‘The us today is like a house where the owners are busy tearing down the walls to throw bricks at the neighbors
PART V: HISTORICAL NETWORK AND INTERACTION PROCESSES p. 20
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- Table 4. Communalities
- Total Variance Explained
- Component Matrix(a)
| PART V: HISTORICAL NETWORK AND INTERACTION PROCESSES p. 20
Turchin (2007) shows evidence for “a great degree of synchrony between the secular cycles in Europe and China during two periods: (1) around the beginning of the Common Era and (2) during the second millennium.” We also find evidence for synchrony in city system rise and fall in common temporal variations in q for the second millennium. The correlations in q by time period follow a single factor model, as shown in Table 4, with China contributing the most to the 47% common variance between the three regions. Table 4. Communalities
Extraction Method: Principal Component Analysis. Total Variance Explained
Component Matrix(a)
Extraction Method: Principal Component Analysis. The evidence from city sizes adds detail on dynamical interaction to that of synchrony for the last millennium. Figure 12 shows that changes in q for Mid-Asia lead those of China by 50 years (the hugely significant correlation at 50-year lag 1; the lead of Mid-Asia over Europe by 150 years (lag 3) is not quite significant), and those of China lead Europe by by 100 years (lag 2).   
Figure 12: Cross-correlations for temporal effects of one region on another Our hypothesis has been Eurasian synchrony has been largely due to trade, particularly that between China and Europe. The cross-correlation in Figure 13, for the effect of Silk Road trade on growth of β in Europe, sustained by the Silk Road trade, for example, suggests that trade is indeed what causes the growth of power-law tails in urban size distributions. 
Figure 13: Cross-correlations for time-lagged effects of the Silk Road trade on Europe Our choice of the last millennium to test the interaction of the city size fluctuations with historical dynamics was motivated by the evolution of globalization in Eurasia in this millennium. Key elements in the transition to market-driven globalization occurred in China starting in the period of 10th century invention of national markets, with currencies, banks and market pricing, a historical sequence that leads, through diffusion and competition, to the global system of today (Modelski and Thompson 1996). The data on credit and liquidity in the Chinese economy also follows closely the rise and fall of q, as shown crudely in Figure 14. Rise of monetization, growth of credit, and development of banking accompany the early Zipfian q~1.5 of Song China, and these mechanisms of liquidity plummet with the Jin conquest of Kaifeng. Circa 7-800 years from 1100 BCE, with long periods of inflation, are required to regain liquidity and banking favoring international trade. During the Qing dynasty the Chinese money was silver coin. The first modern bank, the Rishengchang (Ri Sheng Chang) was established in 1824. It broadened to include banks in every major city, folding in bankruptcy in 1932. (the right end of the liquidity graph, estimated qualitatively in the lower figure, should be higher). 
Figure 14: A crude long-term correlation between Chinese credit and liquidity and q (REDO) We have scant data on total population relative to resources, and we have reliable data for the last millennium only for England in comparison with our Eurasian city data. There are few points of comparison, but temporal synchronies appear in those few points: 1300 and 1625 are the peaks of scarcity for ratios of people to resources and pre-1100, 1450, and 1750 are the troughs of plentiful resources. The peaks correspond to slumps in q and the troughs to rises. It is impossible to rule out at this point the possibility that our urban system fluctuations are interactively linked to Turchin’s secular cycles, particularly if we include both types of fluctuations: those in q, in β, and in our normalized minimum of the two, as wall, which reflects either type of slump. For China, the 800 year lag between urban system collapses in q resemble J. S. Lee’s interpretation of 800-year cycles of internecine conflict in China, as shown by his data, reproduced in Figure 15. There is also a dip in β in the middle of this period that might indicate shorter major fluctuations of the Chinese city system. 9 Mid-Asia also shows 7-800 year lags in our data between urban system collapses, and also has some dips in β in within the longer period. ~ Figure 15: Long-cycle internecine war cycles in China PART VI: CONCLUSIONS p. 24 This study and those that preceded it began as experiments in building from two sets of sources, one in quantitative history and the work of Goldstone (1991), Nefedov (1999), Turchin (2003), and Spufford (2002) and the other in mathematical and measurement concepts that incorporate city size distributions as an object of study in a more meaningful way. The development of unbiased estimates of variations in city size distributions using maximal likelihood (MLE) allowed a level of precision and accuracy even with small samples that led to some useful findings in this study that we think are reliable. By focusing on the 75 largest cities over a series of time periods that go back to antiquity – closely enough spaced to get the quantitative variations of the full cycles of city system oscillations – Chandler makes available a full run of data for studying how city system evolutions couple with agrarian sociopolitical dynamics. Initially, this will not be equally possible in every region at every time period, but only where the density of cities is sufficient for quantitative study. By focusing on China, however, we availed ourselves of one of the richest pockets of Chandler’s comparative data on cities, especially for the early period of globalization, where China had the largest number of large cities. In refining the present