Interpretations of Hyperbolic Growth




Hyperbolic growth describes the historical economic growth and historical growth of population, but their mechanism remains unexplained. Presented here is a brief survey of attempts to understand hyperbolic growth. Mathematical formulations are in general complicated and there is no clear advantage in using them because they do not give better description of data than the simple, two-parameter hyperbolic formula. They also do not explain the mechanism of growth. The well-known simple formula suggests a simple explanation. Two examples show how two independent investigations were on a brink of making an important and breakthrough discovery and how their potential discovery was thwarted by the established knowledge in demography and in economic research. Researchers who could have used their expertise to suggests new research directions and to advance science were constrained by doctrines, which are widely accepted by faith.


Key words: Hyperbolic growth, Mechanism of growth, Population growth, Economic growth, Growth models, Growth theory, Malthusian stagnation

JEL: A10, A12, C02, C12, C20, C50, Y80.

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Aliprantis, C.D., Brown, D.J., & Burkinshaw, O. (1990). Existence and optimality of competitive equilibria. Heidelberg: Springer-Verlag.

Artzrouni, M., & Komlos J. (1985). Population growth through history and the escape from the Malthusian trap: A homeostatic simulation model. Genus, 41, 21-39.

Becker, G.S., Murphy, K.M., & Tamura, R. (1990). Human capital, fertility, and economic growth. Journal of Political Economy, 98(5-2), S12-S37. doi. 10.1086/261723

Ewing, B., Moore, D., Goldfinger, S., Oursler, A., Reed, A., & Wackernagel, M. (2010). The Ecological Footprint Atlas 2010. Oakland: Global Footprint Network.

Galor, O. (2005a). From stagnation to growth: Unified growth theory. In P. Aghion & S. Durlauf (Eds.), Handbook of Economic Growth, (pp. 171-293). Amsterdam: Elsevier.

Galor, O. (2005b). The demographic transition and the emergence of sustained economic growth. Journal of the European Economic Association, 3(2-3), 494-504. doi. 10.1162/jeea.2005.3.2-3.494

Galor, O. (2007). Multiple Growth Regimes - Insights from Unified Growth Theory. Journal of Macroeconomics, 29(3), 470-475. doi. 10.1016/j.jmacro.2007.06.007

Galor, O. (2008a). Comparative Economic Development: Insight from Unified Growth Theory. [Retrieved from].

Galor, O. (2008b). Economic Growth in the Very Long Run. In: Durlauf, S.N. & Blume, L.E., Eds., The New Palgrave Dictionary of Economics, Palgrave Macmillan, New York. doi. 10.1057/9780230226203.0434

Galor, O. (2008c). Comparative Economic Development: Insight from Unified Growth Theory. [Retrieved from].

Galor, O. (2010). The 2008 Lawrence R. Klein Lecture - Comparative economic development: Insights from Unified Growth Theory. International Economic Review, 51(1), 1-44. doi. 10.1111/j.1468-2354.2009.00569.x

Galor, O. (2011). Unified Growth Theory. Princeton, New Jersey: Princeton University Press.

Galor, O. (2012a). Unified Growth Theory and Comparative Economic Development. [Retrieved from].

Galor, O. (2012b). The Demographic Transition: Causes and Consequences. Cliometrica, 6(1), 1-28. doi. 10.1007/s11698-011-0062-7

Galor, O. (2012c). Unified Growth Theory and Comparative Economic Development. [Retrieved from].

Galor, O. & Moav, O. (2002). Natural selection and the origin of economic growth. The Quarterly Journal of Economics, 117(4), 1133-1191. doi. 10.1162/003355302320935007

Galor, O., & Weil, D.N. (1999). From Malthusian stagnation to modern growth. The American Economic Review, 89(2), 150-154. doi. 10.1257/aer.89.2.150

Galor, O., & Weil, D. N. (2000). Population, technology, and growth: From Malthusian stagnation to the demographic transition and beyond. The American Economic Review, 90(4), 806-828. doi. 10.1257/aer.90.4.806

Gilpin, M.E., & Ayala E.J. (1973). Global models of growth and competition. Proc. Nat. Acad. Sci. USA, 70(12), 3590-3593.

Hofbauer, J. & Sigmund. K. (1998). Evolutionary games and population dynamics. Cambridge, UK: Cambridge University Press.

Johansen, A., & Sornette, D. (2001). Finite-time singularity in the dynamics of the world population, economic and & financial indices. Physica A, 294, 465–502. doi. 10.1016/S0378-4371(01)00105-4

Kapitza, S.P. (1992). A Mathematical Model of World Population Growth (in Russian). Matematicheskoe Modelirovanie, 4, 65-79.

Kapitza, S.P. (1996). The phenomenological theory of world population growth. Physics-Uspekhi, 39(1), 57-71.

Kapitza, S.P. (2006). Global Population Blow-up and After. Hamburg: Global Marshall Plan Initiative.

Karev, G.P. (2005a). Dynamics of inhomogeneous populations and global demography models. [Retrieved from].

Karev, G.P. (2005b). Dynamics of Heterogeneous Populations and Communities and Evolution of Distributions. [Retrieved from].

Karev, G.P. (2010). On mathematical theory of selection: Continuous time population dynamics. J. Math. Biol. 60, 107–129. [Retrieved from].

