Contents
1 Trajectories: or common patterns of growth
2 Nature: or growth of living matter
3 Energies: or growth of primary and secondary converters
Steam: Boilers, Engines, and Turbines
4 Artifacts: or growth of man-made objects and their performances
5 Populations, Societies, Economies: or growth of the most complex assemblies
6 What Comes After Growth: or demise and continuity
Retreat of Artifacts and Processes
Scientific Units and Their Multiples and Submultiples
List of Figures
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://
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).
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. xv
Figure 1.1 Evolution of average male body heights in Western Europe, 1550–1980. Data from Clio Infra (2017).
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.
Figure 1.3 Millennium of stalagmite accretion illustrating linear and exponential growth trajectories.
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).
Figure 1.5 Growth of annual global crude oil consumption, 1880–1970: exponential growth plotted on linear and semilog scales. Data from Smil (2017b).
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.
Figure 1.7 Hyperbolic growth curve in comparison with exponential growth.
Figure 1.8 Relay growth of the largest stationary prime mover capacities (Smil 2017b). Overlapping logistic growth of unit ratings of steam engines, water turbines, and steam turbines produces a temporary hyperbolic growth trend with nearly seven-order-magnitude gain in 300 years.
Figure 1.9 Adolphe Quetelet and Pierre-François Verhulst. Steel engravings from the author’s collection of 19th-century images.
Figure 1.10 Verhulst’s (1845) comparison of logistic and logarithmic (exponential) curves.
Figure 1.11 Qualitative characteristics of logistic growth.
Figure 1.12 Robertson’s (1908) comparison of the progress of an autocatalytic reaction with body weight increase of male white rats.
Figure 1.13 Logistic growth (inflection point at 37.1 days, asymptote at 292.9 cm) of a sunflower plant plotted by Reed and Holland (1919).
Figure 1.14 Forecast of US population growth based on the logistic curve (inflection point in 1919, asymptote at 197.3 million) fitted to decennial census data between 1790 and 1910 (Pearl and Reed 1920).
Figure 1.15 The plane that raised a logistic growth ceiling of the cruising speed: Boeing 707. Image from wikimedia.
Figure 1.16 Logistic curve tracing the growth of cruising speed of commercial airliners 1919–2039 (inflection point in 1945, asymptotic cruising speed of 930.8 km/h). Plotted from data on speeds of specific airplanes, starting with KLM’s de Havilland DH-16 in 1919 and ending with Boeing 787 in 2009.
Figure 1.17 Fitting Mozart’s oeuvre into growth curves: symmetrical (a) and asymmetrical (b) logistic functions and quadratic (c) and quartic (d) regression have all high degrees of fit (R2 = 0.99) but predict substantially different long-term outcomes for the year 1806 when Mozart (who died in 1791) would have been 50 years old. Compositions by date listed in Giegling et al. (1964).
Figure 1.18 Marchetti’s (1977) claim of predetermined shares of individual components of the world’s primary energy supply: Fischer-Pry transforms show very regular substitutions.
Figure 1.19 Actual trajectories of primary energy shares show that this has not been a system with an immutable “schedule, a will, and a clock.” Shares plotted from data in Smil (2017b).
Figure 1.20 Logistic growth trajectory (inflection point in 2024, asymptote at 625.5 Wh/kg) of battery energy densities, 1900–2017. Plotted from data in Zu and Li (2011) and from subsequent news reports.
Figure 1.21 Examples of confined exponential growth curves (based on Banks 1994).
Figure 1.22 Carl Friedrich Gauss, Pierre-Simon Laplace, and Abraham de Moivre. Portraits from the author’s collection.
Figure 1.23 Characteristics of the normal distribution curve.
Figure 1.24 Lognormal species abundance distributions (x axes in log2 classes) of North American fish and birds and less regular distributions of North American and Asian vegetation. Simplified from Antão et al. (2017).
