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

by Geoffrey West

In effect, each of us is carrying a device that is keeping track of where we are at any time.

The ubiquitous use of per capita indicators for ranking and comparing cities is particularly egregious because it implicitly assumes that the baseline, or null hypothesis, for any urban characteristic is that it scales linearly with population size.

This provides a meaningful ranking of a city’s individuality and uniqueness beyond what is effectively guaranteed just because it’s a city of a certain size. Without

It goes under many different names including preferential attachment, cumulative advantage, the rich get richer, or the Yule-Simon process.

Thus the energy available for growth is just the difference between the rate at which energy can be supplied and the rate that is needed for maintenance.

On the supply side, metabolic rate in organisms scales sublinearly with the number of cells (following the generic ¾ power exponent derived from network constraints) while the demand increases approximately linearly.

cities are comprised of two generic components: their physical infrastructure, manifested as buildings, roads, et cetera, and their socioeconomic dynamics, manifested as ideas, innovation, wealth creation, and social capital.

This extraordinary process, which can be thought of as the social metabolism of a city, is responsible for increasing our conventional biological metabolic rate derived from the food we eat from just 2,000 food calories a day or 100 watts to about 11,000 watts, the equivalent of 2 million food calories a day.

This is the beauty of the scaling perspective—we don’t need to know the details of what the individual contributions to the metabolism of a city are in order to determine its growth trajectory.

Consequently, the amount available for growth, which is just the difference between its social metabolic rate and the requirements for maintenance, continues to increase as the city gets larger. The bigger the city gets, the faster it grows—a classic signal of open-ended exponential growth. A mathematical analysis indeed confirms that growth driven by superlinear scaling is actually faster than exponential: in fact, it’s superexponential.

Thus there are very few extremely large companies, but an enormous number of very small ones, with all of those in between following a simple systematic power law distribution.

As we’ve seen, growth in both organisms and cities is fueled by the difference between metabolism and maintenance. Using that language, the total income (or sales) of a company can be thought of as its “metabolism” while expenses can be thought of as its “maintenance” costs.

We, too, are finely balanced between metabolism and maintenance costs, a condition biologists refer to as homeostasis.

This revelation echoes the surprise that organisms, ecosystems, and cities are likewise subject to generic constraints, despite the apparent uniqueness and individuality of their life histories.

The half-life of U.S. publicly traded companies was found to be close to 10.5 years, meaning that half of all companies that began trading in any given year have disappeared in 10.5 years.

Companies are surprisingly biological and from an evolutionary perspective their mortality is an important ingredient for generating innovative vitality resulting from “creative destruction” and “the survival of the fittest.”

The fact that companies scale sublinearly, rather than superlinearly like cities, suggests that they epitomize the triumph of economies of scale over innovation and idea creation. Companies typically operate as highly constrained top-down organizations that strive to increase efficiency of production and minimize operational costs so as to maximize profits. In contrast, cities embody the triumph of innovation over the hegemony of economies of scale.

Nevertheless, from analyzing the Compustat data set we found that the relative amount allocated to R&D systematically decreases as company size increases, suggesting that support for innovation does not keep up with bureaucratic and administrative expenses as companies expand.

Check this against Baumol

ACCELERATING TREADMILLS, CYCLES OF INNOVATION, AND FINITE TIME SINGULARITIES

finite time singularity,

Simple power laws and exponentials are continuously increasing functions that also eventually become infinitely large, but they take an infinite time to do so. Another way of saying this is that in these cases the “singularity” has been pushed off to an infinite time into the future, thereby rendering it “harmless” relative to the potential impact of a finite time singularity. In the case of growth driven by superlinear scaling, the approach to the finite time singularity, represented by the solid line in Figure 76, is faster than exponential. This is often referred to as superexponential, a term I’ve already used earlier when discussing the growth of cities.

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.

This can be restated as a sort of “theorem”: to sustain open-ended growth in light of resource limitation requires continuous cycles of paradigm-shifting innovations,

The theory dictates that to sustain continuous growth the time between successive innovations has to get shorter and shorter.

The actuality is qualitatively quite different. As I emphasized earlier, we have been expanding at a superexponential rate rather than “just” exponentially, and this has been driven by the superlinear scaling of socioeconomic activity as a result of the multiplicative enhancement inherent in our social dynamics.

We live our lives on the metaphorical accelerating socioeconomic treadmill.

Until recent times, the time between major innovations far exceeded the productive life span of a human being. Even in my own lifetime it was unconsciously assumed that one would continue working in the same occupation using the same expertise throughout one’s life. This is no longer true; a typical human being now lives significantly longer than the time between major innovations, especially in developing and developed countries. Nowadays young people entering the workforce can expect to see several major changes during their lifetime that will very likely disrupt the continuity of their careers.