model for comparison with other regions we will consider whether to adjust for Chandler’s possible underestimation of walled city populations for China, but the biasing assumption he made for China’s walled cities (Appendix A) does not carry over to other regions. We did find strong evidence of historical periods of rise and fall in the city systems of different regions, and time lagged effects of changes in city size distributions in one region on other regions. These are weak and slow from Mid-Asia to China, and strong and fast from China to Europe, which makes sense in terms of the Silk Roads trade. Perhaps this is the missing evidence of synchronies that Chase-Dunn, Niemeyer, Alvarez, Inoue, Lawrence and Carlson (2006) were looking for but with cruder comparisons. Most of the correlations, however, are time-lagged rather than temporally synchronous. The effects run in the directions suggested by Modelski and Thompson (1996). We are reasonably confident in concluding that the Pareto I and II (q-exponential) measures of city hierarchies through time, especially when used in combination, can provide a measurement paradigm of standardized methods and tests of replication in historical comparisons. The attractive features of the q-measure gain added benefit from the precision of our measures with the use of MLE method. Richness of supporting data would logically take us next to Middle Asia and the larger world from 700 CE that embraced the rise of Islam, the Mongol use of the Silk Roads and development of new towns and cities on those routes to link China and the rest of Middle Asia into a global system. Such a study, modeled on this one, would include the role of the Indic subcontinent, and that of the Mongols (Barfield 1989, Boyle 1977) in trade and conquest, the Arab colonization of North Africa and Spain, and the feeding of urban developments in the Mediterranean, Russia, and Europe. When we compare our results, measurements, and mathematical models to those of the structural demography or secular cycles studies of Goldstone (1991), Nefedov (1999), and Turchin (2003, 2005), we find a novelty that separates our findings from that of the standard Lotka-Volterra oscillation model for historical fluctuations. Turchin (2003, 2004), for example, argues the Lotka-Voltera dynamic works optimally when one of the interactive variables (say, population/resource ratio measure of scarcity and sociopolitical violence) is offset by ¼ cycle. Our cycle of city-size oscillations might be four times as long as Turchin’s secular cycles (J.S. Lee divides his 800 year periods into two periods of 400, seeming to do with an early growth of early forms of “empire” in a region, then a time of turbulence in the second period; then a new cycle of empire. It is possible that the city cycle operates at this level, at the larger civilizational networks of states alternating with forms of empire. Long city-size system oscillations of ca. 800 years would not be offset by a ¼ cycle but by We have been able to discern some of the effects of trade fluctuations (if not trade network structure) in these models. The monetary liquidity variable for China, in one of our tests, showed the effect of a trade-related variable on q. We think it possible to reconstruct trade routes as historical time series, and to do ordinal ranking of trade volumes on these routes. We think that these have strong effects, along with disruptive conflicts and political or empire boundaries, on the economies of individual cities and regions, and that these variables could be shown to have dynamical interactions within the context of secular cycle and urban systems rise and fall. We can be less sure about inferring from empirical results for China or Europe to the real world of Chinese and European history and forward-looking prediction, because we expect to be able to do even better estimations with derivatives, ML estimation, and evaluation or correction of biases in a reconstruction of Chandler’s China dataset. Our hypotheses must remain hypotheses, not yet rejected. Some of patterns we to see in our data as concerns globalizing modernization are consistent with prior knowledge and others are startling. To be expected are the developmental trends of scale – larger M (largest cities), larger Y0 (total urban population), and larger P (total population). With time, the crossover to power-law parameter (Pareto II “scale” or σ) moves further down the tail, so that more and more of the city distribution becomes power law, consistent with much of the previous work on power-law scaling. What is startling is that there might be are long-wave oscillations in q that are very long. Hopefully, a long-term trend and contemporary structure of Zipfian city distributions is an indicator of stability, but even the 20th century data indicate that instabilities are still very much present and thus likely to rest on historical contingencies (somewhat like the occurrence of a next earthquake larger than any seen in x years prior), and very much open to the effects of warfare and internal conflicts that are likely to be affected by population growth, and as opposed to stabilization of trade benefiting per-capita-resources ratios. Our results allow us to consider the edge-of-chaos metaphor of complexity with respect of q as a first but largely insufficient approximation to an explanation for what we see historically. It is a truism to say that complexity, life, history, and complex systems generally stand somewhere between rigidity at one pole, which might be exemplified by q>1.7, and on the other, an exponential random distribution (q≈1) of city sizes, or the heightened unpredictability of chaos (0<q«1 ).10 But we do not see support for equilibrium on the “edge of chaos” in these data. The historical q-periods of China and other regions tend to cluster, somewhat like “edging on chaos,” near an average of q≈1.5, but they do so in terms of oscillations, not far from equilibrium, but