More About “Scale”

Watercolor from life, 2016 (9 x 12)

In my last post on “Scale” by Geoffrey West I didn’t discuss in any detail the results of applying power laws to cities, and entirely avoided the last chapter, which applies scale laws to the issue of growth. I want to address these issues in this essay. The bottom line: we have a limited time to make fundamental changes.

In his approach to cities he quotes the urbanist Lewis Mumford: “The chief function of the city is to convert power info form, energy into culture, dead matter into the living symbols of art, biological reproduction into social creativity.” By analogy with biological systems, West applies the concept of metabolism to cities. But he distinguishes the “physical metabolism,” consisting of electricity, gas, oil, water, materials, products, artifacts and so on, from the “social metabolism” consisting of wealth, information, ideas and social capital.  By analyzing masses of data from many cities, he and his colleagues found that the social metabolism roughly follows a power law with an exponent of 1.15, while the exponent for physical metabolism is roughly 0.85.

What this means is that the larger the city, the more efficient is its infrastructure, by about 15% compared with what would be expected if all cities were equally efficient. By contrast, the social metabolism on average grows at a rate of about 15% greater than expected as cities get bigger. This means that the vitality and creativity of a city (as well as stress and crime) grow faster than expected as cities grow larger. In other words, after providing regular maintenance, the city’s physical metabolism provides a substantial residual of energy for growth. Quoting the author (p. 374) “The bigger the city, 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.” He goes on to discuss how specific cities differ from the average (for example, Corvallis Oregon greatly exceeds the number of patents expected for a city of its size while New York lags well behind expectation).

In the last chapter, he picks up the thread of superexponential growth. The scaling laws for various characteristics of animals (such as metabolism) all had sublinear exponents, meaning that they grew slower at various rates than would be expected if they increased proportionally with size). But cities are growing faster than expected. Analyzed mathematically, such growth leads to a finite time singularity. While exponential growth goes to infinity, but at some infinite time, superexponential growth goes to infinity at a specific time. Analysis by his colleagues estimate that in a growth as usual scenario the cut-off date is around 2045 – 2050.

West goes on to show that periodic innovations have “reset the clock,” effectively postponing the date certain for the system to stagnate and collapse. For example, Malthus’ expectation of imminent starvation was made obsolete by improvements in agriculture, although we may have finally run out of options for improvement (or even maintaining the status quo). However, to keep the wolf from the door, these innovations must occur at closer and closer intervals. At some point the interval between needed innovations become impractically small and the system stagnates and collapses, just somewhat later than without the innovations. Looking at how long it has taken us to make solar and wind energy practical (around 40 years), I personally think we are past the time when we can create technological innovations fast enough to stave off the singularity, for the reason that we have picked the low-hanging fruit, and important innovations may  now take longer than before.

Here I want to fall back on quotes from the book, which express the issues much better than I could summarize then:

P. 424 We live our lives on the metaphorical accelerating socioeconomic treadmill. A major innovation that might have taken hundreds of years to evolve a thousand or more years ago may now take only thirty years. Soon it will have to take twenty-five, then twenty, then seventeen, and so on, and like Sisyphus we are destined to go on doing it, if we insist on continually growing and expanding. The resulting sequence of singularities, each of which threatens stagnation and collapse, will continue to pile up, leading to what mathematicians call an essential singularity – a sort of mother of all singularities.

The great John von Neumann…made the following remarkably prescient observation more than seventy years ago: “The ever accelerating progress of technology and changes in the mode of human life…gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.”

P.425 The increasingly rapid rate of change induces serious stress on all facets of urban life. This is surely not sustainable, and, if nothing changes, we are heading for a major crash and a potential collapse of the entire socioeconomic fabric. The challenges are clear: Can we return to an analog of a more “ecological” phase from which we evolved and be satisfied with some version of sublinear scaling and its attendant natural limiting, or no-growth, stable configuration? Is this even possible?

West acknowledges that many other factors will influence the outcome: he has concentrated on things he can measure, like any good scientist, and discovered unexpected regularities that lead to useful predictions. Climate change, pollution, extinction, pandemics, political and religious turmoil, superstition, corruption,  and so on will obviously have a huge role to play in the outcome, and only the first four can be measured to any useful extent. But taking his results as a sound analysis of one aspect of the problem – availability of energy and resources – it is sobering to realize that even this very restricted slice of a hugely complex system yields a familiar result: we must totally revise our expectations or watch civilization collapse around us. I am not optimistic that we can pull this off, and I believe West’s view is not far from mine.

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