The Dynamics of Cities

Ecological Determinism, Dualism and Chaos

Dimitrios Dendrinos

• Publisher: Routledge
• Year: 2002
• Print ISBN: 9780415077217
• eBook ISBN: 9781134900725
• Edition: 1
• Topic: Architecture
• Subtopic: Urban Planning & Landscaping

Dimitrios Dendrinos, an expert in the application of non-linear dynamics and chaos theory to the subject of urban and regional dynamics, focuses here on fundamental issues in population growth and decline. He approaches the topic of urban growth and decline within a global system perspective, viewing the rise and fall of cities, industries and nations as the result of global interdependencies which lead to unstable dynamics and widespread dualisms. Professor Dendrinos provides valuable insights into the evolution of human settlements and considers the possible futures open to the giant cities of the world.

1: GLOBAL INTERDEPENDENCIES

INTRODUCTION

Frequently, in many regions of the globe and through centuries of human history, the growth and decline of population and wealth in many human settlements has accompanied significant historical incidents. Landmark social economic and political events, ranging from wars to the rise and fall of empires to scientific breakthroughs, have been associated with changes in these two stocks. Such major events have at times triggered, often followed, occasionally coincided, and in other instances simply intermittently interrupted, critical phases in the dynamics of these two variables. Historians have spent significant efforts in attempting to detect such associations. Their emphasis has been, however, on chronicling major events rather than linking them to the underlying population and wealth dynamics in space-time.

To socio-spatial analysis, on the other hand, it is whether such events precede, succeed, coexist or intermittently occur in various identifiable phases in the dynamics of these two key variables which is of importance. When such phases are clearly evident in industries, cities, nations or empires, and contain significant modifications in the size of these two stocks of socio-spatially dominant entities, historians name these periods ‘eras.’

Whether one confronts topics in paleontology, paleoanthropology, archeology or contemporary history, major events and the underlying population stock size (of animals, plants or humans) on the one hand, and the food resource base level (the intake nutrient and energy levels for animals and plants) or the income resources and wealth levels of humans on the other, are closely linked. It is surprising that no systematic study has been undertaken to date connecting such dynamics to the major socio-spatial events in history, let alone prehistory. Clearly, major events affect these dynamics and in turn these dynamics affect the occurrence of such major events in an interactive complex and nonlinear manner.

Changes in population and in the wealth of cities, regions or nations are important causes of events in human history. They are also the outcome of a variety of forces which are at work within a specific social system at a particular location and time-period. Consequently, one cannot expect the dynamics of these two stocks at any point in spacetime to be either uninformative or random. Instead, these dynamics must, in abstract and often succinct form, reveal a comprehensive story of fundamental change in the multifaceted phases of development and evolution of human societies and their settlements. A look at the recent history of these two variables at a number of locations may point to key processes underlying events of the past and foretell events at some time in the future.

That population and wealth are two central variables influencing and being influenced by one another and that in combination they efficiently record various socio-economic growth processes are hypotheses currently affecting theoretical developments in spatial dynamics.¹ Urban, regional, and national development paths are now being studied in view of a dynamic interdependency between population and wealth.

Studying this basic interdependency is nothing new to social science. Demographers,² economists,³ geographers,⁴ sociologists,⁵ anthropologists⁶ and other social scientists and historians have examined this interdependency over the past two centuries. Renewed interest in these two variables’ dynamics has been injected by recent developments in the theory of non-linear difference and differential equations in mathematics. These advances significantly enlarge and possibly modify one's perspective on urban growth, as well as allowing one to reflect more broadly on subjects of socio-spatial development and evolution. They are the sources of some new insights into the study of history.

Briefly, three main themes seem to emerge out of non-linear theory. First, complex socio-spatial processes can be described by simple dynamical models. Second, out of very simple deterministic dynamic model specifications, over a few central variables, extraordinarily complex, powerful and insightful outcomes emerge. These outcomes shed light on the divergent, chaotic, or seemingly stochastic dynamic patterns which describe the qualitative features of real systems dynamics. Third, micro and macro socio-spatial systems alike are marred by an overwhelming likelihood for instability, this being argued here as the main factor contributing to the presence of extreme sociospatial dualisms and disparities. Instability is caused by extensive socioeconomic interdependencies and resulting interactions among social stocks in space-time. Key events in development⁷ or evolution⁸ are the byproducts of this instability. Thus, the framework adopted does not require one to resort to complicated and at times convoluted and largely ideological theories (of Marxist or non-Marxist variety) to describe and account for the presence of such disparities. They are simply found to be inherent in any complex dynamical system.

With this environment as the background, considerable attention has been attracted to the fact that in 1987 the world's population toppled the 5 billion mark. An increase in interest has been shown by urban analysts with regard to the significant growth in absolute population size of the world's largest urban agglomerations and the various predicaments that this has resulted in during the past quarter century or so. Combined with the inevitable question of whether such growth rates are sustainable, one is motivated to explore these relatively recent dynamic events by utilizing the novel analytical methods made available from bifurcation theory. This study is a step toward this direction.