Figure 1.25 Peaks of two asymmetric distributions, one natural and one anthropogenic: there is only one Qomolangma and one Tokyo. Qomolangma image is available at wikimedia and Tokyo’s satellite image is from NASA’s Earth Observatory collection.
Figure 1.26 Benford’s frequency distribution. Plotted from data in Benford (1938).
Figure 1.27 Ranking of the 100 largest US metropolitan districts based on 1940 census (Zipf 1949).
Figure 1.28 Heavy-tailed lognormal distributions of earthquake magnitudes, sizes of forest fires, cities, and the citations of academic papers. Simplified from Clauset et al. (2009).
Figure 2.1 Allometric pattern of autotrophic mass and growth rate. Based on Niklas and Enquist (2001).
Figure 2.2 Logistic growth of Escherichia coli O157:H7. Plotted from data in Buchanan et al. (1997).
Figure 2.3 Algal bloom in the western part of the Lake Erie on July 28, 2015. NASA satellite image is available at https://
Figure 2.4 Progression of the Hong Kong influenza epidemic between May and September 2009. Based on Lee and Wong (2010).
Figure 2.5 Daily influenza mortality time series in New York between February 1918 and April 1920 compared to baseline (1915–1917 and 1921–1923). Simplified from Yang et al. (2014).
Figure 2.6 Bounds of age-related NPP for 18 major forest type groups in the US: the most common annual productivities are between 5 and 7 t C/ha. Modified from He et al. (2012).
Figure 2.7 Group of giant sequoia (Sequoiadendron giganteum) trees, the most massive terrestrial organisms, in Sequoia National Park. National Park Service image is available at https://
Figure 2.8 Age-related and site-dependent growth of merchantable volume for coastal Douglas fir in British Columbia. Based on Martin (1991).
Figure 2.9 Logistic growth (inflection point in 1970, asymptote at 46.5 bushels/acre) of average American wheat yields, 1866–2015. Data from USDA (2017a).
Figure 2.10 Longsheng Rice Terraces in Guangxi province in China: even these small fields now have high yields thanks to intensive fertilization. Photo available at wikimedia.
Figure 2.11 Trends of distinct stages of stagnation and growth of average American grain corn yields, 1866–1997. Based on Crow (1998).
Figure 2.12 Logistic growth trajectory (inflection point in 1988, asymptote at 194.1 bushels/acre) of average American grain corn yields, 1866–2015. Data from USDA (2017a).
Figure 2.13 Universal growth curve, a plot of the dimensionless mass ratio and the dimensionless time variable. Based on West et al. (2001).
Figure 2.14 Wandering albatross (Diomedea exulans) in flight. Photo available at wikimedia.
Figure 2.15 Evolutionary trends of biovolumes for Dinosauria and Mammalia. Simplified from Smith et al. (2016).
Figure 2.16 Growing height and height gain (cm/year) of de Montbeillard’s son. Height data from de Buffon (1753).
Figure 2.17 Quetelet’s loi de le croissance de la femme (law of women’s growth) shows a final average height of 1.58 m. Reproduced from Quetelet (1835), 27.
Figure 2.18 Expected weight-for-age growth of American boys and girls. Based on Kuczmarski et al. (2002).
Figure 2.19 Average height of 18-year-old Japanese males, 1900–2020. Plotted from data in SB (1996). Logistic curve has R2 of 0.98, inflection point in 1961, and asymptote height is 172.8 cm.
Figure 2.20 Growing prevalence of obesity in the US. Data from Ogden et al. (2012) and The State of Obesity (2017). The logistic curve had its inflection point in 1993 and its asymptote is at 37.5% of the total population.
Figure 3.1 Machine de Marly, the largest waterwheel installation of the early modern era, was completed in 1684 to pump water from the River Seine to the gardens of Versailles. Detail from a 1723 painting by Pierre-Denis Martin also shows the aqueduct in the background. The painting’s reproduction is available at wikimedia.
