The elegant law that governs us all
Adog owner weighs twice as much as her German shepherd. Does she at twice as much? Does a big city need twice as many gas stations as one that is half its size? Our first instinct is to say yes. But, alas, we
are wrong. On a per-gram basis, a human
requires about 25% less food than her dog,
and the larger city needs only 85% more
If we double the population of a city, we
also need roughly 15% fewer water pipes and
electrical wires than linear thinking would
predict. In other words, if you wish to live in
a green city, you should forget bucolic rural
settlements and consider Manhattan instead.
Moving to a city that’s twice as big will
not only offer you 15% more income on 15%
less infrastructure, you’ll also be 15% more
likely to patent an invention. It is perhaps
no surprise, then, that Boston, San Francisco, and New York City have emerged as
the unbeatable incubators of creativity.
As Geoffrey West explains in Scale, the
reason behind these intriguing phenomena
is a universal law known as allometry—the
finding that as organisms, cities, and companies grow, many of their characteristics
West is a theoretical physicist who traded
in particle physics for complex systems in
1997. He eventually landed at the Santa Fe
Institute, a hotbed of complexity research,
where he became an eloquent spokesman
on behalf of his newfound subject.
Allometric scaling has deep roots in ecology, dating back to the century-old work of
J. B. S. Haldane, D’Arcy Thompson, and Julian Huxley. Yet, for about a century, it remained a puzzling empirical observation.
This changed two decades ago when West
and collaborators offered the first quantitative explanation of allometric scaling.
With that came a newfound enthusiasm toward the subject as researchers began discovering its relevance to everything from
cities to companies.
Scale offers a fascinating journey into the
genesis, applications, and implications of al-
lometric scaling. Did you know, for example,
that regardless of size, all animals have
about 1.5 billion heartbeats in their lifetime?
And that thanks to this, the bigger an ani-
mal, the longer it lives? Only humans defy
this law, living twice as long as allometric
scaling predicts for our weight.
Readers also learn that, on average, peo-
ple commute about an hour each
day, regardless of city size or mode
of transportation. Our walking
speed, however, depends on the
size of the city we live in: Big-city
residents walk twice as fast as the
locals of small towns, sometimes
creating logjams when the two
populations attempt to traverse
the same streets. This observa-
tion prompted the British city of
Liverpool to create fast walking
lanes, offering an unobstructed
path for city dwellers through the masses of
West’s enduring contribution to our
understanding of complex systems is his
explanation of the roots of allometric scal-
ing. He observes that complex systems—
from cells to cities—require networks to
ensure that every component has access to
the resources needed. These networks have
evolved to optimally transport resources,
minimizing, for example, the energy our
hearts exert to circulate blood or the time
we spend traveling from work to home. In
Scale, West patiently describes these foun-
dational observations, eventually arriving
at the scaling laws that have resisted expla-
nation for more than a century.
Given the central role that networks play
in West’s theoretical framework, it is puz-
zling the degree to which the narrative is
divorced from network science, the field that
focuses on the scaling properties of real net-
works. For example, a universal
feature of all networks discussed
in the book—from the metabolic
network that supplies energy to a
cell, to the social and professional
networks that contribute to the
amazing vitality of a big city—is
the presence of major hubs that
hold the smaller nodes together.
Yet the scale-free property of
these networks, which explains
how the size of these hubs scales
with the number of nodes in the
system, is never considered in allometry.
Scale offers a deeply personal narrative
about the origins and evolution of allometric
scaling that is enriched by West’s distinctive
voice. It’s a journey with many fascinating digressions that do make the nearly 500-page
book a true time investment. Yet, for those
willing to commit, West’s insightful analysis and astute observations patiently build
an intellectual framework that is ultimately
highly rewarding, offering a new perspective
on the many scales with which nature and
society challenge us. j
The reviewer is at the Network Science Institute,
Northeastern University, Boston, MA 02115, USA.
2017. 490 pp.
The metabolic rate of an animal that is twice the size of another is only approximately 75% greater than
that of the smaller creature, an example of allometric scaling known as Kleiber’s law.
A physicist probes a phenomenon seen in cells, cities, and almost everything in between
INSIGHTS | BOOKS
By Albert-László Barabási