For several years, people have been urging me to read Geoffrey West’s book Scale, claiming that his work overlaps with my own. Having read the book, I largely agree (with some caveats below).

Geoffrey West is a physicist who’s become famous for studying ‘scaling’ effects across life on Earth. What is ‘scaling’? It’s best explained through an example. Figure 1 (taken from West’s book) shows how animals’ metabolism varies with body mass. Given the tight relation, scientists say that metabolic rate ‘scales’ with body mass.

Eyeing Figure 1, you might think that metabolism grows linearly with mass … after all, the relation is a straight line. But notice that both the x and y axes use logarithmic scales. When you see a straight line on a double-log plot, the slope of the line actually translates to an exponent. In this case, the slope is 3/4, meaning metabolic rate scales with the 3/4 power of mass:

This metabolic scaling is called Kleiber’s law, and it’s one of the key elements of West’s book. (Unfortunately, as we’ll see below, it’s not actually a universal law.)

As the name suggests, Scale is full of these scaling relations. On that front, the book is worth reading for the data alone. I can’t think of another popular science book that presents so much data. All told, Scale packs a whopping 81 figures.

Continuing with the strengths of the book, West’s writing is clear and accessible. And he does a good job of tracing the origins of his ideas. For instance, it is common knowledge among physicists that when you scale up the size of an object, its properties change. That’s because the volume of the object (which determines mass) grows faster than its cross-section area (which determines strength). (I think I first encountered this idea in Isaac Asimov’s Fantastic Voyage.) Reading Scale, I was surprised to find that this idea was first articulated by Galileo in the 17th century. (That’s a fun fact I would like to have included in my recent essay, The Evolution of ‘Big’.)

Another strength of the book (in my mind) is that West is an unabashed empiricist. On that note, hidden in one of West’s footnotes is this gem from Albert Einstein:

Propositions arrived at by purely logical means are completely empty as regards reality.

To have merit, Einstein implies, logical propositions must be tested against evidence. West agrees with Einstein, as do I.

Trained as a physicist, West is at his best when talking about physical processes. Like most physicists, he identifies the flow of energy as the root driver of complexity. West is weakest when discussing social systems. I agree with him that energy is the basis of human society. Yet I find his worldview a bit too mechanistic. Still, I recommend the book.

When the universal is … not universal

Now to my qualms with Scale. The task of writing a popular book on science is to simplify and generalize, while at the same time not over-simplifying or over-generalizing. It is a difficult act to balance. But overall, West does a good job.

Still, there are places where he oversteps. In particular, I find that West has a bias for ‘universality’. West and I agree that a basic part of doing science is to find similarities that underlie differences. Indeed, discovering a scaling relation that extends across disparate entities is exhilarating … even intoxicating. And for that reason, you must be careful. ‘Universality’ is an extremely strong claim that must be backed by extremely strong evidence. On that front, I think West overstates his case.

In particular, readers should be aware that West’s prime example of a universal scaling relation — Kleiber’s law, the scaling of metabolic rate with the 3/4 power of mass — is not universal. It turns out to be a quirk of mammals and birds.

In their paper ‘Linking scaling laws across eukaryotes’, Ian Hatton and colleagues look at metabolic scaling across all life on Earth. They find that Kleiber’s law does not hold. Figure 2 shows their data relating metabolism to mass across the whole spectrum of non-plant life. The dashed line shows Kleiber’s law. It works well for mammals and birds. It fails everywhere else. In fact, the trend that appears ‘universal’ is a simple linear scaling of metabolism with mass.

So here we see the perils of looking for ‘universality’. West’s generalizations about metabolic scaling come from a small subset of life. For perspective, the pink square in Figure 2 shows the range of West’s data.

Now, this kind of thing happens all the time in science. Conclusions drawn from limited data often change when the data is enlarged. When Edwin Hubble first discovered that the universe was expanding, he pegged the rate at 500 km/s per megaparsec. That’s about 7 times higher than today’s accepted rate (which interestingly enough, is still debated).

The problem comes not from being wrong, but when wrong theories become ‘canonical’. That means they live on, even when the data no longer supports them. Unfortunately, that may be the case with West’s work on metabolism. His explanation of Kleiber’s law has become famous. (He first wrote about it 2 decades ago.) Yet it turns out that Kleiber’s law is not actually a ‘law’ — it’s just a local trend. That puts West’s theory in a tough spot.

Conflating ‘patents’ with ‘innovation’

Another problem with West’s book is that when he turns his attention to human societies, he uses metrics that I consider dubious.

For instance, West measures ‘innovation’ in terms of the number of patents. As Figure 3 shows, he finds that ‘innovation’ scales ‘superlinearly’ with city population. (For every doubling of city size, patents more than double.) Thus, larger cities seem to be more innovative.

I dispute the claim that patents measure ‘innovation’. What patents actually measure is the privatization of innovation. Patents are the act of putting property rights around an idea. So they don’t measure innovation so much as they measure the restriction of new ideas.

Using patents as a proxy for innovations is similar to measuring the spread of ‘knowledge’ using textbook sales. Sure, more textbooks means more knowledge. But higher textbook sales doesn’t necessarily mean that more textbooks are being published. It could be that publishers are simply hiking textbook prices. That’s not the spread of knowledge. That’s monopolistic firms earning more profits by restricting access to knowledge.