Figure 3.2 Logistic growth of maximum water turbine capacities since 1895; inflection point was in 1963. Data from Smil (2008) and ICOLD (2017).
Figure 3.3 Comparison of early growth stages of steam (1885–1913) and wind (1986–2014) turbines shows that the recent expansion is not unprecedented: maximum unit capacities of steam turbines were growing faster (Smil 2017b).
Figure 3.4 Corliss steam engine at America’s Centennial Exposition in Philadelphia in 1876. Photograph from the Library of Congress.
Figure 3.5 Logistic curve of the maximum displacement of transatlantic commercial liners, 1849–1961 (Smil 2017a).
Figure 3.6 Growth of maximum steam turbine capacities since 1884. Five-parameter logistic curve, inflection year in 1954, asymptote has been already reached. Data from Smil (2003, 2017a).
Figure 3.7 Logistic growth (inflection year in 1933, asymptote at 36.9%) of average efficiency of US thermal electricity-generating plants. Data from Schurr and Netschert (1960) and USEIA (2016).
Figure 3.8 Carl Benz (with Josef Brecht) at the wheel of his patent motor car in 1887. Photograph courtesy of Daimler AG, Stuttgart.
Figure 3.9 Linear growth of average power of US passenger vehicles, 1903–2020. Data from Smil (2014b) and USEPA (2016b).
Figure 3.10 OOCL Hong Kong, the world’s largest container ship in 2019, carries an equivalent of 21,413 twenty-foot standard units. Diesels and container vessels have been the key prime movers of globalization. Photo available at wikimedia.
Figure 3.11 Linear fit of the maximum thrust of jet engines. Data from Smil (2010b).
Figure 3.12 Evolution of the bypass ratio in commercial jetliners. Data from specifications for GE, P&W, and Rolls-Royce engines and from Ballal and Zelina (2003). Maximum ratios have seen linear growth that averaged about 2.2 units per decade.
Figure 3.13 Evolution of jetliner efficiency in terms of relative fuel consumption from Boeing 707 (1958) to Boeing 787–10 (2017). Data from Ballal and Zelina (2003) and from www
Figure 3.14 Record conversion efficiencies of research PV cells. Simplified from NREL (2018).
Figure 3.15 Light efficacy (lm/W) since 1930. Based on Osram Sylvania (2009) and subsequent efficacy reports.
Figure 3.16 Logistic fit (inflection point in 1916, asymptote of 89.9%) of the share of power in US manufacturing supplied by electric motors, 1909–1950. Data from Daugherty (1927) and Schurr et al. (1990).
Figure 4.1 Growth of ETOPS for jetliners. In 1988 the three-hour limit opened 95% of the Earth’s surface for commercial air transport, and the longest permissible single-engine operation of 370 minutes in 2018 is just 53 minutes shorter than the flight time from New York to London.
Figure 4.2 Roman crane depicted on a marble relief in the tomb of the Haterii (ca. 100 CE) discovered in 1848 near Porta Maggiore in Rome. The crane is powered by five people treading inside a large wooden wheel. Image available at www
Figure 4.3 K-10000, the world’s largest crane. Maximum hook radius is 100 m, height under the hook is 85 m and capacity is 94 t. Image available at http://
Figure 4.4 Flying Cloud became the most famous clipper ship built by Donald McKay after it clocked the world’s fastest time (89 days and 8 hours) for sailing from New York to San Francisco in 1853. Image available at wikimedia.
Figure 4.5 Four record-holding skyscrapers: Woolworth Building (1913–1930); Empire State Building (1930–1972); Petronas Towers (1998–2004); and Burj Khalifa (2010–2020). All photos available at wikimedia.
Figure 4.6 Logistic curve and polynomial regression of the growth of maximum skyscraper height. Data from Landau and Condit (1996) and Skyscraper Center (2017).
Figure 4.7 Growth of the total number of buildings taller than 200 m. Logistic curve in its early stage of ascent. Data from Emporis (2017).