Karev, G.P. (2015). Private communication

Karev, G.P. & Kareva, I.G. (2014). Replicator equations and models of biological populations and communities. Math. Model. Nat. Phenom., 9(3), 68-95. doi. 10.1051/mmnp/20149305

Khaltourina, D.A. & Korotayev A.V. (2007). A modified version of a compact mathematical model of the World system economic, demographic, and cultural development. In M.G. Dmitriev, A.P. Petrov, & N.P. Tretyakov (Eds.), Mathematical Modelling of Social and Economic Dynamics (pp. 274–277). Moscow: RUDN.

Korotayev, A.V. & Malkov, A.S. (2012). A Compact Mathematical Model of the World System Economic and Demographic Growth, 1 CE – 1973 CE. [Retrieved from].

Korotayev, A. (2005). A compact macromodel of World system evolution. Journal of World-Systems Research, 11(11), 379-393. doi. 10.5195/jwsr.2005.401

Korotayev, A.V. (2015). Private communication.

Korotayev, A., Malkov, A. & Khaltourina, D. (2006a). Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends. Moscow: KomKniga/URSS

Korotayev, A., Malkov, A. & Khaltourina, D. (2006b). Introduction to Social Macrodynamics. Compact Macromodels of the World System Growth. Moscow: URSS Publishers.

Kremer, M. (1993). Population growth and technological change: One million B.C. to 1990. The Quarterly Journal of Economics, 108(3), 681-716. doi. 10.2307/2118405

Lagerlöf, N-P. (2003a). From Malthus to modern growth: Can epidemics explain three regimes? International Economic Review, 44(2), 755-777. doi. 10.1111/1468-2354.t01-1-00088

Lagerlöf, N-P. (2003b). Mortality and early growth in England, France and Sweden. Scand. J. of Economics, 105(3), 419–439. doi. 10.1111/1467-9442.t01-2-00006

Maddison, A. (2001). The World Economy: A Millennial Perspective. Paris: OECD.

Maddison, A. (2010). Historical statistics of the world economy: 1-2008 AD. [Retrieved from].

Manning, S. (2008). Year-by-Year World Population Estimates: 10,000 B.C. to 2007 A.D. [Retrieved from]. and references therein.

Nielsen, R.W. (2014). Changing the Paradigm. Applied Mathematics, 5, 1950-1963. doi. 10.4236/am.2014.513188

Nielsen, R.W. (2015). Unified Growth Theory contradicted by the GDP/cap data. [Retrieved from].

Nielsen, R.W. (2016a). Growth of the world population in the past 12,000 years and its link to the economic growth. Journal of Economics Bibliography, 3(1), 1-12.

Nielsen, R.W. (2016b). Mathematical analysis of the historical economic growth with a search for takeoffs from stagnation to growth. Journal of Economic Library, 3(1), 1-23.

Nielsen, R.W. (2016c). Unified Growth Theory contradicted by the mathematical analysis of the historical growth of human population. Journal of Economics and Political Economy, 3(2), 242-263.

Nielsen, R.W. (2016d). Scientifically unacceptable established knowledge in demography and in economic research. Journal of Economic Library, 3(3), 429-457.

Nielsen, R.W. (2016e). Unified Growth Theory contradicted by the absence of takeoffs in the Gross Domestic Product. Turkish Economic Review, 3(1), 16-27.

Nielsen, R.W. (2016f). The postulate of the three regimes of economic growth contradicted by data. Journal of Economic and Social Thought, 3(1), 1-34.

Nielsen, R.W. (2016g). Mathematical analysis of the historical income per capita distributions. Turkish Economic Review, 3(2), 300-319.

Nielsen, R.W. (2016h). Mathematical analysis of income per capita in the United Kingdom. Turkish Economic Review, 3(4), 551-561.

Nielsen, R.W. (2016i). Demographic Transition Theory and its link to the historical economic growth. Journal of Economic and Political Economy, 3(1), 32-49.

Nielsen, R.W. (2016k). The Law of Growth. Journal of Economic and Social Thought, 3(4), 481-489.

Podlazov, A.V. (2002). Theoretical demography: Models of population growth and global demographic transition (in Russian). In Advances in Synergetics: The Outlook for the Third Millennium (pp. 324–345). Moscow: Nauka.

Shklovskii, J.S. (1962). The universe, life and mind, (in Russian). Moscow: Academy of Science, USSR.

Shklovskii, J.S. (2002). The universe life and mind (5th edn.). John Wiley and Sons, Ltd, New York, US.

Statistics Sweden, (1999). Population development in Sweden in a 250-year perspective. Stockholm: Statistics Sweden. [Retrieved from].

US Census Bureau, (2016). International Data Base. [Retrieved from].

von Foerster, H., Mora, P., & Amiot, L. (1960). Doomsday: Friday, 13 November, A.D. 2026. Science, 132(3436), 255-296. doi. 10.1126/science.132.3436.1291

von Hoerner, S.J. (1975). Population Explosion and Interstellar Expansion. Journal of the British Interplanetary Society, 28, 691-712.

Wrigley, E. A., & Schofield, R.S. (1981). The Population History of England 1541-1871. London: Edward Arnold (Publishers) Ltd.



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