Main Growth : from microorganisms to megacities

Growth : from microorganisms to megacities

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Growth has been both an unspoken and an explicit aim of our individual and collective striving. It governs the lives of microorganisms and galaxies; it shapes the capabilities of our extraordinarily large brains and the fortunes of our economies. Growth is manifested in annual increments of continental crust, a rising gross domestic product, a child's growth chart, the spread of cancerous cells. In this magisterial  Read more...
Year:
2019
Publisher:
The MIT Press
Language:
english
Pages:
664 / 661
ISBN 10:
0262042835
ISBN 13:
9780262042833
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PDF, 16.08 MB
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Growth

Previous works by author
China’s Energy
Energy in the Developing World (edited with W. Knowland)
Energy Analy­sis in Agriculture (with P. Nachman and T. V. Long II)
Biomass Energies
The Bad Earth
Carbon Nitrogen Sulfur
Energy Food Environment
Energy in China’s Modernization
General Energetics
China’s Environmental Crisis
Global Ecol­ogy
Energy in World History
Cycles of Life
Energies
Feeding the World
Enriching the Earth
The Earth’s Biosphere
Energy at the Crossroads
China’s Past, China’s ­Future
Creating the 20th ­Century
Transforming the 20th ­Century
Energy: A Beginner’s Guide
Oil: A Beginner’s Guide
Energy in Nature and Society
Global Catastrophes and Trends
Why Amer­i­ca Is Not a New Rome
Energy Transitions
Energy Myths and Realities
Prime Movers of Globalization
Japan’s Dietary Transition and Its Impacts (with K. Kobayashi)
Harvesting the Biosphere
Should We Eat Meat?
Power Density
Natu­ral Gas
Still the Iron Age
Energy Transitions (new edition)
Energy: A Beginner’s Guide (new edition)
Energy and Civilization: A History
Oil: A Beginner’s Guide (new edition)

Growth
From Microorganisms to Megacities

Vaclav Smil

The MIT Press
Cambridge, Mas­sa­chu­setts
London, ­England

© 2019 Mas­sa­chu­setts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form by any
electronic or mechanical means (including photocopying, recording, or information
storage and retrieval) without permission in writing from the publisher.
This book was set in Stone Serif and Stone Sans by Westchester Publishing Ser­vices.
Printed and bound in the United States of Amer­i­ca.
Library of Congress Cataloging-in-Publication Data
Names: Smil, Vaclav, author.
Title: Growth / Vaclav Smil.
Description: Cambridge, MA : The MIT Press, 2019. | Includes bibliographical references and index.
Identifiers: LCCN 2018059356 | ISBN 9780262042833 (hardcover : alk. paper)
Subjects: LCSH: Civilization, Modern—21st century. | Technology and civilization. | Growth. | Human ecology. | Population. | Energy;  development. | Economic
­development. | Cities and towns—Growth. | Urban ecology (Sociology).
Classification: LCC CB428 .S625 2019 | DDC 909.82—dc23
LC record available at https://lccn.loc.gov/2018059356
10 ​9 ​8 ​7 ​6 ​5 ​4 ​3 ​2 ​1

Contents

Preface vii
1

Trajectories: or common patterns of growth 1
Time Spans 3
Figures of Merit 6
Linear and Exponential Growth 12
Confined Growth Patterns 31
Collective Outcomes of Growth 54

2

Nature: or growth of living m
­ atter 71
Microorganisms and Viruses
Trees and Forests 95
Crops 111
Animals 129
­Humans 151

3

76

Energies: or growth of primary and secondary converters 173
Harnessing ­Water and Wind 176
Steam: Boilers, Engines, and Turbines
Internal Combustion Engines 197
Nuclear Reactors and PV Cells 213
Electric Lights and Motors 217

4

184

Artifacts: or growth of man-­made objects and
their per­for­mances 225
Tools and ­Simple Machines
Structures 239
Infrastructures 252

228

vi

Contents

Transportation 266
Electronics 284

5

Populations, Socie­ties, Economies: or growth of the most complex
assemblies 303
Populations 307
Cities 332
Empires 357
Economies 375
Civilizations 436

6

What Comes ­After Growth: or demise and continuity 449
Life Cycles of Organisms 454
Retreat of Artifacts and Pro­cesses
Populations and Socie­ties 470
Economies 490
Modern Civilization 498

460

Coda 509
Abbreviations 515
Scientific Units and Their Multiples and Submultiples 519
References 521
Index 621

Preface

Growth is an omnipresent protean real­ity of our lives: a marker of evolution, of an increase in size and capabilities of our bodies as we reach adulthood, of gains in our collective capacities to exploit the Earth’s resources
and to or­ga­nize our socie­ties in order to secure a higher quality of life.
Growth has been both an unspoken and an explicit aim of individual and
collective striving throughout the evolution of our species and its still short
recorded history. Its pro­gress governs the lives of microorganisms as well as
of galaxies. Growth determines the extent of oceanic crust and utility of all
artifacts designed to improve our lives as well as the degree of damage any
abnormally developing cells can do inside our bodies. And growth shapes
the capabilities of our extraordinarily large brains as well as the fortunes
of our economies. B
­ ecause of its ubiquity, growth can be studied on levels
ranging from subcellular and cellular (to reveal its metabolic and regulatory
requirements and pro­cesses) to tracing long-­term trajectories of complex
systems, be they geotectonic upheavals, national or global populations, cities,
economies or empires.
Terraforming growth—­geotectonic forces that create the oceanic and
continental crust, volcanoes, and mountain ranges, and that shape watersheds, plains, and coasts—­proceeds very slowly. Its prime mover, the formation of new oceanic crust at mid-­ocean ridges, advances mostly at rates of
less than 55 mm/year, while exceptionally fast new sea-­floor creation can
reach about 20 cm/year (Schwartz et al. 2005). As for the annual increments
of continental crust, Reymer and Schubert (1984) calculated the addition
rate of 1.65 km3 and with the total subduction rate (as the old crust is recycled into the mantle) of 0.59 km3 that yields a net growth rate of 1.06 km3.
That is a minuscule annual increment when considering that the continents cover nearly 150 Gm2 and that the continental crust is mostly
35–40 km thick, but such growth has continued during the entire Phanerozoic eon, that is for the past 542 million years. And one more, this time

viii

Preface

Figure 0.1
Slow but per­sis­tent geotectonic growth. The Himalayas ­were created by the collision of
Indian and Eurasian plates that began more than 50 million year ago and whose continuation now makes the mountain chain grow by as much as 1 cm/year. Photo from
the International Space Station (looking south from above the Tibetan Plateau) taken
in January 2004. Image available at https://­www​.­nasa​.­gov​/­multimedia​/­imagegallery​
/­image​_­feature​_­152​.­html.

vertical, example of inevitably slow tectonic speeds: the uplift of the
Himalayas, the planet’s most imposing mountain range, amounts to about
10 mm/year (Burchfiel and Wang 2008; figure 0.1). Tectonic growth fundamentally constrains the Earth’s climate (as it affects global atmospheric
circulation and the distribution of pressure cells) and ecosystemic productivity (as it affects temperature and precipitation) and hence also h
­ uman
habitation and economic activity. But ­there is nothing we can do about its
timing, location, and pace, nor can we harness it directly for our benefit
and hence it ­will not get more attention in this book.
Organismic growth, the quin­tes­sen­tial expression of life, encompasses
all pro­cesses by which ele­ments and compounds are transformed over time
into new living mass (biomass). ­Human evolution has been existentially
dependent on this natu­ral growth, first just for foraged and hunted food,
­later for fuel and raw materials, and eventually for cultivated food and
feed plants and for large-­scale exploitation of forest phytomass as well as
for the capture of marine species. This growing h
­ uman interference in the

Preface

ix

biosphere has brought a large-­scale transformation of many ecosystems,
above all the conversion of forests and wetlands to croplands and extensive
use of grassland for grazing animals (Smil 2013a).
Growth is also a sign of pro­gress and an embodiment of hope in ­human
affairs. Growth of technical capabilities has harnessed new energy sources,
raised the level and reliability of food supply, and created new materials
and new industries. Economic growth has brought tangible material gains
with the accumulation of private possessions that enrich our brief lives, and
it creates intangible values of accomplishment and satisfaction. But growth
also brings anx­ie­ ties, concerns, and fears. ­People—be it ­children marking
their increasing height on a door frame, countless chief economists preparing dubious forecasts of output and trade per­for­mance, or radiologists looking at magnetic resonance images—­worry about it in myriads of dif­fer­ent
ways.
Growth is commonly seen as too slow or as too excessive; it raises concerns about the limits of adaptation, and fears about personal consequences
and major social dislocations. In response, p
­ eople strive to manage the
growth they can control by altering its pace (to accelerate it, moderate it, or
end it) and dream about, and strive, to extend t­ hese controls to additional
realms. ­These attempts often fail even as they succeed (and seemingly permanent mastery may turn out to be only a temporary success) but they
never end: we can see them pursued at both extreme ends of the size spectrum as scientist try to create new forms of life by expanding the ge­ne­tic code
and including synthetic DNA in new organisms (Malyshev et al. 2014)—as
well as proposing to control the Earth’s climate through geoengineering
interventions (Keith 2013).
Organismic growth is a product of long evolutionary pro­cess and modern science has come to understand its preconditions, pathways, and outcomes and to identify its trajectories that conform, more or less closely, to
specific functions, overwhelmingly to S-­shaped (sigmoid) curves. Finding
common traits and making useful generalizations regarding natu­ral growth
is challenging but quantifying it is relatively straightforward. So is mea­sur­
ing the growth of many man-­made artifacts (tools, machines, productive
systems) by tracing their increase in capacity, per­for­mance, efficiency, or
complexity. In all of t­ hese cases, we deal with basic physical units (length,
mass, time, electric current, temperature, amount of substance, luminous
intensity) and their numerous derivatives, ranging from volume and speed
to energy and power.
Mea­sur­ing the growth phenomena involving ­human judgment, expectations, and peaceful or violent interactions with o
­ thers is much more

x

Preface

challenging. Some complex aggregate pro­
cesses are impossible to mea­
sure without first arbitrarily delimiting the scope of an inquiry and without resorting to more or less questionable concepts: mea­sur­ing the growth
of economies by relying on such variables as gross domestic product or
national income are perfect examples of t­ hese difficulties and indeterminacies. But even when many attributes of what might be called social growth
are readily mea­sur­able (examples range from the average living space per
family and possession of h
­
­ ouse­
hold appliances to destructive power of
stockpiled missiles and the total area controlled by an imperial power),
their true trajectories are still open to diverse interpretations as ­these quantifications hide significant qualitative differences.
Accumulation of material possessions is a particularly fascinating aspect
of growth as it stems from a combination of a laudable quest to improve
quality of life, an understandable but less rational response to position oneself in a broader social milieu, and a rather atavistic impulse to possess,
even to hoard. T
­ here are t­ hose few who remain indifferent to growth and
need, India’s loinclothed or entirely naked sadhus and monks belonging to
sects that espouse austere simplicity. At the other extreme, we have compulsive collectors (however refined their tastes may be) and mentally sick
hoarders who turn their abodes into garbage dumps. But in between, in any
population with rising standards of living, we have less dramatic quotidian
addictions as most p
­ eople want to see more growth, be in material terms or
in intangibles that go ­under ­those elusive labels of satisfaction with life or
personal happiness achieved through amassing fortunes or having extraordinarily unique experiences.
The speeds and scales of t­hese pursuits make it clear how modern is
this pervasive experience and how justified is this growing concern about
growth. A doubling of average sizes has become a common experience
during a single lifetime: the mean area of US h
­ ouses has grown 2.5-­fold
since 1950 (USBC 1975; USCB 2013), the volume of the United Kingdom’s
wine glasses has doubled since 1970 (Zupan et al. 2017), typical mass of
Eu­ro­pean cars had more than doubled since the post–­World War II models
(Citroen 2 CV, Fiat Topolino) weighing less than 600 kg to about 1,200kg
by 2002 (Smil 2014b). Many artifacts and achievements have seen far larger
increases during the same time: the modal area of tele­vi­sion screens grew
about 15-­fold, from the post–­World War II standard of 30 cm diagonal to
the average US size of about 120 cm by 2015, with an increasing share
of sales taken by TVs with diagonals in excess of 150 cm. And even that
impressive increase has been dwarfed by the rise of the largest individual
fortunes: in 2017 the world had 2,043 billionaires (Forbes 2017). Relative

