An Investigation of the Relationships between Empirical Trends in Both Entropy and Maximum Urban Area Size Over the Last 5,000 Years
Almanac: History & Mathematics:Entropy and Destabilization
DOI: https://doi.org/10.30884/978-5-7057-6233-0_02
Abstract
The previous paper (Harper 2017a) revealed a relationship between modeled system entropy and phases of punctuation and stasis of modeled system population sizes over time. This paper investigates the same relationship between system entropy and population, but does so using empirical data for both entropy, based on total world-system population size, maximum urban area population size, and gamma, γ, a fitted constant and natural log-transformed population data for maximum urban area, all over the last 5,000 years. First, basic entropy trends over human history are investigated, and then by selectively removing outlier points, a process called skeletonization, more detailed patterns of entropy are revealed and analysed. It is shown that a pattern of alternating increasing and decreasing system entropy is associated with alternating periods of stasis and punctuation of maximum urban area size. Also, it is shown that embedded within the pattern of alternating increasing and decreasing entropy are linear and non-linear entropy patterns. Some speculation on the adaptive function of such geometries is shared. Further, the potential of the entropy pattern as a standard of comparison for other historical trends is discussed.
Keywords: entropy, maximum urban area size, stasis, punctuation, skeletoni-zation.
Conclusions
1. The macroscopic view of both maximum urban area population and the entropy associated with the world-system supporting those maximum urban areas exhibit the same hyperbolic pattern of growth.
2. The fine scale of the entropy pattern over the last 5,000 years is revealed by a process of skeletonization in which outlier points are removed.
3. Initial skeletonization reveals an alternating pattern of periods, groups of centuries, of entropy decrease followed by entropy increase. The periods of entropy decrease are approximately 1.7 times longer than the periods of entropy increase.
4. At one level of skeletonization there are four periods of decreasing and increasing entropy. Further skeletonization reduces this number to three.
5. Further skeletonization again reveals two parabolic point distributions, which are separated by two shorter periods of linear change.
6. The parabolas by themselves are sequentially concave up followed by concave down, and the periods of linear change alternate between an initial period having a negative slope and a second period, the one we are currently in, having a positive slope.
7. A composite of these four entropy point distributions provides a model against which the types of world-system historical change may be compared.
8. The future of the world-system may in broad terms only be predicted, given the verity of the combined pattern of entropy change.
Acknowledgement
The author wishes to extend his heartfelt gratitude to Evgeniya Stolyarova for very professional editing of this paper.
References
Bailey K. 1990. Social Entropy Theory. Albany, N.Y.: The State University of New York Press.
Bak P. 1996. How Nature Works: The New Science of Self-organized Criticality. New York: Pergamon Press.
Bak P., and Sneppen K. 1993. Punctuated Equilibrium and Criticality in a Simple Model of Evolution. Physical Review Letters 71(24): 4083–4086.
Bardi U. 2019. Before the Collapse: A Guide to the Other Side of Growth. New York: Springer.
Boserup E. 1993. The Conditions of Agricultural Growth: The Economics of Agricultural Change Under Population Pressure. London: Routledge.
Chandler T. 1987. Four Thousand Years of Urban Growth: An Historical Census. Harvard: Edwin Mellin Press.
Chew S. C. 2007. Recurring Dark Ages: Ecological Stress, Climate Changes, and System Transformation. New York: AltaMira Press.
Eigen M., and Schuster P. 1977. The Hypercycle: A Principle of Natural Self-Organization. Part A: Emergence of the Hypercycle. Die Naturwissenschaften 64: 541–565.
Eldredge N., and Gould S. J. 1972. Punctuated Equilibrium: An Alternative to Phyletic Gradualism. Models in Paleobiology / Ed. by T. J. M. Schopf, pp. 82–115. San Francisco: Freeman Cooper.
von Foerster H., Mora P. M., and Amiot L. W. 1960. Doomsday: Friday, November 13, A. D. 2026. Science 132: 1291–1295.
Grinin L., and Korotayev A. 2015. The Great Divergence and the Great Convergence. New York: Springer.
Hardy A. 1908. Mendelian Proportions in a Mixed Population. Science 28: 49–50.
Harper A. 2010. The Trajectory of the World System over the Last 5000 Years. History & Mathematics: Processes and Models of Global Dynamics / Ed. by L. Grinin, P. Herrmann, A. Korotayev, and A. Tausch, pp. 13–63. Volgograd: Uchitel Publishing House.
Harper A. 2017a. An Equation-Based Systems Approach to Modeling Punctuated Equilibria Apparent in the Macropattern of Urbanization over Time. History and Mathematics: Economy, Demography, Culture, and Cosmic Civilizations / Ed. by L. Grinin, and A. Korotayev, pp. 200–217. Volgograd: Uchitel.
Harper A. 2017b. The Punctuated Equilibrium Macropattern of World System Urbanization and the Factors that Give Rise to That Macropattern. Social Evolution and History: Studies in the Evolution of Human Societies 16(1): 86–127.
Harper A. 2019. A Toy Model Mechanism for Greater-Than-Exponential Human Population Growth. History & Mathematics: Big History Aspects / Ed. by L. Grinin, and A. Korotayev, pp. 43–51. Volgograd: Uchitel.
Korotayev A., Malkov A., and Khaltourina D. 2006. Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth. Moscow: Editorial URSS.
Modelski G. 2003. World Cities: –3000 to 2000. Washington. D. C.: FA-ROS 2000.
Padgett J. F., and Powers W. W. 2012. The Emergence of Organizations and Markets. Princeton: Princeton University Press.
Shannon C. 1948. A Mathematical Theory of Communication. Bell System Technical Journal 27(3): 379–423.
Smith J. 1968. Mathematical Ideas in Biology. New York: Cambridge University Press.
Tainter J. 1988. The Collapse of Complex Societies. New York: Cambridge University Press.
Tiner J. 2006. The World of Physics. Green Forest, AR: Master Books.
U.S. Census Bureau. N. d. U.S. Census Bureau Historical Estimates of World Population. URL: http://www.census.gov/population/international/data/worldpop/table/history/php.
Wallerstein I. 2004. World-Systems Analysis: An Introduction. Durham: Duke University Press.
Weinberg W. 1908. Uber den Nachweis der Vererbung beim Menschen. Jahreshefte des Vereins für vaterländische Naturkunde in Württemberg. 64: 369–382.