MACRODYNAMICS OF THE WORLD'S LARGEST URBAN AREAS: ORDER IN CHAOS

A principal finding of this book, and a key stimulus for the deterministic ecological approach theoretical framework adopted here, is that when the relative per capita gross product of the world's major urban areas, recorded as the ratio of their individual per capita product to the pervailing current average of the world's market economies, is plotted against these urban areas’ share of the current world population over a time-period the emerging dynamic paths are not found to be random. Indeed, they turn out to reveal important clues in the study of the evolution of human settlements.

Data from nineteen metropolitan areas are presented in Figure 1.1, with population size greater than five million inhabitants as of 1975.⁹ The dynamics of the world's largest urban agglomerations as shown in the phase portrait (the two-dimensional diagram which records their paths), demonstrate very informative and qualitatively quite robust dynamical features. In Figure 1.1, the observed share of a metropolitan area's population to the current world total (in 10⁴) is recorded along the horizontal axis (x). In the upper diagram the vertical axis depicts ten times the current per capita domestic (or national) product to the world market economies’ prevailing average, y, derived when both are expressed in current US$. Its logarithmic expression, In y, is shown in the upper diagram. The phase portrait contains the signatures from nineteen metropolitan agglomerations, expressed as the simultaneous dynamics of these two variables during the period 1958–80.

Notable is the decrease/increase in relative population above/below a relative per capita product developmental threshold level. Urban areas with a per capita product ratio higher than approximately 74 percent of the world market economies’ current average per capita product, shown by the lines

=7.4 (or in In

=2) in Figure 1.1, exhibit declines in their share of the world's population. Urban areas below this threshold without exception increase their share of global population. This threshold exhibits a resilience throughout the admittedly short study period. However, it enables one to draw certain inferences and mildly strong conclusions about the settings’ macrodynamics, in spite of the possible limitations characterizing United Nations data. The existence of a threshold seems to be confirmed by other researchers as well, although in absolute growth studies.¹⁰

One cannot fail to notice that nations whose urban areas lie underneath the threshold belong without exception to what the UN classify as less-developed countries (LDCs); whereas nations whose urban areas lie above the threshold (with the possible exception of Argentina) are classified by the UN as more developed countries (MDCs). Whether infinitesimal or significant changes in an urban area's per capita relative product have occurred over the 25-year period depends heavily on its past and current location relative to this threshold. Thus, this threshold seems to represent a lift-off level. Below it, urban wealth variations over time are almost negligible. The growth in a particular LDC metropolitan area's population share of the world's total dominates the urban area's dynamics. Above this threshold lie MDC metropolitan agglomerations with very pronounced changes in both population share and relative product, varying during the study period between .9 and 5.5 times the world's average per capita product.

The line

=7.4 seems to be a part of a code which separates two areas with distinctly different dynamics in the relative population-product space. Each metropolitan area's macrodynamics are dictated by its starting value, in reference to this line, on this phase portrait which contains the code. At this scale of analysis and at this point in time dynamic paths depicted in the phase portrait indicate a mild oscillatory motion and a strong indication of irreversibility in their qualitative properties. It is indeed quite interesting to recognize the persistence and non-randomness of the pattern formed in one quarter century as shown in Figure 1.1.

Figure 1.1 The dynamic paths of the world's largest urban agglomerations (mor than 5 million inhabitants in 1975). On the vertical axis the actual raito y of their capita income to the world market economies’ average is plotted (a), along with its logarithmic In y transformation (b); on the horizontal axis their share of the world's population is recorded. The study period is 1958–80. Key: BA (Buenos Aries), BM (Bombay), CH (Chicago), CL (Calcutta), CR (Cairo), J (Jakarata), LA (Los Angeles), LN(London), MC (Mexico City), MO (Moscow), NY (New York), PK (Peking), PR (Paris), R (Rio de Janerio), SH (Shanghai), SL (Seoul), SP(São Paulo), TH(Teheran), TK (Tokyo)

In it many urban agglomerations are depicted as belonging to nations which differ significantly in many dimensions. These nations differ in their political structure, level of economic development, demographic ethnic, cultural and social structures, population and area size. The quantity and type of natural resource abundance varies greatly, their location spans the globe, and in general they differ in many other ways. They share only a few common elements in the historical period these recordings were taken.

During that quarter century, these cities experienced events which locally might be considered as being of large scale with long-term implications. The events, of great historical significance to these cities and the nations they are situated in, ranged from local conflicts involving war and revolution, to radical changes in their economic and political structure, to major socio-cultural transformations, to considerable technological innovation. In view of these myriad local events, and the effects of global events as well, the stability of the code during that period and the largely non-random motion of individual urban areas in the phase portrait of the code are remarkable. This resiliency indicates the presence of certain strong and global forces at work, governing the behavior of this macrosystem beyond the relative microevents just listed and having occurred at many locations at different points in time within the past quarter century.