With that in mind, we could turn West’s claim about innovation on its head. To echo Tim Di Muzio, every patent is a mini tragedy — an enclosure of knowledge that could otherwise be free. So you could argue that it is not ‘innovation’ that scales superlinearly with city size, but rather, the enclosure of the commons. That’s not something to celebrate.

Income, not ‘productivity’

Along the same lines, West shows that income scales superlinearly with city size. Here’s his data for US wages:

That’s interesting. The data tells us that income per capita increases with city size. This is actually a well-known result in urbanism literature. There is almost always an urban-rural income gap. So West generalizes this gap, which is an important thing to do. But then he does something dubious. He claims that this income data shows that productivity increases with city population.

No!

To be fair to West, he is making a mistake that is rife in economics: conflating income with productivity. The mistake dates to the 19th-century work of John Bates Clark, the founder of marginal productivity theory. In the introduction to his book The Distribution of Wealth, Clark declared that if the market worked “without friction” it would “give to every agent of production the amount of wealth which that agent creates.” Since then, the standard practice in economics is to assume that income and productivity are the same thing.

And yet they are not.

To measure productivity, you must differentiate between the quantity of what is produced and the price of this product. Unfortunately, in all but the most trivial examples, you can’t actually make this distinction. So the claim that income reveals productivity is an empty tautology. I’m sad that West falls into it.

That said, West’s income-scaling evidence is important, and it deserves an explanation. What West does not consider is that there is a power dynamic between urban and rural places. Cities are resource-sucking vacuums that, by definition, cannot support their own consumption. So it follows that they must have the power to centralize resources. Could it be that the scaling of income with city size shows this centralization power? Perhaps not, but one should at least consider the possibility.

Or what about the fact that rural folks tend to do more activities outside the market — a fact that would depress income. I grew up in a small town and never paid for a haircut until I moved to the city at 18. Prior to that, my mom cut my hair for free. That kind of thing happens less in the city. In other words, city life comes with specialization, and specialization lends itself to more market transactions, and more income. None of this has to do with productivity, at least not directly.

Firm foibles

Another area where West overstates his case is with firms. Firms, West argues, seem to be different than cities in that their various forms of income scale sublinearly with size (employment). Figure 4 shows his data. The bracketed numbers show the scaling exponents, which are all less than one, indicating sublinear scaling.

The problem is that West is drawing conclusions from a very narrow sample of companies. He’s using the Compustat database, which only includes data for public firms. But these public firms are a tiny sample of the firm universe — a sample that is highly skewed towards large, profitable firms.

In effect, West is doing the same thing that he did with animal metabolism: drawing sweeping conclusions from limited data. If West wants to draw conclusions about scaling ‘laws’ amongst firms, then he needs a representative dataset — one that includes the vast universe of small private firms. I’m guessing that if we included these firms, the scaling relations would change significantly.

Firm survivorship

For one last example of West overstating universality, take the survival of firms over time. The figure below shows West’s data, which demonstrates a remarkable similarity between firms of various size. They all ‘die off’ at a similar rate.

Of course, this data is interesting. But it doesn’t mean firm dynamics are the same everywhere. In fact they are not.

My own research has shown that firm survival tends to vary by energy consumption. As Figure 7 demonstrates, societies that use less energy per capita tend to have more young firms. So here we have another ‘scaling’ relation, but one that emphasizes difference rather than sameness.

Yes, read Scale. No, don’t believe everything it says.

Overall, my thoughts about Scale are similar to my thoughts about Thomas Piketty’s book Capital in the Twenty-First Century. Both books are worth reading for the rich trove of data they present. And both books make theoretical claims that are (in my mind) dubious.

To be fair, it is part of a scientist’s job to convince others that their ideas are correct. The tools for doing so are evidence (which West provides in droves) and good arguments. My worry is that West’s arguments (which are admittedly convincing) are more sweeping than the data warrants.

In a sense, this is a problem with all popular science books. If they are too convincing, they eventually outlive their usefulness. The ideas in a book are forever static. Yet science changes with time. Thus, the continued popularity of books like Marx’s Capital or Dawkin’s Selfish Gene is more of a burden than a boon. These books were long ago made irrelevant by new research.

On that note, a major part of West’s book — his arguments about metabolic scaling — is in danger of becoming irrelevant (or at best, far less universal than West claims). Two years after Scale was published, Hatton’s 2019 study decimated West’s theory. But given the popularity of West’s writing, I suspect that his theory will live on for a long time, evidence be damned.

Problems aside, there is much to like about Scale, and it is certainly a major contribution to science. Just don’t believe everything you read in it.

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Further reading

Di Muzio, T. (2017). The tragedy of human development. A genealogy of capital as power. Rowman & Littlefield International.

Fix, B. (2017). Energy and institution size. PLOS ONE, 12(2), e0171823.

Hatton, I. A., Dobson, A. P., Storch, D., Galbraith, E. D., & Loreau, M. (2019). Linking scaling laws across eukaryotes. Proceedings of the National Academy of Sciences, 116(43), 21616–21622.

Piketty, T. (2014). Capital in the twenty-first century. Cambridge: Harvard University Press.

West, G. B. (2017). Scale: The universal laws of growth, innovation, sustainability, and the pace of life in organisms, cities, economies, and companies. Penguin.

West, G. B., Brown, J. H., & Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science, 276(5309), 122–126.