Preface

xi

differences produced by some of t­ hese phenomena are not unpre­ce­dented,
but the combination of absolute disparities arising from modern growth
and its frequency and speed is new.
Rate of Growth
Of course, individuals and socie­ties have been always surrounded by countless manifestations of natu­ral growth, and the quests for material enrichment and territorial aggrandizement w
­ ere the forces driving socie­ties on
levels ranging from tribal to imperial, from raiding neighboring villages in
the Amazon to subjugating large parts of Eurasia u
­ nder a central rule. But
during antiquity, the medieval period, and a large part of the early ­modern
era (usually delimited as the three centuries between 1500 and 1800),
most ­people everywhere survived as subsistence peasants whose harvest
produced a l­imited and fluctuating surplus sufficient to support only a
­relatively small number of better-­off inhabitants (families of skilled c­ raftsmen
and merchants) of (mostly small) cities and secular and religious ruling
elites.
Annual crop harvests in t­hose simpler, premodern and early modern
socie­ties presented few, if any, signs of notable growth. Similarly, nearly
all fundamental variables of premodern life—be they population totals,
town sizes, longevities and literacy, animal herds, ­house­hold possessions,
and capacities of commonly used machines—­grew at such slow rates that
their pro­gress was evident only in very long-­term perspectives. And often
they ­were ­either completely stagnant or fluctuated erratically around dismal means, experiencing long spells of frequent regressions. For many of
­these phenomena we have the evidence of preserved artifacts and surviving
descriptions, and some developments we can reconstruct from fragmentary
rec­ords spanning centuries.
For example, in ancient Egypt it took more than 2,500 years (from the
age of the ­great pyramids to the post-­Roman era) to double the number of
­people that could be fed from 1 hectare of agricultural land (Butzer 1976).
Stagnant yields w
­ ere the obvious reason, and this real­ity persisted u
­ ntil
the end of the ­Middle Ages: starting in the 14th ­century, it took more than
400 years for average En­glish wheat yields to double, with hardly any gains
during the first 200 years of that period (Stanhill 1976; Clark 1991). Similarly, many technical gains unfolded very slowly. Waterwheels w
­ ere the
most power­ful inanimate prime movers of pre­industrial civilizations but
it took about 17 centuries (from the second c­ entury of the common era to
the late 18th ­century) to raise their typical power tenfold, from 2 kW to

xii

Preface

20 kW (Smil 2017a). Stagnating harvests or, at best, a feeble growth of crop
yields and slowly improving manufacturing and transportation capabilities
restricted the growth of cities: starting in 1300, it took more than three centuries for the population of Paris to double to 400,000—­but during the late
19th ­century the city doubled in just 30 years (1856–1886) to 2.3 million
(Atlas Historique de Paris 2016).
And many realities remained the same for millennia: the maximum
­distance covered daily by horse-­riding messengers (the fastest way of
­long-­distance communication on land before the introduction of railways)
was optimized already in ancient Persia by Cyrus when he linked Susa
and Sardis a
­ fter 550 BCE, and it remained largely unchanged for the next
2,400 years (Minetti 2003). The average speed of relays (13–16 km/h) and a
single animal ridden no more than 18–25 km/day remained near constant.
Many other entries belong to this stagnant category, from the possession of
­house­hold items by poor families to literacy rates prevailing among rural
populations. Again, both of ­these variables began to change substantially
only during the latter part of the early modern era.
Once so many technical and social changes—­growth of railway networks, expansion of steamship travel, rising production of steel, invention and deployment of internal combustion engines and electricity, rapid
urbanization, improved sanitation, rising life expectancy—­began to take
place at unpre­ce­dented rates during the 19th ­century, their rise created
enormous expectations of further continued growth (Smil 2005). And
­these hopes ­were not disappointed as (despite setbacks brought by the two
world wars, other conflicts, and periodic economic downturns) capabilities of individual machines, complicated industrial pro­cesses, and entire
economies continued to grow during the 20th ­century. This growth was
translated into better physical outcomes (increased body heights, higher
life expectancies), greater material security and comfort (be it mea­sured by
disposable incomes or owner­ship of labor-­easing devices), and unpre­ce­
dented degrees of communication and mobility (Smil 2006b).
Nothing has embodied this real­ity and hope during recent de­cades as
prominently as the growth in the number of transistors and other components that we have been able to emplace on a silicon wafer. Widely known
as conforming to Moore’s law, this growth has seen the number of components roughly double ­every two years: as a result, the most power­ful microchips made in 2018 had more than 23 billion components, seven o
­ rders
of magnitude (about 10.2 million times to be more exact) greater than the
first such device (Intel’s 4004, a 4-­bit pro­cessing unit with 2,300 components for a Japa­nese calculator) designed in 1971 (Moore 1965, 1975; Intel

Preface

xiii

100,000,000,000

Stratix 10
10,000,000,000

SPARC M7

Nehalem

number of components

1,000,000,000

100,000,000

Pentium M
Pentium III

10,000,000

1,000,000

100,000

8088
10,000

4004
1,000
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

2020

Figure 0.2
A quin­tes­sen­tial marker of modern growth: Moore’s law, 1971–2018. Semi-­logarithmic
graph shows steady exponential increase from 103 to 1010 components per microchip
(Smil 2017a; IBM 2018b).

2018; Graphcore 2018). As in all cases of exponential growth (see chapter 1), when t­ hese gains are plotted on a linear graph they produce a steeply
ascending curve, while a plot on a semilogarithmic graph transforms them
into a straight line (figure 0.2).
This pro­gress has led to almost unbounded expectations of still greater
advances to come, and the recent rapid diffusion of assorted electronic
devices (and applications they use) has particularly mesmerized ­
those
uncritical commentators who see omnipresent signs of accelerated growth.
To give just one memorable recent example, a report prepared by Oxford
Martin School and published by Citi claims the following time spans ­were
needed to reach 50 million users: telephone 75 years, radio 38 years, TV
13 years, Internet four years, and Angry Birds 35 days (Frey and Osborne
2015). ­These claims are attributed to Citi Digital Strategy Team—­but the
team failed to do its homework and ignored common sense.
Are ­these numbers referring to global or American diffusions? The report
does not say, but the total of 50 million clearly refers to the United States
where that number of telephones was reached in 1953 (1878 + 75 years):
but the number of telephones does not equal the total number of their
users, which, given the average size of families and the ubiquity of phones
in places of work, had to be considerably higher. TV broadcasting did not

xiv

Preface

have just one but a number of beginnings: American transmission, and
sales of first sets, began in 1928, but 13 years ­later, in 1941, TV owner­
ship was still minimal, and the total number of TV sets (again: devices, not
users) reached 50 million only in 1963. The same error is repeated with the
Internet, to which millions of users had access for many years at universities, schools, and workplaces before they got a home connection; besides,
what was the Internet’s “first” year?
All that is just sloppy data gathering, and an uninformed rush to make
an impression, but more impor­tant is an indefensible categorical error made
by comparing a complex system based on a new and extensive infrastructure with an entertaining software. Telephony of the late 19th ­century was
a pioneering system of direct personal communication whose realization
required the first large-­scale electrification of society (from fuel extraction to
thermal generation to transmission, with large parts of rural Amer­ic­ a having
no good connections even during the 1920s), installation of extensive wired
infrastructure, and sales of (initially separate) receivers and speakers.
In contrast, Angry Birds or any other inane app can spread in a viral
fashion b
­ ecause we have spent more than a ­century putting in place the
successive components of a physical system that has made such a diffusion
pos­si­ble: its growth began during the 1880s with electricity generation and
transmission and it has culminated with the post-2000 wave of designing
and manufacturing billions of mobile phones and installing dense networks
of cell towers. Concurrently the increasing reliability of its operation makes
rapid diffusion feats unremarkable. Any number of analogies can be offered
to illustrate that comparative fallacy. For example, instead of telephones
think of the diffusion of micro­wave ovens and instead of an app think
of mass-­produced microwavable popcorn: obviously, diffusion rates of the
most popu­lar brand of the latter ­will be faster than ­were the adoption rates
of the former. In fact, in the US it took about three de­cades for countertop
micro­wave ovens, introduced in 1967, to reach 90% of all h
­ ouse­holds.
The growth of information has proved equally mesmerizing. ­There is
nothing new about its ascent. The invention of movable type (in 1450)
began an exponential rise in book publishing, from about 200,000 volumes during the 16th ­century to about 1 million volumes during the 18th
­century, while recent global annual rate (led by China, the US, and the
United Kingdom) has surpassed 2 million titles (UNESCO 2018). Add to this
pictorial information whose growth was affordably enabled first by lithography, then by rotogravure, and now is dominated by electronic displays
on mobile devices. Sound recordings began with Edison’s fragile phonograph in 1878 (Smil 2018a; figure 0.3) and their enormous se­lection is now

Preface

xv

Figure 0.3
Thomas A. Edison with his phonograph photographed by Mathew Brady in April 1878.
Photo­graph from Brady-­Handy Collection of the Library of Congress.

xvi

Preface

effortlessly accessible to billions of mobile phone users. And information
flow in all t­ hese categories is surpassed by imagery incessantly gathered by
entire fleets of spy, meteorological, and Earth observation satellites. Not
surprisingly, aggregate growth of information has resembled the hyperbolic
expansion trajectory of pre-1960 global population growth.
Recently it has been pos­si­ble to claim that 90% or more of all the extant
information in the world has been generated over the preceding two years.
Seagate (2017) put total information created worldwide at 0.1 zettabytes
(ZB, 1021) in 2005, at 2 ZB in 2010, 16.1 ZB in 2016, and it expected that
the annual increment ­will reach 163 ZB by 2025. A year ­later it raised its
estimate of the global datasphere to 175 ZB by 2025—­and expected that
the total ­will keep on accelerating (Reinsel et al. 2018). But as soon as one
considers the major components of this new data flood, ­those accelerating
claims are hardly impressive. Highly centralized new data inflows include
the incessant movement of electronic cash and investments among major
banks and investment h
­ ouses, as well as sweeping monitoring of telephone
and internet communications by government agencies.
At the same time, billions of mobile phone users participating in social
media voluntarily surrender their privacy so data miners can, without
asking anybody a single question, follow their messages and their web-­
clicking, analyzing the individual personal preferences and foibles they
reveal, comparing them to ­those of their peers, and packaging them to be
bought by advertisers in order to sell more unneeded junk—­and to keep
economic growth intact. And, of course, streams of data are produced
incessantly simply by p
­ eople carry­ing GPS-­enabled mobile phones. Add to
this the flood of inane images, including myriads of selfies and cat videos
(even stills consume bytes rapidly: smartphone photos take up commonly
2–3 MB, that is 2–3 times more than the typescript of this book)—­and
the unpre­ce­dented growth of “information” appears more pitiable than
admirable.
And this is one of the most consequential undesirable consequences of
this information flood: time spent per adult user per day with digital media
doubled between 2008 and 2015 to 5.5 hours (eMarketer 2017), creating
new life forms of screen zombies. But the rapid diffusion of electronics and
software are trivial m
­ atters compared to the expected ultimate achievements of accelerated growth—­
and nobody has expressed them more
expansively than Ray Kurzweil, since 2012 the director of engineering at
Google and long before that the inventor of such electronic devices as the
charged-­couple flat-­bed scanner, the first commercial text-­to-­speech synthesizer, and the first omnifont optical character recognition.