not a stable equilibrium. From that average they may fall into decentralized chaos, here in the metaphoric sense (but with exceptionally low q), in which the power-law tails are absent (with larger cities seemingly crushed in size by internecine wars) and smaller cities are frequent relative to hubs, or rise into regimes are affected by massive external drains on the economy or political policies that seem to put q into abnormally rigid states (exceptionally high q). The directions of change in q are largely predictable as a function of the current-state variables (such as population/resource ratios and sociopolitical violence) in the historical dynamics models up to, but not yet including, the contemporary period. How to derive predictions for the contemporary era is not yet evident given the new configurations of industrial societies, but it is very probable that such predictions as do emerge for the present will contain processes operative in the past. APPENDIX A: Chandler’s Chinese City Data. Many Chinese historians question the estimates of Chinese city population densities given by Chandler (1987:7): "Chinese cities tend to have an especially low density because of the Chinese refusal to sleep below anyone, so their houses are of nearly all of just 1 story. Hence, inland Chinese cities had a density of only about 75 per hectare, and even in seaports or the imperial capital the density hardly exceeded 100.” One such anonymous reviewer considered this an underestimate by half based on current knowledge. To test the effects of these likely underestimates population, we examined the data from the first of our periods, as shown in Table A.3, after checking Chandler’s (1987:417-451) text to note the basis for his estimates for each city. We adjusted the five city estimates affected by raising each by 50% (half the attributed error), recomputed the number of cities for each size category, and then compared the power-law coefficients for the original and the revised data as well changes in estimates of q. Changes were evident and significant in each case. They did not change the r2 for goodness of fit, but for q, for example, the value change from 1.9 to 0.7. Similar tests can be made for other periods, but we may need independent evidence as to the extent to which the critique merits new density computations. Possible errors of this sort in Chandler’s estimation assumptions, then, could change our scaling results. These biases could change the patterns of variation in q seen in our results. Because Chandler uses the common assumptions throughout these historical periods up to 1950, however, it is possible that they may not affect our historical comparisons about relative changes in q, at least up through 1950. For 1962, 1968, and 1970 he has taken the city population data of Richard Forstall of Rand McNally and Co. To test the robustness of our results, however, would entail a project that builds on the Excel spreadsheet for the Chandler data as exemplified above. By consulting his book to pick out each variable used to make multiplicative estimates – such as size of urban area, number soldiers (e.g., times 6), number of streets, etc. – a spreadsheet of calculations with the multiples and their base numbers might be useful to improve Chandler’s estimates using a Bayesian weighting by consistency. Chandler (1987:6) also notes that “the large growth of suburbs outside city walls had not begun before 1850 except in the newly rising industrial conurbations of Britain.” This might cause problems “since the presence of suburbs has been well documented in history with new walls built to enclose a population that had spread beyond the original walls” (Pasciuti and Chase-Dunn 2002:1). Chandler does include suburbs in his criteria for city boundaries, however, and in his estimates throughout the book. References Adamic, Lada A. 1997. Zipf, Power-laws, and Pareto - a ranking tutorial. HP Labs, Palo Alto. http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html Bairoch, Paul. 1988. Cities and Economic Development: From the Dawn of History to the Present. Chicago: University of Chicago Press. Borges, E. P. 2005. Empirical nonextensive laws for the county distribution of total personal income and gross domestic product. Physica A 334-348. Borges, Ernesto P. 2004. Manifestações Dinâmicas e Termodinâmicas de Sistemas Nâo-Extensivos. Tese de Doutorado. Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro. Braudel, Fernand. 1992. Civilization and Capitalism, 15th-18th Century. Vol. 3, The Perspective of the World, translated by S. Reynolds. Berkeley, CA: University of California Press. Chandler, Tertius. 1987. 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______1991 Core, peripheries and civilizations. Pp. 113-166 in Christopher Chase-Dunn and Thomas D. Hall (eds.) Core/Periphery Relations in Precapitalist Worlds, Boulder, CO.: Westview. Zipf, George K. 1949. Human Behavior and the Principle of Least Effort. Cambridge MA: Addison Wesley.  
 
   
THE PAGES BELOW TO BE DELETED Figure 9 shows the autocorrelation functions of q for the three regions. Europe is the most cyclical (as reflected in the runs tests), China less so, and with Mid-Asia showing only 50-year stabilities. The cycling patterns grow weaker in these cases, but the cycling time seems to weakly approximate 800+ years (unit intervals in these graphs are 50-year increments).   
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800 years ~800 years ~800 
th of a cycle, which is a long period of instability (vulnerable to conquest from the outside following internal instabilities). From our perspective, however, sociopolitical instability is not smoothly cyclical but episodic. Rebellions, insurrections, and all sorts of protest are events that mobilize people in a given time and generation, and that impacts that, when repeated frequently, have massive effects. We see this in long-term correlations with SPI, such as internecine wars in China.