Figure 4.8 Growth of the average area of American houses since 1900. Logistic curve had the inflection year in 1979 and its asymptote is about 260 m2. Data from Wilson and Boehland (2005) and USCB (2016a).
Figure 4.9 Growth of the longest railway tunnels, 1840–2020. Data mostly from Beaver (1972) and Onoda (2015).
Figure 4.10 Growth of the longest suspension bridges since 1825. Data mostly from History of Bridges (2017).
Figure 4.11 Growth curve of German Autobahnen, 1935–2015. Data from Zeller (2007) and Bundesamt für Statistik.
Figure 4.12 Growth of the total length of paved US roads since 1905. Plotted from data in USBC (1975) and subsequent volumes of US Statistical Abstract.
Figure 4.13 Growth of the total length of highways in China. Logistic curve with the inflection point in 2007 and asymptote about 30% above the 2015 total. Data from NBS (2000, 2016).
Figure 4.14 Growth curves of the total length of railroads in the US, UK, France, and Japan with some short-term extensions. Plotted from data in Mitchell (1998).
Figure 4.15 Limits of human performance: the world’s 10 best performances annually between 1896 and 2016 in men for the 800 m run, high jump, and shot-put show clear plateaus since the early 1980s. Simplified from Marck et al. (2017).
Figure 4.16 Four-masted paddlewheel liner Great Western designed by Isambard Kingdom Brunel and launched in 1837. Image available at Wikipedia.
Figure 4.17 Passengers on Japan’s trains, 1874–2014. Plotted from data available at SB (1996, 2017a). Logistic curve with the inflection year in 1958 and with the 2015 total only a fraction of 1 percent below the asymptotic level.
Figure 4.18 Logistic fit of the maximum passenger capacity of commercial airplanes: from KLM’s de Havilland DH.16 (four passengers) in 1920 to Airbus 380 (544 passengers in three classes, 868 maximum) in 2007. Plotted from individual airplane specifications.
Figure 4.19 Growth of global civil aviation traffic (domestic and international flights) measured in terms of passenger-kilometers. Logistic curve in its early stage indicates further substantial growth in the decades ahead. Data from ICAO (2016) and from earlier annual reports.
Figure 4.20 The growing power density of successive families of vacuum tubes forms a hyperbolic growth envelope similar to that of Moore’s law. Data from Granatstein et al. (1999).
Figure 4.21 Computing speed records in operations per second and floating point operations per second. Data from Top 500 (2017).
Figure 4.22 Adoption rates of electric stoves, refrigerators, clothes washers, color TVs, and dishwashers. Based on Taylor et al. (2006).
Figure 4.23 Adoption rates of telephones, radios, VCRs, and mobile phones in the US. Based on Taylor et al. (2006).
Figure 4.24 Growth of annual sales of all mobile phones since 1997. The trajectory fits a logistic curve that inflected in 2008 and that is now approaching its asymptotic value. Data from GSMArena (2017).
Figure 4.25 The growth of annual sales of smartphones since the year 2005 has followed perfectly a logistic curve with the inflection year in 2012 and with the asymptote less than 10% above 2016 sales. Data from Canalys (2007) and Meeker (2017).
Figure 4.26 The post-1993 growth of Internet hosts has followed a logistic curve with the inflection year in 2008 and with the asymptotic value less than 10% above the 2017 total. Data from ISC (2017).
Figure 4.27 The growth of Internet hosts also fits a Gaussian curve peaking in 2016 and returning to negligible values before 2040. Such a development seems quite unlikely—unless a new mode of hosting takes over. Data from ISC (2017).
Figure 4.28 Post-1992 growth of Internet traffic in TB/s fits a logistic curve in its early stages of growth indicating further substantial gains in decades ahead. Data from CISCO (2017).
Figure 5.1 Annual rates of GDP growth in Japan, South Korea, and China, 1960–2010. Plotted from World Bank data (World Bank 2018).