Preface

xvii

In 2001 he formulated his law of accelerating returns (Kurzweil 2001, 1):
An analy­sis of the history of technology shows that technological change is exponential, contrary to the common-­sense “intuitive linear” view. So we w
­ on’t experience 100 years of pro­gress in the 21st ­century—it ­will be more like 20,000 years of
pro­gress (at ­today’s rate). The “returns,” such as chip speed and cost-­effectiveness,
also increase exponentially. T
­ here’s even exponential growth in the rate of exponential growth. Within a few de­cades, machine intelligence w
­ ill surpass h
­ uman
intelligence, leading to The Singularity—­
technological change so rapid and
profound it represents a rupture in the fabric of h
­ uman history. The implications include the merger of biological and nonbiological intelligence, immortal
software-­based ­humans, and ultra-­high levels of intelligence that expand outward
in the universe at the speed of light.

In 2005 Kurzweil published The Singularity Is Near—it is to come in 2045, to
be exact—­and ever since he has been promoting ­these views on his website,
Kurzweil Accelerating Intelligence (Kurzweil 2005, 2017). ­There is no doubt,
no hesitation, no humility in Kurzweil’s categorical ­grand pronouncements
­because according to him the state of the biosphere, whose functioning is a
product of billions of years of evolution, has no role in our f­utures, which
are to be completely molded by the surpassing mastery of machine intelligence. But as dif­fer­ent as our civilization may be when compared to any
of its pre­de­ces­sors, it works within the same constraint: it is nothing but a
subset of the biosphere, that relatively very thin and both highly resilient
and highly fragile envelope within which carbon-­based living organisms
can survive (Vernadsky 1929; Smil 2002). Inevitably, their growth, and for
higher organisms also their cognitive and behavioral advances, are fundamentally l­imited by the biosphere’s physical conditions and (wide as it
may seem by comparing its extremes) by the restricted range of metabolic
possibilities.
Studies of Growth
Even when l­ imited to our planet, the scope of growth studies—­from ephemeral cells to a civilization supposedly racing t­ oward the singularity—is too
vast to allow a truly comprehensive single-­volume treatment. Not surprisingly, the published syntheses and overviews of growth pro­cesses and of
their outcomes have been restricted to major disciplines or topics. The g
­ reat
classic of growth lit­er­a­ture, D’Arcy Went­worth Thompson’s On Growth and
Form (whose original edition came out it in 1917 and whose revised and
much expanded form appeared in 1942) is concerned almost solely with
cells and tissues and with many parts (skele­tons, shell, horns, teeth, tusks)

xviii

Preface

of animal bodies (Thompson 1917, 1942). The only time when Thompson
wrote about nonbiogenic materials or man-­made structures (metals, girders, bridges) was when he reviewed the forms and mechanical properties of
such strong biogenic tissues as shells and bones.
The Chemical Basis of Growth and Senescence by T. B. Robertson, published
in 1923, delimits its scope in the book’s title (Robertson 1923). In 1945,
another comprehensive review of organismic growth appeared, Samuel
Brody’s Bioenergetics and Growth, whose content was specifically focused
on the efficiency complex in domestic animals (Brody 1945). In 1994, Robert Banks published a detailed inquiry into Growth and Diffusion Phenomena,
and although this excellent volume provides numerous examples of specific
applications of individual growth trajectories and distribution patterns in
natu­ral and social sciences and in engineering, its principal concern is captured in its subtitle as it deals primarily (and in an exemplarily systematic
fashion) with mathematical frameworks and applications (Banks 1994).
The subtitle of an edited homage to Thompson (with the eponymous
title, On Growth and Form) announced the limits of its inquiry: Spatio-­
temporal Pattern Formation in Biology (Chaplain et al. 1999). As diverse as its
chapters are (including pattern formations on butterfly wings, in cancer,
and in skin and hair, as well as growth models of capillary networks and
wound healing), the book was, once again, about growth of living forms.
And in 2017 Geoffrey West summed up de­cades of his inquiries into universal laws of scaling—­not only of organisms but also cities, economies, and
companies—in a book titled Scale that listed all of ­these subjects in its long
subtitle and whose goal was to discern common patterns and even to offer
the vision of a ­grand unified theory of sustainability (West 2017).
Components of organic growth, be they functional or taxonomic, have
received much attention, and comprehensive treatments deal with cellular growth (Studzinski 2000; Morgan 2007; Verbelen and Vissenberg 2007;
Golitsin and Krylov 2010), growth of plants (Morrison and Morecroft 2006;
Vaganov et al. 2006; Burkhart and Tomé 2012; Gregory and Nortcliff 2013),
and animals (Batt 1980; Campion et al. 1989; Gerrard and Grant 2007; Parks
2011). As expected, t­here is an enormous body of knowledge on h
­ uman
growth in general (Ulijaszek et al. 1998; Bogin 1999; Hoppa and Fitzgerald
1999; Roche and Sun 2003; Hauspie et al. 2004; Tanner 2010; Floud et al.
2011; Fogel 2012).
Healthy growth and nutrition in c­ hildren have received par­tic­u­lar attention, with perspectives ranging from anthropometry to nutrition science,
and from pediatrics and physiology to public health (Martorell and Haschke
2001; Hochberg 2011; Hassan 2017). Malthus (1798) and Verhulst (1845,

Preface

xix

1847) published pioneering inquiries into the nature of population growth,
whose modern evaluations range from Pearl and Reed (1920) and Carr-­
Saunders (1936) to Meadows et al. (1972), Keyfitz and Flieger (1991), Hardin (1992), Cohen (1995), Stanton (2003), Lutz et al. (2004), and numerous
reviews and projections published by the United Nations.
Modern economics has been preoccupied with the rates of output, profit,
investment, and consumption growth. Consequently, t­ here is no shortage
of inquiries pairing economic growth and income (Kuznets 1955; Zhang
2006; Piketty 2014), growth and technical innovation (Ruttan 2000; Mokyr
2002, 2009, 2017; van Geenhuizen et al. 2009), growth and international
trade (Rodriguez and Rodrik 2000; Busse and Königer 2012; Eu­ro­pean Commission 2014), and growth and health (Bloom and Canning 2008; Barro
2013). Many recent studies have focused on links between growth and corruption (Mo 2001; Méndez and Sepúlveda 2006; Bai et al. 2014) and growth
and governance (Kurtz and Schrank 2007; OECD 2016).
Publications are also dispensing advice on how to make all economic
growth sustainable (WCED 1987; Schmandt and Ward 2000; Daly and
­Farley 2010; Enders and Remig 2014) and equitable (Mehrotra and Delamonica 2007; Lavoie and Stockhammer 2013). As already noted, the long
life of Moore’s law has focused interest on the growth of computational
capabilities but, inexplicably, ­there are no comprehensive book-­length
studies on the growth of modern technical and engineering systems, such
as long-­term analyses of capacity and per­for­mance growth in extractive
activities and energy conversions. And even when including papers, ­there
is only a ­limited number of publications dealing explic­itly with the growth
of states, empires, and civilizations (Taagepera 1978, 1979; Turchin 2009;
Marchetti and Ausubel 2012).
What Is (and Is Not) in This Book
The impossibility of a truly comprehensive account of growth in nature and
society should not be an excuse for the paucity of broader inquiries into the
modalities of growth. My intent is to address this omission by examining
growth in its many natu­ral, social, and technical forms. In order to cover
such a wide sweep, a single volume must be restricted in both its scope
and depth of coverage. The focus is on life on Earth and on the accomplishments of h
­ uman socie­ties. This assignment ­will take us from bacterial
invasions and viral infections through forest and animal metabolism to the
growth of energy conversions and megacities to the essentials of the global
economy—­while excluding both the largest and the smallest scales.

xx

Preface

­There ­will be nothing about the growth (the inflationary expansion) of
the universe, galaxies, supernovas, or stars. I have already acknowledged
inherently slow growth rates of terraforming pro­cesses that are primarily
governed by the creation of new oceanic crust with spreading rates ranging between less than two and no more than about 20 cm/year. And while
some short-­lived and spatially l­imited catastrophic events (volcanic eruptions, massive landslides, tsunami waves, enormous floods) can result in
rapid and substantial mass and energy transfers in short periods of time,
ongoing geomorphic activities (erosion and its counterpart, sedimentary
deposition) are as slow or considerably slower than the geotectonic pro­
cesses: erosion in the Himalayas can advance by as much as 1 cm/year,
but the denudation of the British Isles proceeds at just 2–10 cm in ­every
1,000 years (Smil 2008). ­There ­will be no further examination of ­these
terraforming growth rates in this book.
And as the book’s major focus is on the growth of organisms, artifacts,
and complex systems, ­there w
­ ill be also nothing about growth on subcellular level. The enormous intensification of life science research has produced
major advances in our understanding of cellular growth in general and
cancerous growth in par­tic­u­lar. The multidisciplinary nature, the growing
extent, and accelerating pace of t­ hese advances means that new findings are
now reported overwhelmingly in electronic publications and that writing
summary or review books in ­these fields are exercises in near-­instant obsolescence. Still, among the recent books, t­hose by Macieira-­Coelho (2005),
Gewirtz et al. (2007), Kimura (2008), and Kraikivski (2013) offer surveys of
normal and abnormal cellular growth and death.
Consequently, ­there w
­ ill be no systematic treatment of fundamental
ge­ne­tics, epigenet­ics and biochemistry of growth, and I w
­ ill deal with cellular growth only when describing the growth trajectories of unicellular
organisms and the lives of microbial assemblies whose presence constitutes
significant, or even dominant, shares of biomass in some ecosystems. Similarly, the focus with plants, animals, and ­humans ­will not be on biochemical
specificities and complexities of growth at subcellular, cellular, and organ
level—­there are fascinating studies of brain (Brazier 1975; Kretschmann
1986; Schneider 2014; Lagercrantz 2016) or heart (Rosenthal and Harvey
2010; Bruneau 2012) development—­but on entire organisms, including the
environmental settings and outcomes of growth, and I w
­ ill also note some
key environmental ­factors (ranging from micronutrients to infections) that
often limit or derail organismic growth.
­Human physical growth w
­ ill be covered in some detail with focus both
on individual (and sex-­specific) growth trajectories of height and weight

