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Figure from:The World System urbanization dynamics: a quantitative analysis

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As has been mentioned above, Chandler's database does not make it possible to trace the world macrourbanization dynamics after 1400.* That is why in order to obtain an overall picture of the world urbanization dynamics we shall have to rely with respect to Period B2 on Gruebler's estimates (incidentally, let us recollect that because of a very small number of data points in this database the — Figure 10 As has been mentioned above, Chandler's database does not make it possible to trace the world macrourbanization dynamics after 1400.* That is why in order to obtain an overall picture of the world urbanization dynamics we shall have to rely with respect to Period B2 on Gruebler's estimates (incidentally, let us recollect that because of a very small number of data points in this database the

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NOTES. Data sources: Modelski 2003; Gruebler 2006; UN Population Division 2006. Modelski provides his estimates of the world urban population (for cities with >10000 inhabitants) for the period till 1000 BCE, Gruebler's estimates cover the period between 900 and 1950 CE, whereas the UN's estimates cover the period after 1950. The estimates of the world urban population for the period between 1000 BCE and 900 CE were produced on the basis of Chandler's (1987) data on the world urban population living in large cities (with >40000 inhabitants).

NOTES: R = 0.998, R? = 0.996, p << 0.0001. Black markers correspond to empirical estimates of Modelski (2003), Gruebler (2006) and UN Population Division (2006). The solid grey curve was generated by the following equation: Diagram 2. World Urban Population Dynamics (in millions), for cities with > 10000 inhabitants (5000 BCE — 1990 CE): correlation between the dynamics generated by the quadratic-hyperbolic model and empirical estimates

Jiagram 3. Block Scheme of the Nonlinear Second Order Positive Feedback between Technological Development and Demographic Growth As our (both mathematical and empirical) analysis (see, e.g., Kopotaes, Mankos, XantypuHa 2005a, 2005b; Korotayev, Malkov, and Khaltourina 2006a) suggests, up to the 1970s the above mentioned mechanism tended to lead not only to the hyperbolic growth of the World System population, but also to the hyperbolic growth of the per capita surplus’ and also to the quadratic-hyperbolic growth of the world GDP (see Diagram 4):

Jiagram 6. World Urban Population Dynamics (in millions), for cities with >10000 inhabitants (5000 BCE- 2006 CE), with a forecast till 2350 NOTES. Data sources: Modelski 2003; Gruebler 2006; UN Population Division 2006. The curve for 2006-2350 has been calculated on the basis of Gruebler's medium forecast for the dynamics of the world urbanization (i.e., the proportion of the urban population in the overall population of the world) and our own forecast of the world population for this period (Korotayev, Malkov, Khaltourina 2006a).

Diagram 11. Dynamics of the World Macrourbanization (proportion of population living in large, >40,000, cities in the overall population of the world) according to the databases of Modelski, Chandler, and Gruebler (4000 BCE — 1950 CE), logarithmic scale

NOTES: R = 0.997, R? = 0.994, p< 0.0001. The black markers correspond to Gruebler's (2006) empirical estimates. The solid grey curve has been generated by the following equation: Diagram 12. World Macrourbanization Dynamics, 1250-1950 CE: correlation between predictions of the hyperbolic model and empirical estimates