As noted, looking at the phase portrait of Figure 1.1 one detects an oscillatory movement in almost all the urban settings's dynamic paths, these being confined however within their particular field or domain of motion. An obviously irregular path describes each urban area's dynamic within the phase portrait. None the less, each path's oscillations are restrained in their irregular motion. The apparently chaotic movement each trajectory exhibits is not totally random, but rather it is confined within a domain of motion obeying floor and ceiling (capped) dynamics. One does not see either unrestrained chaos or the semi-regularity of quasi-chaos or the strict regularity of periodic movement in these domains.¹¹ When a temporal (lagged or not) mean value is traced for each city's path, these averages seem to behave well within the phase portrait. The temporal average path for each city exhibits certain strong regularities in spite of the apparently chaotic motion that these trajectories collectively demonstrate. Order in chaos is obviously present in these dynamics, as is the case too for the dynamic paths of each among the nineteen cities. These trajectories are not rampantly unruly. Why? What is one to conclude from this? And what for?

Answered briefly, these motions seem to obey some scant regularity possibly because it might not be sustainable for these movements to be either totally chaotic (i.e., purely random), quasi-periodic, or periodic. The observed pattern allows for an ambiguous enough outcome to emerge, not too wildly unruly or fully predictable, so that the system can exist, i.e., survive and evolve, and also tell a number of stories about itself. Ordered chaos may be a prerequisite for socio-spatial evolution. This evolution might be allowed to occur along paths permitted by a code, which contains some flexibility in that some neighboring paths within a given domain assigned to a city may also be possible. The specific paths recorded might be slightly off the statistical averages of these bands in the phase portrait where the actual paths of these two fuzzily measured¹² variables are allowed to move.

It may be concluded that if real (as opposed to model) chaos is present in each city's trajectory then the actual chaotic movement of the two macrovariables’ macrodynamics, i.e., the dynamics of these two aggregates, must also take place within bands for each city. Only the general neighborhood for these bands can be and is outlined, inside which these measurements and movements—based on the UN or any other data sources—are traced. In the phase portrait of Figure 1.1, where the domains of motion for cities belonging to the less and more developed nations converge to or are restrained by roughly identified regions, these latter may be construed respectively as possible ‘strange attractors’ or ‘strange containers’ of these macrodynamics.

Strange attractors (or containers) in non-linear dynamics are areas in the phase portrait where dynamic trajectories wander around (are attracted to or are confined by) in their unstable non-periodic motions. How many attractors exist, where exactly they are located, and what is their approximate size if indeed they really exist beyond their model specification, might have significant implications for each city. To answer these questions, if such answers are ever obtainable, requires the acquisition of far more extensive time series data than that currently available which at present allows only modest speculation about them.

For what reasons do these specific individual trajectories and their possible ‘mean paths’ or their strange containers and attractors exist in the phase portrait? What purpose do they serve now or have they served in the past quarter century? What historical processes are responsible for them? What do they allow by way of dynamic paths for the future? To answer these, as well as address more extensively the previous questions, a general theoretical framework must be set up.

INTERDEPENDENCIES AND ECOLOGICAL DETERMINISM

In social sciences there is a need to address and define in a dynamic context (albeit approximately) the notions of interdependency, interaction, force, and associated concepts. This is done next, in subsection 1 within the framework of what is further defined as ecological determinism. Following these definitions, the analysis focuses on some fundamental forces at work in macro socio-spatial dynamics, in subsection 2. A speculative component inherent in these forces is presented in subsection 3. The distinction between micro and macrodynamics is explored, and in a parallel mode the difference between aggregate and disaggregate social behavior is analyzed in subsection 4. Proximity and overlap among these topics makes for a rather fuzzy set of headings, and a largely artificial segmentation and sequence in these subsections.

Having dealt with the basic theoretical framework of this book, the Malthusian and other demographic models related to the main concerns at hand are looked at in subsection 5, with a critique of the basic economic growth models and some other relevant models about socio-spatial development (from Marxist sociology and cultural anthropology) being supplied in subsection 6.

1 Interactions and interdependencies

No matter which specific discipline they belong to or what their subject of investigation is, development studies address issues of growth or decline in a number of stocks. They also address issues of evolution which typically involve changes of state in the...

Table of contents

• COVER PAGE
• TITLE PAGE
• COPYRIGHT PAGE
• FIGURES
• TABLES
• PREFACE
• ACKNOWLEDGEMENTS
• ABBREVIATIONS
• INTRODUCTION
• 1: GLOBAL INTERDEPENDENCIES
• 2: NATIONS, CITIES, INDUSTRIES, AND THEIR CONNECTANCE
• 3: THE DYNAMIC CODE OF A GLOBAL URBAN HIERARCHY
• 4: EPILOGUE
• APPENDICES
• NOTES
• BIBLIOGRAPHY