublinearly with size, indicating a systematic economy of scale but with an exponent of about 0.85 rather than 0.75...[F]ewer roads and electrical cables are needed per capita the bigger the city. Like organisms, cities are indeed approximately scaled versions of one another, despite their different histories, geographies, and cultures, at least as far as their physical infrastructure is concerned.

As in the case of the circulatory system of living beings, in cities there are similar structures, which must provide water, electricity, gas and communications to each and every one of the homes in the city. Therefore, it is not surprising that the effect is also that of an economy of scale, although with an exponent 0.85 instead of 0.75. West does not explain the reason for this difference, nor why, in the case of companies, the exponent turns out to be a little higher: approximately equal to 0.90. It is curious that the exponent 0.85 also applies approximately to issues such as the number of gas stations in each city based on the number of inhabitants, with very similar slopes regardless of the country in question, as can be seen in figure 33 of West’s book, which I’m showing here:

On the other hand, other particularities associated with cities adjust to a different exponent, approximately equal to 1.15, as in the case of the number of patents as a function of the number of inhabitants of the city, in figure 3 of the book:

West comments on this:

Perhaps even more remarkably they are also scaled socioeconomic versions of one another. Socioeconomic quantities such as wages, wealth, patents, AIDS cases, crime, and educational institutions, which have no analog in biology and did not exist on the planet before humans invented cities ten thousand years ago, also scale with population size but with a superlinear (meaning bigger than one) exponent of approximately 1.15. An example of this is the number of patents produced in a city shown in Figure 3. Thus, on a per capita basis, all of these quantities systematically increase to the same degree as city size increases and, at the same time, there are equivalent savings from economies of scale in all infrastructural quantities. Despite their amazing diversity and complexity across the globe, and despite localized urban planning, cities manifest a surprising coarse-grained simplicity, regularity, and predictability.

The problem with an exponent greater than 1 is that it gives rise to super-exponential growth, which tends to infinity in a finite time. Supporters of the technological singularity (see this post) will jump for joy at this possibility, but West is more restrained and says this:

This is obviously impossible, and that’s why something has to change… This kind of growth behavior is clearly unsustainable because it requires an unlimited, ever-increasing, and eventually infinite supply of energy and resources at some finite time in the future in order to maintain it. Left unchecked, the theory predicts that it triggers a transition to a phase that leads to stagnation and eventual collapse.

This forecast seems much more realistic than the crazy speculations of the supporters of the technological singularity. It is curious that the curve offered by West to describe this situation is practically identical to the curve I proposed to describe the evolution of biological species and civilizations in my two books, Human cultures and evolution (1978) and Evolución biológica y cultural en la historia de la vida y del hombre (2017).

The same post in Spanish

Thematic Thread on Mathematics and Statistics: Previous Next

Manuel Alfonseca