The Science of Interconnectedness: PART II - SCALE

The idea that cities, companies, economies, and ecosystems are macro-organisms—larger complex systems composed from the basic blueprint as individual organisms—is not simply a matter of “woo-woo” wishful projection. For decades, the field of complexity science has been studying the parallels between smaller organisms and larger systems. The data is intriguing, on the surface, and bone-chilling, when fully comprehended. In a nutshell, complexity scientists have found a set of “universal principles” that extend across all living systems. The same laws that govern individual organisms also dictate the behavior of cities, companies, economies, and ecosystems. These larger systems can be thought of as scaled organisms—living, breathing, evolving beings operating on a larger scale.

In his book, Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies, Dr. Geoffrey West, a theoretical physicist and interdisciplinary scientist at the Santa Fe Institute in New Mexico, reveals the underlying simplicity governing all organisms, from bacteria, the smallest organisms, to the blue whale, the largest. For example, metabolic rate—the amount of energy needed per second to keep an organism alive—grows with the size of an animal in a predictable way. As an organism’s body mass index (BMI) increases, so does their metabolic rate. An elephant has a greater metabolic rate than a human; a human greater than a dog; a dog greater than a mouse; and so on. Other mammals fall predictably on this line according to their average BMI (West, 2017).

Source: The Wall Street Journal

https://www.wsj.com/articles/how-nature-scales-up-1498239216

Adapted from: West, G. (2017, p. 3). Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies. New York: Penguin Press. 

An important characteristic of metabolic rate in organisms is that it scales sublinearly: as an organism doubles in size, it only requires a 75% higher metabolic rate—a savings of 25% with each doubling of size (West, 2017). This is known as an “economy of scale.” You are probably familiar with this concept, for example, when purchasing a jar of peanut butter at Costco: instead of paying twice as much for a jar twice as big, you only pay a fraction more than you would for a normal jar of peanut butter. Costco and other big retailers use this same principle as a business model: compared to the small local store, big retailers buy larger quantities of the same item at a fraction of the price, while also reaping savings from bigger warehouses, delivery trucks, and so on (and therefore are able to sell you their products for less money). In the case of organisms, economy of scale is demonstrated at a 3:4 ratio: as size increases by a magnitude of 4, metabolic rate increases by a magnitude of 3. Elephants have roughly 10,000 (104) times more cells than mice—they are heavier than mice by a magnitude of four. However, the metabolic rate of an elephant is only 1,000 (103) times greater than mice—a magnitude of three. Costco has borrowed from nature, except instead of luring customers with apple and orange trees, Costco lulls its modern hunter and gatherers with free samples of puffy rice and fruit snacks.

Amazingly, West and his colleagues discovered that cities and companies demonstrate a similar “economy of scale” as they grow in size. The amount of infrastructure needed to sustain a city (which can be thought of as “metabolic rate”) follows a 0.85 scaling law, markedly close to the 0.75 (3:4 ratio) law observed in organisms (West, 2017). In other words, as a city’s population doubles in size, it only needs 85% more “things” to sustain it. Data compiled from cities across the globe show that, depending on the size of a city, one can reliably predict its number of gas stations, roads, water and gas lines, and other infrastructural components. This is true regardless of a city’s location, history, economy, or culture (West, 2017). The same pattern is demonstrated in companies. Like organisms and cities, the growth of companies follows an economy of scale: as the number of employees increases, most companies’ income, profit, assets, and sales demonstrates sublinear growth. Importantly, because of their sublinear scaling behavior, there are limits to how large organisms, cities, and companies can grow in physical size.

However, while the physical growth of these entities is capped, there seems to be no limit to how large the mind, or metrics of intelligence and innovation, can expand. The mind, as opposed to the body, follows a superlinear scaling pattern. Superlinear patterns are also known as “increasing returns to scale.” Humans, cities, and companies all demonstrate this pattern in regards to metrics of the mind. 

While brain size scales linearly with body size (1:1 ratio) in most animals, something unique began occurring in primates: as body size increased in primates, the brain comprised an increasingly larger portion of the body (Hamilton & Walker, 2019). This phenomenon partly explains primates’ unique social and cognitive abilities. Add on top of this that the number of neurons in the cerebral cortex—which is responsible for “higher order” cognitive functions—also scales superlinearly with size; as primate brain size grows, there is an increasingly larger number of neurons in the cerebral cortex (Herculano-Houzel, 2012). The unique abilities of primates do not stop there: a superlinear correlation exists between brain size and group size; as primates’ brains get bigger, they form increasingly larger social groups. Humans exist in the largest social groups. Because human cognition is highly predicated on this type of social learning, we achieve an “increasing return to scale” on our intelligence as group size grows; our big brains and big social groups have a multiplicative effect. Researchers have multiplied these two factors (brain size*group size) to come up with a measure of “collective brain mass” (Hamilton & Walker, 2019). As expected, we find that collective brain mass scales superlinearly with group size: as group size increases, collective brain mass gets larger per capita of the group (Hamilton & Walker, 2019). In simpler terms, this means that as we bond together, our intelligence becomes more than simply the sum of each part; the quality of our mind emerges from the interconnected, interdependent whole of which we are embedded in.

Perhaps unsurprisingly by now, we see a similar effect occurring in cities. Measures of knowledge, wealth, innovation, and socioeconomic output—measures of social intelligence, as opposed to the physical makeup of an organism or city— all scale superlinearly with a city’s size. Wages, GDP, the number of patents produced, the number of cases of AIDS and infectious diseases, the amount of crime, and the pace of life (e.g., pedestrian walking speed) each demonstrate an increasing return to scale; the bigger the city, the higher these measures on a per capita basis. Data shows this to be reliable for urban cities across the world (Bettencourt, Lobo, Helbing, Kühnert, & West, 2007). Companies follow the same trend: while measures of size (e.g., profit, assets, sales) scale sublinearly with the number of employees, measures of innovation and ideas follow a superlinear trend (West, 2017).

The growth of intelligence in the “collective brain”  mirrors the individual brain. As the brain accumulates more and more neurons and connections, it grows in intelligence; similarly, as we bond together into cities, companies, and social groups, our collective intelligence multiplies. Individuals, cities, and social groups are like neurons in the collective brain, achieving higher and higher density and more and more connections within each cluster. Consider, as well, that these clusters are bound together into larger systems: economic, political, ecological, and other byproducts of technological social connection. Despite any apparent separation, we are each somehow connected to more distal parts of the “collective brain.” Like the body, each part can only be fully understood in relation to its connection to others and the whole.

REFERENCES

Bettencourt, L. M., Lobo, J., Helbing, D., Kühnert, C., & West, G. B. (2007). Growth, innovation, scaling, and the pace of life in cities. Proceedings of the national academy of sciences, 104(17), 7301-7306.

Hamilton, M. J., & Walker, R. S. J. (2019). Unique allometry of group size and collective brain mass in humans and primates relative to other mammals. bioRxiv, 829366.

Herculano-Houzel, S. (2012). The remarkable, yet not extraordinary, human brain as a scaled-up primate brain and its associated cost. Proceedings of the National Academy of Sciences, 109(Supplement 1), 10661-10668.

West, G. (2017). Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies. New York: Penguin Press.