Preface

xxi

(as well as on the undesirable rise of obesity) and on the collective growth
of populations. I ­will pre­sent long-­term historical perspectives of population growth, evaluate current growth patterns, and examine pos­
si­
ble
­future global, and some national, trajectories. But ­there ­will be nothing on
psychosocial growth (developmental stages, personality, aspirations, self-­
actualization) or on the growth of consciousness: psychological and so­cio­
log­i­cal lit­er­a­ture covers that abundantly.
Before proceeding with systematic coverage of growth in nature and
society, I w
­ ill provide a brief introduction into the mea­sures and va­ri­e­ties
of growth trajectories. T
­ hese trajectories include erratic advances with no
easily discernible patterns (often seen in stock market valuations); s­ imple
linear gains (an hourglass adds the same amount of falling sand to the
bottom pile ­every second); growth that is, temporarily, exponential (commonly exhibited by such diverse phenomena as organisms in their infancy,
the most intensive phases in the adoption of technical innovation, and the
creation of stock market ­bubbles); and gains that conform to assorted confined (restrained) growth curves (as do body sizes of all organisms) whose
shape can be captured by mathematical functions.
Most growth processes—be they of organisms, artifacts, or complex
systems—­
follow closely one of t­hese S-­
shaped (sigmoid) growth curves
conforming to the logistic (Verhulst) function (Verhulst 1838, 1845, 1847),
to its precursor (Gompertz 1825), or to one of their derivatives, most commonly ­those formulated by von Bertalanffy (1938, 1957), Richards (1959),
Blumberg (1968), and Turner et al. (1976). But natu­ral variability as well as
unexpected interferences often lead to substantial deviations from a predicted course. That is why the students of growth are best advised to start
with an a
­ ctual more or less completed progression and see which available
growth function comes closest to replicating it.
Proceeding the other way—­taking a few early points of an unfolding
growth trajectory and using them to construct an orderly growth curve
conforming to a specifically selected growth function—­has a high probability of success only when one tries to predict the growth that is very
likely to follow a known pattern that has been repeatedly demonstrated, for
example, by many species of coniferous trees or freshwater fish. But selecting a random S-­curve as the predictor of growth for an organism that does
not belong to one of ­those well-­studied groups is a questionable enterprise
­because a specific function may not be a very sensitive predictive tool for
phenomena seen only in their earliest stage of growth.

xxii

Preface

The Book’s Structure and Goals
The text follows a natu­ral, evolutionary, sequence, from nature to society,
from s­ imple, directly observable growth attributes (numbers of multiplying
cells, dia­meter of trees, mass of animal bodies, progression of ­human statures) to more complex mea­sures marking the development and advances
of socie­ties and economies (population dynamics, destructive powers, creation of wealth). But the sequence cannot be exclusively linear as ­there are
ubiquitous linkages, interdependencies, and feedbacks and t­hese realities
necessitate some returns and detours, some repetitions to emphasize connections seen from other (energetic, demographic, economic) perspectives.
My systematic inquiry into growth ­
will start with organisms whose
mature sizes range from microbes (tiny as individual cells, massive in their
biospheric presence) to lofty coniferous trees and enormous ­whales. I ­will
take closer looks at the growth of some disease-­causing microbes, at the cultivation of staple crops, and at h
­ uman growth from infancy to adulthood.
Then ­will come inquiries into the growth of energy conversions and man-­
made objects that enable food production and all other economic activities.
I ­will also look how this growth changed numerous per­for­mances, efficiencies, and reliabilities b
­ ecause t­hese developments have been essential for
creating our civilization.
Fi­nally, I w
­ ill focus on the growth of complex systems. I ­will start with
the growth of h
­ uman populations and proceed to the growth of cities,
the most obvious concentrated expressions of h
­ uman material and social
advancement, and economies. I ­will end ­these systematic examinations
by noting the challenges of appraising growth trajectories of empires and
civilizations, ending with our global variety characterized by its peculiar
amalgam of planetary and parochial concerns, affluent and impoverished
lives, and confident and uncertain perspectives. The book ­will close with
reviewing what comes a
­ fter growth. When dealing with organisms, the outcomes range from the death of individuals to the perpetuation of species
across evolutionary time spans. When dealing with socie­ties and economies, the outcomes range from decline (gradual to rapid) and demise to
sometimes remarkable renewal. The trajectory of the modern civilization,
coping with contradictory imperatives of material growth and biospheric
limits, remains uncertain.
My aim is to illuminate va­ri­e­ties of growth in evolutionary and historical perspectives and hence to appreciate both the accomplishments and
the limits of growth in modern civilization. This requires quantitative
treatment throughout ­because real understanding can be gained only by

Preface

xxiii

charting ­actual growth trajectories, appreciating common and exceptional
growth rates, and setting accomplished gains and per­for­mance improvements (often so large that they have spanned several ­orders of magnitude!)
into proper (historical and comparative) contexts. Biologists have studied
the growth of numerous organisms and I review scores of such results
for species ranging from bacteria to birds and from algae to staple crops.
Similarly, details of ­human growth from infancy to maturity are readily
available.
In contrast to the studies of organismic growth, quantifications of long-­
term growth trajectories of ­human artifacts (ranging from ­simple tools to
complex machines) and complex systems (ranging from cities to civilizations) are much less systematic and much less common. Merely to review
published growth patterns would not suffice to provide revealing treatments of ­these growth categories. That is why, in order to uncover the best-­
fitting patterns of many kinds of anthropogenic growth, I have assembled
the longest pos­si­ble rec­ords from the best available sources and subjected
them to quantitative analyses. ­Every one of more than 100 original growth
graphs was prepared in this way, and their range makes up, I believe, a
unique collection. Given the commonalities of growth patterns, this is
an unavoidably repetitive pro­cess but systematic pre­sen­ta­tions of specific
results are indispensable in order to provide a clear understanding of realities (commonalities and exceptions), limits, and f­ uture possibilities.
Systematic pre­sen­ta­tion of growth trajectories is a necessary precondition but not the final goal when examining growth. That is why I also
explain the circumstances and limits of the charted growth, provide evolutionary or historical settings of analyzed phenomena, or offer critical comments on recent progression and on their prospects. I also caution about
any simplistic embrace of even the best statistical fits for long-­term forecasting, and the goal of this book is not to provide an extended platform
for time-­specific growth projections. Nevertheless, the presented analyses
contain a variety of conclusions that make for realistic appraisals of what
lies ahead.
In that sense, parts of the book are helpfully predictive. If a ­century
of corn yields shows only linear growth, ­there is not much of a chance
for exponentially rising harvests in the coming de­cades. If the growth efficiency of broilers has been surpassing, for generations, the per­for­mance of
all other terrestrial meat animals, then it is hard to argue that pork should
be the best choice to provide more protein for billions of new consumers. If
unit capacities, production (extraction or generation) rates, and diffusion of
­every energy conversion display logistic pro­gress, then we have very solid

xxiv

Preface

ground to conclude that the coming transition from fossil fuels to renewables ­will not be an exceptionally speedy affair. If the world’s population
is getting inexorably urbanized, its energetic (food, fuels, electricity) and
material needs ­will be ­shaped by ­these restrictive realities dictating the need
for incessant and reliable, mass-­scale flows that are impossible to satisfy
from local or nearby sources.
Simply put, this book deals in realities as it sets the growth of every­thing
into long-­term evolutionary and historical perspectives and does so in rigorous quantitative terms. Documented, historically embedded facts come
first—­cautious conclusions afterward. This is, of course, in contradistinction to many recent ahistoric forecasts and claims that ignore long-­term
trajectories of growth (that is, the requisite energetic and material needs of
unpre­ce­dented scaling pro­cesses) and invoke the fash­ion­able mantra of disruptive innovation that ­will change the world at accelerating speed. Such
examples abound, ranging from all of the world’s entire car fleet (of more
than 1 billion vehicles) becoming electric by 2025 to terraforming Mars
starting in the year 2022, from designer plants and animals (synthetic biology
rules) making the strictures of organismic evolution irrelevant to anticipations of artificial intelligence’s imminent takeover of our civilization.
This book makes no radical claims of that kind; in fact it avoids making any but strongly justified generalizations. This is a deliberate decision
resting on my re­spect for complex and unruly realities (and irregularities)
and on the well-­attested fact that g
­ rand predictions turn out to be, repeatedly, wrong. Infamous examples concerning growth range from ­those of
unchecked expansion of the global population and unpre­ce­dented famines
that ­were to happen during the closing de­cades of the 20th ­century to a
swift takeover of the global energy supply by inexpensive nuclear power
and to a fundamentally mistaken belief that the growth rate under­lying
Moore’s law (doubling ­every two years) can be readily realized through
innovation in other fields of ­human endeavor.
The book is intended to work on several planes. The key intent is to
provide a fairly comprehensive analytical survey of growth trajectories in
nature and in society: in the biosphere, where growth is the result of not
just evolution but, increasingly, of h
­ uman intervention; and in the man-­
made world, where growth has been a key ­factor in the history of populations and economies and in the advancement of technical capabilities.
Given this scope, the book could be also read selectively as a combination
of specific parts, by focusing on living organisms (be they plants, animals,
­humans, or populations) or on ­human designs (be they tools, energy converters, or transportation machinery). And, undoubtedly, some readers w
­ ill

Preface

xxv

be more interested in the settings of growth processes—in preconditions,
­factors, and the evolutionary and historical circumstances of natu­ral, population, economic, and imperial growth—­rather than in specific growth
trajectories.
Yet another option is to focus on the opposite scales of growth. The
book contains plenty of information about the growth of individual organisms, tools, machines, or infrastructures—as well as about the growth of
the most extensive and the most complex systems, culminating in musings
about the growth of civilizations. The book is also a summation of unifying lessons learned about the growth of organisms, artifacts, and complex
systems, and it can be also read as an appraisal of evolutionary outcomes
in nature and as a history of technical and social advances, that is as an
assessment of civilizational pro­gress (rec­ord might be a better, neutral, designation than pro­gress)
As always in my writings, I stay away from any rigid prescriptions—­but I
hope that the book’s careful reading conveys the key conclusion: before it is
too late, we should embark in earnest on the most fundamental existential
(and also truly revolutionary) task facing modern civilization, that of making any f­uture growth compatible with the long-­term preservation of the
only biosphere we have.

