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

Blair Fix

![](https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2021/10/west_cover_2.jpg?w=200&ssl=1){decoding="async"
style="float:right; padding-left: 10px;" recalc-dims="1"}

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](#fig-kleiber) (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.

[]{#fig-kleiber}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2021/10/kleiber_edit.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 1: The scaling of animal metabolism with body
mass. From Scale.</figcaption>
</figure>

Eyeing Figure [1](#fig-kleiber), 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:

::: {style="text-align:center"}
[ \displaystyle \text{metabolic rate} \propto
\text{mass}\^{3/4}]{.katex-eq katex-display="false"}
:::

This metabolic scaling is called [Kleiber's
law](https://en.wikipedia.org/wiki/Kleiber%27s_law){target="_blank"
rel="noopener"}, 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*](https://en.wikipedia.org/wiki/Fantastic_Voyage){target="_blank"
rel="noopener"}.) 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'](https://economicsfromthetopdown.com/2021/08/12/the-evolution-of-big-how-sociality-made-life-larger/){target="_blank"
rel="noopener"}.)

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 {#when-the-universal-is-not-universal target="_blank"}

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'](https://www.pnas.org/content/116/43/21616){target="_blank"
rel="noopener"}, Ian Hatton and colleagues look at metabolic scaling
across all life on Earth. They find that Kleiber's law does not hold.
Figure [2](#fig-hatton) 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.

[]{#fig-hatton}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2021/10/hatton.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 2: Metabolic scaling across all non-plant
life. Data is from Hatten et al (2019). The dashed line is
‘Kleiber’s law’ — the scaling of metabolism with the 3/4 power of mass.
It holds for mammals and birds, but nowhere else. The dark line is the
regression across all species, which is nearly linear (the slope is
0.96.)</figcaption>
</figure>

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](#fig-hatton) 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](https://platosrealm.blog/2020/05/05/the-hubble-tension-a-sign-of-new-physics-in-cosmology/){target="_blank"
rel="noopener"}).

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](https://www.astro.princeton.edu/~burrows/classes/542/papers/Lachlan.West_Brown_Enquist_1997.pdf){target="_blank"
rel="noopener"}.) 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' {#conflating-patents-with-innovation target="_blank"}

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](#fig-patents) 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.

[]{#fig-patents}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2021/10/patents_edit.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 3: The number of patents scales superlinearly
with city size. From Scale.</figcaption>
</figure>

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](https://economicsfromthetopdown.com/2021/03/17/why-are-most-textbooks-still-proprietary/){target="_blank"
rel="noopener"}.

With that in mind, we could turn West's claim about innovation on its
head. To echo [Tim Di
Muzio](https://bnarchives.yorku.ca/530/){target="_blank"
rel="noopener"}, 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' {#income-not-productivity target="_blank"}

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

[]{#fig-firms}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2021/10/wages_edit.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 4: US wages scale superlinearly with city
size. From Scale.</figcaption>
</figure>

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](https://economicsfromthetopdown.com/2019/11/14/productivity-does-not-explain-wages/){target="_blank"
rel="noopener"}. So the claim that income reveals productivity is an
[empty
tautology](https://economicsfromthetopdown.com/2019/07/08/no-productivity-does-not-explain-income/){target="_blank"
rel="noopener"}. 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](https://en.wikipedia.org/wiki/Stettler%2C_Alberta){target="_blank"
rel="noopener"} 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 {#firm-foibles target="_blank"}

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](#fig-firms)
shows his data. The bracketed numbers show the scaling exponents, which
are all less than one, indicating sublinear scaling.

[]{#fig-firms}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2021/10/firm_scale_edit.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 4: Firm income scales sublinearly with
employment. From Scale.</figcaption>
</figure>

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 {#firm-survivorship target="_blank"}

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.

[]{#fig-survive}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2021/10/firm_survive_edit.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 6: Firm survival over time. From
Scale.</figcaption>
</figure>

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](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0171823){target="_blank"
rel="noopener"} has shown that firm survival tends to vary by energy
consumption. As Figure [7](#fig-age-energy) 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.

[]{#fig-age-energy}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2021/10/firm_age.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 7: As societies consume more energy, the
portion of young firms tends to decrease. Data is from <a
href="https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0171823"
target="_blank" rel="noopener">‘Energy and Institution
Size’</a>.</figcaption>
</figure>

### Yes, read *Scale*. No, don't believe everything it says. {#yes-read-scale.-no-dont-believe-everything-it-says. target="_blank"}

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.

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.

Messaggi di Rogue Scholar

A Review of Geoffrey West’s ‘Scale’