Sublinear vs. Superlinear Scaling
Description
Jordan Hall:
"In his book “Scale” theoretical physicist Geoffrey West tells of an investigation into the underlying principles that govern the growth and life spans of everything from plants and animals to companies and cities.
The researchers discovered a remarkably consistent dynamic: a relationship called “Sublinear Scaling”. For example, if you double the mass of a mouse you don’t double its energetic needs at the same rate. Instead, if you increase the mass by a factor of 10 (from 1 to 10 for example) you increase the metabolic rate by only about 5.6. Keep doing this and you can end up with an animal with the mass of an elephant (10 million grams), but with a “metabolic” rate of only 177,000. The ratio of mass to metabolic rate went from 1:1 to 56:1.
The folks working on this project looked at all kinds of systems and they kept noticing this sublinear scaling. They noticed it in cells; in different kinds of animals; in plants; in forests and ecosystems. It was ubiquitous and played a major role in how life operates and grows.
Then they looked at cities.
At first, cities showed the same kind of dynamic. Double the population of the city and you increase infrastructure like roads and electrical lines by around 85%. That same old sublinear scaling. But then a new kind of scaling relationship showed up.
When they looked at things like innovation, productivity and wages, they noticed a completely different kind of scaling relationship: Superlinear Scaling. In the case of these characteristics, if you double the population of a city, you increase the productivity of the city by more than double (roughly 115%). Double the population, increase the productivity by 115%. Double the population, increase innovation by 115%.
Here is my first proposition: superlinear scaling is the generator of cities. The city is, in its essence, the solution to the problem of how to grow the population of a place as large as possible so as to maximally benefit from superlinear scaling."
(https://medium.com/@jordangreenhall/from-city-to-civium-5838e0cdfe31)
Example
Jordan Hall on Cities as the Vehicle for Superlinearity
Jordan Hall:
"Cities and superlinear scaling
Here is my first proposition: superlinear scaling is the generator of cities. The city is, in its essence, the solution to the problem of how to grow the population of a place as large as possible so as to maximally benefit from superlinear scaling.
Consider: if you double the population of a city, you increase several important characteristics like wealth and innovation superlinearly. Move from a village of 10,000 to a town of 20,000 and per capita wages increases by 15%, sort of “automagically”. Double it again and those wages increase by 15% again. After a few doublings, the wealth and innovation gap between the “tiny village” and the “big city” is quite large.
Notably, West and team looked at cities across many periods of time, a wide variety of cultures and across many different levels of population. More or less, none of the particulars mattered that much. The dynamic was there in India, Japan, England and the United States and in cities from the 800’s through to the current age. The key was simply the relationship between population and superlinear scaling.
Notice the implicit feedback loop. Wealth and innovation are profound attractors. Merely by moving from the village to the city, you can participate in this increase and the various qualities of life that stem from increased wealth and innovation. All things being even vaguely equal, many people will choose to move to the city. This increases the population — which then increases the wealth and innovation.
Left to its own devices, this attractor would pull everyone into the city. However, the increase in population isn’t unconstrained. If you want to add more people into a city, you have to find some way to provide food, water and housing, to remove waste, to enable people to move around, etc. If you can’t solve for these constraints, you can’t increase the population of the city.
How do you solve for these constraints? You take advantage of the wealth and innovation produced by superlinear scaling. Having a hard time feeding people? Invent irrigated agriculture. Have a hard time housing people? Invent the elevator and deploy wealth to construct skyscrapers to radically increase the vertical potential of housing.
Thus we have a dynamic tension. Increasing population produces superlinear wealth and innovation. It also produces a variety of new pressures. To the degree that the people of the city can craft and implement solutions to those pressures, the city can continue to grow and produce superlinear results. To the degree that they can’t, stagnation and even collapse."
(https://medium.com/@jordangreenhall/from-city-to-civium-5838e0cdfe31)