Articles | Volume 13, issue 2
https://doi.org/10.5194/esd-13-1021-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-13-1021-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Lotka's wheel and the long arm of history: how does the distant past determine today's global rate of energy consumption?
Department of Atmospheric Sciences, 135 S 1460 E, Rm 819, University of Utah, Salt Lake City, Utah 84112, USA
Matheus R. Grasselli
Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada
Stephen Keen
University College London, London, WC1E 6BT, UK
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Cited articles
Ayres, R. U. and Warr, B.: The economic growth engine, Edward Elgar, Cheltenham, UK, ISBN 978 1 84844 182 8, 2009. a
Ayres, R. U., Ayres, L. W., and Warr, B.:
Exergy, power and work in the US economy, 1900–1998, Energy, 28, 219–273, https://doi.org/10.1016/S0360-5442(02)00089-0, 2003. a
Bettencourt, L. M. A., Lobo, J., Helbing, D., Kühnert, C., and West, G. B.:
Growth, innovation, scaling, and the pace of life in cities, P. Natl. Acad. Sci. USA, 104, 7301–7306, 2007. a
BP: Statistical review of world energy 2020, https://www.bp.com/en/global/corporate/energy-economics/statistical-review-of-world-energy.html (last access: April 2021), 2020. a
Deutch, J.:
Decoupling Economic Growth and Carbon Emissions, Joule, 1, 3–5, https://doi.org/10.1016/j.joule.2017.08.011, 2017. a
DOE:
Annual Energy Review, Tech. rep., Department of Energy, Energy Information Administration, https://www.eia.gov/international/data/world/total-energy/total-energy-production, (last access: November 2020), 2020. a
Feenstra, R. C., Inklaar, R., and Timmer, M. P.: The next generation of the Penn World Table, Am. Econ. Rev., 105, 3150–3182, 2015. a
Garrett, T. J.:
Are there basic physical constraints on future anthropogenic emissions of carbon dioxide?, Climatic Change, 3, 437–455, https://doi.org/10.1007/s10584-009-9717-9, 2011. a
Garrett, T. J.:
No way out? The double-bind in seeking global prosperity alongside mitigated climate change, Earth Syst. Dynam., 3, 1–17, https://doi.org/10.5194/esd-3-1-2012, 2012. a, b
Garrett, T. J.:
Long-run evolution of the global economy: 1. Physical basis, Earths Future, 2, 127–151, https://doi.org/10.1002/2013EF000171, 2014. a, b
Garrett, T. J.:
Long-run evolution of the global economy – Part 2: Hindcasts of innovation and growth, Earth Syst. Dynam., 6, 673–688, https://doi.org/10.5194/esd-6-673-2015, 2015. a
Garrett, T. J., Grasselli, M. R., and Keen, S.: Past world economic production constrains current energy demands: Persistent scaling with implications for economic growth and climate change mitigation, PLoS One, 15, e0237672, https://doi.org/10.1371/journal.pone.0237672, 2020. a, b, c, d
Garrett, T. J., Keen, S., and Grasselli, M.: Supplementary data and code for “Lotka's wheel and the long arm of history: how does the distant past determine today's global rate of energy consumption?”, HIVE [data set and code], https://doi.org/10.7278/S50d-n8p4-ehkb, 2022. a, b
Haff, P.:
Technology as a geological phenomenon: implications for human well-being, Geological Society, London, Special Publications, 395, 301–309, 2014. a
Jarvis, A.:
Energy Returns and The Long-run Growth of Global Industrial Society, Ecol. Econ., 146, 722–729, https://doi.org/10.1016/j.ecolecon.2017.11.005, 2018. a
Keen, S., Ayres, R. U., and Standish, R.:
A Note on the Role of Energy in Production, Ecol. Econ., 157, 40–46, 2019. a
Lamb, D. and Verlinde, J.: Physics and chemistry of clouds, Cambridge University Press, ISBN 10 0521899109, 2011. a
Lindenberger, D. and Kümmel, R.:
Energy and the state of nations, Energy, 36, 6010–6018, https://doi.org/10.1016/j.energy.2011.08.014, 2011. a
Lotka, A. J.:
Contribution to the energetics of evolution, P. Natl. Acad. Sci. USA, 8, 147–151, 1922. a
Maddison, A.: The World Economy: Historical Statistics, OECD, https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-database-2010 (last access: April 2010), 2003. a
Nordhaus, W. D.:
Revisiting the social cost of carbon, P. Natl. Acad. Sci. USA, 114, 1518–1523, https://doi.org/10.1073/pnas.1609244114, 2017. a, b
Oliver, C. D.:
Forest development in North America following major disturbances, Forest Ecol. Manag., 3, 153–168, 1980. a
Oohata, S.-I. and Shinozaki, K.:
A statical model of plant form-Further analysis of the pipe model theory, Japanese Journal of Ecology, 29, 323–335, 1979. a
Piketty, T.: Capital and ideology, Harvard University Press, ISBN 9780674980822, 2020. a
Samuelson, P. A.:
A Summing Up, Q. J. Econ., 80, 568–583, 1966. a
Shinozaki, K., Yoda, K., Hozumi, K., and Kira, T.:
A quantitative analysis of plant form-the pipe model theory: II. Further evidence of the theory and its application in forest ecology, Japanese Journal of Ecology, 14, 133–139, 1964. a
Sorrell, S.:
Energy Substitution, Technical Change and Rebound Effects, Energies, 7, 2850–2873, https://doi.org/10.3390/en7052850, 2014. a
Sraffa, P.: Production of commodities by means of commodities: Prelude to a critique of economic theory, CUP Archive, ISBN 10 0521099692, 1975. a
The World Bank: DataBank, https://databank.worldbank.org (last access: April 2021), 2019. a
Tol, R. S. J.:
The Economic Impacts of Climate Change, Rev. Env. Econ. Policy, 12, 4–25, https://doi.org/10.1093/reep/rex027, 2018. a
United Nations: United Nations Statistical Databases, http://data.un.org (last access: June 2014), 2010. a
United States Census Bureau: Historical Estimates of World Population International Data Base, https://www.census.gov/data/tables/time-series/demo/international-programs/historical-est-worldpop.html (last access: April 2021), 2018. a
Victor, P.:
Questioning economic growth, Nature, 468, 370–371, https://doi.org/10.1038/468370a, 2010. a
Zhang, D. D., Brecke, P., Lee, H. F., He, Y.-Q., and Zhang, J.:
Global climate change, war, and population decline in recent human history, P. Natl. Acad. Sci. USA, 104, 19214–19219, https://doi.org/10.1073/pnas.0703073104, 2007. a
Short summary
Current world economic production is rising relative to energy consumption. This increase in
production efficiencysuggests that carbon dioxide emissions can be decoupled from economic activity through technological change. We show instead a nearly fixed relationship between energy consumption and a new economic quantity, historically cumulative economic production. The strong link to the past implies inertia may play a more dominant role in societal evolution than is generally assumed.
Current world economic production is rising relative to energy consumption. This increase in...
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