1 Trajectories: or common patterns of growth

Growth attracts adjectives. The most common ones have been (alphabetically) anemic, arithmetic, cancerous, chaotic, delayed, disappointing,
erratic, explosive, exponential, fast, geometric, healthy, interrupted, linear,
logistic, low, malignant, moderate, poor, rapid, runaway, slow, S-­shaped,
strong, sudden, tepid, unexpected, vigorous. Most recently, we should also
add sustainable and unsustainable. Sustainable growth is, of course, a clear
contradictio in adjecto as far as any truly long-­run material growth is concerned (I am ignoring any possibilities of migrating to other planets a
­ fter
exhausting the Earth’s resources) and it is highly doubtful that we can keep
on improving such intangibles as happiness or satisfaction. Most of the
adjectives used to describe growth are qualifiers of its rate: often it is not
the growth per se that we worry about but rather its rate, e­ ither too fast or
too slow.
Even a casual news reader knows about the constant worries of assorted
chief economists, forecasters and government officials about securing “vigorous” or “healthy” growth of the gross domestic product (GDP). This
clamoring for high growth rates is based on the most simplistic expectation
of repeating past experiences—as if the intervening growth of GDP had
nothing to do with the expected ­future rate. Put another way, economists
have an implicit expectation of endless, and preferably fairly fast, exponential growth.
But they choose an inappropriate metric when comparing the outcomes.
For example, during the first half of the 1950s the US GDP growth averaged
nearly 5% a year and that per­for­mance translated roughly to additional
$3,500 per capita (for about 160 million p
­ eople) during t­ hose five years. In
contrast, the “slow” GDP growth between 2011 and 2015 (averaging just
2%/year) added about $4,800/capita (for about 317 million ­people) during
­those five years, or nearly 40% more than 60 years ago (all totals are in
constant-­value monies to eliminate the effect of inflation). Consequently,

2

Chapter 1

in terms of a
­ ctual average individual betterment, the recent 2% growth has
been quite superior to the former, 2.5 times higher, rate. This is ­simple algebra, but it is repeatedly ignored by all t­ hose bewailing the “low” post-2000
growth of the US or Eu­ro­pean Union (EU) economies.
Results of the British referendum of June 23, 2016, about remaining in
the EU or leaving it, provided another perfect illustration of how the rate
of change ­matters more than the outcome. In 94% of the areas where the
foreign-­born population increased by more than 200% between 2001 and
2014, ­people voted to leave the Eu­ro­pean Union—­even though the share
of mi­grants in ­those regions had remained comparatively low, mostly less
than 20%. In contrast, most regions where the foreign-­born population was
more than 30% voted to remain. As The Economist concluded, “High numbers of mi­grants ­don’t bother Britons; high rates of change do” (Economist
2016).
Other adjectives used to qualify growth are precisely defined terms describing its specific trajectories that conform (sometimes almost perfectly, often
fairly closely) to vari­ous mathematical functions. T
­ hose close, even perfect, fits are pos­si­ble b
­ ecause most growth pro­cesses are remarkably regular
affairs as their pro­gress follows a ­limited array of patterns. Naturally, ­those
trajectories have many individual and inter-­and intraspecific variations for
organisms, and are marked by historically, technically, and eco­nom­ically
conditioned departures for engineered systems, economies, and socie­ties.
The three basic trajectories encompass linear growth, exponential growth,
and vari­ous finite growth patterns. Linear growth is trivial to grasp and easy
to calculate. Exponential growth is easy to understand but the best way to
calculate it is to use the base of natu­ral logarithms, a mystery to many. The
princi­ple of finite growth patterns, including logistic, Gompertz and confined exponential growth functions, is, again, easy to understand, but their
mathematical solutions require differential calculus.
But before taking a closer look at individual growth functions, their solutions and resulting growth curves, I w
­ ill devote two brief sections to time
spans and to the figures of merit involved in growth studies. In their short
surveys, I w
­ ill note both common and less frequently encountered variables in whose growth we are interested, be it as parents, employees, or
taxpayers, as scientists, engineers, and economists, or as historians, politicians, and planners. T
­ hese mea­sures include such universal concerns as
the weight and height of growing babies and c­ hildren, and the growth of
national economies. And t­ here are also such infrequent but scary concerns
as the diffusion of potentially pandemic infections made worse by mass-­
scale air travel.

Trajectories

3

Time Spans
Growth is always a function of time and during the course of modern
scientific and engineering studies their authors have traced its trajectories
in countless graphs with time usually plotted on the abscissa (horizontal or x axis) and the growing variable mea­sured on the ordinate (vertical or y axis). Of course, we can (and we do) trace growth of physical or
immaterial phenomena against the change of other such variables—we
plot the changing height of growing c­ hildren against their weight or rising
disposable income against the growth of GDP—­but most of the growth
curves (and, in simpler instance, lines) are what James C. Maxwell defined
as diagrams of displacement and what Thompson called time-­diagrams:
“Each has a beginning and an end; and one and the same curve may illustrate the life of a man, the economic history of a kingdom … It depicts a
‘mechanism’ at work, and helps us to see analogous mechanisms in dif­
fer­ent fields; for Nature rings her many changes on a few s­ imple themes”
(Thompson 1942, 139).
Growth of ocean floor or of mountain ranges, whose outcomes are driven
by geotectonic forces and whose examination is outside of this book’s already
large scope, unfolds across tens to hundreds of millions of years. When dealing with organisms, the length of time span u
­ nder consideration is a function of specific growth rates determined by long periods of evolution and,
in the case of domesticated plant and animal species, often accelerated or
enhanced by traditional breeding and, most recently, also by transgenic
interventions. When dealing with the growth of devices, machines, structures or any other ­human artifacts, time spans ­under study depend both on
their longevity and on their suitability to be deployed in new, enhanced
versions ­under changed circumstances.
As a result, growth of some artifacts that w
­ ere in use since the antiquity
is now merely of historical interest. Sails are a good example of this real­ity,
as their development and deployment (excepting t­ hose designed and used
for fast yacht racing) ended fairly abruptly during the second half of the
19th ­century, just a few de­cades a
­ fter the introduction of steam engines,
and a
­ fter more than five millennia of improving designs. But other ancient
designs have seen spectacular advances in order to meet the requirements
of the industrial age: construction cranes and dockyard cranes are perhaps
the best example of this continued evolution. T
­ hese ancient machines have
seen enormous growth in their capacities during the past two centuries in
order to build taller structures and to h
­ andle cargo of increasingly more
voluminous ships.

4

Chapter 1

Microbes, fungi, and insects make up most of the biosphere’s organisms,
and common time spans of interest in microbiology and invertebrate biology are minutes, days, and weeks. Bacterial generations are often shorter
than one hour. Coccolithophores, single-­celled calcifying marine algae that
dominate oceanic phytomass, reach maximum cell density in nitrogen-­
limited environments in one week (Perrin et al. 2016). Commercially cultivated white mushrooms grow to maturity just 15–25 days a
­ fter the growing
medium (straw or other organic m
­ atter) is filled with mycelium. Butterflies
usually spend no more than a week as eggs, two to five weeks as caterpillars
(larval stage), and one to two weeks as chrysalis from which they emerge as
fully grown adults.
In annual plants, days, weeks, and months are time spans of interest. The
fastest growing crops (green onions, lettuces, radishes) may be harvested
less than a month ­after seeding; the shortest period to produce mature staple
grain is about 90 days (spring wheat, also barley and oats), but winter wheat
needs more than 200 days to reach maturity, and a new vineyard w
­ ill start
producing only during the third year ­after its establishment. In trees, the
annual deposition of new wood in rings (secondary growth originating in
two cambial lateral meristems) marks an easily identifiable natu­ral progression: fast-­growing plantation species (eucalypts, poplars, pines) may be
harvested a
­ fter a de­cade of growth (or even sooner), but in natu­ral settings
growth can continue for many de­cades and in most tree species it can be
actually indeterminate.
Gestation growth of larger vertebrates lasts for many months (from 270
days in h
­ umans to 645 days for African elephants), while months, or even
just days, are of interest during the fastest spells of postnatal growth. That
is particularly the case when meat-­producing poultry, pigs, and c­ attle are
fed optimized diets in order to maximize daily weight gain and to raise their
mass to expected slaughter weight in the shortest pos­si­ble time. Months
and then years are the normal span of interest when monitoring growth of
infants and c­ hildren, and a pediatrician w
­ ill compare age-­and sex-­specific
charts of expected growth with a
­ ctual individual growth to determine if a
baby or a toddler is meeting its growth milestones or if it is failing to thrive
fully.
Although the growth of some artifacts—be they sailing ships or construction cranes—­must be traced across millennia, most of the advances
have been concentrated in relatively brief growth spurts separated by long
periods of no growth or marginal gains. Energy converters (engines, turbines, motors), machines, and devices characteristic of modern industrial

Trajectories

5

civilization have much shorter life histories. Growth of steam engines
lasted 200 years, from the early 18th to the early 20th ­century. Growth of
steam turbines (and electric motors) has been g
­ oing on since the 1880s,
that of gas turbines only since the late 1930s. Growth of modern solid-­state
electronics began with the first commercial applications of the 1950s but
it r­eally took off only with microprocessor-­based designs starting in the
1970s.
Studying the collective growth of our species in its evolutionary entirety
would take us back some 200,000 years but our ability to reconstruct the
growth of the global population with a fair degree of accuracy goes back
only to the early modern era (1500–1800), and totals with small ranges of
uncertainty have been available only for the past ­century. In a few countries with a history of censuses (however incomplete, with the counts often
restricted to only adult males) or with availability of other documentary
evidence (birth certificates maintained by parishes), we can re­create revealing population growth trajectories g
­ oing back to the medieval period.
In economic affairs the unfolding growth (of GDP, employment, productivity, output of specific items) is often followed in quarterly intervals,
but statistical compendia report nearly all variables in terms of their annual
totals or gains. Calendar year is the standard choice of time span but the
two most common instances of such departures are fiscal years and crop
years (starting at vari­ous months) used to report annual harvests and yields.
Some studies have tried to reconstruct national economic growth g
­ oing
back for centuries, even for millennia, but (as I ­will emphasize ­later) they
belong more appropriately to the class of qualitative impressions rather
than to the category of true quantitative appraisals. Reliable historical
reconstructions for socie­ties with adequate statistical ser­vices go back only
150–200 years.
Growth rates capture the change of a variable during a specified time
span, with ­percent per year being the most common metric. Unfortunately,
­these frequently cited values are often misleading. No caveats are needed
only if t­ hese rates refer to linear growth, that is to adding identical quantity
during ­every specified period. But when t­ hese rates refer to periods of exponential growth they could be properly assessed only when it is understood
that they are temporary values, while the most common va­ri­e­ties of growth
encountered in nature and throughout civilization—­those following vari­
ous S-­shaped patterns—­are changing their growth rate constantly, from
very low rates to a peak and back to very low rates as the growth pro­cess
approaches its end.