Figure 5.2 World population growth during the past 65,000 years plotted on a semi-logarithmic graph based on Biraben (2003).
Figure 5.3 Annual rates of world population growth, 1675–2018. Calculated from data in USCB (2016a) and World Bank (2018).
Figure 5.4 Average Swedish life expectancy since 1825. Curve fitted from data in Zijdeman and Silva (2014).
Figure 5.5 Global population growth, 1700–2500. Logistic curve with a distant inflection point (in 2105) and asymptote of 45.2 billion.
Figure 5.6 Global share of the urban population, 1800–2050. Plotted from various UN statistics. Logistic curve with the inflection point in 1969 and asymptote of 70.9%.
Figure 5.7 Share of the urban population in the US since 1790. Plotted from data in USBC (1975) and subsequent volumes of US Statistical Abstract. With the logistic curve inflected already in 1910, its asymptotic value is 87.2%.
Figure 5.8 The growth of Shanghai’s Lujiazui financial district epitomizes the rapid urbanization of post-1990 China. Photo available at wikimedia.
Figure 5.9 Tokyo’s population within prefectural boundaries (1900–2020)—a logistic curve with the inflection point in 1932 and asymptote at 13.8 million—and within the Tokyo Major Metropolitan Region since 1920: logistic curve inflection point in 1971 and asymptote at 38.8 million. Data from SB (1996) and TMG (2017).
Figure 5.10 For nearly three centuries Hadrian’s wall, built after 122 CE and crossing from the River Tyne to Bowness-on-Solvay, was the northernmost outpost of the Roman Empire. Photo by English Heritage.
Figure 5.11 Growth of the Roman republic and empire, 509 BCE–117 CE and the implied future trajectory based on a logistic fit. Data from Taagepera (1979) and author’s area measurements based on Talbert (2000). Year zero is 509 BCE.
Figure 5.12 Growth of the Roman republic and empire and the gradual retreat of Byzantium, 509 BCE–1453 CE. Data from Taagepera (1979) and author’s area measurements based on Talbert (2000). Year zero is 509 BCE.
Figure 5.13 Growth of global primary energy supply (including traditional biomass fuels) and fossil fuel and primary electricity supply since 1800. Data from Smil (2017b).
Figure 5.14 Growth of global crude oil production since 1870. Data from Smil (2017b).
Figure 5.15 Growth of global natural gas extraction since 1870. Data from Smil (2017b).
Figure 5.16 Growth of global coal production since 1800. While the two logistic curves for crude oil and natural gas provide a highly plausible indication of future development, coal’s indicated trajectory will almost certainly diverge from the indicated trend. Data from Smil (2017b).
Figure 5.17 Growth of global electricity generation since 1900. Data from Smil (2017b) and BP (2017).
Figure 5.18 Growth of global hydroelectricity generation since 1900. Data from Smil (2017b) and BP (2017).
Figure 5.19 Growth of global nuclear generation since 1960. Data from Smil (2017b) and BP (2017).
Figure 5.20 Growth of global cropland, 1700–2050. Logistic curve had its inflection point in 1876 and the total is now less than 5% below the asymptote. Data from PBL (2010) and FAO (2018).
Figure 5.21 Growth of US cropland, 1700–2050. Inflection point came already in 1876 and the recently cultivated area is very close to the asymptotic level. Data from PBL (2010) and FAO (2018).
Figure 5.22 Growth of global grasslands. The inflection year was in 1923 and the total area is now less than 10% from the asymptotic level. Data from PBL (2010) and FAO (2018).
Figure 5.23 Worldwide production of nitrogenous fertilizers since 1913. Another logistic curve that is very close to its asymptote. Data from Smil (2001) and FAO (2018).
Figure 5.24 Global harvest of staple grain crops since 1900. Data from Smil (2013a) and FAO (2018).
Figure 5.25 Basic oxygen furnaces, such as this one at ThyssenKrupp steelworks in Duisburg, dominate the global production of steel. Photo available at wikimedia.
