FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Ranked analysis of the life cycle of polities |
Guzev M.A., Kradin N.N., Nikitina E.Y. |
2017, issue 2, P. 180-190 |
Abstract |
| Many researchers, from Edward Gibbon to Arnold Toynbee, were interested in how large polities would emerge and collapse. Traditionally, the history of empires was considered both in temporal and spatial dynamics. This article focuses on the study of the external manifestations of polities' structural features which may be expressed by a limited set of mathematical curves described by the specified Zipf’s law. An ideal Zipf’s curve is characteristic of the classical empires with complex economies (China, Rome, and others). However, the curves of some empires have a distinctive feature – an ‘imperial tail’. The simpler the structure of large polities is, the closer is the line describing their livelihoods to a right line. |
Keywords: rank distribution, Zipf’s law |
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References |
| [1] P.T. Turchin, “Arise ‘cliodynamics’”, Nature, 454:7200, (2008), 34–35. [2] P.V. Turchin, Istoricheskaia dinamika: Na puti k teoreticheskoi istorii, KomKniga, Moskva, 2007. [3] R. Taagepera, “Size and Duration of Empires: Systematics of Size”, Social Science Research, 7, (1978), 108–127. [4] R. Taagepera, “Size and Duration of Empires: Growth-Decline Curves, 3000 to 600 B.C.”, Social Science Research, 7, (1978), 115–138. [5] R. Taagepera, “Size and Duration of Empires: Growth-Decline Curves, 600 B.C. to 600 A.D.”, Social Science History, 3:3–4, (1979), 180–196. [6] Ch. Chase-Dunn, T. Hall, R. Niemer, “Middlemen and Marcher States in Central Asia and East/West Empire Synchrony”, Social Evolution & History, 9:2, (2010), 52–79. [7] Ch. Chase-Dunn, A. Alvarez, H. Inoue, R. Niemeyer, A. Carlson, B. Fierro, B. and K. Lawrence, “Upward Sweeps of City and Empire Growth since the Bronze Age”, IROWS Working Paper Available, 2010, http://www.irows.ucr.edu/papers/irows22/irows22.htm. [8] Ch. Chase-Dunn, T. Hall, Rise and Demise: Comparing World-Systems, Boulder, CO: West- view, 1997. [9] C. Marchetti, J.H. Ausubel, “Quantitative Dynamics of Human Empires”, International Journal of Anthropology, 27:1–2, (2012), 1–62. [10] P. Turchin, “A Theory for formation of large empires”, Journal of Global History, 4, (2009), 191–217. [11] P. Turchin, S.A. Nefedov, Secular Cycles, Princeton University Press, Princeton, 2009. [12] F. Auerbach, “The Law of Population Concentration”, Petermann’s Geogr Releases, 59, (1913), 74–76. [13] G.K. Zipf, Human Behavior and the Principle of Least Effort, Addison-Wesley, Cambridge, Mass., 1949. [14] B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman, New York, 1977. [15] A. Clauset, C.R. Shalizi and M.E.J. Newman, “Power-law distributions in empirical data”, E-print: SIAM Rev., 51:4, (2007), 661–703, http://epubs.siam.org/doi/10.1137/070710111. [16] V.P. Maslov, “On a General Theorem of Set Theory Leading to the Gibbs, Bose-Einstein, and Pareto Distributions as well as to the Zipf-Mandelbrot Law for the Stock Market”, Mathematical Notes, 78:5, (2005), 807–813. [17] M.A. Guzev, E.Iu. Nikitina, “Rangovyi analiz Ugolovnogo Kodeksa RF (na primere ekonomicheskikh prestuplenii)”, Dal'nevost. matem. zhurn., 10:2, (2010), 117–129. |