6

Chapter 1

Figures of Merit
­ here is no binding classification of the mea­sures used to quantify growth.
T
The most obvious basic division is into variables tracing physical changes
and immaterial but quantifiable (at least by proxy if not in a direct manner)
developments. The simplest entry in the first category is the increment of
a studied variable counted on hourly, daily, monthly or annual basis. And
when statisticians talk about quantifying the growth of assorted populations, they use the term beyond its strict Latin meaning in order to refer
to assemblages of microbes, plants and animals, indeed to any quantifiable
entities whose growth they wish to study.
As for the fundamental quantities whose growth defines the material
world, the International System of Units (Système international d’unités, SI)
recognizes seven basic entries. They are length (meter, m), mass (kilogram,
kg), time (second, s), electric current (ampere, A) thermodynamic temperature (kelvin, K), amount of substance (mole, mol), and luminous intensity
(candela, cd). Many growth mea­sures deal with quantities derived from the
seven basic units, including area (m2), volume (m3), speed (m/s), mass density (kg/m3), and specific volume (m3/kg). More complex quantity equations yield such common mea­sures of growth as force, pressure, energy,
power or luminous flux.
Most of ­these mea­sures w
­ ill be encountered repeatedly throughout this
book (and their complete list, as well as the list of their multiples and submultiples, are available in Units and Abbreviations). The two basic units,
length and mass, ­will be used to evaluate the growth of organisms (be they
trees, invertebrates or babies), structures, and machines. Height has been
always the most appreciated, admired and emulated among the linear
variables. This preference is demonstrated in ways ranging from clear correlations between height and power in the corporate world (Adams et al.
2016) to the obsession of architects and developers with building ever taller
structures. ­There is no international organ­ization monitoring the growth of
buildings with the largest footprint or the largest internal space—­but ­there
is the Council on Tall Buildings and H
­ uman Habitat, with its specific criteria for defining and mea­sur­ing tall buildings (CTBUH 2018).
Their rec­ord heights r­ose from 42 m for the Home Insurance Building,
the world’s first skyscraper completed in 1884 in Chicago, to 828 m for Burj
Khalifa in Dubai finished in 2009. Jeddah Tower (whose principal building
contractor is Saudi Binladin com­pany, whose ­family name ­will be always
connected to 9/11) ­will reach 1,008 m by 2019 (CTBUH 2018). Length, as
height, rather than mass, has been also a recurrent topic of comparative

Trajectories

7

height (cm)

180

175

170

165

160
1500

1600

1700

1800

1900

2000

Figure 1.1
Evolution of average male body heights in Western Eu­rope, 1550–1980. Data from
Clio Infra (2017).

anthropometric studies, and Clio Infra (2017) and Roser (2017) provide con­
ve­nient summaries of height mea­sure­ments ranging from ­those of ancient
skele­
tons to modern h
­ umans (figure 1.1). Height of Eu­
ro­
pean military
recruits provides some of the most reliable testimonies of ­human growth
during the early modern and modern eras (Ulijaszek et al. 1998; Floud et al.
2011).
Area appears in growth studies frequently on its own in instances as
diverse as the average size of farms, expansion of empires, and annual
installation of photovoltaic panels to generate solar electricity. Changes in
housing development (average areas of h
­ ouses or apartments) are mea­sured
in square meters (m2), except for the nonmetric United States where square
feet are still used. Square kilo­meters (km2, 1,000 × 1,000 m) are used in tracing the growth of states and empires. Area is used even more commonly as
the denominator to quantify productivity of photosynthetic output, that
is yields and harvests in forestry and agriculture. Hectares (100 × 100 m or
10,000 m2) are the most common areal unit in agricultural statistics (except,
again, for the non-­metric US, where acres are still used).
Volume is preferred to mass when surveying the growth of production
and intake of both alcoholic and nonalcoholic beverages (usually in liters),
and mea­sur­ing annual cutting and industrial use of lumber and other wood
products (usually in m3). Volume has been also the indicator of choice
when extracting and transporting crude oil—­and it is also perhaps the best
example of the endurance of a nonmetric mea­sure. A steel container with

8

Chapter 1

the volume of 42 US gallons (or roughly 159.997 liters) was ­adopted by the
US Bureau of the Census in 1872 to mea­sure crude oil output, and barrel
remains the standard output mea­sure in the oil industry—­but converting
this volume variable to its mass equivalent requires the knowledge of specific densities.
Just over six barrels of heavy crude oil (commonly extracted in the ­Middle
East) are needed to make up one tonne of crude oil, but the total may be as
high as 8.5 barrels for the lightest crudes produced in Algeria and Malaysia, with 7.33 barrels per tonne being a commonly used global average.
Similarly, converting volumes of wood to mass equivalents requires the
knowledge of specific wood density. Even for commonly used species, densities differ by up to a f­ actor of two, from light pines (400 kg/m3) to heavy
white ash (800 kg/m3), and the extreme wood densities range from less than
200 kg/m3 for balsa to more than 1.2 t/m3 for ebony (USDA 2010).
The history of ubiquitous artifacts illustrates two opposite mass trends:
miniaturization of commonly used components and devices on one hand
(a trend enabled to an unpre­ce­dented degree by the diffusion of solid-­state
electronics), and a substantial increase in the average mass of the two largest investments modern families make, cars and ­houses, on the other. The
declining mass of computers is, obviously, just an inverse of their growing capability to ­handle information per unit of weight. In August 1969,
the Apollo 11 computer used to land the manned capsule on the Moon
weighed 32 kg and had merely 2 kB of random access memory (RAM), or
about 62 bytes per kg of mass (Hall 1996). Twelve years l­ater, IBM’s first
personal computer weighed 11.3 kg and 16 kB RAM, that is 1.416 kB/kg.
In 2018 the Dell laptop used to write this book weighed 2.83 kg and had
4 GB RAM, or 1.41 GB/kg. Leaving the Apollo machine aside (one-­of-­a-­
kind, noncommercial design), personal computers have seen a millionfold
growth of memory/mass ratio since 1981!
As electronics (except for wall-­size tele­vi­sions) got smaller, ­houses and cars
got bigger. ­People think about ­houses primarily in terms of habitable area but
its substantial increase—in the US from 91 m2 of finished area (99 m2 total)
in 1950 to about 240 m2 by 2015 (Alexander 2000; USCB 2017)—­has resulted
in an even faster growth rate for materials used to build and to furnish them.
A new 240 m2 ­house ­will need at least 35 tonnes of wood, roughly split
between framing lumber and other wood products, including plywood,
glulam, and veneer (Smil 2014b). In contrast, a s­ imple 90 m2 ­house could be
built with no more than 12 tonnes of wood, a threefold difference.
Moreover, modern American h
­ ouses contain more furniture and they
have more, and larger, major appliances (refrigerators, dishwashers, washing

Trajectories

9

machines, clothes dryers): while in 1950 only about 20% of h
­ ouse­holds had
washing machines, less than 10% owned clothes dryers and less than 5%
had air conditioning, now standard even in the northernmost states. In
addition, heavier materials are used in more expensive finishes, including
tiles and stone for flooring and bathrooms, stone kitchen ­counters and large
fireplaces. As a result, new ­houses built in 2015 are about 2.6 times larger
than was the 1950 average, but for many of them the mass of materials
required to build them is four times as large.
The increasing mass of American passenger cars has resulted from a combination of desirable improvements and wasteful changes (figure 1.2). The
world’s first mass-­produced car, Ford’s famous Model T released in October 1908, weighed just 540 kg. Weight gains ­after World War I (WWI) ­were
due to fully enclosed all-­metal bodies, heavier engines, and better seats: by
1938 the mass of Ford’s Model 74 reached 1,090 kg, almost exactly twice
that of the Model T (Smil 2014b). ­These trends (larger cars, heavier engines,
more accessories) continued a
­ fter World War II (WWII) and, a
­ fter a brief
pause and retreat brought by the oil price rises by the Organ­ization of the
Petroleum Exporting Countries (OPEC) in the 1970s, intensified ­after the
mid-1980s with the introduction of sport-­utility vehicles (SUVs, accounting for half of new US vehicle sales in 2019) and the growing popularity of
pick-up trucks and vans.
In 1981 the average mass of American cars and light trucks was 1,452 kg;
by the year 2000 it had reached 1,733 kg; and by 2008 it was 1,852 kg (and
had hardly changed by 2015), a 3.4-­fold increase of average vehicle mass in
100 years (USEPA 2016b). Average car mass growth in Eu­rope and Asia has

Figure 1.2
The bestselling American car in 1908 was Ford Model T weighing 540 kg. The bestselling vehicle in 2018 was not a car but a truck, Ford’s F-150 weighing 2,000 kg.
Images from Ford Motor Com­pany cata­logue for 1909 and from Trucktrend.

10

Chapter 1

been somewhat smaller in absolute terms but the growth rates have been
similar to the US rise. And while the worldwide car sales ­were less than
100,000 vehicles in 1908, they w
­ ere more than 73 million in 2017, roughly
a 700-­fold increase. This means that the total mass of new automobiles sold
globally e­ very year is now about 2,500 larger than it was a ­century ago.
Time is the third ubiquitous basic unit. Time is used to quantify growth
directly (from increased h
­ uman longevity to the duration of the longest
flights, or as time elapsed between product failures that informs us about
the durability and reliability of devices). More importantly, time is used as
the denominator to express such ubiquitous rates as speed (length/time,
m/s), power (energy/time, J/s), average earnings (money/time, $/hour), or
national annual gross domestic product (total value of goods and ser­vices/
time, $/year). Rising temperatures are encountered less frequently in growth
studies, but they mark the still improving per­for­mance of turbogenerators,
while growing total luminosity of illumination informs about the widespread, and intensifying, prob­lem of light pollution (Falchi et al. 2016).
Modern socie­ties have been increasingly concerned about immaterial
variables whose growth trajectories describe changing levels of economic
per­for­mance, affluence, and quality of life. Common variables that the
economists want to see growing include the total industrial output, GDP,
disposable income, l­ abor productivity, exports, trade surplus, ­labor force participation, and total employment. Affluence (GDP, gross earnings, disposable
income, accumulated wealth) is commonly mea­sured in per capita terms,
while the quality of life is assessed by combinations of socioeconomic variables. For example, the ­Human Development Index (HDI, developed and
annually recalculated by the United Nations Development Programme) is
composed of three indices quantifying life expectancy, educational level,
and income (UNDP 2016).
And in 2017 the World Economic Forum introduced a new Inclusive
Development Index (IDI) based on a set of key per­for­mance indicators that
allow a multidimensional assessment of living standards not only according to their current level of development but also taking into account the
recent per­for­mance over five years (World Economic Forum 2017). ­There is
a ­great deal of overlap between HDI for 2016 and IDI for 2017: their rankings share six among the top 10 countries (Norway, Switzerland, Iceland,
Denmark, Netherlands, Australia). Perhaps the most in­ter­est­ing addition to
this new accounting has been the quantifications of happiness or satisfaction
with life.
Small Himalayan Bhutan made news in 1972 when Jigme Singye Wangchuck, the nation’s fourth king, proposed to mea­sure the kingdom’s pro­
gress by using the index of Gross National Happiness (GNH Centre 2016).