Figure 5.26 Worldwide steel production since 1850. Data from Smil (2016b).
Figure 5.27 Worldwide cement production since 1950. Data from Smil (2014b).
Figure 5.28 Logistic curve of worldwide semiconductor sales, 1976–2016. Plotted from data in SIA (2017).
Figure 5.29 Growth and logistic outlook of GDP (expressed in international $2011) in four major economies—France, Japan, and the US since 1870, and China since 1950. Data from World Bank (2018).
Figure 5.30 Growth of per capita income in the US, Japan, and China since 1950. Data from World Bank (2018).
Figure 5.31 Growing shares of international trade in the world economic product since 1870. Data from Klasing and Milionis (2014) and World Bank (2018).
Figure 5.32 Petare slum in Caracas, Venezuela, is an example of a fairly orderly slum development. Photo available at wikimedia.
Figure 6.1 US crude oil extraction forecast based on the 1900–1980 trajectory, and actual 1900–2018 performance. Data from USBC (1975) and USEIA (2019).
Figure 6.2 Population of Greater London: best fits based on 1801–1981 and 1801–2001 totals. Data from Morrey (1978) and GLA (2015).
Figure 6.3 Tardigrada, one of the near-indestructible forms of life capable of cryptobiotic existence. Photo available at wikimedia.
Figure 6.4 Mortality curves for various species as functions of age. Simplified from Jones et al. (2014).
Figure 6.5 Black bakelite phone. Image available at oldphoneworks.com.
Figure 6.6 Complete trajectories of British and Dutch coal extraction. Plotted from data in de Jong (2004) and DECC (2015).
Figure 6.7 British steel output, 1900–2020. Fluctuating output reflects economic downturns, expansions, and wars and hence the normal curve is not a particularly close fit (R2 of 0.79). The production peak came in 1970, with the 2015 output below the level attained first in 1936. Data from https://
Figure 6.8 Steelmaking transitions in the US, 1850–2000. From Smil (2005) and WSA (2017).
Figure 6.9 Number of American draft horses between 1850 and 1970 conforms closely to the normal curve trajectory. Data from USBC (1975).
Figure 6.10 Number of US steam locomotives: a very good Gaussian fit for the nine decades between 1876 and 1967. Data from USBC (1975).
Figure 6.11 The historical growth of the US passenger car fleet can be fitted quite well into a normal curve peaking around 2030. Data from USBC (1975) and from subsequent volumes of the US Statistical Abstract.
Figure 6.12 Successive normal curves chart the US sales of recorded music: vinyl records were displaced by cassette tapes, cassettes were displaced by CDs, and those were largely eliminated by music downloading and then by streaming. Plotted from data in RIAA (2017).
Figure 6.13 Totals of US and Soviet/Russian nuclear warheads, 1953–2010. Norris and Kristensen (2006) and Arms Control Association (2017).
Figure 6.14 Age-sex structures of the Japanese population, 1930, 1950, 2000, and 2050. Simplified from Smil (2007).
Figure 6.15 The beginning of the end of Japan’s short-lived empire: USS West Virginia sinking in Pearl Harbor on December 7, 1941, after the Japanese torpedo and bomb attack. Photo from the Library of Congress.
Figure 6.16 Nikkei 225 average, 1950–2010. Graph based on data available at https://
Figure 6.17 In a photo taken in April 2009 an old man looks from the top floor of Tokyo’s municipal building on the sprawling city: during his lifetime the country rose from defeat and devastation to become a respected, even feared, economic superpower but almost immediately began its gradual economic and demographic retreat. Author’s photo.
Figure 6.18 Few nighttime images from space illustrate the extent of anthropogenic light pollution as stunningly as the view of the most densely populated parts of Western and Central Europe. NASA image.
Figure 6.19 Global CO2 emissions, 1750–2050. Data from Marland et al. (2017).