Trajectories

11

Turning this appealing concept into an indicator that could be monitored
periodically is a dif­fer­ent ­matter. In any case, for the post-­WWII US we
have a fairly convincing proof that happiness has not been a growth variable. Gallup pollsters have been asking Americans irregularly how happy
they feel since 1948 (Carroll 2007). In that year 43% of Americans felt very
happy. The mea­sure’s peak, at 55%, was in 2004, the low point came ­after
9/11 at 37%, but by 2006 it was 49%, hardly any change compared to more
than half a ­century ago (47% in 1952)!
Satisfaction with life is closely connected with a number of qualitative
gains that are not easily captured by resorting to ­simple, and the most commonly available, quantitative mea­sures. Nutrition and housing are certainly
the two best examples of this real­ity. As impor­tant as it may be, tracing the
growth of average daily per capita availability of food energy may deliver
a misleadingly reassuring message. Dietary improvements have lifted food
supply far above the necessary energy needs: they may have delivered a
more than adequate amount of carbohydrates and lipids and may have
satisfied the minimum levels of high-­quality protein—­but could still be
short of essential micronutrients (vitamins and minerals). Most notably,
low intakes of fruit and vegetables (the key sources of micronutrients)
have been identified as a leading risk ­factor for chronic disease, but Siegel
et al. (2014) showed that in most countries their supply falls below recommended levels. In 2009 the global shortfall was 22% with median supply/
need ratios being just 0.42 in low-­income and 1.02 in affluent countries.
During the early modern era, the rise of scientific methods of inquiry
and the invention and deployment of new, power­ful mathematical and
analytical tools (calculus during the mid-17th ­century, advances in theoretical physics and chemistry and the foundations of modern economic and
demographic studies during the 19th ­century) made it eventually pos­si­ble
to analyze growth in purely quantitative terms and to use relevant growth
formulas in order to predict long-­term trajectories of studied phenomena.
Robert Malthus (1766–1834), a pioneer of demographic and economic studies, caused a ­great of concern with his conclusion contrasting the means of
subsistence that grow only at a linear rate with the growth of populations
that proceeds at exponential rates (Malthus 1798).
Unlike Malthus, Pierre-­François Verhulst (1804–1849), a Belgian mathematician, is now known only to historians of science, statisticians, demographers, and biologists. But four de­cades a
­ fter Malthus’s essay, Verhulst
made a fundamental contribution to our understanding of growth when
he published the first realistic formulas devised explic­itly to express the
pro­gress of confined (bounded) growth (Verhulst 1838, 1845, 1847). Such
growth governs not only the development of all organisms but also the

12

Chapter 1

improving per­for­mance of new techniques, diffusion of many innovations
and adoption of many consumer products. Before starting my topical coverage of growth phenomena and their trajectories (in chapter 2), I ­will provide brief, but fairly comprehensive, introductions into the nature of ­these
formal growth patterns and resulting growth curves.
Linear and Exponential Growth
­ hese are two common but very dif­fer­ent forms of growth whose trajectoT
ries are captured by ­simple equations. Relatively slow and steady would be
the best qualitative description of the former, and increasingly rapid and
eventually soaring the best of the latter. Anything subject to linear growth
increases by the same amount during ­every identical period and hence the
equation for linear growth is ­simple:
Nt = N0 + kt
where a quantity at time t (Nt) is calculated by enlarging the initial value
(N0) by the addition of a constant value k per unit of time, t.
Analy­sis of a large number of stalagmites shows that t­ hese tapering columns of calcium salts created on cave floors by dripping ­water often grow
for millennia in a near-­linear fashion (White and Culver 2012). Even a relatively fast growth of 0.1 mm/year would mean that a stalagmite 1 meter
tall would grow just 10 cm in thousand years (1,000 mm + 1,000 × 0.1). The
plotted outcome of its linear growth shows a monotonously ascending line
(figure 1.3). This, of course, means that the growth rate as the share of the
total stalagmite height w
­ ill be constantly declining. In a stalagmite growing
at 0.1 mm/year for 1,000 years it would be 0.01% during the first year but
only 0.009% a millennium ­later.
In contrast, in all cases of exponential growth the quantity increases by
the same rate during ­every identical period. The basic functional dependence is
Nt = N0 (1 + r)t
where r is the rate of growth expressed as a fraction of unity growth per unit
time, for example, for a 7% increase per unit of time, r = 0.07.
This exponential growth can be also expressed—­after a trivial multiplicative unit-­of-­timekeeping adjustment—as
Nt = N0ert
where e (e = 2.7183, the base of natu­ral logarithms) is raised to the power
of rt, an easy operation to do with any scientific hand-­calculator. We can

Trajectories

13

1700

1600

length (mm)

1500

exponential
1400

1300

1200

1100

linear

1000

0

500

1000

Figure 1.3
Millennium of stalagmite accretion illustrating linear and exponential growth
trajectories.

imagine a cave where the amount of dripping ­water carry­ing the same
fraction of dissolved salts keeps on increasing, resulting in an exponential
growth of a stalagmite.
Assuming a very small 0.05% fractional length increase per year,
this stalagmite would have lengthened by nearly 65 cm in 1,000 years
­(1,000 mm × 2.7180.0005 × 1000 = 1,648.6 mm total length, or a length increase
of 64.86 cm), about 50% more than its linearly growing counterpart, and
the plotted exponential growth shows an upward-­bending curve whose
ascent is determined by the rate of increase (figure 1.3). ­After 10,000 years
the linear stalagmite would double its height to 2 m while the exponentially
growing stalagmite would need a g
­ iant cave as it would reach 148.3 m. As
the exponent is the product of growth rate and time, equally large additions can come from lower growth rates over longer intervals of time or
from shorter intervals of higher growth rates.
Another ­simple comparison shows how the trajectories of linear and
exponential growth remain close only during the earliest stage of growth,
when the product of growth rate and time interval is small compared to
unity: soon they begin to diverge and eventually they are far apart. Gold
(1992) assumed that bacterial colonies living deep under­ground fill up to
1% of all porous spaces in the topmost 5 km of the Earth’s crust while
Whitman et al. (1998) put the microbe-­fillable volume at just 0.016% of the

14

Chapter 1

available porous space. That would still translate into enormous aggregate
microbial mass—­but one with exceedingly slow rates of reproduction. Let
us assume (just for the sake of this s­ imple example) that the physical and
chemical constraints make it pos­si­ble for a tiny colony of 100 cells (suddenly squeezed by a seismic event into a new rock pocket) to make the net
addition of just five cells per hour; obviously, ­there ­will be 105 cells at the
end of the first hour, a
­ fter 10 hours of such linear growth the colony w
­ ill
have 150 cells, and the respective totals w
­ ill be 350 and 600 cells a
­ fter 50
and 100 hours.
In comparison to many common bacteria, Mycobacterium tuberculosis—
a remarkably prevalent cause of premature mortality in the pre-­antibiotic era,
and still one of the single largest ­causes of ­human mortality due to infectious disease and the cause of what are now some of the most drug-­resistant
forms of such disease (Gillespie 2002)—­reproduces slowly in most circumstances in infected ­human lungs. But when growing on suitable laboratory
substrates, it ­will double its cell count in 15 hours, implying an hourly
growth rate of roughly 5%. Starting, again, with 100 cells, t­ here w
­ ill be 105
cells at the end of the first hour, the same as with the linear growth of subterranean microbes; ­after 10 hours of exponential growth, the colony ­will
have 165 cells (just 10% more than in the linear case), but the exponential
totals ­will be 1,218 cells a
­ fter 50 hours (roughly 3.5 times as much as in the
linear case) and 14,841 cells ­after 100 hours, almost 25 times more. The
contrast is obvious: without a priori knowledge, we could not tell the difference ­after the first hour—­but ­after 100 hours the gap has become enormous
as the exponential count is an order of magnitude higher.
Instances of linear (constant) growth are ubiquitous. Distance (length)
travelled by light emitted by myriads of stars increases by 300,000,000 m
(299,792,458 m to be exact) ­every second; distance covered by a truck averaging 100 km/h on a night-­time freeway grows by 27.7 m during the same
time. According to Ohm’s law—­voltage (volts, V) equals current (amperes, A)
times the re­sis­tance (ohms, Ω) of the conducting cir­cuit—­when re­sis­tance
remains constant, current increases linearly with increasing voltage. Fixed
(and untaxed) hourly wage ­will bring a linear increase of salary with longer
work time. Cellphone use charged per minute (rather than on an unlimited
plan) ­will produce a linearly increasing monthly bill with linearly increasing chatter.
In nature, linear growth is often encountered temporarily during the
early stages of postnatal development, be it of piglets or c­ hildren. Increasing life expectancies in affluent countries have followed it for more than a
­century, and it is the only long-­term growth trajectory for rising crop yields,
be it of staple grains or fruits. Improvements in the ratings and capabilities

Trajectories

15

of machines have been often linear, including the average power of American cars since the Ford Model T in 1908, maximum thrust and bypass ratio
of jet engines since their origin, maximum train speed and boiler pressure
of steam locomotives (since the beginning of regular ser­vice in 1830), and
maximum ship displacements.
And sometimes s­ imple linear growth is an outcome of complex interactions. Between 1945 and 1978, US gasoline consumption had followed an
almost perfectly linear course—­and ­after a brief four-­year dip it resumed
a slower linear growth in 1983 that continued ­until 2007 (USEIA 2017b).
The two linear trajectories resulted from an interplay of nonlinear changes
as vehicle owner­ship soared, increasing more than seven times between
1945 and 2015, while average fuel-­using efficiency of automotive engines
remained stagnant ­until 1977, then improved significantly between 1978
and 1985 before becoming, once again, stagnant for the next 25 years (USEPA
2015).
Some organisms, including bacteria cultivated in the laboratory and
young c­ hildren, experience periods of linear growth, adding the same
number of new cells or the same height or the same mass increment, during specific periods of time. Bacteria follow that path when provided with
a ­limited but constant supply of a critical nutrient. C
­ hildren have spells
of linear growth both for weight and height. For example, American boys
have brief periods of linear weight growth between 21 and 36 months of
age (Kuczmarski et al. 2002), and the Child Growth Standards of the World
Health Organ­ization (WHO) indicate a perfectly linear growth of height
with age for boys between three and five years, and an almost-­linear trajectory for girls between the same ages (WHO 2006; figure 1.4).
Exponential Growth
Exponential growth, with its gradual takeoff followed by a steep rise, attracts
attention. Properties of this growth, formerly known as geometric ratio or
geometric progression, have been illustrated for hundreds of years—­perhaps
for millennia, although the first written instance comes only from the year
1256—by referring to the request of a man who in­ven­ted chess and asked
his ruler-­patron to reward him by doubling the number of grains of rice (or
wheat?) laid on e­ very square. The total of 128 grains (27) is still trivial at the
end of the first row; ­there are about 2.1 billion grains (231) when reaching
the end of the m
­ iddle, fourth, row; and at the end, it amounts to about 9.2
quintillion (9.2 × 1018) grains.
The key characteristic of advanced exponential growth are the soaring
additions that entirely overwhelm the preceding totals: additions to the
last row of the chessboard are 256 times larger than the total accumulated

16

Chapter 1

125

boys

120

2

height (cm)

115
0

110
105

-2

100
95
90
85
80

2

3

4

5

age (years)
125

girls

120

2

height (cm)

115
0

110
105

-2

100
95
90
85
80

2

3

4

5

age (years)
Figure 1.4
Graphs of expected height-­for-­age growth (averages and values within two standard
deviations) for boys and girls 2–5 years old. Simplified from WHO (2006).

Trajectories

17

at the end of the penultimate row, and they represent 99.61% of all added
grains. Obviously, undesirable exponential growth may be arrested, with
vari­ous degrees of effort, in its early stages, but the task may quickly become
unmanageable as the growth continues. When assuming an average rice
grain mass of 25 milligrams, the ­grand total (all too obviously not able to
fit any chessboard) would equal about 230 Gt of rice, nearly 500 times more
than the grain’s global annual harvest—­which was just short of 500 Mt in
2015.
Over long periods even minuscule growth rates ­will produce impossible
outcomes and ­there is no need to invoke any cosmic time spans—­referring
back to antiquity w
­ ill do. When imperial Rome reached its apogee (in the
second c­ entury of the common era), it needed to harvest about 12 Mt of
grain (much of it grown in Egypt and shipped to Italy) in order to sustain
its population of some 60 million p
­ eople (Garnsey 1988; Erdkamp 2005;
Smil 2010c). When assuming that Rome would have endured and that its
grain harvest would have grown at a mere 0.5% a year its total would have
now reached about 160 Gt, or more than 60 times the world’s grain harvest
of 2.5 Gt in 2015 used to feed more than 7 billion ­people.
Linear scale is a poor choice for charting exponential growth whose
complete trajectory often encompasses many o
­ rders of magnitude. In order
to accommodate the entire range on a linear y axis it becomes impossible to
make out any ­actual values except for the largest order of magnitude, and
the result is always a J-­curve that has a nearly linear section of relatively
slow gains followed by a more or less steep ascent. In contrast, plotting
constant exponential growth on a semilogarithmic graph (with linear x
axis for time and logarithmic y axis for the growing quantity) produces a
perfectly straight line and ­actual values can be easily read off the y axis even
when the entire growth range spans many ­orders of magnitude. Making a
semilog plot is thus an easy graphic way of identifying if a given set of data
has been a result of exponential growth. Figure 1.5 compares the two plots
for such a phenomenon: it charts the growth of one of the key foundations
of modern civilization, the almost perfectly exponential rise of global crude
oil consumption between 1880 and 1970.
The fuel’s commercial production began on a negligible scale in only
three countries, in Rus­sia (starting in 1846) and in Canada and the US
(starting in 1858 and 1859). By 1875 it was still only about 2 Mt and then,
as US and Rus­sian extraction expanded and as other producers entered the
market (Romania, Indonesia, Burma, Iran), the output grew exponentially
to about 170 Mt by 1930. The industry was briefly slowed down by the
economic crisis of the 1930s, but its exponential rise resumed in 1945 and,

18

Chapter 1

world oil consumption (EJ)

90

60

30

0

1880

1900

1920

1940

1960

1970

world oil consumption (EJ)

100

10

1

0.1

1880

1890

1900

1910

1920

1930

1940

1950

1960

1970

Figure 1.5
Growth of annual global crude oil consumption, 1880–1970: exponential growth plotted on linear and semilog scales. Data from Smil (2017b).

propelled by new huge ­Middle Eastern and Rus­sian discoveries, by the mid1970s the output was three ­orders of magnitude (slightly more than 1,000
times) higher than 100 years previous.
Temporary periods of exponential growth have not been uncommon in
modern economies, where they have marked the rise of domestic product
in such rapidly developing nations as Japan, South ­Korea, and post-1985
China, and where they characterized annual sales of electronic consumer
goods whose mass appeal created new global markets. And, of course, fraudulent investing schemes (Ponzi pyramids) are built on the allure of the

Trajectories

19

temporary exponential rise of make-­believe earnings: arresting exponential growth in its early stages can be done in manageable manner, sudden
collapse of Ponzi-­like growth ­will always have undesirable consequences.
Pro­gress of technical advances has been also often marked by distinct exponential spells, but when the exponential growth (and its perils) became a
major topic of public discourse for the first time it was in relation to rising
sizes of populations (Malthus 1798).
That famous work—­An Essay on the Princi­ple of Population—by Thomas
Robert Malthus had pre­ce­dents in the work of Leonhard Euler, a leading scientist of the 18th ­century who left Switzerland to work in Rus­sia and Prus­sia
(Bacaër 2011). In Berlin, ­after his return from Rus­sia, Euler published—
in Latin, at that time still the standard language of scientific writing—­
Introduction to Analy­sis of the Infinite (Euler 1748). Among the prob­lems
addressed in the book was one inspired by Berlin’s 1747 population census
which counted more than 100,000 ­people. Euler wanted to know how large
such a population, growing annually by one thirtieth (3.33% a year), would
be in 100 years. His answer, determined by the use of logarithms, was that
it could grow more than 25 times in a c­ entury: as Pn = P0 (1 + r)n, the total in
100 years w
­ ill be 100,000 × (1 + 1/30)100 or 2,654,874. Euler then proceeded
to show how to calculate the annual rate of population increase and the
doubling periods.
But it was Malthus who elevated the powers of exponential growth to
a major concern of the new disciplines of demography and po­liti­cal economy. His much-­repeated conclusion was that “the power of population is
in­def­initely greater than the power in the earth to produce subsistence for
man” ­because the unchecked population would be rising exponentially
while its means of subsistence would be growing linearly (Malthus 1798, 8):
Taking the population of the world at any number, a thousand millions, for
instance, the h
­ uman species would increase in the ratio of—1, 2, 4, 8, 16, 32,
64, 128, 256, 512, ­etc. and subsistence as—1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ­etc. In two
centuries and a quarter, the population would be to the means of subsistence as
512 to 10: in three centuries as 4096 to 13, and in two thousand years the difference would be almost incalculable, though the produce in that time would have
increased to an im­mense extent.

Charles Darwin illustrated the pro­cess with references to Malthus and Linnaeus and with his own calculation of the consequences of unchecked elephant breeding (Darwin 1861, 63):
­ here is no exception to the rule that e­ very organic being increases at so high a
T
rate, that if not destroyed, the earth would soon be covered by the progeny of
a single pair. Even slow-­breeding man has doubled in twenty-­five years, and at

20

Chapter 1

this rate, in a few thousand years, ­there would literally not be standing room for
his progeny. Linnaeus has calculated that if an annual plant produced only two
seeds—­and ­there is no plant so unproductive as this—­and their seedlings next
year produced two, and so on, then in twenty years ­there would be a million
plants. The elephant is reckoned to be the slowest breeder of all known animals,
and I have taken some pains to estimate its probable minimum rate of natu­ral
increase: it ­will be ­under the mark to assume that it breeds when thirty years old,
and goes on breeding till ninety years old, bringing forth three pairs of young
in this interval; if this be so, at the end of the fifth ­century t­ here would be alive
fifteen million elephants, descended from the first pair.

As I ­will explain in detail in the chapters on the growth of organisms and
artifacts, ­these specific calculations have to be understood with the right
mixture of concern and dismissal, but they share two fundamental attributes. First, and unlike with linear growth where the absolute increment
per unit of time remains the same, exponential growth results in increasing
absolute gains per unit of time as the base gets larger. The US economy grew
by 5.5% in 1957 as well as in 1970, but in the second instance the absolute
gain was 2.27 times larger, $56 vs. $24.7 billion (FRED 2017). In most of the
commonly encountered cases of exponential growth, the rate of increase
is not perfectly constant: it ­either trends slightly over time or it fluctuates
around a long-­term mean.
A slowly declining growth rate w
­ ill produce less pronounced exponential gains. Decadal means of US GDP growth since 1970 are a good example:
they declined from 9.5% during the 1970s to 7.7% during the 1980s, 5.3%
during the 1990s, and to just 4% during the first de­cade of the 21st ­century
(FRED 2017). An increasing growth rate ­will result in a super-­exponential
pace of increase. Growth of China’s real GDP between 1996 and 2010 was
super-­exponential: the annual rate was 8.6% during the first five years,
9.8% between 2001 and 2005, and 11.3% between 2006 and 2010 (NBS
2016). Fluctuating growth rates are the norm with the long-­term expansion of economies: for example, US economic growth (expressed as GDP)
averaged 7% a year during the second half of the 20th ­century, but that
compounded mean rate of change hides substantial annual fluctuations,
with the extreme rates at −0.3% in 1954 (the only year of GDP decline) and
13% in 1978 (FRED 2017).
Second, exponential growth, natu­ral or anthropogenic, is always only
a temporary phenomenon, to be terminated due to a variety of physical,
environmental, economic, technical, or social constraints. Nuclear chain
reactions end as surely (due to the l­imited mass of fissile material) as do
Ponzi (pyramid investment) schemes (once the inflow of new monies sinks

Trajectories

21

below the redemptions). But in the latter case it can take a while: think of
Bernard Madoff, who was able to carry on his fraudulent activities—­a Ponzi
scheme so elaborate that it had eluded the oversight authorities who had
repeatedly investigated his com­pany (although certainly not as diligently
as they should have)—­for more than 30 years and to defraud about $65
billion from his investors before he was fi­nally undone by the greatest post-­
WWII economic crisis in the fall of 2008 (Ross 2016).
That is why it can be so misleading to use exponential growth for longer-­
term forecasting. This could be illustrated by any number of examples based
on ­actual histories, and I have chosen the impressive growth of Amer­i­ca’s
post-1950 airline passenger traffic. During the 1950s its annual exponential
growth averaged 11.1% and the rates for the 1960s and the 1970s ­were,
respectively, 12.4% and 9.4%. A plot of the annual totals of passenger-­
kilometers flown by all US airlines between 1930 and 1980 produces a
trajectory that is almost perfectly captured by a quartic regression (fourth-­
order polynomial with r2 = 0.9998), and continuation of this growth pattern
would have multiplied the 1980 level almost 10 times by 2015 (figure 1.6).
In real­ity, US airline traffic has followed a trajectory of declining growth
(with average annual growth of just 0.9% during the first de­cade of the
21st ­century) and its complete 1930 to 2015 course fits very well into a
four-­parameter (symmetric) logistic curve, with the 2015 total only about
2.3 times higher than in 1980 and with only ­limited further gain expected
by 2030 (figure 1.6). Taking temporarily high rates of annual exponential
growth as indicators of f­uture long-­term developments is a fundamental
­mistake—­but also an enduring habit that is especially favored by uncritical promoters of new devices, designs, or practices: they take early-­stage
growth rates, often impressively exponential, and use them to forecast an
imminent dominance of emerging phenomena.
Many recent examples can illustrate this error, and I have chosen the
capacity growth of Vestas wind turbines, machines leading the shift ­toward
the decarbonization of global electricity generation. This Danish maker
began its sales with a 55 kW machine in 1981; by 1989 it had a turbine
capable of 225 kW; a 600 kW machine was introduced in 1995; and a 2 MW
unit followed in 1999. The best-­fit curve for this rapid growth trajectory of
the last two de­cades of the 20th ­century (five-­parameter logistic fit with
R2 of 0.978) would have predicted designs with capacity of nearly 10 MW
in 2005 and in excess of 100 MW by 2015. But in 2018 the largest Vestas
unit available for onshore installations was 4.2 MW and the largest unit
suitable for offshore wind farms was 8 MW that could be upgraded to 9 MW
(Vestas 2017a), and it is most unlikely that a 100 MW machine ­will be ever

Chapter 1

US air traffic (billion passenger-km)

22

4500

3500

2500

1500

500

0
1930

1940

1950

1960

1970

1980

1990

2000

2010

US air traffic (billion passenger-km)

1200

1000

800

600

400

200

0
1930

1940

1950

1960

1970

1980

1990

2000

2010

2020

2030

Figure 1.6
Predictions of growth of US air travel (in billions of passenger-­kilometers) based on the
period 1930–1980 (top, the best fit is quartic regression) and 1930–2015 (bottom, the
best fit is a logistic curve with the inflection year in 1987). Data from vari­ous annual
reports by the International Civil Aviation Organ­ization.

built. This example of a sobering contrast between early rapid advances of
a technical innovation followed by inevitable formation of sigmoid curves
should be recalled whenever you see news reports about all cars becoming
electric by 2025 or new ba